# Non-Equilibrium Uptake Kinetics of Molecular Cargo into Hollow Hydrogels Tuned by Electrosteric Interactions

## TL;DR

This study models the non-equilibrium uptake kinetics of charged and dipolar molecules into hollow hydrogels, revealing how electrosteric interactions influence encapsulation regimes and rates.

## Contribution

It introduces a combined phenomenological and DFT approach to analyze how electrosteric interactions affect molecular uptake in hydrogels, covering various charge and dipole conditions.

## Key findings

- Polar cosolutes are hindered near collapsed gels due to excluded volume.
- Encapsulation time grows exponentially with cosolute charge for like charges.
- Surface adsorption states can slow down overall uptake.

## Abstract

In this work, we use a combination of a phenomenological effective cosolute-hydrogel interaction potential and Dynamic Density Functional Theory to investigate the full non-equilibrium encapsulation kinetics of charged and dipolar cosolutes by an isolated charged hollow hydrogel immersed in a 1:1 electrolyte aqueous solution. Our analysis covers a broad spectrum of cosolute valences z_c and electric dipole moments mu_c, as well as hydrogel swelling states and hydrogel charge densities. Our calculations show that, close to the collapsed state, the polar cosolutes are predominantly precluded and the encapsulation process is strongly hindered by the excluded-volume interaction exerted by the polymer network. Different equilibrium and kinetic sorption regimes (interface versus interior) are found depending on the value and sign of z_c and the value of mu_c. For cosolutes of the same sign of charge as the gel, the superposition of steric and electrostatic repulsion leads to an "interaction-controlled" encapsulation process, in which the characteristic time to fill the empty core of the hydrogel grows exponentially with z_c. On the other hand, for cosolutes oppositely charged to the gel, we find a "diffusion-controlled" kinetic regime, where cosolutes tend to rapidly absorb into the hydrogel membrane and the encapsulation rate only depends on the cosolute diffusion time across the membrane. Finally, we find that increasing mu_c promotes the appearance of metastable and stable surface adsorption states. For large enough mu_c, the kinetics enters a "adsorption-hindered diffusion", where the enhanced surface adsorption imposes a barrier and slows down the uptake.