Characterizing the Molecular Architecture of Hydrogels and Crosslinked Polymer Networks beyond Flory–Rehner—I. Theory

Abstract

In the early 1940s, Paul Flory and John Rehner published a series of papers on the properties of swellable polymeric networks. Originally intended for vulcanized rubber, their development has since been extensively used and extended to much more complex systems, such as hydrogels, and used to estimate the mesh size of such networks. In this article, we take a look at the development of the Flory−Rehner equation and highlight several issues that arise when using such a theory for the described hydrogel networks. We then propose a new approach and equations to accurately calculate the backbone molecular weight in-between crosslinks while explicitly accounting for the molecular mass of the crosslinker and branch segments. The approach also provides more applicable mesh dimensions, for complex networks with macromeric crosslinkers and/or a high degree of branching, as is the case of biocompatible hydrogels. The approach is finally illustrated by a case study comparing the values obtained with our proposed approach to those using the state-of-the-art approach.

The Influence of Oxidant on Gelatin–Tannin Hydrogel Properties and Structure for Potential Biomedical Application

“…Crosslinking density was calculated according to the Peppas–Barr–Howell equation [ 25 ] in water medium (pH = 7). Derived from the classical Flory–Rehner theory, this equation uses a macromolecular crosslinker in a significantly high concentration and produces more precise results than the original one.…”

Cross-Linked Density Determination of Natural Rubber Compounds by Different Analytical Techniques

“…The Flory-Rehner equation, based on the elastic response to the osmotic stress of the solvent, directly relates the rubber volume fraction at swelling equilibrium to the average molecular weight between cross-links. Thus, the average molecular weight between the cross-links can be determined in a simple way 76 .…”

Mathematical modelling of cross-linked polyacrylic-based hydrogels: physical properties and drug delivery

“…The list of cited works reports also theoretical papers where PDEs numerical methods and algorithms are described. The last type (type 3) of models is actually a large set of semi-empirical relationships available to correlate experimental data [25][26][27][28][29]. This approach appears intrinsically weak since it is not general based on first principles.…”