thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed b ...

, the limit of local stability against

phase separation Phase separation is the creation of two distinct Phase (matter), phases from a single homogeneous mixture. The most common type of phase separation is between two immiscible liquids, such as oil and water. This type of phase separation is kn ...

with respect to small fluctuations is clearly defined by the condition that the

second derivative In calculus, the second derivative, or the second-order derivative, of a function is the derivative of the derivative of . Informally, the second derivative can be phrased as "the rate of change of the rate of change"; for example, the secon ...

Gibbs free energy In thermodynamics, the Gibbs free energy (or Gibbs energy as the recommended name; symbol is a thermodynamic potential that can be used to calculate the maximum amount of Work (thermodynamics), work, other than Work (thermodynamics)#Pressure–v ...

is zero. :

0

The locus of these points (the inflection point within a G-x or G-c curve,

as a function of

composition Composition or Compositions may refer to: Arts and literature *Composition (dance), practice and teaching of choreography * Composition (language), in literature and rhetoric, producing a work in spoken tradition and written discourse, to include ...

) is known as the spinodal curve.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.Koningsveld K., Stockmayer W. H., Nies, E., ''Polymer Phase Diagrams: A Textbook''. 2001 Oxford, p 12. For compositions within this curve, infinitesimally small fluctuations in composition and density will lead to phase separation via

spinodal decomposition Spinodal decomposition is a mechanism by which a single thermodynamic Phase (matter), phase spontaneously separates into two phases (without nucleation). Decomposition occurs when there is no Thermodynamics, thermodynamic barrier to phase separatio ...

. 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 Thermodynamic equilibrium is a notion of thermodynamics with axiomatic status referring to an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable ...

, such as

physical vapor deposition Physical vapor deposition (PVD), sometimes called physical vapor transport (PVT), describes a variety of vacuum deposition methods which can be used to produce thin films and coatings on substrates including metals, ceramics, glass, and polym ...

, will enable one to prepare single phase compositions. 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 A miscibility gap is a region in a phase diagram for a mixture In chemistry, a mixture is a material made up of two or more different chemical substances which can be separated by physical method. It is an impure substance made up of 2 or more ...

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.

Criterion

For binary solutions, the thermodynamic criterion which defines the spinodal curve is that the second derivative of free energy with respect to density or some composition variable is zero.Sandler S. I., ''Chemical and Engineering Thermodynamics''. 1999 John Wiley & Sons, Inc., p 557.

Critical point

Extrema of the spinodal in a temperature vs composition plot coincide with those of the binodal curve, and are known as critical points.Koningsveld K., Stockmayer W. H., Nies, E., ''Polymer Phase Diagrams: A Textbook''. 2001 Oxford, pp 46-47. The spinodal itself can be thought of as a line of pseudocritical points, with the

correlation function A correlation function is a function that gives the statistical correlation between random variables, contingent on the spatial or temporal distance between those variables. If one considers the correlation function between random variables ...

taking a scaling form with non-classical

critical exponents Critical exponents describe the behavior of physical quantities near continuous phase transitions. It is believed, though not proven, that they are universal, i.e. they do not depend on the details of the physical system, but only on some of its g ...

. Strictly speaking, a spinodal is defined as a mean field theoretic object. As such, the spinodal does not exist in real systems, but one can extrapolate to infer the existence of a pseudospinodal that exhibits critical-like behavior such as critical slowing down.

Isothermal liquid-liquid equilibria

In the case of ternary isothermal liquid-liquid equilibria, the spinodal curve (obtained from the Hessian matrix) and the corresponding critical point can be used to help the experimental data correlation process.

References

{{states of matter Thermodynamics