Potential dependence of the capacitance of ionizable bilayers

The effect of the applied potential across a biomimetic model membrane, Δφ, on the extent of dissociation of surface bound ionizable groups has been examined theoretically using a formalism that shares common features with that recently introduced by White and coworkers (Langmuir 9 (1993) 1) to account for the occurrence of peaks in the cyclic voltammetry of self-assembled monolayers rigidly attached to an electrode surface, bearing the same type of ionizable groups facing the electrolyte. Numerical solutions of the governing coupled, highly non-linear system of equations yielded for reasonable membrane parameters, and under conditions of physiological relevance, linear changes in the extent of ionization as a function of Δφ, about Δφ = 0, of ca. 0.07 units/V. Also considered in this work was a more general situation in which the contributions to the total interfacial capacity, C_T, due to the diffuse double layers, C_S^j, and to the fixed charges C^j(f_j) on each of the sides of the membrane-like assembly denoted by 'j', were comparable in magnitude to the potential independent capacity of the intervening hydrophobic layer, i.e. low-electrolyte concentration. In such case, plots of C_T versus Δφ displayed a global minimum at Δφ = 0 and two local maxima at values of Δφ slightly negative and positive to the maxima observed in the corresponding C^j(f_j) versus Δφ plots. Implications of the results obtained to excitable bilayer membranes are briefly discussed.