Scaling laws to predict humidity-induced swelling and stiffness in hydrogels

Abstract

From pasta to biological tissues to contact lenses, gel and gel-like materials inherently soften as they swell with water. In dry, low-relative-humidity environments, these materials stiffen as they de-swell with...

Quantifying the trade-off between stiffness and permeability in hydrogels

“…S3) in accordance with previous testing procedures. 27 Indeed, the stiffness of the hydrogels increases as crosslinker ratio increases (Fig. 2b, blue).…”

“…We and others have shown that changing crosslinking simply changes ϕ poly (or the equilibrium swelling state) and minimally affects other molecular properties. 27,50 That is, in eqn (2), the monomer size, a , and excluded volume, v , do not change with crosslinker amount—only ϕ poly changes. As such, hydrogels that differ only by crosslinking can be viewed as being a part of the same polymer family.…”

“…Previously, we adopted this theory to successfully characterize changes in stiffness, osmotic pressure, and swelling by varying crosslinking density. 27 The semi-dilute theory is a simple, elegant, and experimentally proven description that produces results that are indistinguishable from the more thorough, but complex Flory–Rehner theory that combines Flory–Huggins solution thermodynamics with Gaussian-chain (rubber-like elasticity effects) due to crosslinking. 17,39,40 While the semi-dilute theory does not strictly consider crosslinks, we can assume that the mesh size and corresponding swelling state is set by crosslinking and the osmotic pressure of the environment.…”

“…This modification of the bulk modulus also equivalently changes the osmotic pressure, K ∼ Π . 27,38 In a semi-dilute system, the precise relationship (des Cloiseaux law) between stiffness, osmotic pressure, and polymer volume fraction iswhere k is the Boltzmann constant, T is absolute temperature, a is the monomer size, and v is the excluded volume of the monomer that depends on the Flory interaction parameter, χ , such that 38 v = a 3 (1 − 2 χ ).…”

“…The feasibility of varying crosslinking density to modify stiffness, permeability, as well as a multitude of other properties has been widely confirmed. Stiffness-focused studies [25][26][27] have found that higher crosslinking densities generally result in stiffer gels, which is due to a reduced mesh size of the polymer and a denser network structure. 15,16,28,29 Transport-focused studies have found that crosslinking can modify gas or solute permeability 7,[30][31][32][33] where lower crosslinking densities generally result in higher permeable gels, [34][35][36][37] which is due to the enlarged mesh size and enhanced porosity of the network.…”