Ionic conductivity and hydrodynamic permeability of inhomogeneous (cavity doped) polyelectrolyte hydrogels

Abstract

Ion transport in polyelectrolyte membranes (charged hydrogels) is of significant technological (and biological) importance, but little is known of how micro-structural inhomogeneity affects ionic conductivity. Whereas a uniform electric field drives uni-directional electro-migrative and electro-osmotic ion fluxes in perfectly uniform microstructures, this study considers the influence of spherical inclusions/cavities on the hydrodynamic and ion permeability of charged hydrogels. Such cavities have a high permeability, but they can bear a much lower conductivity due to the partitioning of counter-ions between the cavity and bulk hydrogel phases, also inducing micro-scale electro-osmotic flow. To understand these, perturbations from a nonlinear Poisson–Boltzmann equilibrium state are used to compute the velocity disturbances, and electrostatic and ion-concentration polarization. These furnish three independent Onsager coefficients: one of which is the effective hydrodynamic permeability, and all of which contribute to the two principal electrical conductivities (distinguished by electrode configuration). Cavities with diameters in the range $10$ – $1000$ nm are found to be readily polarized, decreasing the effective conductivity of an otherwise uniform polyelectrolyte. In highly permeable hydrogels, however, electro-osmosis may enhance the electrical conductivity when flow is blocked by impenetrable electrodes. Explicit formulas for the hydrodynamic permeability are provided, complementing a simplified (Maxwell–Donnan) analysis of the conductivity, which neglects diffuse double-layer effects and ion-concentration perturbations.

Ionic Conduction and Dielectric Response of Nanoparticle-Coupled Hydrogel Network Polymer Electrolytes

“…The α 2 relaxation process was also confirmed from the dielectric derivative spectra 38 = ( ) 2 ( ) (ln ) der (11) eliminating the pure-loss conductivity contribution from the ε″(ω) and thereby resolving the dipolar process (see green circle symbols in Figure 5c). The representative ε der (ω) of HPE-NP-0 also shows a single α 2 relaxation at high frequency (Figure 5c), and the dashed and solid curves in Figure 5c are fits of a power law for EP and a derivative form of the HN function for the α 2 process: 38…”

“…The charge transport in hydrogels also plays an important role in the formation of electrical double layers at the electrolyte/ electrode interface of the supercapacitors, but little is known about how the hydrogel microstructure affects the ionic conductivity. 11 Therefore, the rational design of hydrogelbased electrolytes that retain their electrical and mechanical properties is essential to withstand harsh deformations and environments. 12−14 In recent years, the emerging double-network (DN) hydrogels, proposed by Gong and co-workers, 15 have attracted widespread attention because of their robust mechanical properties via the covalent or noncovalent-driven energy dissipation mechanism of two contrasting network structures, composed of one ductile loosely cross-linked network and the other rigid densely cross-linked network.…”

“…Slowing ion transport and becoming fragile and rigid eventually result in supercapacitors with low capacitance retention under mechanical deformations at low and/or high temperatures, limiting the long-term use of the supercapacitors. The charge transport in hydrogels also plays an important role in the formation of electrical double layers at the electrolyte/electrode interface of the supercapacitors, but little is known about how the hydrogel microstructure affects the ionic conductivity . Therefore, the rational design of hydrogel-based electrolytes that retain their electrical and mechanical properties is essential to withstand harsh deformations and environments. − …”

Hydrodynamic permeability of circular-inclusion-doped Brinkman media

“…Polyelectrolytes bearing a nanoscale structure are central to batteries (Harris 2018), fuel cells (Matos 2020), polymeric/soft electronics and sensors (Pan et al 2012) and biomaterials (Brown et al 2020;Zimmerman et al 2021). To explore these from a theoretical perspective, Hill (2022) recently proposed a theory for steady ionic transport in multi-porous charged media. The theory couples disturbances to the electrostatic potential, ion concentrations and electro-osmotic flow arising from a microstructure with heterogeneous charge-and hydrodynamic permeability.…”

“…Along these lines, Hill (2022) employed the ensemble averaging of Koch & Brady (1985) to derive an averaged momentum transport equation for dilute cavity-doped polyelectrolyte hydrogels in which coupled mass and ion fluxes are driven by an external pressure gradient and electric field. The averaged fluid velocity in a charged/polyelectrolyte porous medium that is doped with spherical inclusions (having an arbitrary, contrasting permeability) was expressed in terms of the dipole pressure disturbance of a single inclusion.…”