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Phase Diagrams of Ternary Systems

Phase Diagrams of Ternary Systems

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...

Solid–Solid Solutions

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.

Ellipses

Ellipses

An ellipse is formed when a right circular cone is intersected by an inclined plane that does not cut through its base. This intersection yields a closed, symmetric curve characterized by distinctive geometric properties. Most notably, an ellipse is defined as the collection of all points in a plane for which the combined distances to two fixed points—called the foci—remain constant.The ellipse features two principal axes: the major and the minor axes. The major axis is the longest...

Phase Diagrams

Phase Diagrams

A phase diagram combines plots of pressure versus temperature for the liquid-gas, solid-liquid, and solid-gas phase-transition equilibria of a substance. These diagrams indicate the physical states that exist under specific conditions of pressure and temperature and also provide the pressure dependence of the phase-transition temperatures (melting points, sublimation points, boiling points). Regions or areas labeled solid, liquid, and gas represent single phases, while lines or curves represent...

Phase Diagram

Phase Diagram

A phase diagram is a graphical representation of the physical states of a substance under different conditions of temperature and pressure. It shows the boundaries between solid, liquid, and gas phases and the conditions at which these phases coexist in equilibrium. An area in a phase diagram represents a single phase, whereas lines or phase boundaries represent the equilibrium between two phases.In the phase diagram of water, the boundary line between the solid and liquid states illustrates...

Phase Diagram

Phase Diagram

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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Orientational Transition in a Liquid Crystal Triggered by the Thermodynamic Growth of Interfacial Wetting Sheets

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Phase diagram of two-dimensional hard ellipses.

Gustavo Bautista-Carbajal¹, Gerardo Odriozola²

¹Departamento de Física, Universidad Autónoma Metropolitana-Iztapalapa, 09340 México, Distrito Federal, Mexico and Academia de Matemáticas, Universidad Autónoma de la Ciudad de México, 07160 México, Distrito Federal, Mexico.

The Journal of Chemical Physics

|June 2, 2014

Summary

This study maps the phase diagram of 2D hard ellipses, revealing isotropic, nematic, plastic, and solid phases. Simulations show transitions depend on particle shape and pressure, with evidence supporting first-order phase transitions.

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Area of Science:

Physics
Materials Science
Computational Chemistry

Background:

Understanding phase transitions in anisotropic systems is crucial for materials science.
Two-dimensional hard ellipses provide a fundamental model for studying shape-dependent ordering.

Purpose of the Study:

To determine the phase diagram of two-dimensional hard ellipses.
To investigate the influence of anisotropy and pressure on phase transitions.
To characterize the nature of observed phase transitions.

Main Methods:

Replica exchange Monte Carlo simulations were employed.
The isobaric ensemble was expanded in pressure to implement replica exchange.
Phase regions and transition characteristics were analyzed.

Main Results:

A phase diagram featuring isotropic, nematic, plastic, and solid phases was constructed.
Transitions were observed to be dependent on ellipse anisotropy and pressure (area fraction).
Bimodal probability density functions support first-order transitions for ordering involving quasi-long-range positional order.

Conclusions:

The phase behavior of 2D hard ellipses is complex and highly sensitive to anisotropy.
Simulations provide strong evidence for first-order transitions in several ordering processes.
The study contributes to the fundamental understanding of phase transitions in anisotropic systems.