Structural and electrostatic properties between pH-responsive polyelectrolyte brushes studied by augmented strong stretching theory

Abstract

In this paper, we study electrostatic and structural properties between pH-responsive polyelectrolyte brushes by using a strong stretching theory accounting for excluded volume interactions, the density of polyelectrolyte chargeable sites and the Born energy difference between the inside and outside of the brush layer.In a free energy framework, we obtain self-consistent field equations to determine electrostatic properties between two pH-responsive polyelectrolyte brushes. We elucidate that in the region between two pH-responsive polyelectrolyte brushes, electrostatic potential at the centerline and osmotic pressure increase not only with excluded volume interaction, but also with density of chargeable sites on a polyelectrolyte molecule. Importantly, we clarify that when two pH-responsive polyelectrolyte brushes approach each other, the brush thickness becomes short and that a large excluded volume interaction and a large density of chargeable sites yield the enhanced contract of polyelectrolyte brushes. In addition, we also demonstrate how the influence of such quantities as pH, the number of Kuhn monomers, the density of charged sites, the lateral separation between adjacent polyelectrolyte brushes, Kuhn length on the electrostatic and structural properties between the two polyelectrolyte brushes is affected by the exclusion volume interaction. Finally, we investigate the influence of Born energy difference on the thickness of polyelectrolyte brushes and the osmotic pressure between two pH-responsive polyelectrolyte brushes.

Electric double layer of spherical pH-responsive polyelectrolyte brushes in an electrolyte solution: A strong stretching theory accounting for excluded volume interaction and mass action law

“…[48][49][50][51][52][53][54][55][56] To improve the present theory, we can account for ionic size in electrolyte solutions [57][58][59][60]. However, since we consider the cases where salt concentration and polyelelctrolyte charge density are not high, excluded volume effect of electrolyte ions is negligible, as mentioned in [42]. In the future, we will try to obtain a more complete model of the pH-responsive polyelectrolyte brushes considering other effects such as solvent polarization [61][62][63][64][65][66][67][68], ionic correlation [69] and the polarization of ions [70][71][72].…”

“…Very recently, the author of [42] improved the strong stretching theory by taking into account Born energy and ionic size, and investigated the osmotic pressure between two pH-responsive polyelectrolyte brushes and the height of polyelectrolyte brushes. Although Budkov's group [43][44][45][46][47] addressed probability density functions for star-like molecules or zwitterionic and multipolar molecules by using nonlocal statistical field theory, they did not investigate spherical polyelectrolyte brushes.…”

All-atom molecular dynamics simulations of polymer and polyelectrolyte brushes

“…Distances from the grafted carbon represent the slabs where we perform the averaging. The table has been reproduced from Pial, T. H.; Das, S., Machine learning enabled quantification of the hydrogen bonds inside the polyelectrolyte brush layer probed using all-atom molecular dynamics simulations, Soft Matter, 2022, 18 (47) all-atom MD simulation data and used the machine learningbased clustering approach. Subsequently, we plotted the cluster representing the water-water hydrogen bonds for each case in the v, r space [see Fig.…”

“…While there is a lot of flexibility in synthesizing PE brushes for a specific application, it remains a challenge to predict its exact behavior in each setting due to a large number of microscopic and environmental variables that regulate such behavior. These variables include the molecular weight of the polymer chains, polydispersity, 41 chemical composition of the chains, solvent type, 42 solvent-monomer interactions, 43 screening counterion valence, 44 counterion structure, the position of the functional group in the chain (side chain or main chain 45,46 ), pH of the solution, 47 temperature of the system, concentration and type of the added salt (in addition to the screening counterions), etc. Moreover, additional complexities arise due to the highly non-linear inter-dependence of these different variables.…”