https://doi.org/10.1140/epje/s10189-026-00568-w
Research - Soft Matter
Dynamical networking of polymer networks with dedicated cross-linker particles
1
Department of Physics, Stellenbosch University, 7600, Stellenbosch, South Africa
2
National Institute for Theoretical and Computational Sciences, 7602, Stellenbosch, South Africa
3
School of Chemistry and Physics, University of KwaZulu-Natal, 3209, Pietermaritzburg, Scottsville, South Africa
4
Dipartimento di Scienze Biomediche, Odontoiatrichee delle Immagini Morfologichee Funzionali, Università degli Studi diMessina, 98125, Messina, Italy
a
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Received:
18
November
2025
Accepted:
21
February
2026
Published online:
1
April
2026
Abstract
This paper extends a field-theoretical dynamical networking formalism for mesoscopic polymer dynamics to explicitly include dedicated cross-linker particles. Cross-linkers are represented within a Martin–Siggia–Rose generating functional and reversibly coupled to polymers through Gaussian networking fields, enabling an approximation scheme that reduces their degrees of freedom while remaining compatible with polymer dynamics. The framework is applied to a two-species polymer system in which intra- and inter-species cross-linking are assigned different statistical advantages. Effective networking potentials are derived and used to calculate correlation functions and dynamic structure factors. To validate these results, molecular dynamics simulations of semi-flexible polymers with reversible intra- and inter-species cross-linking are performed. Simulations show that cross-linking decreases polymer persistence lengths and local alignment, and the resulting trajectories yield dynamic structure factors consistent with theoretical predictions. Qualitative comparison reveals that in both approaches, cross-linking broadens the diffusive peaks and enhances the high-frequency tails of the structure factors. Together, theory and simulation provide complementary insights into the dynamics of cross-linked polymers, establishing a tractable framework that captures essential features observed in experiments and offering a basis for exploring more complex synthetic and biological networks.
Supplementary Information The online version contains supplementary material available at https://doi.org/10.1140/epje/s10189-026-00568-w.
© The Author(s) 2026
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