Thermodynamics, electrostatics, and ionic current in nanochannels grafted with pH-responsive end-charged polyelectrolyte brushes

Swelling and shrinking of two opposing polyelectrolyte brushes

Salt concentration and confinement effects affect the configuration of polyelectrolyte (PE) brushes due to electrostatic interactions. In this work, we develop a new theoretical model to analyze the electrostatics and swelling-shrinking behavior of two opposing PE brushes. By comparing three length scales, i.e., equilibrium brush height, separation distance, and Debye length, we obtain distinct scaling laws for brush height in different regimes. We provide explanations for the anomalous shrinkage of the PE brush with added salt reported in experiments and simulations, the applicability of the homogeneous brush assumption, and the confinement effect on the brush height. Our model can be used to shed light on the configuration and functionalities of PE-grafted interfaces, which play important roles in ion selective membranes and organism lubrication. We also anticipate that our method will be useful to understand the functionalities of other charged soft matter systems, such as hydrogel swelling and colloidal stability.

Theoretical Modeling of Chemical Equilibrium in Weak Polyelectrolyte Layers on Curved Nanosystems

Surface functionalization with end-tethered weak polyelectrolytes (PE) is a versatile way to modify and control surface properties, given their ability to alter their degree of charge depending on external cues like pH and salt concentration. Weak PEs find usage in a wide range of applications, from colloidal stabilization, lubrication, adhesion, wetting to biomedical applications such as drug delivery and theranostics applications. They are also ubiquitous in many biological systems. Here, we present an overview of some of the main theoretical methods that we consider key in the field of weak PE at interfaces. Several applications involving engineered nanoparticles, synthetic and biological nanopores, as well as biological macromolecules are discussed to illustrate the salient features of systems involving weak PE near an interface or under (nano)confinement. The key feature is that by confining weak PEs near an interface the degree of charge is different from what would be expected in solution. This is the result of the strong coupling between structural organization of weak PE and its chemical state. The responsiveness of engineered and biological nanomaterials comprising weak PE combined with an adequate level of modeling can provide the keys to a rational design of smart nanosystems.

Ionic current in nanochannels grafted with pH-responsive polyelectrolyte brushes modeled using augmented strong stretching theory

In this paper, we provide a theory to quantify the ionic current ( i ion ) in nanochannels grafted with pH-responsive polyelectrolyte (PE) brushes. We consider the PE brushes to be modeled by our recently proposed augmented strong stretching theory (SST) model that improves the existing SST models by incorporating the effects of excluded volume interactions and an extended mass action law. Use of such augmented SST for this problem implies that this is the first study on computing i ion in PE brush-grafted nanochannels accounting for the appropriate coupled configuration-electrostatic description of the PE brushes. i ion is obtained as functions of PE brush grafting density, medium pH and salt concentration ( c ∞ ), and the density of polyelectrolyte chargeable sites (PECS). For large c ∞ , i ion increases linearly with c ∞ (as for such c ∞ , i ion becomes independent of the PE charge and is dominated by the bulk mobility and number density of the electrolyte ions), whereas i ion is independent of c ∞ at small c ∞ (where the electric double layer electrostatics and the total number of ions in the system is dominated by the hydrogen ions). We further witness an enhancement of i ion for smaller pH and larger grafting density at low and moderate c ∞ , while there is little to no effect of the PECS density on the ionic current except for weakly grafted brushes at low c ∞ . We anticipate that this study will serve as a theoretical foundation for a large number of applications that are based on the brush-induced modification of the ionic current in a nanochannel.