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Excess Gibbs Energy and Local Compositionsin the Mixtures C2, C3 Alkane Diols and Triolswith Water at Various Pressures
Dmitriy M. Makarov1 • Gennadiy I. Egorov1 •
Shiraz A. Markarian2 • Arkadiy M. Kolker1
Received: 20 July 2015 / Accepted: 17 July 2016 / Published online: 26 September 2016� Springer Science+Business Media New York 2016
Abstract In this work the excess molar Gibbs energy of binary mixtures of water with
ethylene glycol, 1,2-propanediol, 1,3-propanediol or glycerol was calculated at 298.15 K
and pressures from 0.1 to 100 MPa. Thermodynamic data were used to calculate the
Kirkwood–Buff integrals and the parameters of local composition (Dnij). The excess Gibbs
energies and parameters of local compositions for aqueous mixtures of the alcohols with
different number of hydroxyl groups and internal structures are compared. Similar char-
acter of intermolecular interactions has been established for all mixtures studied. It was
discovered that external pressure causes an increase of local nonhomogeneity for all
systems. The pressure influence was more pronounced for the aqueous mixtures of
propanediols.
Keywords Aqueous solution � Diols � Glycerol � Kirkwood–Buff integrals � Local
composition � Pressure
1 Introduction
Polyatomic alcohols are an interesting class of compounds from the point of view of
general-theoretical investigations. The presence of several OH-groups gives rise to specific
properties to the alcohol liquid solutions due to the unique properties of hydrogen bonds to
form the strongly self-associated state with developed spatial H-bond networks [1, 2].
Moreover the polyatomic alcohols are inclined to form intramolecular hydrogen bonds
[3, 4].
& Dmitriy M. Makarovdmm@isc-ras.ru
1 G.A. Krestov Institute of Solution Chemistry of the Russian Academy of Sciences, Ivanovo, Russia
2 Department of Physical Chemistry, Yerevan State University, 0025 Yerevan, Armenia
123
J Solution Chem (2016) 45:1679–1688DOI 10.1007/s10953-016-0524-4
The most studied of the polyatomic alcohols are the lower alkyl diols and triols with two
and three carbons. These alcohols were taken as the objects of the present investigation:
1,2-ethanediol (ethylene glycol, EG), 1,2-propanediol (propylene glycol, 1,2-PD), 1,3-
propanediol (1,3-PD), and 1,2,3- propanetriol (glycerol, GL).
Aqueous mixtures of the alcohols under examination are of great importance for biology
and technology. They are widely used as penetrating cryoprotectors [5] to prevent living
cells and tissues from freezing injuries, some of them can be applied to stabilize the third-
order structure of proteins at high temperatures [6] and pressures [7]. However molecular
mechanisms by which polyatomic alcohols inhibit ice formation under cryopreservation
and stabilize the native structure of proteins under a stress are still unclear.
Although the influence of temperature on strongly associated solutions has been studied
in detail [8–10], data on high pressure effects are rarer, probably because of experimental
difficulties. High pressure can be a useful tool for fundamental research as it changes
various equilibria with low energy, making them observable in strongly associated liquids.
At the present work the Kirkwood–Buff (KB) solution theory was applied to examine
the structural features of aqueous solutions of diols and triols. It is a continuation of our
investigations of binary water–alcohol mixtures within the bounds of KB theory [11]. Our
aim was to obtain new data on the influence of the number and location of hydroxyl groups
in the alcohol molecules on structural order and association between the components in
water–alcohol mixtures as functions of the composition and external pressure.
Earlier the KB integrals were calculated for aqueous mixtures of ethylene glycol
[12–15], glycerol [15, 16], and 1,2-propanediol and 1,3-propanediol [17, 18] from ther-
modynamic properties of the appropriate solutions. Unfortunately, the information on
preferential solvation in the mixtures was obtained at atmospheric pressure only.
2 Theory
The Kirkwood–Buff (KB) solution theory [19] links thermodynamic properties with
molecular distribution functions through Kirkwood–Buff integrals (KBIs):
Gij ¼Z1
0
gijðrÞ � 1� �
4pr2dr ð1Þ
where gij—the radial distribution function of i-type molecules within the volume at the
distance r from the central molecule j.
The inverse Kirkwood–Buff approach [20] introduces the following equations for cal-
culation of KBIs:
Gij ¼ Gji ¼ RT jT � ViVj
VmD
� �ð2Þ
Gii ¼ RT jT þ xj
xi
V2j
VmD
!� Vm
xið3Þ
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D ¼ RT þ xixjo2GE
ox2j
!
T ;p
ð4Þ
where R represents the universal gas constant; Vi and Vj the partial molar volumes of
components i and j, respectively; Vm and jT represent the molar volume and the isothermal
compressibility coefficient of the mixture, respectively; GE the excess molar Gibbs energy,
and xi and xj the mole fractions of the components.
One of the key characteristics obtained from KB theory is a parameter of local com-
position, Dnij [21, 22], representing the excess (or deficit) of i-type molecules around the
species j within the range of gij determination, as compared with the number of molecules
i at their completely disordered spatial distribution.
The parameters of local composition were determined by Shulgin and Ruckenstein [23]
as:
Dnij ¼ ciðGij � GVij Þ ð5Þ
Dnii ¼ ciðGii � GVii Þ ð6Þ
where ci represents the molar concentration of the component i, GVij and GV
ii the contri-
butions of the excluded volume calculated by the following equations:
GVij ¼ RTjT � ViVj
Vm
ð7Þ
GVii ¼ GV
ij þ Vj � Vi ð8Þ
3 Results and Discussion
Our experimental and literature data on the concentration dependences of the density,
excess Gibbs energy, and isothermal compressibility coefficient were used to calculate
KBIs. Pressure–volume–temperature-composition (pVTx) relations made it possible to
calculate these properties as functions of pressure. Total inaccuracy of KBI determination
depends, first of all, on the experimental error of the data on the liquid–vapor equilibrium;
secondly, the differentiation procedure also contributes to the magnitude of the total
inaccuracy [24].
The expression for the excess Gibbs energy of water–ethylene glycol mixtures as a
function of composition at 298.15 K was taken from [25]. The densities at atmospheric
pressure and pVTx data for this mixture were obtained by us earlier [26–28].
For water-1,2-propanediol and water-1,3-propanediol mixtures the densities at atmo-
spheric pressure and pVTx data are given in [29] and [30], respectively. The fitting equation
for the excess Gibbs energy of water-1,2-propanediol mixtures [31] was obtained on the
bases of some experimental works [32–37]. GE values for water-1,3-propanediol mixtures
were obtained from the vapor pressure data [38].
For water–glycerol mixtures, the volume properties at atmospheric pressure and pVTx-
properties were obtained by us earlier [39–41]. The Redlich–Kister equation used to fit the
excess Gibbs energy of water–glycerol mixtures [16] was derived from the data by To et al.
[42].
J Solution Chem (2016) 45:1679–1688 1681
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Partial molar volumes of the mixture components were calculated by Eqs. 9 and 10
using the density data:
Vi ¼ Vm � xj dVm=dxj� �
ð9Þ
Vj ¼ Vm þ xi dVm=dxj� �
ð10Þ
The isothermal compressibility coefficients were calculated by the equation:
jT ¼ �1=Vm dVm=dpð ÞT ð11Þ
To calculate the excess Gibbs energy at pressures different from the atmospheric one of
the following expression was applied:
GEp ¼ GE
p0þZp
0
VEmdp ð12Þ
where GEp and GE
p0represent the excess Gibbs energy at high pressure (p) and atmospheric
pressure (p0), respectively, and VEm the excess molar volume of the mixture.
The concentration dependences of the Gibbs energy values at various pressures were
fitted by the following polynomial expression:
GE ¼Xni¼1
aixi ð13Þ
where n, the polynomial degree, is equal to 4 and x is the alcohol molar fraction.
Adjustable coefficients ai at 0.1, 50, and 100 MPa for all mixtures studied are listed in
Table 1.
Table 1 Adjustable coefficientsof Eq. 13 (J�mol-1) used to cal-culate the excess molar Gibbsenergies of aqueous mixtures atT = 298.15 K
Coefficients p/MPa
Ethylene glycol Glycerol
0.1 50 100 0.1 50 100
a1 -899 -997 -1064 -2115 -2225 -2309
a2 1966 2131 2222 4064 4297 4465
a3 -1818 -1889 -1896 -3772 -3943 -4051
a4 751 755 738 1823 1871 1895
Coefficients p/MPa
1,2-Propanediol 1,3-Propanediol
0.1 50 100 0.1 50 100
a1 -425 -615 -756 -331 -400 -440
a2 834 1216 1464 461 466 402
a3 -496 -759 -887 -39 125 351
a4 87 158 179 -91 -191 -313
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The dependences of the excess Gibbs energy for binary mixtures of water with ethylene
glycol, 1,2-propanediol, 1,3-propanediol, or glycerol versus the alcohol content are shown
in Fig. 1. The negative GE values indicate that the hetero-interactions are stronger than the
interactions between identical molecules. The comparison of the excess Gibbs energy of
the systems under examination shows that for all systems, except water–glycerol mixtures,
GE has small negative values and their magnitudes increase within the series: 1,2-
propanediol & 1,3-propanediol\ ethylene glycol\ glycerol. The difference between GE
values for aqueous solution of the alcohols under investigation can probably be explained
by some details of intermolecular interactions; namely, by certain distinctions in their
association degree because of different positions of hydroxyl groups and, of course, by
different sizes of the non-polar groups of the alcohols molecules.
A pressure increase causes an increase of the negative deviation from the ideal state for
these systems and at 100 MPa the series of GE increasing magnitudes is: 1,3-propane-
diol\ 1,2-propanediol\ ethylene glycol\ glycerol. The pressure influence on GE values
is most pronounced for water–1,2-propanediol mixtures.
In Fig. 2 one can see the concentration dependences of KBIs at 298.15 K and pressures
0.1 and 100 MPa for all aqueous mixtures studied (1-water, 2-alcohol). The concentration
behavior of the Kirkwood–Buff integrals for aqueous solutions of the polyhydroxy alco-
hols differs from the behavior of monohydroxy alcohols [11, 23, 43], where strong
extremal dependences of Gij versus the alcohol content were observed because of
microheterogeneity phenomenon in these systems.
The integrals G12 and G22 for all mixtures under consideration are quasi monotonic over
the entire concentration range and are in good agreement with the values obtained earlier
[12–14, 16, 17]. However, there are some discrepancies in the literature data for G11 values
at x2[ 0.5. This is probably connected with using different thermodynamic data for this
integral calculation as it can result as well from the large uncertainty of D value deter-
mination by Eq. 4.
Under the pressure increase up to 100 MPa the dependences of Gij deviate slightly from
the values at atmospheric pressure for all systems in question. Moreover, the positive
values of the integral decrease and negative ones increase with the pressure increase. In
Fig. 1 The molar excess Gibbs energy, GE, at 0.1 MPa (solid line) and 100 MPa (dashed line) atT = 298.15 K for the aqueous alcohol mixtures: ethylene glycol (square); 1,2-propanediol (circle); 1,3-propanediol (triangle); glycerol (inverted triangle)
J Solution Chem (2016) 45:1679–1688 1683
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contrast, for aqueous solutions of monohydroxy alcohols the excess pressure results in
significant deviation of Gij from the value at atmospheric pressure that is the most pro-
nounced in the region of the extremum [11].
In Figs. 3 and 4 the concentration dependences of Dnij parameters, calculated by Eqs. 7
and 8, are presented at atmospheric pressure and at 100 MPa. As one can see, the con-
centration dependences of the local composition parameters are similar for all systems
studied. According to the literature data on aqueous mixtures of ethylene glycol [44] and
glycerol [2], relatively homogeneous distributions of hydroxyl groups are observed, all
over the bulk; the components demonstrate the high degree of their mutual penetration and
form a common infinite hydrogen-bonded cluster across the whole concentration range.
This argues that the fact that the observed deviations of the local compositions from the
bulk concentrations take place, first of all, because of intermolecular hydrogen bonds.
The values of Dn12 (Fig. 3) are positive over the whole concentration range and reach
the maximum at x = 0.1–0.15, i.e. the alcohol molecules are surrounded, in preference, by
water molecules. The maximum at x = 0.15, observed for water–glycerol mixture under
the growth of the water density in the immediate vicinity of the alcohol molecule (Fig. 3),
confirms the scheme of the mixing in this system proposed by Dashnau et al. [10]. In that
work it was stated that the water within the first hydration shell, concentrated around
glycerol polar groups when the alcohol concentration, increases and the average number of
water hydrogen bonds in the bulk falls sharply almost down to 0 at x = 0.15. At lower
glycerol concentrations the quantity of water molecules within the first hydration shell
becomes insufficient to hydrate glycerol molecules completely and the other glycerol
molecules compensate for the water deficiency.
Fig. 2 The Kirkwood–Buff integrals (G12 (square), G11 (circle), G22 (triangle)) at 0.1 MPa (solid line) and100 MPa (dashed line) at T = 298.15 K for the aqueous alcohol mixtures: a ethylene glycol, b glycerol,c 1,2-propanediol, d 1,3-propanediol
1684 J Solution Chem (2016) 45:1679–1688
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The local excess of water around the alcohol molecules increases in the order: 1,3-
propanediol\ 1,2-propanediol\ ethylene glycol\ glycerol. This sequence is in agree-
ment with the conclusions drawn by Zhang et al. [45] on the higher ability of glycerol
molecules, as against ethylene glycol ones, to form hydrogen bonds with water. Apparently
this ability is minimal for propanediols because of the steric effects caused by their non-
polar groups.
The dependences of Dn22 and Dn11 (Figs. 3 and 4) point out the deficiency of the
alcohol or water molecules around their own central molecules, respectively. In some
works the formation of small water clusters around hydroxyl groups of diols [44] and triol
[2, 46] was proposed. The sizes of these clusters depends on the solute concentration in
water. Our data do not contradict the above results as local excess or deficiency is not, by
definition, the increment of water molecules exactly within the first hydration shell. The
value of Dnij can cover the composition changes in several hydration layers but, as a rule,
not larger than in five [47]. Therefore, it can be supposed that the deficit of molecules
around the central molecule of the same nature is determined by the contribution from the
long-range distribution of the proper molecules. The negative Dn11 and Dn22 values show
the absence of clearly pronounced self-association in these systems; alcohol–water
hydrogen bonds efficiently replace water–water hydrogen bonds, thus keeping up the
developed spatial H-bond network regardless of the alcohol content in the mixture.
In the case of aqueous solutions of 1,2- and 1,3-propanediol a sign inversion (from
positive to negative) is observed for Dn11 values at high concentrations of the alcohols
(x[ 0.8). In this concentration range the propanediols behave similarly to monohydric
Fig. 3 Excess (or deficit) molecules around a central alcohol molecule (Dn12 (square), Dn22 (triangle)) at0.1 MPa (solid line) and 100 MPa (dashed line) at T = 298.15 K for the aqueous alcohols mixtures:a ethylene glycol, b glycerol, c 1,2-propanediol, d 1,3-propanediol
J Solution Chem (2016) 45:1679–1688 1685
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alcohols [11]. The data of IR spectroscopic study of these systems [9] show that low water
content does not influence significantly the structure of either diol in the liquid phase.
Under pressure increase up to 100 MPa the molecular packing becomes more compact,
resulting in the increase of the water molecules excess around the alcohol molecules’ in the
systems studied. This may be caused by the increase of stability of water–alcohol bonds, as
was found in molecular dynamics simulation of water–ethylene glycol mixtures under
compression [48]. The pressure results in the destruction of some hydrogen bonds but the
stability of the remaining ones increases because the molecular motions become hampered.
Excess external pressure also results in an increased water deficit around the water
molecules (Dn11) and of the alcohol around its own molecules (Dn22). The strongest
pressure influence is observed for propanediol mixtures, probably because of the weak-
ening of the hydrophobic effects that are weak enough anyway.
Acknowledgments This work was partially financially supported by the Russian Foundation for BasicResearch (Projects 15-43-03092-r_centre_a and 15-43-03093-r_centre_a).
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