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Related Concept Videos

Phase Transitions02:31

Phase Transitions

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Whether solid, liquid, or gas, a substance's state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the solid pack closely together, generally in a pattern. The particles vibrate about their fixed positions but do not move or squeeze past their neighbors. In liquids, although the particles are closely spaced, they are randomly arranged. The position of the particles are not fixed—that is, they are free to move past their neighbors to...
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The phase of a given substance depends on the pressure and temperature. Thus, plots of pressure versus temperature showing the phase in each region provide considerable insights into the thermal properties of substances. Such plots are known as phase diagrams. For instance, in the phase diagram for water (Figure 1), the solid curve boundaries between the phases indicate phase transitions (i.e., temperatures and pressures at which the phases coexist).
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States of Matter and Phase Changes00:59

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The internal energy of a substance—the total kinetic energy of all its molecules and the potential energy of their associated forces—depends on the strength of the intermolecular forces in the condensed phases and the pressure exerted on the substance. The internal energy of a substance is the highest in the gaseous state, the lowest in the solid state, and intermediate in the liquid state. Phase transitions are caused by changes in physical conditions, such as temperature and...
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Phase Changes01:19

Phase Changes

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Phase transitions play an important theoretical and practical role in the study of heat flow. In melting or fusion, a solid turns into a liquid; the opposite process is freezing. In evaporation, a liquid turns into a gas; the opposite process is condensation.
A substance melts or freezes at a temperature called its melting point and boils or condenses at its boiling point. These temperatures depend on pressure. High pressure favors the denser form of the substance, so typically, high pressure...
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Phase Transitions: Melting and Freezing02:39

Phase Transitions: Melting and Freezing

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Heating a crystalline solid increases the average energy of its atoms, molecules, or ions, and the solid gets hotter. At some point, the added energy becomes large enough to partially overcome the forces holding the molecules or ions of the solid in their fixed positions, and the solid begins the process of transitioning to the liquid state or melting. At this point, the temperature of the solid stops rising, despite the continual input of heat, and it remains constant until all of the solid is...
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Phase Transitions: Sublimation and Deposition02:33

Phase Transitions: Sublimation and Deposition

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Some solids can transition directly into the gaseous state, bypassing the liquid state, via a process known as sublimation. At room temperature and standard pressure, a piece of dry ice (solid CO2) sublimes, appearing to gradually disappear without ever forming any liquid. Snow and ice sublimate at temperatures below the melting point of water, a slow process that may be accelerated by winds and the reduced atmospheric pressures at high altitudes. When solid iodine is warmed, the solid sublimes...
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Orientational Transition in a Liquid Crystal Triggered by the Thermodynamic Growth of Interfacial Wetting Sheets
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Geometric structure and information change in phase transitions.

Eun-Jin Kim1, Rainer Hollerbach2

  • 1School of Mathematics and Statistics, University of Sheffield, Sheffield S3 7RH, United Kingdom.

Physical Review. E
|July 16, 2017
PubMed
Summary

We introduce a geometric method to study order-disorder transitions using forward and backward processes. Information length quantifies distinct states, revealing different dynamics for diffusion and advection in phase transitions.

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Area of Science:

  • Statistical Physics
  • Complex Systems
  • Nonlinear Dynamics

Background:

  • Stochastic processes govern many natural phenomena, including phase transitions.
  • Understanding the dynamics of order-disorder transitions is crucial in various scientific fields.

Purpose of the Study:

  • To develop a geometric methodology for analyzing stochastic processes in cyclic order-disorder transitions.
  • To differentiate between forward and backward processes using information length.

Main Methods:

  • A toy model for cyclic order-disorder transitions was developed.
  • Time-dependent probability density functions (PDFs) and information length (L) were calculated.
  • Geometric analysis of stochastic processes was employed.

Main Results:

  • Forward and backward processes exhibit distinct PDF behaviors and information length scalings.
  • Information length (L) scales differently with control parameter deviation (γ) and noise strength (D) for forward (diffusion) and backward (advection) processes.
  • A constant time scale for information change was identified during forward processes, independent of noise.

Conclusions:

  • Information length is a powerful geometric tool to distinguish between diffusion and advection in phase transitions.
  • The findings offer insights into bistable systems and repeated order-disorder transitions.