THE STRUCTURE-FUNCTION OF BRANCHED POLYMERS IN A GOOD SOLVENT - A LATTICE CALCULATION

The fourth 〈r4〉 and the sixth 〈r 6〉 moments of the average monomer-monomer separation of branched polymers is calculated in two and three dimensions in the lattice animal model. The universal ratios ζ≡〈r4〉/(Rg 2)2 and μ≡〈r6〉/(R g2)3 with Rg2 the average squared radius of gyration of the polymers are found to be ζ = 0.550 ± 0.003, μ = 0.201 ± 0.003 in two and ζ = 0.600 ± 0.005, μ = 0.254 ± 0.006 in three dimensions. They are significantly different from the Gaussian values calculated here to be ζ = 0.9204 and μ = 0.7889 in all dimensions. Using the values of ζ and μ the scaled structure function for small values of the momentum transfer can be calculated and compared to that of the Gaussian approximation. © 1990 American Institute of Physics.