The theory of polymer solutions at intermediate concentration

Abstract

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, (ii) intermediate concentrations in which L 9/5 v 3/5 l -3/5 > V/n > v or ( Ll ) 1/2 > V/n > v according to the magnitude of v, i.e. L -1/10 v -1/5 l 7/10 greater than 1 or less than 1, and (iii) dilute solutions in which V/n < L 9/5 v 3/5 l -3/5 . The intermediate case is discussed in detail and the partial pressure of the molecules is found to be given by PV = N κ T {( n / N ) + ½( Nv / V ) - ½π√3( N / V ) ½ ( v 3/2 / l 3 )}. A discussion is given of the way this expression fails as one enters regions (i) and (iii).