# Numerical insights on ionic microgels: structure and swelling behaviour

## TL;DR

This study uses numerical simulations to analyze how charges and counterions influence the structure and swelling behavior of ionic microgels, highlighting the importance of explicit counterion modeling for accuracy.

## Contribution

It extends numerical microgel modeling to ionic systems with explicit counterions, revealing significant structural and transition behavior differences from implicit models.

## Key findings

- Charges significantly alter microgel structure near the VPT.
- Explicit counterion modeling aligns better with experimental data.
- VPT temperature shifts with increased charged monomers.

## Abstract

Recent progress has been made in the numerical modelling of neutral microgel particles with a realistic, disordered structure. In this work we extend this approach to the case of co-polymerised microgels where a thermoresponsive polymer is mixed with acidic groups. We compare the cases where counterions directly interact with microgel charges or are modelled implicitly through a Debye-H\"uckel description. We do so by performing extensive numerical simulations of single microgels across the volume phase transition (VPT) varying the temperature and the fraction of charged monomers. We find that the presence of charges considerably alters the microgel structure, quantified by the monomer density profiles and by the form factors of the microgels, particularly close to the VPT. We observe significant deviations between the implicit and explicit models, with the latter comparing more favourably to available experiments. In particular, we observe a shift of the VPT temperature to larger values as the amount of charged monomers increases. We also find that below the VPT the microgel-counterion complex is almost neutral, while it develops a net charge above the VPT. Interestingly, under these conditions the collapsed microgel still retains a large amount of counterions inside its structure. Since these interesting features cannot be captured by the implicit model, our results show that it is crucial to explicitly include the counterions in order to realistically model ionic thermoresponsive microgels.