Handbook of Solvents - George Wypych - ChemTech - Ventech!

160 Christian Wohlfarth
There is a broad variety of experimental equipment that is based on this procedure (see
below). This isopiestic technique is the recommended method for most polymer solutions
since it is advantageous in nearly all aspects of measurement: It covers the broadest concentration
range. Only very small amounts of polymer are needed (about 30-50 mg with the
classical quartz spring balance, about 100 μg with piezoelectric sorption detector or
microbalance techniques - see below). It is much more rapid than all other methods explained
above, because equilibrium time decreases drastically with such small amounts of
polymer and polymer solution (about 12-24 hours for the quartz spring balance, about 3-4
hours for piezoelectric or microbalance techniques). The complete isotherm can be measured
using a single loading of the apparatus. Equilibrium is easier to obtain since comparatively
small amounts of solvent have to diffuse into the bulk sample solution. Equilibrium
can better be tested by measuring sorption and desorption runs which must lead to equal results
for thermodynamic absorption equilibrium. Supercritical solvents can be investigated
if the piezoelectric detector is used (otherwise buoyancy in dense fluids may cause serious
problems). Much broader pressure and temperature ranges can be covered with relatively
simple equipment, what may again be limited by the weighing system. Isopiestic sorption
measurements can be automated and will allow also kinetic experiments. There are two disadvantages:
First, isopiestic sorption measurements below about 30 wt% polymer are subject
to increasing error because very small temperature differences (vapor pressure
changes) are connected with large changes in concentration. Second, problems may arise
with precise thermostating of both the solvent and the solution at different constant temperatures
over a longer period of time.
Because of their importance, several technical solutions will now be presented in
some detail. The classical concept is the sorption method using a quartz spring balance.
Refs. 81-90 provide some examples, where the concentration (mass) of the solution is measured
by the extension of the quartz spring according to Hook’s law (linear relationship, no
hysteresis). It was not originally developed for polymer solutions but for gas-solid adsorption
measurements by McBain. 91 The principle was introduced into the investigation of
polymer solutions by van der Waals and Hermans 84 and became popular after the work of
Bonner and Prausnitz. 85 In this method, a weighed quantity of the (non-volatile) polymer is
placed on the pan of the quartz spring balance within a measuring cell. The determination of
spring extension vs. mass has to be made in advance as a calibration procedure. Reading of
the spring extension is usually made by means of a cathetometer. The cell is sealed, evacuated
and thermostated to the measuring temperature (T 2), and the solvent is then introduced
into the measuring cell as solvent vapor. The solvent vapor is absorbed by the polymer sample
to form the polymer solution until thermodynamic equilibrium is reached. The solvent
vapor is provided from a reservoir either of pure liquid solvent thermostated at a lower temperature
(T 1) or of a reference liquid solution of known concentration/solvent partial pressure
like in the case of the isothermal distillation procedure as described above. A compact
version of such an apparatus was developed by Illig 82 and widely used within the author’s
own work (see Appendix 4.4A for the corresponding references). Figure 4.4.7a shows the
details of the equilibrium cell, which has a vacuum double-walled jacket.
The following problems have to be solved during the experiment: The equilibrium cell
has to be sealed carefully to avoid any air leakage over the complete duration of the measurements
(to measure one isotherm lasts about 14 days). Specially developed thin Teflon
sealing rings were preferred to grease. The polymer sample has to withstand the tempera-