Handbook of Solvents - George Wypych - ChemTech - Ventech!

302 Kenneth A. Connors
The role of interfacial tension
In all the preceding discussion of terms having the gAγ form, γ has been interpreted as a surface
tension, the factor g serving to correct for the molecular-scale curvature effect. But a
surface tension is measured at the macroscopic air-liquid interface, and in the solution case
we are actually interested in the tension at a molecular scale solute-solvent interface. This
may be more closely related to an interfacial tension than to a surface tension. As a consequence,
if we attempt to find (say) g2A2 by dividing g2A2γ2 by γ2, we may be dividing by the
wrong number.
To estimate numbers approximating to interfacial tensions between a dissolved solute
molecule and a solvent is conjectural, but some general observations may be helpful. Let γX and γY be surface tensions (vs. air) of pure solvents X and Y, and γXY the interfacial tension at
the X-Y interface. Then in general,
γ = γ + γ −W − W
[5.5.56]
XY X Y XY YX
where W XYis the energy of interaction (per unit area) of X acting on Y and W YXis the energy
of Y acting on X. When dispersion forces alone are contributing to the interactions, this
equation becomes 26
d d ( Y)
γ = γ + γ −2 γ γ
XY X Y X
12 /
[5.5.57]
d d
where γX and γY are the dispersion force components of γX and γY. In consequence, γXY is always
smaller than the larger of the two surface tensions, and it may be smaller than either of
them.
Referring now to Table 5.5.8, if we innocently convert g2A2γ2 values to estimates of
g 2A 2 by dividing by γ 2, we find a range in g 2A 2 from 23 Å 2 molecule -1
dimethylsulfoxide) to 118 Å 2 molecule -1 (for isopropanol). But if the preceding argument is
correct, in dividing by γ 2 we were dividing by the wrong value. Taking benzene (γ =28erg
cm -2 ) as a model of supercooled liquid naphthalene, we might anticipate that those
cosolvents in Table 5.5.8 whose γ 2 values are greater than this number will have interfacial
tensions smaller than γ 2, hence should yield g 2A 2 estimates larger than those calculated with
γ 2, and vice versa. Thus, the considerable variability observed in g 2A 2 will be reduced.
On the basis of the preceding arguments it is recommended that gAγ terms (exemplified
by g 1A 1γ 1,g 2A 2γ 2, and gA(γ 2-γ 1)) should not be factored into gA quantities through division
by γ, the surface tension, (except perhaps to confirm that magnitudes are roughly as
expected). This conclusion arises directly from the interfacial tension considerations.
Finally let us consider the possibility of negative gA values in eq. [5.5.23]. Eq.
[5.5.54] shows that a negative gA is indeed a formal possibility, but how can it arise in practice?
We take the water-ethanol-sucrose system as an example; gA was reported to be negative
for this system. Water is solvent 1 and ethanol is solvent 2. This system is unusual
because of the very high polarity of the solute. At the molecular level, the solute in contact
with these solvents is reasonably regarded as supercooled liquid sucrose, whose surface tension
is unknown, but might be modeled by that of glycerol (γ = 63.4 erg cm -2 ). In these very
polar systems capable of hydrogen-bonding eq. [5.5.57] is not applicable, but we can anticipate
that the sucrose-water interaction energies (the W XY and W XY terms in eq. [5.5.56] are
(for