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The Van der Waals Equation

The Van der Waals Equation

The ideal gas law is based on two simplifying assumptions: first, that there are no intermolecular attractions between gas molecules, and second, that the volume occupied by the molecules themselves is negligible compared with the volume of the container. However, these assumptions don't hold up under all conditions - specifically, at high pressures and low temperatures, as gas tends to deviate from ideal gas behavior.The van der Waals equation is an enhanced version of the ideal gas law,...

Van der Waals Equation

Van der Waals Equation

The ideal gas law is an approximation that works well at high temperatures and low pressures. The van der Waals equation of state (named after the Dutch physicist Johannes van der Waals, 1837−1923) improves it by considering two factors.
First, the attractive forces between molecules, which are stronger at higher densities and reduce the pressure, are considered by adding to the pressure a term equal to the square of the molar density multiplied by a positive coefficient a. Second, the volume...

Real Gases: Effects of Intermolecular Forces and Molecular Volume Deriving Van der Waals Equation

Real Gases: Effects of Intermolecular Forces and Molecular Volume Deriving Van der Waals Equation

Thus far, the ideal gas law, PV = nRT, has been applied to a variety of different types of problems, ranging from reaction stoichiometry and empirical and molecular formula problems to determining the density and molar mass of a gas. However, the behavior of a gas is often non-ideal, meaning that the observed relationships between its pressure, volume, and temperature are not accurately described by the gas laws.

Spherical and Cylindrical Capacitor

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Van der Waals Interactions

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Atoms and molecules interact with each other through intermolecular forces. These electrostatic forces arise from attractive or repulsive interactions between particles with permanent, partial, or temporary charges. The intermolecular forces between neutral atoms and molecules are ion–dipole, dipole–dipole, and dispersion forces, collectively known as van der Waals forces.

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Related Experiment Video

Updated: May 22, 2026

Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations

Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations

Published on: October 12, 2019

Approximate scheme for calculating van der Waals interactions between finite cylindrical volume elements.

Ravi P Jaiswal¹, Stephen P Beaudoin

¹School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907-2100, USA.

Langmuir : the ACS Journal of Surfaces and Colloids

|May 25, 2012

Summary

Researchers developed new formulas to accurately calculate van der Waals (vdW) forces between nanoscale objects. This improves simulations of interacting surfaces, especially when they are in close contact or have complex structures.

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Area of Science:

Physics
Materials Science
Surface Science

Background:

Calculating van der Waals (vdW) forces is crucial for understanding interactions between nanoscale objects.
Current methods often approximate vdW forces using parallel plate models, which lack accuracy for cylinders with small radius-to-distance ratios.
This limitation restricts simulations of nanoscale systems with topographical or compositional variations.

Purpose of the Study:

To develop accurate analytical expressions for nonretarded van der Waals (vdW) forces between finite cylinders.
To overcome the limitations of the parallel plate approximation for cylinders with small radius-to-distance ratios.
To enable precise vdW force calculations for contacting or near-contacting nanoscale surfaces with heterogeneous morphology.

Main Methods:

Derived approximate analytical expressions for nonretarded vdW forces between finite cylinders in various orientations.
Validated the derived expressions against full numerical solutions of Hamaker's equations.
Focused on systems with cylinder radius to separation distance ratios of 10 or less.

Main Results:

The derived analytical expressions accurately predict vdW forces between cylinders, showing high agreement with numerical solutions.
The new method overcomes the inaccuracies of the parallel plate approximation for co-axial cylinders with R/D ratios of 10 or less.
Accurate vdW force calculations are now possible for nanoscale systems with heterogeneous surfaces in contact or near contact.

Conclusions:

The developed analytical expressions provide an accurate and computationally efficient method for calculating vdW forces between finite cylinders.
This advancement expands the scope of simulations for nanoscale interactions, particularly for complex surface topographies and compositions.
The findings facilitate more reliable modeling of phenomena involving particle-surface interactions at the nanoscale.