Handbook of Solvents - George Wypych - ChemTech - Ventech!

188 Christian Wohlfarth
χ-function depends only on temperature and concentration, but not on molar mass, the partial
derivative of the chemical potential can be calculated by Equation [4.4.13a] to obtain
values of the χ-function. Scholte carried out experiments for solutions of polystyrene in
cyclohexane or toluene at different temperatures and in a concentration range of 0-80 wt%.
Thus, the sedimentation method is able to cover nearly the total concentration range of
a polymer solution; however, values obtained by this method were slightly higher than values
determined by other methods. Since the measurement of thermodynamic data by sedimentation
equilibrium is not very frequent in the literature this is certainly not a final
statement. A combined determination of second osmotic virial coefficients of poly(ethylene
glycol)s in methanol, water and N,N-dimethylformamide by Elias and Lys 178 using light
scattering, VPO and sedimentation equilibrium showed good agreement between all methods.
This was also confirmed in a recent investigation on poly(1-phenyl-1-propene) in toluene
by Hirao et al., 179 where second virial coefficients were determined by light scattering
and by sedimentation equilibrium over a wide range of molar mass. Some further A2 data
from sedimentation measurements can be found in the tables by Lechner et al. 9 The transformation
of the obtained second virial coefficients into solvent activities is as explained
above.
4.4.3.2.6 Cryoscopy (freezing point depression of the solvent)
In the cryoscopic method, the freezing temperature of a solution is compared with that of the
pure solvent. The polymer must be solvable in the solvent at the freezing temperature and
must not react with the solvent either chemically or physically. Difficulties may arise from
limited solubility and from the formation of solid solutions on freezing. Application of
cryoscopy to polymer solutions is not widespread in literature despite the simplicity of the
required equipment. Cryoscopy was reviewed by Glover, 34 who also discussed technical details
and problems in concern with application to polymer solutions. A detailed review on
cryometers and cryoscopic measurements for low-molar mass systems was recently made
by Doucet. 180 Cryometers are sold commercially, e.g., Knauer. Measurements of thermodynamic
data are infrequent. Applications usually determine molar masses. Accurate data require
precise temperature measurement and control as well as caution with the initiation of
the crystallization process and the subsequent establishment of equilibrium (or steady state)
conditions. High purity is required for the solvent and also for the solute.
Data reduction of cryoscopic measurements is made by applying the relation for the
freezing point depression of a binary mixture to obtain solvent activities:
1 1 R
− =
0
T T Δ H
SL SL
0
1
1 SL 1
ln a
[4.4.55]
1
where:
SL 0
T1 solid-liquid equilibrium melting temperature of the pure solvent
SL
T1 solid-liquid equilibrium melting temperature of the solvent in the polymer solution
0
Δ SLH1 molar enthalpy of fusion of the pure solvent.
Kawai 181 determined some values of the χ-function for benzene solutions of polystyrene
or poly(vinyl acetate) and aqueous solutions of poly(vinyl alcohol). In comparison
with various data from the tables given by Orwoll, 8 larger deviations with respect to other
methods have to be stated. Just recently, Hoei et al. 182 made a more sophisticated analysis of