Lower critical solution temperature

Physical basis

A key physical factor which distinguishes the LCST from other mixture behavior is that the LCST phase separation is driven by unfavorable entropy of mixing. Since mixing of the two phases is spontaneous below the LCST and not above, the Gibbs free energy change (ΔG) for the mixing of these two phases is negative below the LCST and positive above, and the entropy change ΔS = – (dΔG/dT) is negative for this mixing process. This is in contrast to the more common and intuitive case in which entropies drive mixing due to the increased volume accessible to each component upon mixing.

In general, the unfavorable entropy of mixing responsible for the LCST has one of two physical origins. The first is associating interactions between the two components such as strong polar interactions or hydrogen bonds, which prevent random mixing. For example, in the triethylamine-water system, the amine molecules cannot form hydrogen bonds with each other but only with water molecules, so in solution they remain associated to water molecules with loss of entropy. The mixing which occurs below 19 °C is not due to entropy but due to the enthalpy of formation of the hydrogen bonds. Sufficiently strong, geometrically-informed, associative interactions between solute and solvent(s) have been shown to be sufficient to lead to an LCST.

The second physical factor which can lead to an LCST is compressibility effects, especially in polymer-solvent systems. For nonpolar systems such as polystyrene in cyclohexane, phase separation has been observed in sealed tubes (at high pressure) at temperatures approaching the liquid-vapor critical point of the solvent. At such temperatures the solvent expands much more rapidly than the polymer, whose segments are covalently linked. Mixing therefore requires contraction of the solvent for compatibility of the polymer, resulting in a loss of entropy.

Theory

Within statistical mechanics, the LCST may be modeled theoretically via the lattice fluid model, an extension of Flory–Huggins solution theory, that incorporates vacancies, and thus accounts for variable density and compressibility effects.

Newer extensions of the Flory-Huggins solution theory have shown that the inclusion of only geometrically-informed, associative interactions between solute and solvent are sufficient to observe the LCST.

Prediction of LCST (θ)

There are three groups of methods for correlating and predicting LCSTs. The first group proposes models that are based on a solid theoretical background using liquid–liquid or vapor–liquid experimental data. These methods require experimental data to adjust the unknown parameters, resulting in limited predictive ability . Another approach uses empirical equations that correlate θ (LCST) with physicochemical properties such as density, critical properties etc., but suffers from the disadvantage that these properties are not always available. A new approach proposed by Liu and Zhong develops linear models for the prediction of θ(LCST) using molecular connectivity indices, which depends only on the solvent and polymer structures. The latter approach has proven to be a very useful technique in quantitative structure–activity/property relationships (QSAR/QSPR) research for polymers and polymer solutions. QSAR/QSPR studies constitute an attempt to reduce the trial-and-error element in the design of compounds with desired activity/properties by establishing mathematical relationships between the activity/property of interest and measurable or computable parameters, such as topological, physicochemical, stereochemistry, or electronic indices. More recently QSPR models for the prediction of the θ (LCST) using molecular (electronic, physicochemical etc.) descriptors have been published. Using validated robust QSPR models, experimental time and effort can be reduced significantly as reliable estimates of θ (LCST) for polymer solutions can be obtained before they are actually synthesized in the laboratory.