A phase diagram displaying spinodal curves, within the binodal coexistence curves and two critical points: an upper and lower critical solution temperature.
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 (the inflection point within a G-x or G-c curve, Gibbs free energy as a function of composition) is known as the spinodal curve.[1][2][3] 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.[3] In other words, outside the spinodal curve some careful process may obtain a single phase system.[3] Inside it, only processes far from thermodynamic equilibrium, such as physical vapor deposition, will enable one to prepare single phase compositions.[4] The local points of coexisting compositions, defined by the common tangent construction, are known as a 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, and thus the coexisting compositions come closer. The binodal curve forms the basis for the miscibility gap in a phase diagram. The free energy of mixing changes with temperature and concentration, and the binodal and spinodal meet at the critical or consolute temperature and composition.[5]
^G. Astarita: Thermodynamics: An Advanced Textbook for Chemical Engineers (Springer 1990), chaps 4, 8, 9, 12.
^Sandler S. I., Chemical and Engineering Thermodynamics. 1999 John Wiley & Sons, Inc., p 571.
^ abcKoningsveld K., Stockmayer W. H., Nies, E., Polymer Phase Diagrams: A Textbook. 2001 Oxford, p 12.
^P.H. Mayrhofer et al. Progress in Materials Science 51 (2006) 1032-1114 doi:10.1016/j.pmatsci.2006.02.002
curve, Gibbs free energy as a function of composition) is known as the spinodal curve. For compositions within this curve, infinitesimally small fluctuations...
Spinodal decomposition is a mechanism by which a single thermodynamic phase spontaneously separates into two phases (without nucleation). Decomposition...
the emulsion derives its stability from trapping between the binodal and spinodal curves in the phase diagram. However, the microscopic mechanisms responsible...
solution. Phase-transition processes can also be explained in terms of spinodal decomposition, where phase separation is delayed until the system enters...
transition points, states with zero slope, are called spinodal points. Their locus is the spinodal curve that separates the regions of the plane for which...
liquid and smallest possible vapor states are called spinodal points. Their locus forms a spinodal curve which bounds a region where no homogeneous stable...
energy of excess and mixing calculation and activity coefficients Spinodal – Spinodal Curves (Hessian matrix) Standard molar entropy Thermodynamic free...
extremum of a binodal curve in temperature coincides with the one of the spinodal curve and is known as a critical point. In binary (two component) mixtures...
at temperatures ranging from 280 to 500 °C, especially at 475 °C, where spinodal decomposition of the supersaturated solid ferrite solution into Fe-rich...
that specific temperature and pressure, liquid and vapor can coexist. The spinodal line on right is the boundary of absolute instability of a solution to...
region of lower concentration to a region of higher concentration, as in spinodal decomposition. Diffusion is a stochastic process due to the inherent randomness...
fluid's spinodal curve as represented in a pressure–temperature diagram, and the BLEVE onset is a manifestation of explosive boiling, where the spinodal is...
display a miscibility gap. Separation into multiple phases can occur via spinodal decomposition, in which a single phase is cooled and separates into two...
co-exist in the phase diagram. Miscibility gaps in liquid states can cause spinodal decomposition, commonly referred to as oiling out, as commonly occurs in...
mixture components, the UCST is the shared maximum of the concave down spinodal and binodal (or coexistence) curves. The UCST is in general dependent on...
faster in supercritical fluids than in liquids, promoting nucleation or spinodal decomposition over crystal growth and yielding very small and regularly...
{\partial ^{2}\Delta _{\operatorname {mix} }G}{\partial x^{2}}}=0} ), the spinodal curve is defined. The conditions of the mixture in comparison to the two...
the mixture components, the LCST is the shared minimum of the concave up spinodal and binodal (or coexistence) curves. It is in general pressure dependent...
Bar-On, M.; Miller, H.D. (1975), "New computational method in the theory of spinodal decomposition", Phys. Rev. A, 11 (4): 1417–1429, Bibcode:1975PhRvA..11...
shown LSW theory to be robust and accurate. Even some systems that undergo spinodal decomposition have been shown to quantitatively obey LSW theory after initial...
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