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Determination of the self-association and inter-association equilibrium
constants of a carboxylic acid and its mixtures with pyridine derivates
A. Gonzalez a, L. Irusta a, M.J. Fernandez-Berridi a,*, J.J. Iruin a, T. Sierra b, L. Oriol b
a Polymer Science and Technology Department and Institute for Polymer Materials (POLYMAT),
University of the Basque Country, P.O. Box 1072, 20080 San Sebastian, Spainb Polymer and Liquid Crystal Group, Quımica Organica, Instituto de Ciencia de Materiales de Aragon,
Universidad de Zaragoza-CSIC, Pedro Cerbuna 12, 50009 Zaragoza, Spain
Received 11 November 2005; received in revised form 7 December 2005; accepted 8 December 2005
Available online 18 January 2006
This is paper is dedicated to Prof. Cecilia Sarasola
Abstract
Infrared spectroscopy has been employed to determine absorptivity coefficients and the self-association equilibrium constant of 3,4,5-
tris(dodecyloxy)benzoic acid in cyclohexane. The obtained value is consistent with data reported in bibliography for other similar compounds. The
equilibrium constant describing ethylpyridine/carbonyl hydrogen bonds has been determined for mixtures of the above-mentioned acid and two
ethylpyridine isomers. The effect of steric hindrance is discussed.
# 2005 Elsevier B.V. All rights reserved.
Keywords: H-bonding; Supramolecular chemistry; Self-association; Inter-association equilibrium constants; Polycatenar benzoic acid
www.elsevier.com/locate/vibspec
Vibrational Spectroscopy 41 (2006) 21–27
1. Introduction
Intermolecular hydrogen bonding is considered an important
driving force in the formation of supramolecular liquid crystals
[1–3]. Many supramolecules as well as supramolecular
polymers, prepared from components that are appropriately
substituted with functional H-donor and H-acceptor groups, are
able to self-organize into mesophases. In many cases, the
components are not necessarily mesogenic in their own right.
These complexes present the same types of mesophases as
covalently built mesogenic molecules. However, the resulting
organizations may rely on some additional features derived
from the dynamic character of the H-bond.
Most of the mesogenic supramolecular structures described
so far show mesophases of the calamitic type. Several disc-like
supramolecules built through hydrogen bonding have also been
reported to display columnar mesomorphism. This type of
liquid crystalline architecture deserves special attention due to
its applications such as (semi)conducting and photoconducting
materials, chemical sensors, etc. [4–7]. In this work, we have
* Corresponding author. Tel.: +34 943 018194; fax: +34 943 015270.
E-mail address: [email protected] (M.J. Fernandez-Berridi).
0924-2031/$ – see front matter # 2005 Elsevier B.V. All rights reserved.
doi:10.1016/j.vibspec.2005.12.003
studied the hydrogen bonding capability of 3,4,5-tris(dodecy-
loxy)benzoic acid, coded as 1. This acid has a polycatenar
structure and has been widely used on the preparation of
columnar liquid crystals both of low molecular weight and
polymers [8–10]. The study of the self-association and inter-
association of this type of carboxylic acids is the starting point
to understand the complex hydrogen bonding formation that
takes place in the supramolecular liquid crystals [11,12].
Infrared spectroscopy has been an important technique in the
study of both the nature and extent of hydrogen bonding [13] in
organic compounds, in particular on carboxylic acids [14–18].
It is well established in carboxylic acids that the self-
association takes place with the formation of cyclic dimers
(Scheme 1). This self-association equilibrium can be described
by a single equilibrium constant, KB [13,19,20].
The main objective of this work is to obtain the values of the
equilibrium constants describing the formation of 3,4,5-
tris(dodecyloxy)benzoic acid dimers (KB) and the inter-
association 1/pyridine complexes (KA), shown in Scheme 1,
by means of IR spectroscopy.
With the aim in mind, liquid sampling cells of known
thickness were used to obtain infrared spectra of 1 as a function
of concentration in a non-hydrogen bonding hydrocarbon
A. Gonzalez et al. / Vibrational Spectroscopy 41 (2006) 21–2722
Scheme 1. Self-association of the carboxylic acid.
Fig. 1. Infrared spectra in the carbonyl-stretching vibration region for 1/
cyclohexane solutions at different concentrations.
solvent such as cyclohexane. Although most compounds
containing carboxylic acid groups are insoluble in non-polar
solvents, 1 presents a high solubility in cyclohexane, due to the
presence of large non-polar aliphatic chains. This fact offers the
possibility of studying the self-association of a carboxylic acid
in a non-polar inert solvent, which has not been reported on
bibliography so far. For the calculation of the acid/pyridine
inter-association equilibrium constant, mixtures of 1 and
ethylpyridine were prepared at different ratios in cyclohexane.
Infrared spectra of these mixtures were recorded in liquid
sampling cells of known thickness.
2. Experimental
Cyclohexane (Aldrich, HPLC grade), 2-ethylpyridine
(MERCK) and 4-ethylpyridine (Aldrich 98% (GC)) were used
as received. Compound 1 was synthesized according to a
previously reported method [8]. Infrared spectroscopic
measurements were recorded at room temperature in a Nicolet,
model Magna 560 FT-IR spectrometer at a resolution of 2 cm�1
and a minimum of 10 scans. Infrared spectra of 1 solutions
between 0.0003 and 0.14 mol/L were carried out using two
standard liquid cells of 0.1 and 1 mm path length, respectively.
Infrared spectra of 1/ethylpyridine mixtures (1/5, 1/10, 1/20 and
1/40 mol ratio) in cyclohexane were also obtained and in
solutions the concentration of 1 was 2.5 � 10�3 mol/L. Infrared
spectra of these mixture solutions were performed in a cell of
2 mm. All solution spectra were sustracted from the
cyclohexane spectrum obtained in the same liquid cell.
Infrared spectra of a thin film of 1 at different temperatures
were obtained using a variable temperature cell (Harrick) from
150 8C down to room temperature. The thin film of 1 was
prepared by casting from dichloromethane solutions onto a KBr
window.
3. Results and discussion
3.1. Self-association of 3,4,5-tris(dodecyloxy)benzoic acid
3.1.1. Infrared spectra
Fig. 1 shows FT-IR spectra in the carbonyl-stretching
vibration region of 1 in cyclohexane solutions at different
concentrations, recorded at room temperature. In the spectrum
of the most concentrated solution, a single band centred at
1690 cm�1 is observed. This band can be assigned to hydrogen-
bonded carbonyl-stretching vibration in the closed dimeric
form [21]. As the concentration of the solution is decreased a
new band centred at 1740 cm�1 appears. Furthermore, the
lower the solution concentration, the higher the relative
contribution of this band. Therefore, it can be assigned to
the free carbonyl-stretching vibration. The difference in
wavenumbers (about 50 cm�1) between the free and associated
carbonyl bands is very large, confirming that the self-associated
interaction is very strong [22].
The corresponding hydroxyl-stretching vibration band
appears in the region of 3400–3600 cm�1. However, the
resolution is so poor that it is not possible to discern between
associated and free bands, a prerequisite for performing
quantitative analysis. Therefore, only the carbonyl-stretching
region is used for such type of analysis.
3.1.2. Determination of the absorptivity coefficients
In order to quantify the self-association of 1, the relative
contribution of the free and associated carbonyl bands must be
calculated. However, the absorptivity coefficients of these two
vibrations are not the same and, in order to calculate the relative
concentration of free species, at least one of the two coefficients
must be known [14]. In order to quantify the absorptivity
coefficient of the hydrogen-bonded carbonyl vibration, the area
of the associated carbonyl band has been plotted as a function of
concentration. In the more concentrated solutions, where no
free band is observed, a straight line must be obtained. From the
slope of the line the absorptivity coefficient of the associated
band can be readily calculated, according to the Lambert–Beer
A. Gonzalez et al. / Vibrational Spectroscopy 41 (2006) 21–27 23
Fig. 2. Determination of the absorptivity coefficient of bonded carbonyl groups
of 1.
Fig. 3. Determination of the absorptivity coefficient ratio of the carbonyl-
stretching vibration of 1/cyclohexane solutions.
equation. Fig. 2 shows the result of this calculation and a valueof eb = 159 L /mol mm has been obtained.
The fraction of bonded carbonyl groups at different
concentrations can be then determined using Eq. (1) [23,24]:
fB ¼AB
eBlC(1)
where l is the path length of the liquid cell, AB the area of the H-
bonded band and C is the solution concentration. The results of
these calculations are summarized in Table 1. As can be seen,
the fraction of self-associated carbonyl groups increases when
the concentration of [1] increases.
From the values of the associated carbonyl fraction as a
function of the concentration, the ratio between the two
absorption coefficients (r = eB/eF) can be calculated by means
of Eq. (2):
1
fB¼ 1þ r
AF
AB
(2)
where AF and AB are the areas of the free and associated bands,
respectively. Fig. 3 shows the result of this calculation. Only the
Table 1
Fraction of bonded carbonyl groups of 1 obtained at different concentrations
C (mol/L) Area of carbonyl
bonded band, AB
Area of carbonyl
free band, Af
Path length l,
(mm)
fB
0.140 22.38 0.106 0.1 1.00
0.112 16.52 0.070 0.1 0.93
0.088 12.16 0.080 0.1 0.87
0.072 10.70 0.083 0.1 0.93
0.056 8.33 0.064 0.1 0.94
0.046 7.21 0.086 0.1 0.98
0.028 4.19 0.071 0.1 0.94
0.017 2.60 0.062 0.1 0.96
0.010 1.53 0.049 0.1 0.96
0.006 0.84 0.030 0.1 0.88
0.004 3.61 0.213 1.0 0.57
0.002 2.64 0.194 1.0 0.83
0.0008 0.91 0.119 1.0 0.71
0.0005 0.53 0.084 1.0 0.67
0.0003 0.30 0.069 1.0 0.62
most diluted concentrations, where the free carbonyl band is
clearly observed, have been used. From the slope of the straight
line a value of r = 1.9 has been obtained which is consistent
with values previously reported in bibliography (r = 1.6) [13].
3.1.3. Determination of the self-association equilibrium
constant from the carbonyl-stretching region
Knowing the free carbonyl band fraction ( fF) and the
stoichiometry of the acid self-association, the equilibrium
constant can be calculated. The procedure is the following: the
volume fraction (fB) of each concentration can be obtained by
means of Eq. (3):
fB ¼ ciVM (3)
where VM is the molar volume of 1 (708.9 cm3/mol) calculated
using the method of group contributions [13]. The direct
calculation of VM from its density value was not possible
due to the lack of enough sample quantity to perform this
calculation.
From the value of fB and selecting a starting value for KB
and fB1(volume fraction of carboxylic acid monomer) can be
calculated using Eq. (4). From Eq. (5), fF can be calculated for
the whole composition range. The value of KB is systematically
varied and a least square method is employed in order to
determine the best fit of the experimental fF versus fB data
(Fig. 4):
fB ¼ fB1 þ 2KBf2B1
(4)
fF ¼1
1þ 2KBfB1
(5)
The commercial software (Fit K) developed by Painter and
Coleman has been used to perform this calculation.
The least square fit to the equations describing the system
results in a fine match of the experimental data over the entire
composition range considered. The best fit of the data has
A. Gonzalez et al. / Vibrational Spectroscopy 41 (2006) 21–2724
Fig. 5. Infrared spectra in the carbonyl-stretching region of 1/4-ethylpyridine
mixtures.
Fig. 4. Experimental and simulated fractions of free carbonyl groups vs.
volume fraction of 1/cyclohexane solutions.
permitted to obtain a value of KB = 8900. This is a dimentionless
quantity equal to the definition of an equilibrium constant in
terms of molar concentration divided by the molar volume of the
structural unit (708 cm3/mol). It is interesting to note that the
equilibrium constant value determined from 1 is slighly higher to
that determined by Barela et al. [25] for benzoic acid in benzene
(6175). The same authors have reported [26] that the extent of
dimerization of the benzoic acic is lowered by substitution of the
benzene ring and that the effect is more pronounced by ortho
substituents. Taking into account these results a lower value of KB
should be obtained in 1. However, as Marcus [27] pointed out,
there is considerable evidence that aromatic hydrocarbons (as
benzene) interact with molecules containing OH groups,
possibly through the formation of very weak hydrogen bonds,
lowering the value of KB.
3.2. Determination of the inter-association equilibrium
constant in solution
After studying the self-association of 1, we accomplished
the study of the H-bonding equilibrium of the polycatenar acid
[1] and pyridines as H-acceptor. In particular, the inter-
association equilibrium constant, KA, can be calculated from
the infrared spectra of 1/ethylpyridine mixtures. In this study,
two pyridine derivatives, having an ethyl group in position 4 or
2, have been evaluated.
Scheme 2. Inter-association of the carboxylic acid with ethylpyridine.
3.2.1. [1]/4-ethylpyridine mixtures
Fig. 5 shows scale expanded room temperature infrared
spectra of 1/4-ethylpyridine mixtures recorded at different
compositions in the carbonyl-stretching region using cyclo-
hexane solutions having a fixed concentration of 1 (0.0025 M).
As can be seen, IR spectra show the two bands previously
observed for pure 1 and assigned to free and associated dimeric
species [28] (4-ethylpyridine does not present any band in the
carbonyl-stretching vibration region). In addition, the spectra of
the mixtures show a new band at 1710 cm�1, whose intensity
varies systematically as a function of composition [29–31].
This band can be assigned to free carbonyl groups whose OH is
hydrogen-bonded to the pyridine nitrogen, according to
Scheme 2 [32]. The band at 1690 cm�1, assigned to associated
carbonyl groups, decreases as increasing ethylpyridine con-
centration, meanwhile the band at 1740 cm�1 corresponding to
free carbonyl groups is still present but shows a low intensity.
This fact can be explained because the total carbonyl
concentration remains constant in all samples and, therefore,
the increase of the intensity of the 1710 cm�1 band must lead to
a decrease of the other band.
In addition to the three mentioned bands, the spectra of the
mixtures also exhibit a shoulder centered at about 1720 cm�1.
The assignment of this band to a specific interaction is not
straightforward and could be due to opened dimers of the
carboxylic acid. In order to check the origin of this band, a
A. Gonzalez et al. / Vibrational Spectroscopy 41 (2006) 21–27 25
Fig. 6. Infrared spectra in the carbonyl-stretching region of 1 at different
temperatures.
Table 2
Fraction of bonded and free carbonyl groups for different 1/4-ethylpyridine
mixtures
1/4-Ethylpyridine fF fB
1/0 0.13 0.87
1/5 0.54 0.46
1/10 0.70 0.30
1/20 0.82 0.18
1/40 0.86 0.14
Fig. 7. Infrared spectra in the carbonyl-stretching vibration region of [1]/2-
ethylpyridine mixtures.
study of the dependence of the IR spectrum of 1 on the
temperature was accomplished on a thin film sample.
Fig. 6 displays the corresponding spectra in the carbonyl
region of a thin film of 1 at different temperatures. As can be
seen, three variable intensity bands as a function of temperature
appear in all spectra. Thus, at the highest temperature (150 8C)
a band centred at 1690 cm�1 dominates the region. This
position is characteristic of carbonyl groups associated in cyclic
dimers. Moreover, a band at 1738 cm�1 with a shoulder at
1720 cm�1 can be also detected. The band at higher
wavenumbers is due to totally free carbonyl groups. As
temperature decreases, the relative intensity of this shoulder
(1720 cm�1) increases in such a way that, at the lowest
temperature, its intensity predominates over that of 1738 cm�1.
Therefore, this shoulder can respond to carbonyl groups
participating in open dimeric associations.
Taking into account these results, the band at the same
position observed in 1/pyridine mixtures can be assigned to this
type of association (open dimer). It must be stressed out that
this band is centred at higher wavenumbers than the
corresponding to carbonyl groups whose OH is associated
with the nitrogen of pyridine. This fact indicates that the
pyridine-acid inter-association is stronger than the acid/acid
self-association, in accordance with previous results [28,33].
The calculation of KA implies the determination of free
carbonyl fractions for mixtures at different compositions. Due
to the proximity of the frequencies of the bands involved in the
calculation, the determination of their relative contributions
must be done by means of curve resolution. The software
Spectra Fit, developed by Painter and Coleman has been
employed for this purpose. The fractions of free and bonded
carbonyl groups have been determined by Eqs. (7) and (8).
fB ¼AB�
eB
eF1
�AF1þ�
eB
eF2
�AF2þ�
eB
eF3
�AF3þ AB
(7)
fF ¼ 1� fB (8)
where AB, AF1, AF2
and AF3are the areas of associated cyclic
closed dimers, totally free, open dimers and N–H bonded
bands, respectively. eFi (i = 1, 2 or 3) are the corresponding
infrared absorption coefficients.
To calculate the fraction of free and bonded groups the
absorption coefficients must be known. However, although
absorption coefficients of bonded (eB) and totally free carbonyl
groups (eF1) are known, absorption coefficients eF2
and eF3are
unfortunately unknown. Therefore, a linear dependence of the
absorption coefficients with wavenumbers was supposed, in
order to obtain the rest of the coefficients values. Infrared
absorption coefficients of 113 and 135 were obtained for the
open dimer and pyridine-acid carbonyl band, respectively.
Table 2 shows the free carbonyl group fractions at different
compositions. The fraction of bonded carbonyl groups
decreases as increasing pyridine concentration. It is worthwhile
to remember that as the total concentration of carbonyl groups
remains constant, carbonyl groups that are self-associated at
low pyridine concentrations become ‘‘free’’ when increasing
pyridine content.
The equilibrium constant KA can be obtained from free
carbonyl fraction data. Once again, the commercial software Fit
K was applied for this task. Using the self-association KB
previously determined (8900) and stating an initial value of KA,
a least square fit procedure is applied. The value of the free
fraction for the whole composition can be calculated using the
appropriate stoichiometric equations. The value of KA is
systematically varied to fit the experimental curve using a least
A. Gonzalez et al. / Vibrational Spectroscopy 41 (2006) 21–2726
Table 3
Fraction of bonded and free carbonyl groups for 1/2-ethylpyridine mixtures at
different compositions
1/Ethylpyridine fF fB
1/0 0.07 0.93
1/5 0.34 0.66
1/10 0.49 0.51
1/20 0.67 0.33
1/40 0.82 0.18
squares procedure. Other parameters such as molar volume of
components have been employed to fit: V[1] = 708.9; VCHX = 99
and V4-ETPY = 114.8 cm3/mol (calculated by group contribu-
tions as stated previously [13,31]). A value of 335 has been
obtained.
3.2.2. [1]/2-ethylpyridine mixtures
The methodology for the calculation of the equilibrium
constant for 1/2-ethylpyridine system is the same as the
previously employed for 1/4-ethylpyridine mixtures in cyclo-
hexane.
Fig. 7 shows infrared spectra in the carbonyl-stretching
vibration region for 1/2-ethylpyridine mixtures. As can be seen,
the infrared spectra of these mixtures show the same absorption
bands and composition dependence as the observed for
mixtures with 4-ethylpyridine.
Nevertheless, for the same composition, the relative
absorbance of the band assigned to cyclic closed dimer is
higher in 2-ethylpyridine mixtures than the obtained for 4-
ethylpyridine, while the band corresponding to the association
between pyridine and 1 is lower in the former. This behaviour
can be numerically demonstrated when the free carbonyl
fraction is calculated, as can be seen in Table 3.
Applying the previously defined methodology, a value of
standarized equilibrium inter-association constant KA = 152
has been obtained. As expected, this value is lower than the
obtained for 1/4-ethylpyridine system presumably due to a
higher steric hindrance of the nitrogen atom in 2-ethylpyridine
to interact with the hydroxyl group of the carboxylic
compound.
4. Conclusions
The analysis of the infrared carbonyl-stretching vibration
region of 1 has shown different bands due to the presence of two
distinctive absorbing carbonyl groups. Thus, two bands
corresponding to free and hydrogen-bonded carbonyl groups
have been identified.
The constant of the self-association of 1 has been determined
by quantitative analysis of these bands. A value of 8900 has
been obtained, which is in accordance with data reported on in
bibliography.
The analysis of the carbonyl-stretching vibration region of 1/
ethylpyridine mixtures has shown the existence of a new band
assigned to free carbonyl groups generated as a consequence of
OH hydrogen bonding with pyridine nitrogen. This band is
located at lower frequencies than the corresponding to the
‘‘open dimer’’, indicative of a higher strength of the hydrogen
bonding between OH and nitrogen. The position of this band
does not show any dependence on the type of pyridine isomer,
what means that the hydrogen bonding force is about the same
for both isomers. Nevertheless, lower equilibrium constant
values have been obtained for 2-ethylpyridine because the
steric hindrance of the nitrogen in this component.
It is important to recognize that even though the strength of
the interaction between the carboxylic acid and pyridine groups
exceeds that of the carboxylic cyclic closed dimer, the
magnitude of the carboxylic acid dimer equilibrium constant
is greater.
FT-IR results show that the hydrogen bonding strength in
these systems is high enough to be considered the driving force
to achieve supramolecular liquid crystal polymers having
columnar mensomorphism based on this kind of polycatenar
acids.
Acknowledgements
We express our thanks to the University of the Basque
Country and Aragon Government for their continous support
through their respective consolidated research group programs.
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