Simulation of semidilute polymer solutions in planar extensional flow via conformationally averaged Brownian noise

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

Redox-active polymers (RAPs) are a subclass of polyelectrolytes that can store charge and undergo redox self-exchange 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.

Statistical Dynamics of Flow-Driven Globular Polymers

The response of collapsed polymers to the effects of linear mixed flow is studied theoretically in this paper using a model of a self-interacting finitely extensible Gaussian chain that evolves stochastically in the presence of random thermal fluctuations and an external fluid velocity gradient. The interactions that produce compact chain configurations are described by a harmonic pair potential of strength κ that acts between nonbonded sites on the chain backbone. Several chain properties are calculated analytically from this model as a function of κ for elongational and shear flows, including the dependence of the chain's steady-state mean-square end-to-end distance on the Weissenberg number of the flow, the time-dependence of the chain's relaxation to equilibrium from a steady-state of given chain extension, and the nature of the force-extension curves that are obtained from the free energy change between unperturbed and flow-stretched states of the chain. For both elongational and shear flows (but to different degrees), it is found that the greater the value of κ (and the more compact the chain), the more difficult it is, in general, for the imposed flow to induce a transition between compact and extended states, in broad agreement with available data from numerical simulations. For the relaxation process, the differences between the two flow types are more marked. The characteristic decay time for relaxation from a state prepared by elongational flow is essentially independent of κ, whereas in the case of a state prepared by shear flow, it is distinctly κ-dependent, the relaxation becoming faster at larger κ.

The relaxation dynamics of single flow-stretched polymers in semidilute to concentrated solutions

Recent experiments on the return to equilibrium of solutions of entangled polymers stretched by extensional flows [Zhou and Schroeder, Phys. Rev. Lett. 120, 267801 (2018)] have highlighted the possible role of the tube model's two-step mechanism in the process of chain relaxation. In this paper, motivated by these findings, we use a generalized Langevin equation (GLE) to study the time evolution, under linear mixed flow, of the linear dimensions of a single finitely extensible Rouse polymer in a solution of other polymers. Approximating the memory function of the GLE, which contains the details of the interactions of the Rouse polymer with its surroundings, by a power law defined by two parameters, we show that the decay of the chain's fractional extension in the steady state can be expressed in terms of a linear combination of Mittag-Leffler and generalized Mittag-Leffler functions. For the special cases of elongational flow and steady shear flow, and after adjustment of the parameters in the memory function, our calculated decay curves provide satisfactory fits to the experimental decay curves from the work of Zhou and Schroeder and earlier work of Teixeira et al. [Macromolecules 40, 2461 (2007)]. The non-exponential character of the Mittag-Leffler functions and the consequent absence of characteristic decay constants suggest that melt relaxation may proceed by a sequence of steps with an essentially continuous, rather than discrete, spectrum of timescales.

Recent progress in the science of complex coacervation

Complex coacervation is an associative, liquid-liquid phase separation that can occur in solutions of oppositely-charged macromolecular species, such as proteins, polymers, and colloids. This process results in a coacervate phase, which is a dense mix of the oppositely-charged components, and a supernatant phase, which is primarily devoid of these same species. First observed almost a century ago, coacervates have since found relevance in a wide range of applications; they are used in personal care and food products, cutting edge biotechnology, and as a motif for materials design and self-assembly. There has recently been a renaissance in our understanding of this important class of material phenomena, bringing the science of coacervation to the forefront of polymer and colloid science, biophysics, and industrial materials design. In this review, we describe the emergence of a number of these new research directions, specifically in the context of polymer-polymer complex coacervates, which are inspired by a number of key physical and chemical insights and driven by a diverse range of experimental, theoretical, and computational approaches.