Nonlinear taft polar free energy relationship: Reactions of N-substituted benzyl amines with benzyl bromide in methanol

Article abstract of DOI:10.1002/kin.20818

The rates of reactions of N-substituted benzyl amines with benzyl bromide were measured using a conductivity technique in methanol medium. The reaction followed a total second-order path. The end product of the reaction is identified as dibenzyl alkyl amine (C₆H₅CH ₂N(R)CH₂C₆H₅). The rates increased with a decrease in the electron-donating capacity or with an increase in the Taft σ* value of electron-donating alkyl substituents (R) such as t-butyl (σ* = -0.3), i-propyl (σ* = -0.19), n-butyl (σ* = -0.13), and ethyl (σ* = -0.1) on nitrogen of the amine until the Taft σ* value becomes zero for the methyl group (σ CH 3* = 0.00), and then the rates decreased with an increase in the electron-withdrawing capacity or with an increase in the Taft σ* value of electron-withdrawing substituents (R) such H and C₆H ₅ (σH* = 0.49 and σC6H5= 0.6). The locus of the Taft polar free energy relationship has a maximum near the point for N-methyl benzyl amine, showing that there is a sharp change in the rate-determining step. A mechanism involving formation of an S_N2-type transition state between the amine nucleophiles and the benzyl bromide and its subsequent decomposition is proposed. Activation parameters were calculated and are discussed.

Full text of DOI:10.1002/kin.20818

Nonlinear Taft Polar Free
Energy Relationship:
Reactions of N-Substituted
Benzyl Amines with Benzyl
Bromide in Methanol
R. RAVI,1 R. SANJEEV,2 V. JAGANNADHAM1
1Department of Chemistry, Osmania University, Hyderabad, India
2Department of Chemistry, Mizan-Tepi University, Tepi Campus, Tepi, Ethiopia
Received 23 April 2013; revised 23 June 2013; 2 August 2013; accepted 7 August 2013
DOI 10.1002/kin.20818
Published online 31 August 2013 in Wiley Online Library (wileyonlinelibrary.com).
ABSTRACT: The rates of reactions of N-substituted benzyl amines with benzyl bromide were
measured using a conductivity technique in methanol medium. The reaction followed a to-
tal second-order path. The end product of the reaction is identified as dibenzyl alkyl amine
(C6H5CH2N(R)CH2C6H5). The rates increased with a decrease in the electron-donating capac-
ity or with an increase in the Taft σ* value of electron-donating alkyl substituents (R) such
as t-butyl (σ* = −0.3), i-propyl (σ* = −0.19), n-butyl (σ* = −0.13), and ethyl (σ* = −0.1)
on nitrogen of the amine until the Taft σ* value becomes zero for the methyl group (σC∗H
3
= 0.00), and then the rates decreased with an increase in the electron-withdrawing capacity
or with an increase in the Taft σ* value of electron-withdrawing substituents (R) such H and
C6H5 (σH∗ = 0.49 and σC∗ H = 0.6). The locus of the Taft polar free energy relationship has a
6
5
maximum near the point for N-methyl benzyl amine, showing that there is a sharp change in
the rate-determining step. A mechanism involving formation of an SN2-type transition state
between the amine nucleophiles and the benzyl bromide and its subsꢀeCquent decomposition is
proposed. Activation parameters were calculated and are discussed. 2013 Wiley Periodicals,
Inc. Int J Chem Kinet 45: 803–810, 2013
tion for predicting the organic reaction mechanisms
among physical chemists in general and physical or-
ganic chemists in particular. Ever since the Hammett
[1] and Taft [2] equations were developed, several
hundred redox, condensation, disproportionation, nu-
cleophilic, and electrophilic substitution and addition
reactions with meta- and parasubstituted benzene
derivatives have been reported in the literature, in
INTRODUCTION
Although the Hammett [1] and Taft [2] equations are
nearly 75 years old, they enjoy outstanding applica-
Correspondence to: V. Jagannadham; e-mail: jagannad-
ham1950@yahoo.com.
C
ꢀ
2013 Wiley Periodicals, Inc.

804
RAVI, SANJEEV, AND JAGANNADHAM
which the Hammett and Taft reaction (ρ and ρ*) con-
stants were reported. Inclusion of those references here
is beyond the scope of this article as they run to sev-
eral pages. However, readers can find many articles
and reviews in several standard staple physical-organic
chemistry textbooks. But as the title certainly warrants,
it is necessary to mention here the nonlinear Hammett
correlations. There were some reactions that deviate
from linearity of the Hammett ρσ plot and are doc-
umented in detail by Schreck [3]. As mentioned in
the Schreck paper [3], these deviations were primar-
ily attributed to (i) experimental errors, (ii) reactive
and catalytic impurities, (iii) failure to isolate a single
reaction, and (iv) the presence of side reactions and
inconsistent polar and resonance effects. But these are
easily avoidable or could be modified. Another scien-
tifically arguable and solvable deviation is due to the
change in the rate-determining step or a reaction mech-
anism. An example of a nonlinear Hammett ρσ plot is
reported by Crowell et. al. [4] in the reaction of aro-
matic aldehydes with n-butyl amine. The products are
substituted benzylidene-n-butyl amines. This was in-
terpreted in terms of the change in the rate-determining
step from reversible addition of amine to aldehyde to
the subsequent dehydration step, which is favored by
electron-donating substituents. Szmant and Harmuth
tried to explain the V-shaped Hammett locus based on
the same explanations of change in mechanisms of the
Wolf-Kishner reaction of hydrazones [5] and U-shaped
Hammett locus for the rates of solvolysis and thiosul-
fate reactions of α-chloro toluenes [6] for two sets
of electron-donating and electron-withdrawing sub-
stituents. Another notable example of this kind was
from our laboratory [7] wherein the Hammett plot was
again nonlinear for the reactions of monoanion and di-
anion of peroxomonosulfate with benzaldehydes. From
the mechanism and from the Hammett correlation, it is
evident that the reversible addition of monoanion and
dianion of peroxomonosulfate to >C=O is accelerated
by electron-withdrawing groups on a phenyl ring since
the electrophilicity of the carbonyl carbon atom in-
moments of benzoic acids were even reported from
our laboratory [10]. But to the authors’ knowledge,
the present article presents the first of its kind to ob-
serve a nonlinear Taft correlation, though there are sev-
eral reports on nonlinear Hammett correlations in the
literature [11–27].
EXPERIMENTAL
All the chemicals and solvents used in the present
work were purchased from Aldrich (Bangalore, India)
and used as received. The conductivity meter and the
conductivity cell used are from Digison Electronics
(Hyderabad, India) with an accuracy of 0.01 mhos.
The constant temperature bath is from Devi Electronics
(Hyderabad, India) and maintained at constant temper-
ature to an accuracy of 0.1◦C. For studying the reac-
tions at constant temperature, a double-walled Corn-
ing glass inner tube of 3 cm diameter and 8 cm length
was surrounded by a glass jacket with inlets and out-
lets for circulating the water at a given constant tem-
perature from an outside constant temperature bath.
The benzyl amine solution in AR-grade methanol in
this double-walled glass tube and the benzyl bromide
solution in methanol of the required concentration in
another test tube were thermostated for 15 min. The
reactions were initiated by mixing the benzyl bromide
solution of required quantity with benzyl amine solu-
tion with the help of a 1-mL pipette, and a stopwatch
was started immediately. The increase in the conduc-
tivity was recorded periodically at regular intervals of
time. The infinite reading was noted after heating and
cooling the reaction mixture to the required tempera-
ture. The product of the reaction with benzyl amine and
benzyl bromide was identified as N,N-dibenzyl amine
[(C6H5CH2)2NH]. All the kinetic data were stored in a
personal computer and analyzed using KaleidaGraph
software (Synergy Software, Reading, PA). The reac-
tions were also carried out at different temperatures,
and the activation parameters were calculated from the
slope and intercept values of Eyring plots.
−
creases. This is followed by the elimination of HSO4
from the intermediate, a reaction that is helped by the
presence of electron-donating groups in the aromatic
ring. The balance between these two factors could re-
sult in a minimum in the overall rate of the reaction. In
this study the minimum rate was observed with ben-
zaldehyde. There even were nonlinear Hammett corre-
lations observed on physical properties. For example,
quantitative solubility–structure relationships for sev-
eral meta- and parasubstituted benzoic acids in benzene
and cyclohexane [8] and 1,4-dioxane and tetrahydro-
furan [9] were studied. Such kinds of studies using
physical properties such as melting points and dipole
RESULTS AND DISCUSSION
Reaction Order and Rate Equation
The conductivity of the reaction mixture increases with
time as the reaction produces HBr as one of the end
products. Under the conditions [benzyl amine] > [ben-
zyl bromide], the plot of log (C –Ct) versus time was
∞
linear until three half-lives with a correlation coeffi-
cient of 0.9995, indicating that the order in [benzyl
bromide] was unity. Here, C and Ct are the
∞
International Journal of Chemical Kinetics DOI 10.1002/kin.20818

NONLINEAR TAFT POLAR FREE ENERGY RELATIONSHIP
805
Scheme 1
conductivities of the reaction mixture at infinite time
and at regular intervals of time, respectively. From such
plots, the pseudo–first-order rate constants (kobsd, s)
were calculated for all the benzyl amines. The plot of
log (kobsd, s) versus log [benzyl amine] was again found
to be linear with a correlation coefficient of 0.9905, in-
dicating that the order in [benzyl amine] was unity.
Therefore, the simple rate equation of the reaction
would be
ꢀ
ꢁ ꢀ
ꢁ
Rate = k Benzyl amine Benzyl bromide (1)
where k is the second-order rate constant. Under oth-
erwise similar conditions, the solvolysis reaction of
benzyl bromide in the absence of benzyl amine was
checked and the rate was found to be 10 times less
than the rate of the second-order reaction. Hence the
rates of the background reaction of benzyl bromide
were neglected in these studies.
Figure 1 Taft plot of log k versus Taft σ* at 303 K.
Reaction Mechanism and Substituent
Effects
actually be a composite quantity depending on the rate
and equilibrium constant of several reaction steps [7].
The locus in the Taft correlation (Fig. 1) had a maxi-
Since the total order of the reaction is two, a bimolec-
ular type of reaction scheme is proposed as shown in
Scheme 1 via an SN2-type transition state.
mum near the point for N-methyl benzyl amine (σC∗H
=
From the mechanism, one can predict that a linear
correlation would be observed between log k and Taft
σ* with a negative Taft reaction constant (ρ*) because
the rates would increase as the substituent (R) on the
amine nitrogen becomes more and more electron do-
nating that facilitates the availability of the lone pair
of electrons on nitrogen for the attack on the benzylic
carbon of benzyl bromide (see Scheme 1).
But we have observed a nonlinear Taft correlation
(Fig. 1) with two values of Taft ρ*, one negative for
electron-donating alkyl substituents and the other a
positive value for electron-withdrawing substituents.
The origin of the nonlinear Hammett correlations has
been observed and discussed in terms of the relative
degree of bond making and bond breaking in the tran-
sition state and is very popular among solvolysis re-
actions [12]. Also this type of nonlinearity between
structure and reactivity was generally attributed to ei-
ther the change in the rate-determining step of a mul-
tistep reaction or when a measured rate constant may
0.00). This maximum is interpreted as the point wh3ere
the rate-determining step changes from the reversible
reaction of amine with benzyl bromide, which is not
favored by electron-withdrawing groups such as H and
phenyl, whereas the subsequent elimination of the HBr
step is again not accelerated by electron-donating alkyl
substituents.
Alternatively, one can explain this as the electron-
withdrawing substituents (R) on the nitrogen atom of
N-substituted benzyl amines decrease the capacity of
the nitrogen for becoming a more positive center in the
transition state relative to the more availability of the
lone pair of electrons on the same nitrogen atom in
the ground state. This decreases the equilibrium con-
centration of the transition state or decreases the bond-
making process between nitrogen of benzyl amine and
the benzyl carbon atom of benzyl bromide. This is re-
flected in Fig. 1, where for R = H (σ* = 0.49) and C6H5
(σ* = 0.60) the rate constants are lower than for R =
CH3 (σ* = 0.00). On the other hand, electron-donating
International Journal of Chemical Kinetics DOI 10.1002/kin.20818

806
RAVI, SANJEEV, AND JAGANNADHAM
Figure 3 Plot of log k − δEs versus σ* at 303 K.
Figure 2 Plot of log k versus Taft Es at 303 K.
substituents (R) on the nitrogen atom of amine do not
facilitate the removal of proton from the nitrogen in the
transition state. This is reflected in the Taft correlation
(Fig. 1) for R = Et (σ* = –0.1), n-butyl (σ* = – 0.13),
i-propyl (σ* = – 0.19), and t-butyl (σ* = −0.3); the
rate constants are again lower than for R = CH3 (σ∗
CH3
= 0.00). Hence one can see a sharp break in the Taft plot
at R = CH3, the point at which the rate-determining
formation of the transition state (step 1) changes to
its rate-determining decomposition (step 2). The high
values of Taft ρ* (6.44 and –1.73) are consistent with
sensitivity of the rates with substituents.
We have also tried the correlation of rate constants
with Taft Es values (Fig. 2). But the correlation is very
poor (r = 0.46). Furthermore, the rate data are analyzed
using the Taft four-parameter Eq. (2), where R stands
for substituent on nitrogen of benzyl amine):
log kR = log kMe + ρ∗σ∗ + δEs
(2)
Figure 4 Bro¨nsted plot of log k versus pKa of N-substituted
benzyl amines at 303 K.
And using the δ value (0.23) obtained from the plot
in Fig. 2, we tried to plot log k–δEs versus σ*. But
there is no improvement in the correlation except with
electron-donating substituents even after the data are
free of steric effects by subtracting the quantity δEs.
Had there been steric effects in the reaction, this plot
would have been linear separately for both electron-
withdrawing and electron-donating substituents. We
not only have tried with the δ value of 0.23 but tried
arbitrarily different values for δ starting from −0.3
to +1.5. With none of these values was good correla-
tion observed; especially the correlation with electron-
withdrawing groups is not satisfactory (r = 0.815). As a
sample, a plot with δ = −0.3 is shown in Fig. 3. But we
tried the correlation using two different δ values, 1.5 for
electron-donating and zero for electron-withdrawing
substituents, which gave a good correlation (see later
Fig. 7).
Brønsted Correlation. A plot of log k versus pKa val-
ues of amines again showed a linear correlation (Fig. 4)
with two different straight lines with β values of 3.68
and −9.74 for electron-withdrawing substituents and
International Journal of Chemical Kinetics DOI 10.1002/kin.20818

NONLINEAR TAFT POLAR FREE ENERGY RELATIONSHIP
807
Table I Effect of Temperature on Taft ρ*
Taft ρ*
Temperature (K)
Electron-Donating Substituents
Electron-Withdrawing Substituents
298
303
308
313
7.12
6.44
6.36
6.93
−1.76
−1.73
−1.75
−1.83
Table II Activation Parameters
k (M s)
R
Taft σ*
298 K
303 K
308 K
313 K
ꢀH# (kJ mol−1
)
ꢀS# (J (mol K)−1
)
t-Butyl
i-Propyl
n-Butyl
Ethyl
Methyl
H
− 0.300
− 0.190
− 0.130
− 0.100
0.000
0.007
0.017
0.092
0.103
0.453
0.058
0.041
0.008
0.029
0.173
0.166
0.594
0.085
0.055
0.014
0.050
0.209
0.286
1.00
0.019
0.068
0.431
0.405
1.93
53.2
63.2
66.8
64.0
67.7
79.9
57.0
− 109
− 66.1
− 40.4
− 48.9
− 25.1
− 1.20
− 80.4
0.490
0.600
0.135
0.091
0.304
0.139
Phenyl
electron-donating substituents, respectively, similar to
the Taft correlation. This shows that the reactions are
highly sensitive to the basicity of the amines used irre-
spective of the steric hindrances of the substituents on
the amine moiety. Similar observations were made by
Goumont et al. and Um et al. [15,20] in the reactions
of anilines with 4-chloro-7-nitrobenzofuran and pyridi-
nolysis of O-4-nitrophenyl benzoates and thionoben-
zoates. The pKa values of the amines in water with R =
H (9.34), methyl (9.58), and ethyl (9.68) substituents
are from [28]. For other substituents, the pKa values are
computed from the plot of pKa versus ꢁσ* and they
were 9.77 (t-butyl), 9.70 (iso-propyl), 9.67 (n-butyl),
and 9.27 (phenyl).
not by enthalpy factors. This is reflected in the large
variation in ꢀS= values presented in Table II.
This can be seen by getting the final Eq. (4) from
Eyring and Taft equations and assuming no variation
in ꢀH=. In fact in the present work the variation in
magnitude of ꢀS= is very large when compared to that
in ꢀH= (Table II):
ꢀS= − ꢀSo=
= ρ∗σ∗
(4)
R
Equation (4) shows no variation in ρ* with temper-
ature. It is the gain in entropy from benzyl amine with
R = t-butyl to benzyl amine with R = H because the
entropies are negative. This reflects that the more bulky
groups suffer more loss in entropy.
Effect of Temperature on Taft ρ*. From Table I it is
clear that no systematic variation in Taft ρ* values with
temperature is observed. Had there been a systematic
variation in Taft ρ* values with temperature and if the
reaction is an enthalpy-controlled one, and according
to Eq. (3) [29] and with no significant variation in ꢀS=
values, the Taft ρ* values should have a systematic
variation with temperature:
Mechanistic Implications of ꢀS#. From the system-
atic progress of the reaction, the change in crucial con-
figuration of transition state is depicted in Scheme 2.
The formation of the transition state involves the
combination of two reactants to give one species. This
would result in a loss of several translational degrees
of freedom of the reactants, leading to high nega-
tive entropy of activation (Table II). If the deproto-
nation from the transition state is assisted by solvent
methanol, there will be a freezing of solvent molecules,
which leads to the loss of several translational de-
grees of freedom of solvent. This again leads to very
high negative entropy of activation (Table II) as the
ꢂ
ꢃꢄ
log (k/ko) = ꢀH =o − ꢀH = 2.303 RT
= ρ∗σ∗
(3)
But the absence of systematic variation of Taft ρ*
with temperature would indicate that the present reac-
tion series is solely controlled by entropy factors and
International Journal of Chemical Kinetics DOI 10.1002/kin.20818

808
RAVI, SANJEEV, AND JAGANNADHAM
Scheme 2
Figure 6 Exner plot.
It has been asserted that apparently linear corre-
lations of ꢀH# with ꢀS# are sometimes misleading,
and the evaluation of β by means of the equation
ꢀH# = βꢀS# + constant lacks statistical validity [33].
Exner[34]describes analternativemethodforthetreat-
ment of experimental data. If the rates of several re-
actions in a series have been measured at different
temperatures and log k2 (at T2) is linearly related to log
k1 (at T1), i.e., according to the equation, log k2 = a +
b log k1, so that β can be evaluated using the equation,
β = T1T2 (b – 1)/(T2b – T1). We have calculated the
isokinetic temperature β as 228 K by plotting log k2 at
303 K versus log k1 at 298 K as in Fig. 6.
Figure 5 Isokinetic Taft plot.
The value of β (228 K) is lower than the experi-
mental temperature 298 K. This indicates that the rate
is governed by entropy of activation [35].
As seen from Fig. 1, using the δ value = 1.50 for
electron-donating alkyl substituents (R = t-butyl, i-
propyl, n-butyl, and ethyl) and δ = 0 for electron-
withdrawing substituents (R = H and C6H5), the plot
of log kR – δEs versus σ* at 303 K is quite good
(Fig. 7), with a correlation coefficient of 0.9957∗, and
the corresponding relationship is
proton transfer from the neutral molecule to methanol
is exothermic, as evidenced by its proton affinity [30].
A similar situation was encountered by one of authors
in the decomposition of nitroxyl adducts assisted by
solvent water [31].
Isokinetic Relationship. An isokinetic Taft plot is ob-
tained in the present work (Fig. 5) when ꢀH= is plotted
against ꢀS= according to the equation ꢀH# = βꢀS#
+ constant, the slope of which corresponds to an isoki-
netic temperature β of 227 K, which is well below the
experimental temperature range (298–313 K) used in
the present reactions to study the effect of temperature
on reaction rates. According to isokinetic theory [32],
this means that the effect exerted by the substituents
(R) on nitrogen of benzyl amine, both processes, i.e.,
formation and the heterolysis of the transition state, is
controlled predominantly by entropy.
log kR − δEs = log kCH − 1.60 σ∗
(5)
3
The points for i-propyl and ethyl, deviating from
the linear plot, were not included in the correlation of
Eq. (5). Also the same two substituents deviated a little
∗The authors are extremely grateful to Prof. T. Boubaker, Univer-
sity of Monastir, Tunisia, for suggesting this idea.
International Journal of Chemical Kinetics DOI 10.1002/kin.20818

NONLINEAR TAFT POLAR FREE ENERGY RELATIONSHIP
809
reviewers for their constructive comments due to which the
manuscript was improved a lot in its scientific content.
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International Journal of Chemical Kinetics DOI 10.1002/kin.20818

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International Journal of Chemical Kinetics DOI 10.1002/kin.20818