Distance Between Surfaces Given Potential Energy In Limit Of Close-Approach Calculator

Formula Used:

\[ r = \frac{-A \times R1 \times R2}{(R1 + R2) \times 6 \times PE} \]

Hamaker Coefficient (A):

Joule

Radius of Spherical Body 1 (R1):

Meter

Radius of Spherical Body 2 (R2):

Meter

Potential Energy (PE):

Joule

Distance Between Surfaces (r):

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1. What is Distance Between Surfaces Given Potential Energy?

This calculator determines the distance between surfaces of two spherical bodies based on their Van der Waals interaction potential energy in the limit of close approach. It uses the Hamaker coefficient and the radii of the spherical bodies to calculate the separation distance.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r = \frac{-A \times R1 \times R2}{(R1 + R2) \times 6 \times PE} \]

Where:

\( r \) — Distance between surfaces (Meter)
\( A \) — Hamaker coefficient (Joule)
\( R1 \) — Radius of Spherical Body 1 (Meter)
\( R2 \) — Radius of Spherical Body 2 (Meter)
\( PE \) — Potential Energy (Joule)

Explanation: This formula calculates the separation distance between two spherical surfaces based on their Van der Waals interaction energy in the close-approach limit.

3. Importance of Distance Calculation

Details: Calculating the distance between surfaces is crucial for understanding colloidal stability, surface interactions, adhesion forces, and various phenomena in nanotechnology and materials science where Van der Waals forces play a significant role.

4. Using the Calculator

Tips: Enter the Hamaker coefficient in Joules, both radii in meters, and potential energy in Joules. All values must be positive and non-zero for accurate calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the Hamaker coefficient?
A: The Hamaker coefficient is a constant that describes the magnitude of Van der Waals forces between two bodies. It depends on the material properties of the interacting bodies and the intervening medium.

Q2: When is this formula applicable?
A: This formula is specifically applicable in the limit of close approach between two spherical bodies where Van der Waals interactions dominate.

Q3: What are typical values for the Hamaker coefficient?
A: Hamaker coefficients typically range from 10⁻²¹ to 10⁻¹⁹ Joules for most materials interacting across vacuum or air.

Q4: Can this formula be used for non-spherical bodies?
A: No, this specific formula is derived for spherical bodies. Different geometrical relationships apply for other shapes like plates or cylinders.

Q5: What does a negative distance result indicate?
A: A negative distance typically indicates an attractive interaction where the surfaces would theoretically overlap, which may suggest the need for additional repulsive forces in the system to maintain separation.