Regions of the Polymer-Solvent Phase Diagram

A polymer dissolves in two stages. First, solvent molecules diffuse into the polymer, swelling it to a gel state. Then the gel gradually disintegrates, the molecules diffusing into the solvent-rich regions. In this discussion, linear amorphous polymers are assumed. Cross-linked polymers may reach the gel state, but they do not dissolve. 

Notation cp = volume fraction, = correlation length, p= C./6, v= excluded volume parameter, 1 - 2x, N= number of bonds per chain, x= Flory-Huggins polymer-solvent interaction parameter, Vc = cross-over from swollen to ideal. Subscripts cr = critical, / = ideal, d = dilute, s = semi-dilute, m = marginal regime, c = concentrated regime, ov= cross-over from dilute to semi-dilute, cp = cross-over from concentrated to phase separated, sm = cross-over from semi-dilute to marginal, me = cross-over from marginal to concentrated. 

CONCENTFWED SOLUTIONS, PHASE SEPAFWION BEHAVIOR, AND DIFFUSION 

Scaling concepts in polymer physics were brought to their modem state of importance by de Gennes (12). They consist of a series of proportionalities, showing the algebraic relationships between many quantities, particularly between macroscopic and microscopic variables, molecular dimensions, and thermodynamics see Appendix 4.1. 

Another quantity of interest in semidilute solutions is called the blob. It contains a number of mers on the same chain defined by the mesh volume inside of which excluded volume effects are operative. Some texts define the blob as the number of mers between adjacent entanglements, distance s apart. These blobs are large enough to be self-similar to the whole polymer chain coiling characteristics they are coils within a coU. The concept of the blob has been important in theoretical calculations. With increasing concentration, the blobs become smaller, becoming equal to that of an individual mer in polymer melts (no sovent). 

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