Scaling theory of star polymers and general polymer networks in bulk and semi - infinite good solvents

2014 A scaling theory of general polymer networks in bulk and semi-infinite good solvents is derived by using the equivalence between the generating function for the total number of configurations and the multispin correlation function of the classical n-component Heisenberg model in the limit n ~ 0. For general polymer networks with fixed topology G composed of f linear chains with the same length l, the total number of configurations behaves for large f as Ng(l, l, ..., l) ~ l03B3g1 03BClf. The exponent 03B3g is expressed exactly in terms of the corresponding exponents y ( f ) and 03B3s(f) of f-arm (free and center-adsorbed) star polymers. When g of the f arms of the star polymer are attached to the surface at their end points, the exponent 03B3g 03B311 ... 1 (f) is given in terms of that for f-arm star polymers y ( f ) and the exponents of linear chains as 03B311 ... 1 (f) = 03B3 (f) + v + g [03B311 03B31]. Also the exponent 03B3g for comb polymers (with g 3-functional units) is reduced to a linear combination of the exponent of 3-arm star polymers, y (3 ), and the configuration number J. Phys. France 49 (1988) 1329-1351 AOÚT 1988, : Classification Physics Abstracts 36.20 61.40K 05.20 05.50 Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:019880049080132900