Electrostatic Potential Analysis in Polyelectrolyte Brush-Grafted Microchannels Filled with Polyelectrolyte Dispersion

In this study, the model framework that includes almost all relevant parameters of interest has been developed to quantify the electrostatic potential and charge density occurring in microchannels grafted with polyelectrolyte brushes and simultaneously filled with polyelectrolyte dispersion. The brush layer is described by the Alexander-de Gennes model incorporated with the monomer distribution function accompanying the quadratic decay. Each ion concentration due to mobile charges in the bulk and fixed charges in the brush layer can be determined by multi-species ion balance. We solved 2-dimensional Poisson–Nernst–Planck equations adopted for simulating electric field with ion transport in the soft channel, by considering anionic polyelectrolyte of polyacrylic acid (PAA). Remarkable results were obtained regarding the brush height, ionization, electrostatic potential, and charge density profiles with conditions of brush, dispersion, and solution pH. The Donnan potential in the brush channel shows several times higher than the surface potential in the bare channel, whereas it becomes lower with increasing PAA concentration. Our framework is fruitful to provide comparative information regarding electrostatic interaction properties, serving as an important bridge between modeling and experiments, and is possible to couple with governing equations for flow field.

Effect of Counterions on the Interaction among Concentrated Spherical Polyelectrolyte Brushes

The effect of counterions on interactions among spherical polyelectrolyte brushes (SPBs) was systematically investigated by rheology, small-angle X-ray scattering (SAXS) and wide-angle X-ray scattering (WAXS). The SPB particles consist of a solid polystyrene (PS) core with a diameter of ca.100 nm and a chemically grafted poly-(acrylic acid) (PAA) brush layer. Metal ions of different valences (Na+, Mg2+ and Al3+) were used as counterions to study the interactions among concentrated SPBs. The so-called “structure factor peak” in SAXS, the “local ordered structure peak” in WAXS and rheological properties indicated the interactions among concentrated SPBs. Combining SAXS, WAXS and rheology, the formation mechanism of the local ordered structure among PAA chains in the overlapped area of adjacent SPB, which was generated due to the bridge function of counterions, was confirmed. In contrast, excessive counterions shielded the electrostatic interaction among PAA chains and destroyed the local ordered structure. This work enriches our understanding of the polyelectrolyte assembly in concentrated SPBs under the effect of counterions and lays the foundations for SPB applications.

Charge Properties and Electric Field Energy Density of Functional Group-Modified Nanoparticle Interacting with a Flat Substrate

Functionalized nanofluidics devices have recently emerged as a powerful platform for applications of energy conversion. Inspired by biological cells, we theoretically studied the effect of the interaction between the nanoparticle and the plate which formed the brush layer modified by functional zwitterionic polyelectrolyte (PE) on the bulk charge density of the nanoparticle brush layer, and the charge/discharge effect when the distance between the particle and the plate was changed. In this paper, The Poisson–Nernst–Planck equation system is used to build the theoretical model to study the interaction between the nanoparticle and the plate modified by the PE brush layer, considering brush layer charge regulation in the presence of multiple ionic species. The results show that the bulk charge density of the brush layer decreases with the decrease of the distance between the nanoparticle and the flat substrate when the interaction occurs between the nanoparticle and the plate. When the distance between the particle and the plate is about 2 nm, the charge density of the brush layer at the bottom of the particle is about 69% of that at the top, and the electric field energy density reaches the maximum value when the concentration of the background salt solution is 10 mm.