Entropy-driven self-assembly of nanoparticles into strings

Entropy calculations based on the Boltzmann equation reveal that well dispersed systems of nanoparticles have lower entropy than those in which the particles self-assemble into strings which behave as self-avoiding walks (SAWs). These predictions are verified against actual Monte Carlo simulations of the thermal random motion of nanoparticles in solution and in polymer melts. In both systems, simulations indicate a spontaneous aggregation into strings of n particles whose radius of gyration Rg(n) scales as n0.6, as in SAWs. Interestingly, we also observe that the number distribution of string sizes n, weighted by their corresponding gyration volume Rg(n)3, closely follows the entropy profile for SAWs of length n.