Branched Polymers. III. Dimensions of Chains with Small Excluded Volume

Mean-square radii 〈s2〉 for various branched molecules are calculated taking into account the initial effect of segment excluded volume β. Explicit expressions are given for the coefficient of the linear term in the series development of 〈s2〉 in powers of z=(3/2πb2)32n12β, for certain idealized regular star and regular comb structures containing n segments, each of length b. Numerical values of the coefficient, derived primarily through computer calculations, are tabulated as functions of pertinent structural parameters. It is found that at given molecular weight the coil dimensions of star molecules with excluded volume are initially augmented by increase in the number of branches; for comb structures the relationship of size to number of branches and branch-to-backbone length ratio is more complex. For both classes of branched molecules the theoretical quantities evaluated find direct application in analyses of dilute solution data obtained on polymer—solvent systems.