Phase separation in polymers and gels: thermodynamic theory and experiment

Abstract: 

The thermodynamic theory of LCST type phase separation behaviour is presented. The thermodynamic model of the phase separation is derived from a simple two-state model using van’t Hoff type analysis (Figure 1) [1-5]. This approach allows obtaining theoretical curves describing temperature dependence of phase-separated fraction p(T) (for polymer solutions; Figure 1a) or swelling ratio r(T) (for gels; Figure 1b) dependent on physically meaningful parameters, such as enthalpy (ΔHvH) and entropy (ΔSvH) associated with this process. These quantities are called “van’t Hoff transition enthalpy and entropy” and are expressed per mol of cooperative units (i.e. polymer chains or their parts and water molecules that change their phase state simultaneously). The “van’t Hoff” quantities are always obtained from non-calorimetric measurements such as NMR, FTIR or gravimetric analyses. In contrast, “calorimetric enthalpy” obtained from DSC (ΔHcal) can be conveniently expressed per mol of monomeric units. The ratio of these two enthalpies yields the “size” of the cooperative unit (i.e. the number of monomeric units and the number of water molecules in the cooperative unit).

The application of this model will be briefly shown in several systems, such as:

i) polymeric solutions of poly(N‑isopropylacrylamide) (PNIPAAm) (Figure 1a) or poly(vinyl methyl ether) (PVME) or in the presence of various low-molecular additives [1,2] and

ii) single or double network hydrogel systems comprising of PNIPAAm, poly(N,N’-diethylacrylamide) (PDEAAm), polyacrylamide (PAAm) or poly(N-vinylcaprolactam) (PNVCLM) (Figure 1b) [3-5].

We also show a natural extension of the two-state model for UCST, hour-glass or closed-loop type phase behaviour systems, and a description of copolymer systems having several components with different phase separation temperatures.

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