The N-H and O-H bond dissociation energies in 4-hydroxydiphenylamine and its phenoxyl and aminyl radicals

Article abstract of DOI:10.1023/B:RUCB.0000030802.82171.ef

The N-H and O-H bond dissociation energies in 4-hydroxydiphenylamine Ph-NH-C₆H₄-OH (D_NH= 353.4, D_OH=339.3 kJ mol^-1) and its semiquinone radicals D_NH(Ph-NH-C ₆H₄-O^.) = 273.6, D_OH(Ph-N ^.-C₆H₄-OH) = 259.5 kJ mol^-1 were first estimated using the parabolic model and experimental data (rate constants) on two elementary reactions with participation of N-phenyl-1,4- benzoquinonemonoimine (2). One of the reactions, namely, that of 2 with aromatic amines, was studied in this work using a specially developed method.

Full text of DOI:10.1023/B:RUCB.0000030802.82171.ef

306
Russian Chemical Bulletin, International Edition, Vol. 53, No. 2, pp. 306—312, February, 2004
The N—H and O—H bond dissociation energies
in 4ꢀhydroxydiphenylamine and its phenoxyl and aminyl radicals
V. T. Varlamov
Institute of Problems of Chemical Physics, Russian Academy of Sciences,
1 prosp. Akad. Semenova, 142432 Chernogolovka, Moscow Region, Russian Federation.
Fax: (096) 524 9676. Eꢀmail: varlamov@icp.ac.ru
The N—H and O—H bond dissociation energies in 4ꢀhydroxydiphenylamine
Ph—NH—C6H4—OH (DNH= 353.4, DOH=339.3 kJ mol–1) and its semiquinone radicals
DNH(Ph—NH—C6H4—O•) = 273.6, DOH(Ph—N•—C6H4—OH) = 259.5 kJ mol–1 were first
estimated using the parabolic model and experimental data (rate constants) on two elementary
reactions with participation of Nꢀphenylꢀ1,4ꢀbenzoquinonemonoimine (2). One of the reacꢀ
tions, namely, that of 2 with aromatic amines, was studied in this work using a specially
developed method.
Key words: 4ꢀhydroxydiphenylamine, 4ꢀhydroxydiphenylaminyl and 4ꢀanilinophenoxyl
radicals, bond dissociation energies, parabolic model of radical reactions; Nꢀphenylꢀ1,4ꢀ
benzoquinonemonoimine, aromatic amines, rate constants.
4ꢀHydroxydiphenylamine (1) possesses the properties
quinone radicals 2n• and 2o• have not been determined
as yet. Because of this, some problems concerning the
reactivities of these species are still to be solved. These
are, in particular, (i) which group (OH or NH) in molꢀ
ecule 1 is mainly attacked by free radicals and (ii) which
atom (O or N) is more reactive in the hydrogen abstracꢀ
tion reaction during dehydrogenation of organic comꢀ
pounds with quinonemonoimine 2 and is thus to the greatꢀ
est extent involved in the reaction.
of a strong antioxidant and is used for stabilization of
rubbers, fuels, lubricants, and other materials.1 Hydrogen
abstraction from molecule 1 can result in 4ꢀhydroxyꢀ
diphenylaminyl (2n•) or 4ꢀanilinophenoxyl (2o•) radiꢀ
cals depending on which group (NH or OH) is involved
in the reaction.
In this work we first estimated the parameters DNH
and DOH for molecule 1 and the aminyl and phenoxyl
radicals derived from this molecule. They were calculated
using the intersecting paraboles (IP) method,1 some pubꢀ
lished data, and the rate constants for two elementary
reactions involving quinonemonoimine 2 (the lastꢀmenꢀ
tioned parameters were determined in this work).
Among them, there are the reactions of quinoneimine 2
with 4,4´ꢀdimethoxydiphenylamine (3a) and 4,4´ꢀdiꢀ
methyldiphenylamine (3b). The rate constants for these
and related reactions are unavailable as yet because no
relevant methods of their determination were proposed.
Such a procedure was developed in this work. It is based
on the use of the kinetic laws of an initiated chain reacꢀ
tion of quinonemonoimine 2 with 2,5ꢀdiꢀtertꢀbutylꢀ
hydroquinone (4), catalyzed by aromatic amines.
Further oxidation of both radicals (reaction with yet
another radical) results in the same compound, Nꢀpheꢀ
nylꢀ1,4ꢀbenzoquinonemonoimine (2).
The N—H and O—H bond dissociation energies (DNH
and DOH, respectively) for molecule 1 and for the semiꢀ
R1 = R2 = OMe (a), Me (b)
Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 293—299, February, 2004.
1066ꢀ5285/04/5302ꢀ0306 © 2004 Plenum Publishing Corporation

Bond dissociation energies
Russ.Chem.Bull., Int.Ed., Vol. 53, No. 2, February, 2004
307
Experimental
This is due to the fact that the rate constant for the strongly
exothermic reverse reaction (k–1) is 12 to 13 orders of
magnitude greater than k1.
The synthesis and purification of reactants and solvent (chloꢀ
robenzene) were reported earlier.2 Experiments were carried out
in an argon atmosphere in a thermostatted quartz cell reactor of
bubbling type (the volume was 8.5 mL, the optical path length
was 2.0 cm), incorporated into a Specord UVꢀVIS spectroꢀ
photometer. The experiments involved monitoring of the
optical density at λ = 450 nm (ε = 2950 at 321.5 K and
2920 L mol–1 cm–1 at 340.0 K); our previous experiments showed
that only the absorbance of quinoneimine 2 was detected in this
spectral region. To minimize the experimental errors, quinoneꢀ
imine 2 and the initiator (tetraphenylhydrazine) were simultaꢀ
neously introduced into a preheated cell containing solutions of
both hydroquinone and aromatic amine. To this end, we used
coꢀsolutions of quinoneimine 2 and tetraphenylhydrazine with a
prescribed concentration of each component.
The k1 value can be determined reliably if reaction (1)
plays the role of an initiation stage for some chain proꢀ
cess. In this case, provided that all the radicals formed are
accepted, the reaction (1) can contribute largely to the
total rate of the process. This contribution can be meaꢀ
sured experimentally with ease, because an increase in the
rate of the process will be ν times greater than the rate of
the elementary reaction (1), where ν is the chain length.
A convenient example is provided by the chain reacꢀ
tion of quinonemonoimine 2 with 2,5ꢀdiꢀtertꢀbutylꢀ
hydroquinone (4), resulting in 4ꢀhydroxydiphenylamine
(1) and 2,5ꢀdiꢀtertꢀbutylquinone 5 2,3
:
The products accumulated affect the rate of the reaction;2,3
therefore, the reaction kinetics was studied using the initial rates
(w2) of the quinoneimine consumption (in this case, the effect of
the products can be ignored). To increase the accuracy, the w2
values were calculated using the results of approximation of the
kinetic curves of the quinonemonoimine consumption by an
empirical equation
ln(a + ln[2]) = b + ct,
where a, b, and c are constants determined using an iterative
procedure. In this case, one has
w2 = –c [2]0(ln[2]0 + a).
This reaction proceeds by the mechanism presented
below:
Results and Discussion
The most correct estimate of the N—H bond dissociaꢀ
tion energy (DNH/kJ mol–1) for molecule 1 can be obꢀ
tained from the correlation equation proposed4 for substiꢀ
tuted diphenylamines:
Chain initiation*
2 + 4
2
• + 5•
(2)
Chain propagation
DNH = (363.6 0.24) + (11.93 0.42)σ+ (r = 0.995),
2 + 5•
2• + 4
2
• + 5
(3)
(4)
where σ+ is the Brown constant of the substituent in pꢀpoꢀ
sition of the benzene ring of diphenylamine. Using the
same system of σ+ꢀconstants as that employed in Ref. 4
1 + 5•
Chain termination
2• + 2•
(σ+OH = –0.853 5), we get DNH(1) = 353.4 0.6 kJ mol–1
.
2 + 1
(5)
(6)
(7)
Hereafter, this value will be considered as a preꢀ
ferred one.
Method of investigation and determination of the rate
constants for the reactions of quinoneimine 2 with aromatic
amines. For brevity, let us write the equation of this reacꢀ
tion in the form
2 + 4
1 + 5
5 + 4
2• + 5•
5• + 5•
2 + 3
2• + 3•,
(1)
The reaction mechanism is significantly compliꢀ
cated in the presence of aromatic amines. The amine
where 2• are the phenoxyl or aminyl radicals formed from
quinoneimine 2. Reaction (1) cannot be studied immediꢀ
ately by following the consumption of the starting comꢀ
pounds because the reactant concentrations remain virtuꢀ
ally unchanged over a rather long period after mixing.
* Radical 5• is the 2,5ꢀdiꢀtertꢀbutylꢀ4ꢀhydroxyphenoxyl radical
formed upon hydrogen abstraction from hydroquinone 4 or upon
hydrogen addition to quinone 5.

308
Russ.Chem.Bull., Int.Ed., Vol. 53, No. 2, February, 2004
V. T. Varlamov
admixtures act as catalysts and the reaction mechanism
scheme is augmented by the following elementary reacꢀ
tions6:
be determined by following the reaction kinetics. Indeed,
in the presence of an initiator one has
w22 = Φ(i)(k1[2][3] + k2[2][4] + 0.5wi) =
Chain initiation
=Φ(i)(k1[2][3] + k2[2][4]) + Φ(i)0.5wi,
(III)
2 + 3
2
• + 3•
(1)
where Φ(i) is the same function as that appeared in exꢀ
pression (II). The function Φ(i) is independent of wi, and
therefore its value remains constant in a series of runs at
constant concentrations of compounds 2, 4, and 3 and at
variable wi. Then, by plotting a straight line (w22 vs. 0.5wi)
one can determine a = Φ(i)(k1[2][3] + k2[2][4]) from the
Yꢀintercept while the slope gives b = Φ(i). The ratio a/b =
k1[2][3] + k2[2][4] gives the sum of the rates of the reacꢀ
tions (1) and (2). Now, it is possible to determine k1
provided the known k2 value and the concentrations of
the reagents 2 and 4.
Radical exchange
3• + 4
2• + 3
3 + 5•
1 + 3•
(8), (–8)
(9)
Chain termination
2• + 3•
• + 3•
3• + 3•
2 + 3
(–1)
(10)
(11)
This method, which is based on the double mixed
initiation of a chain reaction, was employed in this work
to determine the k1 values for the reactions involving
compounds 3a and 3b. The linear dependence (III) beꢀ
5
5 + 3
Products
The expression for the consumption rate of quinoneꢀ
imine in the presence of a catalyst can be written as
follows:a
2
tween w2 and the initiation rate is quite reasonable
(Fig. 1). The experimental data and the calculated the
rate constants are listed in Table 1.
Calculations of the N—H and O—H bond dissociaꢀ
tion energies for the semiquinone radicals 2n• and 2o•.
Method 1. The O—H and N—H bond dissociation enerꢀ
gies in radicals 2n• and 2o•, respectively, can be calꢀ
culated from the rate constant for the elementary reacꢀ
tion (2) of the mechanism of the chain reaction beꢀ
tween compounds 2 and 4 (see above). The experimenꢀ
tal k2 values at 298.2 and 340.0 K are 3.22•10–3 and
8.61•10–2 L mol–1 s–1, respectively.2
2
,
(I)
w2
=
where
А = k4[4] + k9[3],
B = k2[4][2]+ k1[3][2],
C = k5k82[4]2 + k–1k8k9[4][3] + k9 k11[3]2,
2
w2 •1012/(mol L–1 s–1 2
)
2
D = k6k82[4]2 + k8(k–1
k
–8 + k9k10)[4][3] + 2k–8k9k11[3]2,
3
5
4
3
2
1
E = k7k82[4]2 + k8k–8k10[4][3] + k–8 k11[3]2.
2
1
In expression (I), the factor B equals the sum of the
rates of the reactions (1) and (2) in which radicals are
formed in the system. Let us rewrite expression (I) in
the form:
w22 = Φ(i)B = Φ(i)(k1[2][3] + k2[2][4]),
(II)
where Φ(i) is the function of the concentrations of the
compounds 2 and 4, catalyst 3, and of the rate constants
of all the elementary reactions, except for the initiation
stages (1) and (2). Expressions (I) and (II) show that the
4
0
2
4
0.5wi•109/mol L–1 s–1
dependence of w2 on the concentration of amine 3 canꢀ
2
Fig. 1. The rate of the chain reaction of quinoneimine 2 with
hydroquinone 4 catalyzed by aromatic amines plotted vs. the
radical initiation rate due to decomposition of the initiator
(tetraphenylhydrazine). The straight lines are enumerated exꢀ
actly in the same manner as the series of runs (see Table 1).
not be used to determine k1 because the factor Φ(i) changes
as the parameter [3]0 varies. However, if an initiator caꢀ
pable of generating free radicals at a preset rate wi is introꢀ
duced into the amineꢀcontaining system, the k1 value can

Bond dissociation energies
Russ.Chem.Bull., Int.Ed., Vol. 53, No. 2, February, 2004
309
Table 1. Rate constants k1 (L mol–1 s–1) obtained using double mixed initiation methoda
av
Comꢀ
pound
Series
of runs
T/K
[4]0•104
mol L–1
[3]0•103
0.5wi•1010
mol L–1 s–1
w2•107
k1•103
k1 •103 b
L mol–1 s–1
3a
1
340
4.75
0.57
0
3.88
7.76
15.5
48.5
0
3.88
7.76
48.5
0
7.76
15.5
48.5
0
3.88
7.76
48.5
0
3.88
15.5
38.8
0
8.12
9.44
12.6
14.0
20.1
4.20
6.05
8.18
13.0
5.53
10.1
13.0
17.9
8.68
10.7
12.7
22.7
4.5
3.60 0.90
4.10 1.40
2
3
4
5
6
340
340
340
340
340
2.38
2.38
4.75
2.38
4.75
0.57
5.70
1.90
1.90
1.90
4.80 2.00
0.50 0.23
0.35 0.11
7.35 1.50
9.10 4.90
3b
0.38 0.15
6c
4.4
5.2
6.5
9.6
4.00 1.60d
7.76
8.6
15.5
38.8
0
1.504
4.63
0
9.6
12.3
3.9
4.2
4.4
7
8
321.5
321.5
2.44
2.44
5.85
11.7
1.38 0.40
1.25
0.66 0.20d
4.5
11.1
5.4
a With tetraphenylhydrazine as the initiator; ki (s–1) = 1.475•1014exp(–Ea/RT)2 and Ea = 117.5 kJ mol–1. The concentration of 2 was
1.9•10–4 at 340.0 K and 1.95•10–4 mol L–1 at 321.5 K. The k2 values at 321.5 and 340.0 K are 2.23•10–2 (calculated from the
temperature dependence) and 8.61•10–2 L mol–1 s–1 2
.
av
b k1 denotes the average value.
c Dimethyldiꢀ(4ꢀanilinophenoxy)silane (6).
d Per NH group.
However, the reaction
tion energy in the molecule of hydroquinone 4, DOH(4).
Earlier,7 we estimated this parameter at DOH(4) =
345.1 1 kJ mol–1 by data averaging over four depenꢀ
dences between the logarithm of the rate constants for
elementary reactions of 4,4´ꢀsubstituted diphenylaminyl
radicals 3• with sterically unhindered phenols and the
thermal effects, q, of the reactions (q = DNH – DOH). In
turn, these dependences were plotted using the results of
a laser flash photolysis study of the reactions of four radiꢀ
cals 3• (R1 = R2 = H, Me, Br; R1 = OMe, R2 = H) with
eight different phenols including 4. The characteristics of
the phenols, DOH, used in calculations were somewhat
different from the recommended values1.
2 + 4
2• + 5•
(2)
proceeds involving two channels:
2 + 4
2 + 4
2o•+ 5•,
2n• + 5•,
(2a)
(2b)
exp
where k2 = k(2a) + k(2b)
.
To calculate the DOH and DNH values for radicals 2n•
and 2o• by the IP method, one should know not only
exp
k2 but also the exact value of the O—H bond dissociaꢀ

310
Russ.Chem.Bull., Int.Ed., Vol. 53, No. 2, February, 2004
V. T. Varlamov
The relationship for calculating the rate constant for
the overall reaction (2) by the IP method has the form:
Phenol
DOH/kJ mol–1
Earlier
values
Recommendꢀ
ed values1
k2exp = {2•107e–1/2
γ
(2a)exp[–(337.3 – DNH)/RT ]} +
(2b)exp[–(337.3 – DOH)/RT ]}. (VI)
+ {2•109e– /2
γ
1
C6H4OH
4ꢀMeC6H4OH
4ꢀMeOC6H4OH
2,6ꢀMe2C6H3OH
2,4,6ꢀMe3C6H2OH
2,6ꢀ(MeO)2C6H3OH
369.0
362.2
345.8
354.6
347.5
347.9
367.0
359.8
349.3
356.1
352.3
354.0
Expresion (VI) was used for processing the experiꢀ
exp
mental data for k2 at T = 298.2 and 340.0 K. When
calculating, the bond dissociation energies were deterꢀ
mined iteratively. The following values were obtained
(in kJ mol–1): DNH(2o•) = 273.89 and DOH(2n•) = 259.55
(∆ = 14.34).
The results of comparison of the calculated temperaꢀ
ture dependence of k2 and the experimental data are preꢀ
sented in Fig. 2.
Method 2. The DNH and DOH values for radicals 2o•
and 2n• can be calculated using the rate constants (see
Table 1) for the reactions:
In this work, we consider the DOH(4) value as a referꢀ
ence. Because of this, as well as trying to use the data
from the same source, we revised the experimental data7
and accepted the recommended1 values of DOH in phenols.
As a consequence, the following new value was obtained:
DOH(4) = 337.3 2.3 kJ mol–1
.
This value of DOH(4) is used hereafter in all calculations.
The activation energies of strongly endothermic reacꢀ
tions (2a) and (2b) nearly coincide with the correspondꢀ
ing enthalpies:
2 + 3
2 + 3
2 + 3
2
• + 3•,
(1)
(1a)
(1b)
2o•+ 3•,
2n• + 3•,
Ea(2a) = DOH(4) – DNH(2o•) – 0.5RT =
= 337.3 – DNH — 0.5RT,
k1exp = k(1a) + k(1b). The expression for calculating k1exp is
similar to Eq. (VI), η(1a) = 0.5hNA(vNH – vNH) = 0,
η(1b) = 0.5hNA(vNH – vOH) = –1.5 kJ mol–1, and the
Ea(2b) = DOH(4) – DOH (2n•) – 0.5RT =
= 337.3 – DOH – 0.5RT.
max
max
threshold values are ∆He
= 31.2, ∆He
=
(1a)
(1b)
16.7 kJ mol–1, A(1a) = A(1b) = 1•108 L mol–1 s–1.1 The
N—H bond dissociation energies (DNH) for 3a and 3b are
respectively 348.6 and 357.5 kJ mol–1. The DNH value in
molecules 3a,b was used as independent variable, while
the DNH(2o•) and DOH(2n•) values were fitted. The disꢀ
sociation energies found are as follows: DNH(2o•) = 273.23
and DOH(2n•) = 259.44 kJ mol–1 (∆ = 13.79).
According to the IP method,1 for the classes of reacꢀ
tions similar to those described by Eqns. (2a) and (2b),
the averaged preꢀexponential factors A(2a) and A(2b) are
1•107 and 1•109 L mol–1 s–1, respectively. In the case in
hand, they should be doubled, because molecule 4 conꢀ
tains two equivalent OH groups. For strongly endotherꢀ
mic processes (enthaply of reaction exceeds some threshꢀ
old value ∆Hemax), one should take into account the
change in the collision crossꢀsection using the following
coefficients1:
k2/L mol–1 s–1
0.08
, (IV)
0.06
0.04
0.02
,
(V)
where η = 0.5hNA(vi – vf) is the zeroꢀpoint vibrational
energy difference between the cleaved O—H bond, vi, in
molecule 4 and the forming bond (N—H or O—H) vf in
radicals 2o• or 2n• (h is the Planck constant, NA is the
Avogadro constant, and v is the vibrational frequency). In
the case in hand, we have η(2a) = 0.5hNA(vOH – vNH) =
1.5 kJ mol–1, η(2b) = 0.5hNA(vOH – vOH) = 0,
300
310
320
330
T/K
Fig. 2. Results of calculations of the temperature dependence of
the rate constant k2 using Eq. (VI) (solid line) compared with
the experimental data (points).
max
max
∆He (2a) = 21.9, and ∆He (2b) = 42.1 kJ mol–1
.

Bond dissociation energies
Russ.Chem.Bull., Int.Ed., Vol. 53, No. 2, February, 2004
311
k1•103/L mol–1 s–1
The last equality shows that the N—H bond dissociaꢀ
tion energy for molecule 1 exceeds the O—H bond dissoꢀ
ciation energy for this molecule by the same value as that
by which the N—H bond dissociation energy for radical
2o• exceeds the O—H bond dissociation energy for radiꢀ
3a
4
3
2
1
cal 2n•, i.e., by 14.1 kJ mol–1
.
Test of the results obtained. Estimation of the O—H
bond dissociation energy for molecule 1 from the rate conꢀ
stant for reaction of quinoneimine 2 with 4ꢀhydroxyꢀ
diphenylamine (1). The bond dissociation energies DNH
and DOH for compound 1 and radicals 2o• and 2n• can
also be calculated from the rate constant for the reaction
3b
2 + 1
2
• + 2•.
(–5)
352
356 DNH/kJ mol–1
This reaction proceeds concurrently involving a total
of four channels:
Fig. 3. Rate constant for reaction (1) at 340.0 K plotted vs. the
N—H bond dissociation energy in secondary aromatic amines.
The experimental data for 4,4´ꢀdimethoxydiphenylamine (3a)
and 4,4´ꢀdimethyldiphenylamine (3b) are shown as full circles.
Results of calculations by the IP method are shown by a solid
line (see text ).
The experimental rate constant for the reaction, k–5
equals the sum of the rate constants for the stages (–5a),
(–5b), (–5c), and (–5d).
,
These estimates are in good agreement with the values
listed above. The results of approximation with these DNH
and DOH values are shown in Fig. 3.
Based on the aforesaid, only three rather than four
The averaged values of the N—H and O—H bond
dissociation energies in radicals 2• (DNH = 273.6,
DOH = 259.5 kJ mol–1) can be used for evaluating
the N—H bond dissociation energy in diamine
(PhNHC6H4O)2SiMe2 (6), for which only unreliable data
are known. Calculations using Eq. (VI) and the rate conꢀ
stants k1 for the reactions of 6 with 2 at 340.0 and 321.5 K
unknown parameters DOH and DNH should be determined
exp
from the experimental k–5
values. The experimental
values of k–5exp/(L mol–1 s–1) are (6.23 0.72)•10–3 at
298.2 K and (1.19 0.14)•10–1 at 340.0 K.2
These data are insufficient for correct estimation of
three DOH and DNH values simultaneously. Therefore,
we evaluated only the O—H bond dissociation energy
for molecule 1 DOH(1), while the averaged values
DNH(2o•) = 273.6 and DOH(2n•) = 259.5 kJ mol–1 (see
above) were considered constant. The parameters of the
elementary reactions necessary to perform the IP calculaꢀ
tions are available in the literature.1 The equation for
(see Table 1) gave DNH(6) = 349.1 kJ mol–1
.
As can be seen, calculations of the DNH and DOH
values for the radicals 2o• and 2n• from the rate constants
for two different elementary reactions give very similar
results. Taken altogether with the estimate of DNH for 1
(see above), these data are sufficient for assessing the last
unknown parameter, namely, the OH bond dissociation
energy for molecule 1. This is possible because the DNH
and DOH values for compound 1 and the radicals formed
from molecule 1 are not independent. From the equality
of the thermal effects of the reactions of successive hydroꢀ
gen addition to quinoneimine 2 to give compound 1 as
the end product
exp
calculating the rate constant k–5 is similar to Eq. (VI)
and contains four terms in accord with the number of
concurrent reactions (see above):
k–5exp = {6.065•106
•
•exp(–(DOH – 273.6)/RT )} +
+ {6.065•107
•
2 + H
2 + H
2o• (+H)
2n• (+H)
1,
1,
•exp(–((DOH +14.1) – 273.6)/RT )} +{6.065•107•
•
•
it follows that
DNH(2o•) + DOH(1) = DOH(2n•) + DNH(1)
•exp(–((DOH + 14.1) – 259.5)/RT )} +
+ {6.065•108
•exp(–(DOH – 259.5)/RT )}.
or
•
DNH(1) – DOH(1) = DNH(2o•) – DOH(2n•).
(VII)

312
Russ.Chem.Bull., Int.Ed., Vol. 53, No. 2, February, 2004
V. T. Varlamov
Processing of the data on the temperature depenꢀ
ber of reactions are currently known, which proceed with
violation of the Polanyi—Semenov rule. Thorough analyꢀ
sis of this problem allowed nearly ten factors governing
the Ea value to be established, the heat of reaction being
only one of them (though one of the most important).1
To reveal the role of the other factors, one should comꢀ
pare the activation energy, Ee0, of thermally neutral reacꢀ
tions (the case where the contribution Q to Ea is included
and has no effect on Ea). For the classes of reactions
exp
dence of k–5
using relationship (VII) with iterative
fitting of the optimum DOH value gave DOH(1) =
334.06 0.04 kJ mol–1. Since ∆ = DNH – DOH
=
14.1 kJ mol–1, one gets DNH(1) = 334.06 + 14.1 =
348.16 kJ mol–1, which differs from the preferred estiꢀ
mate of DNH(1) by ∼5 kJ mol–1 only. Such a good agreeꢀ
ment between the results simultaneously points to corꢀ
rectness of the N—H and O—H bond dissociation enerꢀ
gies in the semiquinone radicals 2o• and 2n•, respectively
(see above), which were used in the lastꢀmentioned calꢀ
culations.
under study, Ee0 (NH) = 39.0 and Ee0 (OH) = 43.3 kJ mol–1 1
.
As can be seen, the activation energy of the thermally
neutral reaction following the first route (the transition
state geometry is O...H...N) is 4.3 kJ mol–1 lower comꢀ
pared to the reaction following the second route (the
transition state geometry is O...H...O). The reason for the
Thus, the N—H and O—H bond dissociation energies
for molecule 1 and radicals 2o• and 2n• are as follows:
DNH(1) = 353.4, DOH(1) = 339.3, DNH(2o•) = 273.6, and
•
DOH(2n•) = 259.5 kJ mol–1
.
lower Ee0 value for the reaction between RO2 and 1
These data allow, e.g., the rate constants for the reacꢀ
tions of 1 with alkylperoxide radicals RO2 to be calcuꢀ
involving the N—H bond as compared to the reaction
involving the O—H bond was determined earlier8: this is
the electronegativity difference between the O and N atꢀ
oms in the transition state.
The author expresses his deep gratitude to E. T.
Denisov for helpful discussions.
•
lated, which is of particular interest taking into account
the fact that compound 1 is used as antioxidant. For defiꢀ
niteness sake, we will consider the reactions of secondary
peroxy radicals RO2• with compound 1 at 333 K (60 °C).
Using the recommended1 value of the O—H bond
dissociation energy in secondary hydroperoxides
(DOH(ROOH) = 365.5 kJ mol–1) and the parameters of
the elementary reactions mentioned above, the IP method
gives (k/L mol–1 s–1):
This work was financially supported by the Chemistry
and Materials Science Branch of the Russian Academy of
Sciences (a grant in the framework of the Program "Theoꢀ
retical and experimental investigations on the nature of
the chemical bonding and mechanisms of the most imꢀ
portant chemical reactions and processes").
kNH = k(RO2• + 1) = 5.83•105,
kOH = k(RO2• + 1) = 7.16•105,
kΣ = kNH + kOH = 1.30•106.
References
1. E. T. Denisov and T. G. Denisova, Handbook of Antioxiꢀ
dants, CRC Press, Boca Ration—New York, 2000, 289 pp.
2. V. T. Varlamov, Kinet. Katal., 2001, 42, 836 [Kinet. Catal.,
2001, 42 (Engl. Transl.)].
3. V. T. Varlamov, Dokl. Akad. Nauk, 1993, 332, 457 [Dokl.
Phys. Chem., 1993 (Engl. Transl.)].
4. V. T. Varlamov and E. T. Denisov, Izv. Akad. Nauk SSSR,
Ser. Khim., 1990, 743 [Bull. Acad. Sci. USSR, Div. Chem.
Sci., 1990, 39, 657 (Engl. Transl.)].
As can be seen, the kNH and kOH values are close to each
other. Among other things, this means that 4ꢀhydroxyꢀ
diphenylamine can be considered as an antioxidant of
two classes of compounds (phenols and secondary aroꢀ
matic amines) simultaneously.
It should be pointed out that the kNH and kOH values
differ only slightly, whereas the thermal effects, Q, of
5. A. J. Gordon and R. A. Ford, The Chemist´s Companion,
Wiley, New York—London, 1972.
6. V. T. Varlamov, Dokl. Akad. Nauk, 1995, 345, 339 [Dokl.
Phys. Chem., 1995 (Engl. Transl.)].
7. V. T. Varlamov, N. N. Denisov, V. A. Nadtochenko, and
E. P. Marchenko, Kinet. Katal., 1994, 35, 833 [Kinet. Catal.,
1994, 35 (Engl. Transl.)].
8. E. T. Denisov and V. T. Varlamov, Kinet. Katal., 1997, 38,
36 [Kinet. Catal., 1997, 38 (Engl. Transl.)].
these reactions are significantly different, namely, QNH
D(ROOH) – DNH(1) = 365.5 – 353.4 = 12.1 and QOH
=
=
.
D(ROOH) – DOH(1) = 365.5 – 339.3 = 26.2 kJ mol–1
These results demonstrate that the reactions in question
proceed involving an apparent violation of the Polanyi—
Semenov rule, which relates the activation energy and,
hence, the rate constants to the thermal effect of the
reaction*. Mention may be made that a rather large numꢀ
* The activation energies of the reactions, calculated by the IP
Received February 5, 2003;
in revised form May 20, 2003
method are as follows: ENH = 14.2 and EOH = 10.5 kJ mol–1
.