A thermo-electro-chemo-mechanical model for phase transition of physical hydrogel between solution and gel phases identified by crosslink density - Wu, Tao (2016)
In general, hydrogel is a class of hydrophilic crosslinked polymeric network, consisting of the network matrix and interstitial fluid. Literature search reveals that the previously published studies focused on the bulk (single) phase behavior or the gel-gel phase transition. In this thesis, a thermo-electro-chemo-mechanical model is developed mathematically for simulation of the solution-gel phase transition of physical hydrogels. By coupling the multiphysics effects together, the presently developed model consists of the governing equations for the equilibrium of forces, and the conservations of mass and energy. The constitutive equations are formulated by the second law of thermodynamics, which can reduce to the corresponding constitutive equations based on the non-equilibrium thermodynamic theory developed by Suo’s group (Hong, Zhao et al. 2008, Hong, Liu et al. 2009, Hong, Zhao et al. 2010), if the interface is ignored when only a single bulk phase exists, i.e. no phase transition occurs. Therefore, as the first academic contribution, the presently developed constitutive equations generally accounts for both the bulk phase and interface behavior. In other words, the non-equilibrium model proposed by Suo’s group (Hong, Zhao et al. 2008, Hong, Liu et al. 2009, Hong, Zhao et al. 2010) is just a special case of the present model, when the present two-phase control volume reduces to a single-phase one, in which only the gel phase with constant crosslink density exists in the hydrogel system. As the second contribution, the density of crosslinks is used to identify the phases for the present domain covering the gel and solution states, which are considered as two distinct phases, and an interface between them. The crosslink density is a much more accurate parameter for characterizing the phases, compared with the other options in the previously published studies, such as the volume fraction, temperature, or a simple numerical parameter, since the phase transition of the physical hydrogel between solid and liquid states is directly associated with the forming or breaking of the crosslinks subject to environmental stimuli. As a result, the solution phase is identified as the state when the crosslink density is small, while the gel as the state if the crosslink density becomes large. The interface is treated by two different methods, the sharp interface/configurational forces and the diffuse interface approaches, and an additional kinetic equation is imposed on the interface for its evolution during the phase transition. As the third contribution, a novel Ginzburg-Landau type of free energy is proposed to model the solution-gel phase transition, which accounts for the effects of crosslink density, and consists of the elastic, mixing, binding, polarization and interface contributions. The free energy is in a double-well profile with respect to the crosslink density. As mentioned above, there exist the solution and gel phases and the interface between the two phases, which are identified by the crosslink density. In other words, of the two wells within the free energy density, the one with the smaller crosslink density corresponds to the solution phase, and the other with the larger one to the gel phase. Finally, several case studies are conducted for analysis of the effect of chemical potential, pressure, surface tension and other parameters on the phase transition. After the reduction of the presently developed three-dimensional theoretical model to one-dimensional formulation, a MATLAB source code is developed, and then a spherically symmetrical solution-gel phase transition is numerically simulated both in water and in ionic solution for analysis of the thermal, electrical, chemical and mechanical influences on the solution-gel phase transition.