Coordinated experimental analysis of swollen polymer networks shows linear synthesis-swelling correlations and reveals fundamental inconsistencies in theoretical equations

Hydrogels are water-swollen polymer networks with physical properties that are closely associated with the concentration of polymer in the system at thermodynamic equilibrium. Equilibrium swelling theory estimates the extent to which hydrogels swell in water based on the structure of the polymer network. However, it cannot precisely predict the physical properties of real hydrogels. Here, we show that equilibrium swelling theory overestimates the importance of the equilibrium-swollen polymer volume fraction. Instead, by precisely characterizing the swelling of structurally controlled libraries of crosslinked poly(vinyl alcohol) hydrogels and end-linked poly(ethylene glycol) diacrylate hydrogels, we found that the relaxed polymer volume fraction, immediately following network synthesis, precisely and linearly correlates to the initial polymer volume fraction. Independent of this first relationship, the extent of swelling from the relaxed polymer volume fraction to the equilibrium-swollen polymer volume fraction precisely and linearly correlates to the expected molecular weight between crosslinks of the network. These independent, cross-validated relationships motivate fundamental reanalysis of equilibrium swelling theory.