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Updated: May 20, 2026

Liquid-cell Transmission Electron Microscopy for Tracking Self-assembly of Nanoparticles
Published on: October 16, 2017
Influence of small rings on the thermodynamics of equilibrium self-assembly
1James Franck Institute and Department of Chemistry, University of Chicago, Chicago, Illinois 60637, USA.
Abstract:
The competition between the formation of linear chain clusters and ring structures in an equilibrium self-assembling system is reexamined by developing a new Flory-Huggins type theory that combines an estimate for the loss of configurational entropy ΔS(ring) upon ring formation with the standard treatment of the free energy of a polydisperse solution of linear chains. The excess entropy of ring formation ΔS(ring) is obtained from an analytical fit to exact enumeration data for self-avoiding chains and rings with 30 or fewer steps on a cubic lattice. Illustrative calculations of the spinodal curves and the extent and the average degree of self-assembly highlight the physical conditions for which the cyclic structures impact the thermodynamic characterization of equilibrium self-assembling systems.
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