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Molecular dynamics simulations are used in order to study the self-assembly process and the physical properties of flexible membranes composed of amphiphilic molecules. On molecular scales, these membranes are observed to be rather mobile and to have rough surfaces arising from molecular protrusions, ie, from the relative displacements of individual molecules. On length scales that are only somewhat larger than the membrane thickness, on the other hand, the membranes are found to undergo smooth bending undulations. In this way, our study provides the first explicit connection between computer simulations with molecular resolution and elastic membrane models based on differential geometry.