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Related Concept Videos

Solid–Solid Solutions01:24

Solid–Solid Solutions

The temperature-composition phase diagram of two solids, A and B, which are immiscible in the solid phase but form miscible liquids, shows that when the temperature is low, these two exist as separate, pure solids (A and B). As the temperature increases, they transition into a single-phase liquid solution where A and B coexist. Moving from point a1 to a2 in the phase diagram, the composition changes such that solid B begins to separate from the solution, enriching the remaining liquid with A.
Liquid–Solid Solutions01:29

Liquid–Solid Solutions

The process of a solid dissolving in a liquid to form a solution is governed by the solubility limit, which is the maximum amount of the solid substance, or solute, that can be dissolved in a specific volume of the liquid or solvent. As the solute dissolves, it reaches a point where no more solute can be dissolved at a given temperature - this is known as the saturation point. However, if further solute is added and it manages to dissolve, the solution becomes supersaturated. Supersaturated...
First Law: Particles in Two-dimensional Equilibrium01:18

First Law: Particles in Two-dimensional Equilibrium

Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration; but it is important to remember that these conditions are relative. For instance, an object may be at rest when viewed from one frame of reference, but that same object would appear to be in motion when viewed by someone moving at a constant velocity.
Newton's first law tells us about the...
First Law: Particles in One-dimensional Equilibrium01:10

First Law: Particles in One-dimensional Equilibrium

Newton's first law of motion states that a body at rest remains at rest, or if in motion, remains in motion at constant velocity, unless acted on by a net external force. It also states that there must be a cause for any change in velocity (a change in either magnitude or direction) to occur. This cause is a net external force. For example, consider what happens to an object sliding along a rough horizontal surface. The object quickly grinds to a halt, due to the net force of friction. If we...
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...
The Colloidal State01:29

The Colloidal State

The formation of a colloidal system is exemplified by an aqueous solution containing Cl− ions is introduced to another containing Ag+ ions, resulting in the precipitation of solid AgCl as extremely tiny crystals. Instead of settling out as a filterable precipitate, these crystals remain suspended in the liquid, showcasing a colloidal system.A colloidal system involves colloidal particles within the approximate range of 1 to 1000 nm in at least one dimension, dispersed in a medium called the...

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Related Experiment Video

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Experimental Measurement of Settling Velocity of Spherical Particles in Unconfined and Confined Surfactant-based Shear Thinning Viscoelastic Fluids
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Equilibrium fluid-solid coexistence of hard spheres.

L A Fernández1, V Martín-Mayor, B Seoane

  • 1Departamento de Física Teórica I, Universidad Complutense, 28040 Madrid, Spain.

Physical Review Letters
|June 12, 2012
PubMed
Summary

We developed a new simulation method to accurately calculate the crystallization pressure and interfacial free energy for hard spheres. This advance enables practical studies of crystal formation and properties.

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Area of Science:

  • Computational physics
  • Materials science
  • Statistical mechanics

Background:

  • Understanding the fluid-crystal phase transition is crucial for materials science.
  • Traditional simulation methods face challenges in accurately calculating free energies for large systems.

Purpose of the Study:

  • To develop and validate a novel tethered Monte Carlo simulation technique.
  • To accurately determine the fluid-crystal coexistence pressure and interfacial free energy for hard spheres.

Main Methods:

  • Utilized a tethered Monte Carlo simulation approach.
  • Enhanced traditional umbrella sampling for constrained Gibbs' free energy calculations.
  • Simulated systems with up to 2916 hard spheres to model fluid-solid interfaces.

Main Results:

  • Achieved high-accuracy estimates for fluid-crystal coexistence pressure.
  • Extrapolated coexistence pressure to infinite volume: p(co)=11.5727(10)k(B)T/σ(3).
  • Determined the interfacial free energy for the {100} crystal face: γ({100})=0.636(11)k(B)T/σ(2).

Conclusions:

  • The developed simulation method is practical for studying constrained free energies.
  • Provides accurate thermodynamic data for hard sphere crystallization.
  • Enables precise calculations of coexistence pressures and interfacial energies.