ABSTRACT
Long-chain molecules in dilute solution influence a region of space large with respect to the sum of the volumes of the individual mers. This concept was expressed in terms of the pervaded volume, , in Chapter 5. When the sum of the pervaded volumes of the solute macromolecules equals the macroscopic solution volume, the solution can no longer be considered dilute. It is convenient to define a crossover concentration (
c
*) to the semidilute regime as:
. (6.1)
It will be shown that many of the properties of polymer solutions in the semidilute regime depend in a detailed way on the value of the crossover concentration,
c
*. Two polymer molecules resist overlapping because the presence of one
chain restricts the conformations available to the other chain. This entropically based intermolecular repulsion exists in addition to the segment-segment excluded volume introduced in Chapter 5. If the chains are dissolved in a “good” solvent, the mean-squared radius of gyration is increased in dilute solution due to the intramolecular excluded volume, as discussed in Section 5.2. As the concentration is increased into the semidilute regime, intermolecular repulsion must occur, and the chains are observed to contract in order to reduce intermolecular repulsive energy. It is observed experimentally that the mean-squared radius of gyration in semidilute solutions under good solvent conditions can be described by a scaling law:
V RP G= ( )4 3 2 3 2π/ /
c M
=
. (6.2)
This phenomenon is explained in detail in Section 6.3. Many properties of polymer solutions in the semidilute regime are observed to be described by power-law relationships, and the scaling symbol, ~, reflects this mathematical fact.
