Obtaining effective pair potentials in colloidal monolayers using a thermodynamically consistent inversion scheme.

Area of Science:

• Colloidal science
• Soft matter physics
• Statistical mechanics

Background:

• Colloidal monolayer structure and stability depend on particle interactions.
• Accurate determination of the pair interaction potential u(r) is crucial.
• Extracting u(r) from experimental data is challenging.

Purpose of the Study:

• Develop a novel method to extract the effective pair interaction potential u(r) from the 2D radial distribution function g(r) of colloidal monolayers.
• Evaluate the accuracy of the proposed method against existing techniques and simulation data.
• Assess the robustness of the method in the presence of experimental noise.

Main Methods:

• Utilized the Ornstein-Zernike relation with the HMSA (hydrodynamic approximation) closure.
• Determined the HMSA fitting parameter via thermodynamic consistency (virial and compressibility equations of state).
• Compared the HMSA scheme with a 2D predictor-corrector (HDPC) scheme and conventional HNC and Percus-Yevick (PY) methods.

Main Results:

• The HMSA and HDPC schemes demonstrated superior accuracy compared to HNC and PY, especially at high densities.
• HDPC is accurate for hard-core potentials, while HMSA excels for soft-core potentials at high density.
• Both HMSA and HDPC schemes successfully extracted interaction potentials from noisy g(r) data, preserving key features.

Conclusions:

• The HMSA and HDPC schemes offer accurate and convenient methods for extracting interaction potentials u(r) from experimental g(r) data for 2D colloidal monolayers.
• These complementary methods are robust to experimental noise, facilitating the study of colloidal systems.
• The findings advance the understanding and manipulation of colloidal structures.