The theory of polymer solutions at intermediate concentration

It is argued that polymer solutions can be classified into three broad types which may be characterized in terms of N the total number of (micro) molecules, n the number of polymer chains, l the effective length of a micromolecule, v the excluded volume per micromolecule and V the total volume. The types are: (i) dense solutions in which V/N V/n > v or (Ll) 1/2 > V/n > v according to the magnitude of v, i. e. L-1/10v-1/5l7/10 greater than 1 or less than 1, and (iii) dilute solutions in which V/n < L9/5v3/5l-3/5. The intermediate case is discussed in detail and the partial pressure of the molecules is found to be given by PV = NκT (n/N) + ½ (Nv/V) - ½π√3 (N/V) ½ (v3/2/l3). A discussion is given of the way this expression fails as one enters regions (i) and (iii).