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Topology-mediated conformations and scaling in hierarchical comb polymers via coupling between stiffness and excluded volume

Shelly Bhardwaj and Amit Kumar*

  • Theory & Simulation Laboratory, Department of Chemistry, Jamia Millia Islamia (a Central University), New Delhi 110025, India

  • *Contact author: akumar1@jmi.ac.in
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Phys. Rev. E 114, 055406 – Published 4 November, 2026

DOI: https://doi.org/10.1103/rghw-4dhl

Abstract

We develop a unified theoretical-computational framework to investigate topology-mediated conformations and topology-controlled scaling in semiflexible hierarchical comb polymers. Polymer connectivity is encoded through graph-theoretic operators, while semiflexibility, excluded-volume interactions, and hydrodynamic coupling are incorporated via an effective stiffness metric, self-consistent mean-field renormalization, and a preaveraged Oseen tensor within a generalized Rouse-Zimm description. The resulting spectral formulation provides direct access to global conformational and hydrodynamic observables, including radius of gyration, hydrodynamic size, intrinsic viscosity, and scattering signatures. Across hierarchical generations, we identify an architecture-driven crossover from anisotropic, open conformations at low branching to compact, near space-filling morphologies at higher branching, accompanied by systematic compression of the relaxation spectrum. The proposed framework enables the systematic investigation of a broad range of topology-dependent conformational behavior in hierarchical comb-of-comb polymers. Comparison with coarse-grained molecular dynamics simulations demonstrates that the framework captures both connectivity-controlled and interaction-renormalized regimes. These findings provide a general and experimentally testable description of topology-dynamics coupling in complex macromolecular systems and offer a predictive basis for interpreting scattering, dynamical, and rheological responses in hierarchically branched polymers.

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Phys. Rev. E 114, 055406– Published 4 November, 2026
  • Received 2 April 2026
  • Accepted 20 October 2026
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