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 $Q_{\mathrm{eq}}\approx N_e^{3/5}$ for mean strand lengths ${\overline{N}}_s$ exceeding the melt entanglement length $N_e$. The internal structure of the network strands in the swollen state is characterized by a new exponent $\nu =0.72\mathrm{}\pm 0.02$. Our findings can be rationalized by a Flory argument for a self-similar structure of mutually interpenetrating network strands, agree partially with the classical Flory-Rehner theory, and are in contradiction to de Gennes' $c^{*}$-theorem.