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Related Concept Videos

Van der Waals Equation01:10

Van der Waals Equation

5.9K
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...
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Distribution of Molecular Speeds01:27

Distribution of Molecular Speeds

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The motion of molecules in a gas is random in magnitude and direction for individual molecules, but a gas of many molecules has a predictable distribution of molecular speeds. This predictable distribution of molecular speeds is known as the Maxwell-Boltzmann distribution. The distribution of molecular speeds in liquids is comparable to that of gases but not identical and can help to understand the phenomenon of the boiling and vapor pressure of a liquid. Consider that a molecule requires a...
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Maxwell-Boltzmann Distribution: Problem Solving01:20

Maxwell-Boltzmann Distribution: Problem Solving

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Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
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Equilibrium Conditions for a Particle01:23

Equilibrium Conditions for a Particle

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When an object is in equilibrium, it is either at rest or moving with a constant velocity. There are two types of equilibrium: static and dynamic. Static equilibrium occurs when an object is at rest, while dynamic equilibrium occurs when an object is moving with a constant velocity. In both cases, there must be a balance of forces acting on the object.
To understand the concept of equilibrium, let us first consider the forces acting on an object. When different forces act on an object, they can...
2.0K
Equation of State01:07

Equation of State

2.4K
The equation of state is an equation that relates physical quantities, such as pressure, volume, temperature, and the number of moles, of a thermodynamics system with each other. The equation relating physical quantities with each other can be a simple mathematical expression or too complicated to express in mathematical form. In either case, a relationship between physical quantities exists. If the equation of state cannot be expressed in a mathematical form, then experimental data and...
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Real Gases: Effects of Intermolecular Forces and Molecular Volume Deriving Van der Waals Equation04:01

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

38.1K
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.
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Updated: Dec 4, 2025

Isotopic Effect in Double Proton Transfer Process of Porphycene Investigated by Enhanced QM/MM Method
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Shuttleworth equation: A molecular simulations perspective.

Nicodemo Di Pasquale1, Ruslan L Davidchack1

  • 1School of Mathematics and Actuarial Science, University of Leicester, University Rd., Leicester LE1 7RH, United Kingdom.

The Journal of Chemical Physics
|October 23, 2020
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Summary
This summary is machine-generated.

This study clarifies surface free energy and stress for solid interfaces using statistical mechanics and Molecular Dynamics simulations. It demonstrates consistency between thermodynamic and simulation-based definitions, resolving literature debates.

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Area of Science:

  • Thermodynamics and Statistical Mechanics
  • Materials Science
  • Surface Science

Background:

  • Classical thermodynamics provides a foundation for interfacial phenomena, but concepts like interfacial tension and stress in solids remain debated.
  • Existing debates, particularly concerning the Shuttleworth equation, are primarily within classical thermodynamics, lacking molecular-level validation.

Purpose of the Study:

  • To investigate interfacial phenomena, specifically surface free energy and stress in solids, using a statistical mechanics framework.
  • To bridge the gap between theoretical thermodynamic definitions and practical molecular dynamics (MD) simulations.
  • To resolve ambiguities and validate existing concepts in solid-vacuum interfaces.

Main Methods:

  • Employed Molecular Dynamics (MD) simulations for a one-component system with Lennard-Jones potential.
  • Utilized the cleaving method to calculate the excess free energy of solid-vacuum interfaces under tangential strain.
  • Calculated surface stress by analyzing the difference between normal and tangential forces at the interface.

Main Results:

  • Demonstrated consistency between thermodynamic and statistical mechanical definitions of surface free energy and surface stress.
  • Quantified these properties using interaction-dependent parameters directly from MD simulations.
  • Validated the theoretical relationships within the statistical uncertainty of the simulations.

Conclusions:

  • Statistical mechanics provides a robust framework for understanding solid-vacuum interfacial properties.
  • MD simulations can effectively test and validate thermodynamic concepts of surface energy and stress.
  • The study resolves long-standing debates by showing agreement between theoretical and simulation-derived definitions.