Hamaker Coefficient Calculator

Hamaker Coefficient Formula:

\[ A = \pi^2 \times C \times \rho_1 \times \rho_2 \]

Hamaker Coefficient (A):

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1. What is the Hamaker Coefficient?

The Hamaker Coefficient (A) is a fundamental parameter in colloid and surface science that quantifies the strength of Van der Waals interactions between two particles or surfaces. It represents the magnitude of attraction between macroscopic bodies due to electromagnetic fluctuations.

2. How Does the Calculator Work?

The calculator uses the Hamaker Coefficient formula:

\[ A = \pi^2 \times C \times \rho_1 \times \rho_2 \]

Where:

\( A \) — Hamaker Coefficient (Joules)
\( \pi \) — Archimedes' constant (≈ 3.14159)
\( C \) — Coefficient of particle–particle pair interaction
\( \rho_1 \) — Number density of particle 1 (1/m³)
\( \rho_2 \) — Number density of particle 2 (1/m³)

Explanation: The formula calculates the macroscopic Hamaker constant from microscopic pair interaction parameters and particle number densities.

3. Importance of Hamaker Coefficient Calculation

Details: The Hamaker coefficient is crucial for understanding colloidal stability, adhesion forces, surface tension, and various phenomena in nanotechnology, biophysics, and materials science. It helps predict whether particles will aggregate or remain dispersed.

4. Using the Calculator

Tips: Enter the coefficient of particle-particle pair interaction and both number densities. All values must be positive numbers. Number densities represent the concentration of particles per cubic meter.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for Hamaker coefficients?
A: Hamaker coefficients typically range from 0.4 × 10⁻²⁰ J to 4 × 10⁻¹⁹ J for most materials in vacuum or air, with lower values in liquid media.

Q2: How does the Hamaker coefficient affect colloidal stability?
A: Higher Hamaker coefficients indicate stronger Van der Waals attraction, which can lead to particle aggregation and reduced colloidal stability.

Q3: Can this formula be used for different material combinations?
A: Yes, the formula is general and can be applied to various material pairs, though the interaction coefficient C must be appropriate for the specific materials.

Q4: What are the limitations of this approach?
A: This microscopic approach assumes pairwise additivity of interactions and may not account for many-body effects or retardation effects at larger distances.

Q5: How is the Hamaker coefficient measured experimentally?
A: Experimental methods include surface force apparatus measurements, atomic force microscopy, and analysis of colloidal stability data.