Verification of the hyperscaling law on polymer clusters by neutron-scattering experiments

Measurements of the small-angle neutron scattering by polymer clusters near the gelation threshold have been made possible, in the bulk state, using mixtures of deuterated and hydrogenated polyurethane samples. The exponent which links the scattered intensity to the transfer vector q is predicted to be (3-{τ})Dₚ, where {τ} is the exponent which characterizes the mass distribution and Dₚ the fractal dimension of polymer clusters in the bulk state. This exponent is found to be equal to 2.00±{}0.05. Using this result and the {τ} value determined in a previous experiment on the same system, we verify the hyperscaling law and deduce Dₚ=2.50±{}0.06.