Self-similar chain conformations in polymer gels

We use molecular dynamics simulations to study the swelling of randomly end-cross-linked polymer networks in good solvent conditions. We find that the equilibrium degree of swelling saturates at Q_eq = N_e**(3/5) for mean strand lengths N_s exceeding the melt entanglement length N_e. The internal structure of the network strands in the swollen state is characterized by a new exponent nu=0.72. Our findings are in contradiction to de Gennes' c*-theorem, which predicts Q_eq proportional N_s**(4/5) and nu=0.588. We present a simple Flory argument for a self-similar structure of mutually interpenetrating network strands, which yields nu=7/10 and otherwise recovers the classical Flory-Rehner theory. In particular, Q_eq = N_e**(3/5), if N_e is used as effective strand length.