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Related Concept Videos

Entropy02:39

Entropy

Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
Entropy01:18

Entropy

The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...
Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
Entropy and the Second Law of Thermodynamics01:20

Entropy and the Second Law of Thermodynamics

The second law of thermodynamics can be stated quantitatively using the concept of entropy. Entropy is the measure of disorder of the system.
The relation  between entropy and disorder can be illustrated with the example of the phase change of ice to water. In ice, the molecules are located at specific sites giving a solid state, whereas, in a liquid form, these molecules are much freer to move. The molecular arrangement has therefore become more randomized. Although the change in average...
Entropy and the Second Law of Thermodynamics01:26

Entropy and the Second Law of Thermodynamics

Consider an isolated system in which a hot object is placed in contact with a cold one. This is an irreversible process that eventually leads both objects to reach the same equilibrium temperature. It is crucial to note that the constituents of any substance exhibit increased disorder at higher temperatures. As a cold substance absorbs heat, its constituents become more disordered. The energy transfer from a hotter object to a cooler one increases the system's disorder or randomness. This...
Entropy and Solvation02:05

Entropy and Solvation

The process of surrounding a solute with solvent is called solvation. It involves evenly distributing the solute within the solvent. The rule of thumb for determining a solvent for a given compound is that like dissolves like. A good solvent has molecular characteristics similar to those of the compound to be dissolved. For example, polar solutions dissolve polar solutes, and apolar solvents dissolve apolar solutes. A polar solvent is a solvent that has a high dielectric constant (ϵ ≥ 15); an...

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Updated: May 13, 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

Exploring entropy landscapes using hard particle Monte Carlo metadynamics.

Charlotte Shiqi Zhao1, Sun-Ting Tsai1, Sharon C Glotzer1,2

  • 1Department of Chemical Engineering, University of Michigan, Ann Arbor, MI 48109.

Proceedings of the National Academy of Sciences of the United States of America
|May 11, 2026
PubMed
Summary
This summary is machine-generated.

We introduce hard particle Monte Carlo metadynamics (HPMC-MetaD) to study colloidal crystallization in hard particle systems. This method successfully observed crystallization for five challenging shapes, revealing entropy landscapes.

Keywords:
Monte Carlo simulationscolloidscrystallizationenhanced samplingmetadynamics

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Area of Science:

  • Computational physics and chemistry
  • Soft matter physics
  • Statistical mechanics

Background:

  • Metadynamics is a powerful simulation technique for rare events in molecular systems.
  • Its application to hard particle systems, especially anisotropic ones, has been limited.
  • Crystallization in these systems is primarily driven by entropy.

Purpose of the Study:

  • To develop and validate a novel method, hard particle Monte Carlo metadynamics (HPMC-MetaD), for studying colloidal crystallization.
  • To extend the applicability of metadynamics to entropy-driven phase transitions in hard particle systems.
  • To investigate the crystallization behavior of five specific anisotropic hard particle shapes.

Main Methods:

  • The proposed HPMC-MetaD method combines the hard particle Monte Carlo (HPMC) scheme with metadynamics.
  • The method was applied to simulate five anisotropic hard particle systems known for their resistance to crystallization.
  • Entropy landscapes were constructed to analyze the phase transition mechanisms.

Main Results:

  • HPMC-MetaD successfully induced and observed crystallization for all five studied anisotropic hard particle shapes.
  • The method allowed for the construction of detailed entropy landscapes, providing insights into the crystallization pathways.
  • The simulations demonstrated the effectiveness of HPMC-MetaD in overcoming sampling limitations.

Conclusions:

  • HPMC-MetaD is an effective tool for exploring self-assembly and crystallization in hard particle systems.
  • This method facilitates a deeper understanding of entropy-driven phase transitions in colloidal systems.
  • The approach enables predictive control over self-assembly pathways in complex particle systems.