Binodal

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A phase diagram displaying binodal (coexistence) curves as well as spinodal curves, and lower (LCST) and upper (UCST) critical solution temperatures. LCST-UCST plot.svg
A phase diagram displaying binodal (coexistence) curves as well as spinodal curves, and lower (LCST) and upper (UCST) critical solution temperatures.

In thermodynamics, the binodal, also known as the coexistence curve or binodal curve, denotes the condition at which two distinct phases may coexist. Equivalently, it is the boundary between the set of conditions in which it is thermodynamically favorable for the system to be fully mixed and the set of conditions in which it is thermodynamically favorable for it to phase separate. [1] In general, the binodal is defined by the condition at which the chemical potential of all solution components is equal in each phase. The extremum of a binodal curve in temperature coincides with the one of the spinodal curve and is known as a critical point.

Thermodynamics branch of physics concerned with heat, work, temperature, and thermal or internal energy

Thermodynamics is the branch of physics that deals with heat and temperature, and their relation to energy, work, radiation, and properties of matter. The behavior of these quantities is governed by the four laws of thermodynamics which convey a quantitative description using measurable macroscopic physical quantities, but may be explained in terms of microscopic constituents by statistical mechanics. Thermodynamics applies to a wide variety of topics in science and engineering, especially physical chemistry, chemical engineering and mechanical engineering, but also in fields as complex as meteorology.

Phase (matter) region of space (a thermodynamic system), throughout which all physical properties of a material are essentially uniform; region of material that is chemically uniform, physically distinct, (often) mechanically separable

In the physical sciences, a phase is a region of space, throughout which all physical properties of a material are essentially uniform. Examples of physical properties include density, index of refraction, magnetization and chemical composition. A simple description is that a phase is a region of material that is chemically uniform, physically distinct, and (often) mechanically separable. In a system consisting of ice and water in a glass jar, the ice cubes are one phase, the water is a second phase, and the humid air is a third phase over the ice and water. The glass of the jar is another separate phase.

In thermodynamics, chemical potential of a species is energy that can be absorbed or released due to a change of the particle number of the given species, e.g. in a chemical reaction or phase transition. The chemical potential of a species in a mixture is defined as the rate of change of free energy of a thermodynamic system with respect to the change in the number of atoms or molecules of the species that are added to the system. Thus, it is the partial derivative of the free energy with respect to the amount of the species, all other species' concentrations in the mixture remaining constant. The molar chemical potential is also known as partial molar free energy. When both temperature and pressure are held constant, chemical potential is the partial molar Gibbs free energy. At chemical equilibrium or in phase equilibrium the total sum of the product of chemical potentials and stoichiometric coefficients is zero, as the free energy is at a minimum.

Contents

Binary systems

In binary (two component) mixtures, the binodal can be determined at a given temperature by drawing a tangent line to the free energy. [1]

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Thermodynamic free energy

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The upper critical solution temperature (UCST) or upper consolute temperature is the critical temperature above which the components of a mixture are miscible in all proportions. The word upper indicates that the UCST is an upper bound to a temperature range of partial miscibility, or miscibility for certain compositions only. For example, hexane-nitrobenzene mixtures have a UCST of 19 °C, so that these two substances are miscible in all proportions above 19 °C but not at lower temperatures. Examples at higher temperatures are the aniline-water system at 168 °C, and the lead-zinc system at 798 °C.

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Spinodal

In thermodynamics, the limit of local stability with respect to small fluctuations is clearly defined by the condition that the second derivative of Gibbs free energy is zero. The locus of these points is known as the spinodal curve. For compositions within this curve, infinitesimally small fluctuations in composition and density will lead to phase separation via spinodal decomposition. Outside of the curve, the solution will be at least metastable with respect to fluctuations. In other words, outside the spinodal curve some careful process may obtain a single phase system. Inside it, only processes far from thermodynamic equilibrium, such as physical vapor deposition, will enable one to prepare single phase compositions. The local points of coexisting compositions, defined by the common tangent construction, are known as binodal (coexistence) curve, which denotes the minimum-energy equilibrium state of the system. Increasing temperature results in a decreasing difference between mixing entropy and mixing enthalpy, thus, the coexisting compositions come closer. The binodal curve forms the bases for the miscibility gap in a phase diagram. Since the free energy of mixture changes with temperature and concentration, the binodal and spinodal meet at the critical or consulate temperature and composition.

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A miscibility gap is a region in a phase diagram for a mixture of components where the mixture exists as two or more phases – any region of composition of mixtures where the constituents are not completely miscible.

References

  1. 1 2 IUPAC binodal curve definition http://old.iupac.org/goldbook/BT07273.pdf Archived 2017-05-17 at the Wayback Machine accessed 2/20/13

Redhi, Gyanisavan Govindsamy (2003). "5.7 Fitting Mathematical Equations to the Binodal Curve Data". THERMODYNAMICS OF LIQUID MIXTURES CONTAINING CARBOXYLIC ACIDS (PDF) (Ph.D.). University of Natal, Durban, South Africa. p. 123. Retrieved 22 July 2018.