A New "Quasi-Dynamic" Method for Determining the Hamaker Constant of Solids Using an Atomic Force Microscope

Area of Science:

• Surface Science and Nanotechnology
• Materials Science
• Physical Chemistry

Background:

• Estimating the Hamaker constant (A) is crucial for understanding van der Waals forces in materials.
• Previous quasi-static methods using atomic force microscopy (AFM) are limited by surface roughness, deformation, and dynamic effects.
• The 'jump-into-contact' method, while common, fails at finite approach speeds due to dynamic tip-surface interactions.

Purpose of the Study:

• To develop a novel, more accurate method for determining the Hamaker constant (A) of solids using AFM.
• To overcome the limitations of existing quasi-static methods by accounting for dynamic AFM tip motion.
• To provide guidelines for experimental implementation, ensuring reliable Hamaker constant measurements.

Main Methods:

• Analysis and extension of the quasi-static 'jump-into-contact' method for Hamaker constant determination.
• Development of a dynamic AFM tip motion model to identify limitations of quasi-static approaches.
• Proposal of a 'quasi-dynamic' method using the contact deflection point (d_c) and a double extrapolation procedure for accurate A estimation.

Main Results:

• The quasi-static model fails to represent dynamic tip behavior at close tip-surface separations.
• The new quasi-dynamic method accurately estimates the apparent Hamaker constant (A_app) by using d_c.
• A dimensionless parameter τ was introduced, showing that with appropriate cantilever selection and slow approach speeds, A_app can be within ~3% of the true Hamaker constant, often eliminating the need for extrapolation.

Conclusions:

• The quasi-dynamic method provides a reliable and accurate approach for measuring the Hamaker constant using AFM.
• Experimental validation confirmed excellent agreement with established methods for amorphous silica, polystyrene, and α-Al₂O₃.
• The introduced parameter τ facilitates practical experimental design for precise Hamaker constant determination.