How does flexoelectricity affect static bending and nonlinear dynamic response of nanoscale lipid bilayers?

Patched-clamped oscillating lipid membranes are used as biosensors acting based on the flexoelectric effects of large dipole moments. The variations in the flexoelectric signal from the bilayer lipid membrane can be used to sense the absorbed particles on it. In this study, a size-dependent model based on strain gradient theory is developed for an initially curved lipid bilayer attached to the inner surface of a rectangular capillary. The flexoelectricity and strain gradient viscoelastic effects are considered in this model. Furthermore, the von-Karman strain terms are used to model the deformation of the lipid bilayer more accurately. First, the density of the internal energy, kinetic energy, and external force work are obtained and then the governing equations are derived from Hamilton's principle. The static bending and dynamic response of the nanosystem are studied. In order to solve the dynamic motion equations, the multiple scale method is applied to study the size-dependent electromechanical responses of the lipid bilayer. The results show that for smaller length-scale parameters, the static deflection predicted by the model with flexoelectricity is remarkably higher than the deflection anticipated by the model without the flexoelectricity. However, the deflections of both models approach each other with increasing the length-scale parameter. In addition, for the dynamic response, the flexoelectricity increases the resonance frequencies of lipid membranes up to 4-9 times in comparison to the model without flexoelectric effects. Moreover, the flexoelectricity reduces the dynamic response amplitudes, drastically.