Handbook of Solvents - George Wypych - ChemTech - Ventech!

170 Christian Wohlfarth
avoided. Greater sensitivity can be achieved by using solvents with low enthalpies of vaporization.
This means, for our task, that not all desirable polymer-solvent pairs and not all temperature
(pressure) ranges can be investigated by VPO. Additionally, VPO has some
inherent sources of error. These belong to the possible existence of surface films, to differences
in diffusion coefficients in solutions, to appreciably different solution concentrations,
to differences in heat conductivity, to problems with drop size and shape, to the occurrence
of reactions in the solution, and to the presence of volatile solutes. Of course, most of them
can be avoided by laboratory practice and/or technical improvements, but it must be taken
into account when measuring solvent activities.
Regener and Wohlfarth 125 developed a way to enlarge the applicability range of VPO
to polymer concentrations ≤40wt% for the purpose of measuring solvent activities. An increase
of polymer concentration over the linear steady state working range of VPO causes
some problems. First, no thermodynamically defined ΔT can be obtained and, second, the
calibration constant may become dependent on concentration. Thus, the only way to
achieve higher concentrations is to find methods to minimize the increasing chemical potential
difference of the solvent between the two drops. This can be achieved by using a reference
solution of known solvent activity instead of the pure solvent. The instrument is then
used as a zero-point detector comparing the solvent activity of the reference solution with
solvent activity of the polymer solution. The reference concentration has to be varied until
ΔT=0isfound. The only assumption involved in this method is equal solvent condensation
and diffusion. The extrapolation method to ΔT at zero measuring time can be used to minimize
these influences. It is not really necessary to find the reference solution at exactly
ΔT=0, but it is sufficient to measure a small ΔT < 0 and small ΔT > 0 and to interpolate between
both known solvent activities. An example is shown in Figure 4.4.15, where benzene
was used as solute for the reference solutions.
Since the polymer solution remains quasi unchanged in concentration, this modified
VPO-method is faster than isopiestic isothermal distillation experiments with organic solvents
and polymer solutions. Difficulties
with the increasing viscosity of concentrated
polymer solutions set limits to its applicability,
because solutions should flow
easily to form drops.
Recently, Gaube et al. 126,127 or Eliassi
et al. 128 measured water activities in aqueous
solutions of poly(ethylene glycol) and
showed that the conventional VPO method
also can be used for higher polymer concentrations
with good success.
4.4.3.1.2 Primary data reduction
Figure 4.4.15. Experimental data of the system toluene +
polystyrene, M n = 1380 g/mol, at 323.15K, isopiestic vapor
pressure/sorption measurement (full circles), VPO at
higher concentrations (gray circles), data from authors
own work.
Equation [4.4.7] is the starting relation for
data from VLE-measurements. Two relations
are necessary to obtain the solvent activity
a 1: one for the fugacity coefficient of
the solvent vapor and one for the standard
state fugacity of the liquid solvent. In principle,
every kind of equation of state can be