Influence of small rings on the thermodynamics of equilibrium self-assembly

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 Delta S-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 Delta S-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. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4730161]