Hamaker Coefficient using Van der Waals Interaction Energy Calculator

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Van der Waals Force

Berthelot and Modified Berthelot Model of Real Gas

Clausius Model of Real Gas

Peng Robinson Model of Real Gas

Redlich Kwong Model of Real Gas

Saturation Vapour Pressure

Specific Heat Capacity

Wohl Model of Real Gas

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Hamaker Coefficient

Number Density

✖Van der Waals interaction energy include attraction and repulsions between atoms, molecules, and surfaces, as well as other intermolecular forces.ⓘ Van der Waals interaction energy [U_VWaals]			+10% -10%
✖Radius of Spherical Body 1 represented as R1.ⓘ Radius of Spherical Body 1 [R₁]			+10% -10%
✖Radius of Spherical Body 2 represented as R1.ⓘ Radius of Spherical Body 2 [R₂]			+10% -10%
✖Center-to-center Distance is a concept for distances, also called on-center spacing, z = R1 + R2 + r.ⓘ Center-to-center Distance [z]			+10% -10%

✖Hamaker coefficient A can be defined for a Van der Waals body–body interaction.ⓘ Hamaker Coefficient using Van der Waals Interaction Energy [A]

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Formula

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Hamaker Coefficient using Van der Waals Interaction Energy

Formula

`"A" = (-"U"_{"VWaals"}*6)/(((2*"R"_{"1"}*"R"_{"2"})/(("z"^2)-(("R"_{"1"}+"R"_{"2"})^2)))+((2*"R"_{"1"}*"R"_{"2"})/(("z"^2)-(("R"_{"1"}-"R"_{"2"})^2)))+ln((("z"^2)-(("R"_{"1"}+"R"_{"2"})^2))/(("z"^2)-(("R"_{"1"}-"R"_{"2"})^2))))`

Example

`"-88913.417771J"=(-"550J"*6)/(((2*"12A"*"15A")/((("40A")^2)-(("12A"+"15A")^2)))+((2*"12A"*"15A")/((("40A")^2)-(("12A"-"15A")^2)))+ln(((("40A")^2)-(("12A"+"15A")^2))/((("40A")^2)-(("12A"-"15A")^2))))`

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Hamaker Coefficient using Van der Waals Interaction Energy Solution

STEP 0: Pre-Calculation Summary

Formula Used

Hamaker Coefficient = (-Van der Waals interaction energy*6)/(((2*Radius of Spherical Body 1*Radius of Spherical Body 2)/((Center-to-center Distance^2)-((Radius of Spherical Body 1+Radius of Spherical Body 2)^2)))+((2*Radius of Spherical Body 1*Radius of Spherical Body 2)/((Center-to-center Distance^2)-((Radius of Spherical Body 1-Radius of Spherical Body 2)^2)))+ln(((Center-to-center Distance^2)-((Radius of Spherical Body 1+Radius of Spherical Body 2)^2))/((Center-to-center Distance^2)-((Radius of Spherical Body 1-Radius of Spherical Body 2)^2))))
A = (-U_VWaals*6)/(((2*R₁*R₂)/((z^2)-((R₁+R₂)^2)))+((2*R₁*R₂)/((z^2)-((R₁-R₂)^2)))+ln(((z^2)-((R₁+R₂)^2))/((z^2)-((R₁-R₂)^2))))
This formula uses 1 Functions, 5 Variables

Functions Used

ln - The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function., ln(Number)

Variables Used

Hamaker Coefficient - (Measured in Joule) - Hamaker coefficient A can be defined for a Van der Waals body–body interaction.
Van der Waals interaction energy - (Measured in Joule) - Van der Waals interaction energy include attraction and repulsions between atoms, molecules, and surfaces, as well as other intermolecular forces.
Radius of Spherical Body 1 - (Measured in Meter) - Radius of Spherical Body 1 represented as R1.
Radius of Spherical Body 2 - (Measured in Meter) - Radius of Spherical Body 2 represented as R1.
Center-to-center Distance - (Measured in Meter) - Center-to-center Distance is a concept for distances, also called on-center spacing, z = R1 + R2 + r.

STEP 1: Convert Input(s) to Base Unit

Van der Waals interaction energy: 550 Joule --> 550 Joule No Conversion Required
Radius of Spherical Body 1: 12 Angstrom --> 1.2E-09 Meter (Check conversion here)
Radius of Spherical Body 2: 15 Angstrom --> 1.5E-09 Meter (Check conversion here)
Center-to-center Distance: 40 Angstrom --> 4E-09 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A = (-U_VWaals*6)/(((2*R₁*R₂)/((z^2)-((R₁+R₂)^2)))+((2*R₁*R₂)/((z^2)-((R₁-R₂)^2)))+ln(((z^2)-((R₁+R₂)^2))/((z^2)-((R₁-R₂)^2)))) --> (-550*6)/(((2*1.2E-09*1.5E-09)/((4E-09^2)-((1.2E-09+1.5E-09)^2)))+((2*1.2E-09*1.5E-09)/((4E-09^2)-((1.2E-09-1.5E-09)^2)))+ln(((4E-09^2)-((1.2E-09+1.5E-09)^2))/((4E-09^2)-((1.2E-09-1.5E-09)^2))))

Evaluating ... ...

A = -88913.4177708798

STEP 3: Convert Result to Output's Unit

-88913.4177708798 Joule --> No Conversion Required

FINAL ANSWER

-88913.4177708798 ≈ -88913.417771 Joule <-- Hamaker Coefficient

(Calculation completed in 00.004 seconds)

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< 4 Hamaker Coefficient Calculators

Hamaker Coefficient using Van der Waals Interaction Energy

Go Hamaker Coefficient = (-Van der Waals interaction energy*6)/(((2*Radius of Spherical Body 1*Radius of Spherical Body 2)/((Center-to-center Distance^2)-((Radius of Spherical Body 1+Radius of Spherical Body 2)^2)))+((2*Radius of Spherical Body 1*Radius of Spherical Body 2)/((Center-to-center Distance^2)-((Radius of Spherical Body 1-Radius of Spherical Body 2)^2)))+ln(((Center-to-center Distance^2)-((Radius of Spherical Body 1+Radius of Spherical Body 2)^2))/((Center-to-center Distance^2)-((Radius of Spherical Body 1-Radius of Spherical Body 2)^2))))

Hamaker Coefficient using Van der Waals Forces between Objects

Go Hamaker Coefficient = (-Van der Waals force*(Radius of Spherical Body 1+Radius of Spherical Body 2)*6*(Distance Between Surfaces^2))/(Radius of Spherical Body 1*Radius of Spherical Body 2)

Hamaker Coefficient using Potential Energy in Limit of Closest-Approach

Go Hamaker Coefficient = (-Potential Energy*(Radius of Spherical Body 1+Radius of Spherical Body 2)*6*Distance Between Surfaces)/(Radius of Spherical Body 1*Radius of Spherical Body 2)

Hamaker Coefficient

Go Hamaker Coefficient A = (pi^2)*Coefficient of Particle–Particle Pair Interaction*Number Density of particle 1*Number Density of particle 2

Hamaker Coefficient using Van der Waals Interaction Energy Formula

What are main characteristics of Van der Waals forces?

1) They are weaker than normal covalent and ionic bonds.
2) Van der Waals forces are additive and cannot be saturated.
3) They have no directional characteristic.
4) They are all short-range forces and hence only interactions between the nearest particles need to be considered (instead of all the particles). Van der Waals attraction is greater if the molecules are closer.
5) Van der Waals forces are independent of temperature except for dipole – dipole interactions.

How to Calculate Hamaker Coefficient using Van der Waals Interaction Energy?

Hamaker Coefficient using Van der Waals Interaction Energy calculator uses Hamaker Coefficient = (-Van der Waals interaction energy*6)/(((2*Radius of Spherical Body 1*Radius of Spherical Body 2)/((Center-to-center Distance^2)-((Radius of Spherical Body 1+Radius of Spherical Body 2)^2)))+((2*Radius of Spherical Body 1*Radius of Spherical Body 2)/((Center-to-center Distance^2)-((Radius of Spherical Body 1-Radius of Spherical Body 2)^2)))+ln(((Center-to-center Distance^2)-((Radius of Spherical Body 1+Radius of Spherical Body 2)^2))/((Center-to-center Distance^2)-((Radius of Spherical Body 1-Radius of Spherical Body 2)^2)))) to calculate the Hamaker Coefficient, The Hamaker coefficient using Van der Waals interaction energy A can be defined for a Van der Waals body–body interaction. Hamaker Coefficient is denoted by A symbol.

How to calculate Hamaker Coefficient using Van der Waals Interaction Energy using this online calculator? To use this online calculator for Hamaker Coefficient using Van der Waals Interaction Energy, enter Van der Waals interaction energy (U_VWaals), Radius of Spherical Body 1 (R₁), Radius of Spherical Body 2 (R₂) & Center-to-center Distance (z) and hit the calculate button. Here is how the Hamaker Coefficient using Van der Waals Interaction Energy calculation can be explained with given input values -> -88913.417771 = (-550*6)/(((2*1.2E-09*1.5E-09)/((4E-09^2)-((1.2E-09+1.5E-09)^2)))+((2*1.2E-09*1.5E-09)/((4E-09^2)-((1.2E-09-1.5E-09)^2)))+ln(((4E-09^2)-((1.2E-09+1.5E-09)^2))/((4E-09^2)-((1.2E-09-1.5E-09)^2)))).

FAQ

What is Hamaker Coefficient using Van der Waals Interaction Energy?

The Hamaker coefficient using Van der Waals interaction energy A can be defined for a Van der Waals body–body interaction and is represented as A = (-U_VWaals*6)/(((2*R₁*R₂)/((z^2)-((R₁+R₂)^2)))+((2*R₁*R₂)/((z^2)-((R₁-R₂)^2)))+ln(((z^2)-((R₁+R₂)^2))/((z^2)-((R₁-R₂)^2)))) or Hamaker Coefficient = (-Van der Waals interaction energy*6)/(((2*Radius of Spherical Body 1*Radius of Spherical Body 2)/((Center-to-center Distance^2)-((Radius of Spherical Body 1+Radius of Spherical Body 2)^2)))+((2*Radius of Spherical Body 1*Radius of Spherical Body 2)/((Center-to-center Distance^2)-((Radius of Spherical Body 1-Radius of Spherical Body 2)^2)))+ln(((Center-to-center Distance^2)-((Radius of Spherical Body 1+Radius of Spherical Body 2)^2))/((Center-to-center Distance^2)-((Radius of Spherical Body 1-Radius of Spherical Body 2)^2)))). Van der Waals interaction energy include attraction and repulsions between atoms, molecules, and surfaces, as well as other intermolecular forces, Radius of Spherical Body 1 represented as R1, Radius of Spherical Body 2 represented as R1 & Center-to-center Distance is a concept for distances, also called on-center spacing, z = R1 + R2 + r.

How to calculate Hamaker Coefficient using Van der Waals Interaction Energy?

The Hamaker coefficient using Van der Waals interaction energy A can be defined for a Van der Waals body–body interaction is calculated using Hamaker Coefficient = (-Van der Waals interaction energy*6)/(((2*Radius of Spherical Body 1*Radius of Spherical Body 2)/((Center-to-center Distance^2)-((Radius of Spherical Body 1+Radius of Spherical Body 2)^2)))+((2*Radius of Spherical Body 1*Radius of Spherical Body 2)/((Center-to-center Distance^2)-((Radius of Spherical Body 1-Radius of Spherical Body 2)^2)))+ln(((Center-to-center Distance^2)-((Radius of Spherical Body 1+Radius of Spherical Body 2)^2))/((Center-to-center Distance^2)-((Radius of Spherical Body 1-Radius of Spherical Body 2)^2)))). To calculate Hamaker Coefficient using Van der Waals Interaction Energy, you need Van der Waals interaction energy (U_VWaals), Radius of Spherical Body 1 (R₁), Radius of Spherical Body 2 (R₂) & Center-to-center Distance (z). With our tool, you need to enter the respective value for Van der Waals interaction energy, Radius of Spherical Body 1, Radius of Spherical Body 2 & Center-to-center Distance and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Hamaker Coefficient?

In this formula, Hamaker Coefficient uses Van der Waals interaction energy, Radius of Spherical Body 1, Radius of Spherical Body 2 & Center-to-center Distance. We can use 2 other way(s) to calculate the same, which is/are as follows -

Hamaker Coefficient = (-Potential Energy*(Radius of Spherical Body 1+Radius of Spherical Body 2)*6*Distance Between Surfaces)/(Radius of Spherical Body 1*Radius of Spherical Body 2)
Hamaker Coefficient = (-Van der Waals force*(Radius of Spherical Body 1+Radius of Spherical Body 2)*6*(Distance Between Surfaces^2))/(Radius of Spherical Body 1*Radius of Spherical Body 2)

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