Hamaker Coefficient Calculator

✖Coefficient of particle–particle pair interaction can be determined from the Van der Waals pair potential.ⓘ Coefficient of Particle–Particle Pair Interaction [C]			+10% -10%
✖Number Density of particle 1 is an intensive quantity used to describe the degree of concentration of countable objects (particles, molecules, phonons, cells, galaxies, etc.) in physical space.ⓘ Number Density of particle 1 [ρ₁]			+10% -10%
✖Number Density of particle 2 is an intensive quantity used to describe the degree of concentration of countable objects (particles, molecules, phonons, cells, galaxies, etc.) in physical space.ⓘ Number Density of particle 2 [ρ₂]			+10% -10%

✖Hamaker Coefficient A can be defined for a Van der Waals body–body interaction.ⓘ Hamaker Coefficient [A_HC]

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Hamaker Coefficient Solution

STEP 0: Pre-Calculation Summary

Formula Used

Hamaker Coefficient A = (pi^2)*Coefficient of Particle–Particle Pair Interaction*Number Density of particle 1*Number Density of particle 2
A_HC = (pi^2)*C*ρ₁*ρ₂
This formula uses 1 Constants, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Hamaker Coefficient A - Hamaker Coefficient A can be defined for a Van der Waals body–body interaction.
Coefficient of Particle–Particle Pair Interaction - Coefficient of particle–particle pair interaction can be determined from the Van der Waals pair potential.
Number Density of particle 1 - (Measured in 1 per Cubic Meter) - Number Density of particle 1 is an intensive quantity used to describe the degree of concentration of countable objects (particles, molecules, phonons, cells, galaxies, etc.) in physical space.
Number Density of particle 2 - (Measured in 1 per Cubic Meter) - Number Density of particle 2 is an intensive quantity used to describe the degree of concentration of countable objects (particles, molecules, phonons, cells, galaxies, etc.) in physical space.

STEP 1: Convert Input(s) to Base Unit

Coefficient of Particle–Particle Pair Interaction: 8 --> No Conversion Required
Number Density of particle 1: 3 1 per Cubic Meter --> 3 1 per Cubic Meter No Conversion Required
Number Density of particle 2: 5 1 per Cubic Meter --> 5 1 per Cubic Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A_HC = (pi^2)*C*ρ₁*ρ₂ --> (pi^2)*8*3*5

Evaluating ... ...

A_HC = 1184.35252813072

STEP 3: Convert Result to Output's Unit

1184.35252813072 --> No Conversion Required

FINAL ANSWER

1184.35252813072 ≈ 1184.353 <-- Hamaker Coefficient A

(Calculation completed in 00.004 seconds)

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University of Hawaiʻi at Mānoa (UH Manoa), Hawaii, USA

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< Hamaker Coefficient Calculators

Hamaker Coefficient using Van der Waals Interaction Energy

LaTeX 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

LaTeX 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

LaTeX 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

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

< Important Formulae on Different Models of Real Gas Calculators

Temperature of Real Gas using Peng Robinson Equation

LaTeX Go Temperature given CE = (Pressure+(((Peng–Robinson Parameter a*α-function)/((Molar Volume^2)+(2*Peng–Robinson Parameter b*Molar Volume)-(Peng–Robinson Parameter b^2)))))*((Molar Volume-Peng–Robinson Parameter b)/[R])

Critical Pressure given Peng Robinson Parameter b and other Actual and Reduced Parameters

LaTeX Go Critical Pressure given PRP = 0.07780*[R]*(Temperature of Gas/Reduced Temperature)/Peng–Robinson Parameter b

Actual Temperature given Peng Robinson parameter b, other reduced and critical parameters

LaTeX Go Temperature given PRP = Reduced Temperature*((Peng–Robinson Parameter b*Critical Pressure)/(0.07780*[R]))

Actual Pressure given Peng Robinson Parameter a, and other Reduced and Critical Parameters

LaTeX Go Pressure given PRP = Reduced Pressure*(0.45724*([R]^2)*(Critical Temperature^2)/Peng–Robinson Parameter a)

Hamaker Coefficient Formula

LaTeX Go

Hamaker Coefficient A = (pi^2)*Coefficient of Particle–Particle Pair Interaction*Number Density of particle 1*Number Density of particle 2
A_HC = (pi^2)*C*ρ₁*ρ₂

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?

Hamaker Coefficient calculator uses Hamaker Coefficient A = (pi^2)*Coefficient of Particle–Particle Pair Interaction*Number Density of particle 1*Number Density of particle 2 to calculate the Hamaker Coefficient A, The Hamaker coefficient A can be defined for a Van der Waals (VdW) body–body interaction. The magnitude of this constant reflects the strength of the vdW force between two particles, or between a particle and a substrate. Hamaker Coefficient A is denoted by A_HC symbol.

How to calculate Hamaker Coefficient using this online calculator? To use this online calculator for Hamaker Coefficient, enter Coefficient of Particle–Particle Pair Interaction (C), Number Density of particle 1 (ρ₁) & Number Density of particle 2 (ρ₂) and hit the calculate button. Here is how the Hamaker Coefficient calculation can be explained with given input values -> 1184.353 = (pi^2)*8*3*5.

FAQ

What is Hamaker Coefficient?

The Hamaker coefficient A can be defined for a Van der Waals (VdW) body–body interaction. The magnitude of this constant reflects the strength of the vdW force between two particles, or between a particle and a substrate and is represented as A_HC = (pi^2)*C*ρ₁*ρ₂ or Hamaker Coefficient A = (pi^2)*Coefficient of Particle–Particle Pair Interaction*Number Density of particle 1*Number Density of particle 2. Coefficient of particle–particle pair interaction can be determined from the Van der Waals pair potential, Number Density of particle 1 is an intensive quantity used to describe the degree of concentration of countable objects (particles, molecules, phonons, cells, galaxies, etc.) in physical space & Number Density of particle 2 is an intensive quantity used to describe the degree of concentration of countable objects (particles, molecules, phonons, cells, galaxies, etc.) in physical space.

How to calculate Hamaker Coefficient?

The Hamaker coefficient A can be defined for a Van der Waals (VdW) body–body interaction. The magnitude of this constant reflects the strength of the vdW force between two particles, or between a particle and a substrate is calculated using Hamaker Coefficient A = (pi^2)*Coefficient of Particle–Particle Pair Interaction*Number Density of particle 1*Number Density of particle 2. To calculate Hamaker Coefficient, you need Coefficient of Particle–Particle Pair Interaction (C), Number Density of particle 1 (ρ₁) & Number Density of particle 2 (ρ₂). With our tool, you need to enter the respective value for Coefficient of Particle–Particle Pair Interaction, Number Density of particle 1 & Number Density of particle 2 and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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