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Chemical Physics Letters 379 (2003) 581–587
www.elsevier.com/locate/cplett
Preferential solvation and elasticity of the hydrogen bonds
network in tertiary butyl alcohol–water mixture
Michael Kiselev a, Dmitry Ivlev a, Yurii Puhovski a, Teerakiat Kerdcharoen b,c,*
a
Institute of Solution Chemistry, RAS, Akademicheskaya St. 1, Ivanovo 153045, Russia
b
Department of Physics, Faculty of Science, Mahidol University, Rama 6 Road, Bangkok 10400, Thailand
c
Institute of Science and Technology for Research and Development, Mahidol University, Salaya Campus,
Nakorn Pathom 73170, Thailand
Received 14 July 2003; in final form 26 August 2003
Published online: 19 September 2003
Abstract
Molecular dynamics simulations have been performed for water–tertiary butyl alcohol (TBA) mixtures in the water
rich region. Examination of the Kirkwood–Buff integrals, local composition, and potential mean force for concen-
tration in the range 0.05–0.07 TBA mole fraction leads to insight into the unexpected behaviors of some thermody-
namics properties. Hydrophobic hydration phenomena and solvent–solute association are discussed at the molecular
level. Since the hydrogen bond network elasticity modulus is a quantitative measure of the resistance of the water
hydrogen bonds network to external perturbation arising from solvent–solute interactions, a first principle calculation
of the elasticity modulus was carried out.
Ó 2003 Published by Elsevier B.V.
1. Introduction mixtures have unexpected (peculiar) behaviors in
their physicochemical properties at low alcohol
The study of alcohol–water mixtures provides concentrations. These peculiar behaviors can be
very important clues for understanding the effects explained by the hydrophobic hydration despite
of hetero-functional molecules on the three- alcohol molecules are hetero-functional [1–6].
dimensional hydrogen bonded network of water. Since tertiary butyl alcohol (TBA) has the largest
The reason is that there is a delicate balance be- hydrophobic component among the low-weight
tween Ôstructure-makingÕ and Ôstructure-breakingÕ water-soluble alcohols, it should be an interesting
effects in these mixtures, i.e., both hydrophilic and system to study hydrophobicity.
hydrophobic effects play equally important roles in The process of a nonpolar solute molecule dis-
them. Previous studies have found that these solution in water at low concentration can be di-
vided into three stages [7]: (1) create a cavity in the
solvent to hold the solute; (2) insert the solute
*
Corresponding author. Fax: +66-2-2015842. molecule into the cavity and (3) reorganize the
E-mail address: sctkc@mahidol.ac.th (T. Kerdcharoen). solvent structure in presence of the solute. The first
0009-2614/$ - see front matter Ó 2003 Published by Elsevier B.V.
doi:10.1016/j.cplett.2003.08.082
582 M. Kiselev et al. / Chemical Physics Letters 379 (2003) 581–587
and second stages have been extensively described Table 1
in the literature [8], whereas the third stage is still a The Lennard–Jones parameters of intermolecular interactions
between TBA–TBA and TBA–water moleculesa
matter of controversy. The conventional way to
describe solvent reorganization around a solute is Interaction e (kJ/mol) r (nm)
based on the clathrate-like structure of water in- MeTBA –MeTBA 0.5354 0.3775
troduced by Frank and Evans [9]. The validity of CTBA –CTBA 0.6076 0.4868
OTBA –OTBA 0.2371 0.335
this approach for dissolution of alcohol molecules
MeTBA –OW 2.4390 0.3884
was not supported by the neutron scattering ex- CTBA –OW 1.4325 0.3804
periment by Bowron et al. [10]. In this light, the OTBA –OW 2.6414 0.3439
solute–solvent interactions at low concentration a
Interactions between atoms in different TBA molecules have
might be looked at as being an external pertur- been approximated using the Lorentz–Berthelot mixing rules.
bation on the hydrogen bond network of water.
Looking at the resistance of the water hydrogen
bond network to external perturbations could lead The methyl groups of TBA are considered to be
to an understanding of the reorganization of the a single metal atom MeTBA . The atomic charges
inherent water structure in the mixture. The main 0.00892, 0.29296, )0.75168, 0.43196 a.u., obtained
goal of this Letter is to study this resistance by from ab initio calculations of TBA, are assigned to
making a first principle calculation of the hydro- MeTBA , CTBA , OTBA , and HTBA , respectively. The
gen bond network elasticity modulus since it is a quality of the fit of ab initio data to the potential
quantitative measure of the resistance. functions was judged by its statistical characteris-
tics. 500 additional ab initio energy points for
TBA–TBA and TBA–water dimer configurations
2. Model and details of simulations outside the original set were calculated and com-
pared with the values predicted by the analytical
The SPC2 [11] model was chosen to describe the functions.
water–water interactions. The TBA–TBA and Twenty molecular dynamics simulation runs for
TBA–water potential functions were constructed liquid TBA–water mixture were carried out in the
using ab initio calculations. The interaction ener- canonical NVT ensemble using M O D Y S program
gies were obtained at the RHF/6-31G(d,p) level package [13] covering the concentrations range
using the G A U S S I A N 9 8 program [12]. For a com- between 0 and 0.12 TBA mole fraction. The sim-
plete representation of the potential energy surface ulation cube consists of 1080 solvent molecules
(PES), one molecule was placed at different dis- treated under periodic boundary conditions. The
tances and different relative orientations from system was equilibrated for 300 ps at an average
another fixed molecule, based on molecular sym- temperature of 300 K. The duration of subsequent
metry considerations. Additional configurations runs was 400 ps for data collection. Other simu-
close to the PES local minima were included to lation details have been given in previous papers
improve the model. A set of approximately 1500 [14–16].
interaction energy points was then fitted to an Since a combination of good model potentials
analytical potential function based on the atomic for pure liquids may not lead to reliable results for
coordinates. The total intermolecular interaction the mixture, relevant properties of the mixture
energy was written as a sum of the pair potential obtained from the combined models should be
functions V ðrÞ (r being the distance between the checked. A good agreement of the atom–atom
kth atom of one molecule and the nth atom of radial distribution functions [10], isochoric excess
another molecule) given by heat capacities [17], activation free energies of the
viscous flow [15] and self diffusion coefficients [18]
V ðrÞ ¼ 4eððr=rÞ12 À ðr=rÞ6 Þ þ qk qn =r; ð1Þ
obtained from this potential model with available
where r and e are the Lennard–Jones potential experimental data was achieved for TBA–water
parameters (Table 1), and q denotes the charges. mixtures. Moreover, the present model yields a
M. Kiselev et al. / Chemical Physics Letters 379 (2003) 581–587 583
value of 42.1 Æ 0.4 kJ/mol for heat of vaporization
for pure TBA closer to the experimental value [19]
of 46.5 Æ 0.5 kJ/mol in comparison with the value
of 32.1 kJ/mol obtained from the well-known
OPLS model [20]. Another TBA model introduced
by Tanaka et al. [21] gives fairly good results for
3 mol% aqueous solution of TBA. However this
model predicts immiscibility of the water–TBA
mixture beginning from 0.06 m.f. TBA, whereas
these liquids are miscible over the whole concen-
tration range. Taking into account reliability of
the predicted structural, thermodynamic, dynamic
properties of pure TBA as well as aqueous TBA,
the new model derived from this study is appro-
priate for simulation of water–TBA mixtures.
Ab initio calculations were carried out on a
multiprocessor SGI Origin 2000 workstation at
University of North Caroline at Chapel Hill. MD
simulations were performed on Linux clusters Fig. 1. Kirkwood–Buff integrals G11 ðx2 Þ, G12 ðx2 Þ, and G22 ðx2 Þ
at the Institute of Solution Chemistry, Russian for TBA–water mixture as a function of TBA concentration x2 .
Error bars are shown on the plot.
Academy of Science.
G12 ðx2 Þ, and G22 ðx2 Þ functions are found to have a
3. Results and discussion maximum and an inflection point, respectively,
within the same concentration range.
3.1. Preferential solvation This behavior can be explained by taking into
account two assumptions. First, a maximum of
The Kirkwood–Buff (KB) theory is tradition- heat capacity reflects increasing structural fluctu-
ally applied to the study of hydrophobic phe- ations which arise from there being changes in the
nomena [22]. The KB integrals Gij ðx2 Þ as functions local composition of the water solvation shell.
of concentration x2 indicate a changing of associ- Second, solvent–solute interactions reach compa-
ation between components in solution [23]. rable magnitudes with solvent–solvent ones about
Therefore, its value should be important for de- mole fraction of 0.05. In order to verify the second
termining the preferential solvation. Gij can be assumption, we should estimate the potential mean
directly calculated from gij ðrÞ, the centre of mass force (PMF) of water–tertiary butyl alcohol in-
radial distribution functions (RDF) obtained from teractions in a manner similar to that done in [24].
MD simulations via the formula The depth of the first minimum of PMF DWW–TBA
Z 1 between water and TBA molecules is shown in
Gij ¼ ðgij ðrÞ À 1Þ4pr2 dr; ð2Þ Fig. 2 as a function of the concentration. It has
0
a pronounced minimum around 0.06–0.07 m.f. of
where ij indices refer to solvent–solvent (11), sol- alcohol. Preferable association of water and TBA
vent–solute (12) and solute–solute (22), respec- molecules becomes most probable around this
tively. The calculated G11 ðx2 Þ, G12 ðx2 Þ, and G22 ðx2 Þ concentration. Based on our previous results [15],
as functions of TBA concentration x2 are shown in the reason for the presence of this minimum is due
Fig. 1. The G11 ðx2 Þ curve has a shoulder around to the entropic contribution to the free energy.
0.04–0.07 TBA mole fraction (m.f.). Mixtures in As far as the preferential solvation is concerned,
this region of TBA concentrations have the max- a direct way to estimate it would be to calculate the
imum heat capacity [17]. On the other side, the local composition [22]. The local mole fractions of
584 M. Kiselev et al. / Chemical Physics Letters 379 (2003) 581–587
Fig. 2. The depth of the first minimum DWW–TBA of potential Fig. 3. The local mole fraction xloc of TBA molecules around a
22
mean force versus TBA concentration x2 . Error bars are shown reference TBA molecule as function of binary mixture compo-
on the plot. sition. Error bars do not exceed one percent of the xloc values.
22
the ith component molecule around a reference water molecules near 0.05 m.f. of TBA). Similar
molecule of the jth component xloc are given by
ij results have been reported by Shulgin and Ruc-
xloc ðx2 Þ ¼ nij ðx2 Þ=ðnij ðx2 Þ þ njj ðx2 ÞÞ; kenstein [23], where the local compositions are
ij
calculated from the KB integrals. Since solvent–
solvent associations are the dominant factors in
xloc ðx2 Þ þ xloc ðx2 Þ ¼ 1;
ij jj ð3Þ
determining the values of many thermodynamics
where the number of the ith component molecules properties, replication of the inherent water struc-
near the jth component molecule, nij is calculated ture in response to the presence of a solute molecule
as function of the bulk TBA composition x2 . This must still be the key for understanding of structural
is done by integrating the RDFs of the centre of abnormalities (peculiarities).
mass of the corresponding molecules:
Z rj 3.2. Elasticity of inherent water structure
nij ðx2 Þ ¼ ni ðx2 Þ gji ðr; x2 Þ4pr2 dr; ð4Þ
0 The resistance of the inherent water structure to
where ni is number density of the ith component in structural perturbation from the external effects
solution. We note that the solvent shell radius rj of like external electric field [25], elevated tempera-
the jth component molecule equals the position of ture and pressure [16], and dissolution of nonpolar
the first minimum of the corresponding RDF. solutes [8] are well known in the physics of water.
The local composition around the TBA is shown Rodnikova first introduced an elasticity parameter
in Fig. 3. It can be seen that the local composition of spatial hydrogen bonds network [26–28] for
lies below the iso-solvation line for concentration analysis of liquid structure upon dissolution. This
region around 0.04–0.06 TBA mole fraction. The parameter is defined by different ways through
prefered solute–solute association, which is typical experimental values and can be used as a measure
feature of pure hydrophobic hydration, would of hydrogen bonds network resistance [27,28]. An
therefore not be observed in TBA–water mixture elasticity of spatial hydrogen bonds network has
(TBA molecules are surrounded preferably by been proposed as explanation of series phenomena
M. Kiselev et al. / Chemical Physics Letters 379 (2003) 581–587 585
in solutions [27,28]. On the other hand, an elas- molecules that do not contribute in the hydrogen
ticity parameter may be defined as elasticity bonds networks are excluded from consideration.
modulus of hydrogen bonds network, introduced The resulting l11 ðx2 Þ function for water–TBA
1
within the statistical theory of elasticity in the li- mixture in the water rich region is depicted in
quid state [29]. The generalized HookeÕs law can be Fig. 4. Two interesting features are seen in this
expressed in terms of strain tensors Pab and Pab ~ figure. First, the H-bond elasticity function l11 ðx2 Þ
1
before and after applied stress, respectively, using has a large fluctuation in the concentration range
an assumption of linearity over the shear vector u 0.05–0.06 m.f. of TBA. Such behavior is consistent
at point q: with the maximum of experimental excess heat
capacity [17] and inflection point of viscosity co-
~ oua oub
Pab ðqÞ À Pab ðqÞ ¼ l þ efficient [15] being in the same range. Sato et al.
oqb oqa
[31] has suggested that such fluctuation results
þ dab ðK À 2=3lÞ div uðqÞ; ð5Þ from a transition between different structures in
where K is modulus of compressibility and l is very diluted water–alcohol mixture. The transition
modulus of elasticity, dab – KronekkerÕs symbol, occurs when the number of water molecules nee-
a; b ¼ 1; 2; 3. Both the K and l modulus are in- ded to form the clathrate cage around each alcohol
troduced as adiabatic magnitudes, i.e., external molecules and other structures present before the
stress acts infinitely fast. According to statistical addition of more alcohol molecules is not sufficient
mechanics [29], the expression for strain tensor in a for forming the additional clathrate cages needed
simple isotropy molecular liquid subjected to a fast when the solutions in the range (0.05 – 0.07 m.f.)
shear can be written in a form equivalent to are obtained. Second, the calculated H-bond
Eq. (5). For our situation, the elasticity modulus elasticity exhibits a shallow maximum near 0.1 m.f.
can be expressed in terms of the molecular volume of TBA. The cause of this maximum should be in
3
v ¼ 4=3pr0 (where r0 is position of the first mini- keeping with the results of our previous study of
mum of centre mass RDF), the RDF, and the alcohol solution [15], where for concentration near
potential energy function U ðrÞ. A general expres-
sion [30] which approximates the elasticity modu-
lus l of the binary mixture in terms of the
contributions from the first and second constitu-
ents of the mixtures at infinite frequency of loading
(l1 ), i.e., l11 , l12 , and l22 , is given by
1 1 1
l1 ¼ x2 l11 þ 2x1 x2 l12 þ x2 l22 ;
1 1 1 2 1 ð6Þ
where elasticity modulus lij of mixture compo-
1
nents is calculated from
Z 1
ij 2p d 4 dUij
l1 ¼ r gij ðrÞ dr: ð7Þ
15v2 r0 dr dr
Insofar as the water structure resistance is
concerned, the elasticity modulus contribution
from the water–water interaction l11 can be
1
viewed as a measure of inherent water structure
resistance to any external influence.
In the present Letter, we have studied the hy-
drogen bonds network resistance to solvent–solute Fig. 4. The H-bond network elasticity modulus l11 versus TBA
1
interactions, using the elasticity modulus of concentration x2 . Solid line is a spline approximation of cal-
H-bonded water molecules as its measure. Water culated values. Error bars are shown on the plot.
586 M. Kiselev et al. / Chemical Physics Letters 379 (2003) 581–587
0.1 m.f. of TBA, the results were explained in
terms of the geometrical stabilization. It was found
in that study that the geometrical structure of
water around concentration range of 0.12–0.15 is
even more regular than that in pure water, even if
the effect from alcohol becomes relatively high
[15]. This is the reason for the strengthening of the
H-bond network tension leading to increasing
modulus of elasticity.
It is interested to note that both the excess ac-
tivation free energy function and l11 ðx2 Þ function
1
have inflection points near 0.06 TBA mole frac-
tion. Sato et al. [31] observed an extremum in the
excess activation free energy derived from EiringÕs
approximation of relaxation mechanism in solu-
tion near the concentration range [0.12–0.15]. Our
observations are very interesting since the dielec-
tric relaxation which is a very complicated process,
is dependent on the rotational and translation Fig. 5. Self-diffusion coefficients as calculated from MD simu-
lation (open circles) versus TBA composition in comparison
molecular motions that take place in different time with experimental values [26] (filled circles). Error bars are
scales. shown on the plot.
It is important to know whether the transla-
tional diffusion has unexpected behaviors (pecu-
liarities) in the same concentration range (0.06
m.f. TBA) where peculiarities in other properties 4. Conclusions
occur. The water self diffusion coefficients as de-
rived from well-known Green–Kubo expression A new quantitative measure of inherent water
are plotted versus concentration in Fig. 5. The structure resistance to external perturbations
experimental results published by Harris and Ne- arising from the dissolution of nonpolar solutes
witt [18] are shown in the plot for comparison. based on the H-bond elasticity modulus was pro-
The MD diffusion coefficient is in good agreement posed. The present investigation has also proposed
with the experimental value for concentration new origins of the hydrophobic effect. The unex-
around 0.06 m.f. of TBA. Insofar as diluted wa- pected (peculiar) behaviors of several thermody-
ter–TBA mixture is concerned, it is well known namics characteristics in TBA–water mixture
that SPC2 water overestimates the diffusion coef- around 0.05–0.07 m.f. of TBA result from the
ficient. This would increase the discrepancy be- balance of two types of clusters in solution [30].
tween experimental values and the ones derived This interpretation is in keeping with the conclu-
from MD simulation for very diluted composi- sions given by Bowron et al. [10] that the con-
tions of TBA. The diffusion coefficient as a func- ventional theory of hydrophobicity might not
tion of concentration is expected to decay work for concentration range of 0.05–0.07 in
exponentially without any significant fluctuations. TBA–water mixtures. The H-bond elasticity
The structural fluctuations, which are obtained modulus has a maximum around 0.1 TBA mole
from KB theory (Fig. 1), the local composition fraction indicating the highest stretching of the H-
(Fig. 2) and elasticity modulus (Fig. 4) do not bond network occurs around this concentration.
imply the destruction of structure in solution, but This is taken as being evidence of inherent water
instead indicate an equilibrium between two kind structure resistance, which Sato et al. [31] defines
of clusters, namely TBA(H2 O)n and (TBA)2 (H2 O)n to be due to an entropy–enthalpy compensation
[15]. mechanism.
M. Kiselev et al. / Chemical Physics Letters 379 (2003) 581–587 587
Acknowledgements [11] H.J.C. Berendsen, J.R. Grigera, T.P. Straatsma, J. Phys.
Chem. 91 (1987) 6269.
This work was supported by the Russian [12] M.J. Frish et al., Gaussian 98 (Revision A.10), Gaussian
Inc., Pittsburgh, PA, 2001.
Foundation for Basic Research Grant No. RFBR- [13] I.I. Vaisman, M.G. Kiselev, Y.P. Puhovski, Y.M. Kessler,
02-03-32287, Russian Academy of Sciencies Grant MODYS––molecular dynamics simulator, Institute of
CBO-1.9. T.K. acknowledges the Thailand Re- Non-Aqueous Solutions Chemistry, Ivanovo, 1985.
search Fund for financial support (RSA/13/2545). [14] Y.P. Puhovski, L.P. Safonova, B.M. Rode, J. Mol. Liq.
The authors are thankful to Professors I.M. Tang 103–104 (2003) 15.
[15] M. Kiselev, D. Ivlev, J. Mol. Liq., in press.
and M.N. Rodnikova for reading the paper and [16] S. Krishtal, M. Kiselev, Y. Puhovski, T. Kerdcharoen, S.
fruitful discussions. Hannogbua, K. Heinzinger, Z. Naturforch. 56a (2001) 579.
[17] M.L. Origlia, E.M. Woolley, J. Chem. Thermodyn. 33
(2001) 451.
[18] K.R. Harris, P.J. Newitt, J. Phys. Chem. A 103 (1999) 508.
References [19] J. Polak, G.C. Benson, J. Chem. Thermodyn. 3 (1971) 235.
[20] W.L. Jorgensen, J. Phys. Chem. 90 (1986) 1276.
[1] Y.M. Kessler, A.L. Zaitsev, Solvophobic Effects: Theory, [21] H. Tanaka, K. Nakanishi, H. Touhara, J. Chem. Phys. 81
Experiments and Practice, Khimia, Leningrad, 1989. (1984) 4065.
[2] V.P. Belousov, M.Y. Panov, Thermodynamics of Aqueous [22] A. Ben-Naim, J. Phys. Chem. 93 (1989) 3809.
Non-Electrolyte Solutions, Khimia, Leningrad, 1983. [23] I. Shulgin, E. Ruckenstein, J. Phys. Chem. B 103 (1999)
[3] S. Lamanna, R. Cannistraro, Chem. Phys. 213 (1996) 95. 4900.
[4] A. Wakisaka, H. Abdoul-Carime, Y. Kiyozumi, J. Chem. [24] M.H. New, B.J. Berne, J. Am. Chem. Soc. 117 (1995) 7172.
Soc. Faraday Trans. 94 (1998) 161. [25] M. Kiselev, K. Heinzinger, J. Chem. Phys. 105 (1996) 650.
[5] G. Onori, A. Santucci, J. Mol. Liq. 69 (1996) 161. [26] V. Gaiduk, M.N. Rodnikova, J. Mol. Liq. 82 (1999) 47.
[6] S.Y. Noskov, M.G. Kiselev, A.M. Kolker, J. Struct. Chem. [27] M.N. Rodnikova, Zh. Fiz. Khim. 67 (1993) 275.
40 (1999) 253. [28] M.N. Rodnikova, T.M. ValÕkovskaya, V.N. Kartzev, D.B.
[7] J.A.V. Butler, Trans. Faraday Soc. 33 (1937) 229. Kayumova, J. Mol. Liq. 106 (2003) 219.
[8] F. Franks, in: Water: A Comprehensive Treatise, vol. 1–5, [29] I.Z. Fisher, Statistical Theory of Liquids, University of
Plenum Press, New York, 1973–1975. Chicago Press, Chicago, 1964.
[9] H.S. Frank, M.W. Evans, J. Chem. Phys. 13 (1945) 507. [30] E. Bruck-Levinson, V. Vikhrenko, V. Nemtsov, L. Rott,
[10] D.T. Bowron, A.K. Soper, J.L. Finney, J. Chem. Phys. 114 Izv. Vyssh. Uchebn. Zaved. Fisika 2 (1970) 70.
(2001) 6203. [31] T. Sato, A. Chiba, R. Nozaki, J. Mol. Liq. 101 (2002) 99.
