Solvent and external pressure effects on the ratio of the cyanoisopropyl radical recombination and disproportionation rates

Article abstract of DOI:10.1134/S0023158413040034

A GC-MS analysis of the azobisisobutyronitrile thermal decomposition products of in solutions at 80 C showed that the ratio of recombination and disproportionation rates of the cyanoisopropyl radical does not depend on the medium viscosity, but increases when the internal pressure of the solvent increases according to the log(k _dispr/k _rec) = -1.25 + 0.096 P _int ^0.5 law. This means that the activation volume corresponding to recombination is larger than that corresponding to disproportionation. It follows from the relationship log(k _dispr/k _rec) = (ΔV _rec ^≠ - Δv _dispr ^≠)ΔP/RT that, for the decomposition of the substrate in benzene under a pressure of 0.5-4.0 kbar, the difference between the activation volumes is ΔV _rec ^≠ - ΔV _dispr ^≠ = 8 cm³/mol.

Full text of DOI:10.1134/S0023158413040034

ISSN 0023ꢀ1584, Kinetics and Catalysis, 2013, Vol. 54, No. 4, pp. 404–407. © Pleiades Publishing, Ltd., 2013.
Original Russian Text © V.V. Dubikhin, E.I. Knerel’man, G.M. Nazin, V.G. Prokudin, G.A. Stashina, A.V. Shastin, I.G. Shunina, 2013, published in Kinetika i Kataliz, 2013, Vol. 54,
No. 4, pp. 425–429.
Solvent and External Pressure Effects on the Ratio
of the Cyanoisopropyl Radical Recombination
and Disproportionation Rates
a
a
a
a,
V. V. Dubikhin , E. I. Knerel’man , G. M. Nazin , V. G. Prokudin *,
b
b
b
G. A. Stashina , A. V. Shastin , and I. G. Shunina
a
Institute of Problems of Chemical Physics, Russian Academy of Sciences, Chernogolovka, Moscow oblast, 142432 Russia
b
Zelinsky Institute of Organic Chemistry, Russian Academy of Sciences, Moscow, 119991 Russia
*
eꢀmail: prokud@icp.ac.ru
Received January 16, 2012
Abstract—A GCꢀMS analysis of the azobisisobutyronitrile thermal decomposition products of in solutions
at 80°C showed that the ratio of recombination and disproportionation rates of the cyanoisopropyl radical
does not depend on the medium viscosity, but increases when the internal pressure of the solvent increases
0
.5
according to the log(kdispr/krec) = –1.25 + 0.096
P
law. This means that the activation volume correspondꢀ
int
ing to recombination is larger than that corresponding to disproportionation. It follows from the relationship
≠
≠
log(kdispr/krec) = (ΔVrec − ΔVdispr)ΔP RT that, for the decomposition of the substrate in benzene under a presꢀ
≠
≠
3
sure of 0.5–4.0 kbar, the difference between the activation volumes is ΔVrec − ΔVdispr = 8 cm /mol.
DOI: 10.1134/S0023158413040034
The recombination of alkyl radicals in the gas
There are two possible reasons why the kdispr/krec
phase and in solution usually proceeds considerably ratio increases markedly on passing from solutions to
more rapidly than their disproportionation [1]. This is the solid state. The first reason is the difference
explained not by the different activation energies of between the activation energies of these reactions. The
CIP radical is among the lowꢀactivity free radicals,
and, theoretically, the activation energy Edispr for it can
be noticeably higher than Erec. In the gas phase, this
these processes, which are too low to be determined
experimentally, but by the difference between the actiꢀ
≠
vation entropies
tial factor: А = (
tistical factor of the reaction, еkT
and is the gas constant. Although the
Δ
S , which appears in the preexponenꢀ
≠
difference contributes to the decrease in kdispr
in the solid phase, where the reaction is diffusionꢀconꢀ
trolled, kdispr krec is larger. In this case, kdispr krec in
solutions can depend on the medium viscosity.
/krec, but,
σ
еkT
/h
)exp(
Δ
S
/R
)
, where
= 1.69
value in the
σ
is the staꢀ
1
3 –1
/h
×
10 s ,
/
/
R
σ
disproportionation of alkyl radicals is always larger
than in their recombination, the ratio of these reaction
The other possible reason is the inequality of the
rate constants, kdispr
1]. For example, the kdispr
cal in the gas phase and in benzene is 0.14 [1] at
6
0
/
krec, is typically less than unity volumes of the activated complexes (ACs) in the
[
/
krec ratio for the ethyl radiꢀ recombination and disproportionation reactions. The
σ
=
<
solidꢀstate decay of a radical pair (RP) is described by
the “molten cell” model [4] or by the identical extra
volume model for unimolecular processes [5].
According to these models, both the molecular
decomposition into radicals and the radical pair decay
are preceded by the fluctuationꢀinduced expansion of
the matrix cell up to the size at which the crystal interꢀ
action forces stop acting on the molecule and on the
AC that forms during the reaction and the reactions
proceed at the same rate as in the liquid phase. The
work spent on cell deformation and on the creation of
dispr
(consequently, in the elementary steps kdispr
/
krec
.02), whereas that for the cyanoisopropyl (CIP) radꢀ
C this ratio is 0.06 at
= 12 [2]. At the same time, kdispr krec for the CIP
radical in the solid phase is much larger: this ratio is
.16 in the case of radical generation by the thermal
decomposition of crystalline azobisisobutyronitrile (
at 70 C [2] and is as large as 9 in the photochemical
decomposition of at –78 C [3]. No reliable explanaꢀ
ical Me (CN)C in benzene at 80
°
2
σ
dispr
/
1
I)
°
I
°
tion was suggested for this fact, which possibly reflects
the general regularities of solidꢀstate chemical reacꢀ
≠
the extra volume ΔVext is added to the true activation
tions [4]. For this reason, in the present work we energy, and this causes the retardation of the process.
attempted to experimentally explain why kdispr
crystalline azobisisobutyronitrile is larger.
/
krec in The solidꢀstate increase in kdispr
/krec can be explained
by the effect of solid matrix provided that the activaꢀ
404

SOLVENT AND EXTERNAL PRESSURE EFFECTS
Solvent viscosity and internal pressure effects on the rate constant ratio kdispr krec
kdispr krec
405
/
Viscosity at 80
°
C, cP
kH/kD for the
disproportionation
Solvent
Pint, atm [7]
/
[6]
Acetonitrile
Toluene
Benzene
0.230
0.317
0.318
0.442
0.574
0.890
0.896
1.03
3837
3499
3734
2867
2764
–
–
–
4951
–
0.100
0.070
0.077
0.060
0.054
–
–
–
0.120
–
–*
–
2.17
–
2.03
1.24
1.30
1.36
–
Ethanol
Isopropanol
Naphthalene
Tetralin
Decalin
Ethylene glycol
Cyclohexanol
3.02
3.50
1.33
*
No data (–).
tion volume in recombination is larger than in disproꢀ into the
C
≡
N
bond to form ketenimine
≠
≠
Me (СN)CN=C=СMe(CN), or disproportionated to
isobutyronitrile Me (NC)CH (III and methacryloniꢀ
2
portionation; i.e. ΔVrec
these volumes can be determined from the pressure
dependence of kdispr krec for the reaction conducted in
> ΔVdispr. The ratio between
)
2
trile CH =C(CN)Ме (IV
)
. As an analysis showed,
compounds III and IV always form at equal concenꢀ
trations and, therefore, the kdispr krec ratio can be
determined from the ratio [III]/[II]. The experiments
on decomposition of in deuterated solvents (isoproꢀ
panolꢀ 1, ethanolꢀ 6, tolueneꢀ 3, or a mixture of toluꢀ
eneꢀ 3 (70%) and triphenylmethaneꢀ 1 (30%), where
2
/
inert solvents. Thus, to understand the specific feaꢀ
tures of the competition between the solidꢀstate
recombination and disproportionation, one should
study how these reactions proceed in solutions.
/
I
d
d
d
d
d
the C–D bond strength is low) showed that there is no
EXPERIMENTAL
deuterated Me (NC)CD among the reaction prodꢀ
2
The syntheses of compound I and its fully deuterꢀ ucts. This means that the CIP radicals do not react
ated analog (Iꢀd12) was described by Nonhebel and with the solvent and react only with one another.
Walton [2].
The experimental data are presented in the table.
The products were analyzed by the GCꢀMS The transition of disproportionation to the diffusionꢀ
method. The type of instrument, chromatographic controlled mode was detected as the change in the
conditions, product chromatograms indicating the value of the kinetic isotope effect, which was observed
retention times, product compositions, and their relaꢀ in the decomposition of a mixture of
tive chromatographic sensitivities were reported in our
I
and
I
ꢀ
d
12 in
·
solution. The resulting (CH ) (CN)
C
(RH
)
and
3
2
earlier work [2].
A barostat (working pressure of up to 15 kbar, temꢀ
perature of up to 200 С) was used to perform experiꢀ
ments at high pressures. A tightly sealable Teflon tube
was filled with a solution of the substance to be examꢀ
ined. The tube was placed into a dismountable die as a
thickꢀwalled cylinder made of specialꢀpurpose steel. A
·
(
CD ) (CN)C (RD) radicals undergo conversion via
3 2
reactions involving their free valence at equal rates [2].
Therefore, we can write the following equations:
RH (or R ) + R = HC(CH ) CN (or
°
D
H
3 2
HC(CD ) CN) + CH =C(CH )CN (IV),
3 2
2
3
RH (or R ) + R = DC(CH ) CN (or
D
D
3 2
constant pressure was maintained by means of a 40ꢀton DC(CD ) CN) + CD =C(CD )CN (IVD).
3
2
2
3
hydraulic press.
To measure the kinetic isotope effect kH/kD, the
product concentration ratio [IV]/[IVD] was deterꢀ
mined. The results are given in the table. In benzene,
RESULTS AND DISCUSSION
kH
CIP radicals were generated by decomposition of a reactions, and increases slowly to reach a value of 1.2–
wt % solution of compound at 80 . The solvents 1.3, which is apparently determined by the ratio of preꢀ
/kD is about 2, which is typical of proton transfer
1
I
°С
used differed in their internal pressure and viscosity. exponential factors. Even when the viscosity is 0.9 cP,
The products were analyzed after 3ꢀhꢀlong heating, disproportionation is diffusionꢀcontrolled. In recomꢀ
which ensured virtually complete decomposition of bination, the diffusionꢀcontrolled regime is likely realꢀ
the starting compound. At the early stages of the ized at a much lower viscosity. No dependence of
decomposition of
produced [3], which then recombined to form tetramꢀ the activation energy difference Edispr
ethyl succinimide (NC)Me CCMe (CN) (II), inserted and has no significant effect on the kdispr
I, nitrogen and CIP radicals were kdispr/krec on the viscosity is observed. This means that
–
/
Erec is small
krec ratio.
2
2
KINETICS AND CATALYSIS Vol. 54
No. 4
2013

406
DUBIKHIN et al.
in Pint. An analysis of the products was performed after
the complete decomposition of 1% solutions of at
(the reaction time was 3 h). The data presented
in the table show that disproportionation of the CIP
radical is accelerated by internal pressure to a greater
extent than its recombination, this effect being more
pronounced for the CIP radical than for ethyl [8]. For
example, when replacing ethylene glycol with toluene,
log (kdispr/krec)
I
–0.6
–0.7
–0.8
–0.9
–1.0
–1.1
–1.2
–1.3
1
1
80 С
°
2
2
B
6
4
kdispr/krec increases by a factor of 1.71 for the CIP radꢀ
ical and by a factor of 1.44 for the C H radical. The
2
5
data given in the table obey the equation
А
3
0
.5
4
log(kdispr k ) = −1.25 + 0.096P ,
rec
int
5
whose slope factor is slightly greater than in the case of
the ethyl radical (Fig. 1). This means that VAC in
recombination is larger than in disproportionation and
6
5
2
54 56 58 60 62 64 66 68 70 72
0i n. 5t , atm
Р
≠
≠
the activation volume difference ΔVrec
– ΔVdispr for the
ethyl radical is smaller than for the CIP radical.
Fig. 1. Dependences of kdispr
pressure for the (A) CIP and (B) ethyl radicals [7]: (
ylene glycol, ( ) acetonitrile, ( ) benzene, ( ) toluene,
) ethanol, and ( ) isopropanol.
/
krec on the solvent internal
≠
1
) ethꢀ
If the AC has a linear structure, the fact that ΔVrec
≠
>
2
3
4
(5
6
ΔVdispr is difficult to explain. For this reason, it is
thought that, in disproportionation, the AC has a
cyclic fourꢀcentered structure [1]. The absence of reliꢀ
able data on the structure of AC in this reaction allows
no estimation of its volume by calculation and deterꢀ
≠
The role of the volume factor retarding disproporꢀ
tionation and recombination in the crystal lattice can
be estimated using formula (1), which was derived for
a unimolecular reaction proceeding in the bulk of an
undamaged crystal [5]
mination of the activation volume difference ΔVrec
–
≠
ΔVdispr. However, it can be determined experimentally
from the dependence of kdispr krec on the pressure . To
/
P
2
≠
RT lnKdec = ΔEadd = ΔV
2βVM ,
(1)
ksol is the deceleration coefficient,
Eliq is the additional activation energy,
is the isothermal compressibility factor, VM = М/ is
(
add
)
determine the activation volumes, lowꢀviscosity solꢀ
vents are commonly used and the external pressure is
varied ibetween atmospheric pressure and several kiloꢀ
bars [10]. Under these conditions, the isothermal
compressibility factor of the solvent does not decrease
where Kdec
= kliq/
Δ
Eadd Esol –
=
β
ρ
≠
the molar volume of the substance, and ΔVadd is the significantly and a free volume sufficient for the forꢀ
mation of the activated complex remains in the
medium. In view of the aforesaid, benzene was used as
additional volume for activation in the solid state
ensuring the vibrational–rotational mobility of the
reacting molecule and activated complex. The RP
the solvent in the study of the reaction of
sure. The experiments were performed at 80°C
I
under presꢀ
at a
≠
transforms via two pathways, and the ΔVadd and Kdec
values for each pathway depend on the molar volume
substrate concentration of 1 wt %, and the pressure
range was extended to 10 kbar. This is due to the fact
of AC (VAC). If
β
and VM are constant, a stronger
that, at 80 C and Р > 5 kbar, benzene is in the solid
°
deceleration in the solid state should be observed in
the reaction with a larger VAC or (since the initial state
state and one can see how the solvent solid matrix
influences the competition between the recombinaꢀ
is the same in both cases) a larger activation volume tion and disproportionation reactions.
≠
Δ
V . Thus, the solidꢀstate increase in kdispr/krec can be
The results obtained are shown in Fig. 2. In the presꢀ
sure range from 0.5 to 4.0 kbar, a linear dependence of
explained by the effect of the solid matrix provided
≠
≠
log(kdispr/krec) on P is observed, from which, using the
≠ ≠
that ΔVdispr
<
ΔV . This relationship between the
rec
activation volumes was observed earlier [1] in the reacꢀ
tions of ethyl radicals and some other alkyl radicals.
equation
Δ
log(kdispr
/
krec) = (ΔVrec
–
≠
ΔVdispr
)ΔP/RT,
3
≠
one can determine that ΔVrec
The VAC in these reactions differ by the same value.
When the pressure is 5 kbar, benzene undergoes a
phase transition, after which the decomposition of I
– ΔVdispr = 8 cm /mol.
The kdispr/krec ratio for the ethyl radical was found to
depend on the solvent internal pressure Pint [8], and
0
.5
the linear dependence of log(kdispr
/krec) on
P
was
int
observed, which follows from absolute reactions rate and the radical–radical reaction proceed in the solid
theory [9]. To check if this dependence is fulfilled for matrix of benzene compressed by the high pressure.
the CIP radical formed from
I, we determined the After the solidification of benzene, the kdispr/krec ratio
ratio kdispr krec = [IV]/[III] in several solvents differing increases severalꢀfold (which is due to the drastic
/
KINETICS AND CATALYSIS Vol. 54
No. 4
2013

SOLVENT AND EXTERNAL PRESSURE EFFECTS
407
Thus, we experimentally found that the activation
log (kdispr/krec)
volume in the disproportionation of the CIP radical is
0.4
3
8
cm /mol smaller than in recombination. This is the
first experimental measurement of this kind in the
series of alkyl and substituted alkyl radicals. The data
obtained suggest that the increase in the ratio of rate
0
constants kdispr
crystalline state of
molten cell” model. According to this model, the
/
krec on passing from solutions to the
I
is wellꢀexplained in terms of the
“
0
0
1
.9
.8
.2
solidꢀstate interaction of free radicals is matrixꢀconꢀ
trolled because of the necessity of energy consumption
for mobilization of the reacting molecules and actiꢀ
vated complex. Therefore, among the two competitive
reactions, the reaction in which the activation volume
is smaller is slowed down to a lesser extent.
REFERENCES
0
2
4
6
8
10
, kbar
Р
1. Nonhiebel, D.C. and Walton, J.C., FreeꢀRadical
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Nazina, L.D., Prokudin, V.G., Shastin, A.V., and
Shunina, I.G., Kinet. Catal., 2013, vol. 54, no. 1, p. 18.
Fig. 2. Pressure effect on the kdispr
8
/krec ratio in benzene at
0
°C.
decrease in the isothermal compressibility factor) and
depends weakly on the pressure. This dependence proꢀ
vides no useful information on VAC, since the lowꢀ
compressibility media are not suitable for measureꢀ
ment of activation volumes [10].
3
. McBride, J.M., J. Am. Chem. Soc., 1971, vol. 93,
no. 23, p. 6302.
4. Yakimchenko, O.E. and Lebedev, Ya.B.,
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mekhanizm khimicheskikh reaktsii v tverdom tele. Sb
(Kinetics and Mechanism of SolidꢀPhase Chemical
Reactions), Chernogolovka, Moscow oblast: Ob”edin.
Inst. Khim. Fiz., 1981, p. 27.
≠
The fact that there are no proven ΔVext calculation
methods for reactions with a negative activation volꢀ
5
. Manelis, G.B., Nazin, G.M., and Prokudin, V.G.,
Russ. Chem. Bull., 2011, vol. 60, no. 7, p. 1440.
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. Stefani, A.P., J. Am. Chem. Soc., 1968, vol. 90, no. 7,
p. 1694.
ume and
the RP solid solution in
of Eadd via formula (1). According to experimental
data, the increment of kdispr krec in the solid state is
0 times larger than in ethylene glycol or acetonitrile
solution (solvents in which Pint is closest to Pint in ),
which corresponds to the activation energy difference
Edispr = 6 kJ/mol. This difference results from
the decelerating effect of the solid matrix and, in
essence, is equal to the Eadd value in Eq. (1) deterꢀ
mined at 80 . Due to the increase in the temperature
and compressibility factor Eadd and Kdec also
increase. This explains why the kdispr krec ratio is lartger
the lowꢀtemperature photolysis of [3].
β
cannot be estimated in the microregion of
I
allows no reliable calculation
6.
Δ
/
7. Dack, M.R.J.,
8
1
I
9
. Glasstone, S., Laidler, K.J., and Eyring, H., The Theꢀ
ory of Rate Processes, New York: McGrawꢀHill, 1941.
Erec
–
1
0. Gonikberg, M.G., Khimicheskoe ravnovesie i skorost'
reaktsii pri vysokikh davleniyakh (Chemical Equilibꢀ
rium and Reaction Rates at High Pressures), Moscow:
Khimiya, 1969.
Δ
°С
β,
/
I
Translated by K. Utegenov
KINETICS AND CATALYSIS Vol. 54
No. 4
2013