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Related Concept Videos

Equilibrium Conditions for a Particle01:23

Equilibrium Conditions for a Particle

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...
Fermi Level Dynamics01:12

Fermi Level Dynamics

The vacuum level denotes the energy threshold required for an electron to escape from a material surface. It is usually positioned above the conduction band of a semiconductor and acts as a benchmark for comparing electron energies within various materials.
Electron affinity in semiconductors refers to the energy gap between the minimum of its conduction band and the vacuum level and it is a critical parameter in determining how easily a semiconductor can accept additional electrons.
The work...
Gibbs Free Energy02:39

Gibbs Free Energy

One of the challenges of using the second law of thermodynamics to determine if a process is spontaneous is that it requires measurements of the entropy change for the system and the entropy change for the surroundings. An alternative approach involving a new thermodynamic property defined in terms of system properties only was introduced in the late nineteenth century by American mathematician Josiah Willard Gibbs. This new property is called the Gibbs free energy (G) (or simply the free...
Debye–Huckel–Onsager Conductance Equation01:28

Debye–Huckel–Onsager Conductance Equation

The Debye-Hückel-Onsager equation is a cornerstone of physical chemistry, providing a method to determine the molar conductance (Λm) and molar conductance at infinite dilution (Λ°m) for uni-univalent electrolytes.Uni-univalent electrolytes are electrolytes that dissociate in solution to produce one cation with a +1 charge and one anion with a –1 charge per formula unit.This equation addresses two crucial phenomena: the asymmetry effect and the electrophoretic effect. According to this equation,...
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

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.
Reynolds Transport Theorem01:24

Reynolds Transport Theorem

The Reynolds transport theorem provides a framework to relate the time rate of change of an extensive property within a system to that in a control volume, which is crucial for analyzing fluid dynamics. Extensive properties, such as mass, velocity, acceleration, temperature, and momentum, can be expressed in terms of the mass of a fluid portion. These properties are called extensive because they depend on the system's size, while intensive properties are their corresponding values per unit mass.

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Related Experiment Video

Updated: Jun 16, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Field-theoretic simulations in the Gibbs ensemble.

Robert A Riggleman1, Glenn H Fredrickson

  • 1Department of Chemical Engineering, University of California, Santa Barbara, California 93106, USA.

The Journal of Chemical Physics
|January 26, 2010
PubMed
Summary
This summary is machine-generated.

Field-theoretic simulations can now efficiently model two phases in equilibrium using the Gibbs ensemble. This method allows separate simulation boxes to swap species and volume, improving bulk property calculations.

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Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics
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Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics

Published on: April 12, 2019

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Last Updated: Jun 16, 2026

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
11:03

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids

Published on: December 4, 2017

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics
10:52

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics

Published on: April 12, 2019

Area of Science:

  • Computational physics and chemistry
  • Materials science
  • Statistical mechanics

Background:

  • Field-theoretic simulations are crucial for calculating phase diagrams and equilibrium properties.
  • Simulating two phases in equilibrium within a single box is computationally intensive due to interface effects.
  • Existing methods require large simulations to ensure accurate bulk property estimation.

Purpose of the Study:

  • To introduce an efficient field-theoretic simulation method in the Gibbs ensemble.
  • To enable accurate simulation of bulk properties of coexisting phases.
  • To overcome the computational demands of traditional single-box simulations.

Main Methods:

  • Implementing Gibbs ensemble field-theoretic simulations.
  • Simulating two phases in separate boxes with species and volume exchange.
  • Maintaining chemical and mechanical equilibrium via swapping.
  • Utilizing fixed total species number and volume for canonical ensemble simulation.

Main Results:

  • Demonstrated an efficient method for field-theoretic simulations in the Gibbs ensemble.
  • Successfully applied the method to two-dimensional polymer systems.
  • Validated the approach in both mean-field (self-consistent field theory) and fluctuating field theory regimes.

Conclusions:

  • The Gibbs ensemble offers an efficient alternative for field-theoretic simulations of coexisting phases.
  • This method reduces computational costs while maintaining accuracy for bulk property calculations.
  • The demonstrated approach is applicable to various systems, including polymer models.