(663d) A Thermodynamic Model for Hydrogels

Hydrogels are strongly hydrophilic polymers which are capable of storing immense amounts of water and other hydrophilic solvents. Next to established applications such as drying agents, recent research focuses on unique properties of so-called smart polymers for novel utilisations. Prominent representative of these are hydrogel networks based on poly(N-isopropylacrylamide) PNIPAAm, a biocompatible polymer with high sensitivity towards external stimuli. Based on the thermodynamic phenomenon of a liquid-liquid miscibility gap in the aqueous polymer solution, PNIPAAm hydrogel networks exhibit a characteristic and reversible temperature response: passing a critical temperature of approximately 35 °C (95 °F) the gel drastically switches its degree of swelling from highly swollen to collapsed. Similar swelling transitions are known in response to changes in the surrounding medium composition: the addition of co-solvents or solutes triggers a dramatic change in the degree of swelling. This sensitivity towards physiological substances as well as the thermal instability point near the body temperature make PNIPAAm highly attractive for applications in biological environments; prominent examples are pharmaceutical drug depots, wound moisture regulators or biomechanical sensors and actuators.

It is clear, that for such applications the understanding and modelling of the phase behaviour are essential factors, and a physical explanation of the swelling transition phenomena is required from the point of view of the molecular level. In our approach of a thermodynamic description of such hydrogel systems, we use the Perturbed-Chain Statistical Associating Fluid Theory PC-SAFT for modelling the physical attractive forces between the substances of the system to obtain the Helmholtz energy as significant thermodynamic quantity, and combine the benefits of this general equation of state with an additional elastic contribution for the Helmholtz energy. The distinct consideration of the elastic energy in the polymer network attributes to the stretching of the cross-linked polymer chains, when invading solvent molecules enforce a deformation of the network. Secondary to the elastic energy, an elastic excess pressure is induced in the gel phase depending on the degree of swelling. With an explicit calculation of this pressure difference, we are able to precisely solve modified isofugacity criteria for the equilibrium calculations between the phases of solution and gel. This way considering molecular interactions and elastic forces within the PC-SAFT equation of state, not only fundamental thermodynamic properties of the system can be modelled but also the degree of swelling of hydrogels and the exact gel composition, which is the crucial factor aiming at the applicability of hydrogels. In the present work hydrogel equilibria have been calculated successfully in good accordance with experimental data and a significant predictive capability of our model is proven, while varying both the temperature over a wide range and as well the composition of the surrounding aqueous solution phase, taking binary and ternary systems with PNIPAAm, water, several alcohols (methanol, ethanol, n-propanol, i-propanol), salts (NaCl, NaNO₃, (NH₄)₂SO₄), other organic compounds (acetone) and even oligomers into account (poly(ethylene glycol)), approaching biologically relevant conditions.