We are establishing a comprehensive thermodynamic model to predict swelling behavior of hydrogels in brine solutions at 298 K. Hydrogels are three-dimensional hydrophilic crosslinked viscoelastic network of polymer chains. Depending on surrounding stimuli such as temperature, pressure, solvent composition, salt content, pH; hydrogels exhibit a significant volume change without changing their structural properties [1]. This interesting property is called swelling. Based on a thermodynamic equilibrium condition developed to describe swelling of nonionic hydrogels in brine solutions [2], Electrolyte Non-Radom Two Liquid (eNRTL) liquid activity coefficient model [3] has been utilized to express activity coefficient of solvents and solutes, and a semi empirical expression is derived [4] from the theory of rubber elasticity [5-6] to illustrate Helmholtz energy of crosslinked polymer network. In addition to solvent-ion interactions [3], interactions of solvents/ions with polymer segments [7], and change in long range columbic interactions due to the presence of polymer molecules are considered in the eNRTL model. To account for configurational change in entropy due to addition of polymer molecules, Flory Huggins lattice theory has been adopted. The correlation model for hydrogel swelling requires only two energy interaction parameters per binary and one network functionality parameter per hydrogel system. No concentration dependent binary or ternary interaction parameter is required. The thermodynamic model has been correlated by regressing experimental equilibrium properties [4] (swelling ratio and solute concentration in the gel phase) of the chemically crosslinked poly (N-isopropyl acrylamide) hydrogels in aqueous solutions of NaCl. Swelling of hydrogels in the solution is controlled by the interactions of species present in the gel. Model correlation results show excellent agreement with data up to NaCl saturation at 298 K and atmospheric pressure. Regressed parameters have been used to predict swelling behavior of similar systems [4] only by adjusting the hydrogel network parameter.
References:
[1] O. Okay, "General Properties of Hydrogels," in Springer Series on Chemical Sensors and Biosensors, vol. 6, Springer Berlin Heidelberg, 2009, pp. 1-14.
[2] G. Maurer and J. M. Prausnitz, "Thermodynamics of Phase Equilibrium for Systems Containing Gels," Fluid Phase Equilib, vol. 115, pp. 113-133, 1996.
[3] Y. Song and C.-C. Chen, "Symmetric Electrolyte Nonrandom Two-Liquid Activity Coefficient Model," Ind Eng Chem Res, vol. 48, no. 16, pp. 7788-7797, 2009.
[4] A. Hüther, X. Xu, and G. Maurer, "Swelling of N-isopropyl acrylamide hydrogels in aqueous solutions of sodium chloride," Fluid phase equilib, vol. 240, pp. 186-196, 2006.
[5] P. J. Flory, "Statistical mechanics of swelling of network structures," J Chem Phys, vol. 18, pp. 108-111, 1950.
[6] H. M. James and E. Guth, "Simple presentation of network theory of rubber, with a discussion of other theories," J Polymer Science, vol. 4, pp. 153-182, 1949.
[7] C.-C. Chen, "A Segment-based Local Composition Model for the Gibbs Energy of Polymer Solutions," Fluid Phase Equilib, vol. 83, pp. 301-312, 1993.
