The disjoining pressure (P) versus membrane separation (d_{\mathrm{w}}) in a lamellar structure of DPPC (1,2-dipalmitoyl-sn-glycero-3phosphocholine) bilayers in the gel state in a (30 \mathrm{~m} M \mathrm{CaCl}{2}) solution was analyzed according to a modified Poisson-Boltzmann equation. The observed (P-d{\mathrm{w}}) curve could not be described by a single association constant, but a linear relationship was obtained from the (P-d_{\mathrm{w}}) curve between (\log {10} K) (where (K) is the association constant of (\mathrm{Ca}^{2+}) ion to the DPPC bilayer surface) and the electric field (E{\mathrm{b}}) at the membrane surface. As a result, the binding energy (\Delta U) lies on a straight line in the (\Delta U-E_{\mathrm{b}}) plane, which may be written as (\Delta U=\alpha_{0}+\alpha_{1} \cdot E_{\mathrm{b}}). This linearity can be explained by the electrostatic cation-dipole interaction between bound (\mathrm{Ca}^{2+}) ion and the (\mathrm{P}^{-}-\mathrm{N}^{+})dipole of the polar headgroup of the membrane surface. Two models were formulated for the behavior of the large permanent (\mathrm{P}^{-}-\mathrm{N}^{+})dipole (19 D): one is a continuous change model (CCM) allowing for continuous conformational change and the other is a discrete change model (DCM). In CCM, the (\mathrm{P}^{-}-\mathrm{N}^{+})dipole is trapped in a harmonically approximated potential with parameter (A). The slope (\alpha_{1}) was calculated for both models to investigate whether these models can express the required change of ion affinity. The derived values of (\alpha_{1}) (CCM) and (\alpha_{1}) (DCM) from the models of CCM and DCM, respectively, have the same numerical magnitude in the gel state as (\alpha_{1}\left(\boldsymbol{P}-\boldsymbol{d}{\mathrm{w}}\right)) obtained by analysis of the (P-d{\mathrm{w}}) curve. This (E_{\mathrm{b}}) dependence of (K) may vanish in the liquid crystalline state, especially in the continuous change model in relation to the dielectric constant (D_{1}) of water in the headgroup region. (1994 Academic Press. Inc.