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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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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: Vaporization and Condensation02:39

Phase Transitions: Vaporization and Condensation

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The physical form of a substance changes on changing its temperature. For example, raising the temperature of a liquid causes the liquid to vaporize (convert into vapor). The process is called vaporization—a surface phenomenon. Vaporization occurs when the thermal motion of the molecules overcome the intermolecular forces, and the molecules (at the surface) escape into the gaseous state. When a liquid vaporizes in a closed container, gas molecules cannot escape. As these gas phase...
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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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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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States of Matter and Phase Changes00:59

States of Matter and Phase Changes

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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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Related Experiment Video

Updated: Oct 6, 2025

Combining Microfluidics and Microrheology to Determine Rheological Properties of Soft Matter during Repeated Phase Transitions
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Combining Microfluidics and Microrheology to Determine Rheological Properties of Soft Matter during Repeated Phase Transitions

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Moment-generating function zeros in the study of phase transitions.

R G M Rodrigues1, B V Costa1, L A S Mól1

  • 1Laboratório de Simulação, Departamento de Física, ICEx, Universidade Federal de Minas Gerais, 31720-901 Belo Horizonte, Minas Gerais, Brazil.

Physical Review. E
|January 15, 2022
PubMed
Summary

This study introduces a novel method using energy probability distribution (EPD) zeros to analyze phase transitions more efficiently. The new approach reduces computational cost, enabling studies of complex systems and external field effects.

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Area of Science:

  • Statistical mechanics
  • Computational physics

Background:

  • Partition function zeros are crucial for understanding phase transitions.
  • Fisher zeros method has implementation challenges.
  • Energy probability distribution (EPD) zeros offer an alternative with polynomial reduction.

Purpose of the Study:

  • To present a new formulation based on EPD zeros.
  • To further reduce polynomial degree while maintaining accuracy.
  • To offer a computationally cheaper alternative for studying phase transitions.

Main Methods:

  • Developing a novel formulation utilizing EPD zeros.
  • Implementing polynomial degree reduction techniques.
  • Extending the method for phase transitions in external fields.

Main Results:

  • The proposed method significantly reduces polynomial degree compared to existing EPD zero methods.
  • The approach demonstrates enhanced computational efficiency.
  • The method maintains accuracy in analyzing phase transitions.
  • The formulation is readily extendable to systems with external fields.

Conclusions:

  • The new EPD zero formulation provides a more computationally efficient and accurate method for studying phase transitions.
  • This advancement allows for the analysis of previously intractable systems.
  • The method's adaptability to external fields broadens its applicability in statistical mechanics research.