Flexoelectricity and the Entropic Force between Fluctuating Fluid Membranes



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Biological membranes undergo noticeable thermal fluctuations at physiological temperatures. When two membranes approach each other, they hinder the out of plane fluctuations of the other and thus this hindrance leads to an entropic repulsive force between membranes which, in an interplay with attractive and repulsive forces due to other sources, impact a range of biological functions: cell adhesion, membrane fusion, self-assembly, binding-unbinding transition among others. This topic has attracted extensive attention in the literature spanning nearly five decades. In this work, we take cognizance of the fact that biological membranes are not purely mechanical entities and, due to the phenomenon of flexoelectricity, exhibit a coupling between deformation and electric polarization. The ensuing coupled mechanics-electrostatics-statistical mechanics problem is analytically intractable. We use a variational perturbation method to analyze, in closed-form, the contribution of flexoelectricity to the entropic force between two fluctuating membranes and discuss its possible physical implications. We find that flexoelectricity leads to a correction that switches from an enhanced \emph{attraction} at close membrane separations and an enhanced \emph{repulsion} when the membranes are further apart.



Entropic pressure, Steric pressure, Flexoelectricity, Biological membranes