Stability of the iterative solutions of integral equations as one phase freezing criterion

A recently proposed connection between the threshold for the stability of the iterative solution of integral equations for the pair correlation functions of a classical fluid and the structural instability of the corresponding real fluid is carefully analyzed. Direct calculation of the Lyapunov exponent of the standard iterative solution of HNC and PY integral equations for the 1D hard rods fluid shows the same behavior observed in 3D systems. Since no phase transition is allowed in such 1D system, our analysis shows that the proposed one phase criterion, at least in this case, fails. We argue that the observed proximity between the numerical and the structural instability in 3D originates from the enhanced structure present in the fluid but, in view of the arbitrary dependence on the iteration scheme, it seems uneasy to relate the numerical stability analysis to a robust one-phase criterion for predicting a thermodynamic phase transition.Comment: 11 pages, 2 figure

Phase diagram of self-assembled rigid rods on two-dimensional lattices: Theory and Monte Carlo simulations

Monte Carlo simulations and finite-size scaling analysis have been carried out to study the critical behavior in a two-dimensional system of particles with two bonding sites that, by decreasing temperature or increasing density, polymerize reversibly into chains with discrete orientational degrees of freedom and, at the same time, undergo a continuous isotropic-nematic (IN) transition. A complete phase diagram was obtained as a function of temperature and density. The numerical results were compared with mean field (MF) and real space renormalization group (RSRG) analytical predictions about the IN transformation. While the RSRG approach supports the continuous nature of the transition, the MF solution predicts a first-order transition line and a tricritical point, at variance with the simulation results.Comment: 12 pages, 10 figures, supplementary informatio

Self-assembly of binary nanoparticle dispersions: from square arrays and stripe phases to colloidal corrals

The generation of nanoscale square and stripe patterns is of major technological importance since they are compatible with industry-standard electronic circuitry. Recently, a blend of diblock copolymer interacting via hydrogen-bonding was shown to self-assemble in square arrays. Motivated by those experiments we study, using Monte Carlo simulations, the pattern formation in a two-dimensional binary mixture of colloidal particles interacting via isotropic core-corona potentials. We find a rich variety of patterns that can be grouped mainly in aggregates that self-assemble in regular square lattices or in alternate strips. Other morphologies observed include colloidal corrals that are potentially useful as surface templating agents. This work shows the unexpected versatility of this simple model to produce a variety of patterns with high technological potential.Comment: 13 pages, 5 figures, submitte