Molecular dynamics investigation of percolating membranes

Thermalized tethered membranes are known to have a flat phase, but random perforations may lead to a transition to a crumpled state. This situation arises both in the study of graphene-like materials and in kinetoplast DNA networks that have had minicircles removed by enzymes. Here, we use molecular dynamics simulations to explore the equilibrium properties of randomly perforated tethered membranes at their percolation threshold. We examine the equilibrium radius of gyration and asphericity as a function of molecular weight and compare it to a generalized Flory theory based on the spectral dimension of percolation clusters. While percolation clusters are predicted to have a scaling exponent of 1/2, in between linear polymers and crumpled sheets, our results indicate that their behavior is more sheet-like than polymer-like, consistent with earlier results. We also examine the loss of global surface normal as the degree of perforation increases from pristine sheets towards the percolation threshold.