Scattering by non-ideal solutions of polymers
المؤلف:
Peter Atkins، Julio de Paula
المصدر:
ATKINS PHYSICAL CHEMISTRY
الجزء والصفحة:
ص658-659
2025-12-17
60
Scattering by non-ideal solutions of polymers
The preceding discussion shows that structural properties, such as size and the weight-average molar mass of a macromolecule, can be obtained from measurements of light scattering by a sample at several angles θ relative to the direction of propagation on an incident laser beam. However, eqn 19.8 applies only to ideal solutions. In practice, even relatively dilute polymer dispersions can deviate considerably from ideality. Being so large, macromolecules displace a large quantity of solvent instead of replacing individual solvent molecules with negligible disturbance. In thermodynamic terms, the displacement and reorganization of solvent molecules implies that the entropy change is especially important when a macromolecule dissolves. Furthermore, its great bulk means that a macromolecule is unable to move freely through the solution because the molecule is excluded from the regions occupied by other solute molecules. There are also significant contributions to the Gibbs energy from the enthalpy of solution, largely because solvent–solvent interactions are more favourable than the macromolecule–solvent interactions that replace them. To take deviations from ideality into account, it is common to rewrite eqn 19.8 as
where B is an empirical constant analogous to the osmotic virial coefficient and indicative of the effect of excluded volume. For most solute–solvent systems there is a unique temperature (which is not always experimentally attainable) at which the effects leading to non-ideal behaviour cancel and the solution is virtually ideal. This temperature (the analogue of the Boyle temperature for real gases) is called the q-temperature (theta temperature). At this temperature, B is zero. As an example, for polystyrene in cyclohexane the θ-temperature is approximately 306 K, the exact value depending on the average molar mass of the polymer. A solution at its θ-temperature is called a q-solution. Because a θ-solution behaves nearly ideally, its thermodynamic and structural properties are easier to describe even though the molar concentration is not low. In molecular terms, in a theta solution the molecules are in an unperturbed condition, whereas in other solutions expansion of the coiled molecule takes place as a result of interactions with the solvent.
Fig. 19.5 Plot of the data for Example 19.3.
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