Structural Characterization of Model Gels under Preparation Conditions and at Swelling Equilibrium

We use large-scale computer simulations of star polymer gels to analyze which structural features can be assessed from scattering data of polymer networks. We separate static and dynamic contributions of the scattering intensity I(q), allowing us to determine the correlation length ξ of the corresponding polymer solution and the static correlation length Ξ of network inhomogeneities, combining several properties of the denser cross-link blobs. The dynamic contribution I_dyn is related to the correlation length ξ, incorporating parts of the form factor of the star polymer for polymer volume fractions around the overlap condition. At swelling equilibrium, the cross-link motion is confined within a volume comparable to the size of the somewhat denser cross-link blob. Since the cross-link blob size scales ∝ ξ, we measure Ξ ∝ ξ for our nearly ideal model networks. The motion of the cross-links in a harmonic confining potential implies a Gaussian shape of the static density inhomogeneities, a dependence confirmed by the static contribution to the scattering data of all samples in our study. At swelling equilibrium, dynamic scattering I_dyn(0) from thermal fluctuations is almost identical to the scattering intensity I_stat(0) from static inhomogeneities. At preparation conditions, I_stat(0)/I_dyn(0) decays with a power law following the polymer fraction of the cross-link blobs. Here, the larger volume available for cross-link motion stands out for increasing polymer volume fraction ϕ, reducing the concentration dependence of Ξ.