Monte-Carlo simulation of string-like colloidal assembly

We study structural phase transition of polymer-grafted colloidal particles by Monte Carlo simulations on hard spherical particles. The interaction potential, which has a weak repulsive step outside the hard core, was validated with use of the self-consistent field calculations. With this potential, canonical Monte Carlo simulations have been carried out in two and three dimensions using the Metropolis algorithm. At low temperature and high density, we find that the particles start to self-assemble and finally align in strings. By analyzing the cluster size distribution and string length distribution, we construct a phase diagram and find that this string-like assembly is related to the percolation phenomena. The average string length diverges in the region where the melting transition line and the percolation transition line cross, which is similar to Ising spin systems where the percolation transition line and the order-disorder line meet on the critical point.Comment: 7 pages, 6 figures, Accepted for Europhysics Letter

Particle Monte Carlo simulation of string-like colloidal assembly in 2 dimensions

We simulate structural phase behavior of polymer-grafted colloidal particles by molecular Monte Carlo technique. Interparticle potential, which has a finite repulsive square-step outside a rigid core of the colloid, was previously confirmed via numerical self-consistent field calculation. This model potential is purely repulsive. We simulate these model colloids in the canonical ensemble in 2 dimensions and find that these particles containing no interparticle attraction self-assemble and align in a string-like assembly, at low temperature and high density. This string-like colloidal assembly is related to percolation phenomena. Analyzing the cluster size distribution and the average string length, we build phase diagrams and discover that the average string length diverges around the region where the melting transition line and the percolation transition line cross. This result is similar to Ising spin systems, in which the percolation transition line and the order-disorder line meet at a critical point.Comment: 11 pages, 14 figure

Molecular simulation of 2-dimensional microphase separation of single-component homopolymers grafted onto a planar substrate

The structural phase behavior of polymer brushes, single-component linear homopolymers grafted onto a planar substrate, is studied using the molecular Monte Carlo method in 3 dimensions. When simulation parameters of the system are set in regions of macrophase separation of solution for the corresponding non-grafted homopolymers, the grafted polymers also prefer segregation. However, macrophase separation is disallowed due to the spatially-fixed grafting points of the polymers. Such constraints on the grafting are similar to connecting points between blocks of non-grafted diblock copolymers at the microphase separation in the melt state. This results in "microphase separation" of the homopolymer brush in the lateral direction of the substrate. Here we extensively search the parameter space and reveal various lateral domain patterns that are similar to those found in diblock copolymer melts at microphase separation.Comment: 6 pages, 5 figures, accepted for publication in EP

Soft Spheres Make More Mesophases

We use both mean-field methods and numerical simulation to study the phase diagram of classical particles interacting with a hard-core and repulsive, soft shoulder. Despite the purely repulsive interaction, this system displays a remarkable array of aggregate phases arising from the competition between the hard-core and shoulder length scales. In the limit of large shoulder width to core size, we argue that this phase diagram has a number of universal features, and classify the set of repulsive shoulders that lead to aggregation at high density. Surprisingly, the phase sequence and aggregate size adjusts so as to keep almost constant inter-aggregate separation.Comment: 4 pages, 2 included figure

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

Lane-formation vs. cluster-formation in two dimensional square-shoulder systems: A genetic algorithm approach

Introducing genetic algorithms as a reliable and efficient tool to find ordered equilibrium structures, we predict minimum energy configurations of the square shoulder system for different values of corona width $\lambda$. Varying systematically the pressure for different values of $\lambda$ we obtain complete sequences of minimum energy configurations which provide a deeper understanding of the system's strategies to arrange particles in an energetically optimized fashion, leading to the competing self-assembly scenarios of cluster-formation vs. lane-formation.Comment: 5 pages, 6 figure