ORGANIC COMPLEXES FROM
COPOLYMERIZATION MONOMERSr
PARA SUBSTlTUTED STYRENES AND

MALEIC ANHYDRIDE

Thesis for the beam of Ma. 51.
MICHlGAN STATE COLLEGE
Edward Robert Garret“?

1950

 

 

This is to certify that the

thesis entitled

”Organic Complexes from Copolymerization
Monomers: Para Substitflted Styrenes and
Maleic Anhydride"

presented by

Edward R. Garrett

has been accepted towards fulfillment
of the requirements for

Eb.D. degree inJhnmistry

mac/(793%

{lajor professor

pm July 17 1950

 

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ORGANIC COMPLEXES FROM COPOLYMERIZATION MONOMERS:
PARA SUBSTITUTED STYRENES AND MALEIC ANHYDRIDE

By
EDWARD ROBERT GARRETT

A THESIS
Submitted to the School of Graduate Studies of
Michigan State College of Agriculture and

Applied Science in partial fulfillment
of the requirements for the degree of

DOCTOR OF PHILOSOPHY

Department of Chemistry
1950

ACKNOWLEDGMENT

The writer wishes to express
his appreciation to Dr. Ralph L. Guile
for his counsel and guidance.

****M
*fl'fi'i'
*4?

*-

“Vii-93%

DEDICATION

To my wife, her
patience and 000peration

CONTENTS

page no.
IntrOduCtion o o o o o o o o o o 1

Historical & Theoretical Background.2
EXPERIMENTAL . . . . . . . . . . 27
A. Reagents O O O O O O O O O 27

B. Preparation of Solutions For
Spectrophotometric Studies. 29

C. Preparation of "Complex"
Mixtures For the Study of
Continuous Variations . . . 50

D. Preparation of "Complex"
Mixtures for Other Studies. 31

E. SpectrOphotometric Measure-
ments . 34

F. Investigation of Precipitates
O O 56

G. Summary of the Extent of
SpectrOphotometric Studies. 36

INTERPRETATION OF RESULTS . . . 42

A. The Method of Continuous
variations 0 o o o o o”. o 42

B. Evaluation of the Further
Interaction of a 1:1 Complex
With the Reactants o o o o 46

C. Quantitative Comparison of
the Complexes and Prediction
of Optical Density. . . . . 67

D. Effect of Deoxygenation on
Complex Formation . . . . . 79

E. Effect of Dilution on Complex
Formation . . ... . . . . . 80

F. Interprehtion of the Kinetics:
The Change in Optical Density
of Complexes of p-Dimethyl-
aminostyrene and p-methoxysty-
rnne . . . . . . . . . .81

 

lll‘ylllllll, l t‘ll.

CONTENTS
(Continued)

page no
G. Correlation of the Observed
Kinetics With Structure and
Alternating Tendencies in
Copolymerization. . . . . . . . 98

. 100
. 101

Summary . . . . . . . . . . . . .

Literature Cited . . . . . . . . .

IIIIIIII

 

INTRODUCTION

Complex formation in solution can be investigated
by studies of the change in physical properties of the
solution. Macro properties, such as boiling point and
freezing point changes, viscosity variations etc. have
the disadvantages of not showing detectable variations
when the amount of complex formed is extremely small.
Spectra, however, afford an additive preperty that
allows for the detection of small concentrations.

Color formation has been noted in solutions of
monomers that tend to cepolymerize in alternate fashion.
No exact quantitative study has yet been made on light
absorption, the equilibrium constants (if any) and the
exact composition of the complexes between such monomers
when they are modified by different substituent groups.
Such a study may add to the understanding of the transi-
tion state between attacking radicals and monomers in

the alternating type cepolymerization.

HISTORICAL AND THEORETICAL BACKGROUND

1. Colored Complexes in Solution.
The formation of ”molecular compounds“ or "complexes"

in solution that develop color is a well known phenomenon.

Particular examples are the wurster salts, quinhydrone

structures1’2'5, hydrocarbon-picrate addition compounds

and hydrocarbon-tetranitro methane complexes4'5’6.

Maatman, in a recent study6 on the color forming prop-

erties in solution, has made a rather complete survey

of existent theories and listed an extensive bibliography.

These have also been considered in part by Whelands.

The plausible theories of interaction to form.molecular

compounds have been classified as to covalent, ionic

and polarization theories.

In his discussion of the relative validity of these
theories, Maatman6 states that the covalent theoryv’u'9
appears invalid as bond energies greater than those ob-
tained for molecular compounds are generally associated
with covalence. (The high optical extinction values of
such complexes for small concentrations tend to confirm
this.) He dismisses the ionic theory 10'11 on the
premiSe that it is extreme to postulate a complete
transfer of electrons from donor to acceptor molecules
in non-ionizing solvents and that existent experimental
data could also confirm a polarization hypothesis.
'Maatman contends that a polarization theory 5'12’13’14

based on specific interactions between pairs of mole-

cules is unwarranted when true equilibrium exists and

postulates a "polarization aggregate” to explain low
interaction energy and color formation by stabilization
of resonance contributionsl4. A mechanistic picture of
this aggregate is not presented and the postulate is not
further clarified. Woodward2° has attempted to correlate
a polarization aggregate concept with Weiss' ionic
theory of electron transferlo.

Maatman also states that no absorption peaks
characteristic of the molecular compound have been
observed indicating merely a shift of the absorption

to the red and no apparent correlation between the shift

and the complex's stability.

2. Alternating Type Cepolymerization and the Formation
of Colored Complexes.
In the last decade, the cepolymerization problem
has been studied extensively by Mayo et al and has been

the subject of a thorough review15. The experimental

hlfi'l7 involved the determination of the relative

approac
reactivity of a cepolymerizing radical with a like and
an unlike monomer based on the elementary analysis of
the composition of the copolymer after a noted interval
of copolymerization. On the basis of this treatment an
attempt has been made to fit random type cepolymers
(e.g. styrene - butadiene) and alternating type copoly-
mers (e.g. styrene - maleic anhydride) into an overall
kinetic picture and to provide a quantitative estimate
of the effect of substituents on monomer attack by free

radicals 15-26. In the course of this work, Special

attention was placed on the alternating or 1:1 copolymer-
izing properties of certain monomers.

Bartlett and Nozackiz4 did not discover any character-
istic abnormalities in vapor pressures, mutual solubilities
and viscosities of mixtures of monomers showing tendency
toward 1:1 cepolymerization altho concentrated mixtures
of such monomers as stilbene, styrene, 1,1 diphenyl
ethylene gave decided colors when mdxed in solution with
maleic anhydride. They suggested that resonant structures
and polarities may allow the monomers to act as electron
donors and acceptors respectively. Thus polar chromo-
phoric intermediates may occur that facilitate the alter-
nating tendencies in the cepolymer.

Mayo et a119'22, on the basis of the relative
reactivity ratios of monomers in copolymerization, state
that a relation exists between the relative reactivity
of a monomer, independent of the attacking radical, and
the tendency of substituents on the olefinic carbons
of the monomer to accept electrons from.the double bond.
Relative reactivity is a measure of the rate of radical
attack on the unlike or other monomer in ratio to its
attack on the monomer from which it is furnished.

However, monomers that are of the alternating type show
anomalous divergence from.this series.

Walling et a122 attempted to apply the Hammett
relation25: log Ko/K .- <17“ where no and K are the
rates or equilibrium constants for the reaction of the
unsubstituted and substituted compound reapectively,

‘U—' a parameter having a single value for each ortho,

meta or para aryl substituent and f0 a constant for

any particular reaction. The parameter V is a measure
of the ability of a substituent to withdraw or make
available electrons at the site of the reaction: (’ is

a measure of such electron availability on the reaction
considered. Cepolymerizations of a series of substituted
styrenes with selected monomers were carried out and
relative reactivity of the various styrenes toward the
radical was calculated. A plot of the log of the
relative reactivity against the Hammett V value should
be linear. This is true with the unsubstituted styrene
radical but with radicals derived from methyl methacry-
late and maleic anhydride there is no consistent relation.
Para methyl, para methoxy and para dimethyl amino styrenes
have exceedingly high relative reactivities toward maleic
anhydride but conform to the Hammett linear principle in
being less reactive toward styrene than electron acceptor
substituents.

Mayo and Walling15’21L have attempted to explain this
apparent anomaly: namely that relative reactivities show
the poorest correlation with polar reactions (alternating
capolymerization) where polar phenomena should be most
important, by preposing that "the major driving force
for strong alternation tendencies is not simple polariza-
tion, but arises from contributions to the transition
state of forms in which actual electron transfer between
radical and monomer (or vice versaI has taken place".

In the case of addition of styrene radical (electron
donor) to maleic anhydride, transition structures such

as these could be involved:

 

O O O
R g“' R g C// C/ C/
- - l
\‘4 CH \O-AH/\O-_‘H/\
<- . w- C ‘/l V" i O
9 C HC\C HC\C/
/ 4- .I” \\0 \0, \0,

 

 

In the cenjugate reaction of anhydride radical
(electron acceptor) with monomeric styrene the con-
tributing structures of an anhydridecarbanion (or
relatively stabilized enolate ion) and a benzyl car-
bonium.ion could be constructed. Thus resonance
stabilization of the activated complex may account
for the observed alternating tendencies. This inter-
pretation also explains the increased alternating
effects of p methyl, p methoxy and p dimethylamino
groups on the styrene as a greater number of
additional resonance structures becomes available

on such substitution:

C‘H:= CH2 01.1 - CH2
___3
O *— O
H+ 3H2 H+ C-HZ etc o
C'H= CH2
+
-°\

 

CH3 Otce

 

 

CH -CH2
ll
I ‘
N N’
0113/ Pea;5 0113’ *\CH3 etc.

Qualitative correlation between the tendency of
substituents to influence alternation and the inten-
sity and wave length of the color absorption of
molecular complexes2l showed the similarity in
structures of molecular compounds and the activated
complexes of alternating copolymerizationls’za.
the assumptions of a 1:1 complex and complex stability
being proportional to cptical density, the relative
absorption of similarly concentrated solutions of
substituted styrenes with maleic anhydride, trinitro-
benzene and chlora‘nil were compared in a photometer
using a Corning 511 filter (transmission range:
approximately 350 m”; to 480 my; ; maximum.transmission
at 410 m;(). A radical-ion structure based on the

10

concepts of Weiss was postulated for the complex in

which an electron has been donated by the hydrocarbon

to the carbonyl derivativezg‘rs'z6
t . 11
HO - CH2 “C - c\==0
O
/
CC - 0:0
H I

 

 

 

 

The possibility of alternation proceeding

thru the addition of 1:1 complexes to a growing

chain is deemed improbable by Mayo et a115’23 on

the following bases:
(a) Dilution has small effect on the cepolymeri-

zation27

whereas if true equilibrium exists, the
effect on molecular complexes would be large.

(b) There are no evidences of physical
association.21’25

(c) There is no change in monomer reactivity
ratios on dilution.21’27’28

(d) There is no unequivocal kinetic evidence in
alternating systems.15

Mayo and Walling15 conclude that "growth of
cepolymers by addition of molecular complexes could
either be excluded or could not be demonstrated in
any of a number of strongly alternating systems.
Similar interaction between radicals and monomers,
however, accounts for alternation tendencies."

The arguments against alternating type cepolymeri-
zation depending directly on complex formation are
based on the following premises:

(a) A 1:1 complex is formed.

(b) The molecular complex obeys the laws of true
equilibrium and thus is affected by dilution.

(c) It is intimated15:21v23 that the observed
optical density of similarly concentrated solutions
of substituted styrenes and a conjugated carbonyl
derivative at one absorption band is preportional to
the stability of the formed complex.

(a) and (b) have not been experimentally proven.
(c) is not warranted on the basis of prior Spectro-

photometric investigations of colored complexes6.

3. The Method of Continuous Variations.

The method of continuous variations was
originally developed by P. Job29 to determine the
composition of complexes in solution and their
stability. The following mathematical deveIOpment
is largely based on his work.

Complex formation may be symbolized by an equi-
librium:

(1) mA +- nB e-s AmBn

Let a solution, (a), be [Al° molar in A molecules
and a solution, (b), be lBio : p [Alo molar in n
molecules. The method of continuous variations involves
mixing varying volumes of (a) and (b) and measuring
a property (P) of theSe mixtures. Let l-x be the
fraction (a)r of the total volume of the final
mixture while x is the fraction of (b) asSuth no
contraction or expansion on mixing.

The develOpment of appropriate relations between
a preperty (P) and the volume fraction (x)is based on
finding the value of x for which the concentration
of the complex is a maximum.

The mass action law may be expressed:

(2’; IAlmx [Bin =K lAmBn|

The total number of moles of A in the (a)
fraction is partly combined in the complex after
equilibrium is attained. This amount is given by:

(3) mo (l-x) ' IA|+m IAmBnl

Similarly, for the number of moles of B:
(4) IBIO x 3 piAl 0x =lBl+n IAmBnl

-10-

Taking the derivatives of (2), (3) and (4) with

reSpect to x:

(2') dIBI

dlAI _
mlAim'liBIn dx i-nIBIn liaP' dx

 

dlAmBnl
dx
(5') -lAIo-'-' 9:51 + m d'Aanl
x d

dlBi‘+ n diAmBnl

dx dx

(4') PIAIO

To determine the conditions under which a

maximum.(or minimum) of complex exists, let

dlAmBnl e O and then (2') becomes:
dx

(5) mulm‘limn EliLi-ntmn'luh dIBI .0
dx dx

 

Dividing thru by iAIm'llBln"1,
(6) manila...- nIAIELEL : 0
dx dx

(5') becomes:

(7) dlAl 3 'IAlO
d1

(4') becomes:

Substituting (7) and (8) in (6) gives:
(9) - mIBi IAI °+nIAI piAlo - o

61‘:

(10) iBl : £12m
in

-11-

and substituting (10) in (2):
n men
(11’ (9.2) IAI a KlAmBnl
m.
and substituting (10) in (4):

(12) plAlo x e %§lAhinlAmBnl

where

(15) )AmBnl . gm, x - EIAI

From (3), also:

(14) lAmBnl. iAlo (l-x) - IA]
1!!

Ehuating (15) and (14) and simplifying:

 

(15) IA) : (Ale (n+mp) x-n
n(p-l)

and from (5):
(16) (A) a (Mo (l-x) - mlAmBnl

whereas from (15):
(1'7) (Ale EIAIO X - ElAmBnl
n P

Equating (16) and (17), simplifying and solving

for concentration of complex:

(18) lAmBnle pIAIo 22.3.1132). 8 pm, %_ml)
Substituting (15) and (18) in (11) gives:

n
(19) (3:2)“ is.” {(n;T:):;'}:K KplA,°mfll——L-X((;_;‘;

 

-12-

Simplifying:

(20) (Al .mm'lfl'lhmmh-n} mm

= K n-x(n+m)
m.n"]'nm"l(p-l')m"n"1 3

or:

(21) (A) omn'lpn’l ((n+mp)x-n}m+n . K

m“"1nm'l (p-l) mJ""":"{n-x(n~~111))

Equation 21 is satisfied by values of x
for which the concentration of the complex
[Aan) is a maximum (or minimum).
It can be seen from equation (20) that the
equilibrium constant need not be specified only if
(22) (nemp)x-n : O and thus
(25) n-x(n4m) a 0 and thus

 

(24) x a n e—E— from which it is apparent
n+mp n+m
that
(25) p : 1
Thus the necessary condition for the value of
x to correspond to the preportions of the two con-
stituents that react to form.the complex is that the
molar concentrations of solutions (a) and (b) be equal.
Knowing the formula of the complex AmBn and x for the
greatest complex concentration, the equilibrium constant
can be evaluated using equation (21).
Since the complex concentration cannot be directly
measured in solution, a variation in'a preperty (P)

of the mixture is studied as a function of the mix-

-13-

ture's composition. P is a function of the concen-
trations of the constituents and the complex
(26) P : r( (A) . (BI , IAmBnI)

If the concentrations of the two solutions (a)
and (b) are fixed. P depends only on x. 0n variation
of the volumes of the two solutions, i.e. (x) and
(l-x), P will have a maximum (or minimum) dependent
on the extent of reaction between A and B mole-
cules. To determine the relationship of the var-
iables on the attainment of this property maximum,
differentiate the function (26) with respect to x

. and maximize by equating to zero.

(27) 9-13: ii =iLlLAL+AL |Bl+ 3+ M30
‘1" 31 “Al )3: 3(8) 1:: MAmBnI )x

The necessary postulate is that the property is
a maximum (or minimum) for the maximum concentration

of the complex i.e.:

(28) d (AmBnl . 0
dx

Substituting (7) and (8) in (27) realizing (28) in
(5') and (4'):

(29) air |A|o+SlFBT p Imago

Case (a): If P is a maximum only when the concentration
of the complex is a maximum it follows that, in general,
the function is independent of the equilibrium concentra-

tions of the constituents (i.e. (Al and (BI ) and so

-14-

(50) ill: 0
MA) MB)

Thus the property is a maximum.when the complex
concentration is a maximum. Using a spectrOphoto-
metric prOperty, this case is applicable when the
reactants show no absorption at the wave length used.
If the complex alone absorbs, then the maximum cpti-
cal density (D) corresponds to the maximum in P and
the maximum in complex concentration. The correSpond-

ing volume fraction gives the requisite value of x.

Case (p); If the property is dependent on the concen-
trations of the reactants (e.g. both A and B molecules
absorb at the.Specific wave length used in a Spectro-
photometric method) no interaction between complex and
reactants is postulated. If the preperty studied is
additive then, letting Y be the difference between the
value of the preperty obseryed for the reactants plus
complex and for the initial constituents assuming no

reaction: it follows from (26)

(31) Y:f((AI, (BI. IAanI) - ‘laAlo(1-x),0,0)‘§(0,lflla;,0)

This Y difference is maximized by differentiating (51)

with respect to x and equating to zero:

(52) 3.2!. . .22. 1L“ .1: fli+3_f_ LMIL.
)x' M) )x NB) )x “(1de J x

DilAl n(l-x)l, _2_f__ M:
(S—_-_u)rAl 0(1-xll ) x Hp (Ala!) ) x

-15-

Substituting (7) and (8) in (32) and completing the

 

differentiation:
(33)
-IAl 0.1.1:.+pm.2_£_. Liam «MM 0 9 1?
MA) IISI )IAmBnI 3 x ){Wdl-xfl

- awe—LL— = o
){plAlox}
(28) is the condition to specify for the preperty
difference (Y) to be a maximum when complex concen-

tration is a maximum and (55) becomes:

(:54)

-A‘ 31‘ -___.Lf.___ (A) 1L-_A£_-__=o
| °(3m ){lAia(1-x)] +p °()IBI ){piAlox))

This equation (54) was derived considering the
additivity of the contributions from A, B and Am'Bn

 

to the property (P) (i.e. we consider Beer's law to
hold in the spectrOphotometric method). Thus the rate
of change of the property (P) with reapect to any change

in the concentration of A and B is constant:

(55a) )3 e constant .-. a
)FM

(55b) ) f : constant : b
“BI

and substituting (553) and (35b) into (27):

(36) 9.2. “human + LEA-En)
dx )3: ).x )lAmBnl 3 x

which integrates to:
P. bs_)_f___ BI
(:57) “$11)”de (Ann

where the last term is some function of the complex
concentration \¢lAmPnl )._ Thus, in effect, as per
equation (51) the Y'curve is only a plot of some
function of the complex concentration.

To summarize the method of continuous variations
when only one complex is formed:

1. The mixtures of equimolar solutions of (a)
and (b) are varied to determine the formula of the
complex.

2. The mixtures of non-equimolar solutions of
(a) and (b) are varied to determine the equilibrium
constant of the complex.»

Three cases exist:

Case (a): The measured property is independent of

 

the equilibrium concentrations of the two reactants
and depends only on concentration of the complex.

The curve of property (P) value against mixture
composition (x) passes thru a maximum.or minimum for the
maximum concentration of the complex alone.

Case (b): The measured property is an additive
function of concentrations of the complex and the
reactants. The curve of the difference (Y) between
the experimental values and those that would have
been observed if no complex formation had occurred

is constructed against the mixture composition (x).
This can easily be cone by plotting the difference in
the experimentally observed values and the values

from.a straight line joining the points given by

-17-

the individual reactants. This curve of difference
(Y) gives a maximum or minimum for the maximum con-
centration of the complex.

Case (o): If the measured prOperty depends on some
complicated relation of the constituents present in a
mixture, the variational study does not permit the

determination of maximum complex concentration.

The method as outlined can be applied directly
only if:
1. the two reactants have a well determined mole-
cular formula and there is no dimerization, etc.
2. the complex is unique, i.e. only one species
exists.
3. the law of mass action is applicable.
Experimental verification of these facts can be
obtained by the determined complex formula being the
same for all limits of concentration; no matter how
dilute the solutions of equimolar mixtures. For all
non-equimolar mixtures the obtained value of the
equilibrium constant is a constant for highly divergent

conditions.

Vosburgh and COOper50 deve10ped relations to
specifically apply the spectrOphotometric method.
Consider the Beer-Lambert Law:

(38) I 10101301
where: I 2 the intensity of light transmitted.
I0 is the initial light intensity.

E is the specific extinction or extinction
coefficient per unit concentration per cm.of absorp-

tion cell length.

-18—

C is the concentration
1 is the absorption cell length.
From (58) we get the logarithmic expression:
(59)
D .-.- log—lin— : ECl

where D is defined as the optical density. Let E1,
E2, E3 be the extinction coefficients of A, B and
AmBn at a wave length (A). Then the optical den-
sity (D) is the measured property (P):

(40)
D = 1031 W132 [5| +E3 IAmBnD
Letting‘Y be the difference between the density of
(40) and the density of the solution if there had
been no complex formation:

(41)
Y . [(31 m+ E2 [31+ E3 lfiBnl - E1 [A] 0(1-x) - Egpx m o)

Differentiating (41) with respect to x and maximizing:
(42) d d
A d
aft/«Erin, EZJEL+E3JAnEnL
dx dx dx dx
+E1‘A\o - E2 pwo); 0

Substituting equations (5') and (4'):
(425)
Mm “d'AmBn‘ - mo) +E2 (-n ———-d"‘n3n' +10 w 0)
dx dx

-+ E;5 dlAmBn\.+ E1|A)o - E2 P)A|o = 0
dx

which on simplifying becomes:

-19..

(44) ME!- (ems:l - nEz-t as» = 0
dx

which is generally true when

(45) d'AmBnl _
d1

0

i.e. Y'is maximum or minimum when the concentration
of the complex is a maximum.

If E3 > (m E1+ 11 E2) , Y is a maximum.

If (m E1+n E2)7 E5, Y is a minimum.

Vosburgh and COOper also investigated the re-
lations when two complexes are formed, the second
in the manner:

(46) AmBn-r qB 4—- Ammflq)
then

(4'7) Y :X (E1 ‘A‘ + Ez‘BI + Es'AmBn‘4' E4 ‘AIBn-O-q'
- E1|A)o (1-x) - EzlAlo PX)

Maximizing and simplifying as before:

 

(48)
dY % dIA! fl dlAmBnJ dIAmBn+q|
-': E E _______. E
dxxldx+2dx+3dx *4 dx
+E1lAlo - EglA'o p) = 0
But now

(49) [A]o (l-x) = NH”! )AmBnl +m|AmBn+q‘

(50) plAlox a 1131+ nlAmBnhqlAmqu)

and therefore:

(49') -IA) 0 . 9.51.31. J, mugged +m d’Amin‘rQ’

-20..

(50» p‘AIo . 9.12).... dlAmBnl +q dlAmqul
dx dx dx

Substitute (49') and (50') in (48):

(51)
31 ( 'm —-—d'AmBn' -n flAmBM' - IAI 0)
dx dx

4* E2 {-n d‘an) -q d)A:1:n+gL 4. p'A‘o)

d'AmB d A B
+E3—————-d n)+g4____fl|mn '+Elmo’EglAbp-.:O
x dx
Simplifying:
dIAmBn| (-mEl - nE2+E5)+d(AmBn+q( («31 «1132 +44). 0
dx dx
Now if the reactants have negligible absorption

at the wave lengths used then 31 c Ez‘g’o and the

condition for a maximum.in Y'which is now a maximum

in observed density is:

(533
d
E5 (AmBn‘ +. E4 dlAmBn 9L . 0
dx dx
In general the maximum.value of‘Y (or density

in the last case) will not coincide with the

maximum.in (AmBnl or (AmBn+qlo The value of x

for "33;! s 0 will vary with the extinction

coefficients (R) and thus the wave lengths used.

If in equation (53) E3 2’ E4, the maximum in

density corresponds to a maximum.in the sum of

concentrations of the two complexes then Am3n+q

is negligible if the stability of AmBn is high.

-21-

When volumes of equimolar solutions are mixed,
the maximum in density corresponds to the maxi—
mum in [MBA] as per (55). If Es??? E4, this
latter fact is also true. In dealing with
complexes of low stabiity, however, where E3 and
E4 have no unique relationship, then we may ex-
pect a variation with wave length in the x value corre-
sponding to the maximum density. This would be es-
pecially true with increasing addition of B.

The method of Job29 allows determination of
the complex composition and stability when only one
complex is formed. The treatment of Vosburgh and
Cooper50 only accounts for complex composition in
those cases where unique relations exist among the
extinction coefficients of the several complexes viz.
equal or widely different. They have also suggested
that an asymmetry in the plot of cptical density
against volume fraction of one of the equimolar
solutions is an indication of more than one complex.
Also, a variation in the curve maximum.with wave length

is a valid criterion of the same phenomenon.
4. Other Mathematical Methods of Analysis.

Using spectrophotometric techniques, Hammick and
coworkers3"°2’35 haVe obtained quantities which are
proportional to equilibrium constants when complex
stability is low. They have obtained the constant
itself in a case of relatively high complex stability.

-22-

The following is based on Hammick's derivation which
treats of the case involving only a 1:1 complex.
Consider an equilibrium:
(54) A+ Bee
to be expressed by the mass action law:

(55)
K1: cl ‘3 3-3:-
(Ag - 0;)(Be ' Cl) . 1—
where A. and Bo are the initial molar concentrations
in the solution of A and B molecules and 01 is the

molar concentration of the 1:1 complex.
Differentiating (55) with respect to A0 at
constant Bo results in:
(56)
c 361 D
o : (Ag-ClHBo-Cflg-gt -cl{(A,-cl)(- m)+(Bo'cl)(1')%’}

L2

and thus the numerator is also zero.

 

Dividing thru by Cl and rearranging:

(5'7) 93:; {Me-01) (Bo'cl)

+(Ao-Gl) HBO-01)} : (Bo-Cl)
)Ao Cl

Substituting the equilibrium.constant for its value
(55) and solving for the partial derivatiVe,

(58)

 

 

3 cl Bo'cl Bo-Cl .
0 ii 31

If C; is very small, K1 is very small and thus
l/Kl is very large with respect to the other terms

-23-

of thv denominator and it follows that:

(59) B0

301
3A 1
° 30,0140 K1

1R

 

 

. K1 Bo

At constant cell length (1 e 1 cm.), from

equation (59)
(60) c1 : Dl/El

where E1 is the extinction coefficient of the complex
and D1 is the observed cptical density attributable to
the 1:1 complex. Combining (59) and (60) results in:

) Di
DA. 3 KlElBo

(bl)

 

This equation means that at constant Bo and low
Cl, a plot of D1 against the total unreacted Ao con-
' centration is a straight line of constant slope KlElBo°
Thus K1319 a value proportional to the equilibrium
constant, can be evaluated.

As the amount of C1 increases, the above approx-
imation becomes less valid and a more accurate

approximation of (58) is:

(62)
( 361 :4 Bo " C’1
)‘Ao 'i

 

0 K1

-24-

Thus the second partial derivatives becomes:

 

 

 

 

,.
(as) 1 3c:
3 )A ~ _1_(- 801- 41.3.0}.
L 3A. 39 K1 )Ao DA.
‘/K,"
(64) ,, -

)Ao
‘3 C1 blho

)A.

II
II
I
P1
|-‘

 

 

 

Again applying (60):

(65) F)1n 6%?)

)A. J

.. B,

‘I

 

.Kl

 

 

A plot of the natural log of the instantaneous
slope against the corresponding initial concentration
of Ae should give a straight line, the slope of which
.is the negatiVe value of the equilibrium constant for
complex formation. It is significant that there should
be a decrease in the slope of the curve of optical den-
sity against increasing A0,

Hammick presumed that the ratio of 51K; values for

an homologous series of addition compounds where the K1

-25-

was too small to determine separately, was independent
of the wave length. Such a series qualitatively agreed
with one instance where the equilibrium constants were
known. However, experimental verification can only be
based on constancy of such ratios at varying wave
lengths. Maatman6 contends that such is not the case.

Maatman6

has deve10ped a treatment similar in
principle to that involved in application of equation
(65) to the quantitative isolation of K1 for a 1:1
complex.
Equation (55) can be expanded:
(66)
C1

K1 = 2

Complex concentration (Cl) is assumed to be small
and 012 negligible. Ignoring 012, and rearranging:
(67)

01 K1

Substituting equation (60) in the above and solving
for the extinction coefficient (E1):
(68)

D D 1 D
a..1+__1_+ 1

1‘ .—
A0 B0 K1 AoBo

 

A similar equation exists for another solution of

the same concentration in one reactant, i.e. A but

0!
different in the other, i.e. Bo'

-25-

 

(69)
D ' D i 1 D I
E _ 1
1 ____+ J.‘+ __ 1
I
A0 B0 K1 AOBO'
Equating (68) and (69) and solving for 'E—
results in: 1
(70) L- D1.‘ 'Dl -,
K1 Bl. - D1' 0
Bo 30'

In general, A0 is negligible for small A0 and
K1. Maatman° states that the value of the denominator
in (70) is small compared to the values of its terms
and thus inevitable error in optical measurement

leads to very large error in K Inconsistent results

were obtained by Maatman when the data, or averages of
the obtained data,were substituted in this equation.

In order to circumvent this large experimental
error, Maatman develOped the following approximation
technique. Equation (68) may be rewritten:

('71)

 

Bo BC + A0 + l/K

D1 ADE AOE

Thus for constant A0, .39. may be plotted against Bo

' 1
to approximate a straight line of lepe _lg, . The

line thru the points obtainable from experimefiggl data
should give the necessary "ideal" values that may be
substituted in equation (70) to allow estimation of the
magnitude of the equilibrium constant.

6 contends on the basis of his experimental

Maatman
work that the equilibrium constants so calculated are

independent of the wave length used.

-27-

EXPERIMENTAL

A. REAGENTS

l. Maleic Anhydride (Eastman)

The anhydride was vacuum distilled at 5mm. A
middle fraction of the distillate, b.p. 90°C, was
used.

2. Styrene (Dow) .

The styrene was vacuum distilled thru a 12 inch
Vigreaux column and a fraction 41-45°c at 14-16 mm,
n20°: 1.5446, d2503 0.907 was used.

All other styrenes were fractionally distilled
thru a Fenske column, 10" long and 10 mm in diameter
with an inner jacket packed withl/16" glass helices
and heated with nichrome wire. The fractionating head
was a cold finger type, adapted for collection of small
fractions.

5. p-Chlorostyrene (Monomer-Polymer Co.)

200
The fraction 70-7200 at 4.5-5mm, n = 1.5645;

25°

d4o g

1.086 was used.

Literature values:
b.p. 50-52°c at 6.5mm, n20°z 1.585034
b.p. 58-59°c at 2mm, H200: 1.584855

b.p. ZOO-210°C at 100-120mm

20° 20° 56

b.p. 55-55°c at 5 mm, n ; 1.5658, 840 =_1.09o .
4. p-Methylstyrene (American Cyanamid Co.)
The fraction used:

0
b.p. 60-7000 at 20.5-22mm, n20 = 1.5425, d25

0
a 0.889.
Literature values:
0
b.p. 59.5-59.5°c at 15.5mm, n20 = 1.54.2521

0
b.p. 85-5508 at 18mm, n25 = 1.540237.

-28

5. p-Dimethylaminostyrene (American Cyanamid Co.)

 

The fraction used:
0

b.p. 104-10800 at 4-5mm, n20 a 1.6120,

25°
d = Oo964o

Literature values:
0

b.p. 85-9l°c at 2.5-5mm, n20 = 1.801038;

0
2 20 = 1.512039.

00
6.;p-Methoxystyrene

 

The p-methoxystyrene was prepared in this
laboratory by conversion of 400g. p-anisaldehyde
(Eastman) to the corresponding substituted cinnamic
acid by means of the Doebner reaction (a modified
Perkin reaction with malonic acid, pyridine and ethyl
alcohol)4l. The p-methoxycinnamic acid was subSequently
docarboxylated OVer cOpper powder in quinoline to pre-
pare the p-methoxystyrene according to the method of
Walling and Wolfstirn54. The crude yield on docarboxy-
lation from the quinoline was 255.80 grams. On first
distillation 182.70 grams were collected at 76-85°C
under 6-7mm. This yield is 47.6% based on the
aldehyde.

The fraction used:

20°

b.p. 72-7500 at 4-5mm, n . l.5618-l.5650.

Literature values are:
0 0
b.p. 55-55.8°C at 2mm, n20 = 1.5812 and :120 .

1.552034

0
r120 :la560840.

Twenty-two grams of material were chosen from
the second distillation for use in the spectrOphoto-

metric studies.

-29-

7. Benzene (Merck Thiophene free)
The benzene was distilled immediately prior to
nae. A middle fraction of the distillate was used in

the preparation of solutions.

B. PREPARATION OF SOLUTIONS FOR SPECTROPHOTOMETRIC
STUDIES

The standard solutions (0.25M and 0.125M) of the
substituted styrenes and maleic anhydride for the
study of continuous variations were prepared by
quantitatively weighing the monomer into a tared
beaker, dissolving in the anhydrous benzene and trans-
ferring to a glass st0ppered volumetric flask. The
beaker was subsequently rinsed with successive wash-
ings of benzene until the volumetric flask was filled
Just short of the calibration mark. The flask after
shaking was then immersed in a 25°C electronically
controlled constant temperature bath for several hours
and intermittently agitated to achieve homogenous and
thermal equilibrium.

In the preparation of high molar concentrations
of the monomers in benzene solution (0.5M and greater),
carefully cleaned and dried 50ml. or 100ml. volumetric
flasks were tared and the monomers weighed in the flasks.

In the preparation of dilute monomer solutions,
(less than 0.1M), requisite amounts of the more concen-
trated standardized solutions (0.125M and 0.25M) at 25°C
were pipetted into volumetric flasks and anhydrous
benzene added. '

In all the above cases, after the flasks had
achieved thermal equilibrium.in the 25°C constant

-50..

temperature bath, the few dr0ps of benzene necessary
to bring them up to the mark were added and the
solutions thoroughly mixed.

In some studies it was necessary to use extremely
high concentrations of the substituted styrene (greater
than 2.0M) to obtain the desired cptical densities. In
order to conserve material, the substituted styrene at
25°C was pipetted into a test tube and the number of
moles transferred calculated on the basis of the experi-

mentally determined specific gravity at that temperature.

0. PREPARATION OF "COMPLEX" MIXTURES FOR THE STUDY OF
CONTINUOUS VARIATIONS

Case 1. Complexes of unsubstituted styrene, p-chloro-
styrene and p-methylstyrene with maleic anhydride show
no change of cptical density with time. With these
styrenes, the fractional volumes of the 25°C benzene
solution of the styrene and maleic anhydride were added
by means of a calibrated burette to a clean, dry test
tube fitted with a new, clean cork and then were thoroughly
mixed before the readings. The experimental mixtures were
poured directly into the absorption cells from the test
tubes. The total volume of a mixture was 10ml.

Case 2. In the studies on p-dimethylaminostyrene and
p-methoxystyrene where there is a change in cptical
density with time, two methods were used.

(a) In the majority of the p-dimethylaminostyrene
studies, the volume of styrene solution wanted was
pipetted into the requisite amount of maleic anhydride

solution and the timer started when the transfer began.

-51...

The test tube was corked, shaken several times, and the
mixture immediately transferred to the absorption cell
for reading of the optical density. The time of each
reading was duly recorded.

(b) A modification of (a) to permit quicker
observation of the reaction was made by placing the
desired amounts of styrene and maleic anhydride
solution in separate test tubes, pouring from one to
the other at least three times, corking and shaking
after each transfer. The timer was started at the
moment of the initial transference.

There is no apparent discrepancy in results
attributable to these variations in technique.

In all instances of shaking the corked test tube,
the cork was loosened and tightened at least twice to
prevent loss of material adsorbed on the cork.

The time of mixing and transference usually took
40-70 seconds before the first reading of the optical
density could be made.

D. PREPARATION OF "COMPLEX" MIXTURES FOR OTHER STUDIES
1. Studies Under Nitrogen Atmosphere

It was deemed desirable in view of other work in
this laboratory to show that complex formation would
occur independently of the concentration of absorbed
oxygen in the solution. This Special study was under-
taken with p-methylstyrene.

Nitrogen gas,deoxygenated by passage thru aqueous
alkaline pyrogallol and dried by passing thru sulfuric

acid, was used to replace the air in all Operations.

-52..

The p-methylstyrene was distilled under a vacuum while
a small amount of nitrogen was being introduced into
the system, benzene was distilled under a nitrogen
atmosphere. Both were stored under a positive nitrogen
pressure. .

The maleic anhydride was weighed into a tared
volumetric flask previously evacuated and flushed with
nitrogen. Theilask was then evacuated and flushed
several times with nitrogen and the p-methylstyrene
and benzene were transferred to the flask by positive
nitrogen pressure.

The mixture was transferred by nitrogen pressure
to the absorption cells flushed out by nitrogen. The
cells were capped immediately and readings were taken

as quickly as possible.

2. Effect of Time on Optical Density of "Complex"
Mixtures

As has already been mentioned, the optical density
of p-dimethylamino and p-methoxystyrene complexes
changed rapidly with time and kinetic studies were made
on this transformation. Both intermittent and continuous
exposure to the light beam show no deviations from a
smooth curve when density is plotted against time indicating
no photochemical effects. Visual observation of color
changes in a portion of the solution not introduced into
the light path showed parallel phenomena. Precipitation
occurred in the absorption cell simultaneously with that
noted in the remaining liquid of the test tube.

Readings on Optical density of complexes with

-53..

unsubstituted styrene, p-chlorostyrene and p-methyl-
styrene were continued on the same absorption cell for

a period of several hours. This was done with sample
mixtures of widely varying concentrations. The cells were
subjected to both intermittent and continuous exposure

to the light beam. In no instance was any significant
change in the Optical density manifested that could be
attributed to a photochemical effect or a kinetic effect
in solution.

Mixtures prepared under nitrogen and in the pres-
ence of air were maintained at 25°C for periods of
several weeks and readings taken on portions during
this time. No significant effects were noted.

5. Effect of Dilution on Optical Density of "Complex"
Mixtures.

It was necessary to specifically show the effect
of dilution on optical density and this was done with
p-chloro and p-methylstyrene mixtures. A series of
mixtures was prepared of 5ml. total volume. They
were 0.05M with respect to the anhydride and widely
variant in molarity of the styrene. Density readings
were taken. The contents of the absorption cell were
carefully poured back into the test tube which was
rinsed with 5ml. of anhydrous benzene. This,too,
was poured into the test tube. The tube was shaken
and the absorption cell filled and emptied back into
the test tube. After a final shaking of the tube, the
absorption cell was again filled and the reading taken
on the mixture which now had been diluted by half.

-54-

E. SPECTROPHOTOMETRIC MEASUREMENTS

All cptical density readings below 450 Ina-were
made in fused silica cells of one centimeter light
path with a Model DU Beckman SpectrOphotometer. The
cells were equipped with caps. Readings above 450
were made in Corex cells with one centimeter light
path with a Model B Beckman SpectOphotometer. All
readings were made at room temperature.

Infra red measurements were made in a Beckman
Recording Infra Red SpectrOphotometer using a NaCl
cell at 25°C.

At the ultra violet and visible wave lengths
studied, the absorption of the styrenes did not
significantly interfere with the determination of the
absorption due to the complex. Beer's law was obeyed
by the maleic anhydride solutions (up to 1.00M) and
by all the styrenes. The molar extinction coefficients
(E) for maleic anhydride in benzene solvents were

determined and are listed for the various wave lengths:

-55..

TABLE I

MOLAR EXTINCTION COEFFICIENTS FOR MALEIC ANHYDRIDE

 

 

IN BENZENE
Millimicrons E
575 0.010
570 0.050
565 0.085
560 0.240
555 0.760
550 1.64
545 5.65
540 5.94
555 9.29
550 15.00
525 24.50

520 55.90

-35-

F. INVESTIGATION OF PRECIPITATES FRON SOLUTIONS
OF SUBSTITUTED STYRENE AND MALEIC ANHYDRIDE

The precipitate from the benzene solutions of
p-dimethylaminostyrene and maleic anhydride was
purified by washing with hot benzene in a soxhelet
extractor. It was insoluble in all solvents tried:
dioxane, petroleum ether, benzene, nitromethane,
acetone and methylethylketone. However, the material
is readily soluble in NaOH and H01 showing the expect-
ed amphoteric prOperties of compounds with acid anhy-
dride and dimethylamino groups. A liquifying range
of 120-150°c was noted. '

The precipitate from the benzene solution of
p-methoxystyrene and maleic anhydride was washed with
cold benzene, hot benzene, cooled and filtered from
the liquid. The material is very slightly soluble
in hot benzene, readily soluble in acetone and
alkali, but not in acids or aliphatic hydrocarbons.
The liquifying range was 210-22000. Attempts at
crystallization failed.

G. SUMMARY OF THE EXTENT OF SPECTROPHOTOMETRIC STUDTES

1. Continuous Variations

Benzene solutions of the reactants were prepared,
each containing only a single reactant with molarities
tabulated in Table III.' The given pairs of solutions
were then mixed in a varying series of volume fractions.

The number of such mixtures made in a series from each

pair in the table was 12 to 25. Optical density readings

TABLE II

-37..

SOLUTIONS STUDIED BY CONTINUOUS VARIATIONS:

"R" SUBSTITUTED STYRENE (S) AND MALEIC ANHYDRIDE (M)

R“:

Molarity

S
0.125
0.250
0.250
0.125
2.000
4.275
8.175
8.175

M
0.125
0.250
0.125
0.250
0.155
0.100
0.100
0.250

Wavelengths

studied

550
555
550
555
540
550
560
565

to
to
to
to
to
to
to
to

-Cl
Molarity
S M

Wavelengths

studied

555 0.250 0.250 555 to 580

560 0.500 0.500 545

560
560
575
575
585
590

to 590

* R is the para substituent of the particular styrene.

* . - -
R . CH5 OCHS

Molarity Wavelengths Molarity Wavelengths

studied studied

S M S M
0.125 0.500 550 to 400 0.0500 0.0500 550
0.250 0.250 540 to 400 0.100 0.100 550,575
0.250 0.500 550 to 400 0.0500 00.100 550,575
0.500 0.125 540 to 400 0.100 0.050 550,575,400
0.500 0.500 560 to 400 0.250 0.050 550,575,400
2.000 0.250 570 to 400 0.050 0.250 550,575,400

TABLE II (continued)
-N(CH3)2
Molarity Wave lengths
studied
M

0.250 500 to 890
0.250 550
1.00 550
1.00 500
0.250 550
0.050 500

-59-

on each mixture were made at five millimicron
intervals in the absorption range of the complex.
Many series were duplicated to determine reproduci-
bility and establish techniques.

Preliminary volume mixtures of 1:9, 2:8, 5:7,
etc. were spectrOphotometrically studied to deter-
mine the approximate volume ratio giving a maximwm
Optical density. Fractional ratios were then

investigated in the vicinity of this maximum.

2. Other Studies

(a) Optical densities were determined with maleic
anhydride concentrations ranging up to 1.000M at
constant surene, p-chlorostyrene and p-methylstyrene
concentrations: 0.025M and 0.050M.

(b) Additional solutions were studied with p-chloro-
styrene concentrations ranging up to 6.270M at 0.050M
anhydride concentration. Readings were taken on the
same solution after dilution with an equal volume of
solvent. This was done similarly with p-methylstyrene
concentrations ranging up to 5.5M. All absorbing
ultraviolet and visible wave lengths were considered.

(0) Time studies were made for all substituted
styrene mixtures with anhydride over wide concentration
ranges at all absorbing wave lengths. No density
changes were noted for the following benzene solutions
of p-methylstyrene and maleic anhydride over a period

of three weeks.

-40-

Solutions Molarity Molarity Wave length
p-methylstyrene maleic range
anhydride studied
5 0.250 0.125 555 - 400
4 1.495 0.250 585 - 400

(d) Measurements were taken of change in extinction
with time for all mixtures studied under the contin-
uous variation of p-dimethylaminostyrene and p-methoxy-
styrene with maleic anhydride. In addition solutions
with the following concentrations of reactants were

studied between 550 and 590 m/L .

Solution . Molérity. Molarity
p-dimethy amino- maleic

styrene anhydride

1 0.0250 0.0250

2 0.0250 0.0125

5 0.0125 0.0250

4 0.0125 0.0125

(e) Infra red scannings were made of the following
solutions:

Solution Molarity Molarity
Styrene anhydride

1 0.500M 0.000

2 0.000 0.500

5 0.500 0.500

4 pure styrene 0.000

5 pure styrene 0.500

41-

(f) The following solutions were prepared under

nitrogen and no density dunges were noted over a

period of three weeks.

Molarity
anhydride

0.125
0.125
0.125

Density

0
Complex

Solution Molarity
p-methylstyrene
0.455
0.751
1.500
Readings
m/L Denzity Density
Complex Complex
400 0.058 0.116
590 0.169 0.502
580 0.417 0.717
575 0.627 1.065
570 0.915 1.551
565 1.266 2.092
560 1.716

0.198
0.569
1.575
2.055

INTERPRETATION OF RESULTS

-42-

INTERPRETATION OF RESULTS

A. THE METHOD OF CONTINUOUS VARIATIONS

As has been explained in a prior section, this
method involves the determination of optical densities
of a continuous series of styrene and maleic anhydride
mixtures. The sum.of the values of the optical density
due to the unreacted maleic anhydride and the styrene
are subtracted from the observed density values. This
increase in the value of the optical density is due to
the complex's absorption in the benzene solvent and is
plotted as (D) against the fractional volume of the
maleic anhydride solution in the mixture (x). The (x)
value of the maximum, when equimolar solutions are
continuously varied indicates the ratio of the reactants
in the complex. For non-equimolar solutions where the
equilibrium constant is significant and calculable, the
(x) maximum should be diaplaced from this prior value of
(x). Interpretation of equation (21) shows that for a
more highly concentrated solution of the styrene, the
maximum should be diaplaced toward the greater volume
fraction of the maleic anhydride solution (i.e. greater
(x)) and conversely.

Figures 1 thru 6 are representative of continuous
variations of the various styrene mixtures with maleic

anhydride at all wave lengths where the complexes absorb.

0.8

0&3

 

'ITI'ITI'lrl'ITl'l'I

 

r

o‘F'l'lTi’l

Cur

A

B
C
D

    

CONTINUOUS VARIATIONS
MALEIC ANHYDRIDE AND STYRENE

(560 ml“)
43*1TX\\\\E:

M M
ve Anhydride Styrene

   
 

~ 0.250 0.250
0.155 2.000
0.100 4.275
0.100 8.175(pure

styrene)

 

 

FIGURE 1

OPTICAL DENSITY (D) VS. VOLUME

FRACTION 0F MALEIC ANHYDRIDE (X)

 

CONTINUOUS VARIATIONS
MALEIC ANHYDRIDE AND P-METHYLSTYRENE

 

5751110.
1)
L4 — ’3 O
‘" Q
__ O \D
(.2 —— I M
Curve Anhydride Styrene
‘_ A 0.250 0.250
L0 *“ 0.125 0.500
P— 0.500 0.250
C 0.500 0.500

0.4‘

 

 

I l L l 1 J i
X

0.2 0.4

OPTICAL DENSITY (D) vs. VOLUME
FRACTION 0F MALRIO ANHYDRIDE

FIGURE 2

 

 

CONTINUOUS VARIATIONS
MALEIC ANHYDRIDE AND P-CHLOROSTYRENE

575 nyL
Curve M M
- Anhydride Styrene
0.250 0.250
0.500 0.500

 

0J2‘*‘

 

 

 

 

1 l i Liiililil

M _' am V,‘
PMfl-Mflub J r r J j ‘7“

 

0K) ‘
(12 0:4 X (LG

OPTICAL DENSITY (D) VS. VOLUME
FIGURE 5 FRACTION 0F MALEIC ANHYDRIDE (X)

 

 

 

CO

‘9”

Q(‘

0

CONTINUOUS VARIATIONS
MALEIC ANHYDRIDE AND P-METHOXYSTYRENE
(575 mp )

 

 

 

EXTRAPOLATED
TO
ZERO TIME
m.
0 M M
Curve Anhy- Sty
dride
A 6 0.100 0.050
8 0.050 0.100
H 0.100 0.100
C 0 0.050 0.250
c 0.250 0.050
to
.5
(t.
o

OPTICAL DENSITY (D)
VS. VOL. FRACTION
OF MALEIC ANHYDRIDE

Figure 4

(.5

0.9

0.5

0.0

 

CONTINUOUS VARIATIONS
MALEIC ANRYDRIDE 5

  
 
   

P-DIMETRYLAMINOSTYRE E

1 I I I T

 

IUI'WI‘I'IW‘FTWIWW'

0.250M Styrene
0.250M Anhydride

 

Curve m/A
A 600
B 550
C 500

 

 

 

 

 

A
_ L””#,£LL———v4}—— EEO E7'—_—“‘LF~—~____~“-“
a 1 1 1 1 L 1 1 1 1 1 1 1 1 1 1 1
0.2 0.4 0.5 0.5 5.5 X

OPTICAL DENSITY (D) VS. VOL. FRACTION 0F MALEIC ANHYDRIDE

 

FIGURE 5

 

'[IIUITiIIT‘I’IrTlrrITT

(.2

A—

.3
VIIlTlUlTIrI

I

L

0.8

I
\

h

 

\

 

CONTINUOUS VARIATIONS
MALEIC ANHYDRIDE AND P-DIMETRYLAMINOSTYRENE

Curve M M
Anhydride Styrene
A O 1.000 0.250
O 0.250 0.915
B O 1.000 0.050
O 0.050 0.915

an

550

500

Maximum
11

0.467
0.555
0.450
0.555

 

1

 

 

FIGURE 6

ANRYDRIDE

 

fi‘aliLllilllgillilililgllL‘J
v.2 0.4 x 0.6
OPTICAL DENSITY (D) VS. VOL. FRACTION 0F MALEIC

-45-

There were no discernible deviations in the tynes of
curves obtained by the method of continuous variations.
The choice of wave lengths to represent the method in
the figures was based solely on the advantageous
spanning of the range of Optical densities at the
concentrations studied.

It has been previously mentioned and will be dis- ‘
cussed further in a later section that the light absorp-
tion of p-methoxystyrene and p-dimethylaminostyrene
solutions with maleic anhydride change with time. To
apply this method the extinction values were extrapo-
lated to zero time and these values taken as being due
to the primary complex formation. This necessarily
introduced a large element of error, specifically in
the case of the p-methoxystyrene which gave the greater
rate of change. Also, relatively greater anhydride
concentration of p-methoxystyrene gave a large initial
rate of increase in optical density. Thus, the more
anhydride, the greater was the error and Figure 4 is
not too conclusive.

The equimolar curves (l-A, 2-A, 2-0, 5-A, 5-B,

5-A and 5-C) for the other styrene complexes give a
maximum at x = 0.5 proving conclusively the presence
of a 1:1 complex. Time studies on the comnlexes of
unsubstituted styrene, p-chlorostyrene and p-methyl-
styrene show no change of Optical density and thus
in all cases studied (including the p-dimethylamino-
styrene) the complexes are instantaneously formed.

The continuous variation of non-equimolar sol-

utions show no appreciable shift in the maximum

-44-

(x g 0.5) for the unsubstituted styrene, p-chlorostyrene
and p-methylstyrene cases indicating extremely low
stability of the complexes.

Curvesf2-B, 2-D) for p-methylstyrene are still
symmetrical and give no indication of a shift.

According to Vosburgh and COOper3U

curve symmetry
is a strong argument for a unique complex. Curves (l-C,
l-D) with higher styrene concentration for the unsub-
stituted styrene cases are unsymmetrical. The indicated
shift in the maximum is not toward increasing (x) values
as should be expected for a unique 1:1 complex but to-
ward decreasing (x) values. Application of equation (21)
would result in a negative equilibrium constant! This
is a positive indication of further interaction of the
1:1 complex with styrene.

Only the p-dimethylaminostyrene complex appears
amenable to calculation of the equilibrium constant
in this manner. The symmetrical equimolar curves of
Figure 5 indicate the existence of a unique 1:1 complex.
The direction of the shifts in the maxima of the non-
equimolar curves in Figure 6 are normal. Although the
shifts are small and the error therefore large, yet
the direction of the shifts are Opposed for one or the
other reactant in excess (pairs 6-A and 6-BL. We may
arrive at the magnitude of the complex's stability in
_this case using equation £21).

Since m.= 1, n a 1, equation (21) becomes:

KD . Ho [(1+p)x-112

(p-1)(l-2x)

and using the data where [130 n p [40'

Styrene MA p x

A0 B0

0.250 1.000 4.00 0.467
0.913 0.250 0.274 0.535
0.050 1.000 20.0 0.450

0.915 0.050 0.0548 0.555

KB

2.25
1.98
1.89
2.8

-45-

K1

0.45
0.51
0.55
0.56

KD is the value of a disocciation constant and thus

the average K1 3 l/KD - 0.46 represents the equi-

librium constant.

This calculation of the equilibrium constant is

only valid when a large amount of complex is formed

and only the relative magnitude can be claimed in

this instance. The increased error in extrapolation

to zero time with higher concentration differences

between the dimethylaminostyrene and anhydride did

not warrant such studies.

-A6-

B. EVALUATION OF TEL FURTHER INTERACTION
OF A 1:1 COMPLEX WITH THE REACTANTS

l,ggDeve10pment of g_9uantitative Interaction Theory I

The method of "continuous variations" has shown
that only in one instance (p-dimethylaminostyrene) is
the complex stability sufficient to warrant estimation
of the magnitude of the equilibrium constant by this
method. Certain anomalies in the symmetry of the
curves and the shift in the maxima indicate an inter-
action of the proven 1:1 complex with a reactant (viz.
with styrene in Fig. 1). It may be preposed, on the
basis of’these observations, that another complex is
formed which also absorbs at the wave lengths studied.

Postulating this interaction in terms of a
further equilibrium in addition to (54) i.e.

(72) ~
Cl+’n A'H‘CZ
where C2 a A n+1 B, then

(73) 02
K2 = n
01( A0 - cl)

 

Using the value of C1 in (55) and rearranging:

(74)
K1K2 : C2

0

2

 

(A0 - cl)““1(Bo - cl) 1

-47..

Differentiating (74) with respect to A0 at constant
BO results in

('75)
0 ; (Ac-cpnflmo-clfifé -cg{(Ao-cl>n*1('?fil)

JAG JAG

+ (n+1HBo'Cl)(Ao-01)n (1 .. +01 110)}

Dividing thru by 02 and rearranging:
('76)

c - n+1 -
3 2 [(A0 Cl) (Bo 01)] + &[(Ao_cl)n‘f1

5A0 02 )A0

 

+ (n+1)(Bo-Cl)(Ao-Cl)é] : (n+1)(Bo-Cl)(Ao-Cl)n

Substituting the equilibrium constants for their
values in (55) and (74) and multiplying thru by

 

 

_ K1
-1
Ao'01)n-
('77) ‘
QCkg (2;)
Mo K2 L01
+ K (A 0-01) 2"+0 g (n+1)c

For both K1 and K2 small, the second term is

negligible since (301) ’=‘-'.. K1(Bo-Cl) in equation (.62)

and
('78)BC
Fig : K2(n+1) 01(AO-Cl)n-1

9A0

0

Now the total optical density observed (Dt) is

the sum of the densities attributable to all the
complexes present and thus

(79)

(JEWL_ :‘Dl +.iigg +H£LE§‘+

3A0- 5A0 3A0 3A0

 

 

where D2 is the optical density due to the further

interaction of the 1:1 complex with (n) molecules of

(A). As in equation (60),
(80)
C2 = .2?—
E2
and (78) becomes

(81)

(fl : E2K2(n+1)01 (Ac-01111-1
A
O

-48-

Substituting (61) and (81) into (79) fonsmall K1 and

Cl, assuming only one additional complex,
(82)
2.23 )c A “'1
, = ElKlBO +E2K2(n+l 1 O
3A0
~o
0n the same conditions, (55) allows

(85)
cl , KleBo which modifies (82) to

(84)

) Dt A
3A0 s ElKlBo + E2K1K2(n+l) onBo
O

-49-

Tuking the second partial derivative,
(85)

b '

.____E n-l

J A 2 n E2K1K2(n+l)n A0 B0
0 B0

The (n+1) derivative is
(86)

._____l_ > : E2K1K2(n+l).Bo
+

d A n
0 Bo

If a third complex were present and had significant
absorption the (n+2) derivative would have eliminated
the contributions of the first and second complexes and
the subsequent remarks would then be applicable to the
third since the above treatment can be expanded for its
consideration.

The postulates for the utilization of equations
(82) thru (86)_are very small K1, low Cl and significant
values of EgKgo

For low Bo and A0, 01 concentration is negligible
and equation (22) reduces to the Hammick simplified

case (61) for a unique 1:1 complex.

(87)
D D
iL_£) .;L_i) 2? E K B
0A0 3A0 1 1 o
Bo,Cl_’0 80,0190

This signifies that the initial s10pe of the plot
of the observed cptical density at a constant concen-
tration (Bo) of one reactant against the varied con-

centrations of the second (A0) can be used to

-50-

evaluate the ElKl product for the 1:1 complex.

If further interaction of the 1:1 complex with
more (A) occurs, the curve deviates from linearity
with an increasing slope as shown by equation (84).
If the second complex is A2B (i.e. n a 1), equation
(85) reduces to

(88)

ath

3A..
0
This means that a graphing of the slope in the

 

curve obtained above against the A0 concentration
should approximate a straight line. The s10pe of
this new line should be the value of 2 E2K1K2Bo
since B0 is constant.

If the new line is still a parabola of increasing
sIOpe, the process can be repeated and from the nfl
curves drawn to obtain a straight line the formula
An,1B of the second absorbing complex can be determined.

The value of (n) can be obtained more simply by
plotting the log of the varying s10pes (from the graph
representing equation (84) against the log of the
corresponding A0 concentration. As per

(89)
logP—EE) : nlog Ao+log E2K1K2(n+l)Bo

The sIOpe of this line is the value of (n).
Greater magnitude of K1 with respect to EP in-
validates this treatment of the contribution of

further complex interactions.

-51-

Assuming significant Cl with increasing concen-
trations of the reactants the more accurate equation
(62) should be used instead of (61). Then (78) is
still valid but (82) becomes:

(90)

n-l

 

D
O

+ E1K1(Bo-Cl)+ E2K1K2(n+1) (Ao-01)n(Bo-Cl)

and for A2B where n g 1,
(91)
(ABE) .-. 3131(Bo'01H 2E2K1K2(Ao-Cl)(Bo-Cl)
3A0
B0

The significant value of Cl lessens the slope of
the plot of observed density against A0 in a manner
similar to Hammick's 1:1 complex (equation (62)).

The tendency for the second complex's contribution

to increase the lepe is also lessened. No conclusive
statement as to additional interactions can be made
about such systems where the above plot is linear as
it may be just a fortuitous balancing of effects.

Fow low 01, small K1 and significant values of
EgKg', this development can be used to recognize
dimers in equilibrium.with the complex. Defining
K2' by

C I I
(92) K2' 8 2 02

‘-'- - 2
01(Ao-01)(Bo-01) K1(Ao-Cl)‘(BO-Cl)

 

 

-52.-

Then, corresponding to (88),
(95)

2
(3 D13) 3 2 E2'K1K2'B02
3A0

A similar equation is valid when no and A0 are

 

2

Bo
interchanged. For a series of constant Bo's, the
representative s10pes would have to be divided by
B02 to give equal values rather than by Bo as in

equation (88).

 

 

  
 
  
  
  
     
 

 

05* DENSITY VS. STYRENE
AT CONSTANT ANHYDRIDE
- 5‘70 111/“
Curve Molarity
F Anhydride
1 A 0.04M
B 0.06M
0.4»—
CLE ~—
(2.2—
O.) ——
L-
001 (11(lliLllllLrililg_
I 2 3 4 _ 5

MOLARITY 0F STYRENE
FIGURE 7

 

 

 

 

 

V

U
ct-

9

U]
('9'

0.04

0.00

as.
331:}?

V3. STYRENE AT CONSTANT ANHYDRIDE
370 my

 

 

Molarity

3110 ”MUCH!
O
O
U"

liltiiiiiiihiillt.

Anhydr ids 0

_4J

 

  

 

 

I 2 3 4
MOLARITY 0F STYRENE

Figure 8

 

I

9//
/o////

A
1 L441). L.)

()9

DENSITY
VS.
MALEIC ANHXDRIDE

  
 

 

 

: CONSTANT STYRENE
\o -d) g- 550 my.
\ "*‘
X l,
\ ’0 .9
9 :1 .-
\ \\ j:
“\ - .
\ x a
\' s
x. O\ _i .
- Molarity \\ ‘4 J
Curve Styrene \ -
A 0.025 O\. _. .o
B 0.050 \ "4 o
\\ T
\ --1
C) 0\ -—~
‘1 8'
Jllllllllhlllhlllhll
I?
3 a ”t 9; 0. 3
O O u 0 O

MOLARITY 0F ANHYDRIDE
Figure 9

0.9
0.8
01.7
0.6
0.5
0.4
0.3
0.2
0.l

0.0

DENSITY VS. P-CHLOROSTYRENE
CONSTANT ANHYDRIDE (375111”)

 

 

 

   

Molarity

Curve Anhydride
A 0.025
B 0.050

Figure 10
MOLARITY 0F
P-CHLOROSTYRENE

lljllillllllliiiJii
I 2.

3 4 5

 

 

 

 

5131: F [-7
~— ‘3 VS. P'sCHLOROSTYRENE
..___ A Sty
)— CONSTANT ANHYDRIDE ,. ‘
i ,, ' B
L— (37511),“ ) '
)._.
L /

O 20 , /o

r- /,,
i ,r/
5_ /
l-——' /
(— /
(~—
h- o
.._._f Molarity
L_ CurVe Anhydride

0.I5 b— A 0.025
f..__ B 0.050

 

 

llljilnlh

 

 

MOLARITY OF P~CHLOROSTYRENE
Figure 11

DENSITY VS. MALEIC ANHYDRIDE AT
CONSTANT P-CHLOROSTYRENE

 

 

 

 

 

 

 

 

 

(575mg)
0 "—"1
l
C -——-(> m.
_ C
(I) < —_(
q
O
_.-4
. __ ‘9.
_ O
”'1 MOLARITY OF
‘ W
‘ —-1
_d Figure 12
Curve Molarity " q.
Styrene ' ——" '
_ O
0.025 ..-..
B 0.050 d
0
e __ N
_ O
D...1.(.J.l.1.m
m «r
t o 9 0 8
o o o d

DENSITY VS. P-METHYLSTVRENE
CONSTANT ANHYDRIDE

 

 

(375m/q)
D i,__ ,
tP_ Molarity .6
Curve Anhydride
(.3 n--
~« A 0.025
_ B 0.050
i___
p. B
/,
.———- /O
(.2 8——
)——-
p___
t* ///
0.8 -L———-
L——— // Q/
r______ ‘l/ ,"
5‘ /o/A
i____ ,
5.... /,
»»——— //30
L—— // 9/
004 I”. /,/ ’/I
:«Z/
C>C) P;/)? i 1 i l l 1 J l i L i

 

 

MOLARITY OF P-METHYLSTYRENE
Figure 13

 

DENSITY VS. MALEIC ANHYDRIDE
CONSTANT P-METHYLSTYRENE

 

Molarity
Curve -me thy -
styrene

A 0.025

0.050

MOLARITY OF ANHYDRIDE‘
Figure 14

 

AT

(3751);,“ )

 

 

0.8

0.6

No

0.4

0.2

-55-

2, Application of the Interaction Theory I to the
Studied Complexes

Observed Optical densities (Dt) were plotted
against the molarity of the complexing styrene (So)
at constant maleic anhydride concentration (M0) for
each wave length studied. Typical examples for styrene,
p-chlorostyrene and p-methylstyrene are respectively
shown in Figures 7, 10, and 15. Increasing s10pes
in the first two cases indicate further interaction
with the hydrocarbon as per equation (84). Observed
Optical densities (Dt) plotted against the molarity Of
the maleic anhydride (M0) for the converse case (i.e.
styrene molarity constant) shows no observable devia-
tions from linearity in Figures 9, 12 and 14. No
further interaction of the 1:1 complex with the anhy-
dride can be deduced from this analysis. Because Of
solubility difficulties in handling anhydride concen-
trations greater than 1.0M in benzene, this was the
maximum concentration used.

The value of (n) for the postulated additional
complex with styrene is unity by application of
equation (89) and the only other significant complex is
of the formula M32.

With graphs similar to the sample Figures 7, 10
and 15 for constant anhydride concentration the values
or the initial Slopes and ElKl values can be determined
as per equation (87) for all wave lengths. Division of
each initial sIOpe (E1K1Mo) by its reapective constant

maleic anhydride molarity (Mo) should give a constant

-54-

ElKl if the theory is valid. This is shown to be true
in columns (a), (d) and (g) of Table III for sample
cases. These ElKl values are also shown to be the
same as those determined from Figures 9, 12 and 14
for constant styrene (So) molarities (columns (b),
(e) and (h)).

The theory is applied further in the two cases
Of Observed interaction with the styrene hydrocarbon,
Figures 8 and 11, styrene and p-chlorostyrene. The
straight line resulting from.the plot of )IDt vs.
TS"

molarity of the styrene (So) shows that o
n u l and reduces equation (85) to (88). Division
of the s10pe (2E2K1K2Mo) by twice the respective con-
stant anhydride molarity (2M0) gives the constant
E2K1K2 predicted by the derivation as shown in columns
(0) and (f).

More accurate E1K1Mo values may be obtained from
the intercept of this line.

ElKl values are similarly determined from the

zero time extrapolated density values for the p-methoxy

and p-dimethylaminostyrene complexes.

-55-

. TABLE III
SAMPLES or REPRODUCIBILITY’OF EVALUATED CONSTANTS
BY INTERACTION THEORY I

 

 

Molarity Styrene p-Chlorostyrene p-Methyl-
of the styrene
Constant (a) (b) (c) (d) (e) (f) (g) (h
Reactant ElKl E1Kl EZKQKZ ElKl ElKl EZK1K2 E1K181§1_
0.015 2.05 0.09
(8A) (8A)
0.020 1.98 , 0.15
(88) (88) '
0.025 5.72 p 2.59 2.65 0.25 11.5 11.8
(9A) (10A) (12A) (11A) (15A) (14A)
0.050 1.87 0.10
(80) (80)
0.040 1.81 0.11
(7A,8D) (8D)
0.050 1.74 5 75 0.12 2.40 2.44 0.29 11.1 11.8
(8E) (9B) (SE) (108) (128) (118) (158) (148)
UOUGO 1076 0.11
(78 SF) (SF)
0.070 1 69 0.12
(80-) (so)
0.075 . 11.9 11.2
0.080 1.80 0.14
(8H) (8H)
0.100 10.9 11.4
0.125 11.2 10.7

 

Average 1.85 5.75 0.12 2.40 2.55 0.26 11.5 11.5

(a) and (c) at 570 m/uat constant anhydride molarity
(b) at 360 mfitat constant styrene molarity

(d), (f) and (g) at 575 myIat constant anhydride
molarity

(e) and (h) at 575 m;lat constant dyrene molarity

N.B.
The parenthesis after the datum contains a Figure nump

ber and curve letter to which the constant can be referred.

-55-

5. Another Interaction Theory (II) and its application

The graphical estimation of incremental 810p98 is
a tedious process and a more simplified but less ele-
gant treatment can be deveIOped.
Postulating only a 1:1 complex (54) the express-
ion of the mass action law (66) may be rearranged to:
(94)
K1 32.132 " (Ao+ Bo)K1“‘ Clxl = 1
01
Substituting (60) for CI and rearranging
(95)
E1K1 5.932 g 1+K1(Ao+80) - E}. D1
D1
When K1 is very small and Cl is small (95) can be re-
stated:
(95) AOBO _ 1

D1 131K1

which means that for low A0 and Bo concentrations, the

 

 

product of the initial concentrations of the reactants
divided by optical density attributable to the complex

is a constant.

As the concentrations of one or both of the
reactants increases, only the final term.of (95)
remains negligible and the valid equation is

(97)

A B
° ° . -—-1—-+ "L(Ao+ 80)
1)1 811:1 E

 

where the plot of A030 vs. A0 B0 will give a slope

D1

-57-

Of l/Eland an intercept of l/Eixl. The large values of
intercept and the low value of the s10pe probably will
not warrant the determination of these constants by
this method. However, the resulting curve has a de-
cidedly negative slope. Then it can be surmised that
absorption is occurring beyond that attributable to
the 1:1 complex. Rearranging (95) gives:

(98)

D1 . l

E1K1AOBO 1* K1(A°+Bo) - 9:5;
1

 

 

If the total density (Dt) is the sum of the contri-
butions from several complexes.
(99)
Dt :D1+D2+ e e e e

Considering only two, substituting the value of
D1 into (98) and rearranging
(100) Dt _ 1 '+ D2
KAB "1+1: (A+8)-D1K1 EK A8
E1100 100 3-;- 110°

 

 

As in the interaction theory I, D2 is the optical
density of the second complex 02 and from equation (74)
and (80) when n g 1, K1 and C1 are small.

(101)
D2 1: E2K1K2Ao2P>o

Substituting (101) in (100), simplifying and
putting over a common denominator

(102)

Dt
MOSO

VS. STYRENE
(570m/4)

 

 

 

 

 

 

MOLARITY OF STYRENE

Figure 15

.4“

 

Dt

 

 

 

 

 

 

 

 

 

 

 

 

VS. P-CHLOROSTYRENE
MOSo
(575m,u)
o I
I
._.)
.—+
fl
-—J
:1
Z
O -—()
O |—‘
1111(LliililiiLili E):
“'2 0, In 0.
'0 l0 oi N

MOLARITY OF P-CHLOROSTYRENE (So)
Figure 16

S.

K)

-58-

 

 

 

(102)
DlKl E
D 1+[1+Kl(Ao-(BO) - ____1 2 K
- E1 E1
E K A B
1 1 ° ° liK1(Ao+80) - DlKl
E1

If Ԥ21K2 or A0 is very small relative to K1, (102)
1

reverts to (98). If K1 is also small (97) is valid.

If attempts to use (97) resulted in a line of neg-

ative slope then the converse is true and K1 is very

E
small relative to _§ K2. The final two terms of the

 

 

 

denominator are El negligible and at low BO
(102) reduces to:
(105) E
Dt : l+_2 1(on
ElKleBo E1
or
(104)
pt
: E1K1+ EzKleAo
A0 B0
A plot of Dt vs. A0 will evaluate the same
constants as 0 interaction theory I, a slape

Of E2K1K2 and an intercept of ElK1° Figures 15 and
16 represent such plots for styrene and p-chloro-

styrene complexes and give the predicted straight

line when Dt is plotted against the styrene con-
S M
centration ° 0 (So) at low maleic anhydride concen-

tration (M0). N0 unique relationship was apparent with

the other substituted styrene complexes.

gAN INTERMEDIATE CASE:

Complexes of p-Methylstyrene and Maleic Anhydride.
Interaction Theory III

 

It has been shown in equations (91) and (102)
that if K1 and C1 are too large, the Interaction
Theories (I and II) cannot be satisfactorily
applied. If a second complex strongly absorbs and/or
K1 is not large enough, the method of continuous
variations cannot be applied to the determination of
the equilibrium constant K1. None of these methods
of analysis satisfactorily applied to the p-methyl-
styrene complex at all wave lengths. This indicates
one of the following:

(a) Only a 1:1 complex is formed of low K1 so
that the maximum in optical density is not signifi-
cantly shifted with respect to (x) in non-equimolar
continuous variations, even with large differences
in the molarities of the two solutions (Curve 2D).
(b) Additional complexes are also formed but
K1 and 01 are significant with respect to fig K2
and the previous Interaction Theories El

developed are not applicable.

An attempt to apply Interaction Theory I at
higher wave lengths resulted in approximate E2KIK2
values Of 0.05 at 590, 595 and 400 mg; . As can be
seen from Table III, this is barely within the range
of reproducibility. It cannot be considered as con-

clusive evidence for further interaction, eSpecially

(3135

CX75

' 0.7C)

CLSES

M
-3-vs. MALEIC ANHYDRIDE

 

 

 

    

 

ZONSTANT P METHYLSTYRENE (0.025M)
(550ml!)

8 .

L:

F;

: o
(lilihhhhhh
'02 0.4 0.5 08

MOLARITY 0F MALEIC ANHYDRIDE
Figure 17

 

0.275

0.270

0.255‘

 

 

 

 

0 .250

I I

 

 

 

 

/
_(I(l(i(l(JJl(l)i

.312 vs. P METHYLSTYRENE (so)

D .
CONSTANT ANHYDRIDE (0.125M)
(560m/4)

MOLARITY OF P-METHYLSTYRENE
Figure 18

 

-60..

since the phenomenon can only be observed in one
region of the Spectrum due to complex. An expansion
of Maatman's 6 approximation technique has been
applied in an attempted clarification.

Graphs of equation (71) were made and typical
examples are shown in Figures 17 and 18. The

equation states that a plot of 22, vs. Bo at

constant A0 should give a D1 straight line.
In Figure 17, Bo - Mo (molarity Of anhydride) and

A0 = 80 (molarity of the styrene) in a solution of
density Dt at 550 TW‘- The "ideal" curve drawn thru
these points serves to minimize experimental error in
Optical measurements. ”Ideal" data chosen from.the
extremes of the line is substituted into equation
(70) to calculate K1. Maatman states that for a

1:1 complex the K1 values thus arrived at should not
vary with the wave length.

"K1" values determined in this manner at constant
styrene concentrations are tabulated in Table IV for
the various wave lengths. The plotted data approxi-
mates the predicted straight line only at the lower
wave lengths studied (550 - 560 m/A). At 560-570 m/L
the curves tend to bend over with increasing anhy-
dride concentration (Mo)° NO correlation is per-
ceived at any higher wave length.

According to Maatman's hypothesis, similar plots
of So/Dt vs. 80 at constant MO should give the same
curves as before for a 1:1 complex. Only at these

lowest wave lengths studied did the data hug the

-51-

"ideal" line so that correlation could be ascertained.
Thebeniing over, i.e. decreasing SIOpe of the plots
was also manifested in Figure 18 and in instances
where lines could be objectively drawn, their SIOpes
were much lower than those drawn at constant styrene
concentration. In general, the magnitude of the
deviations from the "ideal" line enormously increases

with increasing wave length.

This surprising discrepancy between the curves at
constant p-methylstyrene and constant anhydride is
shown by the columns for the apparent "K1" values
calculated from (M0) at different wave lengths.

The starred values were calculated from '1d931" lines
that showed very poor correlation with the actual
data.

It will be noted, however, that these apparent
"K1" values show a decided increase with decreasing
wave length. This can be explained by the following
extension of Maatman's thesis.

The optical density D1 in equation (71) is (Dt):
the sum of several contributions (99). Considering
two for purposes of discussion and using the same
postulates that lead to equation (102), we have on
inversion of the equation and dividing thru by

 

(105) A0 80 1/K1
Ao E130 E130

 

-——- s
Dt 1+[1+K1(Ao+80)]§g 1:ng
El

-52-

which is (71) when 22 K2 a 0
E1

This equation shows that if AB interacts further
with A that the plot of Ao/Dt vs. Ao will not give a
Straight line but a curve of decreasing lepe with
increasing A. This leads to the interpretation that
both maleic anhydride and p-methylstyrene interact
with the 1:1 complex, the latter more appreciably
than the former and accounts for the observed
phenomena discussed above. As §§.K2 increases, the
deviation from the linearity expected by equation
(71) becomes more marked. An "ideal" straight line
would average a smaller lepe, and the calculated
apparent "K1" values would decrease. On this basis,
there is strong indication that at the higher wave
lengths the absorption (E2) of the second complex
has increased relative to that (El) of the first.
This also explains the fact that application of Inter-
action Theory I may be possible at higher wave lengths
since the premises of its derivation are more aptly
fulfilled.

The extent of this interaction can be surmised
if an approximate value of the true K1 is known.

Again inverting (102) and dividing by ___}__

 

 

 

D DtAoBo
where 01 - _l and K1 is not too large,
(106) _
1 pt Dt i’ Dt For a second
E1. : K1 Ao'Bo B0 A0 set of values
1+2 K2 A0. at constant Bo,

an equation

(107) can be written with Dt' and A0).

-55-

Equating (106) and (107) and rearranging

 

(108)
—-1- = [Dt"Dt*P.E:EB - DtB°1
K1 A0: A.
El A0: A0
divided by

Bin M] __K2 AO'Dt _ Aopt")
%' El A0 A0'
If 0E K240 then (108) reduces to (70). If
a true E1 value of K1 is known, then from.the
values of Dt9 Dt', A0 and A0' determined from the

"ideal" curve which is a straight line approximation

of (105), an approximation of 32 K2 can be made as:

 

 

 

 

E1
(109) .
[Dt‘-Dt+Dt'Bo _DtBo]_ 1 [Dt _ Dt']

E ._-._- ___
—EK2 . Ao ' Ao Kl A0 A0'
E

1 1 A0 'D A D

K”(O t 0 0% ')_ (A0 Dt' _ AODt+_A_____°B° Dt.’ A' OBODD)
1 A0 A0 ' A

O

and all values are known.

If Bo is small and sinCe Ath'=""5AoD15 then (109)

 

becomes
(110)
Ea (Kl-"K1")(Dt'-Dt)
—K2 =
4E1 AO'Dt _ Ath'

 

 

A0 A0:

-64-

TABLE IV A

REPRODUCIBILITY 0F EVALUATED CONSTANTS FOR
P-METHYLSTYRENE COMPLEXES BY
INTERACTION THEORY III

Molarity At Constant p-Methylstyrene
of the

Constant 575m. 570m
Reactant 4 —_7A
(A) (B) (A) (B)

0.025 as 0.08% 0.50
0.05 ea 0.07 0.50

-:‘

(036-9348) (MWB) (mg-5399‘

0.025 0.18 0.19 0.20 0.14 0.56
0.05 0.16 0.21 0.29 0.09 0.40

* "ideal" lines showed very poor correlation with
available data.

** available data apparently random.

(A) Calculations for "K1" based on equation (70)

(B) Calculations for Ea K2 based on equation (110)
E1
assuming K1 : 0.40

TABLE IV B

 

-65.-

REPRODUCIBILITY 0F EVALUATED CONSTANTS FOR

P-METHYLSTYRENE COMPLEXES BY

INTERACTION THEORY III

 

 

 

 

Mo%a:§ty At Constant Maleic Anhydride

O 6

Constant 575m 57%

Reactant (A) """*K' (B) (A) (B)
0.025 ** 0.015a 0.57
0.05 0.05 0.56 0.022% 0.57
0.075 *%
0.125 0.08% 0.51 0.142b 0.24

560m 555m 550m
(A) ) (A) (B) (AT“179

0.025 0.025» 0.18 0.056a 0.54 0.042s
0.05 0.15% 0.51 0.21s 0.16 0.48b
0.075 0.21 0.54 0.61b as as
0.125 0.55 0.07 0.44b

* "ideal" lines showed very poor correlation with

available-data.

es available data apparently random.

.(A) Calculations for "K1" based on equation (70)

(B) Calculations for E? K2 based on equation (110)
assuming K1 : 0.40

E1

a ="ideal" line was based on points at a high concen-

tration of the styrene

b 3 "ideal" line was based on points at a low concen-

tration of the styrene.

-66..

where "K1" is the apparent value of K1 assuming
equation (70) to be valid.

Assuming a K1 value of 0.4, since at 550mw4the
K1 values from both constant styrene and anhydride

approached each other, equation (110) was used to

calculate the EZKZ values shown in Table IV (A and B).

E1

When the p-methylstyrene concentration

was maintained constant, the increase of the E3 K2
values with increasing ane length confirmed E1
prior qualitative impressions.

The greater parabolic nature of the curves
combined with the inevitable error in Optical measure-
ments did not allow the same consistent results when
the anhydride was held constant. It will be noted in
Table IV that when the available data was at high

styrene molarities, the "K1" values were generally low

and 82E; values high. This is expected since only
K
the 1:1200mplex contributes at very low molarities.

-67-

C. QUANTITATIVE COMPARISON OF THE COMPLEXES
AND PREDICTION OF OPTICAL DENSITY

The constants evaluated by the Interaction
Theories are tabulated in Tables V, VI and VII along
with an estimate of the average deviation in the ex-
perimental data for all wave lengths. The lower wave
length limitation is always due to the increasing
absorption of the anhydride.

The ElKl and E2K1K2 constants show good agree-
ment within the experimental deviation between the
constants derived from both theories I and II. (Tables
v and v1).'

The values of EZKIKZ from Theory I in Table VII
are not expected to have any quantitative meaning
since K1 has been shown to be significant. This would
contradict the premises of the derivation of I. How-
ever, it has significance in that it indicates the in-
creasing absorption of a second complex at higher wave

lengths.

_E.K2' in Table VII can be construed as a more
quantftative measure of the interaction of the 1:1 com-
plex of anhydride and p-methylstyrene with more anhydride,
its validity depending on the validity of the presumed
K1. On the basis of this data, the following may be
true.

(a) The 1:1 complex reacts separately with p-methyl-
styrene and maleic anhydride to form two additional

and distinct 1:2 complexes.

-68-

TABLE V

CONSTANTS FOR MALEIC ANHYDRIDE COMPLEXES WITH

 

STYRENE AS DETERMINED BY INTERACTION THEORIES I AND II

 

 

 

THEORY I THEORY II
ElKl E2K1K2**

Anhydride Styrene* Anhydride ElKl E2K1K2**
Egg Constant Constant Constant
54o 28t5 2515 5.511
545 17:1 1.1710.25
550 14:1 15.510.2 12.711 0.49:0.1
555 , _ 6.811 8.6to.2 0.25:0.02
560 5.5t0.5 5.730.5 0.14:0.05 5.5t0.1 0.195t0.01
565 5.85t0.10 5.1410.06 0.14010.006

570 1.8510.15 1.5010.25 0.1210.02 1.7710.06 0.11010.007
575 1.05:0.10 0.97:0.15 0.09:0.02 0.92:0.05 0.08410.005

580 0.5610.09 0.5It0.02 0.047t0.002
585 0.5010.06 0.01810.006
590 0.18t0.01 0.00710.001
400

e The estimated average deviations were based on
studies made at only two constant syrene concentrations.
we K2 is the equilibrium constant for the interaction
of the 1:1 complex with styrene.

TABLE VI
CONSTANTS FOR MALEIC ANHYDRIDE COMPLEXES
WITH P-CHLOROSTYRENES AS DETERMINED BY INTERACTION

THEORIES I AND II

 

-59-

 

 

 

THEORY I THEORY II
E1K1* IEEE;» E2K1K2**
E/A Anhydride Styrene* Anhydride ElKI E2K1K2**
Constant Constant Constant
555 57::
540 50*?
545 21:? 19.510.4 1.16t0.15
550 15.55t0.05 19t2 0.641: 14.110.5 0.9510.12
555 10.9t0.10 9,410.5 0.710.5 9,810.1 0.8510.06
560 7.5t0.5 6.5to.7 0.7to.1 6,710.4 0.6410.20
565 5.15t0.05 5.15:0.09 0.5810.02 4.5to.2 0.5010.14
570 5.57:0.04 5.64t0.15 0.56t0.1 5.010.15 0.40:0.05
575 2.40t0.01 2.54t0.10 0.26tO.O5 2,110.15 0.281n0015
580 1.6210.04 1.6410.08 0.17:0.07 _1.42#0.12 .174t0.01
585 1.11:0.01 0.1410.04 099410005 0.12210.001
590 0.82:0.05 0.125r7 0.76t0.08 0.10:0.025
595 0.610.2 0.091? 0.5010.06 0.10:0.05
400 0.410.1 0.0561? 0.56t0.04 005910004
410 0.210.1 0.0461? 0.17t0.02 002010004

* The estimated average deviations were based on studies

made at only two constant concentrations.

as K2 is the equilibrium constant for the interaction

of the 1:1 complex with styrene.

-70-

TABLE VII
CONSTANTS FOR MALEIC ANHYDRIDE COMPLEXES WITH P-METHYL-

 

STYRENE AS DETEPMINED BY INTERACTION THEORIES I AND III

 

THEORY I THEORY III***

 

.33. . . 'H' E E
M ,u. Anhydride Styrene Anhydride Anhydride seine...
Constant Constant Constant Constant Constant

 

550 10914

555 9615

540 8112

545 5511

550 55.610.5 55.511.o

555 41.4t1.o 42.6to.5 0,26T$** 0.11:0.05
550 51.sto.3 51.4to.5 0.22t? 0.2oto.01
555 22.8to.5 25.0to.s

570 15.6to.5 15.4to.4 0,52t? 0.50to.oo
575 11.5to.5 11.510.5 0.55t?

580 7.51to.05 7.sto.4

585 4.5510.1 0.0910.05

590 5.0830.04 5.Iito.1

400 1.071o.os 0.05:0.05

404 0.67io.07

410 o.ssto.ov

* K2 is the equilibrium constant for interaction of the
1:1 complex with styrene.

** K2' is the equilibrium constant for interaction of
the 1:1 complex with anhydride.

*** Based on assumed K1 - 0.4.

**** Estimation of deviation is useless due to wide

variation in values obtained.

-vl-

TABLE VIII
CONSTANTS* FOR MALEIC ANHYDRIDE COMPLEXES WITH

 

P-METHOXYSTYRENE AND P-DIMETHYLAMINOSTYRENE

 

ElKl

 

Elk P-METHOXYSTYRENE P-DIMETHYLAMINOSTYRENE

550 157110

560 277113
565 250125
575 7215 261t22
400 5212 255t4
425 22811
450 19735
475 15511
500- 10035.
550 50.511.5
500 4.5to,5
550 2.oto.1

* These values are determined from zero-time
(extrapolated) values with the postulate of a 1:1
complex. The average deviation includes results
from studies at both constant anhydride and constant

styrene concentrations.

-72-

(bl The 1:1 complex reacts with p-methylstyrene
or anhydride to form.a 1:2 complex which reacts
further with the other reactant. A complex equi-
librium is established between the three complexes.

Table IX is a summary of the constants from
Theories I and II. _These are weighted values com-
piled from Tables V, VI, VII and VIII.

Equation (104) can be rearranged to:

(111)

D1, = [ElKlegKlKng] A050

or in our case
(112)
D1; = [ElKl + E2K1K230] M080
Thus, knowing the unreacted substituted styrene con-
centration (So) and the unreacted anhydride concentra-
tion (M0) in benzene, the absorption of the formed
complexes can be predicted using the E1K1 and EQKIKZ
values in Table IX apprOpriate to the wave length con-
sidered. In the p-methylstyrene complexes, the tab-
ulated ElKl alone suffices. The ElKl value also serves
as a good approximation with the p-methoxystyrene and
p-dimethylaminostyrene complexes.

The smooth curves drawn on Figures 1 thru 6
were calculated from equation (112). The excellent
agreement with the experimental points is the final
proof of the reliability of the interaction theories
as applied to these complexes.

Figure 2, Curve C, shows an unwarranted deviation.

However, the dotted pair of points in Figure 14 fall

myl R:
330
335
340
345
350
355
360
365
370
375
380
385
390
395
400
404
410

25

17

13.3
8.4
5.3
3.2
1.8

0.95

0.52
0.30
0.18

TABLE IX A
SUMMARY OF CONSTANTS FROM THEORIES I AND II

37
3O
21
14.9
10.0
7.0
5.1
3.5
2.4
1.6
1.0
0.8
0.5
0.4.

0.2

ElKl

"CH3

1

09
96
81
66
53.5
42.3
31.8
22.9
16.5

11.3

7.4

4.65
3.09
1.75
1.07
0.67
0.38

-OCH5

137

72

32

-N(CH3) 2

277
260

261

236

* R is the para substituent of the styrene in

the complex.

-74-

off the plotted straight lines. This is some of the
same data that comprise (20)! This clearly shows
that the predicted curve is even more valid than
the experimental one in this instance.
Table IX shows the following additional facts:

(a) The ElKl and E2K1K2 values for all complexes
fall off toward the visible. The absorption curves
of the complexes show no discernible maximum. A max-
imum may exist at shorter wave lengths but the absorp-
tion of the reactants makes this impossible to ascertain.

(b) The ElKl ratios clearly show that the absorption
of unsubstituted styrene complex falls off more rapidly
toward the longer wave lengths than the p-chloro and
p-methylstyrene complexes. The ratio between these latter
two remain practically constant so that the contour of
their absorption curves is similar. However, their
absorptions decrease more rapidly than that of the
complex with p-methoxystyrene which decreases more rap-
idly than that of the complex with p-dimethylamino-
styrene.

These phenomena clearly show that a comparison of
the optical densities of substituted styrene-anhydride
mixtures at an arbitrary wave length is no criterion of
complex concentrations or complex stability.

(c) Realizing that the error in these constants
increases below 355 m/Awhere the anhydride has apprecia-
ble absorption, the 1513 K2 values for the complexes with

E
p-chlorostyrene 1 and styrene are relatively

constant for most wave lengths. This indicates that

TABLE IX B

EIK]. Ratios

-75-

 

m/u H : Cl : CH3 : OCH3 : N(CH3\2
335 x 1.0 2.6 x x
340 1.0 1.2 3.2 x x
345 1.0 1.2 3.9 x x
350 1.0 1.12 4.02 10.3 x
355 1.0 1.19 5.05 x x
360 1.0 1.32 6.0 x 52.3
365 1.0 1.59 7.17 x 81.3
370 1.0 1.94 9.18 x x
375 1.0 2.53 11.9 76 275
380 1.0 3.08 14.22 x x
385 1.0 3.33 15.5 x x
390 1.0 4.44 17.17 x x
395 x 1.0 3.5 x x
400 x 1.0 2.7 80 600
404 x x 1.0 x x
410 .x 1.0 1.9 x x

TABLE IX 0

SUMMARY OF CONSTANTS FROM THEORIES I AND II

 

E2K1K2 EaKIKa E2

Ratios ‘ E1
my. R: -H -Cl -H -Cl -H -Cl

340 3.30 1 x 0.13
345 1.2 1.16 1 0.97 0.07 0.06
350 0.50 0.9 1 1.8 0.04 0.06
355 0.23 0.8 1 3.5 0.03 0.08
360 0.18 0.65 1 3.6 0.03 0.09
365 0.14 0.55 l 4.0 0.04 0.11
370 0.11 0.41 1 3.7 0.06 0.12
375 0.084 0.27 1 3.2 0.09 0.11
380 0.047 0.17 1 3.6 0.09 0.11
385 0.018 0.12 1 6.7 0.06 0.12
390 0.007 0.09 1 14.0 0.04 0.11

-77-

ratio of the absorption of the 1:2 complex (E2)

to that of the 1:1 (E1) is relatively constant at
all wave lengths. If we assume that the ratio
E2/E1 is the same for both styrene complexes, then
the stability of the p-chlorostyrene 1:2 complex is
approximately twice that of the 1:2 complex with
unsubstituted styrene.

It may be argued that the observed additional
interaction with the substituted styrene is attribut-
able to the gradual change of solvent, the styrene
replacing benzene and since molarities were used in-
stead of activities. These arguments may be refuted
on several points.

1. The evaluated constants based on the theory allow
calculated predictions to confirm experimental obser-
vations at all concentration ranges and wave lengths.

2. The relations between densities of benzene and
the substituted styrenes show that there are less
molecules of the styrenes per unit volume. This should
be detrimental to interaction and not assist it. For
a given molarity of anhydride there are prOportionally
less molecules of styrene in the more concentrated
styrene solutions per given volume. The styrenes
showed the same absorption as the benzene in the regions
studied.

3. The choice of a benzene solvent is advantageous
as no significant contractions in volume due to
mixing of the hydrocarbons were evident. The complexing

is thru the ethylenic linkages and the independent

-78-

contributions of the aryl rings can probably be
discounted except as they transfer the effect of

the para substituent to the vinyl group.

-79-

D. EFFECT OF DEOXYGENATION ON COMPLEX FORMATION

Application of equation (112) to p-methyIstyrene-
anhydride mixtures prepared under nitrogen and described
in the experimental section shows agreement between the
calculated densities and those experimentally obtained.
No effect of oxygen on complex formation and light

absorption could be determined.

~80-

E. EFFECT OF DILUTION 0N COMPLEX FORMATION

As stated in the experimental section, the Opti-
cal densities were read on 0.05M maleic anhydride
solutions with wide ranges of p-chlorostyrene and
p-methylstyrene. Subsequent dilution of these
solutions to 0.0250M anhydride showed their obedience
to Beer's law and the law of mass action, denoting
true equilibrium.(112) The Figures 10 and 13 show

the respective curves.

-81-

F. INTERPRETATION OF THE KINETICS:
THE CHANGE IN OPTICAL DENSITY OF
COMPLEXES 0F
P-DIMETHYLAMINOSTYRENE AND P-METHOXYSTYRENE

 

 

 

 

The cptical density attributed to complex form-
ation of p-dimethylaminostyrene and p-methoxystyrene
with maleic anhydride changed with time.

In the latter case, the absorption was
principally in the near ultraviolet region, and the
observable density changes occurred so fast that
extremely low concentrations had to be used. Ab-
sorption due to the styrene and the anhydride them-
seves interfered with a quantitative determination
of the density of the complex and a true measure of
its increase. The nature of the density changes
were complex. These reasons made a quantitative
application of kinetic theory infeasible with this
complex.

However, the unique character of the density
changes with p-dimethylaminostyrene warranted such
a study.

1. The color of the formation (yellow-red) is
pronounced and in the visible region where neither
of the complex components absorb.

2. The initial complex, as determined by continuous
variations on extrapolations to zero time, is

definitely 1:1 and, even with the error concomitant

 

 

DENSITY (D) VS. TIME (t)

T

Initial
Curve Styrene OD
Molarity
A 3.27
B 0.125

+4

v

 

/
1,1
2

 

A
k
ill

 

 

 

 

IIIIIJIIJJIJMI Ill JlLll

D “‘2 a. «a

EFFECT OF VARIATIONS IN MOLARITY OF P-DIMETHYLAMINOSTYRENE
CONSTANT ANHYDRIDE (0.125M)

Figure 19 (SOOmAL)
(t) in thousands of
seconds.

 

 

ll
35

EFFECT OF EXCESS REACTANT 0N KINETICS
OF P-DTMETRYLAMTNOSTYRENE
AND MALEIC ANHYDRIDE

INTERACTION

500m

I“ C)

N)
M M

Curve Styrene Anhydride ‘
A 0.175 0.075 *“1
B 0.075 0.175 cu

Total concentrations
of reactants 0.25 4

 

20
k?

I5

10

lllllllllLlllJlllllllJlHllll

 

 

”Till

 

 

 

l.l5

(t) in hundreds of seconds

-82-

with such treatment, shows no clear evidence of
other complexes. (See Figures 5 and 6.)

3. The magnitude of the equilibrium constant for
the 1:1 complex is known. The nature of the kinetic
curves provided positive clues as to the mathematics
to be applied.

a. Figure (19) consists of two curves. Curve A
shows the change in optical density for a mixture
of equal volumes of p-dimethylaminostyrene and 0.25M
maleic anhydride in benzene. Curve B is for a mixture
of equal volumes of the 0.25M styrene and 0.25M anhy-
dride. Notwithstanding the higher initial 1:1 complex
concentration as evidenced by the initial Optical
densities, the absorption of Curve A shows a greater
decrease than that of Curve B. Since 1:1 complex
formation is an equilibrium phenomenon, the decrease in
extinction shows that, at the very least, a reaction
occurs between one part maleic anhydride and two or
more parts of the styrene. Removal of the components
in this ratio decreases the concentration of the 1:1
complex and thus the observed cptical density.

b. Two solutions with the same total sum of
reactant concentrations, (Figure 203 but each with
one reactant in excess of the other, give kinetic
curves of entirely different contours. Curve 20-A,
with excess styrene, shows decreasing density that
tends to level off at a much lower value than the
initial.

Curve (20-B), with excess anhydride, initially

-85-

decreases in density, reaches a minimum and then
increases at a faster rate which subsequently slows.
The slowing in the optical density increase (Note
arrow at curve 20-B) occurs simultaneously with an
observed precipitation. The rate slows regardless
of the increasing turbidity of the solution. With
high excess of styrene (e.g. 20-A) no precipitation
was ever observed.

These experimental observations are conclusive
evidence of two kinetic reactions occurring either
simultaneously or in sequence. One chemical entity
is formed containing an excess of the styrene over
that of the anhydride and has no (or less) absorption
at the studied wave lengths than the 1:1 complex.
Another may subsequently be formed by further reaction
of this entity with anhydride or by simultaneous
formation of a new chemical identity containing an
excess of anhydride over that of the styrene. The
former is the more probable however, as at all con-
centrations studied, an initial dip in density was
always observable notwithstanding the high excesses
of anhydride initially present. The subsequent height-
ening of the rate of density increase clearly demon-
strates that the interaction with anhydride must be
due to a reaction occurring subsequent to a former
reaction with more styrene and not concomitantly.

No such phenomena could be discerned with separate

solutions of the reactants in the benzene solvent.

 

 

w] :14 vol-10 NI 4 _
KINETIC PLOTS OF P-DIMETHYL- f
AMINOSTYRENE-MALEIC ANHYDRIDE
REACTION USING OPTICAL DENSITY (D)

(500mpk)

m Curve Order Plot
A zero D vs. t 41
B second l/D vs. t

 

0.547M styrene
\ O .020M anhydride

\

V

f

w

 

1 1 I 1 1 1 1 l 1 1 111 1 l 1 l 111 1 1 I 1 1 1 I 1 1 1 I 1 1 1 l 1 1 1

 

 

 

Figure 21

(t) time in thousands of
seconds.

k+

-84-

c. The greater the excess styrene concentration,
the greater the tendency for an inverted "S" type
curve with a good portion of the initial plot of the
density (D3 vs. time showing a definite linearity
(Curve 21-A). Density decrease subsequently in-
creased in rate which then diminished as noted above.
Clearly a factor must be considered which affects the
initial rate in such cases.

The above analyses served as clues for the theoreti-
cal kinetic investigation. It may be hypothesized that
the initial linearity of the inverted "S" type curve
may be due to 1:1 complex reacting with styrene and
the equilibrium.relationships necessitating the form,
ation of additional 1:1 complex simultaneously with
its removal. The further decrease in slope may possib-
ly occur when all of the minor constituent (anhydride)
is in the 1:1 complex and no more can be formed. The
remainder of the curve may be investigated kinetically
on an independent basis.

‘With a high excess of the styrene and a low
concentration of the anhydride, the concentration of
the 1:1 complex would be the determining factor in the
kinetics. The reaction can be assumed to be first
order with respect to the complex and so:

(113}
-d01

dt 1 1

where Cl is the concentration of the 1:1 complex.

-85-

But as complex (Cl) is consumed, the equilibrium
creates more complex with the heretofore unreacted
anhydride. The complex concentration is defined as:

(114)

where So and Mo are the respective concentrations of

the styrene and anhydride if no 1:1 complex were

 

formed.
Substituting (114) into (113),
(115)
-d(K18M) -d(K130Mo) d(K101(MO+So) d(K1012)

dt dt dt dt

M0 is presumed to be very small and (115) reduces

to:

 

(116)
d(chlso) d(K1012) dMo
dt dt dt
Expanding,
(117)
dC d8 dC dM
K180 1+ K10] 0 -- 2K161__l. - KlSO_-2 -.-. 1:101
dt dt dt dt

80 is initially very high so that very little
change in its concentration occurs at the start of the
reaction. Assuming so equal to the original styrene

concentration of the prepared mixture and constant,

-86-

(115)
x130 dc1 - 21(101 dc1 - K180 C“"0 : klcl
dt dt dt

To allow integration, an approximation is made
that very small initial Mo concentration is entirely
tied up in the 1:1 complex, i.e. Mo = Cl, and *

(119)
dNo',, dc1

dt dt
It follows from (118) that
(120)
dCl - -k1

dt 2K1

which integrates to
(121)
(cl)2 ‘ (cl)1 _ -kl

 

t2 ‘ t1 231
or since D1
-- : 01
E1

(122)

 

For this substitution we have assumed that if
Dt : D1+ D2 where D2 is the density of the preposed
1:2 complex, the absorption due the second complex

is initially small. This is valid as its extinction

-87-

(E2) has already been shown to be low or nil and its
initial concentration at the point considered is also
low.

Thus the initial straight line portion of a plot
of Density (D) vs. time (t) has a negative lepe of

.EEEE and is of psuedo zero order.
2K1 .

Values of Elkl are tabulated in Table X. Their
constancy is -2E;h corroborative proof of the
theory. The magnitude of k1 is 3 x 10"5 moles/l/sec.
baSed on the assumed K1 : 0.4.

The reaction proceeds in this manner until the
Mo is completely consumed for all practical purposes.
Since the decrease in density is no longer being
retarded by the formation of new complex, the remainder
of the density vs. time curve should be indicative of
the kinetics of the reaction between the 1:1 complex
and p-dimethylaminostyrene.

The rate of a reaction of the nth order is pro-

th power of the concentration of the

portional to the n
reactant. Considering a high excess of p-dimethyl-
aminostyrene we have:

(123)

db

and on integration:

(124) C(1_n)

 

: -k t+L
l-n 1

TABLE x '
DETERMINATION OF FORWARD REACTION RATE CONSTANT
P-DIMETHYLANINOSTYRENE-MALRIC ANHYDRIDR

 

 

 

Initial
Molarity
of the
Reaotants k1 _
Mo 30 slope* Moles/l/sec.**
0.015 0.559 2.2xIO-4 2.7x10‘5
0.020 0.547 2.3 2.9
0.0225 0.501 2.0 2.5
0.0238 0.479 1.7 2.1
0.025 0.456 1.9 2.4
0.0273 0.434 3.1 3.9
0.0275 0.411 2.7 3.4
0.0288 0.388 2.1 2.6
0.030 0.365 2.2 2.7
0.0325 0.319 1.4 1.8
0.0375 0.228 4.2 5.3
Average 2.3x10'4 3 x10"5
* lepe , E1k1 determined from lepes of
initial .7iif straight lines of density plotted
vs. time.
H Elkl .- 311:1 .-.- .131.
K1 K1

ElKl : 100 (See Table VIII) at 500 m}L . For kl

calculation, assumed K1 : 0.4

-88-

KINETIC PLOTS OF P-DIMETHYLAMINOSTYRENE-MALEIC
ANHYDRIDE REACTION USING OPTICAL DENSITY (D)

 

 

 

 

 

(500m/A)
0.547M Styrene ? _-
0.020M Anhydride 0 #
an -
IO
< 4
f////9 —1
21? ~
.4»
Curve Order Plot w
Revers- log(D-D.)
ible lst vs. t ‘7
o A
B lst log D vs.t .a
/ --I
/° De: O. 20 at equilibrium .1
l/Q (see Figure 21) I
O O A
-I-I I LI II I It! I II I I I l I l IIIIJ
0. a! “t '9. 0° 0 N
O o O o O _' ..:
I I I I g I I
LOG VALUES
Figure 22

(t) time in thousands of
seconds

-89..

where L is a constant of integration. Reerranging

and taking logs:

(125) 1
log C1 a 1:; log t 'I' constant
or also
(126)

log D1 u._£_ log t 4-constant
1-n

Log-log plots of density against time give a
slope of l/l-n. This method applied to the latter
portion of the curves for the mixtures in Table X
give an n ~ 1.3.

For higher concentrations of anhydride and for
mixtures that show a mimimum density with a subsequent
rise, values of n g 40 for the falling density portion
have been calculated. With increasing anhydride, (n)
increases, demonstrating the complexity of the kinetics.

Again considering high styrene concentrations and
low anhydride concentrations, first order plottings of
log density (D) vs. time (t) have decreasing negative
slope. This indicates either that the observed density
is greater than warranted by first order kinetics or
the 1:1 complex is not consumed at the expected rate.
(Figure 22-B) Second order plotting of l/density (1/D)
vs. time (t) shows an increasing slope. (See Curve
21-B) This confirms the intermediate order noted
above. An estimate of the situation would be that the
observed density is not decreasing at a fast enough
rate to fully satisfy first order kinetics.

A reverse equilibrium may be postulated:

1:1 complex up. 1:2 complex.

-90-

Assume a first order reversible reaction

(1271
3111+ S -.. $2M

(125)
01+ S L- 02

?

kI
With high concentrations of S, the reaction
rate is first order with reapect to Cl. The rate
expression is:
(129)

32.2.. 1' k (8'02) - k'CZ

dt
where (a) is the initial concentration of C1 (no 02
is present initially) and (k) and (k') are the
respectiVe Specific rates for the forward and Opposing
reactions. At equilibrium
(130)
k(a-(C2)e) g k'(cg)e
where (C2)e is the amount of C2 formed or of Cl
changed to 02 at equilibrium. Substituting the value
of k' of (130) in (129):
(131)

 

 

33?. = Ida-CZ) ~ 1‘ch E'(Cg)e] = kla [(02). - 02]
dt (02)9 (62)e
0n integration, C2 = 0 at t : 0, 02 : C2 at t = t and
(152)
.122. .1 111.1921...
(02). t (62)9-Cg

ak
(c219

 

(133) k+k' -

and (132) is:

-91-

t (02)e-c2
but
(135)

(02)e Do-De

 

(02)e-02 Dt-DO

where Do, Dt and Du are the densities at the beginning,

after time (t), and at equilibrium respectively, and so
(136)

k+k' : l!n___—D°-De
t
Dt’De

Rearranging:
(137)
(k+k')t : 'vpn (Dt‘Du)+’pn(Do'-Du)

If the hypotheses of this derivation are valid,

a plot of the log (Dt‘DeI vs. time (t) should have
_ k+k'
2.303

Curve 22-A is one of a series of curves representative

a negative slope and be a straight line.

 

of the confirmation of the prediction. Such determined
values of k1+-k' are tabulated in Table XI. The value
(De) is determined from.the minimum of the density vs.
time plot and the deviations from linearity depends
on this choice.

As the initial styrene concentration is diminished,
the overall forward reaction rate becomes second order
with first order reversal. The rate expression is:

(138)

392 = k(a-CZ)(b-Cg) - 1:102
dt

where (b) is the initial concentration of uncomplexed
styrene (S) and (a) is the original concentration of
complex on the assumption that all the original anhy-
dride (Mo) is contained within the 1:1 complex.

At equilibrium:

(159)
k(a-C°)(b-Ce) ; k'CU
and thus:
(140)

k' = -g:(a-Ce)(b-Ce)

where as is the concentration of C2 at equilibrium

since 02 = O at the start of the reaction.
Substituting (140) in (138):

(141)
deg k
.——— : k(a-c )(b-c ) -.__ -C b-C C
dt 2 2 03(a g)( a) 2

Expanding and rearranging, this becomes:
(142)

d02 k dt
(COCQ-Eb)(CZ-Ce) Ce

 

Separating by the method of partial fractions,
and setting up (142) for integration with limits as
shown:

143
< 1 02 02 t

__'32_ (d02+_3__( “2:1:de
Caz-ab Cg-ab Caz-ab 02-0 Ce

0 0 °

 

 

-95-

Integrating and evaluating:
(144)

t = Ce JnCe(ab-CGCZ)

ab-Ce2 ab(Cé-Cg)

 

 

1
k

If(b) is large (i.e. original styrene concen-
tration high), 062 is small with respect to ab, (b)
is practically constant and equation (144) reduces
to (132), the first order forward reaction case.
Thus at high styrene concentrations (b) the reaction
is psuedo first order reversible as described, with
kp the apparent forward first order rate constant.

Comparison of equations (132) and (144) shows:

(145)

k+k ' IMO, 021+W+ ' [4941233)
P P P P ab

and if C902 is small (145) can be converted into

an ab equation analagous to (137) where:

(146)
(kp+k'p)t g ant-De) +!n(Do-Du)
Thus the negative s10pe of the plot log (Dt-De) vs.
(t) divided by 2.303 of the above equation is:

(147)
kp+kp' . k‘r”3‘+1:C,;.,-1ce1’=‘=’:kp’3‘ é’ kb+k'

09‘ Ce

It must be realized that these equations were
considered on the basis of high styrene and very

low anhydride concentrations.

-94-

For the general case, the kinetic considerations
lead to the complicated rate expression:
(148)
ng

.71.; = kCl [so - (Cl-0202)] 4:102 =

kKl[M0’(Cl‘I’C2I] [So-(0112023 2 'k'Ce

where So and Mo are the initial molarities of the
styrene and anhydride before any complex formation,
C1 and C2 are the concentrations of the 1:1 and 1:2
complex at any time (t) and K1 is the equilibrium
constant for the formation of the 1:1 complex.

Slight variations of high styrene concentrations
at low anhydride concentrations may allow estimation
of the second order forward rate constant (k) by
means of equation (147).

The calculated values from the curves of the
psuedo rate constants kp+kp' plotted against the
initial styrene concentration (b) should give a
straight line with (k) as the slepe and (k') as the
intercept. The values are tabulated in Table XI.

As the maleic anhydride concentration of the
solution approaches that of the styrene the subsequent
density increase after the minimum can only be caused
by interaction with anhydride to form a chemical
entity of higher extinction. The faster rate can
only be justified on the subsequent interaction of
anhydride with the 1:2 complex. The precipitation
occurring concomitantly with the decrease in rate of

density rise shows that the light absorbing material

-95-

TABLE XI
P-DIMETHYLAMINOSTYRENE (31 AND MALEIC ANHYDRIDE (M)
TABULATION OF APPARENT kfitkp' VALUES
FOR REACTION OF 1:1 COMPLEXES WITH

P-DIMETHYLAMINOSTYRENE

 

 

Initial *
Holarities k +'k '

of the p p
Reactants
Mo 80

0.0275 0.411 1.52 x 10'4
0.02625 0.434 1.88
0.02375 0.479 1.63
0.0225 0.501 1.63
0.020 0.547 1.78
0.015 0.639 1.86

Average 1.7 x 10'4

* Determined by dividing lepe of plot of log (Dt-De)
vs. time (t) by 2.303 according to equation (146)

Plotting kp+-k ' vs. So gives a straight line

P
of positive slope according to equation (147),
I .. I
kp+kp - k I-kso From.this plot

k g 1.9 x 10‘4, k' : 7. x 10'5

EFFECT OF EXCESS REACTANT
0N KINETICS 0F P-METHOXYSTYRENE AND MALEIC ANHYDRIDE
INTERACTION

 

 

 

 

 

 

 

_i (350mfil)
__:’o
DENSITY(D) [0
VS. TIME (t) ‘7
:10
N
A
\ —+
Sq —:.>
o :t
_1_
0 —-4
\O .._....,1_r_w
\ _.
O _
\O i
—9 \< _,o
m _:.n
11 °"‘
1 I 1I1I1I1I1I1 1MP
¢

D , N 0 q (0

M M
': O . ' Curve 8 ty Anhy -
O O dride
A 0.09 0.010
FIGURE 23
(t) time in hundreds B 0.01 0.090
of seconds Total

Molarity : 0.1

-96-

is being removed from solution.

No matter how high the concentrations of p-methoxy-
styrene used with low anhydride concentration, no dip
in Optical density could be observed.

Figure 23 shows two curves at two extremes of
the reactant concentration ratio: anhydride to p-methoxy-
styrene. No ultimate stabilization of Optical density
could be obtained even with very high p-methoxystyrene
concentrations, in contrast to the p-dimethylamino-
styrene. The divers mixtures studied always gave a
precipitate and always showed increasing absorption.
When precipitation started, a sharp decrease in Optical
density was noted approximately prOportional to the
amount of coagulant. (See arrow in Figure 23).

However, the initial rate of density increase
was significantly slower than the subsequent rate
when the styrene concentration was in excess. Con-
versely, with high concentration of anhydride the
high initial rate of increase was subsequently
lessened.

Interaction with a 1:1 complex may be hypothe-
sized. An initial chemical entity with high
p-methoxystyrene may be postulated as 1:2 on the basis
of the well known alternating tendencies of the
monomers in polymerization. This entity has a lower
extinction than any others that are formed simul-
taneously since the slower the increase in density,

the greater the relative p-methoxystyrene concentration.

However, other entities are simultaneously formed,
as is evidenced by the initial high increase of
absorption with high anhydride. It is reasonable
to postulate that a 2:1 complex of the initially
absorbing material (1:1) with another molecule of
anhydride is formed concomitantly. The subsequent
increased rate of density rise can be attributed to
a series of complex reactions between the various
complexes establishing chromOphores. The precipi-
tation removes these chromOphores from solution and
the density decreases at a rate qualitatively estima-
ted as being pr0portional to the rate of decrease in
observed cptical density.

The immediate interaction with greater anhydride
and its pronounced effect on absorption is indicated

by the asymetry of the continuous variation curves

in Figure 4.

G. CORRELATION OF THE OBSERVED KINETICS WITH STRUCTURE
AND ALTERNATING TENDENCIES IN COPOLYMERIZATION

The kinetics of interaction between p-dimethyl-
aminostyrene and maleic anhydride can be explained on
the basis of instantaneous (1:1) complex formation,
its subsequent reaction with a molecule of the sty-
rene followed by reaction with the anhydride.

Certain substituents (p-dimethylamino and p-methoxy)
result in a distinctive polarity and high resonance

stabilizationla’21

of the 1:1 complex. The complex so
stabilized tends to have subsequent selective reaction
with more of the styrene.

This 1:2 complex is not an observable chromophore
and its paramagnetic properties may be substantially
reduced. The achievement of a constant low optical
density in the p-dimethylaminostyrene case suggests
that the 1:2 complex is the only one present with
residual 1:1. It may be stable and hence isolable.
Reaction of the 1:2 complex with maleic anhydride if
sufficient is present subsequently occurs and is
probably accompanied by other heterogenous reactions
between complexes. Very low molecular weight polymers
were indicated. With p-methoxystyrene, the kinetic
curves indicate that there is a simultaneous inter!
action of 1:1 complex with both anhydride and the
styrene.

The high alternation of p-dimethylaminostyrene

and p-methoxystyrene can now be correlated with

-09-

observed kinetic phenomena. The exceptionally great
alternating tendency observed in their COpOlymers
is consistent with kinetically observed selectivity.
Furthermore, the more complete alternation in the
00polymer of maleic anhydride with p-dimethylamino-
styrene could be predicted on the basis of its
kinetically observed selectivity.

The fact that styrene, p-methylstyrene and
p-chlorostyrene when reacted with maleic anhydride
do not give rise to changing absorption with time
clearly shows that a different mechanism must be postu-
lated for the two groups of styrene in contrast to the

overall theory deveIOped by Mayo et a115,

H. RESULTS OF INFRA RED STUDIES

No clarification in the infra red Spectra of
styrene-maleic anhydride complexes was obtainable
with available equipment. Calculation of complex
extinction values by subtracting the extinction
values of the styrene and anhydride was based on
recorded transmission curves. The error was suf-
ficient to account for most deviations. There is a
slight indication, however, of increased conjugated
aromaticity by a very slight shift in the absorp-
tion maximum corresponding to this prOperty of the

styrene.

~100-

SUMMARY

1. The method of continuous variations proves the
existence of instantaneously formed 1:1 complexes
(substituted styrenes with maleic anhydride) and
indicates additional complexes.

2. Generally applicable theories have been developed
to prove the simultaneous existence and composition
of several complexes in solution when the method of
continuous variations fails.

3. These methods have been applied to the complexes
studied.

4. Constants have been evaluated allowing the
prediction of the optical density of such complexes
at all wave lengths.

5. The existence of true equilibrium and the adherence
to Beer's law for the 1:1 complexes has been demon-
strated. This equilibrium is established instantane-
ously.

6. Comparison of solutions of the same concentration
in the substituted styrene and anhydride to Spectro-
photometrically compare complex stability is not
warranted.

7. The kinetics of the interaction of p-dimethyl-
aminostyrene and p-methoxystyrene with maleic anhy-
dride have been studied and interpreted. It has been
shown that other complexes are formed.

8. The observed kinetics have been correlated with
structure and alternating tendencies in 00polymeri-

zation.

-101-

LITERATURE CITED

 

l. Michaelis,L., Chem. Revs., 16, 243 (1935).

2. Michaelis,L. and Schubert,M.P., Chem. Revs.
'32, 437 (1938).

 

3. Wheland,G.W.i Advanced Organic Chemistry,Chapt.
2' 5' J.Wiley and Sons,N.Y., (1949).

4. Hammick,D.L. and YOung,R.P., J. Chem. Soc.,
1463 (1933)

5. Briegleb,G., Zwischenmolekulare Krafte und
Molekulstruktur, Enke, Stuttgart (1937).

 

 

6. Maatman, R.W., Ph.D.Thesis, Michigan State
College (1950).

7. Bennett,O.M. and Willis,G.H., J. Chem. Soc.,
256 (1929).

8. Bennett,G.M. and Wain,R.L., J.Chem. Soc.,
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9. Buehler,C.A., Hisey,A. and Wood,J.H., J. Am. Chem.
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12. Gibson,R.E. and Loeffler,0.H.. J. Am. Chem. Soc.,

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14. Pauling,L. Proc. Nat'l. Acad. Sci. 25,577 (1939).
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-102-

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-103-

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Adams, Organic Reactions, Vol.1, Chapt.8.
6 Perfiin Reaction and Related
Reactions by John R. Johnson
J. Wiley & Sons, Inc., N.Y. 1942.

BITERIERARY LOAN
MAR 1 1 55

JAN14'57
JUN‘IO '58

 

 

 

CHEMISTRY Hanan!

T54l.34ll
G239 Garrett

293698

 

 

4_s_'__-lc-‘