Binodal in the context of LCST

Phase separation is the creation of two distinct phases from a single homogeneous mixture. The most common type of phase separation occurs between two immiscible liquids, such as oil and water. This type of phase separation is known as liquid-liquid equilibrium. Colloids are formed by phase separation, though not all phase separations form colloids - for example, oil and water can form separated layers under gravity rather than remaining as microscopic droplets in suspension.

A common form of spontaneous phase separation is termed spinodal decomposition; Cahn–Hilliard equation describes it. Regions of a phase diagram in which phase separation occurs are called miscibility gaps. There are two boundary curves of note: the binodal coexistence curve and the spinodal curve. On one side of the binodal, mixtures are absolutely stable. In between the binodal and the spinodal, mixtures may be metastable: staying mixed (or unmixed) in the absence of some large disturbance. The region beyond the spinodal curve is absolutely unstable, and (if starting from a mixed state) will spontaneously phase-separate.

In thermodynamics, the limit of local stability against phase separation 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. 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 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.