Effect of Hydrodynamic Interactions and Flow on Charge Transport in Redox-Active Polymer Solutions

Abstract

Redox-active polymers (RAPs) are a subclass of polyelectrolytes that can store charge and undergo redox selfexchange reactions. RAPs are of great interest in the field of redox flow batteries (RFBs) due to their ability to quickly charge and discharge, their chemical modularity, and their molecular size. However, designing RAPs for efficient charge transport at the molecular level requires a fundamental understanding of the charge transport mechanisms that occur in RFBs. Previous work from our group has explored these mechanisms, and in this paper, we seek to improve upon the previous model by incorporating both hydrodynamic interactions (HIs) and out-of-equilibrium dynamics, which are both highly pertinent to flow battery systems. We use a hybrid Brownian dynamics and Monte Carlo simulation to model redox-active polymer chains in both dilute and semidilute solutions. This model is used to show that HI is an important feature when charge hopping is not the major mechanism for charge displacement and leads to more rapid segmental and translational motion of polymer chains that expedites charge transport at low polymer concentrations. We demonstrate that strong extensional flows may result in either enhanced or decreased transport depending on the fraction of charges present on the RAP chain. We show that flow not only can promote charge transport by extending polymer conformations but can also suppress nonadjacent charge hopping processes that are important for transport at high charge fractions. Shear flows can similarly enhance charge transport through chain extension, but tumbling dynamics lead to oscillatory displacements that become dominant features with high charge fractions and strong flows.

Controlling Charge Percolation in Solutions of Metal Redox Active Polymers: Implications of Microscopic Polyelectrolyte Dynamics on Macroscopic Energy Storage

“…Our model uses a “freely draining” model, where polymer diffusion is only related to the number of monomers in the chain; this is known as the Rouse model , and while computationally simple is known to make the incorrect prediction that the polymer diffusion constant is not dependent on its conformational size. Hydrodynamic interactions, if included, would instead lead to the correct result that the diffusion constant of a chain is instead inversely related to the size of the polymer coil (i.e., D ∼ 1/ R G ). , This is directly shown in our DLS results, which are based on the established connection , between coil size and diffusion constant (Figures S11 and S12). As the salt concentration increases, we speculate that the corresponding decrease in coil size (Figure S13) gives rise to a larger diffusion constant and thus a smaller residence time τ res .…”

“…In addition to the role of self-exchange, charge percolation in RAPs is strongly modulated by polyelectrolyte dynamics, arising as a function of the ionic strength of the medium. These effects are known in solutions of polyelectrolytes such as polystyrenesulfonate − but until recently have been described in RAPs by us and others . Studies of viologen- and ferrocene-containing RAPs performed below their overlap concentration have shown a steep increase in the limiting current for electrolysis of RAPs at ultramicroelectrodes as the concentration of supporting electrolyte increases from 0 to ∼100 mM, with a slight decrease afterward up to ∼1 M. A systematic experiment across self-exchange and supporting electrolyte concentration conditions using M-RAPs in combination with molecular dynamics simulations could elucidate the required conditions to improve charge transport in these electrolytes and hence inform NaRFB experiments.…”