Polyelectrolyte nonrandom two-liquid model: Thermodynamic frameworks and applications in ion exchange membranes and polymer swelling equilibrium




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Polyelectrolytes are polymers that have charged functional groups along the backbone chains. The charged polymers are attractive to counterions and repulsive to coions. Such behavior makes polyelectrolytes applicable in processes of separation, purification, biomedical and energy storage systems. Thermodynamic description of phase equilibrium of the mobile ions in polymer and solution phases draws great interest of research. There had been no limiting law for polyelectrolyte solutions like Debye-Hückel theory for simple electrolytes until Manning put forward his counterion condensation theory in 1969. He defined the dimensionless linear charge density of polyelectrolytes as the Manning parameter and stated that counterions would condense on the charged functional groups of polyelectrolytes when charge density was larger than certain critical value. Based on Manning’s limiting law, a few work has been put together to extend the generality of polyelectrolyte thermodynamic models. However, these models either failed capturing the experimental measurements or could not represent nonideality of all species in polyelectrolyte solutions. In this dissertation, a thermodynamic framework for polyelectrolyte solutions is established by introducing Manning’s limiting law to the electrolyte nonrandom two-liquid model (eNRTL). Manning’s limiting law describes the counterion condensation phenomenon by integration of the point-to-line electrostatic potential between mobile ions and polyions. The degree of the condensation ispositively related to the charge density of the polyion. The Pitzer-Debye-Hückel formula is used to capture the point-to-point electrostatic interactions between charged species. The eNRTL short-range equations are used to describe the interactionsbetween particles in their immediate neighborhood. Our model is a comprehensive one that works not only in the limiting case but also for any multicomponent system containing polyelectrolytes with high accuracy. Validation of the model framework is performed on multiple experimental data sets of mobile ion activity and osmotic coefficients for various polyelectrolyte solutions. The polyelectrolyte NRTL model is then applied to solve partitioning of mobile ions in ion exchange membranes and swelling equilibrium of hydrogels in saline solutions. The two cases are similar. Water and mobile ions transfer between the polymer phase and the external saline solutions. At equilibrium, chemical potentials of both water and salt are equal in the two phases. Salt adsorption amounts for membranes with different ion exchange capacities are well correlated with the polyelectrolyte NRTL model with limited number of adjustable parameters. For hydrogels, the extensive change in volume of the polymer structure results in additional excess free energy in the system. With phantom theory calculating the excess free energy from the volume change, degree of swelling data are also correlated with the polyelectrolyte NRTL model with high precision. The polyelectrolyte NRTL model projects nonideality of both the solvent and the mobile ions in polyelectrolyte solutions quantitatively. As validated by the correlation of mentioned experimental measurements, it is a practical and comprehensive model that can be applied to aqueous polyelectrolyte solutions covering the whole concentration range.



Thermodynamics, Polyelectrolyte, Ion exchange membrane, Hydrogels