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].

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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

1682 J Solution Chem (2016) 45:1679–1688

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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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