Van Der Waals Interaction Energy Between Two Spherical Bodies Calculator

Van Der Waals Interaction Energy Formula:

\[ E = -\frac{A}{6} \left( \frac{2R_1R_2}{z^2 - (R_1 + R_2)^2} + \frac{2R_1R_2}{z^2 - (R_1 - R_2)^2} + \ln\left( \frac{z^2 - (R_1 + R_2)^2}{z^2 - (R_1 - R_2)^2} \right) \right) \]

Hamaker Coefficient (A):

Radius of Spherical Body 1 (R1):

Radius of Spherical Body 2 (R2):

Center-to-center Distance (z):

Van Der Waals Interaction Energy (E):

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1. What is Van Der Waals Interaction Energy?

Van Der Waals interaction energy includes attraction and repulsions between atoms, molecules, and surfaces, as well as other intermolecular forces. For two spherical bodies, this energy is calculated using a specific formula that considers their radii, distance, and material properties.

2. How Does the Calculator Work?

The calculator uses the Van Der Waals interaction energy formula:

\[ E = -\frac{A}{6} \left( \frac{2R_1R_2}{z^2 - (R_1 + R_2)^2} + \frac{2R_1R_2}{z^2 - (R_1 - R_2)^2} + \ln\left( \frac{z^2 - (R_1 + R_2)^2}{z^2 - (R_1 - R_2)^2} \right) \right) \]

Where:

\( E \) — Van Der Waals interaction energy (J)
\( A \) — Hamaker coefficient (J)
\( R_1 \) — Radius of Spherical Body 1 (m)
\( R_2 \) — Radius of Spherical Body 2 (m)
\( z \) — Center-to-center distance (m)
\( \ln \) — Natural logarithm function

Explanation: The equation calculates the interaction energy between two spherical bodies based on their physical properties and separation distance.

3. Importance of Van Der Waals Calculation

Details: Accurate calculation of Van Der Waals forces is crucial for understanding colloidal stability, adhesion phenomena, surface interactions, and nanomaterial behavior in various scientific and engineering applications.

4. Using the Calculator

Tips: Enter all values in appropriate SI units. Hamaker coefficient and radii must be positive values. The center-to-center distance must be greater than the sum of the radii for physically meaningful results.

5. Frequently Asked Questions (FAQ)

Q1: What is the Hamaker coefficient?
A: The Hamaker coefficient is a material-specific constant that characterizes the strength of Van Der Waals interactions between two bodies.

Q2: What are typical values for the Hamaker coefficient?
A: Hamaker coefficients typically range from 0.4 × 10⁻²⁰ J to 4 × 10⁻¹⁹ J for most materials in vacuum or air.

Q3: When is this formula applicable?
A: This formula is valid for two spherical bodies and assumes that the materials are isotropic and the interactions are non-retarded.

Q4: What are the limitations of this calculation?
A: The formula doesn't account for retarded Van Der Waals forces at larger distances, surface roughness, or other intermolecular forces beyond Van Der Waals interactions.

Q5: How does distance affect the interaction energy?
A: Van Der Waals interaction energy decreases rapidly with increasing distance between the two spherical bodies, typically following an inverse power law.