Preferential Solvation in Ternary Solutions Containing Methylbenzoate. A Kirkwood-Buff
Fluctuation Theory Study
Begon ˜ a Garcı ´a, Santiago Aparicio, Rafael Alcalde, and Jose ´ M. Leal*
Departamento de Quı ´mica, UniVersidad de Burgos, 09001 Burgos, Spain
ReceiVed: January 30, 2003; In Final Form: July 1, 2003
Density, dynamic viscosity, and refractive index of the hexane/cyclohexane/methylbenzoate ternary solvent
and its binary constituents were measured at 298.15 K over the whole composition range. From the experimental
measurements, excess and mixing properties were evaluated and correlated with composition using different
models. The structure and interactions in the ternary solvent were analyzed starting from the experimental
properties by application of the Kirkwood-Buff fluctuation theory of solutions along with the UNIFAC
group contribution method for predicting activity coefficients. The local composition and excess (or deficit)
number of molecules aggregated around a central one were determined using the Kirkwood-Buff integrals.
The properties of the ternary system were used to test the predictive ability of several models. The volumetric
properties of the binary and ternary systems were correlated and predicted with the cubic equations of state
by Soave and Peng-Robinson combined with two simple mixing rules.
Introduction
Grouping of solvents into classes often is based on the nature
of the intermolecular forces because the manner whereby solute
and solvent molecules are associated with one another brings
about a marked effect on the resulting properties. After the
introduction of the concept of ionization power of solvent,
1
much
work has been devoted to solvent effects on rate and equilibrium
processes.
2
Because of the close connection between liquid
structure and macroscopic properties, determination of volu-
metric, electrical, and rheological properties is a valuable tool
to learn the liquid state.
3
On the other hand, the obtaining of
reliable measurements of solvent properties over a wide range
of composition, pressure, and temperature often is not feasible;
hence, prediction and correlation methods constitute a valuable
option to overcome such difficulties.
4,5
This work contributes to the study of the structure and
interactions of ester-containing ternary mixtures. These solvents
are widely used in polymer science and syntheses operations;
however, the scarce literature existing makes convenient a
systematic research on their properties.
6
Density, dynamic
viscosity, and refractive index data of the methylbenzoate/
cyclohexane/n-hexane ternary solvent and its constituent n-
hexane/cyclohexane, n-hexane/methylbenzoate, and cyclohexane/
methylbenzoate binary components are reported over the full
composition range.
7,8
From these measurements, the excess and
mixing properties were evaluated and interpreted on the basis
of interactions and geometry factors. The volumetric properties
of the binary systems were correlated using the cubic equations
of state by Soave
9
(SRK) and Peng-Robinson
10
(PR) combined
with two simple mixing rules. On the basis of the properties of
the binary components, the same properties of the ternary solvent
were approached using several models. The statistical thermo-
dynamic theory by Kirkwood-Buff (KB)
11
provides a proper
link between macroscopic and microscopic properties and was
used to interpret intermolecular interactions and preferential
solvation effects.
12
This approach describes properly deviations
from ideality, provides a reliable description of the solvation
effect, and can be extended to different types of particles, not
only spherical ones.
13
Also it enables evaluation of the local
composition of the components and has become popular for
binary and multicomponent mixtures.
14
The activity coefficients
were evaluated using the group contribution UNIFAC III
model.
15
The excess molar volumes were applied by deriving
expressions for the Kirkwood-Buff integrals and the corre-
sponding excess number of molecules around a central one.
16
Experimental Section
Reagents. The reactants, methylbenzoate (MB), hexane (hex),
and cyclohexane (cyc), of the highest purity commercially
available were used without further purification. The purity was
assessed by gas chromatography (GC) with a Perkin-Elmer 990
gas chromatograph, equipped with a Hewlett-Packard 3390A
integrator and also by comparing the densities, viscosities, and
refractive indices with literature values (Table S1, Supporting
Information, and refs 17-31 contained therein). The liquids
were degassed with ultrasound for several days before use and
kept out of the light over Fluka Union Carbide 0.4 nm molecular
sieves. To prevent the samples from preferential evaporation,
the mixtures were prepared by syringing amounts, weighed to
Δm ) 10
-5
g with a Mettler AT 261 Delta Range balance, into
suitably stoppered bottles. The mixtures were completely
miscible over the whole composition range.
Instruments and Procedures. The molar excess volumes
((10
-4
cm
3
mol
-1
) were deduced from the densities of the pure
liquids and mixtures. The densities, F, were measured with a
computer-controlled DMA 58 Anton Paar digital density meter
((5 × 10
-6
g cm
-3
) by introducing the samples into a U-shaped
oscillating tube the natural frequency of which is influenced
by the mass of the sample. The proper calibration was achieved
at all working temperatures ((0.01 K) with deionized doubly
distilled water (Milli-Q, Millipore) and n-nonane (Fluka, 99.2%
purity by GC) as reference liquids; the apparatus takes care of
* Corresponding author. E-mail: jmleal@ubu.es. Tel: +34 947 258 819.
Fax: +34 947 258 831.
13478 J. Phys. Chem. B 2003, 107, 13478-13486
10.1021/jp034255l CCC: $25.00 © 2003 American Chemical Society
Published on Web 11/08/2003