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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: Vaporization and Condensation02:39

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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: Melting and Freezing02:39

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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

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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 Transitions01:21

Phase Transitions

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A phase transition is the process in which a substance changes from one state of matter to another, like from a solid to a liquid, liquid to gas, or vice versa, at a specific temperature and under given pressure conditions. This change is spontaneous and is affected by alterations in temperature and pressure. These parameters impact the strength of the forces between molecules (intermolecular forces) in the substance.During a phase transition, both the initial and final phases of the substance...
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Phase Diagrams of Ternary Systems01:28

Phase Diagrams of Ternary Systems

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Consider a ternary system, which is composed of three components: water (W), ethanoic acid (E), and trichloromethane (T). Here, Ethanoic acid (E) is fully miscible with both water (W) and trichloromethane (T), meaning it can mix entirely with either of them. However, water and trichloromethane have partial miscibility, meaning they can only mix to a certain extent, beyond which two separate phases will form.The phase diagram of a ternary system is represented as an equilateral triangle, where...
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The Glass Transition: A Topological Perspective.

Arthur Vesperini1,2, Roberto Franzosi1,2, Marco Pettini3,4,5

  • 1Department of Physical Sciences, Earth and Environment (DSFTA), University of Siena, Via Roma 56, 53100 Siena, Italy.

Entropy (Basel, Switzerland)
|March 28, 2025
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Summary
This summary is machine-generated.

This study reveals that the glass transition in a frustrated network glass-former model is linked to significant changes in the topology of energy landscapes. These findings suggest a new perspective on phase transitions using topological theories.

Keywords:
Monte Carlodifferential topologyglass formerphase transitionsriemannian geometrystatistical mechanics

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Area of Science:

  • Condensed Matter Physics
  • Computational Physics
  • Materials Science

Background:

  • Network glass-formers are complex materials that resist crystallization due to inherent frustration.
  • Understanding the glass transition is crucial for materials science and condensed matter physics.
  • The relationship between geometric properties and topological changes in material states is an active research area.

Purpose of the Study:

  • To investigate the geometric and topological properties of the state space in a frustrated network glass-former model.
  • To explore the connection between thermodynamic singularities and the topology of the potential energy landscape.
  • To determine if topological changes in energy level sets are indicative of the glass transition.

Main Methods:

  • Microcanonical ensemble Monte Carlo simulations were employed to model a Lennard-Jones binary mixture.
  • Analysis focused on geometric markers of potential energy level sets, including mean curvature and scalar curvature variance.
  • The study utilized Pinkall's and Overholt's theorems to link geometric quantities to topological properties.

Main Results:

  • Two peaks in specific heat were identified at equilibrium and low energy, correlating with local ordering changes.
  • Inflection points were observed in geometric markers (mean curvature, principal curvature dispersion, scalar curvature variance) at these singularities.
  • These geometric changes were found to be closely related to the topological properties of the accessible state-space manifold.

Conclusions:

  • The glass transition in this model is strongly associated with significant alterations in the topology of energy level sets.
  • The findings suggest that the topological theory of phase transitions can provide a framework for understanding the glass transition.
  • This research offers new insights into the fundamental nature of glassy states and phase transitions.