Simulation and Theory of Self-Assembled Networks:  Ends, Junctions, and Loops

The equilibrium assembly of chains capable of forming 3-fold junctions, a phenomenon observed in wormlike micelles, microemulsions, and ferromagnetic colloids, is studied by mean-field theory and Monte Carlo simulation. First, the theoretical description formulated by Tlusty and Safran ( Science 2000, 290, 1328) is revisited by treating junctions as the product of end-interior binary interactions rather than the ternary association of chain ends. Although the final results are equivalent, a new perspective is gained in which the gas−liquid transition is easily interpreted as a conventional condensation driven by explicit attractions. Grand canonical Monte Carlo simulation results on a model of hard spheres self-assembling into semiflexible chains with 3-fold junctions are in qualitative agreement with mean-field theory. In contrast, in a flexible model with equivalent chaining and junction association constants, the expected gas−liquid transition is apparently suppressed by the presence of loops, the products of intrachain junction formation. The effects of loop formation on the phase diagram are explored using a simple extension of the mean-field theory.