Stimuli-responsive polyelectrolyte brushes for regulating streaming current magnetic field and energy conversion efficiency in soft nanopores

Abstract

The electrokinetic energy conversion, electroviscous effect, and induced internal and external magnetic fields in a smart polyelectrolyte grafted “soft” nanopore with pH responsiveness are studied here using an efficient molecular theory approach. The analysis is based on writing the total free energy of the system, including the conformational entropy of the flexible, self-avoiding polymer chains and the translational entropy of the mobile species, the electrostatic interactions, and the free energy due to chemical equilibrium reactions. Then, the free energy is minimized, while satisfying the necessary constraints to find the equilibrium state of the system. The predictions of the model are shown to be in excellent agreement with analytical solutions derived for special cases. We discuss the effect of different influential environmental and polymer brush parameters in detail and show that the electrokinetic energy conversion efficiency is optimal at moderate pH values and low background salt concentrations. It is also shown that the electrokinetic energy conversion efficiency is a complex function depending on both the environmental and polymer brush properties. Notably, high slip coefficients or high polymer grafting densities do not necessarily lead to a high energy conversion efficiency. Magnetic field readouts allow to measure streaming currents through nanopores without the need of electrodes and may be utilized as a secondary electronic signature in nanopore sensing techniques. It is shown that in nanopores modified with polyelectrolyte brushes, the induced magnetic fields can be tens of times larger than those in solid-state nanopores having only surface charges. We show that by tuning the pH, background salt concentration, surface charge, and polyelectrolyte grafting density, the magnitude of the internal and external magnetic fields can be significantly changed and controlled in a wide range.