The Study of Swelling Kinetics of Polyelectrolyte Gels

Sen, Swati (2019) The Study of Swelling Kinetics of Polyelectrolyte Gels. PhD thesis, Indian Institute of Science Education and Research Kolkata.

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Abstract

Soft condensed matter is a vast field of interdisciplinary science for which the basic concepts of equilibrium and non-equilibrium statistical mechanics can be applied to systems in which the constituent particles broadly obey Newtonian dynamics. The subject matter of my thesis is the theoretical study of polyelectrolyte (PE) gels, a sub-topic of soft matter and polymer science, which are crosslinked structures of polymer chains containing free and bound ions. Owing to their elastic and viscous properties, these polymeric gels can retain and release a large amount of solvent in response to ambient conditions. In addition, the electrostatic repulsion and ion pressure allow the PE gels to swell to enormous sizes. In my thesis work we study both the equilibrium properties of such phases and kinetics of transition among them. The major focus of this thesis has been to calculate the kinetics of isothermal swelling of polymer gels by developing a theory to address the large deformations of the gels away from Hookean limits. In the process, equipped with the basic understanding of equilibrium properties of polymeric and polyelectrolyte (PE) gels, we theoretically solve the equation of motion for elemental gel volumes undergoing swelling in a salt-free solvent. Before embarking on the swelling kinetics, we first explore further the equilibrium phase behaviour of gels in terms of volume phase transition and two-phase coexistence. We chose the room temperature for the isothermal swelling to avoid the critical slowing down of any kinetic process at the critical temperature, which was well below the swelling temperature for the chosen set of parameters. The mean-field free energy has been modified to include partial ionizability, suitable for many recent experiments. In addition, we derived an analytical expression of charge of the PE gel in the expanded state. Equipped with the free energy, we proceeded with the two methods to solve the constitutive equation of motion for swelling kinetics, which are the Bulk Modulus Method (BMM) that uses a linear stress-strain relationship, and the Stress Relaxation Method (SRM) that uses a phenomenological expression of osmotic stress. These two methods for the swelling kinetics are explored in both the spherical and Cartesian geometries. The calculation provides the spatial and temporal profiles for the displacement variable, polymer density, osmotic stress, and degree of ionization, along with the time evolution of the gel-front location. Comparing the profiles of the same variables obtained from BMM and SRM we estimated the bulk modulus of the PE gel as functions of different ambient conditions. We note that this dynamical method to calculate the elastic modulus is valid only for small deformations. Consequently, an analytical expression of the elastic modulus from the linearized expression of osmotic stress (in the small deformation limit) is derived. To check the applicability of our model, we match the gel-front locations with the experimental data, taken from the measurements of charged RAFT gels, to show an increase in gel-size with charge, and we also match the same for PNIPAM (uncharged) and imidazolium-based (charged) minigels. The agreement between our theoretical analysis and the experiments confirm the decrease of the gel modulus value with the increase of the charge. In addition to the dependency of charge, we further calculate the dependencies of the equilibrium size, total swelling time, and elastic modulus of the PE gel on solvent quality and crosslink density. We then applied SRM, which captures the non-linearities in the osmotic stress, for large deformations of the PE gel, and obtained the total swelling time of such gels with large strains. This result is beyond the scope of traditional linear theories. Intriguingly, a universal power-law dependency of the swelling time on charge and crosslink density is observed for all deformations. Results show that the linear theory underestimates the swelling time, and its deviation progressively increases with the degree of deformation. Further, the effective diffusivity for the swelling PE gels with the same initial polymer density is found to increase with the charge content in line with experiments. We match the time evolution of the gel-front locations for super-adsorbent, partially ionizable hydrogels tuning minimum number of parameters, the dielectric inhomogeneity, in our non-linear model (SRM). The agreement between experimental and theoretical results continues to confirm general diffusive behaviour for swelling of PE gels with a decreasing bulk modulus with increasing degree of ionization (charge). Finally, we study the swelling kinetics around the critical point and capture the deswelling process at a metastable state. Results show a dilation of swelling time at the critical point and a qualitative deviation of all the dynamical profiles for the critical isotherm compared to those from isotherms well-above the critical temperature.

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