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Phase Transitions: Melting and Freezing02:39

Phase Transitions: Melting and Freezing

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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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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Combining Microfluidics and Microrheology to Determine Rheological Properties of Soft Matter during Repeated Phase Transitions
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Exploiting a semi-analytic approach to study first order phase transitions.

Carlos E Fiore1, M G E da Luz

  • 1Departamento de Física, Universidade Federal do Paraná, 81531-980 Curitiba, PR, Brazil. fiore@fisica.ufpr.br

The Journal of Chemical Physics
|January 10, 2013
PubMed
Summary

This study extends a computational method for analyzing first-order phase transitions, enabling accurate calculations of coexistence lines and thermodynamic properties across various models and conditions, even in athermal systems.

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Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Computational Physics

Background:

  • A previous method efficiently treated low-temperature first-order phase transitions using an analytical expression (W) for the order parameter.
  • This expression depended on coefficients derived from small system simulations, offering low computational cost.

Purpose of the Study:

  • To extend the validity of the W expression method beyond low temperatures.
  • To demonstrate its applicability to athermal problems and other thermodynamic quantities.
  • To illustrate its broad applicability across diverse physical models.

Main Methods:

  • Exploiting and extending a previously proposed analytical method for phase transitions.
  • Analyzing the general conditions for the method's validity, including its performance beyond the low-temperature limit.
  • Applying the method to a hard-core lattice gas model and other representative models (Potts, Bell-Lavis, associating gas-lattice).

Main Results:

  • The method's validity is extended to conditions beyond the low-temperature limit for strong first-order phase transitions.
  • The analytical expression (W) can be used to study athermal problems.
  • Relevant thermodynamic quantities such as entropy and energy can be obtained from W.
  • The method accurately determines coexistence lines and response functions.

Conclusions:

  • The generalized method offers a computationally efficient and broadly applicable approach for studying first-order phase transitions.
  • It provides accurate thermodynamic properties and is suitable for both thermal and athermal systems.
  • The method's mathematical features and broad applicability are demonstrated through various models.