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Concept
Upper critical solution temperature
Summary
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 , so that these two substances are miscible in all proportions above but not at lower temperatures. Examples at higher temperatures are the aniline-water system at (at pressures high enough for liquid water to exist at that temperature), and the lead-zinc system at (a temperature where both metals are liquid).
A solid state example is the palladium-hydrogen system which has a solid solution phase (H2 in Pd) in equilibrium with a hydride phase (PdHn) below the UCST at 300 °C. Above this temperature there is a single solid solution phase.
In the phase diagram of the 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 pressure.
The phase separation at the UCST is in general driven by unfavorable energetics; in particular, interactions between components favor a partially demixed state.
Temperature-responsive polymer
Some polymer solutions also have a lower critical solution temperature (LCST) or lower bound to a temperature range of partial miscibility. As shown in the diagram, for polymer solutions the LCST is higher than the UCST, so that there is a temperature interval of complete miscibility, with partial miscibility at both higher and lower temperatures.
The UCST and LCST of polymer mixtures generally depend on polymer degree of polymerization and polydispersity.
The seminal statistical mechanical model for the UCST of polymers is the Flory–Huggins solution theory.
By adding soluble impurities the upper critical solution temperature increases and lower critical solution temperature decreases.
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Lower critical solution temperature
The lower critical solution temperature (LCST) or lower consolute temperature is the critical temperature below which the components of a mixture are miscible in all proportions. The word lower indicates that the LCST is a lower bound to a temperature interval of partial miscibility, or miscibility for certain compositions only. The phase behavior of polymer solutions is an important property involved in the development and design of most polymer-related processes.
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 (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.
Binodal
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. In general, the binodal is defined by the condition at which the chemical potential of all solution components is equal in each phase.