Gel Formation in Reversibly Cross-Linking Polymers

Maud Formanek,Emanuela Zaccarelli,Francesco Sciortino,Angel J Moreno,Lorenzo Rovigatti

doi:10.1021/acs.macromol.0c02670

Abstract

By means of Langevin dynamics simulations, we investigate the gel formation of randomly functionalized polymers in solution, with the ability to form both intra- and intermolecular reversible bonds. Under highly dilute conditions, these polymers form soft nano-objects (so-called single-chain nanoparticles, SCNPs), resulting from the purely intramolecular cross-linking of the reactive functional groups. Here we show that the competition between intra- and intermolecular bonds at finite concentration is governed by a delicate balance of various entropic contributions and leads to a density dependent effective valence. System-spanning networks are formed at relatively low monomer densities and their stability is mediated by just a small number of intermolecular connections per chain. The formation of intermolecular bonds furthermore can induce a non-monotonic dependence of the polymer size on the density for long bond lifetimes. Concomitantly, the polymers in the percolating cluster adopt an intramolecular structure characteristic for self-avoiding chains, which constitutes a strong contrast to the fractal globular behavior of irreversible SCNPs in crowded solutions with purely topological interactions (no intermolecular bonds). Finally, we study the dynamics of the system, which displays signatures expected for reversible gel-forming systems. An interesting behavior emerges in the reorganization dynamics of the percolating cluster. The relaxation is mostly mediated by the diffusion over long distances, through breaking and formation of bonds, of chains that do not leave the percolating cluster. Regarding the few chains that are transiently free, the time they spend until they reattach to the cluster is solely governed by the bond strength.

Highlights

Single-chain nanoparticles (SCNPs) are soft nano-objects synthesized from a linear polymer precursor, which is functionalized with reactive groups capable of forming intramolecular bonds
One would wish to derive a thermodynamic description of the system, for example, according to Wertheim theory,[49,50] using inputs from computer simulations, which would allow us to evaluate the complete K − ρ phase diagram of these reversibly cross-linking polymers and to find the regions in which gel formation is possible
A few fundamental assumptions of thermodynamic perturbation theory (TPT) have to be satisfied in order to be able to describe the system according to its predictions: (i) bonds are strictly monofunctional, (ii) two molecules cannot share more than one bond, and (iii) molecules cannot form bonds with themselves

Summary

INTRODUCTION

Single-chain nanoparticles (SCNPs) are soft nano-objects synthesized from a linear polymer precursor, which is functionalized with reactive groups capable of forming intramolecular bonds. Reversibility means that synthesis is never “complete” and individual SCNPs of this kind can form intermolecular bonds in addition to their intramolecular bonds Article if their concentration is increased above the limit of high dilution. We expect phase separation of the system to be confined to very small densities through the combination of excluded volume interactions and the inherently limited “valence” of the polymers that originates from the locally small number of (monovalent) monomers capable of forming bonds With these ideas in mind, in this article, we present Langevin dynamics simulations of solutions of a bead-spring model for SCNPs with reversible bonds, exploring concentrations from high dilution to far beyond the overlap density.

SIMULATION DETAILS

RESULTS AND DISCUSSION

CONCLUSIONS

■ ACKNOWLEDGMENTS

■ REFERENCES