Determining equilibrium osmolarity in poly(ethylene glycol)/chondrotin sulfate gels mimicking articular cartilage

We present an experimentally guided, multi-phase, multi-species polyelectrolyte gel model to make qualitative predictions on the equilibrium electro-chemical properties of articular cartilage. The mixture theory consists of two different types of polymers: poly(ethylene gylcol) (PEG), chondrotin sulfate (ChS), water (acting as solvent) and several different ions: H(+), Na(+), Cl(-). The polymer chains have covalent cross-links whose effect on the swelling kinetics is modeled via Doi rubber elasticity theory. Numerical studies on equilibrium polymer volume fraction and net osmolarity (difference in the solute concentration across the gel) show a complex interplay between ionic bath concentrations, pH, cross-link fraction and the average charge per monomer. Generally speaking, swelling is aided due to a higher average charge per monomer (or a higher particle fraction of ChS, the charged component of the polymer), low solute concentration in the bath, a high pH or a low cross-link fraction. A peculiar case arises at higher values of cross-link fraction, where it is observed that increasing the average charge per monomer leads to gel deswelling.