Handbook of Solvents - George Wypych - ChemTech - Ventech!

4.4 Measurement of solvent activity 193
05 . 05 .
2
( r ) and ( T ) ( r )
crit crit crit
ϕ = 1/ 1+ χ = 05 . 1+ 1/
2
[4.4.61]
where:
crit
ϕ 2 volume fraction of the polymer at the critical point
T crit
critical temperature
This means that the critical concentration is shifted to lower values with increasing
segment number (molar mass) of the polymer and becomes zero for infinite molar mass.
Equation [4.4.61] explains also why the χ(T)-function becomes 0.5 for infinite molar mass.
The critical temperature of these conditions is then called theta-temperature. Solvent activities
can be calculated from critical χ(T)-function data via Equation [4.4.13]. However,
results are in most cases of approximate quality only.
4.4.3.2.8 Swelling equilibrium
Polymers, crosslinked sufficiently to form a three-dimensional network, can absorb solvent
up to a large extent. The maximum possible solvent concentration, the degree of swelling,
are a function of solvent activity. If solvent is present in excess, this swelling equilibrium is
reached when the chemical potential of the pure solvent outside the network is equal to the
chemical potential inside the swollen sample. This means, there must be an additional contribution
to the Gibbs free energy of mixing (as is the case with the osmotic equilibrium) besides
the common terms caused by mixing the (virtually) infinite-molar-mass polymer and
the solvent. This additional part follows from the elastic deformation of the network. The
different aspects of chemical and physical networks will not be discussed here, for some details
please see Refs. 201-205 The following text is restricted to the aspect of solvent activities
only.
One method to obtain solvent activities in swollen polymer networks in equilibrium is
to apply vapor pressure measurements. This is discussed in detail above in the Subchapter
4.4.3.1.1 and most methods can be used also for network systems, especially all sorption
methods, and need no further explanation. The VPO-technique can be applied for this purpose,
e.g., Arndt. 206,207 IGC-measurements are possible, too, if one realizes a definitely
crosslinked polymer in the column, e.g., Refs. 208-210
Besides vapor sorption/pressure measurements, definite swelling and/or deswelling
experiments lead to information on solvent activities. Swelling experiments work with pure
solvents, deswelling experiments use dilute solutions of macromolecules (which must not
diffuse into or adsorb at the surface of the network) and allow measurements in dependence
on concentration. Deswelling experiments can be made in dialysis cells to prevent diffusion
into the network. The determination of the equilibrium swelling/deswelling concentration
can be made by weighing, but, in most cases, by measuring the swelling degree. Some
methods for measuring the swelling degree are: measuring the buoyancy difference of the
sample in two different liquids of known density, e.g. Rijke and Prins, 211 measuring the volume
change by cathetometer, e.g., Schwarz et al., 212 measuring the volume change by electrical
(inductive) measurements, e.g., Teitelbaum and Garwin. 213
The swelling degree can be defined as the ratio of the masses (mass based degree) or of
the volumes (volume based degree) of the swollen to the dry polymer network sample:
( )
Q = 1+ m / m or Q = 1+ ν / ν = 1+ Q −1
ρ / ρ [4.4.62]
m 1 N v 1 n m n 1