Scattered intensity by a cross-linked polymer blend

Cross-linked mixtures of polystyrene and poly(vinyl methyl ether) exhibit a non-vanishing zero-angle intensity in small-angle neutron scattering experiments. A possible explanation is that fluctuations in composition in the mixture may be frozen by the presence of cross-links. Assuming this, we introduce a screening length κ by the condition that the scattered intensity should not be changed by cross-linking. We find κ² ～ C/(χ ? χ_i), where C is an elastic constant, χ and χ_i, respectively, the inverse temperature and that where cross-linking is performed. When the temperature is varied, we find three regimes. In the first one, the scattered intensity is monotonously decreasing. In the second one, it has a finite maximum. In the last one, the maximum eventually diverges.