Effects of radially dependent parameters on proton transport in polymer electrolyte membrane nanopores

Abstract

A three-dimensional continuum model is explored to investigate the effects of radially dependent system parameters, such as relative permittivity and viscosity, on the transport of proton and water in nanoscale cylindrical pores of a fully hydrated polymer electrolyte membrane (PEM). The model employs Poisson, Nernst-Planck, and Stokes equations. Based on evidence from the literature for the presence of a stagnant water layer near the pore surface, we assume that a no-slip surface is located inside the pore, a few Angstroms from the pore wall. To solve the system numerically, the steady-state solution for the transport of protons and water is considered to be a perturbation around the equilibrium solution. Our results indicate that a radial variation of relative permittivity has the greatest influence on pore conductivity, reducing it by about 50% when compared to that of constant permittivity. On the other hand, viscosity plays the dominant role when the effective water drag within such pores is considered. We conclude that a continuum approach, including constant viscosity, is applicable in nanoscale models provided that the location of the no-slip surface is properly specified and the radial variation of the relative permittivity is taken into consideration.

Contact Resistance at PEM-PEM Interfaces: Charged Fluid Flow between Nanochannels

“…Together with [17] the Stokes equations [4] and [5] simplify here to the ideal gas law for protons in water:…”

“…For the validation of our model, we also examine the electro-osmotic water drag (EOD) over a cross-section ‫ݔ‪ሺ‬ܣ‬ ଷ ሻ, see (4,17),…”

Analytical solution of the Poisson–Nernst–Planck–Stokes equations in a cylindrical channel

“…Also, the value for the proton diffusion coefficient, D, remains a topic of controversy in the literature. In simulations of a PNP-Stokes system for a Nafion pore, Ladipo et al (2011) have shown that a non-constant permittivity, increasing from about 10 near the pore wall to the value of bulk water (80) near the pore centre (Paul & Paddison 2004a,b), can indeed reduce the water drag by a factor of 2. Yet, only the inclusion of a Stern layer, containing immobile water molecules, addresses the water drag discrepancy successfully, bringing its value in line with experimental data.…”

“…To the contrary, there is strong evidence that a Stern layer must be incorporated to reproduce experimental findings. For a discussion of the issues surrounding the modelling of PEM nano-pores, their Stern layers and overlapping electric double layers, we refer to Ladipo et al (2011).…”

Equilibrium shapes of a heterogeneous bubble in an electric field: a variational formulation and numerical verifications

“…Similar problems also arise in the determination of the equilibrium shape of a pore channel embedded in a soft elastomer matrix coupled with electrostatics and diffusion [20][21][22]. To demonstrate our formulation, we focus on a single vapour bubble model for EHD as it represents a simple yet relevant model of EHD-enhanced boiling [10,15,16,[23][24][25][26][27][28].…”