Complex Conductivity Spectra of Nonporous and Porous Hydrogels

This paper reports complex conductivity spectra of two types of hydrogels. The first is a nonporous cross-linked polyacrylamide (PAAm), samples of which are immersed in KCl electrolytes with concentrations up to 100 mmol L^–1. Comparing these spectra with the theory of Hollingsworth and Saville for ideal electrolyte solutions highlights notable differences; these are tentatively attributed to hindered ion mobility and/or ion binding that imparts polyelectrolyte characteristics. The second is a foamed xanthan gum (XG) solution that is gelled by a coexisting polyacrylamide (PAAm) network. These XG-PAAm hydrogels are remarkably compliant, porous polyelectrolytes, which can be subjected to large compressive strain ϵ_x, and used to interpret the conductivity and relative dielectric permittivity on the basis of the void fraction ϕ and aspect ratio γ varying with ϵ_x. Here, ϕ decreases from the initial value ϕ = ϕ₀ ≈ 0.77, where the voids are a dense network of connected spheres, to the limit in which ϕ → 0 as ϵ_x → ϕ₀ ≈ 0.77. The data are very well described by continuum theories for gas spheroids embedded in conducting and dielectric media. However, despite the conductivity spectra bearing qualitative similarities to those of ideal electrolyte solutions, the effective ion mobilities and concentrations required to establish such parallels are profoundly different. Together, the impedance analysis of PAAm and XG-PAAm hydrogels provides quantitative and qualitative evidence that ion transport in hydrogels─even conventionally ideal and uncharged hydrogels─is distinctly different from their ideal electrolyte counterparts. These insights may translate to interpreting complex biological media, pertinent to bioelectrical impedance analysis and studies of subcellular phase-separated domains.