An all-atom MD framework is developed to investigate densely grafted polyelectrolyte (PE) brushes. The solvation water of counterions is replaced by charged functional groups on the PE chains. The complex between counterions and the negatively charged PE segments overwhelms water by weight and volume above a critical grafting density, giving rise to a ''water-in-salt''-like scenario. Furthermore, the counterions and water molecules lose most of their mobility within the PE brushes as a result of electrostatic interactions and brush-induced confinement.

Controlling the direction and strength of nanofluidic electrohydrodyanmic transport in the presence of an externally applied electric field is extremely important in a number of nanotechnological applications. Here, we employ allatom molecular dynamics simulations to discover the possibility of changing the direction of electroosmotic (EOS) liquid flows by merely changing the electric field strength in a nanochannel functionalized with polyelectrolyte (PE) brushes. In exploring this, we have uncovered three facets of nanoconfined PE brush behavior and resulting EOS transport. First, we identify the onset of an overscreening effect: such overscreening refers to the presence of more counterions (Na + ) within the brush layer than needed to neutralize the negative brush charges. Accordingly, as a consequence of the overscreening, in the bulk liquid outside the brush layer, there is a greater number of co-ions (Cl − ) than counterions in the presence of an added salt (NaCl). Second, this specific ion distribution ensures that the overall EOS flow is along the direction of motion of the co-ions. Such coion-dictated EOS transport directly contradicts the notion that EOS flow is always dictated by the motion of the counterions. Finally, for large-enough electric fields, the brush height reduces significantly, causing some of the excess overscreeninginducing counterions to squeeze out of the PE brush layer into the brush-free bulk. As a result, the overscreening effect disappears and the number of co-ions and counterions outside the PE brush layer become similar. Despite that there is an EOS transport, this EOS transport, unlike the standard EOS transport that occurs due to the imbalance of the co-ions and counterions, occurs since a larger residence time of the water molecules in the first solvation shell of the counterions (Na + ) ensures a water transport in the direction of motion of the counterions. The net effect is the reversal of the direction of the EOS transport by merely changing the strength of the electric field.

Multivalent counterion-induced bridging interactions have been identified as the key mechanism of drastic collapse of the height of polyelectrolyte (PE) brushes. In this article, we employ all-atom molecular dynamics simulations to quantify the bridging interactions in PE brushes for counterions of different sizes and valences. We identify that unlike the current notion, bridging interactions are not the sole function of the counterion valence. Rather the bridging interactions depend on the fraction of counterions (of a given type) that get physically condensed on the PE backbone as well as the size of the counterion solvation shell. These mechanisms ensure that certain monovalent counterions demonstrate much stronger bridging interactions than those witnessed for certain divalent and trivalent counterions, while certain counterions of identical valences show drastically different bridging interactions. We argue that these counterion-specific bridging interactions eventually enable not only the significant reduction of the PE brush height in the presence of certain multivalent screening counterions but may also give rise to scenarios where the brush height reduction for certain monovalent counterions is larger than that observed for certain divalent and trivalent counterions. The latter observation contradicts the experimental findings where the multivalent counterions invariably led to a larger decrease in the height of the PE brushes; we argue that this discrepancy stems from the fact that in our simulations we only consider densely grafted and short (and hence less flexible) PE brushes that hinder the formation of different laterally inhomogeneous structures (such as pinned micelles and cylindrical bundles) that would have led to a larger brush height reduction (in experiments, which invariably consider longer and less densely grafted brushes, the formation of such inhomogeneous structures is primarily responsible for the larger brush height reduction in the presence of multivalent counterions). Finally, we also probe the dynamic properties of the counterions (i.e., their time-dependent displacements) and their bridging interactions (i.e., lifetime of bridging interactions).

All atom Molecular Dynamics (MD) simulations of planar Na+-counterion-neutralized Polyacrylic Acid (PAA) brushes are performed for varying degrees of ionization (and thereby varying charge density) and varying grafting density. Variation...

Polyelectrolyte brushes have been modeled using strong stretching theory with excluded volume effects and an expanded mass action law.

We develop a theory to study the generation of the streaming potential and the resulting electrochemomechanical energy conversion (ECMEC) in the presence of pressure-driven transport in nanochannels grafted with end-charged polyelectrolyte (PE) brushes. Our theory gives a thermodynamically self-consistent coupled description of the PE-brush and the electrostatics of the electric double layer (EDL) induced by the PE charges. The end-charged brushes localize the maximum EDL charge density away from the wall, thereby enabling a larger magnitude of pressure-driven transport to stream the ions downstream. This effect is retarded by the drag force imparted by the brushes as well as by the enhanced electroosmotic transport in a direction opposite to the pressure-driven transport. An interplay of these three issues leads to highly non-trivial electrohydrodynamic transport that eventually allows us to converge on appropriate properties of the brushes (e.g., grafting density and the number of monomers) that lead to the generation of a significantly larger streaming potential and a much improved efficiency of the ECMEC as compared to the brush-free nanochannels particularly at medium and high salt concentrations.

The influence of dynamical ion–ion correlations and ion pairing on salt transport in ion exchange membranes remain poorly understood. In this study, we use the framework of Onsager transport coefficients within atomistic molecular dynamics simulations to study the impact of ion–ion correlated motion on salt transport in hydrated polystyrene sulfonate membranes and compare with the results from aqueous salt solutions. At sufficiently high salt concentrations, cation–anion dynamical correlations exert a significant influence on both salt diffusivities and conductivities. Anion–anion distinct correlations, arising from the imbalance between the concentration of free (mobile) cations and anions, and the retarding effect of the fixed charge groups on cations, proves to be an additional important feature for polymer membranes. Our results demonstrate that dynamical correlations should become an important consideration in experimental measurements of salt diffusivities and conductivities for non-dilute salt solutions in polymer membranes.

Augmented strong stretching theory has been employed to establish that functionalization of nanochannels with polyelectrolyte brushes enhances electrokinetic energy conversion.