Conformation of branched polymers

2014 We study the conformation of randomly branched, monodispersed polymers both in dilute and concentrated solutions in their reaction bath. We first extend the Zimm-Stockmayer mean field theory to such properties as elasticity and concentration correlations. We then take this mean field theory as a basis for a Flory approach. In a dilute solution, we recover previous results by Isaacson and Lubensky in a good solvent. In a theta solvent, the critical dimension above which the mean field approach is valid is 6. The exponent for the molecular weight dependence of the radius of gyration, R ~ N03BD, is 03BD = 7/4 (d + 1), where d is the dimension of space. In a melt the polymer chains overlap very weakly, leading to an exponent 03BD = 1/d. In all these regimes, we give scaling laws for the local properties of the chain, and we study the cross-over to linear chain behaviour when the branching fraction is reduced. Tome 42 N° 10 OCTOBRE J. Physique 42 (1981) 1359-1371 OCTOBRE 1981, PAGE 1359 Classification Physics Abstracts 05.50 61.40