Simple transform methods of a force curve obtained by surface force apparatus to the density distribution of a liquid near a surface

We propose two simple methods that transform a force curve obtained by a surface force apparatus (SFA) into a density distribution of a liquid near a surface of the SFA probe. The transform methods are derived based on the statistical mechanics of simple liquids, where the liquid is an ensemble of small spheres. The solvent species is limited to only one component and two-body potential between the solvent spheres is arbitrary. However, two-body potential between the SFA probe and the solvent is restricted to rigid potential (i.e., the transform methods are derived within the restriction of the rigid potential). In addition, Kirkwood and linear superposition approximations are applied in order to derive the transform methods. The transform methods are simply tested in both hard-sphere fluid and Lennard-Jones (LJ) fluid with hard core potential. The tests are computationally practiced using a three-dimensional integral equation theory. It is found that the transform method with Kirkwood superposition approximation (transform method 1) generally reproduces the more precise solvation structure than that with linear superposition approximation (transform method 2). In the test of the hard sphere solvent, it is found that the reproducibility becomes better as the number density of the solvent is lower. Furthermore, it is found in the test of the LJ fluid that the reproducibility becomes better as the two-body potential between the SFA probe and the solvent approaches rigid potential. This is because, the transform methods are derived within the model of the rigid potential. It is verified that the transform methods are useful for obtaining of a rough image of the solvation structure. (However, if evaporation or solidification, a phase transition in a local space sandwiched between the two surfaces, occurs while the experiment, the transform methods should not be used.)