Handbook of Solvents - George Wypych - ChemTech - Ventech!

186 Christian Wohlfarth
ν 2,spez
∞
specific volume of the polymer (more exact, ν2,spez, the partial specific volume at
infinite dilution)
According to the scattering theory of polydisperse polymers, please see, for example,
in the book written by Strobl, 147 the molar mass of the polymer, M 2, is equal to the mass average,
M w, of polydisperse polymers. The contrast factor for neutron scattering takes into
account for the difference in scattering power of solvent molecules and polymer segments.
Again, Zimm plots can be constructed, as was explained above, for light scattering measurements
to take into account for angular and concentration dependence - for a demonstration
see Vennemann et al. 173
The transformation of the obtained second virial coefficients into solvent activities is
as explained above, Equations [4.4.34 and 4.4.35]. A recent example for the determination
of second virial coefficients from SANS is the investigation of aggregation phenomenon in
associating polymer solutions by Pedley et al., 174 where sodium sulfonated polystyrene
ionomers in deuterated xylene were considered. Enthalpic and entropic contributions to A 2
were calculated (as in the paper by Wolf and Adams 149 for A 2 from light scattering) and an
enthalpy of aggregation was estimated from these data. A high-pressure investigation on
aqueous poly(ethylene oxide) solutions was made by Vennemann et al. 173 who measured
second virial coefficients by a SANS experiment for pressures up to 200 MPa and combined
these data with PVT-measurements to obtain also excess and partial excess volumes and
gained information about the pressure dependence of the chemical potential.
4.4.3.2.5 Ultracentrifuge
The analytical ultracentrifuge is a powerful tool for polymer characterization. Technical details
of ultracentrifugation will not be considered here - please see Refs. 26,35-37 for more information.
In a typical ultracentrifuge experiment, the polymer solution is put in a sample
tube and rotated at high speed. Thermodynamic data can be obtained either from the sedimentation
velocity (sedimentation coefficient) or from the sedimentation-diffusion equilibrium
since the centrifugal forces are balanced by the activity gradient. The concentration
gradient is conventionally measured via the refractive index gradient along the axis of the
tube using Schlieren photography or various optics.
The sedimentation coefficient is defined as the sedimentation velocity in a unit force
field:
dh / dt
s =
ω h
2
[4.4.51]
where:
s sedimentation coefficient
h distance from the center of rotation
t time
ω angular velocity
For a given polymer-solvent system, the sedimentation coefficient is dependent on
temperature, pressure and polymer concentration. For obtaining thermodynamic data from
sedimentation coefficients, one additionally has to measure the diffusion coefficient. This
can be made with an ultracentrifuge in special diffusion cells 35 or with dynamic light
scattering 32 based on the theory of Pecora. 175 Nearly all diffusion coefficients have been
measured by this method since it became available in 1970. The determination of sedimen-