AUTOXIDATION INHIBITION OF TETRALIN:

A STUDY BY INDUCTION PERIOD ANALYSIS

By

William Gilbert Lloyd

A THESIS

Submitted to the School for Advanced Graduate Studies of
Michigan State University of Agriculture and
Applied Science in partial fulfillment of
the requirements for the degree of

DOCTOR OF PHILOSOPHY

Department of Chemistry

' 1957

.r ’7 .5."

//

ACKNOWLEDGMENT

The writer is pleased to acknowledge gratefully the
invaluable theoretical counsel, the steady encourage-
ment and the many helpful suggestions of Professor

W} T. Lippincott, under whose guidance this work was
carried out.

Acknowledgment and thanks are also due to Professor
R. M. Herbst for his help and guidance as chairman of
the writer's committee, to Professor F. B. Dutton who
kindly served ig_loco praeceptoris during the summer
term, 1956, and to Professor J. C. Sternberg for many
helpful discussions concerning reaction kinetics.

This work was generously supported by a grant from

The Research Corporation. The recording manometer was
kindly loaned by The Dow Chemical Company.

ii

AUTOXIDATION INHIBITION OF TETRALIN:

A STUDY BY INDUCTION PERIOD ANALYSIS

By

William Gilbert Lloyd

AN ABSTRACT

Submitted to the School for Advanced Graduate Studies of
Michigan State University of Agriculture and
Applied Science in partial fulfillment of
the requirements for the degree of

DOCTOR OF PHILOSOPHY

Department of Chemistry

Year 1957

Approved [fibty/ «i7f=’

 

 

ABSTRACT

The nature of antioxidant interaction with autoxidizable systems
is investigated by means of an intensive study of the effects of various
experimental parameters upon the induction period of inhibited tetralin.

The effect of variation of azoébis-isobutyronitrile initiator
concentration at constant hydroquinone concentration indicates a simple
power relationship. The effect of variation of cobaltous naphthenate
catalyst at constant hydroquinone concentration shows the induction
period to be exponentially dependent upon the cobalt concentration.
This dependency is confirmed by a similar series at constant 2,6-di—
tert-butyl~h-methylphenol concentration. The effect of varying anti-
oxidant concentration at constant cobalt catalyst concentration is
dependent upon the efficacy of the antioxidant and the concentration of
the antioxidant; dependencies vary from first-orde~ to exponential.

At constant concentrations of hydroquinone and cobalt catalyst, the
induction period is inversely proportional to the amount of tetralin-l-
hydroperoxide added to the system. The effects of'variation of oxygen
pressure, substrate concentration and temperature (SO-90°) are also
reported.

These observed relationships are inconsistent with the classical
induction period kinetics derived from assumptions of steady-state
concentrations of intermediates. It is proposed that the steady-state

assumption is not generally applicable to inhibited systems.

iv

In view of the evidence for the occurrence of propagation and branching
reactions during induction periods, a kinetic theory based upon the
branching~chain dynamics of Semenoff is proposed. According to this
concept, application of the steady-state assumption to inhibited systems
is valid only for the special case of retarded linear nonbranching
chains. An approximate kinetic solution for the general case, based
upon the assumption of an inverse relationship between antioxidant

and chain-carrier concentrations, is shown to account qualitatively

for the basic observed relationships.

TABLE OF CONTENTS

Page

INTRODUCTION ....... . ..... . .......... . .................. . .......... l
I. Aims arid scope.. '0 CI... ...... O. O. 00000000000000 .0 IO. 0 I. 0.. 1

II D AutOXid-ation. O O I I O O O O O O C O O O U 0 C O OOOOOOOOOOOOOOOOOO O ........ 2
III. Autoxidation of Tetralin....... .............. . ............ 5
IV. Inhibition and the Induction Period... ...... . ..... ........ 23
EXPERIMENTAL PROCEDURES... ....... ......... ........ .... ..... ....... 39
I. Preliminary Samples ............................. .......... 39

II. Tetralin.Purification....... ........... . ....... ... ........ h3
III. Other Chemicals Used ......... ...... ................. . ..... h?
IV. Apparatus arld MethOd ........ O O O O O O O O O O O O O O l O O ....... O O O O O O S]-

V. Interpretation of a Typical Inhibited Run..... .......... .. 57

VI. Dependency Calculations.. ...... ......... ........ . ......... 63
REBIIIJTS...’ ....... .0... ..... O ........ ......OOO ..... ......OOOOOODO' 70

I. Preliminary Runs.......................................... 70
II. The System Tetralin-Cobalt-Hydroquinone................... 79
III. The System Tetralin-Cobalt-Dibutylcresol.................. 103
IV. Aromatic Amines with Tetralin-CObalt Systems.............. 11b

DISCUSSION... ............ ...... ..... .......... ..... . ......... ..... 125
I. The Claim for Steady-State Conditions..................... 125

II. Objections to the Steady-State Assumption... ............ .. 131
III. The Problem of the NonqSteady-State System................ lh5
CONCLUSIONS.... ............................ . ...... . ....... . ....... 152
BBLIOGMP}IY ........ .....OOIOOO...I.00...........OOOOOOOOOIOOOO...15b

AUTHOR INDEXoo-ooooooocoo-0.000.000.0000.ooooooo00.000900090090000 163

APPENDICES ..... ......DOOOODDOOOIOOOO...... ..... .....OIDOIOOI ......

vi

INTRODUCTION

I. AIMS AND SCOPE
"Frequently the initiation of low temperature oxidation is
preceded by an induction period which is in general non-
reproducible in magnitude."
. C. E. H. Bawn (1)

The aim of the present study is to investigate the nature of anti-
oxidant interaction with autoxidizable systems, by means of an intensive
study of the effects of various parameters upon induction periods.
Although induction periods are well—known phenomena, a thorough study
of inhibition kinetics by induction period analysis has not previously
been reported.

The present work describes a method for the determination of
induction period, for a liquid sample under autoxidizing conditions,
with a fairly high degree of precision and consistency. It presents
the findings of 150 kinetic runs, centering upOn the system: tetralin-
cobalt naphthenate-hydroquinone—oxygen. It undertakes to relate the
observed kinetic dependencies with the general body of kinetic theory
pertaining to autoxidation reactions. It presents an argument against
the application of the steady-state assumption to inhibited systems,
and it offers a general hypothesis for the kinetics of inhibited
systems, extending the concept of branching chain reactions as formu—
lated over twenty years ago by Semenoff (2).

The following sections provide a brief introduction to the general

field of autoxidation, a summary of the considerable body of literature

dealing with tetralin autoxidation, and a discussion of the prior use
of induction periods as kinetically significant criteria in autoxi-

dation studies.

II. AUTOXIDATION

"The Air in which we live, breathe, and move ... is the
menstruum, or universal dissolvent, of all Sulphureous
bodies."

. T. Hooke, 1665 (3)

Man's interest in the phenomenon of chemical oxidation by mole-
cular oxygen antedates the dawn of civilization. His systematic study
of oxygen-oxidation reactions, however, can be dated from the latter
part of the seventeenth century, and particularly from Hooke's
experiments with the combustion of charcoal in limited volumes of air.
For the next hundred years Stahl‘s internally consistent phlogiston
theory dominated scientific thought in this area. But by the end of
the eighteenth century, the cumulative impact of the work of Black,
Priestley (malgre soi) and especially Lavoisier forced the recognition
of oxygen-oxidation as a legitimate chemical reaction, involving no
impalpable entities and obeying classical stoichiometry (h).

The combustion phenomenon, with its characteristic marked exothermal
nature and its emission of visible light, is well known. Less well
known is the subclass of lower-temperature reactions, in which organic
compounds combine slowly with molecular oxygen, in the absence of
flame, to give rise to various oxidation products. It is this sub-
class to which the name autoxidation is given. The relative obscurity

to which autoxidation reactions have been relegated until very recently

is indicated by the paucity of material indexed under the headings,
"Autoxidation," "Oxidation, by Oxygen" and "Oxidation, by Air."

From 1906 through 19b6, a search of Chemical Abstracts under the above
headings leads to a total of one reference to the oxidation of an
organic compound by molecular oxygen (5)-—and this is perhaps dubious
since it involves the mediation of osmium tetroxide. In 19h6, however,
the Faraday Society published the classic symposium on autoxidation (6)
which placed autoxidation phenomena firmly within the body of theoreti—
cal organic chemistry.

Under suitable conditions the majority of known organic compounds
will react with molecular oxygen. This extraordinary scope of reaction
is attributable to the paramagnetic nature of 02; indeed, for the pur-
poses of considering autoxidation reactions, it is often profitable to
consider molecular oxygen as a diradical. Autoxidation of a hydro-
carbon, RH, first requires an initiation process to yield the free

radical R-:
RH + initiator ---—-> R- (1)

Suitable sources of initiation include light, heat and free-
radical sources (7-13), salts of certain transition metals (11,1h-21),
and in some cases the autoxidation products themselves (7-10,22).
Enzymatic initiation is also known (23-25).

Given some initiation process, there is a general concurrence that
the autoxidation reaction sequence involves two discrete steps (11,

26-29): formation of a hydroperoxide and decomposition of hydrOperoxide.

The formation is a simple two-step radical chain process:
R. + .0-0. ---—-> R-O-O- (2)
3-0-0. + RH——-—-> R-O-O-H + R- (3)

in which Reaction 3 is rate-determining for nearly all known systems.
This process may be accelerated, by introducing a chain-transfer agent
such as HBr and thereby replacing Reaction 3 with the energetically

more favored cycle (12,30-32):
R-O-O- + H-Br ———-> R-O-O-H + Br- (3a)
R-H + BrH ——---> R- + H-Br (3b)

so that the over-all rate of peroxide formation is markedly accelerated.
This over-all process (Reactions 2 and 3) may similarly be inhibited
by introducing a chain-transfer agent such as hydroquinone. Chain-
transfer agents which inhibit autoxidations are termed antioxidants,
and the over-all antioxidant-termination step may be designated in the

most general terms as:
R-O-O- + AX -—-—--9 inert products (11.)

The actual nature of Reaction h was once thought to be simply that of
hydrogen transfer, formally analogous to Reaction 3a but leading to

the formation of a molecule of hydroperoxide and a resonance-stabilized
free radical derived from the antioxidant (33). Evidence for other

mechanisms will be discussed later.

The second over-all process in autoxidation, decomposition of the
hydroperoxide, may follow any of at least five routes: spontaneous
homolytic decomposition, metal-ion-catalyzed homolytic decomposition,
acid-catalyzed heterolytic decomposition, base-catalyzed heterolytic
decomposition, or heterogeneous-phase decomposition of the adsorbed
hydroperoxide. These routes are discussed in some detail by recent
reviewers (11,26-29). Of particular interest in the present study are
the first two routes, since these both lead to the formation of radicals
and therefore, in terms of the over-all autoxidation reaction, constitute
chainebranching reactions.

In the case of nonexplosive oxidations, the radicaleproducing
processes of initiation and branching soon become balanced by biradical
termination. ‘Consequently, in the absence of antioxidant the oxidation
rate typically accelerates to a constant value, and thereafter the rate
remains substantially invariant. Most kinetic treatments deal with
this constant-rate range, for which the steady-state assumption may be

invoked reasonably and profitably.

III. AUTOXIDATION OF TETRALIN

"Dasselbe Naphthalintetrahydrur, welches frisch destillirt ...
lieferte drei Tage spater: C 90.11 pCt, H 8.85 pCt...Als die
Analyse nach drei Monaten weiderholt wurde, fanden wir folgen-
de: C 86.51 pCt, H 8.79 PCt."

... C. Graebe and P. Guye, 1883

(311)

The vulnerability of tetralin (1,2,3,h-tetrahydronaphthalene) to
autoxidation was first observed.by Graebe and Guye in the course of a

study of the then-new reduction of naphthalene with HI and phosphorus (3h).

Immediately after fractionation of the product mixture, the tetralin
yielded an excellent elemental analysis, but, notwithstanding careful
storage, the 0-H analysis fell below 99% in three days and to 95.h%
after three months. Distillation of the aged sample from sodium
yielded tops and bottoms giving C-H analyses of 99.5% and 91.9%,
respectively. They offered the reasonable guess that a compound of
empirical formula CIOHIOO was being formed on standing.

Subsequently various measures of the extent of oxidative degrada-
tion were prOposed, based upon determinations of density, reflux boiling
point, viscosity and titratable acids (35). One of the earliest
quantitative measurements suggested was that of peroxide determination
by potassium iodide (36). Many years later George and coeworkers
(17,37) employed potassium iodide in glacial acetic acid to demonstrate
that under moderate conditions peroxide formation accounts nearly
quantitatively for the total oxygen absorbed.

The locus of the oxygen attack and the nature of the peroxide
formed were in doubt for some time, particularly since cyclohexene was
believed to add the elements of molecular oxygen across the>double bond
to form a bicyclic peroxide (38-hO). In the face of this "given"
opinion, Hartmann and Seiberth in 1932 isolated the tetralin peroxide
by vacuum distillation, obtained the correct empirical formula, Cloleoz,
and undertook to establish its structure unambiguously (bl). They
Observed the following: (a) the peroxide was reduced by zinc to yield
1-tetralol, with no traces of a diol; (b) the peroxide was converted

in the presence of ferrous sulfate to l-tetralone; (c) the peroxide

with excess NaHSO3 yielded the Na salt of a sulfonic acid, which on

acidification yielded dihydronaphthalene; and (d) the peroxide, after
being dissolved cautiously in cold dilute alkali, was reprecipitated
unchanged upon careful acidification. The only structure consistent

with these observations is that of tetralin-l-hydrOperoxide, I,

/O-O-H
\\.

[H

In the following year Hook and Susemihl reported a similar study

(b2), confirming structure I_and characterizing the hydroperoxide:
m. 560, d;e.s 1.0988, n;8.8 1.53893. Tetralin 1~hydroperoxide has also
been characterized by its infrared spectrum (R3), and has been at least
partially resolved into its optical enantiomorphs by selective adsorp-
tion on d-quartz (uh).

It was only after this structural determination of tetralin hydro-
peroxide that Hock, Criegee and others reinvestigated cyclohexene
peroxide and found it to be the 3—hydroperoxide (h5-h8). The earlier
confusion may be partially accounted for by the fact that double bonds
are directly attacked in many oxidizing systems. Thus, the benzaldehyde-

O
"activated" oxidation of cyclohexene yields cyclohexanediol monobenzoate

(U9). There is reason to suspect that here the activator is itself

autoxidized to perbenzoic acid, which then makes an electrophilic
attack by an ionic mechanism (50).

In the early work, tetralin hydroperoxide was isolated by careful
fractionation at low temperatures and pressures (h1,h2), and indeed
this is the preferred method according to Organic Syntheses (51).
However, the hydroperoxide can be very easily obtained in high purity
by cold aqueous alkaline extraction followed by cold neutralization
(52,53).

Medvedev (5b) showed that there are two chain processes involved
in tetralin autoxidation, the first involving formation of the hydro-
peroxide and the second involving decomposition of the hydroperoxide to
other secondary products. The peroxide is unusually stable for a
secondary hydrOperoxide; Cook (1h) found it to be stable to 1000,
although the addition of iron salts effected a rapid decomposition even
at 20°, and Ivanov and his co-workers (55) found no appreciable peroxide
decomposition occurring in uncatalyzed tetralin autoxidations at 70°,
and found a substantial increase in peroxide yield upon addition of
manganous naphthenate. Several patents describe the preparation of
tetralin hydrOperoxide by autoxidation at 75—100° (53,56-58), one of
these specifying a suspended cupric carbonate catalyst (58).

Deferring for the present a discussion of metal-catalyzed decompo-
sition, there are several significant observations concerning the decay
of tetralin hydroperoxide. Medvedev (5h) found appreciable decompo—
sition rates only in the presence of oxygen, and Yamada (59) found the

first-order decomposition to be retarded by antioxidants. Both

observations suggest a susceptibility to radical-induced decomposition,
notwithstanding the observed first-order kinetics of the decomposition
(59,60). Further supporting the radical-induction is the observation
by Robertson and'Waters that this first-order decay is followed only A
with peroxide concentrations below about 10% (60). The apparent
anomaly of radical-induced first-order peroxide decay has been noted
before (61,62).

warm alkali readily decomposes the peroxide (58); this is a normal
reaction for secondary hydroperoxides (28,h6,62-66). Hook and Lang (67)
observed that cold (below 100) aqueous sodium bisulfite readily reduces
the hydrOperoxide, yielding chiefly 1-tetralol and dihydronaphthalene,
along with about 10% di-l-tetralyl ether (cf. Hartmann and Seiberth (h0)).
The thermal decomposition of the peroxide is quite medium—sensitive.
Robertson and waters (60) found the rate in chlorobenzene to be about
the same as in tetralin, while successively more rapid decompositions
were Observed in o-dichlorobenzene, cyclohexanone, cyclohexanol and
1-chloronaphthalene. By comparison, Bateman and co-workers (68) found
a similar; medium-sensitivity with cyclohexene-3-hydroperoxide, the
half-life at 800 being 225 hours in benzene, 170 hours in cyclohexane,
72 hours in 1-octene, 56 hours in cyclohexene, and 5.5 hours in
2,6-dimethylhepta-2,5-diene. The very marked effect of the diene may
reflect its unusual properties with respect to autoxidation (69).

A detailed study of the ionic decomposition of tetralin hydro-
peroxide in acidic and basic media has also been reported (70).

The final oxidation products.of tetralin, either from thermal

decomposition of the peroxide or by extended autoxidation in the range

lO

75~1300, are predominantly 1—tetralone (l7,22,5h,7l-73) and, presumably,
water. Similarly, catalyzed autoxidation with manganese or copper salts
(7b) and peroxide decomposition catalyzed by iron salts (lb) or by titan-
ium trichloride (75) yield principally 1-tetralone. At 1000 an
appreciable amount of 1~tetralol is also claimed (76). Peroxide
decomposition at 130-1500 in the absence of air yields, in addition to
the tetralone and tetralol, dihydronaphthalene, uJ-(o-hydroxypheny1)-
butyraldehyde and the corresponding acid, and also uJ-(o-hydroxypheny1)-
propionaldehyde (77). Decomposition of the peroxide in alcoholic sulfuric
acid at 80° yields the u)-(o-hydroxyphenyl)butyric acid (78), though the
initial product is presumed to be the aldehyde which is then readily
oxidized by the aciddperoxide system. Alkaline decomposition (60-800,
aqueous) yields 1-tetralone and l-tetralol in approximately equal quanti-
ties (53,58). Thus the normal breakdown at moderate temperatures does
not lead to 0-0 cleavage; benzylic activation evidently makes the Cl-H
bond more labile than either of the c-c betaebonds.*

The homolytic nature of the in;§itu decomposition of tetralin
hydr0peroxide is indicated by its ability to catalyze tetralin autoxi-
dation. Medvedev (5h,71,80) was the first to explain the autocatalytic
nature of tetralin autoxidation in terms of peroxide homolysis, and
demonstrated this catalysis by adding tetralin hydrOperoxide to pure
tetralin samples. ‘The initial oxidation rate (for about the first five

hours at 75°) was markedly increased by increasing the initial peroxide

 

*"Beta" with respect to the 0-0 bond, following the notation of George
and walsh (79).

11

concentration; however, all runs eventually achieved the same steady-
state rate. This catalytic effect of the peroxide has been confirmed
by R0bertson and waters (22). George and Robertson, in an earlier
paper (81), claimed that the addition of 0.7% tetralin hydroperoxide
had "little" effect upon tetralin autoxidation; however, several claims
in this particular paper (which argued for an energy-chain mechanism in
the low temperature range 65-1200) have been discounted or contradicted
by later workers, including Robertson himself (22,60,77,82).

Several formulations have been proposed to show the actual dependence
of tetralin autoxidation rate upon tetralin peroxide concentration.

'In 1938 Medvedev derived a two-term expression for the autoxidation (5h):

-d(RH)/dt = Iéé38%8;7' + B(RH)(RO0H) (I)

in which A, B and C are combinations of unit rate constants. Once the
autoxidation was well under way, the second term would dominate under
conditions of relatively low temperature and high peroxide content.
According to this development, the dependence of rate upon peroxide
concentration increases from zeroth-order to nearly first-order as the
reaction progresses to steady-state conditions. Robertson and waters
in l9h8 found the initial dependency, by measuring oxygen uptake, to

conform to (82):
-d(02)/dt = k(R00H)°°5 _ (II)

but at later stages in the autoxidation this becomes first-order:

_d(02)/dt = k(RH):(ROOH) (III)

12

where A.is a terminating species such as an antioxidant. More recently,
Bateman and co-workers (68) have derived an expression in the two-term
form of Medvedev but kinetically more akin to the expressions of

Robertson and.Waters:
-d(02)/dt = [ k1(R00H) + k2(R00H)2 loos (IV)

which affords an initial half-order dependency progressing towards a
first-order dependency. It is of interest to note here that in the
presence of metal-ion catalysts, where the peroxide level is generally
low and where therefore the peroxide dependency might be expected to
correspond to the early stages of uncatalyzed autoxidation, Bawn (83)
has independently developed the general rate law for hydrocarbon

autoxidations:
-d(02)/dt = k(RH)(ROOH)°'5(M)°~5 (v)

where 3.15 the metal-ion catalyst concentration. This accords with
EQuations II and IV. However, woodward and Mesrobian (8h), working
with tetralin, developed a somewhat different set of relationships.

For the radical-initiated autoxidation they found:
-d(02)/dt = k<RH)(I)°-5 (VI)

where I_designates a radical-source initiator such as azodbis-isobutyro-
nitrile or benzoyl peroxide. For the case of metal catalysis, using
cobaltous acetate and glacial acetic acid as a solvent-diluent, they

obtained:

13

-d(02)/dt = 'k1(RH)(R00H)°'5(M) ea (VII)

but at steady-state in this system the peroxide concentration is defined
as:

(ROOH) = k2(RH)2/(M)3 (VIII)
So, substituting Equation VIII into Equation VII they obtain:
-d(02)/dt = k3(RH)2 (IX)

The oxidation rate was found to be, in fact, completely independent of
(Co) over the range reported. However, this latter work appears to
represent a special case, probably due to the use of glacial acetic
acid as a medium.

One distinct peculiarity of tetralin, as compared with most other
hydrocarbons which have been studied, is that its principal final
oxidation product, l-tetralone, is a pronounced autoxidation retarder.
Medvedev observed this in his earlier studies (5h,7l,80), noting that
the retarding effect increased with increasing tetralone up to about 3%
tetralone, and thereupon levelled off. He observed an interaction, as
indicated by vapor pressure decrease, upon mixing tetralin hydroperoxide
with l-tetralone (5h), and accordingly postulated a hemieper-acetal
formation:

H
,H 0.
T:CH-O-O-H + T:C:0 -————9- T:C\O-O/C:T (5)

No further characterization of this reaction or of the proposed product

has been found, and the vapor pressure evidence alone seems scanty.

1h

However, the auto-inhibition of tetralin autoxidation has been noted by
others, and has also been traced to l-tetralone by Bateman, Hughes and
Morris (68). This inhibiting effect may be more credibly explained in
the light of Russell's recent work with mixed substrates (85,86); if
tetralone is more reactive than tetralin itself, it may be expected to
retard the tetralin oxidation rate in the same way that a few percent
tetralin retards the oxidation rate of cumene.

The accelerating effect of the salts of iron, manganese, cobalt,
copper and lead upon the decomposition rate of tetralin hydroperoxide
has been noted frequently (1h,17,22,55,87,88). This decomposition is
first-order with respect to both hydrOperoxide and metal ion (22,60).
Yamada (87) observed a second-order dependency with manganous and
cobaltous oleates, but attributed this to a decomposition of the metal
soap at a rate proportional to that of the peroxide decomposition. The
effect of metal-ion catalysis upon over-all oxidation rate has been
explained, in three nearly simultaneous papers by Robertson and co-

workers (17,18,22), in terms of a rate expression of the form:

-d(02)/d'5 = g : 28% (X)

 

other variables being assumed to be held constant. This form has two
particular areas of utility. First, it accounts for the widespread
observations that a given metallic catalyst will increase the oxidation
rate up to a certain level beyond which no additional amount of catalyst
alters the rate (thus in Equation X the limiting rate is D/C). Second,

it accounts for the fairly rare instances of negative catalysis, wherein

15

metal ions essentially inhibit autoxidation reactions (17,89-92) (thus,
in Equation X, where A/B is greater than D/C).

For tetralin and certain other hydrocarbons, George and Robertson
(18) find that a plot of (rate)”1 vs. (M).1 is linear (indicating, for
Equation.X, A.t° be quite small compared with §_and D).

The rationalization of the appearance of M in the denominator in
Equation X has been developed in terms of the hydroxyl radical presumed

to form in the metal-catalyzed peroxide scission:

R-O-O-H + M ; R-O- + H-O- + M (6)

 

Here the radical R-O- proceeds to initiate a new chain, thus giving rise
to the numerator term, but the principal fate of H-O' is termination,
e.g., by collision with R-O-O- radicals (82). According to another
rationalization, H-O- functions not as a terminator but rather as a

"deebrancher" by its own chain process (22):
chH-OOH + H-o- -—-——-> R20-00H + H20 (7)

R2C-OOH a R20:O + H-0- (8)

 

In considering these rationalizations for Equation X, it is of interest
to compare Bawn's general treatment (Equation V), for the special case

of very low metal concentration, for which case Bawn (83) shows:

(ROOH) = k'(RH)2(M) (XI)

substitution of Equation XI into Equation V then gives:

l6

-d(02)/dt = k(k')°-5(RH)2(M) (XII)

-l -1
which also accords with an observed linear plot of (rate) vs. (M) .

However, the nonequivalence of these two preposed kinetic relationships
is obvious. Further, woodward and Mesrobian's kinetics (8b), discussed
earlier, are again different from both of these schemes.

With regard to the mechanism of metal ion catalysis, George, Rideal
and R0bertson (l7), noting that a very little cepper stearate added to
tetralin at 1200 increases the amount of antioxidant (2-naphthol)
required to inhibit the reaction by about one hundred fold, tend to
support the earlier theory of Cook (1b) that the catalysis proceeds via

a complex formation:
A
ROOH ’- M «-=-- (ROOH...M) --—b M + radicals (9)

while R0bertson and waters (22,60), along with Bawn (83) and many others
(11,28) consider the function of the transition metal ion to be
essentially that of an electronebank going through a two-step redox

cycle. Thus, for example, Bawn proposes (83) for cobalt catalysis:
(.
Co(II) + R-O-O-H -——-9- Co(III) + R-0° + H-O‘ ) (10)
Co(III) .. H-oH —-———-> 00(II) + H-Oo (11)

Bawn presents a good summary of evidence for the existence of the
higherevalency form of the metal ion, e.g., spectroscopic evidence for

00(III) in decomposingdperoxide systems (83).

Relatively few antioxidants have been reported to have been tested
with tetralin. In 1933 Hock and Susemihl (88) showed that hydroquinone
inhibits the rate of tetralin peroxide formation under autoxidizing
conditions. The following year Tanaka and co-workers (93) reported
hydroquinone, catechol, and the two naphthols to exhibit inhibitory
action; they found resorcinol to be a pro-oxidant. Phenol itself has
some efficacy (22); and George and his co-workers confirmed 2-naphthol
to be effective (17). waters (20) found chloranil (tetrachloro-
benzoquinone) and mercaptobenzothiazole to be effective at 760. Murata
(9h,95) has made a correlation between the efficacies of a series of
antioxidants, using tetralin as the substrate, with their polariz-
abilities. The best antioxidants include the two phenyl naphthylamine
isomers, and exhibit polarizabilities within a fairly narrow range.

With metal catalysts present, George and co-workers (17) found that
the antioxidant requirements of a tetralin system were greatly increased,
and that low antioxidant concentrations yielded no induction periods*
at all. They developed an ingenious treatment whereby the chain length
of the uninhibited autoxidation reaction can be deduced from the rate
deceleration brought about by addition of a small amount of antioxidant
(see Appendix, Section 1). This elegant mathematical development has,
unfortunately, several severe restrictions which are implicit in the
treatment but which may or may not obtain in the real system. It has,
therefore, not been considered important to the present problem, for

reasons discussed elsewhere.

 

.V—

A

Induction periods are discussed in detail in the section immediately
following.

18

George and Robertson‘s kinetic treatment for thermal (noncatalyzed)
tetralin autoxidation (81) leads to the rate expression:

k(RH)2(02)

_____,____.___ (XIII)
k! (02) + k"(A)

-d(02)/dt

which has the interesting property of introducing an oxygen dependency
for the inhibited rate, but not for the uninhibited rate. This
derivation assumes no chain branching and is therefore of doubtful
applicability to metal~catalyzed systems. Robertson and waters (82),

assuming the general termination step of Reaction h, arrive at:

 

—d(02)/dt = kQEIgLOa) (XIV)

which is the limit for Equation XIII as the second denominator term
dominates. Neither of these expressions, however, account satisfactorily
for all of the data.

While alcohols usually function as chain stoppers or retarders,
Frye and co-workers (96) have observed a striking acceleration in the
uncatalyzed autoxidation of tetralin at h50 upon addition of ethanol.
The apparent explanation is that of chain-transfer which, rather un-
expectedly, serves to expedite the propagation cycle in a manner
analagous to that of HBr (30-32).

A number of activation energy estimates have been made for various
processes associated with tetralin autoxidation. For the first-order

decomposition of tetralin hydroperoxide, the estimates are as follows:

19

 

 

pre-exponential Ea; kcal/mole reference

_- 23. Yamada, 1936 (97)
0.93 x 109 2h. Ivanov, 1939 (55)
2.27 x 109 2h.h Robertson, 19h8 (60)
1.3 x 1011 29.0 Thomas, 1955 (98)

Thomas' rather high value may be due to his use of white mineral
oil as a medium, or to his use of Szwarc's assumption (99) of identical
frequency factors for peroxide decompositions. The activation energy
for the over-all autoxidation was estimated by Medvedev (5h,80) as 26
kcal. for the initial oxidation phase (Equation I) and 9 to 10 kcal.
for the second (steady-state) phase. George, Rideal and Robertson
estimated the activation energy for uncatalyzed autoxidation to be 15
kcal., and that for ferric stearate catalyzed autoxidation to be 6.5
kcal. (17). Bolland (100) estimated the activation energy for benzoyl
peroxide initiated autoxidation to be 2h.8 kcal. Except for one low
estimate (17), the activation energies for the peroxide decomposition
and for the over-all tetralin autoxidation are all quite close to each
other.

‘With respect to unit reactions, Robertson and waters (22) estimated
the energy for the hydrogen-abstraction step (Reaction 3) to be between
11 and 30 kcal., an estimate of only limited utility. Bamford and Dewar
(101) undertook specific calculations for several steps, as summarized

below ("TH" is tetralin):

 

 

 

unit step loglngpge-exponential Ea,gkcal/mole
T- > 02 --> TOO- 7.82 zero
TOO- + TH -e-TOOH + T- h.h0 h.5
T- + To -9 inert 8.711 2.6

20

Both of Bamford and Dewar's termination steps are presumed to be dis-
proportionation. As these last estimates are based upon indirect
reasoning, they should perhaps be taken rather cautiously.

In general, the over-all activation energy estimates compare well
with those obtained for other hydrocarbons. Bolland (100) measured the
over-all energies for a dozen unsaturated hydrocarbons; seven olefins
and cyclo-olefins fell within the range 22.h-2h.5 kcal, ethyl linoleate
was low with 20.5 kcal, and two octenes and a hexadecene grouped high

at 26.8-28.0 kcal. By this analysis:
Ea (over-all) = Ep + 0.5 E1 - 0.5 E.c (XV)

where the right-hand subscripts refer to propagation (H-abstraction),
initiation and termination, respectively. As this work employed benzoyl
peroxide, E1 was known to be 31 kcal. Then.by assuming Et for biradical -
termination to be essentially zero, Ep could be estimated from Ea
(over-all). From Bolland's data the estimate of Ep for tetralin is
about 9.3 kcal. More surprising than the spread between Bolland's and
Bamford.and Dewar's estimates is the fact that both are so low,
considering that C-H bond scission is required.

The question of termination reactions for tetralin is discussed by
R0bertson and waters (82). R- + R- coupling is apparently insignifi-
' cant, since no bitetralyl has ever been obtained from autoxidized
tetralin. The formation of a small amount of dihydronaphthalene, which
could be accounted for by the corresponding disproportionation reaction,

does leave the possibility that some small amount (less than 2%) of

21

termination may occur in this manner. Coupling of two R00: radicals is
considered most improbable; aside from the considerable orientation
requirements, the products, R-O-O-O-O-R or even R—O-O-R cannot be
expected to be highly stable, especially in the presence of peroxide-
decomposers. The cross-termination reaction, R- + R00- to give R-O-O-R
has been invoked for other systems (62,69), but is only important where
the concentrations of the two radical species are of the same order of
magnitude, a rather rare situation which does not apply to tetralin in
most autoxidations (however see George's work, discussed below).
Robertson and waters consider the dominant te~mination.steps for branch-

ing uninhibited autoxidation to be:
R00: + H0: -—-—-> ROH (tetralol) + 02 (12)
R- + H0- -—-—-—-—-> ROH (tetralol) (l3)

and in the presence of an antioxidant they assume Reaction h to dominate.

The dependency of autoxidation rate upon tetralin concentration has
been indicated by a number of preceding formulations (Equations I, V,
VI, IX, XII, XIII and XIV). With or without antioxidants, the rate
dependency is second-order on substrate for metal-catalyzed autoxi-
dations, and is reported variously to be first-order (Equations V, VI),
second-order (Equations XIII, XIV) or somewhere in between (Equation 1)
for autoxidations in the absence of metal ion catalysis.

The oxygen dependency is indicated explicitly only in those
equations wherein (ROOH) is expressed in terms of reactants. Some

treatments (Equations VI, IX, XII) show the rate to be independent of

22

oxygen pressure. George and Robertson's (81) Equation XIII is signifi-
cant in that it introduces a variable oxygen dependency as a concomitant
of inhibition; it is also significant, because it leads to a linear
relationship between reciprocal rate and reciprocal oxygen pressure, a
relationship which has been observed in autoxidations at 1100 with
radical-source initiation, metal catalysis and heterogeneous surface
catalysis (16,18,102). According to this formulation, the rate
dependency on oxygen pressure may vary from zeroth-order (Equations
XIII, k"(A) vanishingly small) to first-order (Equation XIV). Bamford
and Dewar (101), working at 25-h50, found the rate to be independent

of oxygen pressure above 100 mm. These important differences may
reflect the difference in the stability of the peroxide species, a
stable final product under the conditions of Bamford and Dewar, and an
unstable intermediate under the higher-temperature conditions of George's
work.

A unique reduction of the effective energy barrier for tetralin
autoxidation has been found by Wittig and Pieper (103,10h). Small
amounts of dibiphenylene-ethylene (9,9'-bifluorylidene) greatly promote
the autoxidation of tetralin (and of other compounds such as dioxane)
under very mild conditions. They suggest that their substituted
ethylene binds oxygen as a labile adduct which then readily attacks the
substrate. A somewhat similar prOposal has been advanced by von Konow
(105) to explain the pro-oxidant catalysis of certain metal ions;
however, his model system, for the catechol-o-quinone oxidation, does
not appear to be of utility for application to substrates which do not

possess vicinal functional groups.

23

In summary, the autoxidation of tetralin has been studied quite
thoroughly. Certain facts are well established, e.g., the initial
formation of an unexpectedly stable l-hydroperoxide, the decay of this
peroxide to yield (principally) 1-tetralone, and the autocatalytic
nature of the autoxidation as a consequence of peroxide homolysis.

The function of the metal ion catalyst is in part understood: it
catalyzes homolytic decomposition of the peroxide and thereby functions
as a chainebrancher. However, the mechanism of this catalysis has not
been unambiguously proven, and the question of metal-catalyzed initiation
is still open. A number of kinetic formulations have been made, assum-
ing steady-state conditions for the tetralyl and tetralylperoxy radicals
and in some instances assuming steady-state conditions for the hydro-
peroxide also; the variety and disparity of these derivations speaks

for itself. Finally, information on the nature and precise mechanism

of antioxidant inhibition is limited to the kinetic observations of
George and his associates and of Bamford and Dewar, based upon measure-
ments of the retarding effects of certain additives upon steady-state

rates.
IV. INHIBITION AND THE INDUCTION PERIOD

"On sait depuis longtemps que l'oxydation de nombreux hydro-
carbures est caractérisée par une periods d'induction assez
variable."

... C. F. Cullis, 1950 (106)

Perhaps the earliest observation of an induction period in an

autoxidation was made by Lumiere and Seyewitz in 1905 (107). In

studying the autoxidation inhibition of sodium sulfite solutions by

2h

hydroquinone, they noted that the additive did retard the reaction, but
not in the time~independent manner by which retarders often operate:
"L'examen de ces resultats montre que l'effet anti~oxydant n'est pro-
portionnel ni au temps, ni a la quantite d‘hydroquinone." The
peculiarity of their data lay in the fact that, in intermediate inhibitor
concentration ranges, inhibition was very good for a while, and then
deteriorated, allowing finally a rather fast autoxidation of the sub-
strate. This phenomenon, which they did not further identify, was later
to be known as an incubation period, a protection period, an inhibition
period, and (currently) an induction period.

The precise characterization of this time interval between the
beginning of the exposure of the system to autoxidizing conditions and
the beginning of rapid substrate autoxidation has been sought in a number
of ways. Early methods employed, as a criterion, the time elapsed before
some system parameter changed noticeably, e.g., the time required for
free acids to appear (108) or for oxygen pressure to begin to dr0p (109)
or to begin "dropping rapidly" (110). Illustrative of the vagueness of
the earlier preposed characterizations are those of Milas ("An induction
period ... is usually defined as the time necessary for the reaction to
reach its maximum velocity") (111) and of Rescorla and co~workers
("The breakdpoint is indicated by a definite increase in the color in-
tensity of the filter pads when compared with the unoxidized control
samples.") (112). Milas requires specification of the instant that an
asymptotic curve conjoins its asymptote, while Rescorla relies upon .

a purely subjective interpretation of what constitutes a "definite"

increase.

25

A number of pragmatic criteria have been proposed, which are satis-~
factorily specific, e.g., the time required for the attainment of a
certain "peroxide number" (113), for the formation of a certain arbitrary
amount of gum (11h), or for the autoxidative destruction of a certain
percentage of the substrate (115,116). Indeed, the widelyaused
(110,117-122) A.S.T.M. induction period method for gasoline testing
(123) defines the end of the induction.period as the moment when the
rate of pressure drop in a standard oxygen.bomb reaches a value of
eight pounds per square inch per hour, a reasonable quantification of
an earlier method (110). All these are practical criteria for applied
studies, but are in principle ill-suited for theoretical use since the
"induction periods" so measured are actually the sums of the true
induction periods plus portions of post-induction autoxidation, and are
consequently to some extent functions of the post-induction autoxidation

The American literature relevant to induction period studies presents
an additional and perhaps characteristic problem in interpretation: a
surprising number of workers have undertaken to develop indices,
numbers, coefficients or ratios to express their results. Mattill's
"anti-oxygenic index" is obtained simply by dividing the induction
period (with an arbitrary 0.020% antioxidant present) by the induction
period of the control blank (12h). Later expressions have become
progressively more complex (113,11h,1l7,119,125), as illustrated by
the following "inhibitor ratio," where AX is the antioxidant under

study and BAP is the arbitrary standard, p-butylaminophenol (11h):

26

. t AX - ' blank '
R (Ratio) 2 ti BAP _ ti blank (XVI)

Only one of these formulations (119) is demonstrably relevant to the
empirical data; this will be discussed more fully below;

Most recent investigators, however, have employed the method of
graphical intercept: the induction period is then defined as the
projection on the time axis of the intercept of the initial (or
"induction period") rate-awhich may be immeasurably slow and, therefore,
parallel to the time axis--and the post-induction steady-state autoxi-
dation rate. A mathematical definition which is essentially equivalent
to this is as follows: the induction period is terminated when the
second derivative of the reaction variable reaches its maximum, i.e.,
when the third derivative falls from a positive value to zero.* The
degree of correspondence of these two methods of defining the induction
period will be discussed later.

The sum of information available on the induction period phenomenon
in autoxidation reactions is extremely scattered, for several reasons.
First, autoxidation phenomena themselves, as was noted earlier, have
only recently been organized and indexed as such; and as a consequence
recent review papers have been reasonably comprehensive only with
respect to quite recent work. Secondly, terminology has been in a state
of considerable flux, as is indicated in the above discussion. Finally,

the erratic and nonrreproducible nature of much of the data has led

many workers to present their inductioniperiod findings in a purely

 

*The writer is indebted to Professor J. C. Sternberg for this
suggestion.

qualitative manner (17,22,106-lO8,llO,ll3,118,126-l32), incidental to

other autoxidation data. This tendency towards erratic nonreproduci-

bility has been commented on by Bawn,* Cullis,** and a number of other
competent workers. Biggs and Hawkins note that "Even fresh samples of
pure (substrate) vary considerably in the length of the induction
period" (130), and Mattill finds that "There is a great and almost
mysterious variability in the induction periods of different samples
of the same (substrate)" (12h).

It is part of the faith of the scientist, however, that physical
phenomena conform to natural laws, and, therefore, can be explained by
them. In the past decade, on the basis of an accumulating body of
experimental data, Mulcahy and Ridge (133) and others (81,13h,135) have
proposed two general lines of explanation, either or both of which may
be operative in a given instance:

Case (i): The autoxidation proceeds via a slow chainébranching
process, such that the propagation and branching steps
proceed extremely slowly until the concentrations of
the reactive intermediates (radicals and, in some cases,
hydroperoxides) become appreciable, whereupon branching
brings the reaction up to a fast steady-state rate fairly
quickly.

Case (ii): An initial amount of inhibitor reacts sacrificially with
the intermediates, checking the reaction or retarding it
to a very 31 w rate, until the inhibitor is consumed,
whereupon the reaction accelerates up to the steady-state
rate.

The considerable difficulty in obtaining reproducible data may

then be ascribed to the sensitivity of this induction period to slight

 

*Bawn (l), cited above on page 1.
**Cullis (106), cited above on page 23.

28

variations in such factors as initial peroxide content of the substrate,
fractional part-per-million quantities of certain pro~oxidant metal ion
impurities, or exposure to adventitious excitation (even, for example,
diffuse daylight). Conversely, careful control of storage and experi~
mental conditions has led to reasonably good induction period data.
Because of the practical interest in product stabilization under
storage conditions, the most frequently studied relationship has been
that of induction period and antioxidant concentration. Over a wide
range of substrates and conditions, the most common empirical relation-
ship found is a loose curve corresponding to no simple integral de-
pendency (81,112,117,ll9,l20,122,136,137). The most frequently claimed

linear relationship is the simple first-order one:
ti = k(A) (XVII)

which has been reported by half a dozen workers (83,135,137—lh0).
However, in only two of these instances are the actual data convincing
(139,1h0). Kennerly and Patterson (139) oxidized white mineral oil at
155° with no initiator and with a bisphenol antioxidant, and obtained a
good first—order relationship for ti's of 1-30 hours, though they
mention that at higher antioxidant concentrations the response falls

off. Boozer, Hammond and co-workers (lhO) oxidized cumene in chloro-
benzene at 62.50, using massive excesses of azo initiator and two anti-
oxidants, 2,6-di-tert-buty1-h~methylphenol and N,N'-diphenyl-p-phenylene-
diamine, and obtained similar results. It is of particular interest

that they identified the major product of the inductioneperiod reaction

29

with the phenol as the precursor-adduct, 2,6-di-tert-butyl-h-methyl~h—
(cyanoisopropylperoxy)cyclohexadienone. This indicates the high efficacy
of the antioxidant. In this particular instance, the case (ii) explana-
tion is exclusively operative, i.e., substantially no prOpagation or
branching has occurred. This is precisely the necessary restriction

for obtenance of the first—order dependency. For the sizeable number

of other instances wherein a dependency other than first-order is
obtained, contribution of the case (i) explanation is not to be inferred,
since this would tend to predict a higher dependency upon antioxidant
concentration, whereas the observed deviations are in the direction of

a lower-than-first-order dependency.* For these cases, a suggestion
which has received serious consideration is that of a direct antioxidant-
oxygen reaction (33,139,1h3). Even this plausible suggestion, however,
has not led to a fully adequate resolution of the problem of relating
theory to empirical data. For example, Kennerly and Patterson, in
undertaking to account for their first-order dependency and at the

same time to take cognizance of the antioxidant-oxygen reaction, develop

an expression of the form:

-d(A)/dt 771:7 + mod) (XVIII)

where Po represents oxygen pressure. They are then forced to assume

that the values of k_and kl_just happen to be such that the over-all

 

*An exception can be cited, however; Chamberlain andoWalsh (1h2), in a
vapor-phase study of diethyl ether oxidation at 200 , present inhibi-
tion data which appear to best fit the form: 10g ti = k(A).

30

rate of antioxidant consumption is fortuitously constant over their
experimental range (139).

On the other hand, there are some promising signs of convergence
of theory and Observed data. Thus, consider the formal similarity of

George and Robertson's theoretically-deduced relationship (81):
ti = k ln(Ao/A) + k'(AO - A) (XIX)

with the empirical data-fitting equation of Rosenwald and Hoatson

(119):

ti = a + b(A) + c log(A) (XX)

The one-to-one correspondence between these two equations suggests
the possibility of direct relationship between theory and data.

The problem of understanding the mechanisms of antioxidant action
is nevertheless far short of solution. The welter of contrary inferences
regarding mechanism is illustrated by Pedersen's illuminating study of
the effects of antioxidant structure (122). He shows the efficacy of
amine-type antioxidants to be highly sensitive to the electron-donating
properties of N-alkyl substituents (of. references 1h0,lhh), and
proposes an electron-transfer mechanism of chain-stopping for this
class. However, he infers that phenolic antioxidants confer protection
by a different mechanism, probably hydrogen-transfer. It thus seems
probable that no single theory or formulation will prove entirely
adequate to explicate the actions of all chain-stopping antioxidants,

much less to explicate the actions of other types of antioxidants also.

31

The effect of peroxide initiator upon induction period was first
noted qualitatively: peroxidic compounds reduced or eliminated the
induction periods (22,111). For the system white mineral oil-bisphenol
inhibitorebenzoyl peroxide at 1550, Kennerly and Patterson (139)
obtained a smooth curve which they did not interpret. An analysis of
their data, however, indicates a fairly good fit for:

k

ti = (Peroxide)°75' (XXI)

Hammond and co-workers (lhh), working with tetralin in chloro-
benzene, excess azo initiator, and the weak antioxidants, phenol and
N—methylaniline, found the £222.0f retarded oxidation to be proportional
to the square root of peroxide concentration, a general dependency
readily derivable from theoretical considerations (68,82-8h). Since
under their experimental conditions Equation XVII has been shown to
hold, and from this the inference concerning the absence of branching,
their data tend to support Equation XXI also.

The effect of metal-ion catalysts upon the induction period is
less clear. It has been argued (22) that metal salts serve only as
"secondany" or peroxide-decomposing catalysts. The persuasive evidence
to support this claim, i.e., that in a system containing no initial
peroxide and a highly effective antioxidant the induction period should
be unaffected by addition of metal-ion catalyst, has not been forth-
coming. On the contrary, several inhibited systems have been shown to
manifest a sharp induction period dependency upon metal-ion catalyst.

In l9h1 Fenske and co-workers noted that the 15-hour induction period

32

shown by a highly refined lubricating oil at 1300 was completely elimi-
nated by the addition of 0.0018% iron as ferric naphthenate (128).
The post-induction oxidation rate for the oil was unaffected by the
catalyst. More recently, Brook and Matthews have reported fairly con-
vincing data showing the induction period of a paraffinic lubricating
oil at 1250 to vary inversely with the concentration of iron or copper
soaps (1h5). Heaven and co-workers (137), working with transformer oils
at 1200, found that a sample with an induction.period of 72 hours showed
an extremely sharp reduction in ti upon addition of the first few p.p.m.
of cepper naphthenate. Higher additions of catalyst showed progressively
less effect, until by about 150 p.p.m. cOpper the induction period,
reduced to 1.5 hours, was insensitive to further catalyst addition;*
Kreulen (13h), studying the effect of copper filings upon white oil
autoxidation at 100°, round an initial very sharp reduction in
induction period; but again the ti-shortening effect decreased with the
addition of more and more copper. In his syStem the induction period
actually did fall to zero, but then at still higher copper loadings it
re-emerged and increased slowly with further massive additions of copper.
Thus, while the dependency of induction period upon transition metal
catalyst is real and considerable, the present experimental data are
not in mutual agreement, and the exact nature of the relationship is
not clear.

The effect of oxygen pressure upon induction.periods has been most
adequately studied for high-temperature gas-phase autoxidations. Malherbe

and Walsh (lh6), studying butane at 300°, and Mulcahy and Ridge (133),

 

* . .
Cf. discuSSIOn of effect of metal-ion catalysis upon rate, page 1h.

33

studying propylene at 2900, both find approximately reciprocal relation-

ships:
ti = 1?;7. (XXII)

These both accord with the more general formulation of Chamberlain and
welsh (lh7):

ti.(Po)n = k (XXIII)

However, the relevance of high-temperature gasephase data to low-
temperature condensedephase systems is subject to challenge. Liquid-
phase autoxidation rates in the absence of antioxidants are, with few
exceptions (62,69), essentially independent of oxygen pressure above

50 mm. Even ignoring the possibility of direct antioxidant-oxygen
reaction, however, the introduction of an antioxidant to the system may
introduce an oxygen dependency purely as a consequence of the kinetics,
since the oxygen-containing terms of the rate expression no longer
cancel each other (Equations XIII, XIV). In their studies on the
oxidation of lubricating oils, Brook and Matthews (ILS) obtained the

relationship:

k
t. =

1 (po)o.5 (XXIV)

for which, however, the defining data are only fair. Kennerly and
Patterson (139), in their mineral oil study at 155°, report somewhat
irregular data showing an increase in ti by some 20% to 50% upon
reduction of PO by one half. The larger increases in ti were observed

for the runs at higher antioxidant concentrations. This is the sum

3b

of presently available information concerning the effects of oxygen
pressure upon induction period in liquid-phase autoxidation.

The effect of substrate concentration upon induction period has
been found to obey a simple reciprocal relationship for high-temperature
gasephase oxidations (133). Brook and Matthews (th) offer the only
data for low-temperature liquidephase autoxidation; they reported a

well-defined inverse-square dependency:

k

ti =W (XXV)

The effect of temperature upon induction period is analyzed by assuming
the induction period to be inversely proportional to some rate constant
or to some specific rate-constant complex, and then making Arrhenius-type
data plots. Bawn (83), in his low-temperature study of benzaldehyde
autoxidation in glacial acetic acid, measured induction periods at three
temperatures with 2-naphthol, hydroquinone and diphenylamine, and reported
each set to give approximately the same estimate for Ea' This he there-
fore interpreted as being the Ea of the initiation process. Brook and
Matthews (lh5) reported one crude threedpoint determination for their
lubricating oil, leading to an estimated E8 of about 30 kcal. Some
excellent induction period data for a turbine oil over the range lhh-
1560 have been reported by von Fuchs and co-workers (121), but these
data are not linear on an Arrhenius plot. In high temperature gas-
phase oxidations, Malherbe and welsh (lh6) have reported a thorough

study with normal butane, pentane and hexane at 290-3600, but their

data also are nonlinear on an Arrhenius plot. Recently Wilson (135),

35

in a study of the autoxidation of solid polyethylene at 110-160°, has
reported a fairly good induction.period plot, leading to an estimated
Ea of about 25 kcal. A similar plot of his post-induction rates gave a
well-defined Arrhenius SIOpe corresponding to 35 kcal. Thus temperature
effects upon induction periods have been studied with gaseous, liquid
and solid substrates. However, not very much firm activation-energy
information has been Obtained, since the most highly consistent data
(121,1h6)have been collected in ranges where apparently two or more
competing reactions were occurring.

The two general explanations of what an induction period means
have been discussed earlier. Bawn (83), Brook and Matthews (1h5) and
George and Robertson (81) have all taken the induction period to be
reciprocally proportional to the initiation rate; i.e., they have
assumed that case (ii) is exclusively operative and that no propagation
or branching occurs during induction periods. This assumption is not
always acknowledged, however; thus, George and Robertson claim that
"This (inductiondperiod) treatment of the reaction is independent of
any particular reaction mechanism, involving free-radical or energy-
chain carriers, and further makes no assumptions regarding the chemistry
of the inhibitory process" (81). Wilson (135) follows the dualistic
formulation of Mulcahy and Ridge (133); since his induction periods
follow an.Arrhenius dependency, he reasonably assumes that he is
measuring the activation energy of a specific process, but he does not
interpret his Ea as necessarily applying directly to the initiation

process. The convincing proof for the initiation process interpretation

36

would lie in obtaining identical Ea's for several antioxidants in the
same substrate, then in obtaining a different set of identical Ea's for
the same antioxidants in a materially different substrate. Bawn (83)
has claimed to have shown the former; convincing experimental data,
however, have yet to be published.

In the discussion thus far there have been several references to
retardation. It might reasonably be inferred that retardation and
inhibition are two terms describing what is qualitatively the same
kinetic process, that of stopping chain carriers or chain precursors.
However, the continuum between retardation phenomena and inhibition
phenomena can only be postulated. Benzoquinone is a retarder for many
autoxidations, i.e., it slows the autoxidation rate, but it does not
afford a definable induction period followed by a discrete period of
relatively unretarded oxidation. Bawn (83) therefore considers benzo-
quinone-type retarders to be qualitatively different from antioxidant
inhibitors. The fact that benzoquinone (or a benzoquinone) is the
product formed in the course of the consumption of the inhibitor,
hydroquinone, further confuses this particular instance. Possibly
because of this, Moureu and Dufraisse in their pioneering Studies on
acrolein stabilization by hydroquinone (1h8) apparently obtained both
inhibition and retardation, and consequently did not Obtain any well-
characterized induction periods.) In this regard, an interesting
Observation has been made by Burnett and Melville in studying the
polymerization of vinyl acetate (lh9,150): in the photopolymerization

benzoquinone functions as an inhibitor, giving well-defined induction

37

periods proportional to its concentration, but in the peroxide-initiated
polymerization under otherwise comparable conditions benzoquinone is
simply a retarder. They suggest that in the former case the photo-
excited vinyl acetate species is effectively a diradical which may be
terminated readily by a DielseAlder type condensation with the quinone,
whereas in the latter case the monoradicals react much less readily

with the resonance-stabilized quinone system.

An ingenious application of retarded rates has been made by Bamford
and Dewar (101), in the course of obtaining estimates for rate constants
in tetralin autoxidation (discussed in the preceding section). Finding
that the rate was a function of a denominator term in retarder concen-
tration, they measured the rates for a series of retarder concentrations,
and then plotted rate vs. (retarder)-1. *At the ordinate intercept, i.e.,
where the reciprocal of retarder concentration is zero, the extrapolated
rate is the rate at infinite retarder concentration. They found a
finite "infinite concentration" rate by this extrapolation, and they
considered this to be the true initiationeprocess rate. This is
intuitively reasonable, since the contribution from propagation and
branching processes will fall to zero if and only if every precursor
radical is being stOpped by the retarder, and from considerations of
the law of mass action this will occur only at infinite retarder
concentration. Acceptance of the validity of this reasoning is further
strengthened by their data with three different retarders in the same
substrate; the extrapolated lines converge at infinite concentration

to the same intercept.

38

In conclusion, induction periods have been observed for a long
time. The literature is extensive rather than intensive, extremely
variable in quality, and displays a rather sharp dichotomy: induction
periods have been used a great deal in the past two decades as evaluative.
criteria in applied research; yet fundamental studies of the kinetic
significance of induction periods are very few, and these few are not
in general accord with each other. Only two papers have appeared in
which organic liquid substrates have been studied systematically and
with respect to more than one or two of the half dozen fundamental
variables,* the first by Brook and Matthews (1145) in 1951, and the second
by Kennerly and Patterson (139) in 1955. In neither case was a chemically
pure compound employed as a substrate. In each case certain explicit or
implicit assumptions have been made to which serious exception is taken

in the light of the present work.

 

7‘!-

The fundamental variables are concentrations of antioxidant, catalyst,
substrate and substrate peroxide, temperature and oxygen pressure.
In neither of these papers have all six variables been considered.

39

EQERIMENIAL PROCEDURES

 

I. PRELIMINARY SAMPLES

For the purpose of preliminary evaluation of possible substrates
fourteen compounds were selected, including two saturated hydrocarbons
possessing tertiary hydrogens (decahydronaphthalene and 2,2,h-trimethyl-
pentane), two olefins (octene and tetrachloroethylene), three alkaryl
hydrocarbons with benzylic hydrogens (cumene, p-cymene and tetralin),
five ethers (di-n-butyl ether, 1,2-dimethoxyethane, 2,2'-dimethoxydiethyl
ether, 2-ethoxyethanol and phenetole) and two compounds combining the
susceptibilities of ethers with benzylic labilization (dibenzyl ether
and methyl benzyl ether).

Three of these compounds, initially available in lOO-ml. quantities
(just sufficient for a single screening run), were screened without
further purification. The other eleven were fractionally distilled
under nitrogen, the center cuts being collected for screening tests.

In each case the center cut so obtained was bright and colorless.
Refractive indices were measured at 20.00 i 0.10 with an Abbe refracto-
meter (Bausch and Lomb type 33-h5-56). A representative preliminary-
sample purification procedure is given below;

Three hundred seventy-five m1. of C. P. decahydronaphthalene
(decalin), clear and pale amber, was placed in a 500-ml. roundébottom
flask to which was fitted a 10 inch vigreux column and a capillary

nitrogen bleed. At the head of the column an adapter assembly including

hO

a thermometer connected with a water-jacketed condenser, which in turn
was connected via a vented adapter to a 250-ml. receiving flask. All
glassware was connected through tapered glass joints which were
sparingly lubricated with D-C Silicone grease. After a fifteen minute
purge of the system with nitrogen, heat was applied gently by means of
a Variac-controlled Glascol mantle, so that the flask contents were
brought to a medium rolling boil. The first fifty m1. of distillate
was discarded as a fore-run, and a clean receiving flask installed.
The center-out of approximately 225 ml. was then collected, and the
pot bottoms (approximately 100 m1.) discarded. The nitrogen bleed was
maintained throughout the distillation. The center-cut, b. 190. 5°/7h0.8
mm. (uncorr.), was bright and colorless, n20 1.h763. The reported re-
fractive index for "practical" (mixed-isomer) decalin is n;5 1.h753;
for pure cis-decalin it is n;0 l.h780 (151).

Table I presents in summary form the characterizations of the
center-cut fractions obtained, along with the reference refractive
indices. For each sample three to five readings were taken on the
refractometer, using the alternating approach. The reading precision
is indicated by the standard deviation of 0.000,050, calculated (152)
from 36 readings (25 degrees of freedom).

The samples thus purified were tested within h8 hours of distil-
lation, using the autoxidation apparatus and method described in a
later section. The following three samples were screened without pre-
treatment: 2,2'-dimethoxydiethyl ether ("Ether lhl," Ansul Chemical

Corp.), benzyl methyl ether (Eastman Organic Chemicals, White Label

b1

TABLE I

CENTER-CUT FRACTIONS OF PRELIMINARY SAMPLES

 

 

 

 

Compound Boiling Point Index ongefraction
Observed Beilstein Value
(uncorr.) at 20°w (151)
Cumene 151-1520/7h3 mm. 1.h917 n50 l.h920
p-Cymene 175-1760/7b3 mm. 1.h899 n50 1.h903
Decalin 190.50/7hl mm. 1.h763 n55 1.h753*%
Dibenzyl ether 2300/20-25 mm. not determined
Di-n-butyl ether 139-lh00/7h2 mm. 1.399h n65 1.h010
Dimethoxyethane not distilled 1.3791 n50 1.3722;
n29 1.3822
Ethoxyethanol l3u°/7h2 mm. 1.hO77 n50 l.h080
Phenetole 156°/7h0 mm. 1.5069 n50 1.5085
Tetrachloroethene 120-121°/7h2 mm. 1.505h n50 1.5055
Tetralin 2030/7h1 mm. 1.5h05 n60 1.5h02
Trimethylpentane 100-110°/7h0 mm. 1.3912 n50 1.3916

 

*with a polychromatic "white" light source.

**Variab1e according to the cis-trans isomer content.

D2

grade) and octene (Eastman Organic Chemicals, Yellow Label, mixed
octene-l and octene-2). In each case the sample was ordered fresh from
the manufacturer and was taken directly from the sealed reagent bottle
for testing.

A further preliminary purification was carried out with tetrachloro-
ethylene. Industrial chlorinated solvents are usually stabilized with
covolatile inhibitory additives, and consequently distillation-~even
with a highly effective column-~13 often inadequate to remove such
additives. Since the additives employed are amines, the following
procedure was used. Three hundred m1. of the crude tetrachloroethylene
was extracted five times with lOO-ml. portions of 1.5 N aqueous hydro-
chloric acid, then extracted with successive portions of distilled
water until the raffinate was neutral. Two hundred fifty-eight ml. of
the wet extracted solvent was then placed in a clean 500-m1. round-
bottom flask with 38 m1. of C. P. thiophene-free benzene, and the
mixture refluxed under a lO—ml. Dean-Stark trap. Within ten minutes the
trap had collected 0.05 ml. water and within half an hour the trap
contained 0.06 ml. water. .An additional thirty minute reflux yielded
no further water. The trap contents, including about 15 ml. benzene,
were discarded and the solvent, still containing about 25 m1. benzene,
was fractionated in the same manner as the preceding samples, except
that a large fore-run of 85 ml. was collected to ensure removal Of all
benzene. This extracted sample was then tested for autoxidation

stability, as described subsequently.

b3

II. TETRALIN PURIFICATION

.After the selection of tetralin as the substrate for intensive
study, a more elaborate purification procedure was undertaken for this
compound. The procedure employed acid extraction, water washing, drying
and fractionation under nitrogen.

The starting material, Fisher purified tetrahydronaphthalene,
lot no. 761,530, was found to be bright, water-white and clear. Six
gallons of this material was purified batchwise, in l500-ml. portions
as follows.

First, 1500 ml. of the tetralin was placed in a two-liter separatory
flask and was extracted six successive times with 50-ml. portions of
cold concentrated reagent grade sulfuric acid. In each extraction the
flask was given 96 vigorous shakes, bringing about a thorough fine
emulsion, which separated on standing. The first raffinates were con-
sistently a deep reddish-brown. The great bulk of the impurities
(oxygen~containing compounds, dihydronaphthalene and naphthalene), as
indicated by the color of the raffinates, was removed by the third
extraction. The final raffinates were clear and light.

The acid extracted hydrocarbon was then washed once with 100 ml.
of distilled water, once with 100 ml. of 1.0 M aqueous sodium bi-
carbonate, and then five successive times with lOO-ml. portions of

distilled water.* The same vigorous shaking was employed for each

 

‘*In a pilot run the bicarbonate solution was omitted and it was found
that the sixth water raffinate was neutral to litmus.

bl:

extraction process. As the density of tetralin is close to unity,
separation of layers during the water washing was rather slow; for the
first aqueous washes it was often necessary to wait several hours in
order to obtain reasonably good separation. Since the objective was
optimum purity rather than optimum yield, the "scum" zone at the
interface was systematically bled off with the raffinate with each
extraction. Thus about 10-15 m1. of tetralin was discarded per
extraction operation.

The wet extracted tetralin, markedly cloudy due to the water
present, was first dried over fresh anhydrous reagent sodium sulfate.
Two extracted portions of tetralin, 2800-2900 ml. combined, were placed
in a clean dry one-gallon brown glass bottle with 200-250 g. of the
drying agent. The mixture was shaken periodically and allowed to stand
for at least 2h hours. Within six to eight hours the tetralin became
noticeably clearer to the eye, indicating that most of the water had
been absorbed by the desiccant.

The sulfate-dried tetralin was then filtered through Whatman No. 1
paper into a fresh dry one-gallon brown glass bottle. To this bottle
was added approximately 10 g. of sodium chips, pared freshly under
reagent benzene for each drying operation. The tetralin was then
allowed to stand for at least an additional 2h hours, with periodic
swirling of the contents. ‘Within four to six hours the tetralin
became water-white and bright, indicating nearly total removal of water.

A charge of not more than 1800 m1. of the sodium-dried tetralin was

then transferred directly into a three-liter flask equipped with two

hS

tapered seal joints, and the flask connected to the distillation
assembly. The assembly consisted of a 2h inch vigreux-type fractionat-
ing column sealed in a silvered vacuum jacket, an air-cooled head-
connecting tube, and two water-cooled condensers in series leading to
a vented receiving flask. A stream of prepurified oil-pumped dry
nitrogen was passed into the tetralin and flushed through the system
for fifteen minutes before heating. After the first five minutes'
flushing, the nitrogen capillary was partly removed to permit addition
of about five grams of freshly pared sodium chips to the flask contents.
The nitrOgen flush was then continued. At the end of the flushing
period the nitrogen throughput rate was reduced to a trickle and heat
was applied to the flask by means of a Variac-controlled Glascol mantle.
The sodium chips melted and dispersed as small spherical droplets as
the flask‘contents warmed. Usually an appreciable reaction was evident
on the face of the droplets, indicating that traces of water were
still present. The other impurity known to be present at this stage
was reagent benzene, introduced on the surface of the sodium chips.

The flask contents were brought to a slow steady boil, such that
the reflux ratio remained at least 10 to 1. Occasionally the first
few ml. of fore-run were cloudy, notwithstanding the preceding drying
operations. Fore—run fractions were collected until over 100 ml. of
homogeneous and bright distillate was obtained; then the center-cut
was taken. In each case the fore-run.volume was between 125 and 200

m1.; this was discarded.

D6

The center-cutcuflOOO-l200 ml. was then collected, and approxi—
mately hOO ml. of bottoms was discarded. The center-cut material was
then transferred to a twelve-liter storage flask under prepurified
nitrogen. After each addition of freshly distilled tetralin to the
storage flask, a stream of prepurified dry nitrogen was passed through
the flask for a period of two to four hours, in order to purge the
contents of any oxygen which might have been adventitiously admitted
with the tetralin. The purified tetralin was bright, water-white and
colorless, n20 1.5h55, in good agreement with the literature (153);
Eckart reports 1.5hh9 (15b) and Krollpfeiffer reports 1.5h60 (155).

The general technique of using concentrated sulfuric acid extrac-
tion followed by water washing, drying and distillation under nitrogen,
has been favored by several recent workers, including Wbodward and
Mesrobian (8h), HammOnd and Boozer (lhh) and Russell (85,86). Others
have followed different extraction sequences (96), or have relied
entirely upon adsorption of impurities by alumina (68) or upon simple
fractionation (22,101). Many others have not specified what, if any,
purification procedures or criteria of purity were used. Of the three
research groups cited above to employ the general purification scheme
used in the present work, Wbodward and Mesrobian do not report any
refractive index or other criterion of purity (8h), Russell (85)
reports "agreement with the literature," citing Egloff's reference
volume (153), and Hammond and co-workers report n65 of their product to
be 1.5hhh (lhh), which, considering the five degree temperature dif-
ference, is at least qualitatively in agreement with the value obtained

in this work, n20 1.5h55.

III. OTHER CHEMICALS USED

In this study three pro-oxidants and five proposed antioxidants
were used. The compounds used, the characterizations of purity, and
(where necessary) the special purification procedures employed are
described below;

CObalt naphthenate, a commercial pro-oxidant catalyst widely used
in drying oils and lacquers, was obtained from the Nuodex Corporation
under the trade name "Nuodex Cobalt 6." This material is a deep blue
viscous liquid, containing nominally 6.0% by weight cobalt as cobaltous
naphthenate (cobaltous cyclohexanecarboxylate) in naphthenic acid. The
cobalt content was determined* by two methods. A polarographic
w determination of the Co(II)-Co(0) half-wave in 0.5 M pyridine—0.5 M K01
medium indicated 5.68% cobalt, and showed no traces of nickel or other
transition metal impurities. A second portion was digested in concen-
trated nitric acid, taken up in aqueous ammonia and titrated with standard
0.100 M versene (ethylenediaminetetracetic acid disodium salt); this
method yielded a value of 5.70% cobalt, estimated precision i 0.02%.
Thus the actual cobalt content, about 5.7%, is five percent below the
nominal content of 6.0%. Cobalt concentrations reported subsequently
are based upon the nominal cobalt content of the concentrate, and for
purposes of comparison with other work on an absolute concentration

basis should all be reduced by 5.0% of their nominal values.

 

*The writer is indebted to H. G. Scholten of The Dow Chemical Company
for the sample of analyzed Nuodex cObalt naphthenate and for the
analyses.

h8

Azoébis-isobutyronitrile (azo-di-isobutyronitrile), Eastman Organic
Chemicals‘ White Label grade, was obtained as a high-purity white
crystalline solid, m. 101-102O*; Melville and Richards report the m.p.
of the pure compound to be 102-1030 (156). This compound, henceforth
referred to as azo initiator, was stored under refrigeration in the
dark and was used without further purification.

Tetralin hydroperoxide (1,2,3,h-tetrahydronaphthalene-l-hydr0peroxide)
was obtained by the method of Johnson (53) from samples of purified
tetralin which had been autoxidized at 700 with small amounts of azo
initiator. The autoxidation procedure is described in a later section.
To hOO ml. of freshly prepared filtered 10% aqueous reagent sodium
hydroxide, cooled to 100, was added slowly and with vigorous stirring
300 ml. of the autoxidized tetralin. The rate of addition was con-
trolled so that the emulsion temperature remained below 120. The
emulsion was stirred vigorously for an additional thirty minutes, then
allowed to stand overnight in an ice bath. The aqueous alkaline phase
was then separated, cooled to 10°, and neutralized cautiously by drop-
wise addition of concentrated aqueous reagent hydrochloric acid, with
ice-bath cooling and vigorous stirring to maintain the temperature
between 100 and 120. The aqueous solution clouded just before the
endpoint. The neutralization was stopped when the solution became just
neutral to litmus (a readily accessible endpoint due to the buffering

effect of the hydroperoxide). The neutral solution was then cooled to

 

*All m.p.‘s are by capillary in a standard oil-immersion bath.
Temperatures are uncorrected.

A9

00 and allowed to stand overnight in an ice-salt bath, whereupon bright
white crystals of the hydroperoxide were formed. These crystals were
collected by filtration, rinsed sparingly with distilled water, and
dried for eight hours at room temperature and 1-2 mm. pressure. The
dry yield was 2.6 g.

The hydroperoxide was then further purified by recrystallization
from petroleum ether as follows. One and six tenths grams of the dry
hydr0peroxide was dissolved in 900 m1. of refluxing light petroleum
ether (b. h3.0-h3.5o at 736 mm.), the solution filtered to remove
traces of ether-insoluble material (probably sodium chloride), and the
volume reduced to hOO ml. After cooling for two hours in an ice bath
the solution yielded fine white needles of recrystallized tetralin
hydroperoxide, which were collected by filtration and dried overnight
at room temperature and 1-2 mm. pressure. The dry yield was 1.2 g.
The recrystallized hydroperoxide melted at 5h.5-55.5°; the reported
m.p. for the pure compound is 560 (28,h2).

Hydroguinone, Eastman Organic Chemicals‘ White Label grade, was
obtained as high-purity colorless crystals, melting at l72.5-l73.0°.
Andrews and co-workers report the m.p. of the pure compound to be
172.30 (157). This compound was stored in the dark and was used with-
out further purification.

2,6-di-tert-butyl-h-Methylphenol, Shell Chemical Corporation's
C. P. edible grade, was obtained under the trade name "Ionol." The
white colorless crystals melted at 70.0-70.503 the reported m.p. for
the pure phenol is 70° (158,159). It was accordingly used without

further purification.

5O

Diphenylamdne, Matheson, Coleman and Bell, was obtained as color—
less crystals. The portion used for the present work was recrystallized
from absolute ethanol, the preferred method for this compound (160,161).
The recrystallized product was collected by filtration, washed with cold
absolute ethanol, and dried at room temperature and 1-2 mm. for two
days. The purified amine melted at 53.0-53.50. The reported m.p. for
pure diphenylamine is 53.0-53.10 (162), 53.2-53.30 (163), and 53.60 (16h).

p-Phenylenediamine, Eastman Organic Chemicals, was obtained as a
grey-brown powder. Both of two recent purification methods, successive
recrystallization (165) and sublimation (166) were employed. The amine
was dissolved in refluxing absolute ethanol, treated with Norite de-
colorizing charcoal, filtered, and the filtrate chilled in ice for 2h
hours, whereupon bright purple crystals were obtained in good yield.

An identical recrystallization procedure was employed, and the doubly
recrystallized amine was washed twice with cold absolute ethanol, then
dried for five days at room temperature and reduced pressure, shielded
from light. The crystals thus obtained, though still purplish-colored,
melted at lh1-1h2o with decomposition; Callan and Henderson report the
m.p. of the pure amine to be 1h2o (167). A portion of these crystals
was then sublimed at 1210 and 20 mm. for five days, yielding a pale
cream-colored sublimate, which was found to be color-stable on storage
in the dark, as noted by Grammaticakis (166).

Phenyl-2-naphthylamine, R. T. Vanderbilt 00., was obtained under
the trade name "AgeRite Powder" in the form of a grayish powder.

A double recrystallization from ethanol-water (3:1) yielded purple

51

crystals which were dried at room temperature under reduced pressure.
The color cannot be removed by decolorizing agents or by repeated
recrystallizations (168), but the crystals obtained were of good purity,
melting at 108.0-108.5O. The reported m.p. for the pure amine is 107-
108° (168) and 108° (169). A portion of the purified amine was sublimed
at 1000 and 1-2 mm. pressure for five days, whereupon a colorless
crystalline sublimate was formed very slowly. Both the sublimate and
the recrystallized material were used in subsequent tests.

In addition to the above compounds, o-dichlorobenzene and mesitylene
were employed as diluents in several autoxidation runs. Both solvents
were obtained as Eastman Organic Chemicalsi White Label grade, and both
were purified by fractionation at atmospheric pressure under dry pre-
purified nitrogen, using the same equipment described earlier for the
final distillation of tetralin.

Other incidental standard reagents and solvents used were all C.P.
grade or higher. All water used was distilled water. Lubrication of
tapered and spherical joints made use of D-C Silicone Grease and D-C

Silicone High-Vacuum Grease exclusively.
IV. APPARATUS AND METHOD

The apparatus employed in this study is an improved model of an
apparatus described earlier (62). In its essentials it consists of a
two-liter erlenmeyer flask (volume 2061.2 ml. at 250), immersed in a
thermostated bath, and connected via small spherical joints and

capillary tubing to an absolute mercury manometer which is an integral

52

element of a pressure-recording assembly. A 100-m1. sample of tetralin
containing the desired additives is placed in the flask, the atmosphere
of the system is purged thoroughly with pure oxygen or with the desired
gas mixture, and the system is then immersed in the bath and sealed
after a 90-second period to allow for partial thermal equilibration.
The contents of the flask are then mixed in a uniform manner and the
change in oxygen pressure with time is recorded continuously.

Temperature control is maintained with a suitable preset thermo-
regulator (H-B Instrument 00., model 79102A), operating a 750-watt
flexible strip immersion element through an electronic relay (Lumenite
Electronic Corp., model LER-l28l-Al), and holding the bath temperature
constant within i 0.1 degree Centigrade. This type of thermoregulatory
system is independent of external pressure, voltage fluctuations or
electrode surface changes. 'With the five thermoregulators used in the
present study, the bath temperatures have been determined absolutely by
means of a platinum resistance thermometer, using the values of werner
and Frazer (170). The true bath temperatures are shown in Table II.

An early run at 500 gave evidence of a perceptible photocatalytic
effect. .Although this effect was apparently immeasurably small at 700,
the entire bath assembly was masked with triple-gauge aluminum foil as
a precaution.

The tetralin sample was stirred continuously during autoxidation
runs by means of a magnetic stirrer motor placed under the thermostated
bath. A small Bodine constant-speed 300 r.p.m. motor was employed to

ensure uniform stirring rates; this was fitted with a primary alnico

53

TABLE II

TEMPERATURE CALIBRATION OF BATH*

 

 

 

Nominal Mean Absolute
Temperature Centigrade Temperature
50° 50.10°
60° 60.380
70° 70.3s°
80° 80.h6°
90° 9o.t3°

 

*Nominal temperatures are used throughout the discussion as a matter of
convenience, while the absolute Centigrade temperatures shown here are
used in all calculations involving temperature dependency.

Sh

magnet salvaged from a burnt-out Magnestir assembly. Sample mixing was
accomplished by a standard teflon-clad alnico bar magnet, 1~1/8" x 5/16" d.
The recording barometer assembly consisted first of an absolute
mercury manometer connected by capillary tubing to the autoxidation
flask. Encircling the vacuum-leg of the manometer was a floating coil
component of a sensitive inductance tuning circuit, the signal from
which was amplified through a conventional Brown amplifier stage. The
circuit was tuned by adjustment of a variable condenser and with the
floating coil component just tangent to the meniscus of the mercury.
A lowering of the mercury level detuned the oscillator and thereby
tripped a microrelay; this actuated a driving motor which moved the
coil downwards until the circuit was re—tuned, i.e., until the coil
was again tangent to the mercury meniscus. ‘In the event of an increase
in pressure,the mercury rose, the circuit was detuned in the opposite
direction, and the coil was driven upwards until the circuit was again
re-tuned. This sensitive system* maintained the coil continuously
tangent to the mercury meniscus, without perceptibly discontinuous
movements even under conditions of relatively rapid pressure change.
The Brown rotary recorder charted the position of the coil in arbitrary
scale units. The precision and reproducibility of this assembly is
indicated by the calibration data, in which recorder scale units were
compared with the absolute height of the mercury column, as measured

with a standard meter stick. The response throughout the range of

 

*The writer is greatly indebted to 0. Barstow and L. T. Finlayson of
The Dow Chemical Co. for instrumentation of this pressure recording
assembly.

55

519.0 to 77h.5 mm. absolute pressure is linear, with a lepe of
10.210 mm./sca1e unit and a standard deviation of slope (22 DF) of
0.013mm./sca1e unit, less than one part in 750.

The technique of sample preparation, with respect to the rather
small amounts of initiator and inhibitor required for each run, was
adapted to the conditions and purposes of the series being studied.

The method of aliquot dilution was employed in investigating the effect
upon ti of varying cobalt initiator concentration at constant hydro-
quinone concentration. For this method a set of internally-calibrated
volumetric flasks and pipettes was used, along with appropriate stock
solutions, and the 100-m1. samples were mixed volumetrically immediately

prior to their use, for example:

 

 

 

 

 

 

Run A Run B Run 0
HQ 2.500 mM. 50.0 ml. 50.0 ml.. 50.0 ml.
00 0.100 mM| 50.0 h0.0 30.0
Make~up tetralin nil 10.0 20.0
HQ concn. 1.250 mM_ 1.250 mM_ 1.250 mM_
00 concn. 0.050 mM. 0.0h0 mM_ 0.030 mM.

A second technique, of more general utility, made use of a micro-
pipet and a concentrated standard cobalt solution. This solution was
prepared by diluting h7.8028 g. of the cobalt naphthenate reagent (6% Co)
to 100.00 ml. with C.P. reagent thiophene-free benzene, to give a stock
initiator solution of 0.h865 molar 00. Addition of five microliters of

this stock solution to 100.0 m1. tetralin effects a cobalt concentration

56

of 25.0 x 10-6mola1. This is the preferred method of cobalt catalyst
addition as it greatly reduces the likelihood of variability of effective
catalyst concentration due to micelle formation.

In the exploration of effective concentration ranges for several
of the antioxidants, it was most convenient to weigh in a portion of
the antioxidant from a conventional weighing bottle for each run, then
to add the tetralin, dissolve the antioxidant, and finally to add the
five-microliter charge of catalyst. An important requirement of this
method is the ready solubility of the antioxidant. In the case of
hydroquinone, the antioxidant was found not to be rapidly soluble in
tetralin at useful concentrations, and therefore the method of aliquot
dilution, described above, was employed.

It was found necessary to use some precautions in maintaining
stock solutions during any given series of runs. Good results were
obtained by storing the solutions in nitrogen-padded glass-stoppered
flasks which were fitted with tubes so that prepurified nitrogen could
be used to "push" out samples as required. Where lOO-ml. pipettes were
used to charge the apparatus for a run, the stock solution was dis-
charged under nitrOgen pressure into a lOO-ml. cylinder, up to approxi-
mately 103-105 ml. The 100-ml. sample was then withdrawn immediately
by pipette and the small residual portion discarded.

Between runs the cleaning procedure was highly uniformized. The
autoxidation flask, after its contents had been emptied, was rinsed
three times with C. P. acetone, once with water, once with fresh deter-

gent solution (Tide), five times with cold tap water, three times with

S7

distilled water, and again three times with C. P. acetone. The contents
were vigorously shaken during each rinse. At the end of this cleaning
procedure the flask was dried in a stream of filtered compressed air.
The teflon-clad stirrer was similarly cleaned between runs.. The micro-
pipet was cleaned with three successive charges of tetrachloroethylene
followed by four successive charges of acetone. Between each run the
spherical joints were relubricated sparingly with D-C Silicone High-
Vacuum grease. At no time was sulfuric or chromic acid permitted to

contact any of the equipment used in the autoxidation assembly.
V. INTERPRETATION OF A TYPICAL INHIBITED AUTOXIDATION RUN

The treatment of raw experimental data is most clearly illustrated
by example. For the run under consideration, h1.l mg. (0.2503 milli-
mole) of azoébis-isobutyronitrile was added to 100.0 m1. of a 2.000
millimolar solution of hydroquinone in tetralin, affording an azo
initiator concentration of 2.571 millimolal. The results of autoxi-
dation of this sample at 700 under oxygen are presented in the follow-
ing tables and figures.

Table III presents the raw pressure-time data. A plot of these
data, shown in Figure 1, permits the determination of induction period
by the method of graphical intercept. In this instance the indicated
ti is 7.97 hours. As the dataplot shows, the induction period is
quite sharply defined, the precision of the graphical intercept method
permitting a variation of less than 1% for these data. The estimated

weighing error for the h1.1 mg. of azo initiator is 0.5% (0.2 mg.).

58

TABLE III

RAW'DATA FOR A TYPICAL INHIBITED AUT0XIDATI0N*

 

 

 

Time, Hrs. P, m. Time, Hrs. P, m. Time, Hrs. P, m.
0.17 7A8.7 5.17 7A6.2 10.17 667.6
0.112 71:8.7 51:2 7145.? 10.12 659.9
0.67 7h8.7 5.67 7&5.7 10.67 652.3
0.92 7h8.7 5.92 7h5.7 10.92 6h5.1
1.17 7h8.7 6.17 7h5.2 11.17 637.h
l.h2 7h8.7 6.h2 7h5.2 11.h2 630.3
1.67 7h8.7 6.67 7hh.6 11.67 622.6
1.92 7h8.2 6.92 7hh.6 11.92 616.0
2.17 7&8.2 7.17 7hh.1 12.17 609.h
2.h2 7A8.2 7.h2 7A3.6 12.h2 601.7
2.67 7A7.7 7.67 7A3.1 12.67 595.6
2.92 787.7 7.92 7h1.6 12.92 589.h
3.17 7&7.7 8.17 735.0 13.17 582.3
3.h2 7A7.2 8.h2 725.8 13.h2 576.2
3.67 7b7.2 8.67 717.1 -- end of run --
3.92 7h7.2 8.92 708.h
14.17 7146.7 9.17 699.7
h.h2 7A6.7 9.h2 691.5
b.67 7h6.7 9.67 683.h
h.92 7h6.2 9.92 675.2

 

*Tetralin, 2.00o m!,hydroquinone, 2.571 MH.aZ° initiator. 700: 1 atm- 02°

59

.Another method of computing induction periods consists of determin-
ing by interpolation the time at which the third derivative of pressure
with respect to time falls from a positive value to zero. Table IV
illustrates the calculations from the appropriate Table III data. The
value for ti by this third-derivative method is 8.02 hours. Differences
of this magnitude between graphical and third-derivative estimates of
ti are typical (v.i.).

Inspection of Figure 1 shows a noticeable deceleration in the post-
induction rate. As has been noted earlier, this is characteristic of
tetralin and is attributable to the retarding effect of the principal
autoxidation product, l-tetralone. A fairly good estimate of the steady-
state rate in the absence of tetralone may be inferred from a plot
(Figure 2) of the rate of autoxidation against pressure drop (as a
measure of total autoxidation).

The zero-time rate may be determined by graphical extrapolation to
the ordinate axis, as in Figure 2, or may be computed from the first-
derivative data vs. (PO -'P) in a more rigorous manner, estimating the
intercept mathematically from the least-squares fit, and permitting
determination of the standard deviation of intercept (152). The present
study is primarily concerned with induction periods, however, and the
use of rate measurements has been restricted to a series of runs to
determine the range of rates in this apparatus for which diffusion

processes may safely be ignored (v.i.).

6O

 

61

TABLE IV

INDUCTION PERIOD BY THE THIRD-DERIVATIVE METHOD*

 

 

 

L1

 

I

 

 

Time, Hrs. P, mm. dP/dt dzP/dt2 d3P/dt3
(mm/hr) (mm/hr?) (mm/hrs)
5.17 7h6.2
5.h2 1.0
5.67 7h5.7 0.0
5.92 1.0 + 0.2
6.17 7bS.2 + 0.2
6.h2 1.2 - 0.h
6.67 7th.6 - 0.2
6.92 1.0 + 1 2
7-17 7th.l + 1.0
. 7.h2 2.0 . 13.2
7.67 7A3.1 + 1h.2
7.92 16.2 + 5.h
8.17 735.0 + 19.6
8.h2 35.8 - 20.6
8.67 717.1 - 1.0
8.92 3h.8 - 1.2
9.17 699.7 - 2.2
9.h2 32.6
9.67 683.h
ti = 7.92 + (0.50 x 5.h/26.0) hrs.
t = 8.02 hrs.

 

*Raw data taken from Table III.

6.2

 

63

VI. DEPENDENCY CALCULATIONS

The preceding section has shown methods of calculating the induction
period from the raw data of a single autoxidation run. This section
illustrates the method employed for the interpretation of a series of
induction periods obtained from a series of autoxidation runs.

The effect of varying the concentration of azo initiator upon the
induction period of tetralin with other factors constant (T = 700, 1 atm.
02, hydroquinone 2.000 mM) was investigated by a series of seven runs.
The induction periods Obtained in these runs are shown in Table V.

These data well illustrate the close agreement between the values of
ti computed by the graphical and the third-derivative methods.

In general, a linear relationship between ti and the variable under
’study is sought by trial plots of various functions, e.g., 1n ti vs.
(variable) or 1n ti vs. ln.(variable).g In this instance a log-log plot
of the Table V data affords a good linearity for the five runs with
excess initiator present. No simple trial plot renders all seven
points linear.

The series chosen for this example is the most complicated series
of the present study, in that the two runs with less initiator than
inhibitor present a unique problem. Three conceptions of the system
.1ead to three different relationships between the two loweinitiator
runs and the other runs. First, if hydroquinone is an extremely
effective inhibitor, even at very low concentrations, then no significant

propagation or branching occurs until the last hydroquinone is consumed

TABLE V

VARIATION OF INDUCTION PERIOD WITH AZO INITIATOR CONCENTRATION*

6h

 

 

Azo Initiator Added

Observed Induction Period

 

mmoles 1n mmoles ti 1n ti ti 1n ti

mg. per Kg. per Kg. graphical graphical 3rd-deriv 3rd-deriv
10h.3 6.528 1.876 3.11 1.135 3.13 1.1hl
73.7 h.613 1.529 h.28 1.h5h b.3h 1.h68
61.2 3.830 1.3h3 5.2t 1.656 5.23 1.65h
50.0 3.129 1.1h1 6.50 1.872 6.52 1.875
hl.l 2.572 0.9h5 7.97 2.076 8.02 2.082
30.0 1.878 0.630 11.52 2.hh5 11.62 2.h53
2h.0 1.502 0.h07 15.15 2.718 15.37 2.727

 

*In tetralin contg. 2.000 mg hydroquinone, 70°, 1 atm. 02.

6S

sacrificially. For this case the low-initiator runs should yield a
sharp discontinuity, their induction periods becoming extremely long in
comparison with the others. Second, if there is some natural inhibitor
present, compared to which the hydroquinone is either ineffective or

at best offering only supplementary protection, then the low-initiator
runs should yield ti's in agreement with the extrapolated relationship
defined by the five other runs. Third(and this is an intermediate
position between the two extreme interpretations), if the hydroquinone
is reasonably effective but not totally effective at low concentrations
in inhibiting propagation, then after the initiator is used up an ad-
ditional and somewhat slower supply of free radicals is provided the
system by homolysis of the substrate hydrOperoxide, and in this case

an appreciable lengthening of the induction period, over and above the
extrapolated values, should be observed for low-initiator runs.

Figure 3 shows a log-log plot of the Table V data, indicating a relation-
ship consistent with this third conception of the system.

The linear portion of the data (and for all other series to be dis-
cussed, this will include all of the data in each series unless it is
explicitly noted otherwise) may then be analyzed to yield the best~fit
slope and the standard deviation of slope, according to standard
procedures (152). A representative calculation of slope is shown in
Table VI, using the data from the first five runs in Table V, and
fitting 1n ti (third-derivative) vs. 1n (initiator concn.). The value

obtained is:

d(1n ti)/d(ln initiator) = - 1.013; standard deviation i 0.020

66

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

« . 1H . . 1 44 4 ..
9..4#YO.-ini¢.o-§103.01.... 4‘s; .Al.o -.1.). o acvovpt»? ....415767.WFI.721
#.:..VA VA.. ...; Y...i.... . .A d........ . . .vv.w.(..o¢..(xr ...:¢7+&.f(o
st 0 II ...c . 0 4 0 VII ..4 . 0.0 u v . clfiu. . n . v 6 A u o O a c c t n c o a o . P < v 0.14 V. :6 c o 6 .11.
«#11774... ..ir ..-. .vo. ..... ...vl.5.. . $1.... o...1..+(?~ .£«.vvblfi.
i L e. r , s» a
q a A A
V o .7? 0 7,1,8 . 7.1.4 o a . . c o r . u 0 ol 1 4 . c 9 7 v 4 u . . . . p o y at o o r 4 c o a . .98 If.
_ i .
a... .V.. .v‘otlu..n. A... ... ...YAA... - v ...:c o... VIVA. -¢.A(.I5.
code 01.. at. .o .... c... A..- .rt. . orécoxcy.v.a. ....(nnot ..-
..uolcllvo .. Alt... .... ....4 ....o . avtio.o>.vic. ..o. lo». ‘7.
, a 4 4 4 .
036......11 at. u A-.. .v.4 p...w+¢.. . o .+,¢. .... v.(oti.4.v 9.?a
.... ..r. ... . v... ..o. ....l... A . .... -... I... ...b olw
otco .Iv' or. o #.6. ...c‘ ..vvlo... . o .....t... «19.0: novvxolo
. ,1
. v . a 01?... ' T+ v c o . w . slob v r I . w c v F . . . o t c r o a ..Q T; . u c Ho 1 v1 9 a c
y r I) ) r ,
t )«J a 1
.»V?c....vi.+t. c c.1wv +... .....4... . ...... ,l.. .... coco oi.
.4)... u.oT no," : ..Po .. l..... 91.,9 . [J n a 6.... 7..» .... too
9... I9... P... : .oo. loves .... .... 5 . o... 5th )9... ..».y¢.c
Iota. 0.1.77va. 0 ....Y...IH ..c¢ ycofi v 4+...7lrv‘r.XV+clc.ro v.»
i 1 \r \P 1
4 i 4 la
77.. ch c . two. 6‘... ...1‘ $.74. » . (19¢. vnVo. coo. .... .VO
..-. ..-v...0 .. .. . .... o... t... . 41.... . . ...» .... ...
. c o n o e a 4 ‘15. . . 7 . . o . . v. c o In J o c . o A. o . o . b . . . (1.. ,o . . . c c .
, .,
v.6- .17-... O . ... .0... tool.l.v.l . 76.. .v0. .... |.. ...
.(VOcdooYt 0.6 t.. .... ....111.. o-.. u o v... n. 0 16.. ....(ch
yt.. +... co , .... ... .... ..-. . ...... ..o o» . ...$ ...
.
-..!1It... .9 ..1.... ...(o .... .. . . . .. . ........ ..-. ...
.....o ...?t.; n.. v... .7.-. ...-. ... . . 7... . .. .J.. ..
1 4 7.
.... .-.v .1 o y. .Y... -... ...... v . .. ...» .. ....1 o.
p...vitnc c1 #1.. . . .... 7?... . ..... 9... .... ...9.o..
o..!7..o.a 0c. qu ... .... ..-. .... v t u! . .... ..-.4 .... ...
I... .... .‘I. .+ ...vi.... v... .c. . .... . ... v .
1400 A11>IOQV 4 0 O 90in. Va?’ .... n b 0.9 .. . p .0
o:.0 . II ct .. .....904. ..)V ... . ... . . . .
-....v: o I ...y .-.. .7: ..... . .. .. .. m
4 1 l a a 1
... 4..Iva.. i . >.+. ...- .Ho. .... c .. . a... ... o... .... 1* . ... . ..r... 9... ..Y. Q... oclq..§»v ....170056 $7.10.... .(VIVAquOITA Iii.I.o-VI..n
.... u.I. . . _U . (......4c .... .... .. . . .. . . .. ... I... t «1-. .Tv. .-.? ... V... ..O. fie.5..179... ‘.ii.ii.vvtlyq O vict..l?o.o.4¢4¢.¢
. l
v... o... c». .. .... .... 68.. v». . . . .... . O . ..9 .. s c ‘.v' I. . a$.. .... ....v.(.ct 0.7.46, .0...(¢u.c )lOtic OoV‘IYcantvalo
.
.... 7.... ft. a.. .7... ..r.)..k. 91v. . , .. . .... .. . .. . ., .1..»-.«l. v. .T‘. ....Tob. .q .14 .IobT- (...+lrr..v...o.11.v.§.ir 00‘9‘1 tvaolTpIQ.
»
4 1 4 l l 4 11
.. o .....L o+q r ...;c.. A.... 4'... . a. . . I... .... ... ..o . o. w. o. v.. .... ...ch .o.. ......a... .... .o.TY-.r..|voo .oo.1....fi|?9.1liv1 JlrélI 01071.7.oarq
.... 0.. c? .v .... .. . .... .. . . . .... .. .... .. . v... c. .. v.o .7 etc... 0.1.. ..u. 1.....- +.v¢l_uv... I... .v.-.v..avl .1 .7.A£...i119-;11
... ....17I¢. . a... .... .... .. . . .. .. . . . .. v... .. .7 ... o .. ....1.... ..v. 1. .. ...- .Y.. +:.. 1.. .7.¢ .vii twt..1.¢oov..l.
.V... .1 vi; n (T .... $706. so... ... c . ...o . o. wovif....1 .r. to at Int 0.. ..Va -.v.7...v n..(-. .... .... cacti].-. -(7..+.¢4.- oltoL). VIOLILT9.YIIA.!JI7..
I‘ll! ZVTOIQIv ,
A a a .
... I... e . ...... .... ...» .... . .... .... .-.. .... .... X .. o. .. .... ....A...t .... Iv. . ..7.....cvt..§.1¢li.... 61... .11 oJViTA.¢lOAYoO:3.o
.. Ovvu.. 0.. d... o... .... 0.... . s... . .. a... .... .1 . .. .. .o.06 o... ..... ....o... ... .... ...: 717.. .11. ...ciT+.O¢ I ,_¢¢(-.v.-Ynt...
... .- .0. .. ..tv I... c... ... . . v.. .... o... v... .«o. .. c. o Toto .... v... c «6 .... .... oncoluuéllwciri v. . .JiicubolV ..8)Jn.locV Cod.
... o v... .. tb.. .... .... .... , . . .. . .. .... .... ..v. ... .v on- o... Jwéc .... 9. v coy. .v.7-v).y 9a.:Tb..- .7:»o..v..,9lva.o o ..tIV 0.091.000)
n ,
.Iololo n
I {I41 1 4 a A 4 i a
... a. c». Oct ...v .... n... .. . . . ....v.... ... .... .... .. .o <.. ..Is. .tvo .... .... 01.. ...Jv...v.«... .iol dildo taublvfi ....uiwiriio .6..
c» ob. u.cCo. ..t. .5... .... ... . ... v .... .9. .v0. .... 09 a 41.9.. 9..» .01... .‘é. ..-o :9. ....A - .... Inc... ...-Yin... o c....oii9~.u 6.1..
.. .. .. .. .... c. . .... ... . . ... .... ... ....i.... .. r 9.. .... .... v c. ..v. ... .... l. . .... .... O ’r... so)... .1168: . ....
l _
.f. err. ... .c 9.7. ...t ..I» o .. . . .... .... .... o...ln.4cla on Io co.» t..o...7¢ 7... 3.01 ooY. ...: .uvclviii. .-.; Avoiollaltvlo 1.7.1.1..)TIt 1
t r ’
IIHII 1 .. 7 I. . a l 4 O , 04 4
0 vv ac. c .... .... ..r. .... . . .r .... ...v .... a... .. .. ...1'v.. ...l .c.. 9... cl... ...AIT.... .... ....Iét T... o.o|ol9 .¢7..v k3... 60....A
000 v. ... o o .... .vo. .... .1 . . .... .. . .... .v... .... I. .. ..b .... 0... ..o. ....Y»... .. . .ovx.l...a blocoullfi 3.60v.(udaio 00.0.74... $3..
to. o? 6.0 T. .... L... n... ... . .. . ... ... .... .... .. . . . .03. ...~ 071v. can: 9... .... Y. . v.77. .... iv..1...b)0 90.11....4 00-...
.70. +7. 7.. to. .o‘. .... .... ... . ... ... u... .... ...o .. on on.i'¢vt cl... ottlc...... v.10. v... ...o .4». ..na .ovoi .on « vso‘irtl<i Yttr
III. {I >
I .
at. .v ... . .... .... .... .... .. . . .... .. .... .u . .... .... .67.. .... (... ....i....v.. . ..T? ....lvv\.. .... t... .... ....
...F.» ...o— . v... ,.... ..1. ... . .... ... .... .... . .. .. .... .. . .... ......... ... .... .... .... .... .... -... . O...v.5... .. .
.... a. .a. o ...v k... .... I . . . ... . .. .o.. c . . . . v... n .. ... .... u. . ... . .. .... .... ...!A...n .... ....L.. o ...
... lao.t .0 ....ib... .... . . . . .. o... . .I r ..r . .. ... .vvt 0.. ..4. T.tsvoo.. I... 7A9. ..vl’lrh... A... ..t. ....IT ..IA.0 A 87...
Tell, I . < 4 a a
... aicowai v o... Vcc4 .... .... . . .... . .. . .. .. .. ...97..c. .... ..ttl.... v... .7....... ..b. a... .... 05.. o.o.vl(v.. ..A
...797..rc ... . ..cw... .... . . . . . . .. . ..‘c . . . ... ..H. ccic .... ..V- ...? .... .... v.¢u ...4 .... .... ..41..1.900 .. . ....
60.t 4|...n. cos .. .... 4...: o c. .. . . . . . a.. .. o. . . ... .. a «6.10 I... .v.' ...0. .... .... noctfnoavcuou . .rl..o‘ . .O‘It.... ...».
nit. ¢on ...I .. .... o... c. . .v.. . . .. ... . . . c .. . o. «.610... 60.35... .... 1‘s. .... o... v?!- n..V ....v’b.» .660... "tcx..cb at...
I r r
4 a 4 1 i III I I O
a... .... ... .. .... .... .... n . .... . . .. ...a a. c . Q..4 no. 7 c. c... c. A .... 9‘. 0+4. . ..1... our: .... . notvvlvco.. .' .
V .
.... .... ... o .. .c . . .. .... . . . . .... . ... .. . C o \ ) I ..v.... .. .... ....L- ..olol...o v.0
. .. .v.. ... z . .... .... .... . . .. . ., ... .. ... 9.-. .... .. . .... . -—....1665. ....i
y
4 l
.... .... .. . .... .... .... . .... .... .. .... . . c . . . ... c. . .. ... .... .... ovo' ao.o.n. .
.... .... .. .. .... .. . . . .. . .. .. ... . . . ...v .... .c.. ... .... . .... .... .... ... t... . Z ......61. . .
...r .... . f .9 ..... . ... ... . . . . . . . v... ...1 .. . .. .. .. . ... .... .... .-.. 1.... .... a... 9...
t L
a u 4 l
...alv... ... .. .... ... . . . .. .. . ... .. .. . ,. c-.. .... . . . . .... . . ... ....A..... ..boilfic.i.|7. o
...A ......o. .. to . .. .... . . .... . . .. I. . .. ... . . .... . . .... .... co. . .. . .. .... ( fincAoonOAcv.r
l
... not. ... .. .... ... . , 1. A. . . . . . I . . .. .v.. .... . .: .... 1. ..Au .vv! .... ... .... .ocuuvooo 1....
.... ..y) .....t .... . .... .. ..... . .. ,. .. .. .. . ..... . . . ..... I... ....y.:I.7....
{'1 l 4 4
.... .... to. .. .... .. . .... ...,. . .... .. . . .. . . ... .... . .. .... ... .... u I ... ....v.. . .... ...» ! .7.o 5.9.4....4.
.... ... e .. .... .. .. \, . .., . . . . .. ..ev .. . . ., .... .. .... .... .... -... ...7. ... ...? -.Il
. ..vrl. .. ..... . .. . . .. . . . . ... .....tv. .... ...... .77. ..v .... .91. .... . .. ...o . .... $9.... 0...
i
.... ...f . ... .. .... .. . . . .. .. . .. .. ...?.. .... .... ........ ..-. .... -. . ....» .. . .... . ...Tr.... (All
e L
l 4 4
v... .... ... .. . .« .... .... .. . .... .... ... . .. . .. b . .0.74 ...?lbo.. v .- .ovo .... .... ...9 ....v.... .... co . .An- .09. 00'? ...o
. .... . E . .... .... .... .. . . .... ..-. . .. ... .... . .. ... .... .ac. ..n......a.ot ...- ... «... .tI. v. .. .... 4... .... .o?. ...
. . .... t .. .... . .. .... ... . .. . .... .... .'.. ...fi .. . ..V.... «-.. .1: i...- o.. ... ..oo 7. . 111.2 ....1 . . .07.. w... .v.. ...»
.. ... . . ... . .. vv.. . .. . . .. ..., ... .... ....a .. .. ... ..b. ...: .-.. .....7 n... ... ... .... .... i!.vl.... v... .(.c .... tic.
. LI
I4 4] 1 J .
.1... ... . .. . a... a... . . . ... .. . .... . .. .... _ .. c4. ....Yv... |> . ..O. ...I ... 9. . ..., ...VO 0.9. on . .... .9c. tactvarfo
.... ...A .04 .. ..u. .v.. .. . . . . ... v. .+ . .... v. .. . . ..V4 8... .. o. ..7 . n. .. . .... . .. o... _. . ... s .- .... c...
...a .... ... . .... ..c. .... .... . . . .. .... .4. .... ..7 . ... T on 6.91.... .... v. . .... ... I .v . u. ..c. ...AV... a... A...
.. ...4 ... . . a r. .. . . .v. ..yc .. . . i. .. o.v .... v... .... .... . . . u. t. . . I . . .. .... ..v: (.5. l. ...a
L
.1 4 J] 4
. .... . .. . .. Au, . . ... .. .. . .. 7 . .. ... .... .0.. cc). ... ..o.. ..-. ... . o .... ... .. . .-.. .... .... .otv
.. o... ... .. .. ... . . v .. .. . . ... .... .... ...L «... .. . ... . .. . ..... .... .... . .. .. . . .o o .... a...
.... .. .. , . ,. .... ..... ... .. . ........ . .. .. .. . . . .. ... ... ... . .. ...A....
.. .... .. .. ... . .. . . . . . .. ...: .... .... .. . . ... ... .... ...v ..» .... c .. .... - ... 0(oo
4
.. ... .. . . .. . . . . .. . . . .. . .. .... ..~. .. .. . ......... .... ...- ....
.
. . . .. . . .. . ... id .... . . . . 1 .. ... , .. .... a... .... ., . ...a .. .. .YA...
. ., . ... 9. . . . . . c . . v . ... . ... .... a. . .ofi'... .... ...: 41-5 .... . .lcda.
. ... .... . . .. .. .. . .... . . uv ... . . ..41 ..tt Ac.. .... . .: ... .... .. .l.(onl)V
4 1 4
.. .... .. . . .. . . .... .. .... ... . .. . .... ..Y. ... c .. .. . o c. . . ..o o .
.. . . . . , .. .... .. ... .. .. ., .. . ... .... ... ... .... . , ...V o .. c... .. . ... ....
-.. . , ....
. .. . .. .. . . . i . ... .... . .. ..... . .. . .. .. . . ... .. . ... . . x.... .1 . ..... .
... .. . . . .. . . . . . . ... u .. . .. . . . .... ... .. . .... . . .... .o.. .. . .... .... ... .... .--.
rl LII» ,'

 

 

 

TABLE VI

67

MODEL DETERMINATION OF SLOPE AND OF STANDARD DEVIATION OF SLOPE*

 

 

 

 

 

x Y XY x2 Y2
1.876 1.1h1 2.180,516 3.519,376 1,301,881
1.529 l.h68 2.2hh,572 2.337,8u1 2.1ss,o2u
1.3h3 1.6Sb 2.221,322 1.803,6u9 2,735,716
1.1u1 1.87s 2.139,375 1.301,881 3.515,62s
0.9h5 2.082 1.967,h90 0.893,025 b.33h,72h
6.83u 8.220 10.713,275 . 9.855,772 1h.ou2,97o sums
OPERATIONS:
1. '3? 1.3668 8. Y-ZY 13.513,68o
2. f-Z Y 11.23S,O96 9. (3)-(6) 0,528,669,928
3 XY -(2) -o.521,821 10. (8)+(9) 1h.0u2,3h9,928
L.. f-Zx 9.3uo,711,2 11. Ex? -(10) o.ooo,62o,072
s. Zfzxz -(u) 0.515,060,8 12. (11)/(n-2) o.ooo,206,69o,66,,
6 (3)/(5) -1.013,125,052 13. (12)/(5) o.ooo,h01,293,724

7. Y’ 1.6hh

1h. (13)°°5

0.020,032,316,99

 

SLOPE (From operation 6)

DEGREES OF FREEDOM (n-2)

STANDARD DEVIATION (1h)

*Data from Table v; method

adapted

3.

i0.0ZO

from Youden (152).

68

A similar calculation using the graphical ti data yields:
d(ln ti)/d(ln initiator) = -1.017; standard deviation 1" 0.022

Thus, as can be qialitatively inferred from Figure 3, these data give a

good first-order fit, the empirical relationship being:
k
ti = T (XXVI)

for the linear portion of the curve in Figure 3. Further interpretation
of §.in Equation XXVI and of the deviations at low initiator concen-
trations will be deferred to the general discussion.

The data in Table V are illustrative of a number of trial calcu-
lations in-which both graphical and third-derivative methods have been
employed to estimate ti. Calculations by the two methods uniformly
yield results in close agreement with each other, and for most purposes
the methods may be considered equivalent in terms of the results
Obtained. There are, however, three considerations which favor the use
of the third-derivative method. First, a slightly better precision is
Obtained in defining slopes from series of data. Second, it avoids the
subjective factor in the operation of arbitrary line-fitting, and conse~
quently it is the more objective method and is entirely independent of
the operator. Finally, the third-derivative method has the potential of
permitting direct computation of induction period from any given theo-
retical construct. Thus for any hypothesized kinetic sequence the
expression dO/dt can be obtained and can be differentiated twice with

respect to time, and the resulting expression set equal to zero and

solved for ti analytically. For these several reasons, the third-
derivative method is employed in the treatment of subsequent data,

except as noted otherwise.

69

70

RESULTS

The experimental results are organized into four sections. The
first section reports briefly on a number of preliminary runs. Included
in this section for comparison with later data is the result of a series
of runs with an ostensibly nonbranching initiator, azo4bis-isobutyro-
nitrile. The second and major section reports in some detail the
induction period characteristics of the system tetralin-cobalt
naphthenate-hydroquinone. The third section reports some relationships
observed when hydroquinone is replaced with a somewhat different phenolic
antioxidant, 2,6-di-tert-butyl-h-methylphenol (dibutylcresol). The
final section reports the results of a survey of three aromatic amine
antioxidants with the tetralin-cobalt naphthenate system.

In the course of presenting the results, the empirical interpre-
tations of the observed dependencies have been indicated. For the
most part, however, consideration of the theoretical implications of

these dependencies has been deferred to the Discussion.

I. PRELIMINARY RUNS

Three groups of preliminary runs were made: a miscellaneous group
of runs with various substrates, a series of uninhibited runs with
varying concentrations of the cobaltous naphthenate catalyst, and a
series of hydroquinone-inhibited runs with varying concentrations of
azo initiator. In each case the data are reported in terms of pressure

drop in millimeters of mercury (mm.), or rate of pressure drop.

71

For this system at 700 and with a lOO-ml. charge of substrate, a dr0p
of 1 mm. is equivalent to an oxygen uptake of 0.9299 millimoles per
liter of substrate.

substrates. The substrates tested are described in Section I of
Experimental Procedures, and are reported in the same groupings. All
runs are at 700.

The two saturated hydrocarbons were found to be substantially inert
towards autoxidation under the experimental conditions. Decalin showed
no perceptible oxygen uptake in eight hours, with or without the presence
of 10 millimolal (mfl) cobalt catalyst. ISO-octane underwent an extremely
slow autoxidation, the rate being less than 0.1 mm./hr. This rate was
unaffected by the addition of 10 mg cobalt catalyst. The somewhat
surprising inertness of iso-octane towards low temperature autoxidation
has recently been noted by Wibaut and Strang (171) and by Bateman (26).
It may be attributable to steric hindrance, in view of the neopentyl
structure attached to the tertiary carbon. In summary, both saturated
hydrocarbons were found to be insufficiently reactive to serve as suit-
able substrates under the moderate conditions employed.

Of the two ethylenic compounds tested, one was extremely reactive
and the other inert. Octene, in the presence of 11 m! cobalt catalyst,
oxidized autocatalytically and very rapidly; the terminal rate surpassed
300 mm./hr., and was still increasing at the end of the run. With rates
of this order of magnitude, the observed rates are probably nonsignifi-
cant because of the limiting factor of the rate of oxygen diffusion into

the substrate (v.i.). The other olefin, tetrachloroethylene, was inert

72

to autoxidation under the present conditions, even after the addition
of 3.92 m!_benzoyl peroxide. The specially purified sample of tetra-
chloroethylene was similarly inert. In summary, of the two olefins
tested, octene was found to be satisfactorily reactive. Indeed, its
reactivity was such that anti-explosion precautions would appear to be
indicated for any extended study of this compound.

Of the three alkaryl hydrocarbons tested, cumene was the least
reactive. In the absence of initiator the cumene sample took up no
oxygen in thirteen hours. In the presence of 10 mfl_cobalt a very slow
autoxidation was obtained, the rate being close to 0.5 mm./hr. Its
methylated homolog, p-cymene, was markedly more reactive. A slow autoxi-
dation rate of about 1.0 mm./hr. was obtained in the absence of
initiator; the same rate was obtained in the presence of 2.18 WM benzoyl
peroxide. The addition of cobalt catalyst, however, greatly accelerated
the rate; in the presence of 0.10 mg cObalt the Observed rate was about
lb mm./hr., and in the presence of 1.00 WE cobalt the rate was greater
than 80 mm./hr. Further increases in cObalt concentration effected only
relatively slight further increases in autoxidation rate, probably
reflecting a diffusion effect. Crude tetralin (used "as is"), in the
absence of initiator, afforded a slow autoxidation rate of h mm./hr.,
suggesting the preSence of some natural retarder (very possibly
naphthalene). The redistilled tetralin, after a short induction period,
attained an autoxidation rate of about 20 mm./hr. In the presence of
1.00 mg cobalt catalyst, the rate obtained was greater than 80 mm./hr.

As in the case of p-cymene, higher concentrations of cobalt had little

73

further effect upon rate. A trial inhibition run with redistilled
tetralin and 10 m!_hydroquinone showed complete resistance to autoxi-
dation for the duration of the run (hO hours). In summary, two of the
three alkaryl hydrocarbons tested, p-cymene and tetralin, were found to
be satisfactorily susceptible to autoxidation and to autoxidation
catalysis under the present conditions.

0f the five ethers tested, only phenetole was found to be com-
pletely inert. Neither benzoyl peroxide nor cobaltous naphthenate
brought about measurable autoxidation under the test conditions.
Di-nébutyl ether appeared to be inert in the presence of cobalt catalyst,
but underwent a smooth slow autoxidation at a rate of h mm./hr. upon
initiation with 1.95 mg benzoyl peroxide. Ethoxyethanol, in the
absence of initiator, commenced autoxidation.very slowly, gradually
accelerating in fifteen hours to a rate of h mm./hr. In the presence of
1.63 mg benzoyl peroxide the induction period was eliminated and a slow
smooth autoxidation was obtained, again at a rate of about u mm./hr.
Dimethoxyethane in the absence of initiator underwent an induction
period of about four hours, then accelerated smoothly, giving a maximum
autoxidation rate of about 9 mm./hr. Near the end of this autoxidation
run (after a pressure drop of over 100 mm.) an appreciable deceleration
of rate was noticeable. Dimethoxydiethyl ether in the absence of initiator
was still more reactive, affording an induction period of about two hours
followed by a smooth acceleration to a maximum rate of about hO mm./hr.
Again an appreciable deceleration of rate was observable near the end

of the run. These decelerations may reflect an unusual oxygen dependency.

7h

Although most substrates have been observed to autoxidize at rates
independent of oxygen pressure at pressures above 50-100 mm., a similar
ether, 2,2'-dihydroxydiethyl ether, has recently been shown to be
sharply pressure-dependent in its autoxidation under comparable con-
ditions (62). In summary, of the five ethers tested, two (dimethoxy-
ethane and dimethoxydiethyl ether) have been found to be satisfactorily
susceptible to autoxidation under these conditions, two others (ethoxy-
ethanol and di-n4butyl ether) appear to be somewhat less susceptible
although they still yield appreciable and measurable rates, and one
(phenetole) has been found to be inert under the test conditions.

The two benzylic ethers have been classed separately because of the
double activating effects of ether linkages and benzylic labilization.
Both compounds readily autoxidized in the absence of initiators. Benzyl
methyl ether commenced autoxidation at a rate of about 12 mm./hr., this
rate gradually accelerating with time. Dibenzyl ether commenced very
rapid autoxidation, with an initial rate in excess of 100 mm./hr., and
near the end of the run exhibited the deceleration which was noted with
the two fast-oxidizing ethers in the preceding group. In summary, as
might be expected, both benzylic ethers were found to be satisfactorily
susceptible to autoxidation under the test conditions.

At the conclusion of these screening runs it was decided to select
tetralin as the substrate for intensive study, in view of its ready
availability, its moderately high susceptibility to autoxidation, and
the detailed information already available concerning its autoxidation

characteristics.

75

Catalyst concentration and rate. The effect of cobaltous
naphthenate catalyst concentration upon rate of tetralin autoxidation in
the absence of inhibitors was determined by a series of runs* at 70°,
in which the cobalt catalyst concentration was varied from 2.5 x 10"6
to 2.5 x 10-4 molal. The results of these runs are shown in Table VII.
These data show the rate of autoxidation to increase markedly with
increasing cobalt concentration up to 2.5 x 10.5 M_cobalt. No further
acceleration is obtained by further increases in cobalt concentration.
This levelling effect may be attributable to either (or both) of two
factors. It was noted in Section III of the Introduction that metal-ion
catalysts characteristically accelerate hydrocarbon autoxidation up to
a certain maximum rate which appears to be limiting; this phenomenon
has been rationalized in terms of the presumed reaction kinetics by
RObertson and his co-workers (17,18,22). Secondly, in any heterogeneous
reaction of this nature, the rate of autoxidation will ultimately be
limited by the rate of diffusion of oxygen into the liqiid phase, this
being a purely physical limitation imposed by such experimental details
as mixing efficiency, area of contact, and so forth.

A log-10g plot of the Table VII data is shown in Figure b. Two
significant relationships are shown in this data plot. First, the six
runs at the low-concentration end of the scale (2.5 to 25 micromolal Co)
show a linear increase. The best-fit (least squares) slope for these

data is:

 

7‘For this series and all subsequent data reported, the tetralin used is
specially purified according to the method outlined in Section II of
Experimental Procedures.

TABLE VII

EFFECT OF COBALT CONCENTRATION UPON AUTOXIDATION RATE*

 

__
L— —

 

CO concn., Autoxidation rate:
micromolal P drop in mm. per first hr.
2.50 _ hS.3
5.00 67.0
7.50 81.7
12.5 109.9
25.0 15h.4
25.0 160.9
50.0 1h5.4
75.0 131.1
250.0 1214.6

 

*Cobaltous naphthenate in tetralin, 700, 1 atm. 02.

77

d(ln rate)/d(ln CO concn.) = 0.5h0; s.d. i 0.0086
This indicates a slightly greater than square root dependency:
Rate = k(CO)°'5+ (XXVII)

The second Observation Of interest in Figure h is that at higher
concentrations of cobalt catalyst, the autoxidation rate does not merely
level off, but appears definitely to decline. A somewhat similar anomaly
has been noted by Kreulen (13h), who Observed the induction period of
white mineral oil to increase slowly with increasing Cu at very high Cu
loadings.

Of particular relevance to the subsequent experimental work was the
selection of a reasonable concentration range of cobalt. 0n the basis
of these data, the reference concentration selected was 25 x 10.6 M,
This concentration was selected as being low enough to Obey Equation
XXVII, and yet high enough to minimize possible error due to the
presence of trace amounts of adventitious initiator in the substrate.

Azo initiator concentration and induction period. The majority Of
autoxidation runs in the present study have been carried out in the
presence of cobaltous naphthenate, a known branching-type catalyst.

It was therefore desired to carry out a reference series of runs in
which a simple chemical radical-source initiator was used in lieu of
the cobalt catalyst. A series of seven runs was carried out, with
aliquots of tetralin containing 2.000 mfl_hydroquinone and with varying

amounts of the initiator, azoébis-isobutyronitrile.

78

Go

see

I!

4.4

sentence easnoo me some
.. .

s dsxmawz-

 

79

This series Of runs was selected to illustrate the methods of data
treatment in Sections V and VI of Experimental Procedures. The results
are shown in Table V and Figure 3, and are discussed in the adjacent
text. 'Where the azo initiator concentration exceeded the hydroquinone

concentration, a good reciprocal dependency was obtained:
-1
ti = k( Initiator) (XXVI)

.At low concentrations of the azo initiator, the induction periods
became appreciably longer than those predicted by extrapolation (see
Figure 3). An interpretation of this ti-lengthening is Offered in the

original discussion of these data.
II. THE SYSTEM TETRALIN-COBALT NAPHTHENATE-HYDROQUINONE

This system has been studied with respect to the effect upon in—
duction period of variation in cObalt concentration, hydroquinone
concentration, oxygen pressure, tetralin concentration, temperature and
initial tetralin hydrOperoxide content. Following are the results
Obtained.

Effect of cobalt concentration. The effect of cobaltous naphthenate
concentration at constant hydroquinone concentration was studied by a
series of six runs in which the cobalt concentration was increased from
zero to 50 micromolal in uniform increments of 10 micromolal. The
results of this series are shown in Table VIII. The effect of cobalt
concentration upon induction period is very sharp, and is nonlinear by

either a direct plot or a log-10g plot. However, a plot of ln ti vs.

TABLE VIII

EFFECT OF COBALT CONCENTRATION UPON INDUCTION PERIOD*

80

 

 

 

CO concn., Induction.Period

molal x 106 (Hours) 1n ti
nil 30.65 3 .h23
10. 12.05 2.h89
20. h.51 1.506
30. . 1.55%r 0.h38
ho. O.5h** -O.612
50. 0.23*% -l.h70

 

*Cogaltous naphthenate in tetralin containing 1.250 m! hydroquinone,
70 , 1 atm. 02.

**For short-t. runs the ti is estimated by the method of graphical
intercept Since the initial third-derivative values are not

adequately established. This makes no significant difference in
the results obtained.

81

cobalt concentration, shown in Figure 5, affords a linear relationship.
The consistency of this relationship is also shown by the good fit of

the least-squares slope:
d(ln ti)/d(CO concn.) = -0.0996 Kg./micromole; s.d. i 0.0015
This indicates the novel and unexpected relationship:
0 \

where t: is the induction period in the absence of cobalt (in this
system about 30.6 hours) and k, which is dependent upon the units of
cobalt concentration, has a value of 0.10 when concentration units are
micromoles/Kg.

Effect of hydroquinone concentration. The effect of hydroquinone
concentration at a constant cobalt catalyst concentration of 25'x lO-éfl
was investigated by'a series of seven runs in which the hydroquinone
concentration was varied from 0.50 to 2.50 mg, The results of this
series are shown in Table IX. As indicated in this table, the two
lowest-concentration runs have somewhat less confidence attached to them
than do the other data, both because these two were among the earliest
runs made and also because the induction periods were so short that the
precision Of ti determination was inherently poor. A direct plot of
the Table IX data is shown in Figure 6.

This plot indicates that at higher concentrations of hydnaquinone
(above 1.25 m!) the dependency reflects a simple power relationship,

about first-order or a little less. HOwever, the Observation of a

82

a
r
t
n
e
C
n
O
C
+0
1
a
b
O
C
f
O
+u
C
e
f
f
E

 

TABLE IX

EFFECT OF HYDROQUINONE CONCENTRATION UPON INDUCTION PERIOD*

 

83

 

 

 

 

TA:—

 

 

Hydroquinone Concn., Induction Period
molal x 103 (Hours)
(0.50 0.23)**
(1.00 0.50)**
1.25 5.1
1.50 12.1
1.75 ‘ 19.0
2.00 23.1
2.50 3h.0

 

*Hygroquinone in tetralin containing 0.025 m! cobaltous naphthenate,
70 , 1 atm. 02.

**As these were early runs with very short ti's, the results should be
interpreted with caution. '

8L;

 

85

finite (though short) induction period at 0.50 mfl_hydroquinone suggests
another relationship in the low concentration zone.

The results of four empirical treatments of these data are shown
in Figures 7a-7d. Figure 7a shows a direct log-log plot, the non-
linearity of which indicates the failure of an unmodified power relation-
ship of the form ti = k(HQ)n to account for the data. A second approach
works with the five high—ti data on the assumption that the system has
a fixed initial inhibitor-demand (e.g., in the form of a little initial
peroxide). The magnitude of this demand is estimated by getting the
best fit for the five data points, by trial and error. Table X illus-
trates the set of computations used to conclude that the best fit by

this approach is for:

ti = k((HQ) - 1.11; Flips/4 (XXIX)

As Figure 7b shows, this method linearizes the data quite well. There
are, however, three objections to this method. First, it requires the
above special assumption. Second, it ignores the Observed existence
of short but appreciable ti's at concentrations below 1.1h mu, Finally,
although the Observed data fit is good (s.d. is 1.96% of slope), it is
not that much better than the first-order fit (Figure 6, s.d. is 3.51%
of slope) or the half-order fit (Figure 7c, s.d. 3.6h% of slope). This
difference in fit over the range n = 0.5 to n = 1.0 is not sufficient
to specify a particular value of E;with a high degree of confidence.
Figure 7d illustrates the exponential dependency plot, which in

the case of cObalt variation (Figure 5) was found to be linear. It is

86.

y,

.:r:'v~;-};-1 I z . ,
ln- (HQ concn. -1.13

y...

HQ concn.

 

87

TABLE X

DATA-FITTING FOR THE HYDROQUINONE POWER DEPENDENCY*

 

 

 

Percent

Value of a in Power Dependency: s.d. of s.d. of
1n(HQ ~ 5) d(1n ti)/d(HQ - a) Slope Slope
1.0h nu_ 0.976 0.0h5 n.59
1.06 0.935 0.037 3.9b
1.08 0.893 0.029 3.28
1.10 0.8118 0.022 2.59
1.13 0.777 0.015 1.96
1.16 0.699 0.019 2.70
1.19 0.608 0.030 b.92

 

3 4
The approximate best fit is for: ti = k((HQ) - 1.1h) /

 

*Data from Table Ix, fixed initial inhibitor-demand treatment (see
Figure 7b).

88

tentatively proposed at this point that the hydroquinone concentration
dependency changes character over the range of concentrations studied,
and more specifically that an initial exponential dependency gives way
to a simple power dependency--approximately first-order--at higher
inhibitor concentrations. Further support for this prOposal will be
adduced later.

Effect of oxygengpressure. It was noted earlier that, although
uninhibited substrates seldom exhibit an oxygen pressure dependency
above very low oxygen pressures, the introduction Of an inhibitor is
liable to introduce an oxygen dependency (Equation XIII). This pos-
sibility was investigated by a series Of runs at constant solute
composition (1.25O mfl hydroquinone and 0.025 mfl_cobaltous naphthenate)
and with varying initial oxygen pressure. Four runs were made, using
nitrOgen as the diluent gas, with initial oxygen pressures varying
from 37.9 to 738.5 mm. The results of these runs are shown in Table XI
and Figure 8.

The approximate linearity Of the IOg-log plot in Figure 8 indicates
a power dependency, for which the best~fit slope is -0.l7, s.d. i 0.017.
Exclusion of the poorest data point improves the fit but does not
significantly alter the dependency. The approximate empirical relation-

ship may then be represented by the equation:
ti = k(Po)"°'17 (XXX)

Effect of substrate concentration. The effect of tetralin concen-

tration.upon induction period was investigated by additions of inert

TABLE XI

EFFECT OF OXYGEN PRESSURE UPON INDUCTION PERIOD*

89

 

 

Initial Oxygen Induction
Pressure, mm. Period, Hrs.
738.5 5.36
371.8 6.11
158.3 6.9
37.9 9.1%-

 

*Tetralin contaigling 1.250 mg hydroquinone and 0.025 ml}. cobaltous
naphthenate, 70 .

**Determined graphically-~the third derivative method is difficult
to apply accurately for small pressure changes.

9O

0
e
m
S
S
e
r
P

 

91

diluent to the tetralin solution, maintaining the concentrations Of
cobalt initiator and hydroquinone inhibitor constant. This investi-
gation ran into several experimental difficulties. Nitrobenzene was
first used as a trial diluent, and it was found that 20% by volume
rutrObenzene increased the induction period from five to 16.0 hours.
A.repeat run.with 15% nitrobenzene yielded substantially the same
lengthened ti, 15.7 hours. It was evident from these runs that nitro-
benzene was functioning as more than an inert diluent. It is inferred
that nitrobenzene was interfering either as a radical—complexing
retarder Or as a cobalt-complexing catalystepoisoner. The retarded
post-induction rates would be consistent with either explanation.

A second attempt was undertaken with o-dichlorobenzene as a diluent.
Here an unexpected reverse effect was noted; the induction periods were
sharply reduced. 'With 20% by volume dichlorobenzene the induction
period was diminished from five hours to 1.9 hours, and with h0%
diluent to only 0.9 hours. At dilutions of 60% and higher, no
induction period at all was Obtained. As the hydroquinone inhibitor
was maintained at constant concentration relative to the total volume,
this ti-shortening effect is difficult to interpret; it may reflect
deactivation of the hydroquinone by molecular complex formation, or
catalytic enhancement of the cobalt via complex formation (177,178).
In any case these Observations indicate an activity on the part Of
the dichlorobenzene that is incompatible with its intended role as

inert diluent.

92

The final attempt to study the dilution effect was made with a
solvent carefully selected for its similarity to the substrate material.
Mesitflene, like tetralin, is a nonpolar alkylaromatic hydrocarbon, of
similar molecular weight (mesitylene 121, tetralin 132) and molar volume
(mesitylene lhO, tetralin 137). Possessing only nuclear and.primary
hydrogens, it is not itself susceptible to autoxidation at temperatures
below 1000. Three runs were carried out with mesitylene and tetralin,
at constant concentrations of hydroquinone and cobalt catalyst. The
addition of mesitylene not only lengthened the induction period but
also-«as Figure 9 shows-had the effect of blurring the end of the
induction period, making the precise determination'of ti more difficult.
The results Of these runs are shown in Table XII and in Figure 10.

Unfortunately, due to limitations on the amount of tetralin avail~
able and to consumption on "unsuccessful" runs with the earlier trial
diluents, it was not feasible to extend this set in order to define the
dilution effect more precisely. As Figure 10 shows, however, the
increase in ti appears to be approximately linear with diluent concen-
tration. The magnitude of the increase in ti (about sixfold for 50%
dilution) may be rationalized in terms of the hydroquinone-tetralin
balance. At constant total hydroquinone concentration, the hydro-
quinone-tetralin ratio was doubled at 50% dilution. As has been shown
earlier (Figure 6), doubling of the hydroquinone concentration over
the linear portion of that relationship (e.g., from 1.25 to 2. 50 ml‘_’I_

hydroquinone) results in an approximately sixfold increase in the

93

R s lu

ction Peri

n
O
.1
m
l
.1
D
f
0
t
C
.m
f
E

Undilut

P

Inducti

tion Tetra 'n

 

TABLE XII

EFFECT OF SUBSTRATE DILUTION UPON INDUCTION PERIOD*

9).:

 

‘—

 

Tetralin: Mesitylene:
Volume Tetralin: Volume Induction Period,
Percent Mole Fraction Percent Hours
100. - 1.000 nil 17.9
75. 0.7514 25. 65.0
50. 0.505 50. 106.5

 

*At constant solute concengrations: 3.50 m! hydroquinone, 0.025 m!_
cobaltous naphthenate, 70 , 1 atm. 02.

95

magnitude of the induction period. Thus the present dilution data appear
to accord well with the relationship noted earlier.

Effect of temperature. The effect of temperature upon induction
period was investigated by a series Of runs at constant concentrations
Of hydroquinone and cobalt and at ten-degree intervals over the range
50-900. In the course of this series, some erratic behavior was
Observed at 500 and 600; specifically, the post~induction rates varied
diurnally, the high rates being consistently Observed during the day—
light hours. This phenomenon, and the corrective action taken, is
discussed earlier under Experimental Procedures. For these two runs,
therefore, the induction periods were determined by the graphical
method, using the "dark" post-induction rates. The results of this
series are shown in Table XIII.

If the induction period in any reaction is a simple reciprocal
function of the rate of a process, then data at various temperatures
may be plotted according to a simple modification of the Arrhenius
equation, and the slope, d(ln ti)/d(1/T), may be expected to afford the
basis for an activation energy estimate. A number of induction period
plots of this nature have been found to be nonlinear; however, three
workers (83,135,1h5) have reported induction period data to obey the
Arrhenius equation in this manner. Two of the determinations involve
only three points, but Wilson's data (135) on the induction.periods of
a sample of polyethylene at six temperatures are sufficiently good to
lend considerable empirical support to this treatment. A modified

Arrhenius plot of the data in Table XIII is shown in Figure 11.

96

TABLE XIII

EFFECT OF TEMPERATURE UPON INDUCTION PERIOD*

 

 

Temperature, OC.%* Induction.PeriOd, Hrs.
90.113 2 .05
80.h6 3.27
70-35 5-36
60.38 10. res:—
50.10 28 *%*

 

*Tetralin containing 1.250 ml; hydroquinone and 0.025 mg cobaltous
naphthenate, 1 atm. 02.

”From Table II .
%**Determined by the graphical method.

97

 

98

A fairly good Arrhenius linearity is shown for this system over the
range 60-900, while the 500 induction period is appreciably displaced.
This displacement may represent the emergence of another process into
prominence in connection with the antioxidant consumption reaction;
thus, for example, the catalytic activity of cobalt salts in another
system has been shown to drop very abruptly from 750 to 500 (89).

The activation energy of the rate-determining induction period
reaction, as computed from the least-squares fit of the data at 60°,
70°, 80° and 90°, is 12.6 kcal., s.d. i 0.hO kcal. A facile interpre-
tation could be made, i.e., that the energy barrier so measured is that
for the reaction between hydroquinone and a tetralylperoxy radical.

An Obvious requirement of any antioxidant is that it react more readily
“with a substratedperoxy radical than does the substrate itself. This,
for practical purposes, means that it must have a markedly lower acti-
vation energy. The over-all activation energy for tetralin autoxi~
dation has been estimated by Medvedev (Sh,80) as 26 kcal., and by
Bolland (100) as 2h.8 kcal. However, as will be pointed out in the
Discussion, the actual process of antioxidant consumption, dA/dt, the
integral of which is being measured by the induction period, is a com-
plex expression involving initiation, propagation and branching as well
as the antioxidant-radical termination step. Consequently it is very
doubtful that such a simple interpretation of the Arrhenius activation
energy may be validly inferred.

Effect of tetralin hydroperoxide. A major function (and possibly

the only function) of metal-ion initiator catalysts is that of catalyzing

99

the homolytic decay Of peroxides; therefore, in the presence of cobaltous
naphthenate these peroxides may be expected to serve as free-radical
sources. Tetralin hydrOperoxide, although quite stable at 700 in the
absence of catalysis (the activation energy for its noncatalyzed
decomposition is about 2h kcal. (55,60,97,98)), would be anticipated to
undergo decomposition in the presence of the cobalt catalyst to produce
free radicals. At a fixed inhibitor level, increasing amounts of initial
tetralin hydroperoxide may be expected to shorten the observed induction
period.

To investigate this effect, five runs were carried out using uniform
samples Of tetralin containing 2.000 mm hydroquinone and 0.025 mg
cobaltous naphthenate. The purified peroxide was weighed into each
sample, then the cobalt catalyst added by micropipet, immediately prior
to each autoxidation run. The results of this series of runs, in which
initial peroxide concentrations ranged from 0.59 to b.78 m!, are shown
in Table XIV.

Inspection of these data show the induction period to be some in-
verse function of the initial peroxide concentration. A log-10g plot
of these data is shown in Figure 12. Its linearity indicates conformity
to a simple power relationship. Calculation of this relationship by
the method of least squares leads to a dependency slightly greater than
minus unity. For the third—derivative ti data, 2;: -1.106, s.d. i 0.068.
For the graphical ti data, n.= -1.080, s.d. i 0.069. The slight devi-
ation from unity in either case is not statistically significant; i.e.,

the null hypothesis has a prObability between 20% and 30% in both cases.

100

TABLE XIV

EFFECT OF TETRALIN HYDROPEROXIDE UPON INDUCTION PERIOD%

 

 

Initial Peroxide Induction Period Induction Period
Concn. , millimolal (Graphical), Hrs . ( 3rd-deriv . ) , Hrs .
h-77a 3°65 3-U7
2 .737 6 .35 6.23
1.350 12.1 12.06
0.961 22.95 22.99
0 .590 33 .1 33 . 2

 

*In tetralin congaining 2.000 mg hydroquinone and 0.025 ml! cobaltous
naphthenate, 70 , 1 atm. 02.

101

 

102

The approximate empirical relationship then is:
-1
ti = k(Hydroperoxide) (XXXI)

wherein th e hydroperoxide concentration referred to is, of course, the
initial 2 e :ro-time concentration. This relationship is similar to that
found for ‘the azo initiator (Equation XXVI).

A fI-Lr ‘ther Observation may be made in View of this relationship.
The variation in induction period has already been shown to be prOpor-
tional to hydroquinone concentration in this range (Figure 6)- If, as
a consequence of peroxide addition and subsequent homolysis, the only
irnportaht reaction was one of precursor-termination with hydroquinone,
then. a given increment of tetralin hydroperOxide would be kinetically
equiv alent to a given decrement of hydroquinone inhibitor (With a simple
corPeQ tion factor to account for radical recombination owing to the
saga S:f.‘fect). Under these conditions the relationship between ti and

etb
t e‘:L:I'._n hydroperoxide concentration, at constant hydroquinone concen-

tra ~
tion, would be of the form:

ti = t; - k(Hydroperoxide) (XXXII)

The Jl"elationship of Equation XXXII is not even approximately obeyed,
hbvever.
A second line of defense for the precursor-termination concept, as
outlined above, might be drawn by asserting that Equation XXXII is not
Ob eyed because the cobalt-catalyzed decomposition of tetralin hydro-

e . . .
p P03tide is for some unknown reason very slow in thls system.

103

The immedi ate Objection to this proposition is the consistency of the

observed :- elationship for even the low-peroxide runs. In these latter

runs, hydr- cquinone is in stoichiometric excess, even taking the unlikely
assumption that no biradical recombination occurs. Thus the relation-
ship obser-Ved in Table XIV and Figure 12 is inconsistent with the denial
or prOpaga ‘tion and branching reactions during the induction period.

The case for propagation and branching reactions during the induction

period will be developed more fully later.
I .
II THE: SYSTm TETRALIN-COBALT NAPHTHENATE-DIBUTYLCRESOL

ThQ preceding section has undertaken to explore in some detail the
emit-1Q Q1 relationships between various experimental parameters and the
induction period, for the cobalt~cata1yzed tetralin system in the
pres elice of a well-known antioXidant, hydroquinone. In order to

genébmize some of this information, and particularly to avoid erroneous
gen%:b alizations based upon some distinctive character of hydroquinone,
S€v§b a1 crucial relationships have been reinvestigated using other
amt’3Lt3’3-Cidants. These are reported in the present and following sections.
This section reports the results of tests with one of the best

Si
Triple phenolic antioxidants, 2 ,6-di~tert-buty1-h~methylphenol (here-

of:
tel" called dibutylcresol). Three series Of runs were carried out,

'l -
m “11cm cobalt concentration, dibutylcresol concentration and

temperature were varied systematically. The results of these series are

I"epor‘ted below.

10h

Preliminary tests with dibutylcresol showed two characteristic
differenc e s between it and hydroquinone. First, appreciably higher
concentra‘tz. ions of the dibutylcresol were required in order to afford
measurable induction periods under otherwise identical conditions.
Secondly , :‘Lnduction periods with dibutylcresol are defined extremely
sharply, the transition between very slow oxidation and fast steady-
state Oxidation typically occurring within a few minutes. This latter
Characte1“."x.stic,_which makes dibutylcresol an ideal antioxidant for
studies by induction period analysis, is no doubt due in part to the
fa“ i153 oxidized product is not itself a retarder, as was the case
With 1Vlir‘fimoquinone.

A second possible reason for this fast transition may be adduced
from the known chemistry of its reaction with peroxy radicals. The
131.0(1th of reaction of this phenol with tert-butyl hydrOperoxide was I

firSt .
shown to be of the form Of Structure II by Campbell and Copplnger
(17 2 3

\h‘XS Was confirmed by Bickel and Kooyman (173) for reactions with a
11“an91" of other hydroperoxides, including tetralin hydrOperoxide.
Recently an adduct of this same form has been Obtained and characterized

b
y BOozer, Hammond and co-workers (1110). This type of adduct is stable

105

in the presence of metal-ion catalyst; many were isolated in good yield

from metal-ion catalyzed decompositions of hydroperoxides in the

Presence of the dibutylcresol (173). This cyclohexadienone structure

is the end result of interaction of the phenol with two radicals, only
one 01' mich adds to the nucleus. The other apparently hydrOgen~
abstracts to form a molecule Of substrate hydrOperoxide, a branching-
precursor in the present system. The chemistry of hydroquinone inter-
action in similar conditions is more varied; it may hydrogen-transfer
or it “Way form di-adducts. If the latter should apply significantly
t° hydI‘Qquinone in this system, then both the higher threshold concen-
traai on needed with dibutylcresol and the sharp-breaking character of
lmjllc‘t’ion periods with dibutylcresol may be accounted for in terms of
its 113"fire gen-transf er function.
gifect of cobalt concentration. The first series of runs with
dibutylcresol investigated the effect of varying cobalt catalyst
cont: e‘ntration at constant inhibitor concentration. It will be recalled
that for the comparable series with hydroquinone, the Observed relation-
Ship was exponential (Figure 5). The results of five runs at a constant
dibutylcresol concentration of 7.50 mfl and with cobaltous naphthenate
cone entration varying from 0.010 to 0.050 m_1‘_4_ are shown in Table XV.
The induction period, it will be noted, is extremely sensitive to
QB\EZL‘C concentration, varying considerably more sharply than was the
case at constant hydroquinone concentration. A semilOg plot of the
Table XV data is shown in Figure 13. Here the mean value was taken

for the very short induction period Obtained with 0.035 "‘13. cobalt

106

TABLE XV

EITECT OF COBALT CONCENTRATION UPON INDUCTION PERIOD)?

-.-—_-— l: !

-‘U-‘L- l

 

 

 

‘ _. J

Ob 3.3— ‘t Naphthenate Induction Period

file 11 . , millimolar (Hours) 1n ti
0.010 107.? 11.681
0.020 8.19 2.103
0.025 2.29 0.829
0.035 0.15-0.20><~x- -1._7h3-x—:s:-
0.050 < 0.05 ---

\

 

“:bann containing 7. 50 mM 2 ,,6—di~tert-buty1-h-methylphen01 700,
Qty]. 02

fit. estimate by comparison with uninhibited autoxidation curves.

8 ti is too short to measure with precision by the present
SI‘L‘ohods.

' Qge of the mean estimated value of 0.175 hours.

....I II

107

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

44 4 . 1 4 4 4 , 4 4 4 41
o o . . {stick Viol--. .. v . VI . 00..» I O 4 M. . . u 9 u .6 .IO M. ...... 90. b IJYA to . quail? o I» v r r T; .. 9.01.9 o o 0 6 . . o. v v o . o . . a . I . on 3 é o . . . - . . . .. v . n . . . . . a. v. . v .... I .....i v Q a 7... 'IOIQIOA
... 4 oo- . +0.0‘o 4 9 f6. .0 vac. Io.t.A . . o .t.... .40.. 4.041100 ‘6. .94 o v >v0141144.$ I. .0..LY¢IIJ .L .O .0 . .... . . .. o . . C ..I . . . .I .t . . . . v . T. .4 .1 .. t . I ... ‘va' 01¢ o.lon..I. .htog
Y.|5I.t Icebb ..o o 91.9.. co. Yo... .... ..iTY4.It ....txar.6117+.oa +oo.+.r19§.§\IifIloAv.o.v a... .v...I....:.O oo¢< .-.t . .. Iot. .II I...- a..| 16.10.16700o..I9....g'704
. . .IIYO ..b . . o . v Q o » a ...v. ..4 lo. . v v I t . fl. . 1.9.10 o . .v .I a. a o lit} .5 9 0 Y XII- 1+. YLYO o Yiilll . ... o .. .Iv-I Alivb . o I o . . T61 a . c . vitAal OI . - 0|- .tl. .AIv -. .A 11 . 19.0 .11. t T. .1. . .I. 7...;
Hr A L f y t , LL
, 44 l a 4 A.) ,4
. .u 9 I» . n . I . ..9..1 . .o, ... VI. A P . . . . . .1... a. 7.9.0 .4 at v11.§ I. . .o o .AIF..I¢ 7:. 1-.- c. .o 4. .« .. o.lT?v|.> . .. ... .411. . o o o .1 96.0 .0... o no! Iot‘.xv.f. .Iwol'. . ‘99.. . 001.;
v.... .3.. ... . . .v.o ... .... .Y o. .... .... .4t. .... “.....6... ...-Y.o.-.1. ...... ..ol ...» ....v'Toc .... .-.... .... ole. .... .... .- . I...|.v..f.. Io.9+1w90?1+l
.... .... 1-. . . ...4...... ... .... .... ..... ..vI....... c... .... ...l. ...I. v..7.-v4.9.. ...r 9... .....Yfro. .... i.-. .-9. -..oo.$I.I¢o... I.--n1.-.. .0... ..61.
o. r . ,0 . u . . I o ' . o . . . . 9 . VI. . . o . . . . . . . . . ... . v--. . c 1,. o . ... ...1 ...... o b V‘A.1Vb1.l.x.¢a.ot .V. . . l. ...O .1... . ..IOI.... o . ..6 II... I .-IAYO.-- YVX . .. A o . . b . .. vv- 7 It. .. 0.05!
l . . I l
140 .Alv+,. . u v . . . . . o. o . . . . o . . . . . ..v. . . . . 4. .11 do. .. .8... o . . . .i.31.‘i . . .1 title. 4 1 4 on- 00.. a; 01.4.1.7)! I... r 1 . ..IOI O. .9 DI.‘. fintlttl o 1. .L. . It: . o '1 ..-. . v .69 .1
...8..-v.. ... . . I.... ... .-.. .. .... .... ...- f... -... .... II.§+.O 6... .....1... > fvxv.o..,r..,900'..... ...I. .I.4..Ti--?r.¢.03v.... ....I.... .Q... Iol.
.... I... ov. v o . .... ... ..9... .. . .... -... n.9t Y... -... .... -9..1’..9..¢I .t.. ...41‘. 91-101II01.4101Y1-.1 ..‘...I .0... ....1:... .940‘.. u..i. .. . ...... 4'.. ..-.. I......
....v.... .... . . .... ... .... .. . no. 3.4. t... «.10 T14. ..-. ..n-.1vv.vf...uo. .....n. J. $-frf...0.& 7o..v1v1o. A11 -14.?. n..¢ ..IIHQ ..I ..I r1..1. 36.91
, _ l 4
.-.¢. ..II ... n . I... ... .... '11. ... .. .I9.1.II.. ....1réio. ...)....04.. ....o r.0|?- a... ...-tilltaboétloc. ..I. .
8.1.. .... .... . .... .Ov .... .1 .... V... ...q..... ..431 1.... .... a... 9V?..Ir..o.. r... $.41. c.11TvI. ct o.vlo .
I... .... k.o . . .... .... .... .0 ..- I... ..v. .v... .... 99.. ...... ...1 7...? .1v.. .....Ikll.....-n1$-o.. r...
...1. ...ac ... . .... ..A. ... .n . FIol ...I .1... ......lev0 .I7. ... . .... 1.19. ...I.. .... Y...‘ VII .Ivla.¢.| O... .
... 9.1!. I .....Y..' .... .. . 4.6v ... ..I. ....x ..z. . I .... l.vA TtIvtb I‘vvi .801. thlifiIith‘ ..IQLv IO. . I
.... I-.. v. .. -.. u. I .. .... . ...-A . t l.- .. I . ..VOqu.... IV... ..|O I Iol. .--..I... .
. . I . a o v . . . i o . . . . - . . . . . . . . . . 9.. I . t I . . . c I . . . . . . I . II . .1 . v v I I). .1... . It . . I .II 1 A .. . o . .
.i..n.v.v . . o... .0 c . . .. ... ... 9..$1.I.. ... Io. . ..I oIcI I..- TI..11.01 ....L..9¢Alv..fu
..l.o .... ... l . ...I 4 . ... .. ... .... .V... 0 .o ... I I .. I I A..-t1.c.. ....f.4.-v.-.. .
-. . . . ... o .. v . . I 1.. . . o . . . . a I . . . . . . . . . . . . . . . . . £1 v . . . . v . . . . . . . . . . . a . 6 q . o I.-- . . .
AODIWQ‘O. I ~. . . n . Ann u .> .0! O O?" ..Ii 0.... Q a n h .v. cub; ...}- h-OI IV. 140' .
...9 «...? . . .... .. . .. .... .. .v.. .. . . .. . . ... -.fr..-... -.. v..TI.I... .
Q
.... ..-. _U . .. -.. o. . . . ... . .. ... . . . . ..- ..I .I .... ...-4. . .
... .... . . I .. .. .. . . . . .. . ... I. . I ...+ v..-b I
.... ..- n u .I- . . . .... . 4 v. . . ... ... .....I. .. . a. .--. I . ...... .
.... ... o I.I...Q .. . .I. . .. .... . ... . ...... ... .. . II . .... . .. ..-} .
.|.l 0...». .. .... I ... .. . .... .... ... .... ... ... ... . .. a. n
. . n . A . . . VL n . v . . . . A A . . . . 4 o . .. . . . .II o I)- . . . . . . . . IL . . a . . . . . . . . . AI. .. n l .
.... Tv.. O .... .. . ... ....v... . .. ..-. .... ...Ilf-.4.s..v.
.-.. .... cl .. . . .. . -. --..1...- .... ...- .-. .z..tirf-r.-.... ..Tl-..... .... ..6
I: .:. “H ..;..: . . ....:..;.-. .: .:- .. :..:..: . .:,.:- :.-::-III:..:;.1II:..z-:-
.... oIII a“ . ....71.. . I... .... ..I.... ... ..cv .... .. .. ... fiII.. ... .0.). .... o. .! . ..-Ili Ifi.ltf.4.-)1w.v.... .‘
r t o . . a. . ... .. . ... . .. ..11... . ... .. ... .. . . 9. 1.0. ... IvIII. . .. o. 1 . ...o ......u W..1!1..... ..--—
-... .... r. .. .. .. v... ...... .-. . . . ..-..II..--.-... . ...-.... .I.v.-. ...I.)......
....A...... ~ ...... ... . . .1 . .... -.. r... ... .. .. .... I71.1 .. .... ... ...-. .. .-.-....vr1oIVI|¢ro.. ..o
T +U x
..l. n“ . . . . .. .. . . .... | oTAI ... .... v .. ..-r.oI§. .... 9-9. . ......I: .... ... --..Is 1I1110l ItInvIv.'o.IY‘I
. v. . . II . ... . . ... i... ... . . v ..Iv .-.!» .... ...II 9.. .. .II. .. . . ...I I..IA.IIP01..,....YIV«I. ..r
_F... . I I .... ... ...: ..... .... . . ... 1.... .¢.. I....-.II . ... .I.Iol... ...IrITIITI... fI¢1$$IIAv.6I
v r c a
.v . n I . . . . 1 . . . .... . . ... . . IIO. .. .... .. II.. v.VIr... .. .5..I?1401 ..v .|.1TI —
c....l . . .. . .. .. ...I I ...... I.r . . ... v . . ...-1 .9 .4 ..v...... .IT‘- . ttclo..rlofit.1 T.
e .... O . . .1 ... . . I o ...I . .- .. I.|t .... . ..awoln...-. ... . . . . 5.1... ...vAVIolli 6.1.4 11AI9I? O
r . I I‘ll . I . . u .1 . c . . . . . . .. 0| . 1 I . . on v . . 1010I. .. . o .. I. I v. v . . . I If. I II. . . . . . 6!..«1111Iv.g 0 p o )1 ...l
1 III-cl. C p 0 T'- m
..T1 at . . . .. ... . .... .....- . ... ..I . . ..-.. -.Isl-I. ...I ...-.. ’
.l1vv1 . .. .. .. . . .... ....-..-.. i--.1......II.-.. .... .-.-II. ..- .to I.
7.1 IIOIjr 1 i .
“H ......oi a .. . .. .... . . . . ... I.-| ... ...I .... I . 1.....r .. . .. ..-. ..I .I.. I... vaI1TY. n
v.11 . . . . I. .. ... ... ..I. . . . -.. ... ... o... . .. . .I--. .. .... 1:9...9. 4....L v..
v 1.... b . 6..1. I . .. . ... .. o. . . . . . .. . . . I... ... .. . .I .... ......6-.- . y-|.0u|i|...t .4 c
.041 . $1111.. ... . ... .v. .... . . .. . .I .... ..Iv.1... ....Y.. .q . . ......I. 0.. .....YTI.1AI.II c.... .6
It 0 n
fil wtt‘l C . . .... ... A... . . . .v .. . . . . . . a. 4 .. . . In.x .. .... . .-.. ... 4. . ... 9.0.17.1910... ..l O
..A... ...v; A I .PyI. ... . . ..II . .. . .. -.. . ..v. . . . .-. I . I. .I.. .... 1.14 ct... It!
3:1 . .. . . .- .. .. I .. .-IIII . 111.21.... .....-) C
v...4 ..olxvoo‘oIA n — . . . v I c . c . . . y . I . . o . . . . .I . 4 a . . I o . VII .0 I . n .-..-.H .1. . .0. . I.1.1 .-- u .. nI¢1v..vt . an! FAXYWO‘... o.
...I 4..( O . . . .. I . . .-. .. . . .. .. - . .. ... .. .. .I -.. . . .-. .. . ..V. we... I. o
vocatvv..1 i... ... .4 v . I . . . ... . . I I ...I I I. ... . . ... n.90. . .... ..II ... ... v.1. I... .-.1.V.vo. .7
o... ....A I. .. ... ... .. . . . .. .. . ... .. ... .. . .... ... . . . ..I .14. I . .v..|.11.v..l I ... .0 C
..v . . I.‘ 0 I . . . . . Y. . . . I . . . v . . . . .‘ I. 1. . . Iv! . .7 .7. . n . . . I v n I . . . o ..v . w! YO . . . A . . ... 11-.- . I . . . v.I 1.... .IA .5 . . .36 I #61» (.Y‘I.
t .
.... .. . . .. . . . . ... . .... ... ..OOT... . .. .-....O. . .... .p .1.I . .. . ... T.I ... ._ . I4...ioo.. .-Iv 9‘.+. ..
.... .III e . . .. I . . .... ... ... a... ..I . I .0 A..I. .: .xl. ... . I . . . . .‘ v- . ... .vv.1.-.. .I'IAIY..0.¢I. ...S
. t. I... n— a .1 . . . I . u. .. . . . .. .IOIAI... . .II! ..v ... ...v ... ....TO..O. .... a... .It1!01. [Ana
.... . . D. . . ... .... .... .. .. . .. ..v. .-.. .. . .1.-. I - Q
. . ...V. . I . . . .. . .. . . I a .. . . . ... .
.... ..I . . . . . . . . . . ..... ... I. .. .. I .
... I... . .. ... ... . . . ..YDO.» .. . w. . . I
u p V . ll.’ I.vl o‘ol It: In! Ly
. ..- . .. I. .. . .. .. .. .. .lrov .... Iv! . .I
.. . .. or. . . .. I . . ...I . . I I. .... ..ln 9.. .... 41.14 .I
. . I t. . . . . Ii... 1 .. ... .. .... . .. .. ...tfinall Tv4.. .a IlJlIoc ....
. ... . J . -... ...... v....:...l...o-1-..
. . .. .. . ... ...I ...I. ..vIviol it... ....T..O.. ...
a
I-.. .....J. . ...: Ioo1tli.I.I .IIYII. .-.. ....
.. ... 1....-. .-.. --I- -I..... .
I . 6...I . I............ 91 . ..
_. .7... ..w.-.... . .v.... .... ..I .. . T... ....
. . ~u an . .. ..
._ ...‘l I ..-. A...
. ._ ... ‘
.. w. . ..vlo .n. 0....
‘ .. .... . .. . .
T. t. 4
v _. §
, .. _. .... .9..
.. ..
... -‘
. . 2 ..

 

108

iting Values for this ti are indicated by the vertical bar through
data. jpoint). Again a good exponential dependency is obtained,
east -—squares slope being -O.2569 Kg./micromole, s.d. i 0.00032
acisi on which is probably fortuitous).

‘hus -this series well confirms the exponential relationship of
.on U111, derived from the comparable series with hydroquinone.
of interest, though, that the exponential coefficient with di-

creSol is some two and a half times that obtained with hydro-

ne

‘

Er\tect of dibutylcresol concentration. The one relationship in

)re Ceding section that was ambiguous and almost noninterpretable
Lhat obtained upon varying the hydroquinone concentration at
tfilfit cobalt concentration (Figures 6 and 7). It was then noted
the relationship might reflect an initial exponential dependency
‘qu falling to a simple power dependency at higher hydroquinone
: QYI:11:.rations. The results of a comparable series of eight runs at
ying dibutylcresol concentrations are shown in Table XVI. The
y steep dependency of induction period upon dibutylcresol concen-
Lt'Z‘Lon accords best with a semilog plot, shown in Figure lb. The good
; f or four of the five data points is indicated also by the precision
the least-squares slope. The slope obtained is + 0.866 Kg./milli-
“S‘- , s.d. i 0.010. The datum for 9.19 mg inhibitor is assumed to be

rratic, as no alternative treatment of the data brings it into accord

1th the other four data.

109

TABLE XVI

EFFECT OF DIBUTYLCRESOL CONCENTRATION UPON INDUCTION PERIOD*

 

Eibutylcresol Concn. , Induction Period,
__¥ Millimolal Hours
1.666 nil
3 .111 nil
S.h88 0.60
6.6h4 1.63
7.888 h.66
8.150 7 .93
9 .189 1‘23;
17 .56 >> 110.
""““-~.___

 

With

‘betralin containing 0.025 ”E cobaltous naphthenate, 70°, 1 atm. 02.

110

t
n
O
n
O

.l

t
a
r

t
n
e
C
n
O

C

l
O
S
e
r.
C

1

t

m

.l

D

f
0

+0
C
e

f

f

E

3
Q—. $

Molal x 103

Dibu lcresol Concn.

 

111

This then indicates another exponential relationship:
ti = k exp(k'A) (XXXIII)

where §.is the concentration of dibutylcresol antioxidant and k' has a
value of 0.87 Kg./m;llimole. It is suggested that this exponential
relationship of Equation XXXIII may initially hold for hydroquinone also
(see Figure 7—d), yielding at higher concentrations to an approximately
first-order dependency expression.

Effect of temperature. The preceding data have shown the induction
period in dibutylcresol systems to be more sharply dependent upon the
concentration variables than was observed with the corresponding hydro-
quinone systems. A similar sharp dependency was observed with respect
to temperature. Thus a sample giving a satisfactory induction period
of 5.9 hours at 900 was found to give unfeasibly long induction periods
at 600 and 700. After several range-finding attempts, a series of three
runs in the range 700 to 900 was carried out, for which measurable
induction periods were obtained. The resulting data are shown in
Table XVII. These data indicate a much higher activation energy, about
36.? kcal. Although the three data points happen to be in very good
agreement (s.d. = i 0.05 kcal.), this determination can be considered
only approximate, in.view of the small size of the data set and the
difficulty of measuring with precision induction periods shorter than
0.5 hours.

This sharp increase in temperature dependency in going from hydro~

quinone to dibutylcresol occasioned a rough recheck of the hydroquinone

I“

 

112

TABLE XVII

EFFECT OF TEMPERATURE UPON INDUCTION PERIOD*

 

 

 

 

JT

 

Tempgrature , Induction Period,
C . Hours
70.35 2.33
80 .h6 O . SO
90.h3 0.12

 

*With tetralin containing 1;.209 m! dibutylcresol and 0.025 mg cobaltous
naphthenate, 1 atm. 02; ti's by graphical method.

1"- .A“' .1 .
i
1
l

113

temperature dependency. The reason for the recheck was to determine if
tme method of sample preparation was influencing the results. The
hydroquinone samples had been prepared by the aliquot dilution method,
whereas the dibutylcresol samples had been prepared by the method of
terminal addition of cobalt via micropipet. A rapid recheck at 600,
700 and 800, using the newer method, gave a rough Ea for hydroquinone
of 13.9 kcal., s.d. i 2.9 kcal. This was considered good confirmation
of the previously-determined Ea for hydroquinone of 12.6 kcal., s.d.

i 0.h kcal.

It has been mentioned earlier that the observed Ea's probably
represent complex combinations of rate constants and cannot validly be
assigned to the peroxy radical-antioxidant termination step. This
observation may now be underscored by the observation that the measured
Ea with dibutylcresol exceeds by about 12 kcal. the Ea for the over-all
uninhibited_tetralin autoxidation. It seems most unlikely that any
compound exhibiting such a high energy barrier to the reaction with
perdxy radicals would function as an effective antioxidant at the
nmderate temperature of 70°.

In summary, the results of these tests with dibutylcresol confirm
the exponential relationship earlier found between induction period
and cObalt catalyst concentration. Dibutylcresol appears to be less
effective as an antioxidant in this system than hydroquinone; higher
threshold concentrations are required to give protection to the system,
and the activation energy of the induction period reaction is markedly

higher. The clean exponential dependency of induction period upon

14—4"

run

11h

dibutylcresol concentration strengthens the interpretation suggested
earlier for hydroquinone. A theory adequate to explain these observ-
ations must, it would seem, involve at least a two~term expression in
Iduch either the exponential or the power term may dominate, the
latter being favored by high antioxidant efficacy and high antioxidant
concentration. Such a theory must also account for the exponential
dependency upon cobalt concentration, found in both systems over the

entire ranges of concentrations studied.
1N2 AROMATIC AMINES WITH TETRALIN-COBALT NAPHTHENATE SYSTEMS

Sections II and III have reported some characteristics of cobalt-
catalyzed tetralin systems in which phenolic inhibitors were present.
The other major class of antioxidants is the aromatic—amine class.
Three representative members of this class, p-phenylenediamine, di-
phenylamine and phenyl-Z-naphthylamine, have been examined in this
system at 70°. .Although these antioxidants are widely employed at
higher temperatures, and are in general superior to phenolics in the
temperature range 125-1500, it will be seen from the following results
that none of them are comparable in efficacy to hydroquinone or di-
butylcresol under the present experimental conditions. Consequently
no highly intensive studies were undertaken with these amines.

Diphenylamine. The first trial runs with amine inhibitors were
carried out with diphenylamine. In the presence of 0.025 mg cobalt,
the standard catalyst concentration in this study, a 2.500 mg amine

solution gave no measurable induction period. A second run was made

115

vdth a fivefold increase in amine concentration to 12.50 mfl_(over 2 g./
Kg. tetralin), and this again gave no induction period, although the
autoxidation rate was retarded appreciably. For this latter run the
oxidation proceeded at 12~15 mm./hr., about one-tenth of the control
rate (cf. Table VII). At this point it was considered possible that
the inefficacy of the amine was attributable to some specific inter-
action with the catalyst, e.g., cobalt-catalyzed autoxidation of the
amine. Therefore, an additional run was carried out, again with 12.50
m§_diphenylamine but with no initiator present. Even under these con-
ditions no induction period was obtained; autoxidation commenced
immediately at a slow rate (about 3 mm./hr.) and gradually accelerated
to 10 mm./hr. at forty hours. These results indicated diphenylamine

to be an ineffective inhibitor under the present experimental conditions,
and, therefore, no further runs were made.

p-Phenylenediamine. The effect of p-phenylenediamine upon the

 

cobalt-catalyzed tetralin autoxidation was found to be again different.
Like diphenylamine, p-phenylenediamine did not afford an induction

period in the usual sense; that is, in all cases appreciable oxidation
occurred within the first hour of the the runs. 'With p-phenylenediamine,
however, an interesting variation on the usual autoxidation curve was
obtained. The initial autoxidation rate-—which was appreciably retarded
even with only 0.50 mg p-phenylenediamine--decelerated within the first
2h hours to a temporarily stationary minimum rate. Then ultimately the
autoxidation rate commenced a gradual acceleration which was maintained

until the end of the run. A typical autoxidation curve, with 2.00 mg.

116

p-phenylenediamine, is shown in Figure lS.*

Due to the failure of deveIOpment of a final steady-state maximum
rate, it was unfeasible to assign a meaningful pseudo-induction period
to any of the p-phenylenediamine runs. However, the retarding effect
of pdphenylenediamine was studied by a series of runs in which the
amine concentration was varied from 0.50 to 2.50 mfl,and the minimum
rates determined graphically. The results of this series are shown in
Table XVIII.

In the introductory discussion, the work of Bamford and Dewar (101)
in.studying retarded rates has been discussed. Based upon an argument
similar to that of Robertson and waters (82) (see Equation.XIV), they
deduced that at infinite retarder concentration propagation contribu-
tions to the over-all rate of autoxidation would become nil, and‘that
the Observed rate would be that of the pure initiation process. In View
of the empirically-noted linear relationship between rate and reciprocal
retarder concentration, the rate at infinite retarder concentration was
easily attainable by extrapolation from a group of rates at finite
concentrations. Following their empirical treatment, the rate data in
Table XVIII was plotted against reciprocal amine concentration. This
plot is shown in Figure 16.

It should first be noted that the reciprocal relationship is
followed rather well in Figure 16, particularly in view of a certain

inexactitude associated with measurement of the minimum rate

 

*Figure 15 shows data points at five-hour intervals, for clarity. For
the purposes of defining minimum rate, however, it should be recalled
that there are twentyfold more data points than shown in this Figure.

 

117

VhO

leml
Time in Hours

 

118

TABLE XVIII

RATE RETARDATION WITH p-PHENYLENEDIAMINE*

 

 

 

 

 

 

 

 

 

Amine Concn., Observed Stationar
Millimoles/Kg. Minimum Rate, mm. hr.
nil (ca. 150.)

0.50 8.1
l .00 3 .h
1.50 1.96
2.00 1.32
2.50 0.72

 

*With tetralin containing 0.025 m}! cobaltous naphthenate, 70°, 1 atm. 02.

119

Rate

lamine upon

d
e
n
e

1
Va
n
e

h

9..
p

f
O
t
C
e

f

f

E

’ le

11710

, Kg./Mill

-1

ne)

nylenediami

(Phe

 

120

(see Figure 15). 0f greater theoretical interest, however, is the
conclusion to which the Figure 16 plot leads upon extrapolation to
infinite retarder concentration. The intercept quite clearly defines a
negative rate.

It may be taken for granted, then, that the theoretical interpre-
tation of Bamford and Dewar cannot be applied to these data. There is,
however, an important experimental difference between the present work
and that of RObertson and waters (82) and Bamford and Dewar (101).
Rdbertson and waters studied tetralin autoxidation initiated solely by
the slow thermal decomposition of tetralin hydroperoxide. Bamford and
Dewar studied the low-temperature (ZSO-hSO) photosensitized autoxidation
of tetralin, using benzoyl peroxide as the sensitizer. In each case a
simple nonbranching initiation process was employed, and in each case
tetralin hydroperoxide was a relatively stable product. The present
conditions, however, involve autoxidation in the presence of a strong
branching catalyst. In the Discussion it will be attempted to show
that this difference is a highly relevant one, and that the intro-
duction of significant branching would be likely to lead to an appar-
ently negative initiation rate according to this treatment.

Phenyl-2-naphthylamine. The last amine examined was phenyl-2-
.rmphthylamine, one of the most widely employed of all antioxidants.
Unlike the preceding amines, phenyl-2-naphthy1amine was found to afford
real induction periods. However, the concentration of the amine
required to give an induction period of one hour was high compared to

either of the phenolic antioxidants, approximately 12 mfl_(more than

121 L“*“”

2.6 g./Kg.). The results of a series of runs with phenyl-2-naphthyl-
amine at varying concentrations are shown in Table XIX.

In addition to the induction periods listed in Table XIX, those
runs with 11 mg or more of the amine yielded delayed minimum rate
regions, very similar to those obtained with phenylenediamine. These
minimum rates did not, however, appear at lower concentrations of
phenyl-2-naphthylamine, and consequently the data afforded no opportunity
to study the rate—concentration relationship as was done with the diamine.

The effect of phenyl-2-naphthylamine concentration upon induction
period is shown graphically in Figure 17. Reproducibility for these
short induction periods is rather poor, due in part to the poor defini-
tion of the induction period with this amine. However, several com-
parisons may be noted between the amine concentration plot and the
corresponding plots for the data with phenolic inhibitors (Figures 6,
1h). First, the threshold concentration required to give an induction
period is markedly higher for the amine than for the phenolics. Second,
the initial concentration dependency, in the short-ti range, appears to
be substantially a simple linear one over a range of about h mg in con-
centration. Third, a further concentration increase leads to a sharp
increase in ti, indicating a change in dependency, possibly a modulation
to an exponential dependency.

Based upon considerations of threshold concentration and of the
amount of protection conferred by given antioxidant concentrations, the
ranking of the antioxidants examined, in order of decreasing antioxidant

efficacy, is: hydroquinone, dibutylcresol, p-phenylenediamine,

122

TABLE XIX

INHIBITION WITH PHENIL-2-NAPHTHILAHINH*

 

 

Amine Concn., Induction Period,
Millimoles/Kg. Hours
1.99 nil
b.95 nil
5.58 nil
9.8h 0.72
10.3h 0.62
10.9h . 0.95
ll.h7 1.30
12.08 0.95
13.07 1.13
1h.8 1.86
15.1 > 96.

 

*With tetralin containing 0.025 mg cobaltous naphthenate, 70°, 1 atm. 02-

123

 

 

 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4 4 77 4 , c. .. . . 9909 $0757.70 79 7VI
wo yo . . t... . v .7" a . . . . . . . .,¢o a 7:9 ..7 7o%.o 79707.6. 7.. . .. .7 . .o 7. . v . . 4 . . . . . . .74 . a 6 0.140 n k
, , I , A 7 . . . 7 . . . . . - ... Y¢.- 77v¢ .. . v.46...
c .<. . ... . . ... .... .... .7.v 7... co. bola. .... .... ... ..-¢ .7. 7... . .7.
, , -7 . .7. .. 7 . .70 .0 3... ..o‘
. . . . 7. . > o . . o . . .9 o . . 771.47. 0 .... «L7. 3|? . 7- ..IO 7 .... .41 7 . .7. . .97. ... . . . . 7 . . . 7 1 I i §.¢.¢
. 7.. ‘ O 'h .77 . 7‘
n ... 7 0.. ‘ .7 I 7 «a 77" a 0.1. a 0 Von Oobol
. — .. 70 o. . .t . 7. .
o ... 77 7.. m o .77. .... 77.. . . 7. .7. 7....
, . . u - .7..l.7-. A r .
. ... .. .77 .77. .... vu.‘ . .7 . c o 6 col
.7 . . . 7 .7 .... .77. 7.7077
7 . . . . . . . . o . c. - o . . . o . o . 7 . 7b 7 . .701 94.0.0 37. . . v. . . 4 a 70 . ... Y7. - . 7.. . .77... .74. v 7 ... . . . 7 . 7
1 . D A. n a. 7 a I .0 00-1! 01". I40.
. 7 ... . . ... . .. .... .... ...! .7 . 77.9v..o- .45vvco.. ..t. n... .... c.» 7.7... ... v....
7 7
. 7.... . .. .. - 7 . u. .7.. .77. .777
. ... . ... . . .. .... .... .... on . .... .77.. ...; V's. ..c..o~w7 ... o.. .-O. 777.7Y-7 7.
. 7A . . . .. .... 777.7 77..
. . . . . . 7 . . . . .. . . . 7 . . . . I. . 7 . . . 7 l . . . . 777. . . 7 . . . v..- . . 7 A . 7o . I. oi. Y. y h 9.7- .7 . . .167 . . . . v
, u 7: u 7 . c. .u. 70¢..nn..
. . . . .. .... .7 .. .... .7 7... .77. 7... ...-.7.74 o... t. 4... .07. o... o7..47...rv
.. 7. 77 7 . 7. 7. Ab.
. o . . . . . 7 v. V 77 . . . 7. . c . .77. v. .190. . so 7 0 u. . v. 7 ti 7 odv .70. 0: 4‘3 96 '70 09:10 o .7 7. act 7 A A. v. .
4
.vv .7 7. 77 . .7 .. .97. 7.7.7.7...
. 4 . ... 7 V ... .... .0 o ..7. .7 . .77717o77 77.. -... .... 007. no. it. ..‘7 771. . 7.
v. .7 .. o .7. I. ..-! 9 .... .7ooo
7 «A . ... . o7. .... ... ... ... .V - .7..7V3v.l -.¢79 v.7.a .... ..c .7T? ..7. .7 . 7
7. . . 7 7 7 . .7 77s. a ....
A. ..o c .7. c v .49 .v0. ..ol. .... .v.~ . 7 .... 77¢.‘A.-Jv 17 . 7... .Q 4's. ..tl . .. .
. . 7 t o .7 I.
. ... . 7.. A . 9777.... 74.. 7... ... .o . .77. 7.77 .... 77.. ... . 7 77... 7... 7 .77. T7
7 . 7 7i . 4-7
. ... .7. 7 .1 ........ 7.74. . . 7. .7 7.. 77.71.... -77.. . . 7... t.. ..b. .... .
7. 07 o . .7 .7
. ... ... . 7 7 . 7.77 77.7 ... . 7 .7. 7.. 7. 7... .7. . .77 9.. .7 . .7 . .
. ... v. 7 . . .7.7 ... .. 7.. 7 ... .. 77.57.77. . . . . . . -... .... . 7. - 7. .7 7 7V
7 .7 7 7‘1. 7 7.
77.. .. 7 ... .7 7. 7 ... 77 (.7 7... .7 .777- .7 7 ..7 7.7.- 7.-. 77 7 .. 7
. 77. . 7. . ... . 7.. . .7 7 7. . 7 . 7. 7.7.. 7.. 7.7. .1.7 77.. 7 7
. . ..t .‘v.0.o 87-7. .Ial.|
..- ... 7 7. 7. .77. 7. 7. 7 7.7 . 7 .... 7.. 77. 47.7 .7 .77 -. . .
7 7 .A. .7 .7777. .009 7‘.-
. 77. . . . .. . .. .... .. .. 7 7. ... .... ...7 .. .. .... .77 . 7
. .7 7 7x7 .117... 77:77.7777
... . 7 . .7 .. . 7. . 7.. . .7 v. . . .7 .77 .7. .7- . .7. 7
7 7 -1..77 07-! A7-
7 .. . .. ... ... . . . . .. 7 . A 7 v .7 .
. 7 . . .. ..Ac 777.1...7
. .7. . .. . . . 7 7. 7.. . . . . 7 7 . 7 . . .77 . 7
.. . 7 . .d .770 A....?.. x
. .. 7 .. . 7. . . . . . 7 .
. 7 . 7 o..- .7 7
... 77 7 . . 7.. .7- . 7. .. . 7.77...7 . ..r. . 7 r .
. . . 7 . . . 7 . 7 c. 7 7 . . . . . 7 . 7 7 . . 7 .1 t. . . 7 7 . 7 . . . 7. .7. H77. 7LY. . .7.
. 7 7 7.. .. . ..v . . .7 7 .... 7 .7.77 7.. ...- x7-..1. . - .7 7. .7.7.7. 717.. .7...
7 . . . . . .7 . 7v... .7. .. . . . . -. 7.... . 7Y7 .. 7 . . .. .74. 07.. 7....
.. . 7. 7. .7 7 .7. .... ... .7 7 7. . . .. 7. . .7111 7.77-7.77 77 .. . . . .. .077. 70.01. I.
. . . . . . . 7 7 77 7v 7. .. . . 7. . .7 771777. 7 7 .. . a .....77 4.-....767
. O b . 0. - . '75 .... o I. A . . . D c .- .... .. )7.- .'.O a I I. . 7 o 4‘ lnn‘ ‘tVl’ l.‘7"
. ... 7.. . . .7 7.. ... 7.7 ... 77 7. I... .. I. ...7. 7 .. 7 7 . .. 7.70 9.07. .75..
. . . . . . . . 7 . . . . . . 7 . 7 7 . . . . . . . 7 7 . ill. . 7 7. . 7. . . 7 . 7 . . . 7 . 7. 7 T. .7oir- 77‘ ...
. . . . n 7 .7. . . 7 7 ... 7.. . . ... .... . . 77 . .7 . 7 7 .- .O...¢.Vn 70-.1.
.. 7 7 . ... ... ... . 7 . . . . . .. 7 .7 . . . . . . . 7 . .7 . 77xw9..7T...
.. . ‘7. ... 7 .. . . . . 7 . . .7 . 7... _ . . 7 7 . .7 .... 9.00 701.7
7 i
. a . , . .. . .. . . . . . .7 . . . . .. . . 7 7 7 . - 7 . . . .7 . 7 7 o .4 - . . ' vowe.4 . I‘l7ox
.. . . 7 . .7 ... .77. . 7 . 7 . . .- .77-c.7...vo ....
... . . . .. . . .. 7 . .. . 7 . ... ..77 . .7 . . . .. .7714.ov .7.7o7...
7 . . . . . 7 . 7 . . . . . 7 . . . 7 7 7 7 . . . . . . 7 . . . . 7 7 . . . 7 . . 7 7 7 7 .7. . . . 7 .1 7 lo. .o . L o 77.97. .. .70..
7. . .. . ,. . . . ... 7. . n . .. .7 . . .. . .. .... ... . 7 .7 7 7 . .. 7.... ..9......
. . . . 7 .7. . . 7 .. . , . .7 7 7. . . .. 7-. ..7 7.7 . . . 7 . V. .7574 .7 ....
. .7 . . . . . ... .71. . 7 7 .7. .7 . . . . . ..7.v.917 . .7..1
o . 7 . v . . 7 ... . . . . . . . . . 7 o 7 . . . . t. . .7 .i s . 7 1. . . . .. .. u 7 . 77 77177 7 q 75 7 . A 77 . . c .0 77-091 - 177. 7.
D
7 . . . 7.. 7 7 7. . . . ..77x ... . .77 . . . . 7.7 v. 7 Q .7 7 A - 7 . .t .o.o . I .601
a 7 . . . . . . . 7 7 7. . . 7. . . 7 77 . x . . . .77. . .4v707..
v. ... . 7. .7 . . 7 .. 7. . . .. . l. . .7 i . o ....7 0?.7 7.7-
. ... . 7 . .. 7 . . . . . . . 7 . 7 7 .. .. 777 7. . . . . o. .7717 A... 777.
f
v a. V 7 . . . .7 I!» I. 7.. V: .7 v.77 1 7 w . I}. A cOv-QIO‘CI
. ... . . 7 . 7 . .. . 7. . 7 . .A. 7......-.vv
... . . . . . 7. . . .7 .7. . 7. . .7...¢.. .777.
v. ... . . . . h 7 7. . 7. . .7.L .7 7 . .. . .4 . x....kvtfit.
b
47
. . . 7 . . . . .. . . . 7 .. .7 . . . . .. ..lo... .717
7 ... . ... . .. 7x .. . .. .7 ... . . . .4 7. o .... A
. ... .7 . . . . ... ... .. 7. . .7. . . . . . ..
v. ... - 7. .-. 77 7 7 . . ...7 ..v. . . c..x . 7.? 7 . 7-7 7.. 7 7. . .-
7 7 7. . . . . . .. . 7 . . 7..7 7 . . o . 7.
I7 7 . .... . 7 7. . . 7 .. . . 7 7.. . . . .
77 . 7 . 7... .7 . 7 7 - v 7.. .7 .. . . . 7 .7. . .77. .7 7 777 . A . . . 7. A
. . . . . . . 7 . . 7 77. .. . . . . . . ..777 . .. 7 . . . . . .. 4
. .. . . . . 7 . . . . 7 Al... .7 .7 7
. 7 . . .. 7 7. . . . .7 . . . .7 7 . . .
A
. 7.. . . . . 7 . . . 7 7. 7 ..7 . 7 7 . .-.. . .7 . 7.77 .777 .
. . . .7 7 .. 7 . . .. 7 .. 7 ... Y... i
. . . . . .. . 7 . . 7. 7 .77. . . . . 7... .77. .
7 7 7 .. ... 7 7 .. 7. .. o.-.
. . . . 7 . . 7 77 . .7 7 . . 7.. .I.. ....
. . .. . . . . .... . .. . . 77 . . 7 .7 7 . . - .... 7... ....
. . . 77.. . .7 7 . ... .7 .. . . . . 7. .... ...7179..77
7 , 7. . . .7 7 . . .7. . 77 7... ... ... .7. .7 7 .. 7A7... . 7 . 7 .L .. .... .07: 7...
7 7. .. o . 7 7 . .7 7.77v..u. .... . . .7 . . A..l.v9|.17o .7 .. . . . 7. .n- o a. .o..
7 . .. .. . .. . 7 . 7 77. . .. .... 7. .7 7. . . . ... .... 7 . . ... .. .....7 ..+...
7. .. ... . . . 7. .. 7 .7. ... 7. . ..73 0.07.717... .77c7x .v. .... . . .7v7... 7 .. . 77 7... 9 4...
747 7
. ..77 . 7. . .... .7 . . .no . 7 .07 .o.0v7onlyv 7. ..oil .. .. .. .77. 7 . 7. 7 . .. .... o +970.
.. 7 . . .o.. .. . 7 . x. 7 ... 7 7 97 .... 1-0. ..7.. ...7 ... 7.. . . .7 7 .. . 7 .... . .. 9...
. H v u .7 . . . a v 7.... .v.. 0.7.4
o. 7 .. 7 . 7 . .... .-.. o...
7 b .7 . n o o '5 .i- . O. 0.00
\ .7 I .974 t 7 . . .7 4- .00 ...?
. . _ .. 7 7. 7. .. . 7 . .7 . . ... ...77 . . . . ... 7. 7...
7 7. . . . . . . . . 777. .. ... ...A ...7 .. . .7 .. ... . 7. . .. 7. .. .. . . . .. . 7. ...o
.7 . 7. 7 .. 77 . 7 7 . ... . . . .. . 7 .a.. . . . . . . . 7.. ....o
. . .. . . .7. .. .7 7. . . .7 .. .... . .7 . .. .7 7 . .. . . .7..-
7 77.- . . .7 n. 77.. 7 u 7. .7 . . . .r .. c ...»1...o
m 0H In . .7. ... ... .. . 7... . . . 7 7 7. 7.. .. 70..
. O
... . ...7 7. 7 7... .-.7 7 7. .. 7 . .7 .. 7. . ...
. . . . ... .... .. .7.. ... . .. .. 7 . .. ... . .. 7.7
_. .n. .77. . 7
7 . n A . . .7 u 7.. u 7 I. 7 . . O u 7 ... 7 7..
r . .... .77 7.. . . .. .7 . . 7 7. 7. . 7.7. . .

 

 

 

1217

phenyl-Z-naphthylamine and diphenylamine. The marked difference in the
observed concentration dependencies for the three antioxidants which
give induction periods is the most peculiar aspect of the experimental
results. The latter portion of the Discussion will undertake to formu-
late a unified treatment which will account qualitatively for these
different dependencies, and for the dependencies reported by some other

workers.

125

DISCUSSION

I. THE CLAIM FOR STEADY-S‘I‘ATE CONDITIONS

As was noted in the introduction, the great weight of theoretical
efiTort which has been expended in explicating the phenomenon of the
induction period has taken as an a priori assumption the existence of
steady—state concentrations of unstable intermediates during the
induction period.

The first theoretical treatment of ti in autoxidations was presented
in.l9h6 by George, Rideal and Robertson (1?). In this treatment, which
is elaborated in Appendix A, the steady-state assumption is taken for
the case of a simple nonbranching chain reaction, and by a series of

algebraic transformations an equation of the general form:

ti = $3on - A, + E—ln if (XXXIV)
is adduced, whereinAo and Ai are the concentrations of antioxidant at
the beginning and at the end of the induction period, respectively, and
the constants a, b and g_represent the initiation rate, the termination
rate, and ka(R), respectively.

A more widelydused treatment, developed by George and Robertson (81)

and published.concurrently with the above, takes formal c0gnizance of

chain branching. The four generalized reactions are considered:

126

 

 

RH ,— R (k1) (1h)
RH + R -—-—-—e- P + R (kp) (15)
P ,— 2R (kb) (16)
R + A —-—-, inert (ka) (17)

wherein Reaction lh is a general initiation reaction, Reaction 15 is an
elision of Reactions 2 and 3, representing the propagation cycle

(a legitimate simplification of notation for other than low-oxygen-
pressure studies), Reaction 16 is a generalized chain-branching decompo-
sition of the hydroperoxide P, and Reaction 1? is the antioxidant
termination reaction, assumed to effectively dominate biradical termi-
nation during the induction period. The steady-state assumption with

respect to R and §_leads to the simultaneous equations:

ll
0
ll

dP/dt kp(RH)(R) - kb(P) (XXXV)

I
O
I

dR/dt - - ki(RH) + 2kb(P) - ka(A)(R) (XXXVI)

Substitution for the value of §.in Equation XXXV into Equation XXXVI

permits solution for R;

ki(RH)

(R) = kaCA) - 2kp(RH) (XXXVH)

The rate of antioxidant consumption, from Reaction 17, is simply:
dA/dt = -ka(A)(R) (XXXVIII)

Substitution of Equation XXXVII into Equation XXXVIII, and rearrange-

ment of terms, gives:

127

ka(A) - 2kEfiRH)
kam .kimHT

 

dA = - dt (XXXIX)

Integration of Equation XXXIX between limits, from A0 and t = O to A1

and t = ti, then yields:
._ A _ 2k lnAO A1 + 2k 1mm XL
WW n’é-r‘ W JET— H

where the two right-hand terms are small constants, functions of the
concentration of the antioxidant at the end of the induction period.
This equation corresponds directly to Equation XIX, and is isomorphous
with the empirical deta-fitting Equation XX developed by Rosenwald and
Hoatson (119) to describe gasoline stability data.

Equation XL is subject to two simplifications. First, where ka(A)
is much greater than kp(RH), the latter term may be neglected in
Equation XXXVII, and final integration then yields the simpler

expression:

= A0 _ Ai

ti m ms— (m)
Secondly, where Ai is very small compared with A0 (and it is often
considered to be negligible by comparison), the two right-hand terms
of Equation XL, or the right-hand term of Equation XLI, may be drOpped.
In the latter case, the final relationship is the simple first-order
dependency of ti on (A), claimed by a number of workers (83,135,137-lu0)
and represented by Equation.XVII, where E_is the reciprocal of the
initiation.process rate ki(RH). This simple relationship has been
fbund to obtain in the data of Boozer, Hammond, Hamilton and Sen (lbO)

and that of Kennerly and.Patterson (139).

128

An alternative explanation of Equation XVII has been advanced by
Kennerly and Patterson. Taking the kinetic formulation of Bolland and

ten Have (179) as:

-95- =k(P)[1+%)] (XLII)

dt
they assume the existence of a further direct reaction between the anti-

cmidant and molecular CXygen, and obtain a final equation of the form:

- 3% = M?) I 1 + 11%] + k"(oz)(A) (mu)

Since their results accord with Equation XVII, it follows that - dA/dt
must be substantially constant over their experimental range. This
constancy, they suggest, is fortuitous (139). .

Hammond, Boozer and co-workers (lhO,lhh) found that in the azo-
initiated autoxidation of cumene in chlorobenzene at 62.50, inhibited
with dibutylcresol and with N,N'-diphenyl-p-pheny1enediamine, "both
inhibitors gave sharply defined inhibition periods which are exactly
proportional to the inhibitor concentrations" (IhO). No data were
presented on this point. They also propose (lhh) a more complex

antioxidant termination mechanism, replacing Reaction 1? with:

R00. + A -—-=. (ROO...A) (18)
<—-—-
(ROO...A) + ROO- --> inert products (19)
Reaction 18 is assumed to be reversible, so that the termination process

rate may be designated as ka(ROO)2(A), where ka in this instance is the

product of the equilibrium constant for Reaction 18 and the rate constant

129

for Reaction l9. Ignoring branching and considering only initiation
and branching (Reactions 1b and 15) along with this termination

mechanism, (R00) may be solved for via the steady-state assumption,
giving:

0.5
EH ] (XLIV)

k-
(ROO) = [ka

Substitution of this value for (ROO) into the propagation expression
gives:

'- dO/dt = kp(RH) [5.1% Jo's (XLv)

Equation XLV, describing the rate of oxidation in the presence of an
antioxidant, could not be effectively tested in the presence of potent
inhibiting antioxidants, as the inductionaperiod rates would be extremely
low. Equation XLV was, however, found to be obeyed by the weak anti-
oxidant, N-methylaniline, in the azo-initiated cumene system, the
especially significant evidence being a good inverse square-root
dependency of rate upon the N-methylaniline concentration. These
workers had already shown, as has been discussed earlier, that the
potent antioxidant dibutylcresol stopped two radicals per molecule (lbO).
It was implied, therefore, that potent antioxidants might also follow
the termination mechanism described by Reactions 18 and 19.

The method of retarded rate analysis developed by Bamford and
Dewar (101) may prOperly be considered as another major facet of the
steady-state theory of inhibited autoxidation systems. In this scheme
consisting essentially of Reactions 1h, 15 and 17, for which retardation

rather than inhibition is observed, the steady-state assumption forER

130

leads to the simple solution:

k- RH)

(R) = ka A (XLVI)

The rate of oxygen consumption, making the common and usually safe
assumption that alkyl radicals will react very readily with oxygen to

give peroxy radicals, is then:
- dO/dt = ki(RH) + kp(RH)(R) (XLVII)
Substitution of Equation XLVI into Equation XLVII yields:

k (RH)

= k- RR 1 +
l( ) [ ka A

I (XLVIII)

I
910--
C“ C)

Assuming substrate concentration to be constant, it is evident that
Enuation XIVIII is of the form: y = mx + b, where x_is reciprocal anti~
oxidant concentration. Bamford and Dewar showed experimentally that a
plot of reciprocal retarder concentration vs. time did give a linear
relationship. Extrapolation of this linear relationship to infinite
retarder concentration (i.e., to l/(A) = 0) gives the rate of the pure
initiation process, as Equation XLVIII shows.

Further empirical support for the steady-state treatment of inhibited
autoxidation is given by the clean reciprocal dependency of induction
period upon metal soap concentration, reported by Brook and Matthews
(its) in their study of lubricating oil oxidation. This accords with
Equations XVII and XLI, wherein the initiator concentration would

appear as a multiplicand of ki°

The foregoing has outlined the arguments and principal ramifications
of the steady-state assumption as it is specifically applied to inhibited
mnmxidations. This treatment is not generally considered to be based
upon limiting assumptions; thus George and Robertson state that their
treatment is "independent of any particular reaction mechanism" and
"makes no assumptions regarding the chemistry of the inhibitory process"
(81). The following section will attempt to show that the steady-state
assumptions as applied to inhibited autoxidation systems, and all of
the kinetic ramifications which follow from these assumptions, rest
upon logically dubious grounds and are incapable of explaining the-
general behavior of inhibited autoxidation systems except under special

and highly restrictive conditions.
II. OBJECTIONS TO THE STEADY-STATE ASSUMPTION

The steady-state assumption is perhaps the single most valuable
tool to students of complex chain processes. Its reasonableness, as
well as its great utility, has been amply demonstrated for many systems.
Indeed, the tendency for most autoxidizing systems to attain and then
hold an essentially constant rate of autoxidation would be difficult to
explain in the absence of this assumption. Perhaps because of its
great utility, and particularly its great resolving power in complex
systems, the steady-state assumption has been applied generally to all
types of autoxidizing systems, including inhibited systems. The pre-
ceding section discussed specifically the theory of inhibited autoxi-

dation as it has been developed and ramified from this central assumption.

132

This section presents the argument against the application of the
steady-state assumption to inhibited systems. This argument is
develOped along three lines: a discussion of the illogic of application
of this assumption to this area, a critical evaluation of the theory and
experimental support presented in the preceding section, and a survey
of some important empirical relationships (both from the present study
and from the work of others) which cannot be explained or accounted for
in terms of steady-state kinetics.

The logical objection. This will be presented on two levels, first,

 

a heuristic appeal to reason, and secondly, a mathematical demonstration
of inconsistency. For the first, let us consider the scheme of

Reactions lh-l7, and particularly the fate of radicals produced in this
scheme. The fraction of radicals formed which will enter the propagation
cycle, at any time, is given by:

3(RH)
£13 = kp(RH) . ka(A)

 

(XLIX)

Now at the beginning of the inhibited autoxidation, ka(A) is much
greater than kp(RH); otherwise there would be no inhibition. At the
end of the induction period, kp(RH) is of the same order of magnitude
as ka(A), and perhaps larger; otherwise the induction period would not
'be terminated. Consequently, as we progress from t = O to t = ti, the
fraction fp increases from an initial value very close to zero to a
final value approaching unity. This prOpagation step is the peroxide~
forming step, and so not only are peroxides increasing with time, but

the rate of formation of peroxides is increasing with time, as fp grows.

 

 

133

we may now take either of two positions with respect to the peroxide:

it is maintained at a steady-state concentration by the branching re-
action, or it is essentially an inert stable product to which the
steady-state treatment does not apply. If we take the first position
and assume the branching reaction to hold the §_concentration constant,
then the rate of R_formation by branching must not only increase with
time but must increase at an increasing rate with time. If on the other
hand we take the second position and invoke the steady-state assumption
only with respect to radical concentration, a consideration of Equation
XLIX shows that as A.is gradually depleted, the rate constant ka must
increase correspondingly in order for ka(A) to remain constant, this
being a clear violation of the law of mass action. If ka(A) is not
constant, then the fraction of radicals being stopped per unit time is
decreasing and the radical concentration cannot be maintained at steady-
state.

A mathematical demonstration of the internal inconsistency of the
steady-state assumption in this application may be shown by a rederiva-
tion of ti using the scheme of Equations XXXV-XL. As a first-approxi-
mation correction, let us take the expression for R given by Equation
XXXVII and differentiate it with respect to time. This gives:

__ ki(RH)-ka(dA/dt)
[ka(A) - 2kp(RH)]2

dR/dt =

 

(L)

substitution.by Equation.XXXVIII for dA/dt into Equation L gives a simple
algebraic expression for dR/dt. Let us set this, instead of zero, equal

to the sum of unit terms in Equation XXXVI. This gives us:

13h

.Eéiii(RH)(A)(R) = ki(RH) + 2kp(RH)(R) - ka(A)(R) (LI)

[ka(A) - 2kp(RH) 3'

 

Solution of Equation LI for R_and substitution into Equation XXXVIII

yields:

95. z _ ki<RH> (ka(A) - 2kp(RH))2
dt kaki(RH) + TkaIA) - 2kp(§H))s (LII)

 

Integration of Equation LII between limits yields the new equation

defining ti:

k k
t = a A2 -- ~2-E-P A - 1 ‘ a A?
i "T'Tzki RH 0 xi 0 ka(kaAo - 2kaRR) 2ki(RH) 1

1
' ka(kaAi - 2kp(RH)) (LIII)

 

+ik2A.+
ki 1

The very marked difference between Equations XL and LIII shows that
the "first approximation correction" completely changes the character
of the relationship between ti and A0. If Equation XXXVI had been a
good approximation to begin with, this re-working through should have
added a small correction term or corrective factor to Equation XL. In
both operations the only assumptions made were those of Equations XXXV
and XXXVI, i.e., the steady-state assumptions. The nonequivalence of
the two derived expressions indicates the self-contradictory nature of
these assumptions.

This self-contradiction may be seen even by direct inspection of
the adjacent Equations XXXVI and XXXVII in the original treatment.

If Equation.XXXVII is differentiated with respect to time, the result-

ing differential is obviously not zero, since A_is necessarily a

135

function of time. Yet Equation XXXVI equates dR/dt to zero. That this
difference is not a trivial one has been shown by the development of
Eqwations L-LIII.

An.appraisal of the steady-state arguments. The following critical
discussion of the reasoning for and the evidence supporting the steady-
state assumption in this application will follow the chronology of the
preceding section.

The first treatment by George and co~workers (17), leading to
EQuation.XXXIV, is based upon three reactions. The initiation and
propagation reactions follow the form of Reactions lb and 15. The
termination reaction in the absence of antioxidant is "monomolecular,"

i.e.,
R -————————e, inert (kg) (20)

Not only is no mention made of branching reactions, but this treat-
ment is incapable of accommodating itself to a branching-chain reaction.
In the first place, there is an implicit "hidden denial" of branching,
in that the rate of antioxidant consumption is defined as the product
of the fraction of chains stopped by the antioxidant (fa would be equal
to l - fp as defined in Equation XLIX) multiplied by the initiation
rate. Thus, if branching occurred, the radicals so formed would
essentially not be counted among those eligible to react with the anti-
oxidant. Secondly, this treatment is subject to the internal contra-

dictions discussed earlier with respect to the George and Robertson

treatment. Finally, the use of a "monomolecular" termination step

136

makes this treatment hazardous even when applying it to uninhibited
autoxidations, for which steady-state approaches are usually fruitful.
For unless kt in Reaction 20 is more than twice the magnitude of the
product of kp and substrate concentration, there will be no steady-state.
To put it another way, bonafide steady-state conditions apply in free
amtoxidations, notwithstanding branching, because termination proceeds
at a rate proportional to the square of the radical concentration. In
simplifying the kinetics according to Reaction 20, the power of the
square-term is lost, the potency of the termination process as an over-
all rate-controller is vitiated, and the attainment of equilibrium
steady-state conditions is dependent upon the propagation and branching
reactions' being sluggish. This treatment, finally, does not accord
with overwhelming evidence that the uninhibited autoxidation rates are
proportional to the square root of the initiation process and inversely
proportional to the square root of the termination rate constant.

The George and Robertson treatment represented by Equations XXXV~XL
is a substantial improvement over the above treatment, in that it takes
cognizance of chain branching. However, the superimposition onto the
reasonable scheme of Reactions 1h-17 of the steady-state requirements
for both §_and §_leads to the internal inconsistencies discussed above
and demonstrated in the development of Equation.LIII. ‘

The alternative explanation offered by Kennerly and.Patterson (139)
(Equations XLII, XLIII) aptly illustrates the strain of cumulative
Special assumptions which become necessary to account for the facts in
terms of a theory based upon a faulty premise. First of all, in order

to derive an expression of the form:

137

do__ kRH
- dt - Rl [ l + Ejézjl' J (LIV)

from the kinetics of Bolland and ten Have (179), they have been obliged
1m make two unacknowledged special assumptions: that the initiating
species is an alkyl radical rather thanenlalkylperoxy radical or any
other form, and that termination is exclusively by alkylperoxy radicals.
It is also required that no propagation occurs, since they equate -dO/dt
with -dA/dt. Then, in order to convert Equation LIV to their form,
Enuation XLII, they are obliged to factor P_out of Bolland‘s Ri- Ris
the over-all initiation rate, is defined by Bolland as the sum of the
thermal rate (zeroth order on peroxide), a bimolecular branching rate
(second order on peroxide) and an acid-catalyzed rate which is unique

to his linoleic acid system. The factoring out of a firsteorder
dependency on E.was neither deduced nor demonstrated by experimental
data. Given all these assumptions, they were then obliged to add a

new reaction with molecular oxygen (Equation.XLIII), solely to counter-
act the second term of Equation XLII, so that -dA/dt can be found to be
"fortuitously" constant over the range of observations. This range of
observations included a tenfold change in the concentration of A_and a
corresponding change in the observed induction periods.

- According to the treatment of Bolland and ten Have (179), k3 and k9
correspond to kp and ka in the present notation. 'Consequently, if (as
Kennerly and Patterson explicitly assume) -dO/dt = -dA/dt, the chain
length is zero and the second term in Equation LIV is zero; i.e., the

term k'/(A) in Equation XLII is zero. Thus,the problem which they

 

138

undertook to solve by invoking the antioxidant—oxygen reaction appears
to have arisen from a misapprehension of the kinetics upon which their
argument was based.

The observed constancy of ~dA/dt can be much more simply explained
in terms of a consideration of the effect of (A) upon (R). First, the
restriction will be made that the system under consideration is sub-
stantially a nonbranching system. With this restriction made, R_can be
considered to be produced at a rate entirely independent of A; that is,
E;is produced essentially only by the initiation process(es), which
exclude branching. R, however, is consumed at a rate directly pro-
portional to the concentration of A, The equilibrium concentration of

B, then, will be an inverse function of the concentration of A:
(R) = k/(A) (LV)

Now, from a combination of Equations XXXVIII and LV, it follows that
the rate of antioxidant consumption will be constant under the con-
ditions of the restriction noted above. It will be noted that this
simple alternate explanation makes no steady-state assumption; on the
contrary, Equation LV is not consistent with the steady-state assumption.
The remaining major kinetic study dealing with the steady-state
treatment of induction periods is that of Hammond and Boozer (1h0,1hh).
This work, employing cumene and tetralin in chlorobenzene at 62.50, is
rather unique in that massive excesses of azo4bis-isobutyronitrile
initiator were employed in all cases. In the absence of branching
agents and with this powerful initiation process, this particular work

constitutes in effect a special study of the dynamics of interaction of

 

 

139

a chain precursor with various antioxidants. The function of the sub-
strate in these tests was essentially that of an indicator: the com-
mencing of oxidation of the substrate signalled the completion of
consumption of the inhibitor. Evidence for the nonparticipation of the
substrate during the induction period is afforded by the detailed study
of the oxidation product of the dibutylcresol antioxidant, discussed
earlier. Aside from the precursor-adduct, h-methyl-h-(2-Cyan0-2dpropyl-
peroxy)-2,S-cyclohexadienone (Structure II, R = (CH3)EC(CN)-O-O- ),
which was obtained in good yield, the authors state that "it is unlikely
that other products were formed in significant amounts" (lhO).

The magnitude of excess of azo initiator was such that the rate of
production of cyanoisopropyl radicals was essentially constant through-
out the induction periods. Under these conditions, and again in the
absence of branching, the linear relationship between A0 and ti is
rational. The authors chose to explain this relationship in terms of
steady-state kinetics, to which the same objections apply as have been
made earlier in this section. The linear first—order relationship can
be readily explained in terms of Equation LV, without encountering the
inconsistencies discussed at length in the preceding pages.

“With regard to the retarder treatment of Hammond, Boozer and co-
workers (lhh), it should be noted that the objections which have been
raised here against invoking the steady-state assumption in inhibited
autoxidations do not necessarily apply to retarded systems. In particu-
lar, where a relatively high concentration of weak retarder is employed
to shorten the kinetic chain length of the autoxidation, the rate

measurements are commonly made over a period of time in which the

 

 

lhO

concentration of the retarder is substantially invariant. Therefore,

in the absence of branching conditions, there is no reason why the steady-
state assumption should be less valid for retarded autoxidations than

for free autoxidations.

However, even in considering retarded systems, the importance of
the nonbranching condition is readily demonstrable. Consider, for
example, the rate analysis developed by Bamford and Dewar and shown
in Equations XLVI-XLVIII. If this is worked through again, based upon
the scheme of Reactions lh-17 inclusive (and thus including the branch-
ing step, Reaction 16), then the steady—state assumption leads to the
expression for (R) shown in Equation XXXVII, rather than that shown in
Equation XLVI. Substitution of Equation XXXVII into the oxygen uptake

rate expression, Equation XLVII, yields the equation:

d0 _ _ k RH -k A
‘ dt ' 1‘10“” [ kaxéRHg - kahg ] (LVI)

Equation LVI is not considered, in the present discussion, as a valid
equation, for it makes use of the steady~state assumption in a branching
system and is therefore subject to the same inconsistencies as have

been discussed above. It is, however, significant, that this is the
fate of the Bamford and Dewar treatment if it is applied to branching
systems. Quite evidently it is substantially different from Equation
XLVIII; it will certainly not lead to an extrapolated value of the
initiation rate at infinite retarder concentration, even though the
limit of the expression as (A) approaches infinity is k1(RH).

In retarder studies the chain length is almost always substantially

 

 

lbi

greater than unity. If Equation LVI is used literally, extrapolation
of data will lead to some negative value for rate at infinite retarder
concentration, so long as the chain length, kp(RH)/ka(A), is greater
than 0.5 in the experimental data. It is of interest to note that the
data plot obtained in a system containing a branching catalyst does
indeed lead to an apparent negative value at infinite retarder
concentration (Figure 16).

In summary, the arguments based upon the steady-state assumption
and applied to induction period treatments of inhibited autoxidations
are fundamentally inconsistent with the law of mass action, and, there-
fore, inevitably lead to internal inconsistencies. Where branching
reactions occur, these arguments completely break down and are in-
applicable. ‘With respect to retarder treatments, the steady-state
assumption appears to be valid if and only if no branching reactions
occur.

The preceding arguments have been develOped primarily on a_theo-
retical level. The following will undertake to show that on the
pragmatic level of explaining and accounting for observed empirical
relationships in induction period studies, the theoretical treatments
based upon steady-state assumptions are often impotent.

Empirical objections to the steady-state assumption. The first
portion of the Discussion presented some observations selected to
support the theories based upon the steady-state assumption. It is
axiomatic, however, that any theory, however frivolous or ridiculous,

can be supported by selected observational data. The empirical test

 

 

 

lh2

for adequacy of a theory, therefore, is its power to account for the
universe of observational data within its domain. Below are presented
some important observed relationships from the present work, along with
several Observations by others, which appear to be inexplicable in terms
of steady-state kinetics.

The increase in induction period with increasing inhibitor concen-
tration is often greater than can be accounted for in terms of the
power dependency predicted by steady-state kinetics. This has been
observed in the present work in the case of low concentrations of hydro-
quinone (Figure 6) and high concentrations of phenyl-2-naphthylamine
(Figure 17), and most dramatically in the case of dibuylcresol (Figure lb).
Earlier data by Chamberlain and Walsh (lh2), obtained in the course of
a gasaphase study of diethyl ether oxidation at 200°, include a non-
interpreted curve of ti vs. inhibitor, the data points of which are
fOund to Obey Equation XXXIII. More recently, in some unpublished work
(l7h,l75) presented simultaneously with the first report of the present
researches (176), Harle has shown an accelerating increase of ti with
increasing antioxidant concentration in a mineral oil system. All of
these observations indicate suppression of branching reactions, and
cannot be accounted for in terms of steady—state kinetics.

Further powerful support for this contention is afforded by the
careful measurements of Harle and Thomas (17h) of the decrease in
phenyl-l-naphthylamine concentration during a single inhibited autoxi-
dation. This increase was shown to be nonlinear with time and to be
accelerating climactically towards the end of the induction period,

clearly contrary to the steady~state behavior.

1&3

The effect of increments in the metal-ion catalyst concentration
upon induction period is likewise greater than would be predicted
from steady-state considerations. Earlier work already discussed (128,
13h, 137) has reported extremely sharp decreases in ti with the first
few thousandths of a percent of catalyst added, the rate of decrease
then falling off in a manner which nowe-in the light of the present
data-~can be seen to be exponential. The exponential nature of this
fall-off is clearly shown in Figure 5 and 13. Again the concurrent
work of Harle (175) supports this relationship, although he did not
appear to notice the exponential nature of his data with iron and copper
naphthenate.

In addition, three other relationships observed in the present
study appear to be irreconcilable with steady-state kinetics. The
effect of azo initiator upon induction period should, if steady-state

kinetics are followed, conform with the equation:

k ln I
O = A
tl Io _ a (LVII)

where a|is the equivalent concentration of antioxidant inhibitor
present. As I0 falls towards a, ti increases towards a limit of
infinity. The data in Table V and Figure 3 show this prognosis to be
wrong, and show the data to follow Equation.XXVI.

The effect of addition of tetralin hydrOperoxide to the cobalt-
catalyzed hydroquinone-inhibited system could lead to any of three
results in terms of steady-state kinetics. If the peroxide were

unaccountably stable, no effect upon ti would be observed. If the

1th

peroxide underwent rapid homolysis in the presence of the catalyst,

the net effect would be the stoichiometric reduction of inhibitor con-
centration and Equation XXXII would be obeyed. If the peroxide were
slowLy decomposed homolytically, affording a trickle of radicals similar
to that Obtained with azo initiator, then the kinetics of Equation LVII
vmmfld obtain. (Other objections to this third possibility are discussed
under Results.) The Observed relationship (Figure 12), however, con~
forms to none of these, but rather to Equation XXXI.

Finally, the effect of retarder concentration in the case of
steady-state kinetics should conform to Equation XLVIII and should
permit determination of initiation rate by extrapolation. Instead,l
extrapolation leads to an apparent negative rate of oxidation at
infinite retarder concentration, a consequence which is not only mean-
ingless but inexplicable in terms of the Bamford and Dewar treatment.
The extrapolated negative rate has, however, been accounted for quali-
tatively in terms of postulation of a branching step which, however,
also destroys the kinetic framework of this treatment.

In summary, there are serious logical objections to the application
of steady-state kinetics to inhibited autoxidation systems. A study
of the evidence and arguments developed for these systems in terms of
steady-state kinetics shows the former to be severely limited in the
nature and scope of conditions, and the latter to be sharply restricted
to linear nonbranching systems, and even there to display internal in-
consistencies. Finally, a significant body of empirical relationships,
drawn from the present work and from the work of others, is noninterpret-

able and, therefore, inexplicable in terms of steady-state kinetics.

 

 

1145

III. THE PROBLEM OF THE NON-STEADY-STATE SYSTEM

The preceding section has undertaken to prove the inadequacy of
steady-state kinetics in treating inhibited autoxidation systems.

It has been implied, and it will be said explicitly now, that steady-
state treatments are applicable only for the special limiting case of
linear nonbranching reactions. Even for this limiting case, steady-
state treatments are only approximations, and may not in all cases be
good enough approximations to be useful. Thus, steady—state kinetics
comprise a body of limited, approximate and subordinate laws, which are
subsumed under a higher and more general body of laws governing inhibited
autoxidations 3‘

It is proposed that, rather than attempting to overextend the
brilliant simplifications of Hinshelwood and the English school to
areas wherein these simplifications do not afford even rough approxi-
mations of state descriptions, it will be more profitable to attempt to
extend the theory of branching chains, following the basic formulations
of Semenoff (2).

The fundamental problem to which this proposal leads is that of
handling a dynamic complex of reactions without having at our disposal
a resolving tool analagous to the steady-state assumption. Thus, if

we consider the following reaction scheme:

S + I --—--> R + I (ki) '(21)
s + R —----> P + R (lop) (22)
P + I -——-> 2R + I (kb) (23)

 

*This same general body of laws would apply to other dynamic analogs
of the system in nuclear physics, population growth and other eco-
logical problems, econometrics, and so forth.

1116

R + A -—-—-9- inert (ka) (2h)

along with a generalized biradical termination step:
R + R ---ev inert (kt) (25)

(wherein the notation has been further simplified: S is substrate, 1
is the initiating and branching catalyst, R is the unspecified free
radical, P is the substrate hydroperoxide and.A is antioxidant), we

can readily derive the following simultaneous differential equations:

dR/dt = kiSI + .2ka - kaAR - 2ktR2 (LVIII)
dP/dt = kpSR - kaP (Lu)
dA/dt = - kaAR (LX)

Although these are three independent equations in three variables, and
are, therefore, in principle soluble, there appears to be no exact
solution known, and furthermore there is no known route to a good

\

approximate solution of these simultaneous equation3.*

 

1‘IThe writer wishes to acknowledge with deep thanks the time and interest
given to this particular problem by those well-qualified in this area:
Professors C. P. wells (Mathematics), R. S. Rudner (Philosophy), C. Ip
(Engineering) and J. C. Sternberg (Chemistry) of this University, and
Bro. Anselm Peter, LaSalle Academy, New York. Special work on an
approximate solution to this problem was also contracted to Mr. F. C.
Sherburne, Jr. of the Department of Mathematics. A number of approxi-
mation methods have been investigated, but thus far none has proven

adequate.

 

 

lb?

An indication of the form of the true solution is given by the
following non-rigorous treatment, adapted from Brook and Matthews (IhS).
Assuming Reaction 25 to be unimportant as compared with Reaction 2b,
the steady-state approximation for R_leads to:

kiSI + 21¢pr
kaA

R = (LXI)

The rate of change of peroxide concentration may now be expressed by
substituting the EQuation LXI value for R_into Equation.LIX. This gives,

on rearrangement of terms:

 

d? dt Ix
ka(2kpS - kaA)P + kikpSZI kaA ( )

Integration of Equation LXII between limits, assuming that P: O at
t = 0, yields:
(2kpS - kaA)kat

. . k A
(2kpS - kaAkaI

 

Now, if the rate of prOpagation is taken as a criterion of the rate of

oxidation reaction occurring during the induction period:
dX/dt = kpSR (LXIV)

we can first substitute in the Equation LXI value for R and thereby

express the rate in terms of P}

dX/dt = £31223+ .P..‘____. (LXV)

“a

 

11:8

and we can then substitute the EQuation LXIII value for P to obtain the
final over-all expression for the induction period reaction rate:
(31:13-5- - 1)k It
dX/dt = kiSI-kES + kiSI-ka e kaA b _ (LXVI)
kaA k aA( mops ~kaD

Equation LXVI exhibits a fair correspondence with several observed re-
lamonships. Where kaA and kiSI completely dominate the reaction, and
propagation and branching are insignificantly small (e.g., in Hammond's
work) , the pre-exponential term with (kaA)2 in the denominator essen-

tially drops out, and the exponential itself is also very small, so

that the approximate relationship becomes simply ‘

k-SI- s
dX/dt = 3171:2- (LXVI-a)
a

and tile induction period, being inversely proportional to the induction
periOd reaction rate, becomes directly proportional to antioxidant
conc, entration (as found by Hammond and Boozer and by Kennerly and
Patter son) and inversely proportional to the initiating catalyst concen-
tration (as found by Brook and Matthews), and inversely proportional to
the Squzare of substrate concentration (also found by Brook and Matthews).
A second case may be considered, wherein kaA is still very unich

larger than kpS, but because of significant propagation and branching,
the ea‘l‘Lmnential term cannot be ignored. Here the approximate relation-
ship is:

~kat

slit/at -.- k_.i___p__SI'k S . 1.21.5232}. (1 - e ) (LXVI-b)
.kaA (kept)2

 

 

 

1&9

This leads to an exponential dependence on initiating catalyst, but
only a simple lOdeower dependence upon antioxidant concentration.

These relationships correspond to those found in the present work using
hydroquinone as the antioxidant.

If kaA is still smaller, so that the full equation LXXII must be
considered, the exponential term is of the form exp(kI/A), correspond-
ing to the direct exponential dependence of induction period upon anti~
oxidant concentration and the inverse exponential dependence of
induction period upon initiating catalyst. These are the dependencies
observed with dibutylcresol antioxidant.

Finally, if kaA is so small as to approach the value of 2kpS, the
exponential term itself goes to zero, causing the pre-exponential to
drop out also, and the expression again regresses to the character of
Equation LXVI-a. This, it is suggested, is illustrated by the observed
relationship with phenyl-2-naphthylamine. At very high amine concen-
trations, kaA is of course increased severalfold, tending to throw the
expression into the dibutylcresol-type dependence. This too is con~
sistent with the sharply increasing dependency at the high-cOncentration
end of the phenyl-2-naphthylamine series.

In support of this approximate interpretation, it should be noted
that the assignment of experimental results to these several modified
cases was by no means arbitrary. Hydroquinone, on the basis of both
its low threshold concentration and its activation energy, is quite
evidently the most effective of the antioxidants examined in the present

work, and thus has the highest ka. At the loweconcentration.end of the

 

150

hydroquinone test series, kaA was at its lowest for hydroquinone, and
imuld be reasonably expected to fall into the range of magnitude of

the dibutylcresol kaA values. The experimental data show that at the
low-concentration end of the hydroquinone series the dependency did in
fact shift from about first-order to something of an exponential
character (Figure 6). The dibutylcresol is intermediate in efficacy as
judged by threshold concentrations, and over the range of concentrations
studied its dependencies all corresponded to the intermediate case. The
amine is least effective, and its relationship fits the low -kaA case
except at its highest concentrations.

The foregoing treatment provides a fairly consistent rationaliza-
tion of the major observed relationships. It is not, however, without
serious faults. Two assumptions made in the development of Equation
LXVI warrant examination. The first, an approximate steady-state
assumption for R_(Equation LXI), is perhaps not too serious, since some
initial simplification was needed in order to obtain a working grip on
the problem, and since the peroxide level, which was employed to develop
the general expression, was specifically not assumed to be at steady-
state. The second and more serious assumption is implicit in the
integration of Equation LXII to yield Equation LXIII: in order to
integrate, the antioxidant concentration was assumed to be constant.

As an excuse for this assumption, it may be pointed out that the A_term
appears in two places in Equation LXII in such a manner that it tends to
cancel out, so that an.integrating error in.A_should not be too critical.
Nevertheless this latter assumption is undoubtedly the weak link of

the above development. . -

151

Another development of an approximate solution, which avoids making
either of these two objectionable assumptions, is shown in Appendix B.
The final expressions obtained are similar to the above, and account
for the experimentally observed relationships equally well.

At present it appears that an entirely adequate general solution
to the problem as formulated in Equations LVIII-LX may have to await
the further development of mathematical knowledge in the area of non-
linear differential equations. Lacking the exact general solution to
these equations, we may take encouragement from the operational simplic-
ity of the individual terms. Because of this simplicity, these equa-
tions may be readily programmed on computers. The assignment to a
computer of a family of specific systems with identical constants but
with, e.g., varying initial concentrations of A, should lead to a
pragmatic solution for the dependency of ti upon.A5 similarly, other
variables might be investigated. In this manner a general solution for
Equations 20-25 may be evolved. The evolution of a general method for
a general solution would greatly clarify the implications of various
detailed mechanism proposals: for example, Hammond's complex termination
step might be shown to be generally valid or generally invalid by a
formal treatment evolved in this manner. The future of non-steady-state
kinetics, in this area as well as in others, may well rest upon exacting
computational studies made upon the mathematical analogs of complex
chemical systems. The results of such studies would be of the greatest

fundamental importance to chemical kinetics.

 

 

152

CONCLUSIONS

 

l. A method has been developed whereby the induction periods of
inhibited liquid substrates under autoxidizing conditions may be measured
with a high degree of precision and reproducibility.

2. Studies of the data obtained from one hundred fifty autoxidation
runs show that the induction period is systematically related, by a
power or exponential dependency, to each of the major experimental
variables. Consequently, the magnitude of the induction period is of
major significance as an observational variable in the study of
inhibited reactions and inhibition kinetics.

3. Studies with a branching type metal-ion catalyst, cobaltous
naphthenate, show the induction periods of inhibited solutions of
tetralin to be exponentially dependent upon cobalt concentration.

h. The effect of antioxidant concentration upon induction period,
in the presence of cobaltous naphthenate, is shown to vary according
to the antioxidant used, from a linear and approximately first-order
relationship to an exponential relationship.

5. These relationships, as well as others involving substrate
hydroperoxide, weak-antioxidant retardation and the use of nonbranching
initiation, demonstrate the presence of propagation and branching
reactions to be significant during induction periods.

6. The observed kinetic relationships have been shown to be

incompatible with the classical kinetics of inhibited autoxidations.

 

 

 

153

The basis for this incompatibility is the widely-employed steady-state
assumption, which is shown to be invalid for the present system.

7. It is proposed that the steady-state assumption is in general
not valid for inhibited systems. A more general theory is proposed,
based upon the branching—chain kinetics of Semenoff. According to this
concept, the steady-state approximation may be permissible only for
the special case of linear nonbranching chain reactions.

8. A first approximation to a solution of the general theory is
presented, accounting qualitatively for the major empirical relation-

ships observed.

 

 

l.

2.

3.

h.

10.
ll.
12.
13.
1h.
15.
16.

17.

18.
19.

20.

15h

 

BIBLIOGRAPHY

C. E. H. Bawn, J. Oil Colour Chem. Assoc., 36, hh3 (1953).

N. Semenoff, "Chemical Kinetics and Chain.Reactions," Oxford
University Press, 1935, pp. hlff, h5hff.

T. Hooke, "Micrographia," The Royal Society, 1665, cited in
reference h.

WK P. D. Wightman, "The Growth of Scientific Ideas," Yale
University Press, 1953, Cht XVI.

. R. Willstatter and E. Sonnenfeld, Ber., BED 2952 (1913).

. Discussions Faraday Soc., 2_(l9h7)3 Trans. Faraday Soc., 52, 99-398

(19h6)-

. J. L. Bolland, Proc. Roy. Soc., A 186, 218 (l9h6).

J. L. Bolland, Quart. Rev., 2, 1 (19119).

. J. L. Bolland and G. Gee, Trans. Faraday Soc., _L_;_2_, 2th (191.6).

J. L. Bolland and G. Gee, ibid,, 236.

C. E. Frank, Chem. Rev., Q9, 155 (1950).

F. F. Rust and w. E. Vaughan, Ind. Eng. Chem., y_1_, 2595 (1919).
W2 A. waters, Ann, Repts. Prog. Chem., Q2, 130 (19h5).

A. H. Cook, J. Chem. Soc., 1223, 17714.

E. H. Farmer and A. Sundrilangham, J. Chem. Soc., 12y251137.

P. George, Trans. Faraday Soc., 32, 210 (l9h6).

P. George E. H. Rideal and A. RObertson, Proc. Roy. Soc., A 185,
288 (19h6).

P. George and A. Robertson, Trans. Faraday Soc., Q2, 217 (l9h6).
C. Paquot, Bull. Soc. chim., 8, 695 (l9hl).

W2 A. waters, Trans. Faraday Soc., Q2, 18h (l9h6).

21.

22.
23.
2h.
25.

26.
27.
28.

29.

30.

31.

32.

33.

3h.
35.
36.

37.
38.
39.
ho.
hl.

155

W2 A. Waters, "The Chemistry of Free Radicals," Oxford University
Press, 2nd ed., 19Q8, pp. 226-258.

A. Robertson and W} A. Waters, Trans. Faraday Soc., Q2, 201 (19Q6).
S. Bergstrom and R. T. Holman, Adv. in Enzymol., Q, Q25 (19Q8).
D. J. Mackinnon and W} A. Waters, J. Chem. Soc., 1252, 323.

V. Stannett and R. B. Mesrobian, "The Low-Temperature Autoxidation
of Hydrocarbons," U. s. ONR Report 033-292 (1950).

L. Bateman, Quart. Rev., 8, 1Q7 (195Q).
J. E. Leffler, Chem. Rev., Q5, 385 (19Q9).

A. V. Tobolsky and R. B. Mesrobian, "Organic Peroxides," Inter-
science, 195Q, pp. 96ff.

J. P. “fibaut and A. Strang, Koninkl. Ned. Akad. wetenschap. Proc.,
55B, 207 (1952).

E. R. Bell, G. E. Irish, J. H. Raley, F. F. Rust and w. E. Vaughan,
Ind. Eng. Chem., Q}, 2609 (19Q9).

P. J. Nawrocki, J. H. Raley, F. F. Rust and W} E. Vaughan, ibid.,
260k.

F. F. Rust, U. s. patents 2,369,181-2 (19u5); 2,380,675 (19u5);
2,395,523 (19u6); and 2,u21,392 (19u7).

J. L. Bolland and P. ten Have, Discussions Faraday Soc., 2, 252

(19h?)-
C. Graebe and P. A. Guye, Ber., 325 3028 (1883).
L. Piatti, Angew; Chem., QED 638 (1933).

C. Moureu, C. Dufraisse and R. Chaux, Ann. Office nat. comb.
Liquides,2 _, 233 (1927); Chem. Abs., 2;, 311516 (1927).

P. George and A. Robertson, J. Inst. Petroleum, 2, Q00 (19Q6).
H. N. Stephens, J. Am. Chem. Soc., 59, 568 (1928).

H. Hook and H. Schrader, Angew. Chem., 32, 565 (1936).

H. Hock and H. Schrader, Naturwissenschaften, 2Qg 159 (19h6)-

M. Hartmann and M. Seiberth, Helv. Chim. Acta, $2, 1390 (1932).

h2.
h3.
ht.

us.
A6.
b7.
ha.
A9.
50.
51.
52.

53-

55.

S6.

58.

59.

60.
61.

156

H. Hook and W} Susemihl, Ber., 66B, 61 (1933).
G. J. Minkoff, Proc. Roy. Soc., A 22h, 176 (195Q).

Y. Ikeda Bull. Liberal Arts Coll.,‘Wakayama Univ. (Nat. Sci.), Q,
27 (19515; Chem. Abs., g2, 95831 (1955).

R. Criegee, H. Pilz and H. Flygare, Ber., 122, 1799 (1939).
E. H. Farmer and A. Sundrilangham, J. Chem. Soc., l2Q2, 121.
H. Hock, Oel u. Kohle, 13, 697 (1937).

H. Hook and A. Neuwirth, Ber., 222, 2516 (1939).

‘w. Treibs and L. Schulz, Chem. Ber., gg, 21L (19h7).

I. M. Roitt and W. A. Waters, J. Chem. Soc., l2Q2, 3060.

H. B. Knight and D. Swern, Org. Syn., 3Q, 90 (19Sh).

J. E. Wicklatz and T. J. Kennedy, U. S. patent 2,511,957 (1950);
Chem, Abs., QQ, 8952j (1950).

R. Johnson, U. S. patent 2,568,639 (1951); Chem. Abs., Q6, 5089d
(1952).

. s. s. Medvedev, Acta Physicochimica U.R.S.S., 9, 395 (1938).

K. I. Ivanov, V. K. Savinova and E. G. Mikhailova, Compt. rend.
acad.)sci. U.R.S.S., 255 3L, Lo (1939); Chem. Abs., 3Q, 39739
<19uo .

Soc. pour 1'ind. chim. a Bale, Swiss patent 162,998 (1933); Chem.
Abs., 2g, 27307 (193A).

. W. Nussle, Jr., G. W. Perkins, J. A. Glovis and G. Toennies, Am.

J. Pharm., 10 , 29 (1935).

R. Johnson, U. S. patent 2,Q5Q,8OQ (l9h8); Chem. Abs., Q2, 1808d
(19h9).

T. Yamada, Researches Electrotech. Lab. (Tokyo), Qh3, l (19Q0);
Chem. Abs., 3§, 22583 (19QQ).

A. Robertson and W} A. Waters, J. Chem. Soc., 12Q8, 1578.

C. G. Swain,'W} H. Stockmayer and J. T. Clarke, J. Am. Chem. Soc.,
13, 5&26 (1950).

157

62. w. G. Lloyd, 2.232., 78, 72 (1956).

63. N. Kornblum and H. E. DeLamare, _3;_b_1_d_., 13, 880 (1951).
6Q. E. E. Royals and S. E. Horne, Jr., 2222,, 11, 187 (1955).
65. H. Hock and K. Ganicke, Ber., 1_1J_3_, 11130 (1938).

66. M. S. Kharasch, A. Fono and W. Nudenberg, J. Org. Chem., l_6_, 113
(1951)-

67. H. Hook and S. Lang, Ber., 15B, 300, 313 (19Q2).

68. L. Bateman, H. Hughes and A. L. Morris, Discussions Faraday Soc.,
_]_-_)._L_, 190 (1953)-

69. L. Bateman and A. L. Morris, Trans. Faraday Soc., Q2, 1026 (1953).

70. J. E. Hay, N. M. Johnstone, C. F. H. Tipper and R. K. Williams,
J. Chem. Soc., 1251;, 629.

71. S. Medvedev and A. POd'yapol'skaya, J. Phys. Chem. U.S.S.R., 1.3,
719 (1939); Chem. 1193-: 2,11,, 77075 (191:0)-

72. E. Ibuki, J. Chem. Soc. Japan, Pure Chem. Sect., 72, 221 (19h9);
Chem. Abs., Q5, Q702e (1951).

73. T. Kusama and D. Koike, ibid., :72, 683 (1951); Chem. Abs., Q_6_,
1116148. (1952).

7Q. L. Hess and S. Felser, to J. D. Riede1~E. de Haen A.-G., German
patent 520,290 (1925); Chem. Abs., 25, 271,03 (1931).

75. H. Hock and O. Schrader, Brennstoff-Chem., _l_8_, 6 (1937).

76. T. Yamada, Researches Electrotech. Lab. (Tokyo), Q11, 1 (1937);
Chem. Abs., 32, 911622 (1938).

77. A. Robertson and W. A. Waters, J. Chem. Soc., 19118, 15711.
78. H. Hook and s. Lang, Ber., 178, 257 (19th).
79. P. George and'A. D. Walsh, Trans. Faraday Soc., Q2, 91; (191(6).

80. S. S. Medvedev, Khim. Referat. Zhur., Q, No. 2, 35 (19141); Chem.
Abs., 3}, 30801 (19h3).

81. P. George and A. Robertson, Proc. Roy. Soc., A 185, 309 (19176).

82. A. Robertson and W. A. Waters, J. Chem. Soc., 12Q8, 1585.

83.
8Q.

85.
86.
87.

88.
89.
90.
91.
92.

93-

9Q.

95-

96.

97.

98.
99.
100 .
101 .
102 .

103 .

158

C. E. H. Bawn, Discussions Faraday Soc., 2Q, 181 (1953).

A. E. W00dward and R. B. Mesrobian, J. Am. Chem. Soc., 15, 6189
(1953).

G. A. Russell, ibid., 33, u583 (1955).
G. A. Russell, ibid., 16, 10L7 (1956).

T. Yamada, J. Soc. Chem. Ind. Japan, Q9, suppl. binding, Q22 (1937);
Chem. Abs., 22, 28156 (1938).

H. Hock and‘W) Susemihl, Brennstoff-Chem., 2Q, 106 (1933).

W. G. Lloyd, unpublished work.

P. George and A. Robertson, Trans. Faraday Soc., Q2, 227 (19Q6).
E

. Berl and K. Winnacker, Zeit. physik. Chem., 1Q8, 261 (1930).

CC")

. Dufraisse and R. Horclois, Compt. rend., 121, 1126 (1930);
. Moureu, C. Dufraisse and M. Badoche, ibid., 182, 685 (1926).

Y. Tanaka, T. Kuwata and M. Aoki, J. Soc. Chem. Ind. Japan, 37
suppl. binding, QAS, uh? (193A); Chem. Abs., 26, 7253,,3 (193Q).

N. Murata, J. Soc. Rubber Ind. Japan, 22, L2 (1989): Chem. Abs.,
Q6, 1791d (1952).

N. Murata and N. Sashio, J. Chem. Soc. Japan, Ind. Chem. Sect., 55,
5Q6 (1952); Chem. Abs., Q2, 981d (1955).

C. F. Frye, C. B. Kretschmer and R. Wiebe, Ind. Eng. Chem., Q6,
1517 (1958).

T. Yamada, J. Soc. Chem. Ind. Japan, 22, suppl. binding, Q50, Q52,
Q55 (1936); Chem. AbS-: 2}; U57h3,5 (1937)-

J; R. Thomas, J..Am. Chem. Soc., 11, 2R6 (1955).

M. Szwarc, Chem. Rev., Q1, 75 (1950).

J. L. Bolland, Trans. Faraday Soc., Q6, 358 (1950).
C. H. Bamford and M. J. s. Dewar, Proc. Roy. Soc., g_l9§, 252 (19h9).
P. George, ibid., g_;§5, 337 (19Q6).

. Wittig and G» Peiper, Ann., 5Q6, 172 (19Q1).

C)

 

lOQ.
105.
106.
107.
108.
109.

110.

111.

112.

113.
11Q.
115.

116.
117.

118.
119.
120.

121.
122.

123.

159

G. Wittig and G. Peiper, gpgg,, 556, 218 (19h7).

R. von Konow, Finska Kemistsamfundets Medd., 62, Q2 (195Q).
C. F. Cullis, Bull. Soc. chim. France (5), 11; 863 (1950).
A. L. Lumiere and A. Seyewitz, 2222-: (3), 33, huh (1905).
R.

. Haslam and P. K. Frolich, Ind. Eng. Chem., 22, 292 (1927).

*3

G. R. Greenbank and G. E. Holm, ibid., 11; 625 (1925).
C. D. Lowry, Jr., C. Egloff, J. C. Morrell and C. G. Dryer, ibid.,

25, 80b (1933).
N. A. Milas, Chem. Rev., $9, 295 (1932)-

A. R. Rescorla, J. H. Cromwell and D. Milsom, Anal. Chem., 2Q,
1959 (1952).

H. Morawetz, Ind. Eng. Chem., Q2, 1QQ2 (19Q9).
J.‘W; Thompson, Oil Gas. J., July 5, 195Q, p. 15h-
E. M. Bickoff, J. Am. Oil Chem. Soc., 2g, 65 (1951).

K. T. Williams, E. Bickoff and B. Lowrimore, Oil and Soap, 22, 161
(19QQ).

C. G. Dryer, C. D. Lowry, Jr., C. Egloff and J. C. Morrell, Ind.
Eng. Chem., 21, 315 (1935).

'W. W. Scheumann and J. H. Haslam, ibid., 2Q, Q85 (19Q2).
R. H. Rosenwald and J. R. Hoatson, ibid., Q}, 91h (19Q9)o
J.‘W} Thompson, Oil Gas J., June 28, 195Q, p. 125-

G. H. von Fuchs, E. L. Claridge and H. H. Zuidema, A.S.T.M.
Bulletin 186, Q3 (1952).

C. J. Pedersen, in "The Use of Additives in Petroleum Fuels,"
Petroleum Division (A.C.S.) Symposium 36-8, 103 (1955).

"Oxidation Stability of Gasoline (Induction Period Method),"
A.S.T.M. Method D525-Q9, in "A.S.T.M. Standards," 19h9 ed.,
Vol. V, p. 930.

 

 

l2u”
12EL
126.

127.

128.

129.

,130.

131.
132.

133.

13Q.
135.
136.
137.0

138.
139.
1QO.

lQl.
1Q2.

1h3-

1QQ.

160

H. A. Mattill, J. Biol. Chem., 26, 1Q1 (1931).
H. s. Olcott, J. Am. Chem. Soc., 6, 2Q92 (193A).
G. M. Henderson, Discussions Faraday Soc., 19, 291 (1951).

M. F. R. Mulcahy and M. J. Ridge, Trans. Faraday Soc., Q2, 906
(1953)

M. R. Fenske, C. E. Stevenson, N. D. Lawson, G. Herbolsheimer and
E. F. Koch, Ind. Eng. Chem., 22, 516 (19Q1).

G. H. Denison and P. C. Condit, 1b16,, Q1, 9QQ (19Q9).

B. S. Biggs and W. L. Hawkins, Modern Plastics, 21, No. 1, 121
(1953)-

A. J. Ham and C. N. Thompson, J. Inst. Petroleum, 26, 673 (1950).
D. J. H; Kreulen, ibid., 38, QQS (1952).

M. F. R. Mulcahy and M. J. Ridge, Trans. Faraday Soc., Q25 1297
(1953)

D. J. w; Kreulen, J. Inst. Petroleum, 26, QQ9 (1952).
J. E. Wilson, Ind. Eng. Chem., Q1, 2201 (1955).
R. W. Dornte, ibid., 2_8_, 26 (1936).

.H. Beaven R. Irving and C. N. Thompson, J. Inst. Petroleum,
37, 25 (19513.

G. H. von Fuchs and H. Diamond, Ind. Eng. Chem., 2Q, 927 (19Q2).
G.‘W3 Kennerly and W3 L. Patterson, Jr., in reference 122, p. 191.

C. E. Boozer, G. S. Hammond, C. E. Hamilton and J. N. Sen, J. Am.
Chem. Soc., 11, 3233 (1955)-

C. E. Boozer and G. S. Hammond, ibid., 16, 3861 (195Q).

G. H. N. Chamberlain and A. D. Welsh, Trans. Faraday Soc., Q5,
1032 (19Q9)-

J. L. Bolland and P. ten Have, ibid., Q3, 201 (19Q7).

G. S. Hammond, C. E. Boozer, C. E. Hamilton and J. N. Sen, J. Am.
Chem. Soc., 11, 3238 (1955).

lQS.

1Q6.
1Q7.

1Q8.
1Q9.
150.

151.

152.

153.

lSQ.
155.
156.
157.

161

J. H. T. Brook and J. B. Matthews, Discussions Faraday Soc., 19,

298 (1951).
F. E. Malherbe and A. D. Welsh, Trans. Faraday Soc., Q6, 82Q (1950).

G. H. N. Chamberlain and A. D. walsh, Rev. Inst. Franqais du Pétrole,
Q, 301 (19149)-

C._Moureu and C. Dufraisse, Compt. rend., 115, 127 (1922).
G. M. Burnett and H. W3 Melville, Proc. Roy. Soc., A 182, Q56 (19Q7).
G. M. Burnett and H. W) Melville, ibid., Q81.

Beilsteins Handbuch der organischen Chemie, Julius Springer, 1919,

1929, 1939-

W; J. Youden, "Statistical Methods for Chemists," John Wiley and
Sons, 1951.

G. Egloff, "Physical Constants of Hydrocarbons," Reinhold, 19Q7,
vol. IV, p. 30.

H. Eckart, Brennstoff-Chem., Q, 2Q (1923).
F. Krollpfeiffer, Ann., Q30, 161 (1923).
H. W. Melville and S. Richards, J. Chem. Soc., 125Q, 9QQ.

D. H. Andrews, G. Lynn and J. Johnston, J. Am. Chem. Soc., Q6,
127A (1926).

158. w; Heinrich, Ind. Eng. Chem., 55, 26h (19Q3).

159. w. A. Pardee and w. Weinrich, ibid., 16, 595 (19th).

160.
161.
162.
163.

16Q.
165.

D. P. Craig and I. G. Ross, J. Chem. Soc., 125Q, 1589.
M. A. Paul, J. Am. Chem. Soc., 16, 3236 (195Q).
H. Rogers and'W} C. Holmes, J. Ind. Eng. Chem., 12, 31Q (1921).

N. Puschin and I. Grebenschtschikow, J. Russ. Phys.-Chem. Soc.,
QQ, 112 (1912); Chem. zentr., 1212 1, 19Q6.

H. Block, 2. phys. Chem., 16, 385 (1912).

K. B. Everard, L. Kumar and L. E. Sutton, J. Chem. Soc., 1251, 2807.

166.
167.

168.
169.
170.

171.

172.

173.

17Q.

175.

176.

177.
178.

179.

162

P. Grammaticakis, Bull. Soc. chim. France, 1251, 538.

T. Callan and J. A. R. Henderson, J. Soc. Chem. Ind., 26, Q08T
(1919).

W; C. McCrone, Anal. Chem., 22, 188Q (1951).
E. Knoevenagel, J. prakt. Chem. (2), 62, 1 (191Q).
F. D. Werner and.A. C. Frazer, Rev. Sci. Instruments, 22, 163 (1952).

J. P. Wfibaut and A. Strang, Koninkl. Ned. Akad. wetenschap. Proc.,
51g, 229 (1951).

T. W} Campbell and G. M. Coppinger, J. Am. Chem. Soc., 1Q, 1Q69
(1952).

A. F. Bickel and E. C. Kooyman, J. Chem. Soc., 1252, 3211.
0. L. Harle and J. R. Thomas, "Inhibition of Oxidation. I.
Kinetics of the Inhibition Period," American Chemical Society,

Miami, April, 1957.

O. L. Harle, "Inhibition of Oxidation. II. Mechanism of Auxiliary
Inhibition," American Chemical Society, Miami, April, 1957.

w; G. Lloyd and w; T. Lippincott, "Antioxidant Studies by Induction
Period Analysis. I. Cobalt Naphthenate Initiated Tetralin Autoxi-
dation," American Chemical Society, Miami, April, 1957.

A. Pirie and R. van Heyningen, Nature, 112, 873 (195Q).

A. J. Chalk and J. F. Smith, ibid., 178, 802 (1958).

J. L. Bolland and P. ten Have, Trans. Faraday Soc., Q2, 201 (19Q7).

 

163

 

 

 

AUTHOR INDEX

222292. REFERENCE NUMBERS PAGE REFERENCE IN THESIS

Aoki, M. 93 17

Andrews, D. H. 157 Q9

Badoche, M. 92 15

Bamford, C. H. 101 19, 22, 37, Q6, 116, 120,
129, 1QO

Bateman, L. 26, 68, 69 i6 5, 9, 12, 1Q, 21, 31, 33,

Bawn, C. E. H. 1, 83 1, 12, 15, 16, 27, 28, 31,
3Q, 35, 36, 95, 12?

Beaven, G. H. 137 28, 32, 127, 183

Bell, E. R. 30 Q, 18

Bergstrom, S. 23 3

Berl, E. 91 15

Bickel, A. F. 173 lOQ, 105

Bickoff, E. M. 115, 116 25

Biggs, B. S. 130 27

Block, H. 16Q 50

Bolland, J. L. 7, 8, 9, 10, 33, 3, 8, 19, 20, 29, 98, 128,

100, 183, 179 137

Boozer, C. E. lQO, lQl, 1QQ 28, 30, 31, Q6, lOQ, 127,
128, 129, 138, 139, 1Q8

Brook, J. H. T. 185 32, 33, 3Q, 35, 38, 95, 130,
187, 188

Burnett, G. M. 1Q9, 150 36

Callan, T. 167 50

 

 

AUTHOR INDEX - Continued

 

AUTHOR REFERENCE NUMBERS
Campbell, T. W} 172
Chalk, A. J. 178

Chamberlain, G. H. N. 1Q2

Chaux, R. 36
Claridge, E. L. 121
Clarke, J. T. 61

Condit, P. C. 129

Cook, A. H. 1Q
Coppinger, G. M. 172

Craig, D. P. 160
Criegee, R. Q5
Cromwell, J. H. 112

Cullis, C. F. 106
DeLamare, H. E. 63

Denison, G. H. 129

Dewar, M. J. S. 101
Diamond, H. 138

Dornte, R. W} 136

Dryer, C. G. 110, 117
Dufraisse, G. 36, 92, 1Q8
Eckart, H. 15Q

Egloff, G. 110, 117, 153

Everard, K . B. 165

168

PAGE REFERENCE IN THESIS
lOQ

91

29, 33, 182

6

25, 38, 35

9

27

3, 8, 10, 1Q, 16
lOQ

50

7

28, 28

23, 27

9

27

19, 22, 37, Q6, 116, 120,
129, 180

28, 127

28

2Q, 25, 27, 28

6, 15, 36

86

2Q, 25, 27, 28, Q6
50‘

 

AUTHOR INDEX - Continued

 

AUTHOR REFERENCE NUMBERS

Farmer, E. H. 15, Q6

Felser, S. 78

Fenske, M. R. . 128

Flygare, H. 85

Fono, A. 66

Frank, C. E. 11

Frazer, A. C. 170

Frolich, P. K. 108

Frye, C. F. 96

von Fuchs, G. H. 121, 138

Ganicke, K. 65

Gee, G. 9, 10

George, P. 16, 17, 18, 37, 79:
81, 90, 102

Glovis, J. A. 57

Graebe, C. 38

Grammaticakis, P. 166

Grebenschtschikow, I. 163

Greenbank, G. R. 109

Guys, P. A. 38

Ham, A. J. 131

Hamilton, C. E. 1Q0, 1QQ

Hammond, G. s. 180, 181, 188

165

PAGE REFERENCE IN THESIS

3, 7, 9
10

27, 32, 183

7

9

3, 5, 16

52

2h, 27

18, 86

25, 28, 38, 35, 127

9

3

3, 6, 10, 11, 1Q, 15, 16, 17,
18, 19, 22, 27, 28, 30, 35,
75, 125, 131, 135

8

5

50

50

28

5

27

28, 30, 31, 86, 108, 127,
128, 129, 138, 139

28, 30, 31, 86, 108, 127,
128, 129, 138, 139, 1Q8, 151

 

 

166

 

AUTHOR INDEX - Continued

 

 

2E2§9§_ REFERENCE NUMBERS PAGE REFERENCE IN THESIS
Harle, 0. L. 178, 175 182, 183
Hartmann, M. 81 6, 8, 9
Haslam, J. H. 118 25, 27
Haslam, R. T. 108 28, 27
ten Have, P. 33, 1Q3, 179 Q, 29, 128, 137
Hankins,‘w. L. 130 27
Hay, J. E. 70 9
Henderson, G. M. 126 27
Henderson, J. A. R. 167 50
Herbolsheimer, G. 128 27, 32, 1Q3
Hess, L. 7Q 10
van Heyningen, R. 177 91 .
Hoatson, J. R. 119 25, 26, 28, 30, 127
Hock, H. 39, 80, 82, 87, 6, 7, 8, 9, 10, 18, 17, 89
88, 65, 67, 75:
78, 88
Holm, G. E. 109 28
Holman, R. T. 23 3
Holmes, W} C. 162 50
Hooke, T. 3 2
Horclois, R. 92 15
Horne, S. E., Jr. 6Q 9
Hughes, H. 68 9, 12, 18, 31, 86
Ibuki, E. 72 10

Ikeda, Y. 88 ~ 7

 

AUTHOR INDEX - Continued

 

AUTHOR REFERENCE NUMBERS
Irish, G. E. 30
Irving, R. 137
Ivanov, K. I. 55
Johnson, R. 53, 58
Johnston, J. 157
Johnstone, N. M. 70
Kennedy, T. J. 52
Kennerly, G. W} 139
Kharasch, M. S. 66
Knight, H. B. 51
Knoevenagel, E. 169
Koch, E. F. 128
Koike, D. 73

von Konow, R. 105
Kooyman, E. C. 173
Kornblum, N. 9
Kretschmer, C. B. 96
Kreulen, D. J. W. 132, l3Q
Krollpfeiffer, F. 155
Kumar, L. 165
Kusama, T. 73
Kuwata, T. 93
Lang, S. 67, 78

167

PAGE REFERENCE IN THESIS
8, 18

28, 32, 127, 183

8, 18, 19, 99

8, 9, 10, 88

89

9

8

28, 29, 30, 31, 33, 38, 127,
128, 136, 188

9

8

51

27, 32, 183
10

22

108, 105

9

18, 86

27, 32, 77, 183
86

50

10

17

9, 10

 

AUTHOR INDEX - Continued

Elia
Lawson, N. D.
Leffler, J. E.
Lippincott, W. T.
Lloyd, W3 G.
Lowrimore, B.
Lowry, C. D., Jr.
Lumiere, A. L.
Lynn, G.
Mackinnon, D. J.
Malherbe, F. E.

Matthews, J. B.

Mattill, H. A.
McCrone, W. C.
Medvedev, S. S.
Melville, H. W}
Mesrobian, R. B.
Mikhailova, E. G.
Milas, N. A.
Milsom, D.
Minkoff, G. J.
Morawetz, H.
Morrell, J. C.
Morris, A. L.

Moureu, C.

REFERENCE NUMBERS
128

27

176

62, 89, 176
116

110, 117
107

157

28

186

185

128

168

58, 71, 80
189, 150, 156
25, 28, 88
55

111

112

83

113

110, 117
68, 69

36, 92, 188

168

PAGE REFERENCE IN THESIS
27, 32, 183

3, S

182

9, 21, 33, 51, 78, 98, 182
25

28, 25, 27, 28

23, 27

89

3

32, 38, 35

32, 33, 3h, 35, 38, 95, 130,
187, 188

25

51

8, 10, 11, 13, 19, 98

36, 88

3, 5, 9, 12, 16, 31, 86, 89
8, 18, 19, 99

28, 31

28, 28

7

25, 27

28, 25, 27, 28

9, 12, 18, 21, 31, 33, 86
6, 15, 36

AUTHOR INDEX - Continued

Elli-i
Mulcahy, M. F. R.
Murata, N.
Nawrocki, P. J.
Neuwirth, A.
Nudenberg, W,
Nussle, W., Jr.
Olcott, H. S.
Paquot, C.

Pardee, W} A.

Patterson, W2 L., Jr.

‘Paul, M. A.
Pedersen, C. J.
Peiper, G.
Pakhm,G.W.
Piatti, L.
Pilz, H.

Pirie, A.
Pod'yapol'skaya, A.
Puschin, N.
Raley, J. H.
Rescorla, A. R.
Richards, S.

Rideal, E. K.»

REFERENCE NUMBERS

 

127, 133
98, 95
31

88

66

S7

125

19

lS9

139

161

122

103, 108
57

35

85

' 177

71

163
30, 31
112
156

17

169

PAGE REFERENCE IN THESIS

 

27, 32, 38, 35
17

L, 18

7

9

8

25

3

89

28, 29, 30, 31, 33, 38, 127,
128, 136, 188

50

25, 28, 30
22

8

6

7

91

10, 13
50

8, 18
28, 28
88

3, 6, 10, 18, 16, 17, 19, 27,
7S. 125, 135

AUTHOR INDEX - Continued

AUTHOR
Ridge, M. J.

RObertson, A.

Rogers, H.
Roitt, I. M.
Rosenwald, R. H.
Ross, I. G.
Royals, E. E.
Russell, G. A.
Rust, F. F.
Sashio, N.
Savinova, V. K.
Scheumann, W} W}
Schrader, H.
Schulz, L.
Seiberth, M.
Semenoff, N.

Sen, J. N.

Seyewitz, A.
Smith, J. F.
Smmmfidd,E.
Stannett, V.

Stephens, H. N.

REFERENCE NUMBERS

127, 133
17, 18, 22, 37,

6o, 77, 81, 82,
90

162

so

119

160

68

85, 86

12, 3o, 31, 32
95

SS

118

39, 80, 75
89

81

2

180, 188

107
178
5
25
38

170

PAGE REFERENCE IN THESIS

 

27, 32, 38, 35

3, 6, 9, 1o, 11, 18, 15, 16,
17, 18, 19, 20, 21, 22, 27,
28, 30, 31, 35, 86, 75, 99,
116, 120, 125, 131, 135

so

8

25, 26, 28, 30, 127

50

9

18, 86

3, 8, 18

17

8, 18, 19, 99

25, 27

6, 10

7

6, 8, 9

1, 185, 153

28, 3o, 31, 86, 108, 127,
128, 129, 138, 139

23, 27
91
3

 

AUTHOR INDEX - Continued

AUTHOR
Stevenson, C. E.
Stockmayer, W. H.
Strang, A.
Sundrilangham, A.
Susemihl, W.
Sutton, L. E.
Swain, C. G.
Swern, D.

Szwarc, M.
Tanaka, Y.
Thomas, J. R.
Thompson, C. N.
Thompson, J. W.
Tipper, C. F. H.
Tobolsky, A. V.
Toennies, G.
Treibs,‘W.
Vaughan, W} E.
walsh, A. D.

‘Waters, W. A.

'Weinrich,‘w.
‘Werner, F. D.

Wibaut, J. P.

REFERENCE NUMBERS

171

PAGE REFERENCE IN THESIS

 

128

61

29, 171

15, 86

82, 88

165

61

51

99

93

98, 178

131, 137

118, 120

70

28

57

89

12, 3o, 31

79, 182, 186, 187
13, 2o, 21, 22, 28,
so, 60, 77, 82
158, 159

170

29, 171

 

27, 32, 183

9

3, S

3, 7, 9

7, 8, 18, 17, 89

so

9

8

19

17

19, 99, 182

27, 28, 32, 127, 183

25, 28

9

3, S, 9, 16, 89

8

7

3, 8, 18

10, 29, 32, 33, 38, 35, 182
3, 8, 9, 1o, 11, 18, 15, 16,
17, 18, 19, 20, 21, 27, 31,
86, 75, 99, 116, 120

89

52

3, S

 

AUTHOR INDEX - Continued

81.1898
Wicklatz, J. E.
Wiebe, R.
Wightman, W. P.
Williams, K. T.
Williams, R. K.
Willstatter, R.
Wilson, J. E.
Winnacker, K.
Wittig, G.
Woodward, A. E.
Yamada, T.
Youden, W. J.

Zuidema, H. H.

REFERENCE NUMBERS
52

96

8

116

70

S

135

91

103, 108

88

59, 76, 87, 97
152

121

172

PAGE REFERENCE IN THESIS
8

18, 86

2

25

9

3

27, 28, 38, 35, 9S, 12?
15

22

12, 16, 31, 86

8, 9, 10, 18, 19, 99
80, S9, 65

25, 38, 3S

 

 

 

173

APPENDIX A

 

THE ANALYSIS OF INHIBITION BY GEORGE, RIDEAL AND ROBERTSON

The following treatment of autoxidation inhibition, published by
George, Rideal and Robertson in early 1986 (17), is the first attempt
to Rake a rigorous kinetic treatment of inhibited systems. Most of the
inhibition kinetics which have been subsequently developed and which
are based upon the assumption of steady-state conditions are heavily
indebted to this original work.

In a chain reaction in which the rates of the processes of chain
initiation, propagation and termination may be represented by a, p and

b, respectively, the over-all rate RO may be defined as:

If an inhibitor at concentration I_reacts with the chain carrier,
and the velocity constant of this reaction is represented by the symbol

2;

the inhibited rate Ri may be expressed as:

. = __§R__
R1 b + CI (II)

Now at any time the fraction of chains stopped that are being
stopped by the inhibitor is cI/(b » cl). If one inhibitor molecule is

removed per chain stopped, the rate of inhibitor consumption is given

by:

CL

I

m
a
P1

 

(III)

0..
0"
.4.
O
H

178
Integration of Equation III between limits, representing the initial
concentration of inhibitor as IO, yields the following expression:
t=-2:-(IO-I+p-ln%°-) (1v)

For the purposes of considering retardation, if t is small and I
not too different from IO, Equation IV may be simplified by ignoring

the logarithmic term, yielding:

I = ID - at (V)
Now from Equation II,

1 b + cI

... = ...—... VI

R1 ap < >

Appropriate substitution of Equation V into Equation VI yields:

 

= b + CID - cat

1
RI; ap (VII)

which can be rewritten in terms of the initial inhibited rate, Rio, as:

1...}.
31 Rio

*dlg

(VII-a)

From Equation VII-a it can be seen that a plot of reciprocal rate vs.
time for a retarded autoxidation should be linear, the slope giving
the ratio of the antioxidant termination rate constant to the rate of
propagation, c/p.

Now from a consideration of Equations I and II we may write the

ratio of uninhibited rate to initial inhibited rate as:

3.0. = 11.3.1.9. (VIII)

Rio b

175

This may be rearranged:
3.2.. -1 = 4:1 (VIII—a)

Rio
The chain length of the uninhibited reaction, p/b, may be represented

as:

 

(IX)

Now substitution of Equation VIII—a into Equation IX yields the final

expression:

g=-—-a-o-—— (x)

In Equation.X, R0 and Rio are determined experimentally, I0 is of
course known experimentally, and the ratio c/p is determinable graphic-
ally in accordance with Equation VII—a. Thus the absolute chain length
of the uninhibited reaction is determined by a direct study of the
effect of retarders upon rate. The only assumption necessary is that
concerning the stoichiometry of reaction between retarder and chain
carrier.

As an alternative treatment, George and co-workers developed an
induction period method of obtaining the same information. Dividing

Equation IV by IO yields:

_t__1 b1n;Q+IQ-I
IO ~ a [cIO (I ) Io J (XI)

-—-— = --—-- (XII)

176

Substitution of Equation XII into Equation XI then yields:

t l 1 ln I I - I
I0 a Ea _ 1 I " Io (XIII)
Rio

For the conditions in which an induction period is obtained,
however, the initial inhibited rate, R10: is necessarily very small
compared with the uninhibited rate, R0; this is a definitional require-
ment in the characterization of an induction period. Therefore, the
coefficient of the legarithmic term has, for these cases, a very large
number in its denominator, RO/Rio. And, therefore, the logarithmic
term in Equation XIII may be legitimately neglected, permitting this
equation to be simplified--for the case of inhibitors yielding

induction periods-~to:

At the end of the induction period, when t = ti, the inhibitor concen-
tration I is approaching zero, and may be considered to be extremely
small compared to its initial concentration, IO. Therefore, for the
case of strong inhibition, Equation XIV may be further simplified to
the relationship:

(XV)

9:
II
.515“

From Equation I, the expression for chain length, p/b, is given as:

2.:
b

WB‘U

(XVI)

177

Substitution of Equation XV into Equation XVI then yields the final
equation for chain length of the uninhibited autoxidation in terms of

induction period:

5- = 5935- (XVII)

Equation XVII thus gives a direct estimate of chain length from
the directly observable terms: rate of free uninhibited autoxidation,
time of induction period with a given amount of some effective inhibitor,
and concentration of inhibitor used.

This careful development of the theoretical aspects of inhibition
was quite well supported'by data obtained with low-temperature autoxi—
dations urder nonbranching conditions. The clarity and logic of these
kinetics are unlikely to be surpassed by later workers. Unfortunately,
however, there are implicit in this treatment no less than three
assumptions which, for reasons expanded upon elsewhere, are not accept-
able for any general theory of autoxidation inhibition. Equations I
and II specifically presuppose a "monomolecular" radical termination
step. Equations I, II and IV rest upon the steady-state assumption.
Equation III implicitly denies the possibility of branching in the
system. In addition, the assumption leading to the simplification of
Equation XIV to Equation.XV is not always a good one, as has been shown
not only in the present work but also by some of the experimental
results reported by George and his co-workers in the same paper which

presented this kinetic analysis (17).

178

APPENDIX B
AN APPROXIMATE SOLUTION TO THE NON-STEADY#STATE PROBLEM

Considering the reactions:

S -—--—-——-—> R (ki)
S + R ——------> P + R (kp)
P + I --------9- 2R, + I (kb)
R + A -—-——-9 inert (ka)
R + R -————-—4> inert (kt)

Considering biradical termination to be unimportant during the
induction period of an inhibited reaction, the differential equations
for R and E are:

dR/dt = kiS + ZkaP - kaAR (I)

dP/dt

kpSR - kaP (11)

Rejecting any steady-state assumption, let it be assumed instead
that a dynamic equilibrium obtains between the intermediate species,

after Semenoff. In this instance the assumption may be expressed as:
dP/dt = n(dR/dt) (111)

where n will be a constant for a given system, substantially greater

than unity since the species P_is much more stable than species R,

179

Then, substitution of Equations I and II into Equation III and

solving for R_yields:

nkiS + 2%]?

R=__E
nkaA+kpS

 

(IV)

Now since kaA must be much greater than kpS during the induction period,
and furthermore since Q_is much greater than unity, it follows that kpS
is an extremely small term compared with nkaA, and may, therefore, be
neglected. This permits simplification of Equation IV to give an
expression for R independent of 2?

kiS + 21(pr

kaA

 

(V)

Substitution of Equation V into Equation II then yields an expression

for dP/dt in terms of 2_and A:

dP/dtz _p.__1._k S'k's + _p_____2k S'kaP - kaP (VI)
kaA kaA

In the final treatment presented in the Discussion, an expression
of the general form of Equation VI was rearranged and integrated, making
the questionable assumption that A may be taken as a constant through
the integration. The second important difference in the present treat-
ment is that A_is assumed to be a variable which may be expressed as a
function of E: For a branching system, in which peroxide level is in
equilibrium with radical level, it is evident that these levels will
be some inverse function of antioxidant concentration. Taking the

simplest inverse function, the following relationship is proposed:

P(mA + 1) = PSS (VII)

180

where m_is a constant of proportionality and PSS is the steady—state
peroxide level for free autoxidation in the absence of antioxidant A.
Thus, at very large values of A, §_is very small, and as A goes to zero,

2 converges to Pss’ This may be rearranged to give A.as a function of E;

A = 3.33.;3 (VIII)

The steady-state expression for P derived for this scheme under the

ss’
conditions of free autoxidation (the only conditions under which it
will be conceded that the steady-state assumption is justified), for
the usual long kinetic chain process, is:

Fee = £83,1—; (Ix)

Substitution of Equation IX into Equation VIII yields A_in terms ofgg
alone:

(kgs)2 - ka-ktP

A = mka.ktP (X)

 

Now, returning to Equation VI, the above expression may be substituted

for A, Expansion and collection of terms then yields:

g§_=.(ka)2.kt(2mkps + Ra)?2 + ka.kpS(mkiS.kt - ka.kpS)P (XI)

t - ka.ka.ktP + ka(kpS)2

 

0..

Further treatment is simplified by temporarily replacing the aggregates

of constants with single letter symbols, thus:

181

B for (ka)2.kt(2mkpS L ka)
C for ka.kpS(mkiS.kt - kakpS)
D for - ka-ka-kt

E for ka(kpS)2
whereupon Equation XI may be rewritten as:

BP2 + CP
DP + E

0..
“U

I

(XI-a)

Q.
(....

The general integration of Equation XI-a, from t = O and P0 negligibly

small to t = t and P = P, gives:

B c BP+CJ=t<XII>

Ufl

For practical solution of Equation XII there will be two general cases.

If DC is greater than BE, Equation XII will be approximated by:

D ln BP + C
Rearranging: P = B exp(Bt/D) - C/B (XIII-a)

And in the original notation:
ka
(XIV—a)

 

= kpS (ka.kpS - mkiSkt) + (ka)2kt(2mkpS . ka) e

ka.kt(2mkpS + ka)

P

If on the other hand BE is greater than DC, Equation XII will be
approximated by:

1n [ ---1-D-— ] = t (XII-b)

cane

FF I
"‘ I
U,“ S;
A n
#8.: (3

182

P = C exp<93/E) (XIII-b)

Rearranging: l _ B expTC t /ET

And in the original notation:

mk.
- ( 1.-._;fiEE ) kat

 

 

kakp
P = (kakpS - mkiSkt)ka.kpS e (XIV_b)
_ _ mkikt
(ka)2kt(2mkpS : ka) e a p - 1

Now Since dA/dt is simply - kaAR, substitution of the Equation V value

for R_defines dA/dt in terms of P:

- dA/dt = kiS + 2kaP (xv)

and for the two extreme cases of Equation XII considered above, 2_may
be replaced by the value given by Equation XIV-a or XIV-b. The inter-
mediate cases of Equation XII are difficult to express in this form but
will yield expressions for 2 intermediate between these two forms.

The antioxidant concentration term, A, does not appear explicitly
in the final equations of this development, but for the purposes of
examining the qualitative relationships involved one may look for the
ka terms; for instance, if the concentration of (A) were doubled, this
would change the system in substantially the same manner as if ka were
doubled. With this in mind, inspection of the combination of Equations
XV and XIV-a shows a surprisingly close correspondence to the form of
the final equation evolved in the Discussion section, and may be used
similarly to interpret the data. Thus, at very large ka's, the ka

term drops out of the exponent but (I) remains; as ka decreases both

IV and XIV-
in View of
at very la:

while at i

183

the ka and the (I) terms are important in the exponential, and the slope
of the exponential dependency term at constant ka gets steeper (compare
the cobalt dependency slopes of hydroquinone and dibutylcresol). As ka
gets very small, —dA/dt again becomes equal to a collection of constant
terms. For the second case, represented by the combination of Equations
XV and XIVéb, the over-all effect is a little more difficult to ascertain
in view of the two somewhat countervailing exponential terms. Again

at very large values of k8 the ka term drops out of both exponentials,
while at intermediate ka's it remains in both exponentials. When ka
decreases further, approaching the value of mkikt/kp, the exponential
term goes to zero. In this second case the exponential dependency on

(I) again remains through high and intermediate values of ka’ being

lost only as the entire exponential term drops out.

Thus, this derivation appears to account at least as well for the
various experimental relationships as does that developed in the
Discussion. This derivation has the advantages that it has avoided the
two weak approximations of the earlier derivation: it has made no form
of steady-state assumption except for free post—induction-period autoxi-
dation, and it has avoided making undesireable assumptions about the
constancy of A_or of any other variable for the purposes of integration.
The only assumption made which cannot be demonstrated to be reasonably
correct is that of Equation VII. This relationship was postulated as
a reasonable one, and appears to be very much better than the assumption
of constant concentrations. It is possible, however, that some other

inverse function may better characterize this relationship.