Effect of Propanol-1 on the Reaction between Thiophenol and N,N'-Diphenyl-1,4-Benzoquinone Diimine in Chlorobenzene

Article abstract of DOI:10.1134/S0036024419040289

Abstract: It is found that the interaction between thiophenol and N,N '-diphenyl-1,4-benzoquinone diimine proceeds by two routes, one of which is a radical chain reaction and the other is a nonchain reaction between the reagents. The kinetic patterns of the reaction depend substantially on the concentration of propanol-1 in mixtures of it and chlorobenzene. It is shown that at 343 K, replacing chlorobenzene with propanol-1 results in an almost twentyfold increase in the total rate of the reaction. Increasing the concentration of propanol-1 raises the rate of both routes of the reaction, but that of the nonchain route grows more than that of the chain route. It is concluded that increasing the concentration of propanol-1 results in a simultaneous 20–30 times rise in the rate constants of both the stage of radical generation by the reaction between the reagents as well as the rate constant of the nonchain bimolecular reaction, and the chain length of the chain reaction is shortened. When chlorobenzene is replaced with propanol-1, the rate constant of the limiting stage of chain propagation (the reaction of quinone diimine with a phenylthiyl radical) is halved, due to the formation of H complexes between the π system of quinone diimine and the proton of propanol-1.

Full text of DOI:10.1134/S0036024419040289

ISSN 0036-0244, Russian Journal of Physical Chemistry A, 2019, Vol. 93, No. 4, pp. 644–651. © Pleiades Publishing, Ltd., 2019.
Russian Text © V.T. Varlamov, 2019, published in Zhurnal Fizicheskoi Khimii, 2019, Vol. 93, No. 4, pp. 521–528.
CHEMICAL KINETICS
AND CATALYSIS
Effect of Propanol-1 on the Reaction between Thiophenol
and N,N'-Diphenyl-1,4-Benzoquinone Diimine in Chlorobenzene
V. T. Varlamova,*
a Institute of Problems of Chemical Physics, Russian Academy of Sciences, Chernogolovka, Moscow oblast, 142432 Russia
*e-mail: varlamov@icp.ac.ru
Received July 11, 2018; revised July 11, 2018; accepted July 11, 2018
Abstract—It is found that the interaction between thiophenol and N,N'-diphenyl-1,4-benzoquinone diimine
proceeds by two routes, one of which is a radical chain reaction and the other is a nonchain reaction between
the reagents. The kinetic patterns of the reaction depend substantially on the concentration of propanol-1 in
mixtures of it and chlorobenzene. It is shown that at 343 K, replacing chlorobenzene with propanol-1 results
in an almost twentyfold increase in the total rate of the reaction. Increasing the concentration of propanol-1
raises the rate of both routes of the reaction, but that of the nonchain route grows more than that of the chain
route. It is concluded that increasing the concentration of propanol-1 results in a simultaneous 20–30 times
rise in the rate constants of both the stage of radical generation by the reaction between the reagents as well
as the rate constant of the nonchain bimolecular reaction, and the chain length of the chain reaction is short-
ened. When chlorobenzene is replaced with propanol-1, the rate constant of the limiting stage of chain prop-
agation (the reaction of quinone diimine with a phenylthiyl radical) is halved, due to the formation of H com-
plexes between the π system of quinone diimine and the proton of propanol-1.
Keywords: N,N'-diphenyl-1,4-benzoquinone diimine, thiophenol, bidirectional reaction, kinetics, mecha-
nism, rate constants, chlorobenzene + propanol-1 binary solvents
DOI: 10.1134/S0036024419040289
INTRODUCTION
example of reactions involving quinone imines [15–
19]. Literature data stating that the specified reactions
proceed by two routes were confirmed from the start.
It was a great surprise when the previously unknown
radical chain mechanism of one of the routes was
proven. It should be noted that the formation of radi-
cals during reactions between quinoid compounds and
thiols was noted earlier [20, 21]. These observations
did not attract attention, however, and the chain
mechanism of the reaction was not considered.
Reactions between thiols and quinoid compounds
(quinones and quinone imines) are of great impor-
tance in chemistry and biochemistry. Such reactions
transform biologically important thiols (e.g., glutathi-
one and cysteine residues of proteins) into compounds
with covalent C–S bonds, from which the initial thiols
cannot be regenerated. This is one of the main reasons
for the high toxicity of quinoid compounds [1–7].
Reactions between thiols and quinone compounds
in alcohol and water–alcohol solutions were studied in
detail for the first time in [8] through the example of
reactions involving 1,4-benzoquinone and its deriva-
tives. Based on the data on the composition and yield
of the products, it was concluded that the specified
reactions proceed by two routes: (a) an oxidation–
reduction transformation of quinone to hydroquinone
and thiol to disulfide and (b) via the addition of thiol
to the ring of quinone (route (b) predominates). The
mechanism of the nucleophilic 1,4-addition of thiol to
the cyclohexadiene ring of quinone or quinone imine
was later accepted for route (b) [9–12].
EXPERIMENTAL
Studies show that the rate and composition of the
reaction products depend on the nature of the solvent.
The rate of the reaction between thiophenol and N,N'-
diphenyl-1,4-benzoquinone diimine thus grows by
almost an order of magnitude when chlorobenzene is
replaced with propanol-1 [19]. It follows from these
data that the kinetic patterns of the reaction in chloro-
benzene + propanol-1 binary solvents can be used to
obtain additional information on the mechanisms of
both routes of the reaction. Considering the great
practical importance of these reactions, we decided to
consider this problem in more detail in this work.
The kinetics of the reactions between quinoid com-
pounds and thiols remains poorly studied; until
recently, there were very few works [13, 14]. Detailed
studies in this field have only just begun through the
We therefore analyzed the results from studying the
reaction between thiophenol (C6H5SH, PhSH) and
644

EFFECT OF PROPANOL-1 ON THE REACTION
645
Table 1. Rate constants of stages (I), (Inc), and (II); parameter k2/(2k4)1/2 [19]; and dielectric constants of PhCl + PrOH
binary solvents, depending on the molar fraction of PrOH in mixture NPrOH, calculated according to formulas (1) and (2)
(T = 343 K, argon bubbling)
k2
(2k4 )1/2
k2 × 10−6
*
k1
k1nc
NPrOH
ε(298 K)
ε(343 K)
L mol−1 s−1
(L mol−1 s−1 1/2
)
L mol−1 s−1
0
0.0084 0.0015
0.021 0.0063
0.0414 0.019
0.196 0.081
0.25 0.04
0.50 0.06
0.96 0.42
3.2 1.5
10.8 0.3
9.54
8.0 0.13
6.87 0.13
5.6 0.65
1.2
5.62
6.78
7.79
16.5
20.1
4.89
5.82
6.60
12.0
13.7
0.106
0.194
0.803
1
1.05
0.88
0.75
0.61
0.196 0.072
4.8 1.0
9
−1 −1
* Calculations at k = 6 × 10 L mol
s ; see text.
4
N,N'-diphenyl-1,4-benzoquinone diimine (C6H5–
N=C6H4=N–C6H5, QDI) in mixed chlorobenzene
(PhCl) + propanol-1 (PrOH) solvents [17–19]. This
study was performed at T = 343 K with argon bub-
bling, and the kinetic patterns were determined from
initial rates wQDI of the consumption of quinone dii-
mine.
where
are the volume fractions of
vPhCl and vPrOH
chlorobenzene and propanol-1, respectively, calcu-
lated in [22] and presented in Table 1.
RESULTS AND DISCUSSION
The reaction between PhSH and QDI proceeds
according to the equation
Densities d and relative dielectric permeabilities ε
of chlorobenzene and propanol-1, which are needed
for further investigations, are presented below [22]:
PhSH +
N
N
Products
QDI
dPhCl = 1. 10 k g L−1,
εPhCl 298 K = 5.62
The products are N,N'-diphenyl-1,4-phenylenedi-
amines (I) phenylthio-substituted by the central ring
and phenylthio-substituted quinone diimines (II),
along with N,N'-diphenyl-1,4-phenylenediamine
(H2QDI) and diphenyl disulfide (PhSSPh) [8–10, 23,
24]. Earlier than others, compounds I are formed,
which are then converted into thiosubstituted qui-
nonediimines II under the action of the initial diimine
QDI and/or other oxidizing agents. At the initial
stages under conditions [PhSH] > [QDI], the reaction
does not proceed farther than the formation of
monothio-substituted N,N'-diphenyl-1,4-phenylene-
diamine I, n = 1.
(
)
(∂ε/∂T = −0.0168 K−1),
dPrOH = 0.800 kg L−1,
εPrOH 298 K = 20.1
(
)
(∂ε/∂T = −0.142 K−1).
Using these data, the dielectric permeabilities of
chlorobenzene εPhCl and propanol-1 εPrOH at 343 K,
(1)
ε(343 K) = ε(298 K) + 45(∂ε/∂T)
The kinetic scheme of the reaction at not deep
along with dielectric permeabilities ε of mixtures com- stages is presented below [16, 17]:
posed of them,
(I )
nc
Nonchain reaction QDI +PhSH →(I, n=1), k1nc
;
(2)
ε = vPhClεPhCl + vPrOHεPrOH
,
•
•
+PhSH
(i)
TPH → Ph2N ⎯⎯⎯→ PhS , ki;
QDI + PhSH → HQDI· + PhS•, k1;
HQDI· + PhSH → H2QDI + PhS•,
(I)
Ph
HN
Ph
NH
Ph
Ph
N
N
PhS• + QDI ↔ RA• → AmN•Ph, k2;
AmN•Ph + PhSH → (I, n = 1) + PhS•, k3;
PhS• + PhS• → PhSSPh, k4.
(II)
(III)
(IV)
(SPh)n
(SPh)n
n = 1−4
n = 1−4
(I)
(II)
Scheme 1.
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646
VARLAMOV
•
aminyl (C H – •–C H –NH–C H , HQD ) rad-
Tetraphenylhydrazine (Ph2N–NPh2, TPH) is
N
I
6
5
6
5
icals in the absence of6an4initiator proceeds according
specified here as the initiator, which decomposes upon
•
heating to diphenylaminyl Ph
2N
radicals that do not
to bimolecular reaction (I) between QDI and PhSH.
interact with QDI but are very active in the abstraction
of mobile H atoms [25]. In Scheme 1, we assume the
total reaction proceeds by two routes, one chain and
one nonchain. Stage (Inc) is a bimolecular reaction of
nonchain interaction between the reagents, and the
remaining stages belong to a chain reaction.
HQD • radicals are then replaced with Ph radicals,
•
I
S
one of the two types of radicals that lead the chain of
the total chain reaction, according to the reaction
•
with PhSH. Ph radicals propagate the chain by
S
participating in complex reaction (II), which
According to Scheme 1, the formation of primary
•
includes the formation of an unstable R
adduct:
radical
A
phenylthiyl (C H •, Ph •) and 4-anilinodiphenyl-
5S
S
6
Ph
Ph
N
N
N
H
N
+ PhS
Ph
Ph
(a, f)
S
Ph
RA
Reversible reaction (a, f) of the association and transfer of the highly mobile H atom of the C–H
•
bond of the ring to the nitrogen atoms of QDI (or to
fragmentation of the R
adduct is introduced into
A
the O and N atoms in the case of the reaction of
PhSH with N-phenyl-1,4-benzoquinone monoi-
mine (C6H5–N=C6H4=O, QMI)). For example, the
energy of activation of the monomolecular isomeriza-
tion of the adduct formed when
the mechanism in analogy with the reversible reaction
of adduct formation between thiyl radicals and unsat-
urated hydrocarbons known from the literature [26–
29]. In the above mechanism (see Scheme 1), we
•
assume that the R
radical adduct can not only
A
defragment into the initial reagents but also isomerize
Ph N−
O
Ph N−
OH
to an Am •Ph thio-substituted diarylaminyl radical
N
(iso)
that acts as the second type of radicals which lead the
chain at stage (III)
PhS
RA
H
SPh
AmN Ph
Ph
Ph
HN
•
a Ph radical “adheres” to QMI is ~200 kJ/mol,
S
N
H
N
N
Ph
Ph
which even exceeds the strength of the C–H bond that
breaks as the reaction proceeds (~160 kJ/mol) [30].
For reaction (iso), an alternative bimolecular mecha-
nism was proposed that included embedding a thiol
into a four-membered transition state, thereby
(iso)
S
S
Ph
Ph
AmN Ph
RA
Reaction (iso) was specially considered by means expanding it to a six-membered transition state favor-
of quantum chemistry in [30]. It was found that as a ing the reaction. When the reaction is complete, the
result of its high energy of activation, this reaction thiol regenerates; i.e., it acts as a catalyst for the chain
barely proceeds along the route of intramolecular reaction at complex stage (II) of chain propagation:
kadd
O
Ph N
RA + PhSH
AmN Ph + PhSH
H
(isocat)
S
PhS
H
Ph
wAmNPh of the formation of Am •Ph) depends on the
Experimental data testify to reaction (II) being the
limiting stage of chain propagation [16, 17]. The form
of the expression for the rate of this stage (i.e., rate
N
ratio of the rate constants of the reactions of associa-
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EFFECT OF PROPANOL-1 ON THE REACTION
647
tion ka, fragmentation kf, and isomerization kadd of the above that PhSH efficiently catalyzes the isomeri-
zation of RA• to AmN•Ph even at the lowest experi-
mental concentrations; i.e., inequality kadd[PhSH] ≫
kf holds.
radical adduct R •. If kadd[PhSH] ≫ kf, then
A
w2 = k2[QDI][PhS•] = wAmNPh
= kadd[PhSH][RA•] = ka[QDI][PhSi ],
k2 = ka.
The opposite inhibitory action of propanol-1 on
stage (II) can be expected as a result of the complex
formation of quinone imine with propanol-1. Qui-
none imines form complexes with both chlorobenzene
and propanol-1, and the complexes with propanol-1
are much stronger [34]. Complex formation is mainly
due to the formation of H complexes; in quinone
imines, both their heteroatoms (N atoms in QDI,
along with N and O atoms in QMI) and π electron sys-
tems act as proton acceptors. Enthalpies of formation
ΔH of hydrogen-bound complexes of quinone imines
with propanol-1, in which the heteroatoms of quinone
imines are proton acceptors, were determined in [34]
by means of quantum chemistry and the additive–
multiplicative model of hydrogen bonds [35]. Values
that were quite high and close to each other were
obtained for both quinone imines: ΔH = −23 kJ mol−1.
(3a)
=
RA•
If kf
≫
kadd[PhSH], then
(ka/kf)[QDI][Ph S• ], so
w2 = k2[QDI][PhS•] = wAmNPh
= kadd[PhSH][RA•]
(3b)
= k k /k PhSH QDI [PhS•],
(
)
add
[
][
]
add
a
f
k = k k /k PhSH .
(
)
[
]
2
a
f
The experiment shows that the main parameter of
the chain reaction between QDI and PhSH
1/2(see below) does not depend on the concentra-
k2 /k4
tion of PhSH [17–19]. This indicates that when the
reaction occurs, correlation (3a) is observed; i.e.,
inequality kadd[PhSH] ≫ kf holds at the lowest experi-
mental concentrations of PhSH. We would therefore
expect that the value of k2, determined by the kinetic
patterns of the chain reaction between QDI and PhSH
is the same as that of ka, i.e., the rate constant of the
When discussing the effect of propanol-1 on k2, the
thermodynamic characteristics of the H-complexes
formed during the interaction between the protons of
alcohol and π-electron systems of quinone imines, the
reaction centers of the reaction, are of much greater
interest. These data were not presented in [34], so we
calculated enthalpy of formation ΔH of such com-
plexes in this work using the additive–multiplicative
model for this as well [35]. This model allowed us to
calculate the enthalpy of H complex formation of two
particles with one hydrogen bridge under the standard
PhS• radical “sticking” to the double C=C bond of the
cyclohexadiene ring of quinone diimine QDI. Let us
k2 /k41/2
estimate k2 from the values of
in Table 1.
Assuming that the rate constant of the recombination
of the PhS• phenylthiyl radicals is close to diffusion conditions (1) a composition of the complex of 1 : 1;
limit k4 = 6 × 109 L mol−1 s−1 [31, 32], we obtain k2 =
(2) a temperature of 298 K; and (3) CCl4 as the sol-
1.2 × 106 L mol−1 s−1 in chlorobenzene. This estimate
falls in the range of experimentally measured rate con-
vent. We calculate ΔH using the formula
ΔH, kJ mol−1 = 4.96EaEd,
stants of the reactions of PhS• addtion to olefins of dif-
ferent structures in various solvents [32]. By assuming
that k4 does not depend on the concentration of pro-
where Ea and Ed are empirical enthalpic proton-
accepting (for the π system of quinone imines) and
proton-donating (propanol-1) factors that character-
ize the relative capability of compounds to form
hydrogen bonds. We found the values of Ea and Ed
using the HYBOT program [36]:
panol-1,1 we obtained the values of k2 in chloroben-
zene + propanol-1 mixed solvents that are presented in
Table 1. It is seen that the value of k2 is halved when the
solvent changes from chlorobenzene to propanol-1.
E = 0.38 for the π system of quinone imines ,
(
)
Let us discuss the possible reasons for the drop in
k2. In principle, we can expect dual action of propa-
nol-1 on k2. Propanol-1 can evidently accelerate the
isomerization of the RA• radical adduct to the
AmN•Ph radical catalytically, similar to that of thio-
phenol (PhSH) considered above [30]. However, no
notable effect of propanol-1 on the reaction rate
should be expected, despite the much higher concen-
tration of the alcohol, relative to PhSH. It follows from
a
E = −1.54 for the H atom of propanol-1 .
(
)
d
Based on these values of Ea and Ed, we obtain
ΔH(π…HO) = −2.90 kJ mol−1.
As we can see, the reaction of formation of π com-
plexes is weakly exothermic. Despite the estimated
nature of the obtained value of ΔH, these data show
this reaction can indeed make some contribution to
the processes in the system. The formation of com-
plexes with propanol-1 blocks the π systems of qui-
none imines; i.e., it lowers their effective concentra-
1
When studying reactions with the participation of thiyl radicals,
their solvation by solvents (particularly alcohols) is generally not
considered [28, 33].
RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY A Vol. 93 No. 4 2019

648
VARLAMOV
tions, the reaction centers in reaction (2) of PhS• rad-
icals “sticking” to the cyclohexadiene rings of quinone
imine. A consequence of the formation of π complex
could be a drop in k2 when the solvent is changed from
chlorobenzene to propanol-1. The data in Table 1
agree with this conclusion.
An alternative interpretation of the effect of propa-
nol-1 on k2 can also be obtained with the electrostatic
models of nonspecific solvation. Using the data in
Table 1, we built the dependence of lg k2 on the Kirk-
wood function (ε − 1)/(2ε + 1) (see Fig. 1):
logk2
6.1
6.0
5.9
5.8
log k2 = log k2(0)
2
μQ2 DI
3

2 
μ≠
μPhS•
(4)
1
ε −1
2.303kT 2ε + 1
−
+
−
,


0.36
0.40
0.44
3

3 
r
PhS•
rQDI r≠


(ε − 1)/(2ε +1)
where μ and r are the dipole moments and radii of
reagents PhS• and QDI, along with the activated com-
Fig. 1. Dependence of log k on function (ε − 1)/(2ε + 1)
2
of binary solvent chlorobenzene + propanol-1 at 343 K.
plex of reaction (2) between PhS• and QDI. It is seen
that the experimental points satisfactorily fall on a
straight line:
Table 1 presents the average values of k1 and k1nc
obtained in [19] from processing the results from
experiments with and without the initiator, according
to Eq. (5). Table 1 shows that upon moving from chlo-
robenzene to propanol-1, the values of k1 and k1nc
grow to almost the same extent (by approximately
20 times), and the absolute values of k1 are 20–
30 times lower than those of k1nc, regardless of the
composition of the mixed solvent.
log k = 7.2 0.2 − 3.0 0.4 (ε −1)/(2ε + 1),
(
)
(
)
2
R = 0.969.
As might be expected, this line has a gentle slope,
as is characteristic of radical reactions. The negative
value of the slope testifies to the activated complex
being less polar than the total polarity of the reagents.
It is, however, difficult to obtain additional informa-
tion, due largely to quinone diimine (QDI) existing in
two of its forms: syn- and anti-, which differ strongly
Using the rate constants of the reactions from
Table 1, we calculated rates wQDI of the total reaction
and both its routes (nonchain wnc and chain wc) at sev-
eral concentrations of reagents [QDI]0 and [PhSH]0
from the range of variation of their values in actual
experiments. Our results are presented in Table 2. For
comparison, Table 2 also presents the experimental
data for the experiments at [QDI]0 = 8.6 × 10−5 and
with respect to their properties (in the gas phase, μsyn
=
2.11 D and μanti = 0 D [30]). In solutions, both forms
are present in comparable concentrations but their
absolute values are unknown
Ph
Ph Ph
N
N
N
N
[PhSH]0 = 2.75 × 10−3 mol L−1.
Ph
syn-QDI
anti-QDI
It is seen from Table 2 that the rates of both routes
of the reactions grow along with NPrOH, and the rate of
the nonchain route wnc grows faster than that of chain
route wc. This is also indicated by the results from cal-
culating the ratio of the rate of the chain route to the
rate of total reaction wc/wQDI (see Table 2). One con-
sequence of the drop in the wc/wQDI ratio with the
growth in NPrOH is apparently an increase in the yield
of the products of the nonchain reaction when the sol-
vent is changed from chlorobenzene to propanol-1. In
addition, it follows from the data of Table 2 that
replacing the solvent is accompanied by a reduction in
chain length ν of the chain reaction. This means that
when chlorobenzene is replaced with propanol-1, an
increase is observed in the yield of the products
formed at the stages of chain initiation and termina-
tion (i.e., H2QDI and PhSSPh). This agrees with the
Let us discuss the effect the solvent has on the rates
of the reaction by each route and the composition of
the products. The following expression for the total
rate wQDI of the reaction is obtained from kinetic
scheme of the reaction:
wQDI = (k1 + knc)[QDI][PhSH]
(5)
k2
+
[QDI] 0.5w + k [QDI][PhSH] 1/2
,
{
}
i
1
k41/2
where wi is the rate of initiation upon the decomposi-
tion of the initiator. Expression (5) considers the con-
sumption of QDI in the chain reaction, by the non-
chain channel (Inc), and in stage (I) of radical forma-
tion (we must consider the rate of this stage for short
chains).
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EFFECT OF PROPANOL-1 ON THE REACTION
649
Table 2. Kinetic parameters of the reaction between QDI and PhSH, depending on the molar fraction of propanol-1 NPrOH
in PhCl + PrOH binary solvents and the experimental reaction rates (the values in brackets) at [QDI]0 = 8.6 × 10−5 and
[PhSH]0 = 2.75 × 10−3 mol L−1 [19] (T = 343 0.2 K; argon bubbling)
wi(0) × 109
wQDI × 108
mol L−1 s−1
NPrOH = 0
1.66
wnc × 108
wc × 108
[QDI] × 104 [PhSH] × 104
mol L−1
wc/wQDI
Chain length
1
3
1
1
0.168
0.504
0.84
2.52
0.252
0.756
1.26
1.41
7.30
3.17
16.4
6.05
0.848
0.906
0.716
0.813
0.504
83.3
144.3
37.3
64.5
14.7
8.05
4.43
1
5
3
5
20.2
3.78
0.86
0.86
27.5
27.5
3.97
12.0
5.96
(13.7)
NPrOH = 0.194
1
3
1
3
0.86
0.86
1
1
5
5
27.5
27.5
0.828
2.48
4.14
12.4
19.6
3.30
15.0
10.2
41.8
33.3
0.96
2.88
4.80
14.4
22.7
2.34
12.1
5.35
27.4
10.6
0.709
0.808
0.527
0.655
0.318
27.8
48.2
12.4
21.5
4.9
(23.7)
NPrOH = 0.803
7.70 3.20
32.6
26.6
101.0
1
3
1
3
0.86
0.86
1
1
5
5
27.5
27.5
3.93
11.8
19.7
58.9
92.9
4.50
23.0
10.6
53.0
22.7
0.585
0.705
0.399
0.525
0.230
11.0
19.0
4.9
8.5
1.9
9.6
16.0
48.0
75.7
98.3
(124.5)
NPrOH = 1
1
3
1
3
0.86
0.86
1
1
5
5
27.5
27.5
3.93
11.8
19.6
58.9
92.8
8.51
33.2
32.8
115.7
132.8
(180.9)
4.8
14.4
24.0
72.0
113.5
3.71
18.8
8.83
43.7
19.3
0.436
0.567
0.269
0.378
0.145
8.9
15.5
4.0
6.9
1.6
w
= 2k [QDI][PhSH], w = k [QDI][PhSH], w = w
− w chain length ν = (w /w ) − 0.5.
QDI nc, c i(0)
i(0)
1
nc
1nc
c
scarce literature data, which were, however, obtained
at relatively great depths of conversion. The consider-
able effect the nature of the solvent has on the compo-
sition of the products of the reaction of QMI with thi-
ols was thus observed in [12].
The data in Tables 2 and 1 apparently do not con-
tradict one another. Indeed, when NPrOH is increased,
the values of k1 and k1nc in Table 1 grow in proportion
to one another. At the same time, it follows from
Table 2 that the rate of the nonchain route wnc in this
case grows faster than that of chain route wc. In fact,
this “contradiction” is explained by a decrease in the
chain length ν of the chain reaction with an increase in
NPrOH (see the last column of Table 2).
Let us consider the expression for chain length ν in
more detail. For this we obtain the expression for the
rate of chain reaction wc = wQDI − wnc = wQDI
k1nc[QDI][PhSH] from Eq. (5) and divide it by the
−
rate of chain initiation in non-initiated reaction wi(0)
2k1[QDI][PhSH]:
=
wQDI − wnc
wc
ν =
=
wi(0) 2k1[QDI][PhSH]
(6)
 [QDI] 1/2
k2
= 0.5 +
.
1/2 

2k41/2k1
[PhSH]


RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY A Vol. 93 No. 4 2019

650
VARLAMOV
The first summand 0.5 in the right part of (5) con-
ACKNOWLEDGMENTS
This work was supported by the Russian Academy
siders the consumption of QDI in reaction (I) of radi-
cal formation, and this summand can be ignored for
fairly long chains.
of Sciences.
It is seen from (6) that the second member in the
right part depends on cofactor k2/2(k4k1)1/2 at the
same ratio of the concentrations of QDI and PhSH.
Table 1 shows that upon moving from chlorobenzene
to propanol-1, parameter k2/(2k4)1/2 is only halved.
This is insufficient for explaining the fairly large drop
in chain length upon an increase in NPrOH. The growth
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RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY A Vol. 93 No. 4 2019