Chemistry Reference
In-Depth Information
yield values of
M
2
1
n
and slopes that are measures of the second virial coefficient
of the polymer solution. Theories of polymer solutions can be judged by their
success in predicting nonideality. This means predictions of second virial coeffi-
cients in practice, because this is the coefficient that can be measured most accu-
rately. Note in this connection that the intercept of a straight line can usually be
determined with more accuracy than the slope. Thus, many experiments that are
accurate enough for reasonable average molecular weights do not yield reliable
virial coefficients. Many more data points are needed if the experiment is
intended to produce a reliable slope and consequent measure of the second virial
coefficient.
A number of factors influence the magnitude of the second virial coefficient.
These include the nature of the polymer and solvent, the molecular weight distri-
bution of the polymer and its mean molecular weight, concentration and tempera-
ture of the solution, and the presence or absence of branching in the polymer
chain.
The second virial coefficient decreases with increasing molecular weight of
the solute and with increased branching. Both factors tend to result in more com-
pact structures which are less swollen by solvent, and it is generally true that bet-
ter solvents result in more highly swollen macromolecules and higher virial
coefficients. The virial coefficients reflect interactions between polymer solute
molecules because such a solute excludes other molecules from the space that it
pervades. The
excluded volume
of a hypothetical rigid spherical solute is easily
calculated, since the closest distance that the center of one sphere can approach
the center of another is twice the radius of the sphere. Estimation of the excluded
volume of flexible polymeric coils is a much more formidable task, but it has
been shown that it is directly proportional to the second virial coefficient, at given
solute molecular weight.
Most polymers are more soluble in their solvents the higher the solution tem-
perature. This is reflected in a reduction of the virial coefficient as the tempera-
ture is reduced. At a sufficiently low temperature, the second virial coefficient
may actually be zero. This is the Flory theta temperature, which is defined as that
temperature at which a given polymer species of infinite molecular weight would
be insoluble at great dilution in a particular solvent. A solvent, or mixture of sol-
vents, for which such a temperature is experimentally attainable is a theta solvent
for the particular polymer.
Theta conditions are of great theoretical interest because the diameter of the
polymer chain random coil in solution is then equal to the diameter it would have
in the amorphous bulk polymer at the same temperature. The solvent neither
expands nor contracts the macromolecule, which is said to be in its “unperturbed”
state. The theta solution allows the experimenter to obtain polymer molecules
which are unperturbed by solvent but separated from each other far enough not to
be entangled. Theta solutions are not normally used for molecular weight mea-
surements, because they are on the verge of precipitation. The excluded volume
vanishes under theta conditions, along with the second virial coefficient.
