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
AHC = (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
AHC = (pi^2)*C*ρ12 --> (pi^2)*8*3*5
Evaluating ... ...
AHC = 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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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

20 Important Formulae on Different Models of Real Gas Calculators

Critical Temperature using Peng Robinson Equation given Reduced and Actual Parameters
Go Real Gas Temperature = ((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]))/Reduced Temperature
Temperature of Real Gas using Peng Robinson Equation
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 of Real Gas using Reduced Redlich Kwong Equation
Go Critical Pressure = Pressure/(((3*Reduced Temperature)/(Reduced Molar Volume-0.26))-(1/(0.26*sqrt(Temperature of Gas)*Reduced Molar Volume*(Reduced Molar Volume+0.26))))
Critical Temperature of Real Gas using Reduced Redlich Kwong Equation
Go Critical Temperature given RKE = Temperature of Gas/(((Reduced Pressure+(1/(0.26*Reduced Molar Volume*(Reduced Molar Volume+0.26))))*((Reduced Molar Volume-0.26)/3))^(2/3))
Actual Temperature of Real Gas using Reduced Redlich Kwong Equation
Go Temperature of Gas = Critical Temperature*(((Reduced Pressure+(1/(0.26*Reduced Molar Volume*(Reduced Molar Volume+0.26))))*((Reduced Molar Volume-0.26)/3))^(2/3))
Reduced Pressure given Peng Robinson Parameter b, other Actual and Reduced Parameters
Go Critical Pressure given PRP = Pressure/(0.07780*[R]*(Temperature of Gas/Reduced Temperature)/Peng–Robinson Parameter b)
Reduced Temperature using Redlich Kwong Equation given of 'a' and 'b'
Go Temperature given PRP = Temperature of Gas/((3^(2/3))*(((2^(1/3))-1)^(4/3))*((Redlich–Kwong Parameter a/(Redlich–Kwong parameter b*[R]))^(2/3)))
Critical Pressure given Peng Robinson Parameter b and other Actual and Reduced Parameters
Go Critical Pressure given PRP = 0.07780*[R]*(Temperature of Gas/Reduced Temperature)/Peng–Robinson Parameter b
Hamaker Coefficient
Go Hamaker Coefficient A = (pi^2)*Coefficient of Particle–Particle Pair Interaction*Number Density of particle 1*Number Density of particle 2
Actual Temperature given Peng Robinson parameter b, other reduced and critical parameters
Go Temperature given PRP = Reduced Temperature*((Peng–Robinson Parameter b*Critical Pressure)/(0.07780*[R]))
Actual Temperature of Real Gas using Redlich Kwong Equation given 'b'
Go Real Gas Temperature = Reduced Temperature*((Redlich–Kwong parameter b*Critical Pressure)/(0.08664*[R]))
Reduced Temperature given Peng Robinson Parameter a, and other Actual and Critical Parameters
Go Temperature of Gas = Temperature/(sqrt((Peng–Robinson Parameter a*Critical Pressure)/(0.45724*([R]^2))))
Radius of Spherical Body 1 given Center-to-Center Distance
Go Radius of Spherical Body 1 = Center-to-center Distance-Distance Between Surfaces-Radius of Spherical Body 2
Radius of Spherical Body 2 given Center-to-Center Distance
Go Radius of Spherical Body 2 = Center-to-center Distance-Distance Between Surfaces-Radius of Spherical Body 1
Distance between Surfaces given Center-to-Center Distance
Go Distance Between Surfaces = Center-to-center Distance-Radius of Spherical Body 1-Radius of Spherical Body 2
Center-to-Center Distance
Go Center-to-center Distance = Radius of Spherical Body 1+Radius of Spherical Body 2+Distance Between Surfaces
Actual Pressure given Peng Robinson Parameter a, and other Reduced and Critical Parameters
Go Pressure given PRP = Reduced Pressure*(0.45724*([R]^2)*(Critical Temperature^2)/Peng–Robinson Parameter a)
Critical Temperature of Real Gas using Redlich Kwong Equation given 'b'
Go Critical Temperature given RKE and b = (Redlich–Kwong parameter b*Critical Pressure)/(0.08664*[R])
Redlich Kwong Parameter b at Critical Point
Go Parameter b = (0.08664*[R]*Critical Temperature)/Critical Pressure
Peng Robinson Parameter b of Real Gas given Critical Parameters
Go Parameter b = 0.07780*[R]*Critical Temperature/Critical Pressure

Hamaker Coefficient Formula

Hamaker Coefficient A = (pi^2)*Coefficient of Particle–Particle Pair Interaction*Number Density of particle 1*Number Density of particle 2
AHC = (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 AHC 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 1) & Number Density of particle 2 2) 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 AHC = (pi^2)*C*ρ12 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 1) & Number Density of particle 2 2). 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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