  Biomembranes are thin capacitors with the unique feature of displaying phase
transitions in a physiologically relevant regime. We investigate the voltage
and lateral pressure dependence of their capacitance close to their chain
melting transition. Since the gel and the fluid membrane have different area
and thickness, the capacitance of the two membrane phases is different. In the
presence of external fields, charges exert forces that can influence the state
of the membrane, thereby influencing the transition temperature. This
phenomenon is called electrostriction. We show that this effect allows us to
introduce a capacitive susceptibility that assumes a maximum in the melting
transition with an associated excess charge. As a consequence, there exist
voltage regimes where a small change in voltage can lead to a large uptake of
charge and a large capacitive current. Furthermore, we consider
electromechanical behavior such as pressure-induced changes in capacitance, and
the application of such concepts in biology.
