”fi'fgqu

ABSTRACT

A COMPUTER-INTERFACED SCANNING STOPPED-PLOW
SYSTEM AND ITS APPLICATION TO THE KINETICS

OF AIR-SENSITIVE REACTIONS

By

Nicholas Papadakis

A double-beam, vacuum tight, thermostated stopped-flow
apparatus has been constructed and computer interfaced.
A specially designed all quartz mixing and observation cell,
equipped with a double mixer and two optical path lengths
has been used. The syringes were made out of heavy-walled
precision bore tubing. Steel plungers with adjustable
Teflon tips were machined to fit them. Metal flags mounted
on the stopping plunger provide useful timing pulses by
interrupting two light beams which are detected by photo-
transistors. The entire apparatus was constructed such
that the solutions contact only Pyrex, quartz and Teflon.
A thermostat bath which surrounds the flow system allows
for temperature dependent studies and helps to establish
thermal equilibrium between the solutions and the system

in order to eliminate thermal artifacts. After dispersion

Nicholas Papadakis

with a rapid—scan monochromator, light beams are transmitted
gig quartz fiber optics to the flow cell and reference cell
and then to a pair of photomultipliers. Sample and reference
photocurrents are converted to absorbance by means of opera—
tional amplifiers. The absorbance is sampled and digitized
at a nominal 20.“ KHz rate which is controlled by the rota-
tion of the monochromator mirror with the aid of a phase-
locked loop circuit. Parallel digital transmission is
utilized to send the absorbance signal and the required
control signals to (and from) a remote PDP8-I computer,

with line-drivers and receivers in a "party-line" structure.
A versatile real-time averaging scheme is used to store
complete time-dependent spectra with enhanced signal-to-
noise ratio at long times. Any spectrum or combination of
spectra can be examined on a CRT display terminal. Time
cuts can be displayed at any desired wavelength and then
punched onto computer cards for rigorous data analysis with
a CDC-6500 computer. The system has been tested extensively
by studying a number of well characterized chemical reac—
tions and its performance characteristics are excellent.

The effect of the cation complexing agents dicyclohexyl—
lS-crown-B ("Crown") and H,7,13,16,21,2H-hexaoxa-l,lO-diaza—
bicyclic (8,8,8) hexacosane ("2,2,2 Crypt") upon the rate
of protonation of potassium-anthracenide (K+,An7) with
ethanol (EtOH) in tetrahydrofuran (THF) was examined with

the stopped-flow system. In the absence of complexing agent,

Nicholas Papadakis

pseudo-parallel first and second order reactions were
observed, in agreement with the results of other investi-
gators. The contribution of the second order component
was controlled by the addition of various amounts of the
complexing agents to the K+,An7 solution prior to reaction.
The results obtained, showed conclusively that two contact
ion pairs (K+,An7) are required for the second order process.
The alcohol dependence of the pseudo-first order rate con—
stant (without complexing agent) as computed from the data
at low concentration of K+,An7 (m5 x 10-5 M), was found to
be second order. When "Crown" (C) or "2,2,2 Crypt" (CR)
was added to the solution of K+,An7, a very slow pseudo-
first order process was observed together with the regular
protonation of K+,An7. This slow step was attributed to
the protonation of the species K+C,An7 and K+CR,An7. The
corresponding rate constant was larger for K+C,An7 than for
K+CR,An7 at all the alcohol concentrations used. This was
expected from the presumed difference in charge localiza-
tion caused by the structures of the "Crown" and "2,2,2

Crypt" complexes.

A COMPUTER-INTERFACED SCANNING STOPPED-FLOW
SYSTEM AND ITS APPLICATION TO THE KINETICS

OF AIR-SENSITIVE REACTIONS

By

Nicholas Papadakis

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements

for the degree of

DOCTOR OF PHILOSOPHY

Department of Chemistry

197”

To

Euridici and My Parents

ii

ACKNOWLEDGMENTS

The author wishes to express his special gratitude to
Professor James L. Dye for his guidance, assistance and
encouragement throughout the course of this work.

He would also like to thank Mr. Richard B. Coolen for
his collaboration in the construction and interfacing of
the stopped-flow apparatus and Mr. James Avery for his
assistance in the development of the hardware and software.
Thanks go to professor C. G. Enke for his valuable sugges—
tions on the interface and to Mr. R. E. Teets for his help
with the display software. The helpful suggestions and
criticisms of Professor S. R. Crouch who served as my second
reader are appreciated.

The author also wishes to acknowledge the help of J. M.
Ceraso, M. T. Lok, L. D. Long, E. Mei, and F. J. Tehan.

The cooperation of the MSU glass shop and the Chemistry
Department machine shop is acknowledged. Financial sup-
port from the Atomic Energy Commission is also acknowledged.

Last, but not least, many thanks go to my wife, Euridici,
for her understanding and patience which made attainment of

this goal possible.

iii

TABLE OF CONTENTS

Page
LIST OF TABLES . . . . . . . . . . . . . . viii
LIST OF FIGURES . . . . . . . . . . . . . ix
I. INTRODUCTION . . . . . . . . . . . . . . . 1
II. HISTORICAL . . . . . . . . . . . . . . . . u

II.l. Protonation of Aromatic Radical
Anions in Ethereal Solvents.

II.1.1.The Work of Minnich and Long

II.1.2. The Results of Bank and
Bockrath . . . . . . . . . . . 10

II.1.3. The Work of Szwarc and Co-
workers. . . . . . . .

II.2. Reaction of Sodium-Ethylenediamine

Solutions with Water . . . . . . . 14
II.2.l. The Work of Feldman and
Hansen . . . . . . . . . . . . 1n
11.2.2. The Work of DeBacker . . . . . 16
II.3. The Stopped-flow Apparatus . . . . l7
II.3.l. First Systematic Development by
Chance and Gibson. . . . 18
II.3.2. Commercially Available Instru-
ments. . . . . . . . . . . . . 20
II.3.2.l. Durrum—Gibson Stopped
Flow Spectrophotometer . 20
II.3.2.2. Aminco-Morrow Stopped
Flow Apparatus . . . . . 21
II.3.3. Scanning Stopped-flow System
of Dye and Feldman . . . . . . 21
11.3.4. Thermostated Stopped-flow System
of Dewald and Brooks . . . . . 2H
II.H. Computer-assisted Data Analysis. . 25
III. EXPERIMENTAL. . . . . . . . . . . . . . . 28
III.l. General Techniques. . . . . . . . 28
III.l.l. Glassware Cleaning. . . . . . 28

iv

Page

III.l.2. Vacuum Techniques . . . . . . 29
111.1.3. Metal Purification . .'. . . 29
111.2. Solvent Purification and Solution
Preparation. . . . . . . . . . . 29
III.2.l. Tetrahydrofuran (THF). . . . 29
III.2.2 Ethylenediamine (EDA). . . . 30
III.2.3. Pre-rinsing Techniques . . . 31
III.2.4 Solutions of Sodium in Ethylene-
d1am1ne. . . . . . . . . . . 32
III.2.5. Solution of NH3 in EDA . . . 32
III.2.6. Aromatic Anion Solutions 33
III.2.7. '2,2,2 Crypt: "Crown" and
Alcohol Solutions. . . . . . 33
IV. THE STOPPED-FLOW APPARATUS . . . . . . . 36
IV.1. Introduction. . . . . . . . . . . 36
IV.2. Flow System Design. . . . . . . . 37
IV.2.l. General Description . . . . . 37
IV.2.2. Flow Cell and Reference Cell. 39
IV.2.2.l. Drilling of Quartz. . . 39
IV.2.2.2. Cell Construction . . . Ml
IV.2.2.3. Cell Mounting . . . . . HM
IV.2.3. Pushing and Stopping System . H6
IV.2.3.l. Syringe Design. . . . . #6
IV.2.3.2. Mechanical System and
Framework . . . . . . . H8
IV.2.3.3. Stopping Syringe and
Waste Lines . . . . . 51
IV.2.3.u. Delivery System . . . . 53
IV.2.H. Solution-handling System. . . 6M
IV.3. Optical System Design . . . . . . 66
IV.3.l. Overall Characteristics . . . 56
IV.3.2. Light Sources, Monochromator,
Fibers............ 57
IV.3.3. Detectors . . . . . . . . . . 59
IV.3.u.' Absorbance Circuitry. . . . . 60

IV.H. P

IV.H.1.
IV.#.2.
IV.H.3.

IV.

IV.H.H.

IV.4
IV.H

IV.
IV.

IV.5. U

IV.5.1.
IV.5.2.
IV.5.3.
IV.
IV.

COMPUTER-
PROCESSI

V.l. Ge

V.l.l.
V.l.l.
V.l.l.

V.l.2.

erformance Tests.
Optical Calibration Data

Flow Calibration Data.
Mode . .
Isosbestic Point

Wavelength
.H.l. Dead Time.

.u.2. Mixing Efficiency and
Stopping Time. .

se of the Computer Interface.
General Characteristics.
Solution Requirements.
Calculation Schemes Used

5.3.1. Program ABSTIM

5.3.2. Program KINFIT

ASSISTED DATA ACQUISITION AND

NG. . . . . . . . . .

neral Description

Signal Enhancement in Real Time

1. Maximum Sampling Rate

2. Averaging Scheme.

Control and Timing Signals.

V.2. Hardware.

V.2.l.
V.2.2.
V.2.3.

v.2.u.
v.3. So
v.3.1.

Digital Transmission Lines.
Flag Circuits

Use of the Phase- locked— —1oop
Circuit . . . . .

Overall System.
ftware.

Data Acquisition.

vi

General Performance, Scanning
9.3.1. Clean Stoichiometry and

Flow Cell, Performance, Fixed

u.u.3. Reliability of the System.

u.u.u. Quantitative Measurements.

Page

60
60
65

66
67

75
75

76
78
81
87
87
89
92
92
93

95
95
96
96
98
101
102
102
10”

105
107
108
109

V.3.2. Description of Output Options

VI. RESULTS

VI.1. Dissociation of Na- in Ethylene-
diamine (EDA) - . . . . .

VI.1.l. Equilibrium Studies of the
Effect of Ammonia Addition

VI.1.2. Kinetics Studies

VI.2. Effect of Cation Complexing Agents

Page

Page
113
11H
11”

11H
116

on the Protonation of K+,An7 in THE 120

VI.2.l. Effect of "Crown" on the ESR
Spectrum of Na+,An7 in Di—
ethylether (Et20)-

VI.2.2. Kinetics Studies

VI.2.2.l. Short Path Length Cell
Data (Path Length of

the Optical Cell=2.0mm).

VI.2.2.2. Long Path Length Cell

Data (Path Length of the

Optical Ce11=l.85 cm).

VII. DISCUSSION-
VII.1. Dissociation of Na" in EDA.
VII.2. Effect of "Crown" and "2,2,2

Crypt" on the Protonation of K+,

An7 with EtOH in THF.

VII.2.l. Dependence of the Pseudo—
first Order Rate Constant
(kés) on [EtOH]

VII.2.2. Conclusions
APPENDIX A-
APPENDIX B-
REFERENCES-

vii

120
122

129

130

142
192

luu

150
150

155

158
160

Table

II

III

IV

VI

VII

LIST OF TABLES

Page

Observed pseudo-first order rate

constants and calculated third order

rate constants for the reaction:

Hero; + 211202 + H+ + CrOS + 3H20. . . 82

Effect of the averaging scheme on
the rate constant of a pseudo-first
order reaction. . . . . . . . . . . . 90

Rate constants computed by fitting

the data obtained in the absence

of complexing agent to Equation

(19). . . . . . . . . . . . . . . . . 127

Rate constants computed by fitting

the data obtained in the presence

of complexing agent, to Equations
(21a)-(21d) . . . . . . . . . . . . . 132

Results obtained with low potassium
anthracenide concentration in the
absence of complexing agent . . . . . 136

Results obtained with the long
path length cell in the presence
of "Crown" or "2,2,2 Crypt" . . . . . 139

Summary of the protonation rate
constants for various ion pairs . . . 15u

viii

Figure

LIST OF FIGURES

Page
Vessels used for the preparation
of (a) K+,An7 solutions, (b) all
other solutions 3H

Schematic diagram of the thermostated
stopped-flow apparatus. A - joints for
rinsing solutions, B - joints for re-
actants, C - thermostated burettes,

D - reactant reservoirs, E - mixing

and observation cell, F - reference
cell, G - pushing syringes, H - pneu-
matic pistons, I - stopping syringe,

J - quartz light fibers, K - thermostat
bath, L - to vacuum, M - to vacuum

and "waste", 1, 2, 3, H, 5-flow

valves 38

Set-up for the drilling of quartz
capillaries. A - indexing head, B -

to the airbrasive unit, C - capillary
tube. H0

Schematic diagram of the mixing and
observation cell. A - Fisher-

Porter 2 mm quartz joints, 8 - ~0.5

cm, C - cross-section of a mixer H3

Reference cell and its holder. A -
quartz fiber optics, B — observation
windows. H5

Detailed view of a syringe used in

the stopped-flow system. A — Teflon

tip, B - threaded rod, C - Viton "0"
rings, D - fill position, E - rinse
position, F - locking nut. H7

Timing pulses from the flow—flags.

A - start flag, 8 - flow velocity
profile, C - stop flag, D - location

of the metal flags on the stopping
plunger, E - location of the photo-
transistors, F, G - data collection

can be initiated at one of these

points, H - constant flow velocity

has been reached at this point. 52

ix

Figure

10

11

12

13

1H

15

16

17

Page

Absorbance circuitry. A - variable
gain potentiometer, B - high fre-
quency noise filters, (controlled
with toggle switches). All the major
components are from Philbrick/Nexus
Research.

Holmium oxide spectrum recorded while
scanning at 75 spectra/sec. Solvent
background has not been subtracted

Absorbance from the stopped-flow
system gs absorbance from a CARY

15 spectrophotometer for aqueous
solutions of KMnOu. The line drawn
has a slope of 2.0

Overall spectrall changes for the
formation of peroxychromic acid.
Solvent background has not been
subtracted

Characteristic spectra isolated
from Figure 11. Solvent background
has been subtracted

Time cuts for the formation of peroxy-
chromic acid. A - 35H nm, B - 600
mm, C — H80 nm.

Time cuts for the formation of peroxy-
chromic acid, showing the slow decom-
position process

Time developments during the first
2.1 seconds from Figure 1H

Plots of £n(IA-Aw|) vs time at various
wavelengths for the formation of
peroxychromic acid. [HCrOHJ° = 0.5
mM, [H202]° = n.5u mM EH+J° = 10.u

mM, a,(3, n are decays while ¢, p,

A are growths.

Semilogarithmic plot of [A(tm) -
A(t°)]/[A(tm) - A(t)] vs time for

the dead time computatIEn (concentra-
tions of the solutions: [HCrOE] =

5 mm, [H202] = uu.97 mM, [H+] = 22.5
mM

61

62

SH

68

69

70

72

73

7H

77

Figure Page

18 Decay of the 732 nm peak of K+An7

after mixing with ethanol, showing

the constancy of absorbance during

flow (fixed wavelength technique) 79
19 Growth of the FeSCN2+ complex at

H55 nm for the stopping time esti-

mation 80

20 Decay of HCrOu vs time at 35H nm
after mixing with H202. [H20 1°

u. 5H mM, [HCr0;]° = 0. 5 mM EH+J°
10.0 mM

85

21 Growth of peroxychromic acid X§
time at 600 nm during the reaction
of HCrO' with JHZOZ. A - fixed wave-
length HCrOE¥ = 5.0 mM, [H 021° =
HH. 97 mM, = 22.5 mM. - fixed
wavelength [HCrOfi]° = 1.0 mM, [H202]°
= 9.085 mM, [H+J° = 20. 0 mM. 0 -

Scanning at 75 spectra/sec [HCrO 3°

0. 5 mM, [H202 ]° = u. 5n mM, [H 3°
10.0 mM 86

22 Plots of £n(IAm-AI) vs time at 580
nm and 376 nm for the reaction of
HCrOE and H . A - fixed wave-
length growfh2 at 580 nm, the line
drawn has the computed slope of 5.3
sec'l. B - fixed wavelength decay
at 376 nm, the line drawn has a
slope] of 6.1 sec‘l. In both cases
= 9.085 mM, [H+]° = 20.0 mM,
%Cr0§]° = 1.0 mM 88

23 Block diagram of the computer inter-
faced scanning stopped-flow system 106

2H Flow-chart for the data acquisition
routines 110

25 Time cuts from the dissociation of
Na' in EDA at A — N660 nm and B -
~1000 nm 117

26 Typical computer fit for the decay
of Na' at m660 nm 119

27 Cation complexing agents. (I)
"Crown", (II) "2,2,2 Crypt" 121

xi

Figure Page

28 Effect of "Crown" on the ESR spectrum
of Na+,An7 in Et20 123

29 Time development of the spectrum of
K+,An7 during reaction with 0.083
M EtOH in THE 125

30 Computer fits for the reaction of
K+,An7 with EtOH in THF in the ab-
sence of complexing agent. For all
computer fits x - experimental point,
0 - calculated point, = - experimental
and calculated are the same. 126

31 Computer fits for the reaction of
K+,An7 with EtOH in the presence of
"Crown“ Contribution of K+C,An7 to
the second order protonation 131

32 Representative computer fits for the
reaction of K+,An7 with EtOH in the
presence of various "Crown" concen-
trations 133

33 Representative computer fits for the
reaction of K+,An7 with EtOH in the
presence of various "2,2,2 Crypt"
concentrations 13H

3H Plots of £n(A-Aw) vs time for the
reaction of K+,An7-T05x10'5M) with
EtOH in THF. A - [Et0H1°=0.209M,
the line was drawn with the computed
slope of ~15.7 see-l. B - [Et0H1°=
0.293M, the line was drawn with the
computed slope of ~28.9 sec‘l. C -
[EtOH]°=0.H18M, the line was drawn
with the computed slope of ~65 sec'1 137

35 Representative computer fits for
the reaction of K+,An7 (m5x10‘5M)
with EtOH in the presence of A -
"Crown", B - "2,2,2 Crypt" 1H1

36 Effect of the complexing agent
separated ion pair on the second
order protonation of K+,An7 in THF.
X-experimental points, A - points
calculated from Equation (30), a -
points calculated from Equation (31),
o - points computed from Equations
(21a)-(21d). Note that this is only

xii

Figure

Page

36 Cont. the first 2.3H sec out of 7H.0 sec

37

required for the reaction to go to
completion 1H7

Dependence of the pseudo-first order

rate constant (k's) on [EtOH]. The
drawn line has a slope of 2.12 151

xiii

I. INTRODUCTION

Utilization of the stopped-flow method for the study

(1). The

of chemical reactions has been well established
coupling of a stOpped-flow apparatus with a rapid scanning
spectrometer has produced a very versatile instrument,
developed primarily for the study of chemical reactions.
which involve short-lived intermediates(2’3). Scanning of
the appropriate spectral region can provide information
about the number and types of intermediate species present
as well as the kinetics of the formation and decay of these
species. For studies with very reactive air-sensitive
systems, the stopped-flow apparatus must be evacuable
and constructed such that only quartz, Pyrex and Teflon
come into contact with the reacting solutions.

The advantages of on-line laboratory computers for
high speed data acquisition, rapid data handling or data
processing have been demonstrated for a variety of instru-

<u,s,s,9u>. I

ments in a great number of applications n a

well programmed interactive computer system, the computer
can execute a variety of tedius processing operations

under the continuous guidance of the experimenter. Thus,
the experimenter can impose his experienced judgment and
make important decisions during the data acquisition and

analysis. For routine applications, where the boundary

conditions are well defined, a high degree of automation

is usually desirable<52). However, for research and develop-
ment projects, when the information obtained may be un-
predictable,it is important that the experimenter communi-
cates with the computer and establishes “the best procedure
for data acquisition and processing, such that the informa-
tion necessary for characterizing the system under study

can be obtained.

The purpose of the present research was to:

(1) Develop a rapid scanning, variable temperature,
vacuum tight stopped-flow system for kinetics studies with
air-sensitive systems. Two optical path lengths were
desirable for the apparatus in order to be able to carry
out studies over a wide concentration range.

(2) Interface the stopped-flow system to a remote PDP—
81 computer and write a sophisticated set of computer
routines to collect, average, modify and output the kinetics
data. These routines had to fully utilize the scanning
ability of the instrument and provide sufficient inter-
action between computer and experimenter that important
decisions could be made during the actual experiment.

(3) Extensively test and calibrate the entire system,
utilizing well-studied chemical reactions.

(H) Apply the system to the study of:

(a) The dissociation of sodium anion (Na‘) in ethylene-
diamine (EDA). The results of this work could help us to

better understand the nature of metal-amine solutions.

(b) The effect of the complexing agents dicyclohexyl—
18-Crown-6 ("Crown") and H,7,13,16,2l,2H-hexaoxa-l,10-
diazabicyclic (8,8,8) hexacosane ("2,2,2 Crypt") on the
protonation of potassium anthracenide with ethanol in
tetrahydrofuran. This would further elucidate the important
role of ion-pairs in the protonation of aromatic radical
anions.

Because of the complexity and the size of the project,
the construction and interfacing of the stopped—flow ap-
paratus was carried out in collaboration with Mr. Richard
B. Coolen, who demonstrated the applicability of the
instrument to the study of transients in enzyme kinetics.
His Ph.D. thesis should be consulted for additional informa-

tion.

II. HISTORICAL

Since a large amount of work has been done on each of
the subjects included in this work, it is not feasible to
give a detailed historical development. Instead, only
the necessary information is given to establish a con—
nection between past work and our studies.

This section is divided into four main parts. In
the first two parts recent studies on the protonation of
aromatic radical anions and the reaction of sodium-ethylene-
diamine solutions with water are presented. The develop-
ment of the stopped-flow method to a very important tool
for kinetics studies follows in the third part. Finally,
a brief presentation on the use of on—line computers for

data acquisition and analysis is given in the fourth part.

II.1. Protonation of aromatic radical anions in ethereal

 

solvents
Various techniques have been used to produce aromatic

radical anions in solution and to study their properties

and reactions(7’8). The stopped-flow method has been used

by several investigators for the study of the protonation

of such anions in ethereal solvents(9-15).

II.1.1. The work of Minnich and Long

A scanning stopped-flow apparatus<2)

was employed
by Minnich and Long for their kinetics studies. The radical

u

anions were produced by reduction of the parent hydrocar-
bons with alkali-metals.

Minnich studied the reactions of the radical anions of an-
thracene (An) and terphenyl (Te) with various alcohols (ROH) and
water in tetrahydrofuran (THF) and dimethoxyethane (DME).

The reactions of potassium-anthracenide (K+,An7) with
ethanol (EtOH), methanol (MeOH), t-butanol (t—BuOH),
i-propanol (i-PrOH) and water (H20) in THF, were reported
to be second order in the anion and about half-order in
ROH(7’9). The concentration of An was kept nearly the same
in many experiments and the ROH concentration was varied
within limited ranges. No dependence of the reaction rates
upon the alkoxide (R0-) concentration was found.

For the reactions in DME, similar results were ob-
served, but with lower pseudo-second order rate constants.

In THF, the reactions of sodium-anthracenide (Na+,
An?) with EtOH were similar to those with K+,An7 in the
same solvent. However, the reaction with H20 did not give
consistent results; namely a pseudo-second order decay
was observed in one experiment but a mixed pseudo—first
and -second order decay was found in the other one.

In DME, the reactions of Na+,AnT with EtOH or H O,

2

were found to be slower by a factor of 10 than those of

K+,An7, and moreover the decay of Na+,An7 was first order.
The reaction of potassium-terphenylide with EtOH

in THF appeared to be first order in each reactant.

The above results were consistent with the proposed

general mechanism:

kl
M+,Ar7 + M+,Ar7 fié (M+,Ar7)2 la
+ - k1 + _ + _
(M ,AP')2 + ROH -* M APH + M ,R0 + AP 1b
M+A H“ + ROH 53 A H + M+ R0‘ 1
r fast r 2 ’ C
+ _ k3 . + ._
M ,Ar° + ROH -+ ArH + M ,RO 1d
kn
+ - . + -
M ,Ar' + ArH f + M ArH + Ar 1e
ast

The following general rate law was derived, assuming a

. . + -
steady state concentrat1on for the spec1es (M ,Ar°)2:

2k'
- dEM+,Ar7] _ +
dt ' 1+<kLTkltR0H

 

 

])[M+,An7]2 + k3[R0H][K+,An7]

Under conditions which favor ion-pair formation, the second
order process dominates (equations la, b, c), but where ion-
pairing is not favored, the first order process is observed
(equations 1d, e, c).

At about the same time, Bank and Bockrath report-
ed(11) a pseudo-first order rate law for the protonation
of Na- Napthalenide with H20 in THF. Also, Levin, et

a1.(l3)

had observed a second order decay for sodium-
perylenide in its reaction with various alcohols in

THF. They also found the reaction to be inverse first

order in the perylene (Pe) concentration, which was con-
sistent with the protonation of the ion-paired perylene
dianion (Pe=,2Na+) as the intermediate species.

In order to further investigate the second order
behavior in the protonation reactions, Long and Ceraso
extended Minnich's work. The reaction of K+,An7 with
EtOH in THF was studied over a wide concentration range

of EtOH and An(8’10).

At low EtOH concentrations (<0.01 M)
the rate was found to depend upon the ratio [EtOHJ/[An],
consistent with the formation and subsequent protonation

of the anthracene dianion (An:,2M+). The pseudo-second
order rate constant increased with EtOH concentration,

but became essentially independent of An concentration at
higher concentrations of EtOH. Above an EtOH concentration
of ~0.1 M, a first order contribution to the decay became
apparent. All the above observations were consistent

with the following proposed dianion and ion-cluster mechan-

ism:

H
K k+ _
2(K+,An7 29 (K+,An7)2 I" 2K+,An- + An 2a
k- .
+ = kl + — + —
2K ,An + ROH -+ K AnH + K ,RO 2b
+ .. k2 + .- + ..
(K ,An‘)2 + ROH -+ K AnH + K ,R0 + An 2c

+ _ fast + _
K AnH + ROH -+ AnH2 + K ,RO 2d

+ - k3 , + _

K ,An' + ROH -+ AnH + K ,RO 2e
+ _ fast + -

K ,An' + AnH' -+ K AnH + An 2f

which leads to the general rate law:

 

 

 

 

+ 7 v
- dEKdéAn J = 2k'KQ + 2k2KQIR0H] (K+,An7)2
k2 [An]
1+——
kl [ROH]
L J
+ k3[R0H][K+,An7] 2g

provided that a steady-state concentration of the dianion
is obtained.

At high values of [ROH], the second term dominates in
the second order component and the decay becomes pseudo—
second order in [K+,An7] and first order in [ROH], after
correction for the first order (in[K+,An7]) protonation.
At low [ROH], the second term becomes less important and
the rate expression reverts to that of the dianion mechanism.
An alternative mechanism introduced by Minnich et al.10
was the cation solvation mechanism. According to this
mechanism, potassium ion is solvated by ROH as follows:

K+ + ROH K5 KTROH 3a
+

01‘

K

+ + ROH 3 An7,K‘-‘R0H 3b

An7,K

Substitution of KtROH for the THF—solvated cation in the
contact ion pair with An7 could increase the charge localiza—
tion on the radical anion in the vicinity of the cation.
Whether this leads to an increased rate of formation of the
dianion or to a concerted protonation of the quadruple
ion-cluster is difficult to assess, because rate expressions
derived by using either assumption fit the experimental data
as well as equation (2g). However, the apparent insensitivity
to the nature of the proton donor suggests that a cation-
solvation mechanism may be responsible for the breakdown
of the dianion mechanism at high concentrations of the
proton donor.

The important role played by contact ion pairing in
the protonation of aromatic radical anions was further
tested by Long and Ceraso. They added "Crown" to a solution

(8)

of K+,An7 in THF prior to protonation The "Crown" had been

proven to be a good complexing agent for alkali metal cat-
ions(16). They observed a dramatic effect on the protonation
rate. WheanCrown"] >> IK+,An7] only a slow first order
protonation remained, while when ["Crown"] < [K+,An7], a fast
initial decay followed by a much slower first order decay

was observed. Although the studies with "Crown" were only
preliminary, it was noticed that the first order protona-
tion of the solvent (and/or "Crown") separated ion pairs (in

THF) was “100 times slower than the similar reaction of the

contact ion pairs (in THF).

10

II.1.2. The results of Bank and Bockrath

 

Bank and Bockrath produced sodium naphthalenide (Na+,

Nap7) in THF by reduction of naphthalene (Nap) with metallic

(11)

sodium and studied its reaction with H2O They found

that the reaction followed a pseudo-first order rate law
similar to the one reported by Paul, Lipkin and Weissman<69),

namely:

k

Nap7 + H20 -} NapH' + OH_ Ha
_ k2 -
NapH' + Nap' -+ NapH + Nap Hb
- k3 _
NapH + H20 -+ NapH2 + OH Hc

If a steady-state concentration is assumed for [NapH'],

the following pseudo-first order rate law is derived:

- dENa ‘3 e 2kiENap7]; with k' = klEH20] 5

dt 1
. o _ H -1 -1
At 20 C they computed: kl - 0.01 x 10 M sec .
They also studied the protonation of Na+,An7 with H O

2

(12)

in THF, DME and mixtures of these solvents In this

case the following reaction was used to produce Na+,An7:
+ - 1 + —
Na ,Nap° + An + Na ,An- + Nap 6

Of course appropriate assumptions were made to justify

ll

subsequent protonation of Na+,An7 without significant
interference from the other species present in solution.
The reaction of Na+,An7 with H20 in THF was reported to be
similar to the same reaction of Na+,Nap7, but “200 times
slower. The stopped-flow method was employed in all of
their kinetics work.

The above results do not agree well with the observa-

tions of Szwarc in DME and Minnich et al. in THF.

II.1.3. The work of Szwarc and co-workers
(1H,15)

 

Rainis, Tung and Szwarc , have studied the effect
of cation, alcohol and solvent on the protonation of aromatic
radical anions by the stopped-flow method. Solutions of the
aromatic anions were prepared by reacting the parent hydro-
carbon with the appropriate alkali metal. In most of their
experiments the corresponding alkali metal salt of tetra—
phenylborate was added in excess to the M+,Ar7 solution,
in order to repress the dissociation of M+,Ar7 ion pairs
into the less reactive free Ar7 ions.

The following results were reported: The protonation
of Li+,An7 was first order in [Li+,An7] regardless of solvent
or alcohol used. The protonation of Na+,An7 by MeOH in DME
was also first order in [Na+,An7], while a simultaneous
first and second order reaction was observed in THF. With
the less reactive t-BuOH, the first and second order re-
actions contribute simultaneously to the protonation in DME,

but only the second order reaction was observed in THF.

12

Finally, in the protonation of the least reactive K+,An7

by MeOH, contributions from both first and second order
reactions were seen in both solvents, while only the second
order dependence was observed when t-BuOH was used.

The reaction with Li+,An7 was also found to be first
order in alcohol, with MeOH being more reactive than t-BuOH
and with rates slightly higher in THF than in DME. A
second order alcohol dependence became evident in the
protonation of Na+,An7 with MeOH, while in the K+,An7-

MeOH system the alcohol dependence was purely second order.
When t-BuOH was used, only first order alcohol dependence
was observed. They proposed the following mechanisms in

order to explain the alcohol dependence:

k
(A) M+,An7 + ROH +pm AnH' + M+,RO- 7a
1<
2ROH Q (ROH)2 7b
+ - k d + +
M ,An- + (ROH)2 P» AnH' + R0 ,M ,ROH 70
+ — - +
(B) M ,An' + ROH zAn',M (ROH) 8a
- + . _ +
An-,M (ROH) +AnH + R0 ,M 8b
An7,M+(ROH) + ROH +AnH' + RO-,M+,ROH 8c

It was noted that the first order dependence on t-BuOH

13

would be expected according to mechanism A because the
bulkiness of t-BuOH prevents the reaction (7b) which in-
troduces the second order dependence.

The following mechanism was suggested for the dianion

protonation:
K _ k2
2An-°',M+ #1 (An-,M+; An7,M+) k:
-2
+ - + k3 - +
(An; M ,An’,M ) k2 An + An_,2M
-3
+ +
kpl I ROH] kp2 I ROH] 9

 

 

, v
Protonat1on Products

The contribution of dianions to the protonation, then depends

Dispr : K1K2K3'

The above mechanism is basically identical with the first
(10)

upon the disproportionation constant K
of the mechanisms proposed by Minnich et a1. and there
is a very good qualitative and in many cases quantitative
agreement between the results reported from the two groups.
In summary, the studies presented have demonstrated
the validity of a general mechanism for the protonation

of aromatic anions over a very wide range of conditions

(10) (15)

for one system as well as for several different systems
The pronounced effect of ion pair formation upon the protona-
tion is undeniable. The free ions are the least reactive,
while the reactivity of ion pairs increases with their
tightness, as was demonstrated by the effect of "Crown"

(8).

on the protonation of K+,An7

1H

II.2. Reaction of Sodium-ethylenediamine Solutions With

 

Water

Alkali or alkaline earth metals when dissolved in
liquid ammonia, aliphatic amines and certain ethers, form
metastable blue solutions with no chemical reaction.
These solutions have been the subject of very extensive
study since the first characteristic blue color was ob-

(17). The nature of metal-ammonia

served in 186H by Weyl
solutions is still a subject of controversy. However,
there is general agreement that the optical absorption

band can be attributed to the solvated electron (esolv)

and its loosely-bound aggregates. The optical spectra of
metal-amine solutions are more complicated and their inter-
pretation has been simplified only with the results of the
past few years. The species responsible for the IR-band in
metal-amine solutions are probably the same as in the
metal-ammonia case, while the anionic species M- has been

shown to be responsible for the metal dependent band(18).

II.2.1. The Work of Feldman and Hansen

 

The first direct observation of the hydrated electron

(19)

in 1962 initiated a great deal of work related to the

kinetics of reactionscfi’solvated electrons. The rate

constant for the reaction of the hydrated electron (egq)

with water

e + H

aq 20 *‘H + OH

15

has been found to be 16 M.1 sec-1(2O).

Dewald(21) (22)

and Feldman utilized the stopped-flow
technique in trying to measure the rate of reaction of the
solvated electron with water in ethylenediamine (EDA).

(23)

Feldman extended the work of Dewald et a1. and

found the following: The reaction of cesium with H20 in

EDA gave a rate constant similar to the one reported before<23),
but in many cases showed the presence of a slower pseudo-
first order process. Similar results were found for the
corresponding reactions of rubidium and potassium. The
reaction of sodium with H20 in EDA was found to be first
order in the metal absorbance, but the order in water
varied with the H20 concentration. The lithium-H20 reactions
yielded as many as three pseudo-first-order rate constants.

(2”) used the scanning stopped-flow system

(2)

Hansen
introduced by Dye and Feldman but a better data analysis
process, utilizing a Varian C-102H Computer of Average

)(57).

Transients (CAT He found that the reaction of sodium
with H20 in EDA was second order in water at [H20] greater
than 1M, and the decay of the metal band was nearly first
order. However, the corresponding reactions of potassium,
rubidium and cesium were all apparently first order in

[H20], but the decay of the metal band was not simply first
or second order. All the above results combined with studies
with EDA labelled at the a-position with tritium, convinced

(2H) '

Hansen that the reactions of alkali metals with H20 in

EDA are faster than and proceed via a different mechanism

16

from similar reactions in dilute metal—ammonia solutions.

(2H)

The mechanism proposed by Hansen was consistent with
the observed rates and the existing models for metal-amine
solutions. To describe the sodium abnormality, he suggested

the following mechanism:

 

 

Na‘ + H20 : Na'-H+ + 0H‘ 10a
fast
+ k1 _
Na °H + H20 + Na + OH + H2 10b
which yields:
dEHzl _ k K [Na-JEH2012 10
dt-ll C
[OH‘I
if equilibrium is maintained in (10a). The validity of

(10c) could be tested by observing the effect of sodium

hydroxide (NaOH) on the reaction rate.

11.2.2. The Work of DeBacker:

 

Using the stopped-flow method, DeBacker studied the
effect of NaOH on the reaction of sodium with H20 in EDA<25).
He did not observe any hydroxide effect upon the reaction
rate and found a first order dependence on metal and close
to third order dependence on the H20 concentration. No

simple mechanism could account for these observations and

a shift of the equilibrium

17

_ + -
Na 2 Na + 2e
solv

to the right by the addition of large amounts of H20 was
suggested. Stopped-flow results combined with pulse-
(26)

radiolysis studies indicated that the reaction

Na' + Na+ + 2
solv

might be the rate determining step in the reaction of
sodium with H20 in EDA.

Summarizing, the complicated nature of metal-amine
solutions and their high instability make kinetics studies
difficult. However, it is hoped that the current models
for metal-amine solutions, combined with results such as

those presented here, will help us to better understand

the nature of metal-EDA solutions.

II.3. The Stopped-flow Apparatus

 

Since the earliest kinetics investigation in 1850(27),

a variety of methods have been developed for the study of

chemical reactions in solution, and the range now extends

9 ec(l).

to reactions with half-lives as short as 10- 8 Al-

though the continuous-flow method had been introduced by

Hartridge and Roughton in 1923(28), it was in 19H0 that

(29)

Chance introduced the first systematic development of

the stopped-flow method. Today the stopped-flow method is

widely used because of its simplicity and real time data

presentation The method is, however generally

18

limited to reactions with half-lives of about a millisecond

or longer.

II.3.1. First Systematic Development by Chance and Gibson
In the continuous-flow method, the two reactants are
mixed and the resulting solution flows at a constant velocity
through an observation tube of uniform geometry. The progress

of the reaction can then be monitored by measuring some
property of the system at various points along the observa-
tion tube. At constant flow velocity the extent of reac-
tion will remain constant at any fixed distance from the
point of mixing. Thus a method of rapid detection is not
essential. Of course the efficiency of mixing determines
the time resolution of such an apparatus. Also, the con-
tinuous-flow method requires large volumes (liters) of solu-
tions to obtain one rate curve. In the stopped-flow method,
the reactants are forced through a mixing chamber into an
observation area and the flow is then abruptly stopped. At
the time of stopping, the mixture is only a few milliseconds
old, and the remaining progress of the reaction is monitored.
In this case we need a detection system with very rapid
response because the extent of reaction changes according
to the corresponding rate constant.

By 19H0 adequately rapid methods of observation
were available to permit the first systematic development
and application of a stopped-flow apparatus.

(29)

Chance worked mainly on the development of an

l9

accelerated-flow apparatus, which could also be used for
stopped-flow measurements after the flow had been stopped.

He gives a detailed analysis of all the factors influencing
the performance of the apparatus as well as kinetics data
which illustrate its applicability. Chance's apparatus
utilized two tuberculin type pushing syringes, screwed into

a polystyrene mixer at the end of which the glass observation
tube was sealed. Many mixers of various types were made and
tested for mixing efficiency. A rotary potentiometer attach-
ed by a chain to the sliding pushing block was used to measure
the flow velocity. An appropriately stabilized tungsten
filament lamp was used with the necessary filters for wave-
length selection. The light passing through the observation
tube was detected by a photocell for absorption measurements.
The output was amplified and fed into a cathode ray oscillo—
scope where the record of the kinetics curve was displayed
and photographed. This apparatus was used for accelerated-
flow measurements with times from 0.2 to 10 milliseconds and
for stopped-flow measurements with times greater than 30 milli-
seconds and up to 60 seconds (30 msec was the time required
for the solutions to leave the mixing chamber and stop at

the observation point - dead time). Very efficient mixing
was reported with no cavitation phenomena. Even though this
stopped-flow apparatus had a large dead volume, it had a
major advantage over the continuous-flow method; namely,

the much smaller volumes of reactants required for a set

20

of measurements. In 1951(37)

Chance introduced a new stopped—
flow apparatus with a dead time of “I20 milliseconds.
The stopped-flow method owes its wide adoption to

the stopping device introduced by Gibson<38).

A small piston
at the end of the observation tube is pushed along by the
reaction mixture, and is suddenly stopped by coming against

a seat or an external stop. This simple arrangement was
found to be extremely effective, with stopping times of 1-2
msec, resulting in dead times of m3-5 msec. The apparatus

(33)

used by Gibson has been the prototype of most of the

stopped-flow systems now in existence.

II.3.2. Commercially Available Instruments

 

II.3.2.l. Durrum-Gibson Stopped Flow Spectrophotometer
(33)

 

has
(H0)

The instrument initially developed by Gibson
been manufactured by Durrum Instrument Corp. since 1966
A large number of improvements and options have been added
to the originally manufactured instrument and have made it
an easy to operate, versatile and reliable apparatus. The
entire block containing the reservoir syringes and the flow
system can be thermostated by circulating a constant tempera-
ture liquid through the appropriate channels. Some problems
with studies at other than ambient temperatures have been
reported<u2). The horizontal position of the flow system

can cause bubble problems; studies regarding this problem

together with cavitation artifacts have been carried out in a

21

similar apparatus and in the flow rate range of 5—10 m/sec(39).

Even though it has been used for studies with air-sensitive

(11,1H)

systems , its applicability to very reactive unstable

chemical systems is questionable. The instrument has been
used widely in biochemical studies, where two of the offered

(H0)

options (Fluorescence measurements , and multi-mixing

system("l)) are very useful.

11.3.2.2. Aminco-Morrow Stopped-flow Apparatus
(36)

 

Developed by J. I. Morrow and manufactured by

American Instruments Company since 1971(H3)

, this apparatus
employs a solution delivering arrangement (which connects
the reservoir and drive syringes) which minimizes bubble
problems and allows solutions to be easily changed. The
reacting solutions contact only KEL-F, Teflon and quartz,
and the observation cell offers two path lengths for following
absorption changes of the reacting mixture. (However, no
performance data for the short path length have been pub-
lished).

From the reported performance characteristics the
apparatus seems to be very good for biochemical applications,

but its applicability to very reactive, air-sensitive systems

is also questionable.

II.3.3. Scanning St0pped-flow System of Dye and Feldman
Rapid scanning spectroscopy is a technique in which a
selected region of the electromagnetic spectrum is scanned

on a time scale ranging from several seconds down to a few

22

microseconds. The advantages to be gained from such a
technique (especially for the study of chemical reactions
which involve short-lived intermediates) have led to the
development of several rapid scanning spectrometers(Hu-u7).
Earlier studies of the kinetics of electron attachment
reactions in ethylenediamine by the stopped-flow method
convinced Dye and Feldman that due to the complexity of
metal-amine solutions (overlapping of various absorption
bands) a rapid scanning spectrometer was necessary in order

(2).

to obtain clean kinetics data They used a Perkin-

Elmer model 108 rapid scan monochromator coupled with a
home built stopped-flow apparatus. The entire flow system
was evacuable and all the manipulations could be carried
out in the absence of air. Thermostated burettes were used
for making dilutions into a thermostated storage vessel.

The pushing syringes could also be thermostated by circulat—
ing a constant temperature liquid through the appropriate
plastic jackets. The entire flow system was vertical in
order to eliminate bubbles. The mixing chamber and observa-
tion cell was constructed from precision bore heavy walled

capillary by a Very elaborate procedure(2’22)

, and was shown
to perform satisfactorily.

The scanning monochromator could in principle (with
the appropriate prism) scan a selected spectral region

between 0.2 and 10 Um, with from 3 to 150 scans per second.

External controls permitted selection both of the interval

23

to be scanned and the center of scan. The spectral scan

was produced by a modified double pass Littrow system with

a rotating tilted mirror. The light after leaving the mono-
chromator impinged on a beam splitter from a BausCh 8 Lomb
Spectronic 505 spectrometer. The parallel beams from the
splitter were focussed with spherical mirrors onto the
center of the flow cell and a reference cell and then were
directed to two photomultiplier tubes. The anode currents,
which were balanced as well as possible over the region of
interest, were then input to a logarithmic amplifier circuit.
This circuit gave an output voltage which was directly propor-
tional to the logarithm of the ratio of the current from

the reference phototube to that from the sample, and hence
to the absorbance of the sample.

During a run, all pertinent data were stored on magnetic
tape by utilizing an Ampex SP-300 FM direct recorder/repro-
ducer. A synchronization signal from the monochromator was
also stored in one of the recorder channels. The recorded
information was played back into a Tektronix type 56H storage
oscilloscope with the time base triggered by the channel
which contained the synchronization signal (which indicated
the beginning of each revolution). The data on the scope
were then photographed, using a Polaroid camera, and the
resulting transparencies were magnified with a photographic
enlarger and traced on graph paper. The greased glass
syringes and stopcocks of the flow system introduced many

difficulties because of the slow attack upon the silicone

21+

grease by the metal—amine solutions. This problem was solved

later(7,2H,25)

by using syringe plungers with Teflon tips,
Fisher-porter "solv-seal" joints and various types of valves
with Teflon stopcocks. Also the data analysis procedure was
modified by introducing the use of a Varian C-102H Computer
of Average Transients (CAT)(2u). In this way, the data
could be read from the tape recorder onto graph paper in
analog form for display purpose, and onto computer cards

in digital form for the purpose of rigorous analysis. This
system has been used successfully for various kinetics

studies(7’8’2u’25).

II.3.H. Thermostated Stopped-flow System of Dewald and

 

Brooks
In order to increase the temperature range over which
reactions could be studied by the stopped-flow technique,

Allen et al.(u8)

had constructed a stainless steel apparatus,
capable of operating at —120° C. However, stainless steel

is not compatible with a number of reactive systems such as
metal-ammonia solutions.

To adapt the flow method for use with very reactive
chemical systems at low temperatures, Dewald and Brooks
constructed an all-Pyrex thermostated system capable
of operating from -H0° C to above room temperature<3u).
The system could be evacuated and all the manipulations
were carried out in vacuum and at low temperatures.

The entire flow system as well as the storage vessels were

surrounded by a Plexiglass thermostated bath. Three-way

25

greased stepcocks were used to connect the pushing syringes
to the mixing chamber and reactant reservoirs. Three-turn
spirals of 2 mm tubing were used to connect the mixing chamber
with the stopcocks. These spirals were found to be necessary
to prevent breakage of the glass when the apparatus was
cooled, probably because of the difference in the coefficients
of thermal expansion of the metal frame (on which the entire
glass assembly was mounted) and the glass. Light wires
(BauschiiLomb 321306) were used to transmit the light through
the bath fluid to the observation tube and then to the photo-
tube. The system has been used successfully in the study of
electron attachment reactions in liquid ammonia solutions at
N -35° c(”9).
In summary, the stopped-flow technique has been used
for kinetics studies with a variety of systems. A great
number of instruments have been constructed and successfully
used. The coupling of such an apparatus with a rapid scann-
ing spectrometer has produced a very efficient system, which

has proven to be of great importance for the study of reactions

involving transient intermediates.

II.H. Computer-assisted Data Analysis

 

It appears that it was in the middle 1960's when
scientists first realized that computer handling of experi-
mental data would soon be an absolute necessity, because of
the large amounts of raw data being generated by modern

instrumental techniques. The earliest solutions to these

26

problems involved the construction of off-line (data process—
ing with no real-time requirements) data acquisition (in
digital or analog form) and data-logging hardware<50).
Even though the off-line computer-assisted data analysis
was much better than prior methods, it still was frustrating
for the researcher who could turn out mountains of data in
minutes, but then had to wait as long as a few days to analyze
the results of these experiments. It then became obvious
that a more direct line of communication between the experi-
ment and the computer was necessary. The earliest extensive
use of on-line (direct coupling of computer and instrument)
computers was in the field of nuclear chemistry(51). These
first types of laboratory computer applications were passive
- no significant computer control of the experiment. Today
active on-line computer systems (the computer is involved
to some significant extent in the control of the experiment)
can be found in many chemistry laboratories, especially the
ones for analytical applications.

Of course, calculation problems in theoretical chemistry
as well as in reaction kinetics and spectroscopy, may still
require off-line computers with large core memory, but the
data acquisition can be carried out much more efficiently
with on-line laboratory computers. The number of published
applications of small laboratory computers is increasing very
rapidly. Small dedicated systems (one instrument per com-

(H,6,539H)

puter) for a variety of instruments up to complex

satellite systems (large computer, H8K; several small

27

computers; extensive periphery)(5)

have been reported to
be used in chemical and biochemical laboratories. It is
in clinical routine analyses that automation has almost
reached the ultimate; the operator just starts the system
and provides the appropriate samples(52).
Recent advances in integrated circuit technology have
made it possible to manufacture minicomputer systems which
possess tremendous real-time data acquisition and control
capabilities(su). Unfortunately the task of connecting or
interfacing the computer to a particular instrument or to
a set of instruments is still a problem. One might consider
it irrelevant whether a card reader, a magnetic tape or an
analytical instrument (commonly via an Analog-to-Digital
converter) were connected to the computer. However, whereas
conventional devices such as card readers and magnetic tapes
transmit data to the computer according to the needs of the
appropriate program, the data from an analytical instrument
must be taken by the computer at times which are determined
by the on-line experiment (real-time data acquisition).
A day-by-day increasing number of basic commercially avail-

able elements,make the interfacing barrier surmountab1e(su).

III. EXPERIMENTAL

1II.l. General Techniques

III.l.l. Glassware Cleaning
All glassware was first cleaned with an HF cleaning

solution (33% HNO 5% HP, 2% acid soluble detergent, 60%

3,
water) followed by thorough rinsing with distilled water.

The item was then filled with boiling aqua regia, which

was allowed to remain in it for at least 10 hours. After
rinsing six times with distilled water and six times with
conductance water, the glassware was dried in an oven (110°
C) overnight.

All the parts of the stopped-flow apparatus were cleaned
in the same way before assembling the system. Prior to each
run, the entire system was washed by allowing boiling aqua
regia to remain in it for NE hours and then rinsing it with
distilled and conductance water until no change of pH of
the water could be detected. The system was dried by
evacuation. All the glassware destined to be used in the
kinetics experiments as well as the stopped-flow apparatus

was again rinsed after the above cleaning procedure, as

described in Section III.2.3.

28

29

III.l.2. Vacuum Techniques

 

All of our work was carried out with standard high
vacuum techniques. The vacuum lines were evacuated by
using dual-stage mechanical pumps and two stage oil diffusion
pumps, with Dow Corning 70H diffusion pump fluid. Liquid
nitrogen cooled traps were positioned between the vacuum
line and the diffusion pump. Pressure measurements were
made with a Veeco RG75P glass ionization tube and a Veeco
RGLL6 or a Granville-Phillips 260-001 gauge controller.
Greaseless Teflon valves (Fisher-Porter, Delmar, Kontes
and Rotaflo types) some of which were specially modified

(55)

for high vacuum work , were extensively used.

III.l.3. Metal Purification
Alkali metals were purchased as follows:
Na : J. T. Baker Co. (99.99%)
K : J. T. Baker Co. (99.99%)

The metals were distilled several times prior to actual
use.

The technique used for preparing and storing small
quantities of these metals in small tubes has been given

elsewhere<18).

III.2. Solvent Purification and Solution Preparation

III.2.l. Tetrahydrofuran (THF)

 

"Distilledin Glass" type THF was purchased from Burdick

and Jackson. About 3 liters of THF were poured into a large

30

glass vessel containing mlO grams of purified grade CaH2
(from Fisher scientific company). The vessel was then cooled
with an ice bath and the solvent was thoroughly degassed by
pumping through a liquid nitrogen cooled trap. A Teflon-
coated magnet in the vessel was used to stir the mixture
for several days and then the degassing procedure was re-
peated. The THF was then vacuum distilled into a flask
containing m6 grams of benzOphenone (Eastman-Kodak Company)
and an excess of sodium-potassium alloy (1:3). A dry-ice
isopropanol bath was used to help the distillation, while
the vessel with THF over CaH2 was kept at room temperature.
The excess of Na—K alloy was necessary in order to make
sure that only the non-volatile benzophenone ketyl and not
benzophenone was left. The formation of benzophenone

ketyl resulted in a dark purple solution. Because of its
reactivity with water, the benzophenone ketyl served both
as a drying agent and as an indicator of dryness. This
purple solution was stable for months at room temperature.
The solvent used for the experiments was vacuum distilled

from such purple solutions.

III.2.2. Ethylenediamine (EDA)

 

EDA of 99% stated purity was obtained as a gift from
the Dow Chemical Co. After a freeze purification step(25),
the solvent was transferred under vacuum into small bottles
(«300 ml at a time) through a medium porosity glass fPit

There EDA was degassed by successive freeze-pump—thaw cycles

31

until the pressure change between two successive cycles

was ‘2 x 10-6 torr. The solvent was then transferred in
the same way as above, into vessels containing Na-K alloy
(1:3), which were kept in a dry-ice isopropanol bath. A
very dark blue solution was formed as soon as the solvent
was brought to room temperature. After keeping the solvent
over the alloy for N1 week, the desired amounts of EDA
were vacuum distilled into the appropriate bottles for

preparing the required solutions.

III.2.3. Pre-rinsing Techniques

 

All the vessels destined to be used for solution prepa-
ration as well as the solvent bottles were pre-rinsed with

(8). The bottles

a solution of potassium-anthracenide in THF
used in the study of the reaction of Na- in EDA were further
dried by distilling liquid ammonia from a storage vessel

into them 3 or H times(2u’25).

The vessels were then pumped
to ‘2 x 10"6 torr and used as required.

Before all the runs (except the first one with Na-EDA
solutions) the stopped-flow apparatus was evacuated (pres-

H torr) and then rinsed with a dilute solution

sure <1 x 10-
of K-anthracenide in THF ([K+,An7] m'lO-QM) as follows:

The entire flow system as well as the storage vessels and
the thermostated burettes were filled with the rinsing solu-
tion and allowed to sit for N20 minutes. After that, the

system was rinsed thoroughly with THF and pumped to

p‘ l x 10'“ torr, through liquid nitrogen cooled traps,

32

before being used. This rinsing proved to be very helpful,
because we did not detect any decomposition of our solutions

while filling the system.

III.2.H. Solutions of Sodium in Ethylenediamine

 

Solutions of Na in EDA were prepared in vessels similar
to the ones used for the K+,An7 solutions (Figure la),
but without the glass frit and the side arm for the anthra-
cene. Sodium was distilled into the bottles through the ap-
propriate side arm (after the bottle had been pumped to
NS x 10'"6 torr), then EDA was vacuum distilled into the
non-metal side of the vessel using a dry-ice isopropanol
bath. After bringing the vessel to room temperature, a
small amount of EDA was transferred over the metal and a dark
blue solution was formed. This blue solution was then mixed
with the rest of the solvent without any detectable decom-
position. This step was repeated until it was judged that
the absorption of the solution was appropriate for our
kinetics studies. Solutions made in this way were stable

at room temperatures for «12 hours.

III.2.5. Solution of NH in EDA

3
Ammonia (Baker Chemical Co.) was distilled onto Na-K

 

alloy yielding a blue solution. After several days of
freeze-pump-thaw cycles, it was stored over Na—K alloy at
liquid nitrogen temperature. The desired amount of NH3 was
vacuum distilled from the storage vessel into a preweighed

33

heavy-walled bottle and after its exact weight had been
determined, it was distilled into another heavy-walled

vessel with a known amount of EDA.

III.2.6. Aromatic Anion Solutions

 

Solutions of K-anthracenide in THF were prepared in
vessels such as those shown in Figure 1a. The procedure was
nearly the same as for sodium solutions in EDA. The only
difference was that the break-seal containing a known amount
of anthracene was broken by a Teflon enclosed magnet and the
anthracene was dissolved in THF just before the formation
of the blue solution. PAR grade anthracene from Princeton
Organics was used without further purification and enclosed

<e>_

in the break-seal as described elsewhere From the weight
of the bottle empty and with solvent, the amount of THF
used was determined. Solutions made in this way were stable

with no detectable change in absorbance for days at room

temperatures.

III.2.7. "2,2,2 Crypt", "Crown" and Alcohol Solutions

(56) and "Crown" from E. I.

Zone-refined "2,2,2 Crypt"
duPontckaNemours 8 Co. were used without further purifica-
tion. Weighed amounts of "Crown" (or "2,2,2 Crypt") were put
into preweighed glass tubes which had a break-seal on one
end and a 5 mm Fisher-Porter joint on the other. The tubes
were then connected to the vacuum line via the 5 mm joints
and pumped to 05 x 10'6 torr. After that, anhydrous ammonia

was condensed onto them and distilled away several times to

3H

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35

complete the drying process. Pumping was continued for
N2 days after the NH3 condensation, and then the tubes were
sealed off under vacuum, weighed and attached to the ap-
propriate bottles (Figure 1b).

Spectral grade ethanol (Gold Shield grade from Commercial
Solvents Corporation) was further purified by distillation
over a sodium mirror followed by degassing through freeze-

(8). Pure alcohol was then distilled into

pump-thaw cycles
a preweighed glass tube with a breakseal in one end. This
tube had been dried by condensing anhydrous NH3 into it
several times, followed by pumping for N2 days. The alcohol
was then frozen in the tube with liquid nitrogen, pumped to

5

W2 x 10- torr, sealed off, weighed and connected to the

solution make up bottle (Figure lb).

After rinsing (Section III.2.3), solvent distillation
and solution preparation were carried out as described else-
where(8).

All the solutions were pressurized with m0.5 atm of

(8)

appropriately purified helium gas , before being con-

nected to the stopped-flow apparatus.

IV. THE STOPPED-FLOW APPARATUS

IV.1. Introduction

 

Since the initial measurement of the rate of reaction

of the solvated electron (e—

solv ) With water 1n ethylene-
(23)

diamine , Dye and co-workers have continued to work on
the development and improvement of stopped-flow systems for
work with very reactive air-sensitive solutions. Three
major improvements were, the incorporation of a scanning
monochromator which permits the entire spectrum to be

(2)

examined during reaction , the development of all-quartz

mixing and observation chambers by the use of an air—

(2H)

brasive drilling unit , and the acquisition of data with

an FM tape recorder for subsequent analysis by computer<2u’25’57).
However, the kinetics studies were still limited by the neces-
sity to work at or near room temperature and by analog
storage of the data. Also another major disadvantage was
the inability to analyze data rapidly during a particular
experiment so that important decisions could be made and
conditions modified if required.

A major effort has been made during the last three years
to develop a variable temperature, vacuum-tight, stopped-
flow system which is on-line with a remote PDP—BI computer.
An appropriately planned averaging scheme could increase
substantially the signal-to-noise ratio, especially in the

"tail" of a reaction and thus increase the sensitivity of

36

37

the instrument. At the same time, two easily interchange-
able path lengths were desirable for the stopped-flow appa-
ratus, such that a much wider concentration range could be
studied. Finally, the system had to be constructed not only
for use with reactive systems but also for the study of

transient state enzyme-kinetics(58).

IV.2. Flow System Design

 

A schematic diagram of the system is shown in Figure

2.

IV.2.l. General Description

 

Because of the nature of the solutions, the flow
apparatus had to be constructed such that only quartz,
Pyrex and Teflon come into contact with the reacting systems,
and the entire system could be evacuated. Also temperature
insensitive seals had to be made, to permit variable tempera-
ture studies. This introduces a major problem because the
Teflon seals had to be adjustable in order to maintain a
vacuum at temperatures below about 10° C. Since temperature

(SQ’HZ) the thermostat

artifacts are common with flow systems
bath was constructed to include the entire flow apparatus
in order to keep the reacting solutions at the same tempera-
ture as the flow system. A reference cell which could be

filled easily with any solution was necessary since we

wished to utilize double-beam operation.

Figure 2.

38

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I a
C C

| H
L.

5 I.

J‘HEI E J
0 HT, 0 F
3 I 2 : 4 M
‘ ll G G ll r K

 

 

 

 

 

 

 

III * I.
I H F"
1

Schematic diagram of the thermostated stopped-flow
apparatus. A - Joints for rinsing solutions, B -
Joints for reactants, C - thermostated burettes,

D - reactant reservoirs, E - mixing and observation
cell, F - reference cell, G — pushing syringes,

H - pneumatic pistons, I - stopping syringe,

J - quartz light fibers, K - thermostat bath, L -
to vacuum, M - to vacuum and "waste", 1, 2, 3, H,
5-flow valves.

 

 

 

 

39

IV.2.2. Flow Cell and Reference Cell

 

IV.2.2.l. Drilling onguartz

 

The earlier mixing cells were constructed from Plexi-
glas, and the observation tube with the in-coming lines was

sealed to it by using epoxy resin(21).

Since this mixing
chamber was attacked by the solutions, an all Pyrex mixing
and observation cell was constructed by a very elaborate

(2,22)

technique Also, all quartz cells were made by the

(22) (2H)

same technique , but their cost was very high. Hansen
describes a better way to construct quartz cells which utilizes
Airbrasive drilling of heavy-walled 1 mm i.d. quartz capil-
laries. The performance of cells constructed in this way
has proven to be very good(7’8’10’25).
In constructing the cells we followed the method des-
cribed by Hansen, with some modifications, which were neces-
sary because of the complexity of our cells. The starting
materials were 7.7 cm lengths of heavy-walled 1 or 2 mm i.d.
quartz capillaries (purchased from Engelhard Industries, Inc.,
Amersil Quartz Division, Hillside, N.J., at the price of $2-3/ft
for tubing selected to be close to l or 2 mm, or $25/ft for
tubes exactly 1.0 mm i.d.). These lengths of capillaries
were polished flat on two opposite sides (by Precision Glass
Products Co., Oreland, PA). ‘The drilling of the inlets and
outlets was accomplished by utilizing an Airbrasive unit

(8. S. White Industrial Division, New York, NY, a model C

unit was used with No. 1 Airbrasive powder). This instrument

H0

 

Figure 3. Set-up for the drilling of quartz capillaries.
A - indexing head, B - to the airbrasive unit,
C - capillary tube.

01

outputs a high speed stream of nitrogen gas, which contains
finely divided aluminum oxide (or another powder) and may
be used to drill holes of the desired shape and size (this
depends upon the nozzle tip used and the distance of the

tip from the item to be drilled<60)

). The capillaries were
mounted on a horizontal drilling table utilizing an indexing
head for very accurate positioning. The drilling set-up

is shown in Figure 3.

IV.2.2.2. Cell Construction

 

IV.2.2.2.1. Drilling

 

In order to achieve more complete mixing, we wanted to
divide the solution into four streams after initial mixing
and then mix them again. This had to be accomplished with
a very little increase in dead volume. Also we wanted two
path lengths for each cell.

To accomplish this, first the capillary for the double
mixer was drilled as follows. A 0.5 cm quartz rod was
inserted and sealed into the central bore about one cm
from one end. Then, using the device described above
(Section IV.2.2.l), the four inlet holes were drilled,
entering the central bore of the capillary almost tan-
gentially and at an angle of about 105° to it. The
capillary was rotated 90° between successive holes,
until all four holes had been drilled. To prevent un-
wanted drilling of the capillary wall opposite the hole
being drilled, a piece of polyethylene medical tubing was in-

serted in the central bore of the capillary tube. By using the

H2

appropriate nozzle tip and positioning it at the proper
distance from the tube, we were able to drill holes which
were slightly tapered from the outside surface of the
capillary to the central bore. The entrance diameters were
just under half the bore diameter. At a distance of one cm
above these inlets, four similar holes were drilled at an
angle of ”135° to the central bore, and 0.5 cm lower (also
0.5 cm from the inlets) four more holes were drilled at an
angle of mH5° (see Figure H). To enlarge these holes to
an entrance diameter equal to half the bore diameter, we
used an appropriate diameter tungsten rod coated with a
mixture of water and Airbrasive powder in a drill press.
For the long path length optical cell, another capil-
lary was utilized. 0n the two flat sides of this capillary
two parallel holes were drilled at an angle of m135°. The
entrance diameters of these holes were equal to the bore

diameter and at the desired distance apart (W1 or W2 cm).

IV.2.2.2.2. GlassblOWing(61)

 

The capillaries drilled as above were then cut to
the appropriate lengths (Figure H). The mixer was finished
by attaching the vacuum joints (Fisher-Porter 2 mm "solv-
seal" quartz joints) and sealing the unwanted holes with
appropriately ground quartz rods. The capillary destined
to form the long path length cell was then connected to
the mixer with the top joint as shown in Figure H. Finally,

the two ends of the long path length were ground such that

H3

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the two parallel holes were just uncovered and then two
flat optical windows were sealed on. These windows were
cut from transparent fused quartz cover slips of m0.2 mm
thickness (purchased from Thermal American Fused Quartz,
Montvill, N.J.). Also, thicker windows were used, but they

had to be ground and polished after being sealed on.

IV.2.2.2.3. Description of the Reference Cell
The reference cell was constructed the same way as the
sample cell but, of course, without the mixer (see Figure 5).
We have constructed sample and reference cells from
1 mm (long path length is m1 cm) as well as 2 mm capil-
lary tubing (long path length is m2 cm). The latter was
used more extensively, because it had better optical charac-

teristics with the weak light sources used initially.

IV.2.2.3. Cell Mounting

 

Individual holders were machined from stock-aluminum
for each of the cells. Each holder consists of four
separate pieces which fit around the cell, as closely as
possible, and are held together by six screws (see, for
example, Figure 5). To make_sure that the cell did not
move inside the holder we wrapped it with Teflon tape.
The holder has openings into which the light fibers fit.
Each opening has a light window of the appropriate size
at the cell end. The light windows are round (1 or 2 mm

in diameter) for the long path lengths and rectangular

H5

I
8
l
l
I
I
I
I
I
I
I
.
b
u
-
o

“...-..--.-.-.
an...
. an.

 

Figure 5. Reference cell and its holder. A — quartz fiber
optics, B - observation windows.

H6

(0.5 x 2 or 1 x 2 mm) for the short path lengths. The
short path length is located ml mm above the second mixer.
With this set-up we have been able to obtain very efficient

mixing as well as good light transmission.
IV.2.3. Pushing and Stopping System

IV.2.3.1. Syringe Design

Glass syringes, lubricated with Dow-Corning silicone

(21’22), but caused many problems

(2H)

grease, were used previously
because the metal solutions attacked the silicone grease
Greaseless plungers were then made by mounting Teflon tips

on plungers from Hamilton glass syringes. The tips had been
machined appropriately to insure a vacuum tight liquid sea1(2u).
Uranium glass was used to seal these Hamilton "gas tight"

syringes to Pyrex joints. A side arm was introduced later
with a new type plunger to eliminate the problem of the high

(7,25)

permeability of Teflon to oxygen Even better results

were obtained by making special syringes with precision bore

(8’25) and similar plungers.

tubing
We have modified this last technique in making our

syringe and plungers, in order to permit compensation for

changes in the dimensions of Teflon with temperature (see

Figure 6). The syringes were made out of heavy-walled

precision bore tubing (Trubore 8700-765, I.D. = 0.553",

ACE Glass Inc., Vineland NJ) and the plungers were machined

to fit these syringes. They are vacuum tight down to -30° C

(tested), and have solved the recurring problems associated

H7

 

.. /

H/ C\t

 

I
I
A
U

 

To vacuum
and “we ste"

45—6

1

 

é———Stee| Plunger

 

 

 

'LZIIZLTJIZZ’E

;_J_

‘1“
J

 

 

 

 

 

 

Figure 6. Detailed view of a syringe used in the stopped-
flow system. A - Teflon tip, B - threaded rod,
C - Viton "0" rings, D - fill position, E - rinse
position, F - locking nut.

H8

with leaky syringes. The Teflon seals are forced against
the glass walls by Viton "0" rings held under compression.
To further insure against leakage, the Teflon wipers can

be pulled down by the adjusting threaded rod, thus maintain-
ing a good vacuum seal. By using the side-arm for back
pumping, we insure that the section between the Teflon
wiper and the second "0" ring is constantly evacuated during
the motion of the plungers.

An operation which wastes solution in many stopped-
flow systems is that required to rinse the previous solution
from the syringe and to introduce a new solution of known
composition. We use the back-pumping side-arms of the
syringes as exit ports for the purpose of rinsing the system
prior to re-filling. Special care was taken in drilling
a small hole on the glass wall (utilizing the Airbrasive
unit; Section IV.2.2.l) and sealing the side arm, such that
the barrel is not distorted and a good seal is maintained,
even when the Teflon wiper is lowered to the rinsing posi-

tion.

IV.2.3.2. Mechanical System and Framework

The flow system was mounted on a framework of suitably
machined aluminum plates, which were bolted in place to
four threaded rods (3/8"). One of the plates was bolted to
a sturdy angle iron table. Onithe same table were mounted
the monochromator, the lamp and the detectors. As can be

seen in Figure 2, the flow system is mounted vertically.

H9

This position eliminates bubble formation, but it can cause

back diffusion problems as described in a later section.
The plungers of the pushing syringes were bolted to

an aluminum block, which has the appropriate holes to allow

easy adjustment of the Teflon tips. This block was then

(62)

connected to a pneumatic piston via a threaded rod passing
through an aluminum plate. The plate was used for stopping
the plungers when they were lowered to the rinsing position,
while small aluminum blocks were inserted between the
pushing block and the plate in order to stop the plungers
at the filling position.

The pneumatic piston could be operated manually (with
a H-way, 3—position valve<62)) or automatically by utilizing

solenoid operated valves(62).

Usually we fill the syringes
by using the manually actuated valves and then have the
scanning monochromator control signals (beginning of scan
pulses) trigger the pushing operation by setting the ap-
propriate logic gate to "1" when we are ready. In this
way, we synchronize the scanning monochromator with the
stopped-flow apparatus. When fixed wavelength experiments
were performed, the pushing was actuated manually (a minor
modification could be introduced to allow for automatic
pushing when the monochromator is not scanning).

A miniature pneumatic cylinder operated with a manual
valve was used to expel the waste solution from the stopping

syringe. All of these operations could be easily computer

controlled if the manually operated flow valves were replaced

50

with solenoid operated ones (see Section IV.H.H.3).

The thermostat bath, which surrounds the entire flow
system (see Figure 2), was constructed from 3/8" Plexiglas
sheets (Plexiglas gives good visibility and insulating

characteristics<3u>

). Three bath walls were permanently
sealed to the bottom piece, while the fourth one was mounted
on with screws, such that it could be taken off easily.
Also, part of another wall could be removed to allow work

to be done in the bath. The flow valves were mounted on

one of the permanent bath walls and utilized small Plexiglas
blocks, which were fit firmly around each valve (with the
appropriate length of Teflon tape) and then connected to

the wall with screws. This way of mounting has proven to

be very efficient and allows for removal of the valves

when necessary.

The pushing syringes pass through the bottom Plexiglas
piece together with their side-arms. The syringes were
mounted on an aluminum plate which was forced against the
bath with an "O" ring in order to make a liquid-tight seal.
Having the side-arms coming out through the syringe mounting
plate allows for easy replacement of the syringes.

Holes were drilled in the Plexiglas walls for the
fibers and the waste lines. Dow Corning 3110 RTV encapsulat—
ing compound was used as required to make liquid-tight seals.

Two air-driven magnetic stirrers (Arthur H. Thomas
Company, 8612-850) were used in the bath to mix the solu-

tions in the reservoir vessels.

51

A lab-line Hi—Lo Tempmobile unit was available for
circulating the thermostatting fluid. For work at or above
room temperature, a water bath was thermostated by circulat—
ing a 50:50 mixture of water and antifreeze from the Temp-
mobile unit through copper coils in the water bath. The
water was then circulated through the Plexiglas bath with
a centrifugal pump. In this way the temperature of the

Plexiglas bath could be controlled to within i0.l° C(58).

1V. 2.3.3. Stopping Syringe and Waste Lines

 

The stopping syringe was similar to the pushing syringes
with an adjustable Teflon plunger. An aluminum plate located
at the desired distance above the syringe was used to
abruptly stop the plunger during an experiment. The stopping
plate can be easily moved to a different position; however,
we have found that the optimum position is one which allows
the plunger to move about 1 cm. This traveling distance
allows for maximum flow velocity to be obtained (with
moderate air pressures), and gives three successive pushes
per filling of the pushing syringes. Two metal flags were
mounted on the stOpping plunger. These flags interrupt
light beams which strike two phototransistors (GELlHB) to
give timing pulses from which the flow velocity can be
accurately calculated (see Figure 7). These pulses were
used to trigger the data collection. We can start collect—
ing data either as soon as the maximum flow velocity has

been reached (trigger with the start flag, which had to be

52

 

 

 

 

 

 

 

 

 

(A)
1
x434 \
/
/ / Decelerotion —,‘
1’ \
/
, ’ “Acceleration \\———-(8)
JG

 

 

 

 

Stopping Plunger

 

 

 

 

 

L 1
6“ tr— 0‘- .J
0/1— I ":5
\[a u

 

 

 

WW4

 

 

Figure 7.

Timing pulses from the flow-flags. A - start
flag, 8 - flow velocity profile, C - stop flag,
D - location of the metal flags on the stopping
plunger, E - location of the phototransistors,
F, G - data collection can be initiated at one
of these points, H - constant flow velocity has
been reached at this point.

53

inverted in order to trigger our circuitry), or just a few
milliseconds before the stopping occurred (trigger with
the stop flag). In this way we always collect some data
during flow and thus have a better estimate of the initial
absorbance. Also by utilizing these pulses to start and
stop a clock, and knowing the exact separation of the two
phototransistors as well as the thickness of each metal
flag we have been able to compute (within the experimental
error) the zero of time; that is, the time when the mixed
solutions come to complete rest.

The waste line coming out from the exhaust valve was
connected via two valves to the reference cell. In this
way we have been able to make a reference solution of the
desired composition in the flow system and then fill the
reference cell with it. This would be useful when observing
the formation of unstable compounds in the presence of large

amounts of interfering reagents.

IV.2.3.H. Delivery System

 

The pushing syringes were connected to the flow control
valves (Kontes Teflon valves) via two-turn spirals made
out of 2 mm regular wall tubing. These spirals have been

(3H). Two

found to be necessary for low temperature work
flow control valves (1,2 Figure 2) connected the syringes
with the mixing and observation cell and two more (3,H
Figure 2) were used in the lines to the storage vessels.

Between the valves and the cell, we have inserted two

more (3 turn) spirals, which are coupled to the cell with

5H

2 mm Fisher-Porter joints. The same kind of joints have

been used in connecting the top of the cell with the ex-

haust valve (5 Figure 2) and the stopping syringe.

IV.2.H. Solution-handling System

 

Up to four solution bottles could be mounted on each
side of the apparatus (Figure 2). The bottles were con-
nected to the system via 5 mm Fisher-Porter joints and at
an angle which allowed for transfer of their entire contents
if so required. Each bottle was attached to a 10 ml thermo-
stated burette, such that accurate dilutions could be made.
The burettes were connected to the vacuum line at the upper
end (via Kontes valves) and to the mixing vessel at the
lower end (via Rotaflo adjustable Teflon valves with small
dead-volumes).

All four burettes on each side were connected with
”1 mm tips to a funnel-shaped tube which drained into the
storage vessel (WHO ml vessel).

After the solution bottles were mounted, the system was
evacuated (low vacuum for non-air-sensitive systems or high
vacuum for unstable solutions). After the necessary vacuum
was obtained, the system was isolated from the vacuum line,
and solvent was admitted into both storage vessels. Sub-
sequently, the pushing syringes were filled and pushed
slowly to fill the system with solvent. Appropriate adjust-
ments were made (light, absorbance circuitry, amplification,
etc.) and the solvent background spectrum was collected.

Any solvent left in the storage vessels was then removed

55

(either pushed out or through the side-arms of the syringes),
the desired solutions were transferred into the storage ves-
sels, where they were mixed (with a Teflon enclosed magnet)
and allowed to reach thermal equilibrium with the bath (“10
minutes, depending upon the temperature difference and the
volume of the solutions). The system was then ready for

the kinetics experiment to begin.

Commonly, small volumes of the concentrations to be
studied were prepared in order to rinse the storage vessels
and the syringes before starting the data collection. After
the pushing syringes were rinsed and the solutions to be
studied were prepared in the storage vessels, the data col-
lection was carried out as follows:

Valves 1 and 2 were closed and valves 3 and H were
opened. The pushing plungers were then lowered to the
filling position and the syringes were filled with the
solutions. Valves 3 and H were closed, valves 1 and 2
were opened and the "push ready" logic gate was set to "l".
The next beginning of the scan pulse from the monochromator
activated the pneumatic piston which forced the plungers to
move upward. This caused the reactants to flow through the
mixing and observation cell to the stopping syringe. The
stopping plunger was thus forced to move upward and strike
the stopping plate to halt the flow and the advance of the
pushing plungers. After the data collection was over
valves 1 and 2 were closed, while the pneumatic piston was

returned to the hold position. Valve 5 was opened and the

56

reacted solutions were expelled to the "waste". With valve
5 closed, valves 1 and 2 were re-opened and the pneumatic
piston was activated for a second push. A third kinetics
record was obtained in the same way before refilling the

bottom syringes.

IV.3. Optical System Design

 

IV.3.l. Overall Characteristics
(63)

 

Quartz fiber optics transfer the dispersed light
from the monochromator, through the bath fluid, to the cells
and then to the photomultiplier detectors. The use of

fibers also helps to overcome problems associated with align-
ment of the optical components and allowed for a more
convenient positioning of the monochromator and the photo-
tubes. At the same time, we eliminated errors resulting

from vibration of the cell out of and into the light beam,
since, if vibration occurred, the fiber end could move with
the cell. As mentioned before, double beam operation and
analog conversion of intensities to absorbance were employed
in order to permit a wide dynamic range of input intensities,
to cancel out lamp intensity and photomultiplier voltage
fluctuations and to allow for observation of small absorbance
changes over large background contributions. Small Pyrex
fibers were used to illuminate the phototransistors (with

a miniature bulb) for the timing pulses of the stopping

plunger (Section IV.2.2.3).

57

IV.3.2. Light Sources, Monochromator, Fibers

 

In the early stages of our work we used either a Tungsten
(Quartz Iodine) or a 150-watt Xenon light source (both
Bausch 8 Lomb products). Their low intensities, combined
with inefficient matching of their output with the mono-
chromator input, gave low signal—to-noise ratio values.
Later, we were able to utilize a 1000-watt Xenon arc lamp
with the appropriate optics to match its output to the mono—
chromator input and this improved our results dramatically.
This lamp was mounted in a model C-60—50 Universal Lamp
housing and powered from a model C-72-50 Universal Lamp power
supply (all from Oriel Optics Corporation, Stamford, CT).
A Perkin-Elmer model 108 rapid scanning monochromator(2)
was coupled with the system, and allowed us to scan a
selected spectral region between 280 and 1050 nm with 3 to
150 scans per second (a new prism to be mounted soon should
lower the U.V. limit to N220 mm, which is the cut-off wave-
length of the fibers). Two kinds of triggering signals are
produced by the scanning monochromator. One of them marks
the beginning of each revolution (BS-signal) while the other
one is related to the rotation angle of the nutating mirror
(GT-signal). To generate these signals we utilize a minia-
ture lamp to illuminate the gear which is directly attached
to the nutating mirror. This light beam is reflected from
a small polished spot on the black (painted) gear and strikes
a phototransistor (GELlHB) to give the BS-signal. Another

phototransistor, located behind the gear, is used to detect

58

the light beam as it is interrupted by the gear teeth, and
gives the GT-signal (136 teeth on the gear give 136 pulses
per revolution). The frequency of the GT—signal is then
appropriately multiplied (see Section V.2.3), and the
resultant signal is used to trigger the sample-and-hold
amplifier and the analog-to-digital converter (ADC). In
this way, data points are collected at equal increments of
rotational angle of the mirror, and since wavelength is
determined by the angle of rotation, corrections are auto-
matically made for slight changes in rotational velocity
(due to "play" in the gear train).

The output of the monochromator was coupled to the fibers
by use of a metal tube which was mounted on the monochromator
cover. The fibers were held in place with small set-screws,
while the mounting assembly allowed for adjustments (slotted
mounting holes) to be made in optimizing the light intensity
on the reference and sample fibers. An attempt to combine
four fiber—bundles into a slit-shaped end was aborted because
the quartz fibers are very fragile, making their handling
almost impossible. Commercially available 2 mm round end,

(63)

50 cm long, quartz fibers were used. The present fiber
set-up introduces a problem because the sample and reference
fibers "see" different regions of the Xenon arc, so that
spatial fluctuations are not averaged out. A factory-made

(63) with a slit shaped end has been ordered

beam splitter
and will be attached to the monochromator to minimize this

problem.

59

IV.3.3. .Detectors

The use of either quartz-envelope RCA photomultiplier
tubes (RCA 6903, 8-13 response; from RCA, Harrison, NJ), or
EMI photomultiplier tubes (EMI 968HB, S-l response; from
Gencom Division/Emitronics, Inc., Plainview, NY), allowed
us to detect light in any spectral region between 220 and
1050 nm. In order to reduce the dark current of the EMI
photomultipliers (PMT's) we used the appropriate magnetic
lens assembly (supplied by the manufacturer) and also en-
closed them in a specially made, dry-ice cooled, housing.
This was a two compartment housing designed so that we
could add dry-ice during the experiment without exposing
the PMT's to ambient light. Styroform insulation was used
in the cooling compartment and a double quartz window was
mounted at the two ends of the magnetic lens assembly to
avoid condensation on the PMT window when the tubes were
kept at low temperatures. Since two fibers are used for
each PMT (short and long path length), a sliding bar was
mounted between the tubes and the fiber ends, which allowed
for isolation of one beam at a time. Provision was also
made for calibration filters to be inserted into the sample
beam, while a V-shaped vane positioned in front of the
reference tube allowed for intensity adjustments. This
cooled housing has been used successfully from -70° C
up to room temperatures.

The detectors were powered with a regulated power

supply from Furst Electronics (model 710-P).

60

IV.3.H. Absorbance Circuitry

 

The outputs of the PMT'S were the inputs to a loga-
rithmic ratio amplifier, whose circuit diagram is shown in
Figure 8. All components used in this circuit are from
Philbrick/Nexus research, Dedham, Mass. The output voltage
is proportional to the logarithm of the ratio of the refer-
ence to the sample intensity. At 27° C and gain 1, the out-
put is actually m0.982H volts per absorbance unit (the
variable gain switch allows for gains of 1,2,5,10,20).

This voltage was then converted to absolute absorbance by
utilizing calibrated neutral density filters (Optical
Industries, Inc., Santa Ana, CA) as described in Section
IV.5.3. The output of the absorbance circuit was appro-
priately biased to allow for utilization of the entire range

of the data acquisition system (from -5 to +5 volts).

IV.H. Performance Tests

 

Performance tests have been made with the entire system
in a variety of ways, including the study of a number of

standard reactions.

IV.H.l. Optical Calibration Data

The wavelength resolution of the instrument depends
upon the instrumental settings. An example is given in
Figure 9, which shows a portion of a 128 points holmium
oxide spectrum collected while scanning at 75 scans per
sec (26.66 msec per revolution; 13.33 msec per spectrum).

The effective path lengths of the cell were determined

61

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63

by utilizing Beer's law tests. For the short path length,
freshly prepared aqueous solutions of KMnOu were used.

The solutions were calibrated with a Cary model 15 spec-
trophotometer by using 1.00:0.01 mm SCC cells, just before
being used. In Figure 10, the results obtained with our
instrument at 52H nm have been plotted against the corres-
ponding results from the Cary. It can be seen that Beer's
law is obeyed for absorbances up to m2.0, and that the path
length calculated by using least squares for the first 6
points is l.9910.02 mm.

Similar tests for the long path length with aqueous
solutions of 2,H-dinitrophenolate at 360 nm, gave an effec-
tive path length of 1.85 cm<58).

The lack of linearity for absorbances greater than 2.0,
could result from non-linear response of the absorbance

3 to 10.9 amps

circuit (it is linear over the range of 10-
of photocurrent).

Scattered light problems were minimized by positioning
the appropriate cut-off filters in the light beam between the
lamp and the monochromator (e.g. for the Na- work a CS 3-66
Corning filter was found to perform satisfactorily, while
for the anthracenide work a Pyrex glass filter was used).

No light leaks were detected in any of the experiments.

The signal-to-noise ratio depends of course upon the

wavelength region examined. With the 1000-watt Xenon arc

lamp we have studied total absorbance changes at 330-H50

nm, of 0.08 absorbance units on a 0.2-0.6 absorbance units

lead

An.

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«y-/\

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Absorbance from the Stopped-flow Apparatus

6H

 

 

 

4
3.0.4

l
2.0-4
100 d
0.0 I I I

0.0 0.5 1.0 1.5

Absorbance from CARY 15
Figure 10. Absorbance from the stopped-flow system ys

absorbance from a CARY 15 spectrophotometer
for aqueous solutions of KMnOu. The line
drawn has a slope of 2.0.

 

65

(58). For this case, the

background at 75 spectra/sec
r.m.s. noise as estimated from an analog storage oscillo-
scope was ~0.002 absorbance units.

Two major sources of noise are limiting at the present time.
One arises from vibrations of the scanning mirror and can be re-
moved only by collecting data at fixed wavelengths. However,
the second one is associated with the position of the fibers
at the exit slit of the monochromator (see Section IV.3.2)
and could probably be minimized by using an appropriate
beam-splitter. This second source sometimes gave us r.m.s.

noise as high as 0.02 absorbance units, for absorbance

changes of ml.0 units over no background absorbance.

IV.H.2. Flow Calibration Data

 

Utilizing the flow flags described in Section IV.2.3.3
we were able to compute the flow velocity for each push.
We actually measured the flow time; that is the time required
for the stopping plunger to travel a given distance (depending
upon the separation of the two phototransistors); and then
computed the flow velocity. For example in one set of pushes
we had (air pressure m50 PSI):

(a) Flow time for 25 successive pushes = 76.5:H.3 msec.

(b) Distance to travel (for stopping plunger) within

5 mm.

this time
These resulted in a flow velocity in the stopping syringe:

USS = 0.06510.003 m sec—l, or a flow velocity in the mixing

chamber: Umc = 3.2210.15 m secIl. Note that the critical

velocity for turbulent flow for water at 20° C in a 2 mm

66
tube isvnl m sec-1(la’ pg. 715).
The time between the pulse which started the flow time
clock and the next BS-pulse (for scanning experiments) was
found to vary from a few msec to the time corresponding to
a complete revolution. This time was always measured by the
computer with a real time clock<6u).
From these measurements and the instrumental stopping
time we were able to compute the time which elapsed between
the initiation of the data collection and the actual stopping
of the solution. In this way, the appropriate time corrections
could be made to our data.
Vibrational artifacts appeared to be absent, and cavita-

tion did not occur during flow or upon stopping. Trapped

gas bubbles are easily swept out of the system.

IV.H.3. General Performance, Scanning Mode

 

As mentioned earlier, one source of error results
from vibrations of the scanning monochromator. As expected,
the size of the error depends upon the scan speed. We
have been able to collect scanning data at speeds up to
150 spectra per second (13.3H msec per revolution), with
satisfactory signal-to-noise ratios. However, the system
operates much better at lower scan speeds and most of our

¢

work has been carried out at 75 spectra per second.

The peak positions for successive unaveraged spectra were

found to be very reproducible, generally within 11 core memory

location for sharp peaks and over the range covered in

67

Figure 9. Also the absorbance of calibration filters or

solutions did not change between successive scans.

IV.H.3.1. Clean Stoichiometry and Isobestic Point

One of the systems used to test the performance of
the instrument, was the production of peroxychromic acid
from hydrogen peroxide and acidified solutions of dichromate,
according to the reaction: HCrOE + 2H202 + H+ z CrO5 +
3H20(65). Figure 11 shows the results obtained while scann-
ing at 75 spectra/sec from N300 to N600 nm. At low wave-
lengths we observe the decay of Cr(VI) while at high wave-
lengths the growth of the peroxychromic acid gives an in-

crease in absorbance. For this particular experiment we

used the following initial concentrations:

[HCrO;]° = 0.5 mM
[H202]° = n.5u mM
[H*]° = 10.0 mM

In Figure 12 we have isolated only a few spectra from the
same experiment, and here we can see better the decay'at
N35H, nm the growth at N600 nm and the isosbestic point at
NH80 nm. Also in this figure can be seen the effect of
the averaging scheme in smoothing the data. Starting from
the top (of the decay) each spectrum is the average of l,
2,H,8,16 (13.3 msec) spectra respectively, and the effect
of averaging on the signal-to-noise ratio is profound.

In Figure 13 are shown the time cuts for the first

9 seconds, from the same experiment, at wavelengths which

68

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71

correspond to the maximum of the decay, the isosbestic
point and the maximum of the growth.
When the initial concentrations of the reactants are

changed to the values:

[H0r0;]° = 1.0 mM
[H202]° = 1.817 mM
[H+]° = 52.0 mM

the reaction reaches equilibrium, then the decomposition of
peroxychromic acid starts and both peaks decay. Time develop-
ments from these data for a total of 90 seconds are shown in
Figure lH. We can observe the fast growth (or decay),
followed by the slow decomposition process. In Figure 15

is shown the first 2.1 seconds of the reaction which dis-
plays a small anomaly for the decay. This was also ob-

(65)

served by Wilkins et al. who attributed it to small

amounts of Crzog'

in the solutions.

A simple test for an "uncomplicated" reaction in which
both reactant and product absorb, can be made by plotting
£n|A(t) - A(tm)l ys time at different wavelengths. If the
reaction is "uncomplicated" these plots must be wavelength
independent (see Appendix A). In Figure 16 we see such plots
from data corresponding to the experimental conditions given

for Figure 11. It is evident that under these conditions

the reaction which gives peroxychromic acid is "uncomplicated".

72
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75

IV.H.H. Flow Cell Performance, Fixed Wavelength

IV.H.H.l. Dead Time

The dead time of a stopped-flow apparatus is the time
required to transfer the solutions from the mixing chamber
to the observation point and bring them to a complete stop.
The dead time therefore depends upon the mixing efficiency
and the stopping time of the apparatus as well as the flow
velocity obtained for a particular experiment. If the
stopping time has been found to be very small and the mixing
is very efficient, then the dead time can be estimated from

the equation: t = V/U(36)

, where V = dead volume = volume
from the point of mixing to the end of the observation win-
dow, and U = average flow velocity in ml/sec.

For our mixing and observation cell we have:

(1) V1 volume from the first to the second mixer
m0.015 ml
V2 = volume of the second mixer N0.02H ml
V3 = volume from the second mixer to the end of
the short path length window’V0.009 m1.
So: V = Vl + V2 + V3 m 0.0H8 m1
Our typical flow velocity was N18 ml/sec and re-
sulted in a calculated dead time for the short path
length equal to N2.66 msec.
(2) For the long path length we had the additional

volume of N0.073 ml and the corresponding dead

time is “6.7 msec.

76

The dead time was also computed from data obtained by study-
ing the formation of peroxychromic acid at N600 nm, under
pseudo-first order conditions (initial concentrations:
[HCr0;] = 5 mM; [H202] = HH.97 mM, [H+] = 22.5 mM). A semi-
logarithmic plot of (A(tm) - A(t°)/(A(tm) - A(t)) yg time
has been made with the use of our time zero (see Figure 17).
An extrapolation of the resulting straight line to the value
of the absorbance that could have been observed if reaction
had not occurred at time zero, gives the dead time as the
difference between our time zero and the true time zero

of the reaction<36). From Figure 17 we extract 2.5 msec

as the dead time of the short path length for this particular

experiment. Similar plots gave a dead time for the long

path length of N5.5 msec.

IV.H.H.2 Mixing Efficiency and Stopping Time

 

The mixing efficiency is good enough that we have not
yet been able to measure its deviation from 100% complete
mixing at the time of observation in the short path length
cell (perhaps because of the double mixer we are using).

We mixed equal amounts of 2 x 10'‘4 molar paranitrophenolate
and 1 x 10'“ molar hydrochloric acid and observed the absor-
bance through the short path length cell at H00 nm where

the p-nitrophenolate absorbs. The resultant absorbance was
a flat straight line. This means that the reaction, which

(30)

is diffusion controlled , is over by the time the mixed

solutions reach the observation point. Such results could

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78

not have been obtained unless complete mixing had occurred
before the solution reached the observation window.

No mixing artifacts were detected by pushing solvent
gs solvent and the absorbance during flow stays reasonably
constant after the constant flow velocity has been reached.
In Figure18 we see the trace from a fixed wavelength re-
action of potassium anthracenide with ethanol as photographed
from our display scope. In this case the data collection
was triggered with the stop flag.

The stopping time was found to be reproducible and
less than one millisecond. Recall that stopping time is
the time required for the mixed solutions to come to com-
plete rest, after the flow has been stopped. One of the

reactions studied was the following:

3+ 2+

Fe (0.01M) + SCN- (0.01M) + FeSCN

The absorbance change was followed at H55 nm. In Figure
19 we see the first 200 msec of the reaction, while in
the inset is a closer look at the time of flow stop (from
10 to 1H msec after the stop flag had triggered the data
collection). The rounding, which results from non-abrupt
stopping of the solutions when the stopping plunger stops,

seems to be very small.

IV.H.H.3. Reliability of the System
Successive pushes with the same solutions were very

reproducible and we did not have to discard any of them.

79

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81

No leaking problems were detected when the syringe plungers
were properly adjusted. The entire system could be pumped

to p 5.1 x 10'”

torr, and stayed evacuated long enough for
a complete run with air-sensitive materials to be made
(N12 hours). It has been used at temperatures up to H0° C
with good results and no detectable thermal artifacts.
Low temperature studies have not yet been made because the
flow valves do not perform well at temperatures below N10° C
(Kontes type valves with Teflon stopcocks). Special adjust-
able Teflon inserts can be constructed and used in the same
valves for low temperature work. One such valve is ready
to be tested with a push-pull type insert, similar to the
syringe plungers.

One problem which remains is the relatively large hold-up
volume; that is, the volume between the pushing syringes
and the observation point. This is important, especially
for biological applications where the volume of reactants
is limited. However, the hold-up volume could be de-
creased with a slight modification of the present design.
Also, some back diffusion from the mixing chamber occurred,
depending upon the solution densities and the duration of
the observation. Because of this problem we were sometimes
forced to use only two pushes per filling of the syringes

and to discard the middle one.

IV.H.H.H. Quantitative Measurements

 

The formation of blue peroxychromic acid was investi-

gated at N30° C and the results are summarized in Table I.

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(65)

Wilkins et al have~shown that the rate expression for

this reaction is

dECrO5 (aq.)1
dt

 

+ -
- k[H ][H202][HCrOu] 11
so that under pseudo-first order conditions

dECrO5 (aq.)]
dt

 

= kpSEHCrOu] 12

with
+
kpS - k[H 1EH202] 13
They also reported the following expression for the rate
constant as a function of temperature:

exp(-H5001200/RT) M-Z seo’l 18

At 30° C this equation yields a third order rate constant

-1

of 2.26 x 10" M.2 sec with limits of 1.5 x 10H and 3.76 x

H M'2 sec-l.

10
In order to compute the rate constants included in

Table I, we fitted the observed data either to a growth

or a decay pseudo-first order expression. For this we

utilized a non-linear least squares computer program (see

Section IV.5.3.2). The third order rate constant was then

calculated from Equation.Cl3). Representative computer

fittings are given in Figures 20 and 21. Also plots of

the logarithm of the absorbance yg time are given in

85

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86

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87

Figure 22.

0
served the same initial deviation from pseudo-first order

At concentrations of HCrO higher than 0.5 mM we ob-
decay as reported elsewhere<65) (Figure 22, B).

Data from experiments with no pseudo-first order conditions
were not analyzed kinetically, since our intention was to
demonstrate the ability of our system and not to study ex—

tensively the formation of peroxychromic acid.

IV.5. Use of the Computer Interface

 

IV.5.l. General Characteristics

 

The only way one can really appreciate the on-line data
acquisition, is to run an experiment with and without the
computer. In fact, it would have been very difficult if
not impossible, to obtain some of the results discussed in
Chapter VI without utilizing long time averaging to improve
the signal-to-noise ratio. Our averaging scheme is very
versatile and the experimenter can choose how much averaging
to do by setting the apprOpriate parameters (see Section
V.l.2). However, the choice is important because we do
not want to affect the rate constant(s) of the reaction by
starting the averaging process too soon. The experimenter
must choose the appropriate averaging parameters carefully
because unaveraged data are not available after the experiment
is over.

We used the reaction of aqueous NaOH with 2,H-dinitro-

phenyl acetate (DNPA) as an example to test the effect of

88

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89

averaging on the reaction rate constant. This was a fixed-
wavelength experiment at H00 nm. The parameters used and
the computed pseudo-first order rate constants are given
in Table II. From these results we conclude that the rate
constant, at least for this fixed wavelength case, is re-
markably insensitive to the averaging scheme used. However,
the results obtained for a grouping factor of four might
indicate an effect caused by excessive early averaging.
Generally we collect scanning data (if the reaction rate
is slow enough to permit it) in order to follow the absor-
bance changes at various wavelengths and to check for clean
stoichiometry (see Appendix A). However5the scanning mode
introduces an inherent source of error; namely, vibrations
of the nutating mirror. For this reason, it is probably
good practice to study the kinetics at fixed wavelengths
after the reaction has been proven to be "uncomplicated".
As we can see from the results in Table I, there is no
significant effect on the reaction rate when we go from one

mode to the other.

IV.5.2. Solution Requirements

 

Combination of the scanning capability with the very
efficient data acquisition system, reduces drastically the
volume of reactants required for the complete study of a
particular problem. Only about 8 milliliters of each re-
actant are enough to run a complete test for transient

intermediates or to show clean stoichiometry. Also, of

90

 

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92

course, the same data can be analyzed to determine the rate
constants. With the currently available averaging scheme,
we can study fast initial changes followed by slower processes.
This can be seen with the data for the non-pseudo-first order
peroxychromic acid formation and will be analyzed more fully
in Section V1.2. This ability to observe both fast and slow
processes in a single push also decreases the required amounts
of reactants. Also the fact that we generally find no need
to discard any pushes (except when back diffusion becomes
a limiting factor), increases confidence in the results
obtained with only a few pushes.

In summary, the performance of the entire system shows
that an experienced investigator can run a well-planned
experiment and make the most efficient use of the available

reactants.

IV.5.3. Calculation Schemes Used

 

IV.5.3.1. Program ABSTIM<66)

 

As mentioned already, we utilize calibrated neutral
density filters in order to convert the output voltage of
the logarithmic amplifier to absolute absorbance. This
is done on the CDC 6500 computer with the aid of a multiple
regression program (MULTREG(7)), which fits the ratio
Aabs/Aobs to a polynomial in Aobs of degree up to five,
keeping only the most significant terms. Aabs is the
absolute absorbance and Aobs is the voltage (proportional

to absorbance) as measured with our system. This fitting

93

is first done for the calibration filters for which absolute
absorbance is known (from measurements with a CARY 15
spectrometer). Then the coefficients, which result from

it, are used to fit the actual data to the same polynomial
and to compute the absorbance for each data point. Note
that the Aobs values are collected under the same conditions
for both the calibration filters and the actual kinetics
data.

After the absolute absorbance has been computed, the
time corresponding to each data point is calculated from
the experimental parameters with the program TIMER (Ap-
pendix B).

Finally,the time correction for actual zero of time is
done and the relative variances for each data point are
computed from deviations supplied by the experimenter.

All the data are then printed, and data from the actual
time zero and later are punched onto computer cards ready
to be used for kinetics calculations (MULTREG and TIMER
are included in the main program ABSTIM).
NOTE: As will be described in Section V.3.H, the raw data
are automatically punched by the PDP-81 computer, together
with the core-page which contains all the experimental

parameters, in a format compatible with ABSTIM.

IV.5.3.2. Program KINFIT

This program was written by Dye and Nicely and has

been described elsewhere<67). The program estimates the

9H

set of parameters which give the optimum correlation be-
tween a particular rate law and a set of data. From the
information printed out, an experienced user can see how
applicable the trial rate law is and decide whether to
accept, modify or reject it.

A new version of the program (KINFIT2<18C)) makes it
possible to determine the kind and accuracy of information
required in order to be able to make decisions regarding

a particular mechanism.

V. COMPUTER-ASSISTED DATA ACQUISITION

AND PROCESSING

V.l. General Description

 

As already mentioned, an interactive on-line system was
necessary for efficient acquisition and processing of the
data generated by the rapid scanning stopped-flow apparatus.
Because of the nature of our experiments, the following con-
straints had to be imposed on the system.

The absorbance data from the stopped-flow apparatus
are functions of both time and wavelength and must be col-
lected by the computer on a real-time basis without losing
any of their important features. Since the chemical reactions
to be studied can have duration ranging from a few msec up
to several minutes, the data acquisition system had to be
designed so that the information necessary to characterize a
particular system, could be obtained without exceeding the
available storage capacity of the computer. At the same
time the signal-to-noise ratio could be improved by approp-
riate averaging. After collection, the data had to be
stored properly for subsequent retrieval and analysis, and
options for rapid computations and display were needed so
that decisions could be made during the experiment. Finally,
convenient editing and output options had to be available

for more complex computations on a large computer.

95

96

Also, since our experiments require long preparation
and data analysis times, the on-line computer was justified
only on a part-time basis. Therefore it was necessary to
interface our instrument with an available small computer
with the features required for our experiments. A PDP8-I
computer in one of Professor Enke's research labs on the fourth
floor was ideally suited to our needs. However, this required
transmission of data and control signals from (or to) the
experiment over a long distance, since the stopped-flow
apparatus is located in the basement. Parallel digital
transmission of the data was found to be most efficient in
our case, because it is fast and does not lead to any signal

degradation.

V.l.l. Signal Enhancement in Real Time

 

V.l.l.l. Maximum Sampling Rate

 

The data sampling rate is a function of the time scale
of the experiment, the computer speed and the rate of analog-
to-digital conversion. The frequency at which the signal
changes in a kinetics experiment depends not only upon the
rate constant(s) of the reaction(s), but also upon thetime
elapsed since the initiation of the reaction(s). At the
beginning of the reaction, the signal changes with time
much faster than it does near the end. This means that a
variable sampling frequency bandpass would be useful during
a particular reaction as well as for different reactions.

Traditionally, clock oscillators have been used to generate

97

a convenient sampling frequency which remains constant
during a particular experiment. Programmable clocks which
permit the sampling frequency to be changed during an experi-
ment provide another solution. However, decreasing the
sampling rate as a reaction proceeds, ignores useful informa-
tion while permitting the computer to "idle".
One solution to this problem as emphasized by deMaeyer<83)
is to sample the signal at the maximum possible rate and sub-
sequently to reduce the necessary storage and improve the
signal-to-noise ratio by appropriate digital averaging. Either
intermediate storage registers to "hardware-average" the data
or software averaging by the on-line computer could be used.
The former is required for very fast signal changes (e.g.
relaxation experiments), while the latter can be employed
for stopped-flow experiments.

It was estimated that NHO microseconds would be required
by the computer to complete the data acquisition, averaging and
storage cycle. Thus, the maximum sampling frequency possible
was N25 KHz. We also wanted to couple the sampling with the
nutating mirror of the monochromator in order to correct for
small changes in the rotational velocity of the monochromator.
The GT-signal generated by the gear, which is attached to
the nutating mirror (see Section IV.3.2), would then be
used to trigger the sampling process. However, the fre-
quency of this signal varies with the scan speed and has
a maximum value of 10.2 KHz (75 revolutions/sec x 136

gear teeth/rev x l pulse/gear tooth = 10,200 pulses/sec).

98

Multiplication of the frequency of this signal was sug-
gested by Prof. C. G. Enke and this was accomplished as
described in section V.2.3. These considerations led to a
nominal sampling rate of 20.H KHz (=2 x 10.2), which has
proven to give very good results in both wavelength and

time resolution.

V.l.l.2. Averaging Scheme

 

In typical rate studies, the signal varies rapidly at
first and then changes progressively more slowly as the
reaction approaches completion (or equilibrium). It is
therefore advantageous to use a wide bandpass at the beginning
of a reaction, but to decrease it as time increases. Most
instruments are designed to operate with a fixed bandpass;
that is, filters are selected prior to the experiment and
then not changed during the experiment. Even in these cases,
one must be careful in selection of the filters, since analog
filtering can distort the signal shape. In contrast to this,
digital filtering (appropriate averaging or smoothing) can
provide a bandpass which varies with time as needed.

As an example, consider a fixed wavelength experiment in
which the absorbance varies with time. If the half-life of a
fast reaction is 5 msec, then one point every 200 usec
would yield 25 points during the first half-life. Since the
data acquisition time is N50 IBec (Section V.l.1.l), each
200 Isec "point" would actually be the average of four

samples. If a slow process occurs at the same time, we

99

might want to continue to follow the absorbance for a total
of, say, 10 sec. Continuation of the 200 usec/point rate
would give a total of 50,000 points - truly a formidable
storage problem! However, after collecting the first 25
points it is a simple matter to obtain 25 additional points
during the next 10 msec, each of which is an average of 8
samples at the 50 Usec rate. The next set of 25 would
require 20 msec, then H0, 80, etc. Ultimately we could
collect 11 sets of 25 points each. This would require only
275 storage locations. The first set of 25 points would
extend out to 5 msec and each point would be the average

of H samples. The last set of 25 points would extend out
to 10.2H sec and each point would be the average of H096
samples. If the noise were random, the signal-to-noise
enhancement of the last set over the first would be 32 to

1 [=(H096)l/2/(H)l/2].

With the ability to scan wavelength during reactions,
another dimension is added to the averaging problem. We
have programmed the computer to provide a number of possible
averaging schemes. In all cases, data collection at
A50 Usec/sample continues. But we are able to select the
number of points per spectrum by averaging an appropriate
number of adjacent samples, with the number chosen to avoid
serious loss of spectral resolution. After this selection
has been made, averaging in time according to the scheme
outlined above is also done by averaging appropriate numbers

of adjacent spectra together. Our scanning system produces

100

a forward and a back-scan on each revolution (one is the
mirror image of the other). According to our data acquisi-
tion routines, averaging of adjacent spectra does not take
place in the first group of collected spectra (corresponding
to the first set of 25 points in the fixed wavelength
example). In this way we can collect both the forward and
back-scans and thus obtain a better time resolution in the
early stages of the reaction. In the rest of the groups,
back-scans cannot be collected, because we need that time
for the spectral averaging process. If back-scans are
collected in the first group they are reversed automatically
in order to be used for kinetics computations.

In order to accomplish the above averaging scheme, the
experimenter has to set a number of parameters which are used

by the computer as counters to control the data acquisition.

V.l.l.2.l. Data Acquisition Parameters

 

Samples/point (SP): The number of adjacent samples
which are averaged together into a single data point.

(a) Fixed-wavelength data.

 

A group is a set of points each having the same number
of samples averaged per point.

Points/Group (PG): The number of points in the group;
all groups have the same number of points.

Number of Groups (NG): The number of groups the experi-
menter wants to collect in order to follow the reaction up

to the required time.

101

Grouping Factor (FC): Determines the modulus by which
the number of samples/point is increased for each successive
group, according to the equation: (SP)G=(SP)G=1(FC)G'1,
where G=Group number.

(b) Scanning Data.

 

A group is a set of spectra each being the average of
NG consecutive spectra (NG=l for the first group).

Spectra per group (8G): The number of spectra in each
group. Determines the time length of each group, as
governed by the scan speed.

Grouping factor (FC): The modulus by which the
number of consecutive spectra averaged together to form one
spectrum is increased for successive groups; according to
the equation: NG=(FC)G_l where G=Group number.

The value for each parameter depends upon the particular
experiment to be performed. Their effect upon the rate

constant is discussed in Section IV.5.1.

V.l.2. Control and Timing Signals

The signals generated by the scanning monochromator
and the stopped-flow apparatus are used to initiate data
acquisition and to synchronize the computer with the experi-
ment. The pulses produced by the stopping plunger (Section
IV.2.3.3) are used to trigger data acquisition and also as
timing marks for time computations.

The BS and GT-signals of the scanning monochromator

(Section IV.3.2) gave very reproducible wavelength markers

102

whenever scanning data were collected.

v.2. Hardware

 

The interfacing of our stopped-flow apparatus with a
remote computer, is very complex and possesses some charac-
teristic features. Because we scan the spectrum of absorbing
species during the reaction, we had to overcome problems of
timing and control which are not present in a fixed wave-
length experiment. Also the location of the computer in
regard to the experiment introduced the problem of trans-
mitting and receiving information and control signals over
a large distance. It was necessary to construct and assemble
a large number of circuit boards, since data and control
signals were handled at two locations. Only the most charac-
teristic parts of the interface will be presented here.
Details of construction are described in a "hardware manual"

which is available to users of our system(72).

V.2.l. Digital Transmission Lines

 

The long distance between computer and experiment,
combined with the noisy environmental conditions make im-
practical the analog transmission of data and control
signals. Noise pick-up and signal degradation would result
from analog transmission and decrease the quality of the
experimental data. The instrumentation available at the
time of construction made impossible serial digital trans-
mission becauseit was too slow for our experiments ($20,000

(5Hb)).

bits per second Parallel digital transmission

103

through twisted-pair cables appeared an attractive alter-
native. Recall that in parallel transmission each of the
binary bits that make up a word is transmitted simultaneously,
while serial transmission involves the output of each bit of
a word, one bit at a time. In order to decrease the cost of
the transmission system a "party line" structure was

employed in which two or more line drivers and receivers
shared a common transmission line. Line drivers and .
receivers from Texas Instruments Inc. were utilized because
of their performance characteristics (types SN75107 and
SN75109)(70). They permit high speed transmission (<10

MHz), high sensitivity (<50 mV) at the receiver input, high
common-mode rejection at the receiver input, strobe capability
for the receiver and inhibit capability for the driver. The
driver is composed of a stage that converts input logic
levels to voltage levels that control a current switch.

The current switch unbalances the voltage on the transmis-
sion lines, resulting in a voltage difference at the re-
ceiver input. The input stage of the receiver is a dif-
ferential-input stage that exhibits high rejection of common-
mode input signals. An intermediate stage converts the
polarity of the line signal to the appropriate logic levels
at the receiver output. Since the driver output is not
affected by common-mode signals induced on the line, error-
free transmission and recovery of data results. The driver
inhibit logic is computer controlled and permits data to

be transmitted to, or received from the computer via the

10H

same lines. All drivers and receivers, required at each
end of the transmission line (computer and experiment),
were mounted on a single (9" x 6") circuit board which was
connected to the interface with 3M type flat connection
cables. The transmission line is a Belden 8769 cable (ob-
tained from Newark Electronics), which contains 19 twisted
pairs of #22 conductors. Each pair of conductors is
shielded with stranded wire and foil wrapping. All of the
stranded shields were connected together at one end and
grounded. This prevents ground loops in the transmission
cable. Each conductor is terminated at both ends with 2H

ohm resistors (the characteristic impedance of each line).

V.2.2. Flag Circuits

As previously mentioned, it was necessary to utilize
synchronization pulses (from the stopped-flow apparatus and
the scanning monochromator) to clock the data into the com-
puter such that the correct wavelength and time could be
associated with each data point. Also, in order to output
the data from the computer onto various devices (scope,
plotter, cardpunch), the status of the device (ready or not
Iready) had to be checked by the computer before outputing
any data. All of the input/output (I/O) control was achieved
by a system of device flags and device codes. Each device
was assigned a code number and associated with a flag cir-
cuit. In this way, the computer could recognize the device

and determineiitsstatus by checking the appropriate flag.

105

At the appropriate time, each device must generate a "ready"
pulse which triggers the corresponding flag and notifies the
computer of its readiness to send or receive data, or simply
to set a timing mark (Flow and BS Flags). These pulses are
produced by the interruption or reflection of a light beam
(see Sections IV.2.3.3, and IV.3.2) or simply by changing
the state of a logic gate. The main component of each flag
circuit is a J-K Master-Slave Flip-Flop (type SN7H73 or
SN7H76), which is set by the trigger pulse of the correspond-
ing device and cleared by the computer after the device has
been serviced as well as at the initiation of the experi-

ment<71’72).

V.2.3. Use of the Phase-locked-loop Circuit

 

For synchronization and automatic wavelength correc-
tion we used the GT-signal (IV.3.2) to control the data
acquisition. Since the frequency of this signal is lower
than the desired sampling rate (V.l.1.l) (and varies with
the scan speed of the monochromator), it was necessary to
construct a circuit for frequency multiplication of the
fundamental GT-signal. At the suggestion of Prof. C. G.
Enke, a phase-locked-loop (PLL) and divide by N circuit was
constructed. With this system we maintain all sampling
triggers synchronous to the experiment by integer multiplica-
tion of the GT-signal to achieve the 20.H KHz sampling
frequency. Figure 23 shows the basic principle of the

circuit. The PLL (NE 565A from Signetics<73)) corrects

106

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107

its output frequency such that the two input signals are in
phase and of equal frequency. Thus by changing the divide
by N number (Motorola MC HOlBP 7110 programmable counters),
the output frequency can be made the desired multiple of the
input frequency. It was necessary to "clean" the GT-signal
of high frequency noise, before feeding it to the PLL cir-
cuit. For this purpose, a voltage comparator (LM3ll by
National Semiconductors) was used.

The above circuit was found to perform very well when

(72) and "tracked" changes in gear speed

properly adjusted
effectively. Whenever fixed-wavelength experiments were
performed, the output of a Wavetek Model 116 Signal Generator

was utilized at 20.H KHz to control the data acquisition.

V.2.H. Overall System

 

A block diagram of the overall system is shown in
Figure 23.

Commercially available integrated circuits (IC's)
were utilized to construct the control logic centers<72).
In order to sample and digitize the voltage output of the
logarthmic amplifier, two interchangeable types of sample-

(7H) were used in conjunction with a high

and-hold amplifiers
speed, programmable, 12-bit Analog-to-Digital-Converter
(ADC)(75). To output analog data for the display scope or
the incremental plotter, lO-bit Digital-to-Analog—Converters
(DAC's)(76) were used, because of the inability of these

devices to resolve a 12-bit from a lO-bit word. However,

108

lZ-bit words were punched onto computer cards for rigorous
data analysis.

In order to control the devices located near the experi-
ment, a number of control signals had to be transmitted
from the computer to the devices. To do this on a one-for-
one basis would have required more transmission lines than
we had available. To overcome this problem, a complex
Coding-Decoding system was designed and constructed from
commercially available IC's. From our experience with the
design and testing problems involved, we would simply install
more transmission lines if we had to do it over. All circuits

(77)

were constructed on standard circuit boards , which were

then mounted in a Computer Interface Analog Digital Designer
(ADD)(78).

The computer is remotely controlled by a Teletype unit
and has an operating system resident on a dual magnetic
tape unit (from DEC) for software and data storage. Also,
the following peripherals were available for data output:

An IBM 526 card punch equipped with a Varian C-lOOl coupler

(79)

which was modified appropriately and an RCA 301 line

printer<80). Both of these peripherals are located near

the computer. A Model 611 ll-inch storage Display Scope<81)

and a Model 6550 Omnigraphic high speed point plotter<82)

are located near the stopped-flow apparatus.

v.3. Software

 

In order to perform the desired data acquisition,

processing and output, a long and sophisticated set of

109

computer programs was required. Since, at the time, only
2 fields of core memory (8K or 8192 12—bit words) were
available and we wanted to save field 1 (MK) for data storage,
it became necessary to develop our software such that it
could be loaded in the available core memory. To overcome
this problem, we divided our software into two main parts:
(a) Core resident routines, which are in core memory
during the entire experiment and data treatment period
(these are various utility subroutines).
(b) Non-core resident routines (called Modes or Seg-
ments), which are called into core memory (from the
magnetic tape) as needed and only one at a time.
A core resident routine supervises the loading of the
appropriate Mode according to the experimenter's command (as
controlled via the Teletype and the display scope). This
has proven to be a very efficient way to utilize 4K of core

memory for W18K of software.

V.3.l. Data Acquisition

 

The flow-chart for the data acquisition mode is shown
in Figure 2%. Only the two main options have been included
in this flow chart; namely, scanning and fixed-wavelength
data. In addition, data for absorbance calibration with
neutral density filters, wavelength calibration with ab-
sorbing glasses, solvent background and background at
infinite time (tad can be easily collected. The experi-

menter simply sets the data collection parameters (V.l.l.2.l),

110

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111

or just changes any of them as required, selects the ap-

propriate option and initiates the stopped-flow experiment

(Push). The digital sample collection then takes place

according to the following sequence of events:

(i)

(ii)

(iii),

(iv)

(v)

(vi)

(vii)

Start Flag occurs - push has begun, real time
clock is started.

Data collection begins on the falling edge of
the next BS-pulse, real time clock is read and
stored with the experimental parameters.

The next sample trigger (from PLL) activates

the HOLD mode of the sample_and-hold amplifier
(SHA).

The same sample trigger is delayed m5 usec (with
a monostable multivibrator) in order to allow
the SHA to "settle", and then triggers the ADC.
100 nsec before the 12 parallel digital bits

are ready, the ADC generates an End of Conversion
pulse. This pulse, after suitable delay through
a monostable multivibrator, opens the data latch
(temporary 12-bit word register) and sends a
SAMPLE READY signal to the sample flag.

The computer recognizes the SAMPLE READY FLAG,
the inhibit on the data line drivers is removed
and the sample is clocked into the accumulator.
The computer clears the sample flag and proceeds
to average and store the data.

The next sample trigger begins the process again.

112

Since the computer keeps track of BS-pulses,
the samples are averaged and stored in the cor-
rect sequence with respect to both time and wave-
length.

When the fixed-wavelength option is selected the
sampling and digitization process starts with the
STOP Flag and goes through steps (ii)-(vii).

The data as collected during a push are stored in field
1 (WHK of core memory), and after the collection is over
they can be stored permanently on magnetic tape. A file
name is associated with each push when stored on tape. This
file name consists of a date code, a run code (characterizes
a set of pushes), a push code and the operator's initials to
make future reference easy.

After the raw data have been stored on tape, the experi-
menter can ask for quick computations to be performed and
examine the data before continuing the experiment. The
desired data during flow can be averaged to give the ab-
sorbance at to, which then can be subtracted from the raw
data. Solvent background and absorbance at tm (if collected)
can also be subtracted. After these computations, the desired
wavelength or time displays can be examined, which may in-
dicate that modifications in the experiment are required.
Future options, such as logarithmic computations, can be

introduced, if more core memory is available.

113

V.3.2. Description of Output Options

Displays of spectral growth and decay with arbitrary
scale expansion and selection of particular spectral scans
individually or collectively can be obtained on the storage
scope. Time developments at any particular wavelength
covered in the experiment, with arbitrary starting and ending
times as well as scaleexpanSionScan also be examined on the
scope. In this way, any desired time period, at any point
from the beginning of the reaction and at any wavelength
can be analyzed as soon as the push is over. Hardware and
software are also available to plot on the incremental
plotter whatever is displayed on the scope.

Finally, the time displays from the scope can be punched
onto computer cards for more detailed data analysis. The
decimal number corresponding to each data point on the time-
cut is punched. The time corresponding to each point is
computed on the CDC 6500 computer from the experimental
parameters, which are also punched for each data file
(IV.5.3.l). An option for punching entire spectra can be
easily added, such that spectral shapes could be analyzed
on a large computer.

The performance of the interface has been tested together
with the stopped-flow apparatus and the results are discussed

in Section IV.H.

VI. RESULTS

V1.1. Dissociation of Na- in Ethylenediamine (EDA)

Based upon the equilibrium constant and the reverse

rate constant from pulse radiolysis studies<26>, the for-
ward rate of the reaction
N‘ N++2- 15
a 2 a esolv

in EDA should be slow enough to permit its study by stopped-flow

methods. We hoped to be able to examine the disappearance of

the optical band of Na' and the appearance of that of esolv

by mixing a solution of Na in EDA with a solution of ammonia
in EDA. Small amounts of ammonia should shift the equilibrium
to the right. Another method of shifting the equilibrium

to the right is the addition of small concentrations of "2,2,2

"(16{ This would have the advantage that it would not

Crypt
alter the solvent properties as drastically as would the

addition of large amounts of ammonia.

VI.1.l. Equilibrium Studies of the Effect of Ammonia

 

Addition

Solutions of Na in EDA were prepared in a cell which
consisted of a 2.0 mm quartz optical cell and two quartz
side vessels. Sodium was distilled into one side vessel
and EDA into the other. A solution of the appropriate
concentration was then made by dissolving the required amount

of metal in EDA. Various amounts of ammonia were added to

11%

115

this metal solution and its effect upon equilibrium (15)
was studied by recording the optical spectra at room tem-
perature with a Beckman DK-2 spectrophotometer.

The following results were obtained: The solution

without any ammonia had only one absorption band at m660 nm

-(18)

corresponding to Na When about 1.7 weight % ammonia

was added, a second band started growing in at W13OO nm

- (18)

solv . As the concentration of ammonia

corresponding to e
was increased (up to ~9.3 weight %) the absorbance of the

e band continued to increase. Equilibrium constants

solv

for reaction (15) were computed from the equation:

solv
[Na’]

+
[Na ]x[e J2 YNa+x 72

7<

ll

X
(D
(HI
0
...:
<

16

 

Conservation of charge gives:

+ _ _ _
[Na J - [Na 3 + [esolv

]

Thus equation (16) becomes (for YNa' = YNa+ = _ = 1.0):
solv

(D

{[Na’1+[e' J}x[e' )2

K : solv - solv 17
[Na ]

 

The concentrations of Na- and esolv were calculated from

the absorbance measurements at “660 nm and Wl3OO nm respectively.

The corresponding molar absorptivities have been reported

elsewhere(25). The following values were obtained for the

116

equilibrium constant at three ammonia concentrations:

K = 1 x 10‘7 M2 with ~9.3 weight % NH3
K = 5 X 10-8 M2 " 418.7 N n n
K = l X 10-9 M2 " “1.7 n n n

By extrapolating these results to 0% NH3 we obtained K in

EDA ~10"10 M2 (from pulse radiolysis studies K 5 10-10 M2).
From the above results we see that, ammonia shifts equilibrium

(15) to the right as expected.

VI.1.2. Kinetics Studies

 

One experiment was done by mixing a solution of Na in

EDA ([Na‘] ml x 10‘”

M), with a solution of ammonia in EDA
(8.9 weight % NH3), in the stopped-flow system at room
temperature. Solution stability was not good and the high
vapor pressure of ammonia over the solutions (”2.56 atm

if Raoult's Law is obeyed) caused problems. The decay of

the Na- band was observed (probably due to decomposition),
but no esolv band was detected. A time cut at m660 nm (A)
and another one at mlOOO nm (B) is shown in Figure 25.

The small growth observed during flow in B corresponds to the
tail of the Na- band. We were able to analyze kinetically,

some of the decays of the Na' band by fitting the data to a

first order decay equation, namely

_ -kt
At - Ao e 18
where At = absorbance at time t
A = absorbance at time t=0

117

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118

A representative computer fitting is shown in Figure 26.
A first order rate constant of 1.7 sec"1 was obtained.

It was thought at the time that small amounts of im-
purities in the solvent or the stopped-flow apparatus caused
the decomposition of the solution. Because of the problems
caused by the high ammonia vapor pressure, we decided to repeat
the experiment with a solution of "2,2,2 Crypt" and with more
carefully purified solvent. Also, the flow apparatus was
prerinsed as described in Section III.2.3.

Two experiments were done with "2,2,2 Crypt" solutions

u M and 8.6 x 10-”

(8.9% x 10- M). Similar results were
obtained in both cases as with the ammonia solution.

We were unable to find the reason for the decomposition
at the time and turned to the studies with the more stable
solutions of aromatic anions. However, in the first experi-
ment with potassium-anthracenide in THF we were faced with
the same decomposition problem. A systematic check of the
flow apparatus, showed that the Teflon insert in one of the
Fisher—Porter joints located between the mixing cell and the
flow valves did not maintain a vacuum tight seal when the
reacting solutions were pushed through the system. This
resulted in contamination of the ammonia (or "2,2,2 Crypt")
solution with oxygen or water followed by decomposition of
the Na' solution. Because of the time required to purify

the EDA and to prepare the solutions,we abandoned further

studies on the dissociation of Na' in EDA.

119

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Nn.: wH.m Hm.H mo.o

 

 

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120

VI.2. Effect of Cation Complexing Agents on the Protonation

 

of K+,An7 in THF

 

A number of studies(7-15’8u)

have shown that the protona-
tion of aromatic radical anions in solution depends not only
upon the acidity of the proton donor but also very strongly
upon the state of aggregation of the ions in solution.
Changes in the state of aggregation and the structure of

the solvation shell of the protonated species, affect the
rates and the free energies of the protonation processes.
For this reason the addition of complexing agents which
would destroy the contact ion pairs of the type M+,A7

(e.g. K+,An7) is expected to drastically affect the protona-
tion rates. Two complexing agents (Figure 27), WhiCh have

(18)

proven to effectively complex metal cations , were used

in this work.

VI.2.l. Effect of "Crown" on the ESR Spectrum of Na+lAn7

 

in Diethylether (Etzgl

 

The ESR spectra of alkali salts of many aromatic radi-
cal anions show hyperfine splitting by the alkali cation,

(85,86). Com_

presumably because of contact pair formation
plexation of the cation should be able to prevent such contact
pair formation. To demonstrate this effect the ESR spectrum
of Na+, An7 in EtZO was recorded at -70° C without and with
"Crown" present. The solution of Na+,An7 was prepared in

a cell which consisted of_a 2.8 mm i.d. ESR tube sealed

to an inverted U-tube. A break-seal was attached on one arm

121

Figure 27. Cation complexing agents. (I) "Crown", (II)
"2,2,2 Crypt".

122

of the U-tube, and a sidearm on the other one. First the
required amount of "Crown" (always in excess) was enclosed
under vacuum in the break-seal. Anthracene was then intro-
duced into one arm of the U-tube (close to the break-seal),
and the metal was vacuum-distilled through the sidearm

into the other arm. After distillation of the solvent,

the solution was prepared and kept away from the metal.

The ESR spectrum of this solution was measured at -70° C
(Figure 28a) with an X-band Varian E-H spectrometer. The
hyperfine splitting by Na+ is in agreement with the results

of Hirota<85’86).

Subsequently the break-seal was broken
and the "Crown" dissolved in the above solution. The addi-
tion of "Crown" to the solution caused the disappearance Of
the Na+ hyperfine splitting as shown in Figure 28b, in
complete accord with expectation. These results are similar
to those obtained when alkali solvating agents such as

"glymes" are added to similar solutions<87).

VI.2.2. Kinetics Studies

 

To further investigate the effect of metal-cation
complexing agents upon the protonation of aromatic radical

anions in ethereal solvents(8’10)

, the reaction of K+,An7
with EtOH in THF was studied in the presence of various

amounts of "Crown" or "2,2,2 Crypt". Two sets of experi-
ments were carried out. In the first case, the concentra—

tions of K+,An7 and EtOH were such that, both first and

second order contributions were observed in the absence of

123

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C

o
0) Nc°,An" In £920 at -10 c.

Io—moso I

 

lofl—ol

l-——¢——-l

b) Soln. a 0 'Crown' at —70°C

Figure 28. Effect of "Crown" on the ESR spectrum of Na+,An7
in Et20.

12H

the complexing agent (short path length cell data). In
contrast the second set of experiments was carried out at
low K+,An7 concentration and high [EtOH], such that only
the pseudo-first order reaction was detected (long path

length cell data).

VI.2.2.1. Short Path Length Cell Data (Path Length of the

 

Optical Cell=2.0 mm)

 

First the solution of K+,An7, as diluted by various
amounts with THF, was allowed to react with EtOH in the
flow system. An example of the spectrum of K+,An7 taken
from the observed decays is shown in Figure 29. Subsequently,
the same dilutions of the K+,An7 solution were prepared with
each complexing agent present and allowed to react with EtOH.
The data collected in the absence of complexing agent
were fit to a pseudo-parallel first and second order rate

law. The integrated form of the equation

- d[K+,An7]
dt

 

_. + 7 2 I + 7
- kpSEK ,An 1 + kps[K ,An 1 19

was fit to the data by using the computer program KINFIT.
Three parameters were adjusted: [K+,An7]o, the pseudo-
second order rate constant (kps) and the pseudo-first order
rate constant (kés). Representative fits are shown in
Figure 30, and the results obtained are listed in Table

III.

The data obtained in the presence of complexing agent were

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126

 

 

 

 

 

 

 

 

 

 

 

 

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in." . .3
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m. "‘1 ........... . . J
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Figure 30.

Computer fits for the reaction of K+,An7 with

EtOH in THF in the absence of complexing agent.

For all computer fits x - experimental point,
0 - calculated point,

- experimental and
calculated are the same.

127

 

 

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129

analyzed as follows:
The equilibrium
+.. K+ -

K ,An- + C 2 K C,An° 20
was assumed to exist between contact ion pairs (K+,An7)
and complexing agent separated ion pairs (K+ C,An7; C =
"Crown" or "2,2,2 Crypt"). Protonation of the species
K+,An7 occurred as in the case with no complexing agent in
the solution, while the ion pairs K+C,An7 were protonated

via a pseudo-first order pathway. The following equations

were then combined to fit the experimental data:

 

+ -
K = EK+C1AE J (from Equation (20)) 21a
[K ,An'JXECJ
+ _ + - -
[K C,An°] + [K ,An°] = [An-1T 21b
[0] + [K+c,AnT] = C0 21c
dEAn71
' T - + T 2 I + 7
dt - kpSEK ,An 1 + kpSEK ,An J +
II + T
kpSEK C,An 1 21d

Total anthracenide concentration

where: [An°1T

C

0 Initial concentration of the complexing

agent

For the cases with CO< [An7];, three parameters were

130

_ o
adjusted; namely, K, [An']T and the pseudo-first order rate

constant for the species K+C,An7 (kps)' The values of kpS

and kés, computed from the data without complexing agent,
were introduced as constants. For alcohol concentrations

higher than 0.083 M, the values of k were calculated from

133
(8310), while values of kDS were computed

from the long path length cell data (VI.2.2.2). The data with

data reported elsewhere

CO >> [An7]; were fit to the same equations, with K used as
a constant (computed for the CO 3 [An7]; case), because
there was not enough information to compute three parameters.
Finally, for very slow reactions at which [An7]T did not
decay to zero within the duration of the observation, one
more parameter was adjusted; namely, [An7];.

Attempts to introduce the term kg; [K+,An7] x EK+C,An7],
into equation (21d) were abandoned because a negative value
for kg; was obtained without significant change in the fitting
(see Figure 31). Even when only the portion of the data with
high [An71T (data up to m2.3 sec) was used, the computed
value for kg; was negative.

The results obtained when "Crown" or "2,2,2 Crypt" was
added to the K+,An7 solution prior to protonation are sum-

marized in Table IV. Some representative computer fittings

are shown in Figures 32 and 33.

VI.2.2.2. Long Path Length Cell Data (Path Length of the

Optical Cell = 1.85 cm)

 

The potassium anthracenide solution, which was used

for the work with the short path length cell, was diluted

131

 

 

 

 

 

 

 

0.00 ,
. I
wt], . 0.0 II 10“"
c. - 1;” I: 10"II
0... (EM) 0 0.0.3 I
IOII ‘
g .
I
I
C
.
I.
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.
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p
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..u . ' .
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...u 1 - 1 f - .
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a... : O
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I
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1 . .
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..n- .... ..u o..- 1.» 1.“ I... a...

Figure 31.

 

 

W
"..iifiino:bi .I. -.A I

,1!

..u , ° ,

 

 

 

I v . v v
0.0). LI! 3... II.) 53.6 6)..

flu. (..c)

A - second order protonation gig
two contact ion pairs.

B - Second order protonation gig
one contact ion pair and a
"Crown" separated ion pair.

C - Same as B, but only up to
N2 sec.

Computer fits for the reaction of K+,An7 with

EtOH in the presence of "Crow Q,Contribution of
K C,An7 at the second order protonation.

.> QHAUH Baku coxokaov

 

 

 

 

 

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133

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135

by a factor of 10 in order to be utilized for the low
[K+,An7] studies (5 days after the previous work) with no
significant change in absorbance.

The protonation in the absence of complexing agent was
examined first with four alcohol concentrations. The data
with low ethanol concentration ([BtOH] = 0.10u5 M), showed
a small pseudo-second order contribution, but a predominantely
pseudo-first order rate law, and were fit to the integrated
form of Equation (19). Two parameters were adjusted in
this case; namely, [K+,An7]o and kés, while kps was intro-
duced as a constant, because the second order contribution
was very small. However, the data with [EtOH] > 0.2 M showed

only a pseudo-first order dependence and were fit to the

equation:
_ '
A = Ace kpst + Am 22
where A0 = absorbance at the beginning of the reaction
A0° = absorbance at infinite time
Three parameters were adjusted in this case: A0, A00 and

kés, the pseudo-first order rate constant. A0° was always»
No.1 A0.

The results obtained are listed in Table V. In Figure
3% 2n (A—Aw) is plotted versus time, for three alcohol con-
centrations.

The effect of "Crown" and "2,2,2 Crypt" was investigated

0
at two concentrations of complexing agent, with [EtOH] =0.u18 M.

136

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.ANNV coflpmsemc smome pmepo pmgflm-oesmma m op mums mo was sogmfiuv
.H magme 509% Ans myocpoou ..mloc

 

 

 

 

 

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137

 

-3.0—

2n(A-Am)

-u.o-

-5.0-

 

 

Figure 3n.

 

T I I I
100 200

Time (sec)

Plots of £n(A-Aw) XE time for the reaction of

K ,An? (~5x10-5 M) with EtOH in THF. A - [EtOH]°=
0.209 M, the line was drawn with the computed
slope of ~15.7 sec-l. B - [EtOH]° = 0.293 M,

the line was drawn with the computed slope of
~28.9 sec‘l. C-[EtOH]° = 0.H18 M, the line

was drawn with the computed slope of ~65 sec'l.

138

o _ o
The data obtained with ["Crown"] $0.5 [K+,An°] were fit

to the Equations (21a) - (21c) and (23).

- dEAn7JT + _ + _
= v . n .
dt kpSEK ,An 3 + kpSEK C,An ] 23
_ 0
Three parameters were adjusted: K, [An']T and kBS. Also

[An7]; was introduced as a parameter whenever the absorbance
had not decayed to zero. kps was used as a constant. For
the data with ["2,2,2 Crypt"]o ~0.5 [K+,An7]o it was impos-
sible to use the same rate law as that used for the "Crown"

case. However, a pseudo-first order decay of the form
_k" t
A = Aoe PS 2”

was used successfully. Two parameters were adjusted in

this case: A the absorbance at the beginning and k"

PS’
the pseudo—first order rate constant for the complexing

0,

agent separated ion pair (K+C,An7).

Finally, the data with CO >>> [K+,An7]o were fit to
Equation (2n) for both complexing agents.

The results are summarized in Table VI. Characteristic

fits are shown in Figure 35.

139

 

 

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VII. DISCUSSION

VII.1. Dissociation of Na- in EDA

 

Since no detectable formation of esolv occurred during
the slow decomposition of the Na' solution, its rate of
production could not be measured. However, if we assume

the following possible pathways for the decomposition:

k1
Na“ 2 moi + 2e;01V 25
k-l
k2 k3

Decomposition products
an estimate of the maximum value of k1 can be calculated.
If the dissociation process had reached equilibrium,

the concentration of esolv’ as computed from Equation (17)
8 H

with K=6 x 10' M2 and [Na‘] «10' M, should be:

u

[e' 1 = 1.21x10' M

solv

n

This would result in an absorbance of 1.21 x 10' x 0.2 x

1.51 x 10“ = 0.37 absorbance units at W1000 nm (the molar

absorptivity of 1.51 x 10u M-l cm'1 was computed from

(25)).

previously reported results Calibration experiments
have shown that absorbances 2'0.02 should be easily
measured with the instrument. This indicates that the re-
action did not reach equilibrium, because no detectable

absorbance changes occurred at «lOOO nm. Thus the

142

1H3

concentration of e was:

solv

M 6

] £ 0.02/0.2xl.51x10 = 6.62x10- M 26

[e

solv

for all three experiments.
The rate of decomposition of Na- as derived from

Equation (25) is:

gigall = -(kl+k2)[Na'] + k_1[Na*][e‘32 = -l.7[Na']

OP

(kl+k2-l.7)[Na-] = k_lINa*J[e‘]2 27

(26)

From pulse radiolysis studies a value of k_l[Na+]

9 M"1 sec-l was calculated at [Na+]

M. Since, in this work [Na+] Ni x 10‘”,

8 M"1 sec-l.

(0.132t0.015) x 10

0.7 x 10'3

a good approximation for k_l[Na+] is W10
By substitution of the known values into Equation (27),

the following result is obtained:

108x(6.6x10'6)2 1

_u = 1.7+uu = ”5.7 sec-
10

= 1.7 +

 

1 2

This indicates that kl could be as high as ~50 sec.1 and
still no formation of esolv would be detected because of
the decomposition problems.

With this information we cannot conclude whether the
reaction of Na with water in EDA proceeds via the dissocia-

tion of Na' or not. The performance of the stopped-flow

luu

system as tested with the protonation of K+,An7 in THF,

indicates that further studies on the dissociation of Na-
in EDA are possible. A solution of "2,2,2 Crypt" should
be used in order to eliminate the problems caused by the
high vapor pressure of ammonia, and in order not to alter

drastically the properties of the solvent.

VII.2. Effect of "Crown" and "2,2,2 Crypt" on the Protona-
tion of K+,An7 with EtOH in THF

It is clear from the results presented in the last
chapter, that both complexing agents affect the rate of
protonation of K+,An7 in THF in the same direction but by
different amounts. The following equilibria and reaction
steps should be considered.to predict the species present in
a solution of K+,An7 in THF to which a cation complexing

agent (C) has been added:

K K
+ - .3 + - 2 + _
K ,An:+C + K C,An' I K C+An~ 28a
'2' — K+Q — + 1:; = +
2(K ,An“) 4- (An',K )2 4- An ,2K +An 28b
k"
K. k"!
+ - + - 2Q + — + — +
K C,An-+K ,An' (K C,An°;K ,An') 1
k"!
= +
An ,2K C + An 28c

It is assumed that dissociation of contact ion pairs

(K+,An7) is negligible in THF<89).

/ 195

If the formation of "loose" ion pairs involves only

electrostatic forces, the value of the equilibrium constant

K2 can be estimated from the Fouss equation(90)

;L_ z unasNexp(b)
3000

 

29

K

e2

aDkT

where: N = Avogadro's number
a = ionic diameter
e = charge on an electron
D = dielectric constant

k = Boltzmann's constant

The ionic diameter of the species K+C,An7 can be computed
as follows (for C = "2,2,2 Crypt"). K+ to oxygen distance
in K+-2,2,2 Cryptate is equal to 2.79 3(92). Also for the
ion pair K+,An7 in THF an ionic radius of 5.7 A has been

calculated(101

3(91).

, while the potassium ionic radius is 1.33

Thus a m2.79 + 5.7 - 1.33 m 7.15 K for K+C,An7.

The value of fL-= 3.68 x 10” M-1
2

Equation (29) at 25° C. This indicates that the dissocia-

is then computed from

tion of the "2,2,2 Crypt" separated ion pairs is very small

5

(K = 2.7 x 10- M). A similar dissociation constant can

2
be expected for the "Crown" separated ion pairs.
The contribution of the equilibrium (28c) to the protona-
tion reaction can be examined as follows. ~As was shown in

Section VI.2.2.1 the second order term k" [K+,An7] x [K+C,An7]

I
ps

196

did not improve the computer fits when used (together with
the term kpSEK+,An7]2) and actually resulted in a negative
value for kgé. Now we may assume two more cases. Either the
second order step requires two contact ion pairs (K+,An7),

or it requires only one K+,An7 and any other ion pair in

the solution; either K+C,An7 or K+,An7. If we let CO be

defined by CO = [K+C,An7], then the second order protonation

will be:
T = 'kps([An.]T " CO) A 30
or
d[An7]T _ _
—_5¥——— : -k2([An']T — Co)x [An°]T 31

where Equation (30) requires two K+,An7, while Equation
(31) requires only one contact ion pair. Let us now con-

sider the limiting case k = k2, and compute the curves

ps
corresponding to Equations (30) and (31), for the case

u _ -u -
M, CO - 1.76 x 10 M and kps -

x sec-1. The results are shown in Figure

where [An7]; = H.064 x 10-
3.53 x 10” M"1
36 and indicate that the second order protonation of K+,An7

with EtOH in THF requires two contact ion pairs.

In summary it seems justified to neglect the equilibrium
(28c) and to assume that the dissociation of the speciele+C,An7
is insignificant in THF.

Let us now propose a general mechanism in conjunction with

the results reported elsewhere(10’15).

JTxlou M

[An7

H.16

3.69 .

3.21 d

2.7” ‘

2.27

1.795

1H7

 

 

 

'1‘ 9 ,6:

 

 

0

0.239

Figure 36.

r r I I I m I I

0.H68 0.702 0.936 1.17 l.H04 1.638 1.872 2.106 2.3M

Time (sec)
Effect of the complexing agent separated ion pair
on the second order protonation of K+,An7 in
THF. X-experimental points, A - points calcu-
lated from Equation (30), a - points calculated
from Equation (31), o - points computed from
Equations (21a)-(21d). Note that this is only
the first 2.39 sec out of 79.0 sec required for
the reaction to go to completion.

108

K
K+,An7 + cl: K+C,An7
KQ k:
+ - + - + = +
2(K ,An“) + (An-,K )2 1 An ,2K + An
k"
k1

An‘,2K+ + ROH -> K+AnH- + K+RO-
k
.. + 2 + — + .-
(An-,K )2 + ROH -» K AnH + K R0 + An
k
+ - 3 . + .-
K ,An- + nROH -* AnH + K R0 (ROH)n_l

+- oku"-
K ,An: + AnH ‘* K AnH + An
fast
k5
K+C,An7 + nROH -+ K+CRO-(ROH)D_1 + AnH°
k
+ - . 6 + -
K C,An- + AnH -* K CAnH + An
fast
k
K+CA H’ + ROH -2 K+CR0' + A H
n fast n 2
k8
+- .,+-
K AnH + ROH fast K R0 + AnH2

The above mechanism leads to the general rate law:

dEAn7JT
dt

32a

32b

32c

32d

32e

32f

32g

32h

32i

- _ + 7 2 _ I + 7 _ II 4' 7

if a steady-state concentration of the dianion (An=,2K+) is

assumed.

The rate constant expressions are:

 

*
n=1 for t-BuOH(15), while n=2 for MeOH<15)

work VII.2.1).

and EtOH (this

199

 

k S = kfi+ Q + 2k2KQ[ROH] 39a
p 1+ "’ [All]
k1.[ROHI
' - H. II .. 1’1
kps - k3[ROH] , kps - kSEROH] 39b

One more equilibrium must be considered during the protona-

tion process; namely,

KROH

K+RO- + c z K+C+RO' 35

The equilibrium constant KROH could be determined from
conductance measurements. However, it can be assumed to
be very small, because the dissociation equilibrium constant

for K+RO',

KI
+ ROH

KRo‘ z K++Ro'

is very lOW- This can be justified as follows. The
equilibrium constant for the formation of the ion pair

F07, Na+ in DMF-DME 1:1 mixture has been reported to be

M-l(93)

1.3 x 109 (F07 is the Fluorenone radical anion,

DMF = dimethylformamide, DME = dimethoxyethane). Since THF

is a less polar solvent than either DMF or DME, KKOH
-9

should be ‘ 10 M.

150

VII.2.l. Dependence of the Pseudo-first Order Rate Constant
' 0
$553) on [EtOH].
The reproducibility of the results summarized in Table
V and Figure 3”, indicates that only the first order protona-

5 M and [EtOH] 2

tion of K+,An7 occurs when [K+,An7] ~10—
0.2 M [The noise observed in Figure 3” is a result of the
problems associated with the present fiber configuration
(Section IV.H.1)]. A plot of log kés vs log [EtOH] is shown

in Figure 37. Even though we have only three points, it appears
that the alcohol dependence is second order. ‘Similar dependence

(15) for the protonation of K+,AnT

was observed by Szwarc et a1.
with methanol in THF.

Not enough information is available to calculate the de-
pendence of kgs upon the ethanol concentration; however,

analysis (VI.2.2.1) of the data for the short path length cell

indicates a dependence similar to that of kés.

VII.2.2. Conclusions

 

The reproducibility of the results reported in Table III
indicates the reliability of the computer-interfaced scanning
stopped-flow system (Chapters III and IV) for the study of
reactions with air-sensitive solutions. The observed values
for kps seem to be wavelength independent. From the concentra-

tions given in Table III and Equation (3ua), a value of 3.1a

x 10“ M-1 sec-l was calculated for kps’ with the use of results

reported elsewhere(10). This compares very well with the

observed value of kps = (3.6310.15) x 10” M'1 sec-1 (overall

151

 

 

 

 

2.0
I}
(D
~o.
x 1.5-
b0
0
H
1.0 T t ' ' l
-100 -008 -006 -0.”
log [EtOH]
Figure 37.

Dependence of the pseudo-first order rate constant
kég) on [EtOH].

The drawn line has a slope of

152

average from Table III). Note that the computation of the
pseudo-first order rate constant at these low ethanol and
anthracenide concentrations could not be done efficiently
without the versatile computer-assisted data acquisition
system.

The proposed general mechanism fits the short path length
cell data reasonably well, but shows some discrepancies when
the second order protonation is absent (long path length cell
data). The mechanism for the pseudo—first order protonation
is very important in these concentration ranges. The following
mechanism might explain the inconsistency associated with the
pseudo-first order data:

K
1
K+,An7 + ROH 2 K+,An7(ROH)

Km

K+C,An7 + ROH I K+,An7(R0H) + (2

kn

K+,An7(ROH) + ROH 1 products (via fast steps)

Note that this is actually the "cation solvation" mechanism

as introduced by Dye et al.(10)

to explain the alcohol de-'
pendence of the pseudo-first order protonation step. This
mechanism gives a second order dependence on ethanol, in
agreement with the observed behavior (VII.2.1), and is cur-
rently under further study.

These studies have clearly shown that the second order

protonation requires two contact ion pairs, which is an

153

important result. In general, the requirement of contact
ion pairs for the second—order protonation is in agreement
with the results obtained in solvents more polar than THF
and with the cation dependence of the mechanism(10’15’8u).
The computed rate constants indicate that the "Crown"
separated ion pairs are protonated more rapidly than the
"2,2,2 Crypt" separated ion pairs. This is expected, since
the structure of "Crown" (Figure 27) allows for stronger
charge localization than does "2,2,2 Crypt". The average

rate constants computed from Table IV are m2.2 M-l sec.1

for the "Crown" and $0.72 M.1 sec-1 for the "2,2,2 Crypt"
separated ion pairs.

Even though specific solvent effects may alter the protona-
tion rates significantly, the results to date (excluding those
from pulse radiolysis in the pure alcohols) are consistent
with an overall scheme in which the dominant factor is the
degree of charge localization in the aromatic system. This
is clearly shown from the rate constants listed in Table VII,

since we expect the charge localization to decrease in the

order:

(An=,2M+) > (An7,M+)2 > (An7,M+) > (An7||M+) > (An7,
"Crown" M+) > (An7, "2,2,2 Crypt" M+) > (An7); [(An7,||M+)

is a solvent separated ion pair].

15H

Table VII. Summary of the protonation rate constants for various

 

 

 

ion pairs
Ion Pair ' k M‘1 see"l
(An=,2m*) ml.5 x 109 (a)
(9.117,sz «2.5 x 103 (b)
(An7,M+) msuu (d)
(An7l IM“) me (c)
(1%, "Crown" M+) «2.2 (d)
(An7, "2,2,2 Crypt" M”) «0.72 (d)
(An?) «2 x 10'” (e)

 

 

Notes :

(a) From reference (10).

(b) From reference (10). This could be as high as ml.7 x 1010

depending upon the mechanism.

(0) From reference (11+), if Na+An7 is assumed to exist in DME largely
as the solvent separated ion pair.

(d) This work.
(e) Prom reference (84).

(f) Note that the rate constants depend also upon the metal cation (15) .

APPENDICES

APPENDIX A

TEST FOR AN "UNmMPLICATED" REACTION

Suppose that both the reactant (R) and the product (P) absorb
and that the only other absorption is background absorption, AB ,
which does not change with time. Then at any wavelength, A, we can

mite
A(A,t) = eR(l)’R(t) + eP(A)'P(t) + A80.) (A1)

in which 8R0.) and 6PM) are the molar absorptivities of R and P
(normalized to unit path length) R(t), P(t) represent the concentra—
tions of these species. If the stoichiometry of the overall reaction

also holds during the reaction then we have
[P(t) - P(O)] = v[R(O) - R(t)] (A2)

in which v is simply a ratio of balancing coefficients and P(O),
R(O) represent initial concentrations . It is usually convenient to
measure A(A,°°), that is, the absorbance at long times. Equations
(A1) and (A2) give

A(A,t) - A0,“) = [sRm - vepcmtmu - R(°°)J (A3)

Equation (A3) shows that the difference in absorbance at any
tineandattheendofthereactioncanbewrittenastheproductof
a function which depends only upon wavelength and a function which
depends only upon time (for a given set of initial concentrations and

155

156

conditions). Let us re-write Equation (A3) as
F(A,t) = G().)’H(t) (An)

A convenient way to test for the validity of this equation is to take

logarithms of both sides to give
2n[F(A,t)] = 2n[G(>.)] + [2mm] (A5)

Note that the absolute values of F()(,t) and GO.) must be used. This

gives
£n[F(A,t2)] - £n[F(A,t1)] = Rn[H(t2)] - £n[H(tl)] (A6)

Therefore, the difference in the logarithm of the function A(A,t)
- A(A,°°) at two different times should be independent of wavelength.
Similarly,

ILnEF0.2,t)] - mthm = 211E602” - 2n[G(Al)] (A7)

Therefore, the difference in the logarithm of the function A(A,t)

- A(A,°°) at two different wavelengths should be independent of time.
For a scanning system, it is easier to use Equation (A7) than Equa-
tion (A6). This is because a given scan of A y_s_ A takes time.

This derivation suggests a simple test for an "uncanplicated"
reaction in which both a reactant and a product absorb. (The same
test is validifnorethanonepmductormrethanonereactant
absorb.) Plots of 2.n(A) - 2.n(A,,) y_s_ time are constructed at various
wavelengths. Regardless of the rate law, these plots will be parallel.

A very sensitive technique would be to plot the difference ,

157

more - A(12,°°)] - mumps - my»): (A8)

m time. A constant value should result if the reaction is "un-
complicated". When this proves to be the case, then the logical
procedure is to study the kinetics at fixed wavelength .

If the spectrum during reaction shows the presence of other
absorptions, the methods of factor analysisws) can be used to

determine how many independent species are involved as well as the

nature of their spectra.

158

Amv><mH n m><mH

H u A
mm u oszZm
o.H u mo90<m
o.o u mmomZm

o.N\N><m<+AHIZDzveN><m<+m><m< u Hm<m<

mmem><m< H mm

mw><m<\o.oomo: u Mm

oo: 09 ow Ao.om.nmav><mHv MH

Awmv><mH u mm><m<

Amav><mH u NH><m<

Amv><mH u m><m¢

Amv><mH u m><m<

Amv><mHuN><m<

szsz<om mom HuAmHv><mHv HszHmmmxm .4.3 meHm mo wszz<om mom xommo

HzmxmmozH .mZm u UZHmZm
mDomw mmm Qmw<mmm¢ <mHommm mo .02 n MOBU<M
<meommm Qmw<mm>< OB MDQ Bmmmmo .mZm n mmomZm

ZOHHDAO>MM mo<m mo wszszmm H< Qmmmem w.m£muam<m<

m.mZm QMmm<Am u mm ZOHHDAO>MM mum m.m£m u mm
wm34<> MNHA<HBHZH

abomw mum mBZHom u AoHv><mH

moao<m wszDomw u ANHV><mH mDomw mum <mHommm u nmv><mH
w<qm z<omI¥o<m n A3V><mH mBzHom mo .02 u z
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z<om mum QmHXm m.m2m u Amv><mH Qmmmem mz<om A<HBHZH u Amv><mH
Qmmmm z<om u Ammv><mH mmmZDz HzHom u 232

BDU MZHH mewzmqm><2 m<ADoHBM<m <

mom ammm<dm mmqmz<m mo .02 2H MZHH Qmmm<4m MHDmZOU OB MZHBDommDm
szmzHB ZOHmZMZHQ

nm~Hv><mH\m><m\zo£Zoo

AZNMXHHASDZV MMSHB mzHBDommDm

mmEHB mzHHDommDm
m xHszmm<

mm

OUUUOUUUUOUUOUU

159

sz

mm OH 00

H u A3v><mH

Aoav><mH u Amv><mH
o.N\N><m<+o><m< u Bm<m<

0.0 u mm

Auv><mH u Mm

om OH ow

om<3mom mm AA< AAH3 mz<om mmh mo Emma mma
m><mH+H u a
o.N\AMm¢Ao.HIMOHo<mVV u whomzw
moav<memm u UZHAZm
NH><m<¢mOBU<h u m090<m

<myommm Qm0<mm>< mom mZOHBommmoo NHDmZOU
Hm<m<ImMuAH+va2HB

mm+mMHmm

z<omlxo<m mesmzoo 302

Bm<m<+mmMava2HH

BmMHm z<om Qm<3mom MBDmZOU

~.m><mH.HuH com on

quo maomw HmmHm 2H mm qu3 mz<omeo<m mom mMZHH MHDQZOU
ZMDHmm

o.w\Amm«Ao.HIMOHU<mvv u whomxm

moeu<m¢Mm u UZHmZm

NH><m<emoeo<m u mOHo<h

<maommm Qmw<mm>< mom mZOHHommmoo

02Hm2m+mm u mm

mm0m2m+9m<m<+mMuaxvm2HB

SHANHux oma on

HIAm><mH+Hv u 2H4

z<omlxo<m HDOmHH3 mDomw mzo 2H MZHB MBDmZOU
m><mH.z.AuH ooH on

mmomZm 3mz Mme szm CH BzHom HmmHm mmB mH A
mDomw mo<m mom mozo mooa on

com OB ow AH.MZ.A:V><mHV MH

AQMHUMAJOU mz<omI¥U<m mH mua:v><mHv z<omlxo<m < mom xommo

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0000

REFERENCES

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The author is grateful to Mr. A. E. Seer of the Michigan
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By Schrader, Scovill Fluid Power Division, Wake Forest,
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For more information on device flags see any small
computer handbook.

For more information on our particular system see "An
Interactive Computer Interface for Rapid Scanning
Stopped-flow Kinetics". This is a laboratory manual
for our instrument.

SE/NE SSS-Phase Locked Loop-Linear Integrated Circuits,
Signetics Corporation, 1970.

(a) SHA 1A, Sample and Hold Module, Analog Devices Inc.,
Norwood, Mass.

(b) SAMPAC MP250 0.01% fast acquisition Sample and
Hold, Analogic, Wakefield, Mass.

75.

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79.

80.
81.

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83.

89.

85.
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165

ADPAC MP2212 15V, high speed 12 bit A/D Converter,
Analogic, Wakefield, Mass.

DACPAC MP1810-2C, high speed 10 bit D/A Converter,
Analogic, Wakefield, Mass.

Two types were used, both from Heath Company, Benton
Harbor, Michigan.

(a) Model EU-SO-MG, ready to use PC boards with place
for 11-16 pin IC's.

(b) Pre-sensitized single sided foils for circuit
boards.

From Heath Company. The ADD used includes a Digital
Power Module (EU-801-ll), a Binary Information-
Module (EU—801-12), and.an Auxiliary Module (EU-801-19).
Modified by Mr. M. Rabb and Interfaced with help from
B. Hahn, K. Caserta, R. Coolen, T. Niemczk and N.
Papadakis.

Interfaced by Dr. Enke's group.

From Tektronix Inc., Beaverton, Oregon.

From Houston Instrument, Division of Bausch 6 Lomb,
Bellaire, Texas.

Personal communication to J. L. Dye from L. deMaeyer.

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