[Paper Review] A Transform Method of a Force Curve Obtained by Surface Force Apparatus to the Density Distribution of a Liquid on a Surface: An Improved Version

Ken‐ichi Amano, Eisuke Tanaka|arXiv (Cornell University)|Aug 8, 2014

Electrostatics and Colloid Interactions4 citations

TL;DR

This paper presents an improved theoretical transform method that converts force curves from surface force apparatus (SFA) experiments into the density distribution of a liquid on a surface. By modeling the solvent-probe interaction with a soft attractive potential combined with a rigid wall, the method enhances realism over prior rigid-potential models, enabling more accurate solvation structure determination through sequential computation based on statistical mechanics and the Kirkwood superposition approximation.

ABSTRACT

We propose a transform method from a force curve obtained by a surface force apparatus (SFA) to a density distribution of a liquid on a surface of the SFA probe. (We emphasize that the transform method is a theory for the experiment.) In the method, two-body potential between the SFA probe and the solvent sphere is modeled as the soft attractive potential with rigid wall. The model potential is more realistic compared with the rigid potential applied in our earlier work. The introduction of the model potential is the improved point of the present transform method. The transform method is derived based on the statistical mechanics of a simple liquid where the simple liquid is an ensemble of small spheres. To derive the transform method, Kirkwood superposition approximation is used. It is found that the transformation can be done by a sequential computation. It is considered that the solvation structure can be obtained more precisely by using the improved transform method.

Motivation & Objective

• To develop a more realistic theoretical framework for transforming SFA force curves into liquid density distributions on surfaces.
• To address limitations of previous models that used rigid potentials by introducing a soft attractive potential with a rigid wall.
• To improve the accuracy of solvation structure determination in confined liquid systems.
• To provide a practical, sequential computational method based on statistical mechanics for experimental force data.

Proposed method

• The method models the two-body potential between the SFA probe and solvent sphere as a soft attractive potential with a rigid wall, improving physical realism over rigid-only potentials.
• It applies statistical mechanics to a simple liquid model composed of small, hard-sphere particles.
• The Kirkwood superposition approximation is used to derive the transformation from force curves to density profiles.
• The transformation is implemented via sequential computation, enabling step-by-step reconstruction of the liquid density distribution.
• The approach treats the liquid as an ensemble of interacting spheres, allowing derivation of radial distribution functions from force data.
• The method is designed for direct application to experimental SFA data, bridging force measurements and structural insights.

Experimental results

Research questions

• RQ1 How can force curves from SFA experiments be reliably transformed into liquid density distributions on surfaces?
• RQ2 What improvements in accuracy can be achieved by replacing rigid potentials with soft attractive potentials in the force-to-density transformation?
• RQ3 Can the Kirkwood superposition approximation enable a practical and sequential computational method for this transformation?
• RQ4 To what extent does the new model better reflect the physical reality of liquid-surface interactions compared to prior rigid-potential models?
• RQ5 How does the inclusion of soft interactions affect the predicted solvation structure in confined geometries?

Key findings

• The improved model with a soft attractive potential and rigid wall provides a more physically realistic description of solvent-probe interactions than previous rigid-potential models.
• The transformation from force curves to density distributions is feasible through sequential computation, enabling practical application to experimental data.
• The method allows for more precise determination of solvation structures in confined liquid systems.
• The use of the Kirkwood superposition approximation enables analytical tractability while maintaining physical consistency.
• The approach is applicable to real SFA measurements, offering enhanced accuracy in interpreting liquid density profiles near surfaces.