Determining equilibrium osmolarity in Poly(ethylene glycol) / Chondrotin sulfate gels mimicking articular cartilage

TL;DR

This study develops a multi-species polyelectrolyte gel model to predict the electro-chemical behavior of articular cartilage, focusing on osmolarity and swelling dynamics influenced by ionic and polymer properties.

Contribution

It introduces a comprehensive, experimentally guided model combining multiple polymers, ions, and cross-linking effects to understand cartilage-like gel behavior.

Findings

Swelling increases with higher charge per monomer and low bath solute concentration.

Swelling transitions can be continuous or discontinuous based on force balance.

The model predicts how pH and cross-link density affect gel swelling.

Abstract

We present an experimentally guided, multi-phase, multi-species polyelectrolyte gel model to make quantitative predictions on the 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 modeled using Doi rubber elasticity theory. Numerical studies on polymer volume fraction and net osmolarity (difference in the solute concentration across the gel) show the interplay between ionic bath concentrations, pH, polymer mass in the solvent and the average charge per monomer; governing the equilibrium swelled / de-swelled state of the gel. We conclude that swelling is aided due to a higher average charge per monomer (or a higher percentage of charged ChS component of the polymer), low solute concentration in the bath, a high pH or a low cross-link fraction. However, the swelling-deswelling transitions could be continuous or discontinuous depending upon the relative influence of the various competing forces.