Entropic Forces in the Mechanics of Solids

The molecules that comprise biological structures are joined together by chemical bonds that are relatively weak com- pared to the ionic, covalent and metallic atomic bonds of traditional engineering materials. Both the large size of these molecules and the relatively low energies of these bonds account for the softness of the resulting material structures. When immersed in water at a temperature on the order of 35 °C, a biological membrane undergo random transverse fluctuations, driven by Brownian motion of the water molecules. If not constrained in any way, a soft elastic structure will deform so that the mean elastic energy induced just balances the mean entropic energy acquired through fluctua- tion. If the elastic structure is constrained kinematically, the forces necessary to maintain such constraints are entropic forces. The estimation of such forces, as well as some of their consequences, are discussed here, mainly for the case of bio-membranes with elastic bending resistance.