摘要利用原子力显微镜研究生物膜力学性质，已经成为研究生物膜稳定性的重要技术。通常，原子力显微镜探针和磷脂双层膜相互作用力谱曲线包括非线性部分和线性部分，其中线性部分的物理机制仍不完全清楚。将磷脂双层膜看作弹性半空间，基于相互作用原理，系统地研究了原子力显微镜探针与磷脂双层膜相互作用过程，理论结果包含了能够表征磷脂双层膜稳定性的重要参数：杨氏模量和泊松系数，以及原子力显微镜探针尖端半径。不仅合理地揭示了H. J. Bütt的实验结果曲线中线性部分的物理机制，还指出，通过增加离子浓度，磷脂双层膜的杨氏模量增大和泊松系数减小，从而导致原子力显微镜探针与磷脂双层膜之间的相互作用力随着离子浓度增加而增加。
Abstract：To determine the mechanical properties of lipid bilayers at nanoscale by atomic force microscopy has become an important technique for investigating the stability of lipid bilayers. Generally, the force spectroscopy involves the interaction between the atomic force microscopy and lipid bilayers, which consists of a linear part and a nonlinear part. So far, the mechanism about the linear part is not totally clear. Taking the lipid bilayers as a half elastic space, the interaction of the atomic force microscopy with the lipid bilayers is analyzed systematically based on the reciprocal theorem. The theoretical results contain Young's module and Poisson's ratios, as important parameters for lipid bilayers, which are related to the ion concentration of solution. Young's module and Poisson's ratios increase and decrease, respectively, with the increase of the ion concentration of the solution. So the theoretical results not only give a reasonable explanation of the linear part of the experimental results obtained by H. J. Bütt, but also indicate how the ion concentration affects the stability of lipid bilayers. The radius of atomic force microscopy tip enters also the theoretical consideration with its square root as a parameter, which reasonably explains the increase of the force between the atomic force microscopy and lipid bilayers with the increase of the radius of atomic force microscopy tip in H. J. Bütt's experimental results.