Electrohydrodynamics and Surface Force Analysis in AFM Imaging of a Charged, Deformable Biological Membrane in a Dilute Electrolyte Solution

Abstract

Surface forces arising in atomic force microscopy (AFM) imaging of a deformable, negatively charged biological membrane in an electrolyte solution are investigated in the limit of continuous electrohydrodynamics. Specifically, we extend our previous analysis (Fan, T.-H.; Fedorov, A. G. Langmuir 2003, 19, 1347−1356) of purely hydrodynamic interactions between an AFM tip and the elastic cell membrane by accounting for electric double-layer forces under the assumptions of a dilute electrolyte solution and local electrochemical equilibrium. The solution of the problem is obtained by integrating the quasi-steady, electrically forced Stokes equation for the electrohydrodynamic field, the linearized Poisson−Boltzmann equation for the electrostatic field in the electrolyte inside and outside of the cell, and the Laplace equation for the electrostatic field within a dielectric AFM tip. Helfrich and Zhong-can's equation for an equilibrium shape of the cell membrane is employed as a quasi-steady, nonlinear boundary condition linking the stress fields on both sides of the cell membrane augmented by the local membrane incompressibility condition in order to find the local tension/compression force acting on the membrane. An integrated framework for the dynamic coupling of the membrane double-layer effects and the AFM tip−electrolyte−membrane motion is established that allows for characterizing of the local electrolyte flow field, the electrostatic field, the elastic deformation of the membrane, and the electrohydrodynamic surface force acting on the AFM tip in great detail. The results of the analysis provide information on the motion of the membrane and the surface forces induced by both an electrolyte motion and the Maxwell stresses resulting from the electric double layer for a full cycle motion of the AFM tip during noncontact, nonresonant mode imaging of a simple cell membrane.