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Three-dimensional single-component ideal gas systems composed of model homogeneous rigid molecules in various molecular shapes and sizes are simulated by a molecular Monte Carlo simulation technique. We reveal that percolation thresholds of such single-component systems result in, when the molecular volume is fixed, power-law decreasing functions of the radius of gyration (gyradius) of the molecules. The systems with the same parameter set of the molecular volume and radius of gyration, but in different molecular shapes, show the identical value of the percolation threshold. Moreover, we also reveal that a dimensionless scale-free parameter, which is the ratio between the radius of gyration and real cube root of the molecular volume, uniquely determines the percolation threshold., 7 pages, 4 figures

Simulating percolation and critical phenomena of labelled species inside films composed of single-component linear homogeneous macromolecules using molecular Monte Carlo method in 3 dimensions, we study dependence of these conducting transition and critical phenomena upon both thermal movement, i.e. spontaneous mobility, and extra-molecular topological constraints of the molecules. Systems containing topological constraints and/or composed of immobile particles, e.g. lattice models and chemical gelation, were studied in conventional works on percolation. Coordinates of the randomly distributed particles in the conventional lattice models are limited to discrete lattice points. Moreover, each particle is spatially fixed at the distributed position, which results in a temporally unchanged network structure. Although each polymer in the chemical gels can spontaneously move in the continuous space, the network structure is fixed when cross-linking reaction ends. By contrast to these conventional systems, all the molecules in the present system freely move and spontaneously diffuse in the continuous space. The network structure of the present molecules continues changing dynamically. The percolation and critical phenomena of such dynamic network structures are examined here. We reveal that these phenomena also occur in the present system, and that both the universality class and percolation threshold are independent from the extra-molecular topological constraints., Comment: 10 pages, 6 figures

Percolation phenomena of homopolymer brushes on a planar substrate are simulated using the molecular Monte Carlo method in 3 dimensions. The grafted polymers are isolated from each other at extremely low grafting density, whereas a continuous polymer layer covers the whole substrate when the density rises to extremely high values. This indicates that percolation clusters of the grafted polymers, bridging both the edges of the substrate, appear at an intermediate density. We construct phase diagrams of this percolation phenomenon. Critical phenomena at the transition are also studied., Comment: 6 pages, 5 figures, accepted for publication in J. Chem. Phys

In conventional molecular simulation, metastable structures often survive over considerable computational time, resulting in difficulties in simulating equilibrium states. In order to overcome this difficulty, here we propose a newly devised method, molecular Monte Carlo simulation of systems connected to three reservoirs: chemical potential, pressure, and temperature. Gibbs-Duhem equation thermodynamically limits the number of reservoirs to 2 for single component systems. However, in conventional simulations utilizing 2 or fewer reservoirs, the system tends to be trapped in metastable states. Even if the system is allowed to escape from such metastable states in conventional simulations, the fixed system size and/or the fixed number of particles result in creation of defects in ordered structures. This situation breaks global anisotropy of ordered structures and forces the periodicity of the structure to be commensurate to the system size. Here we connect the such three reservoirs to overcome these difficulties. A method of adjusting the three reservoirs and obtaining thermodynamically stable states is also designed, based on Gibbs-Duhem equation. Unlike the other conventional simulation techniques utilizing no more than 2 reservoirs, our method allows the system itself to simultaneously tune the system size and the number of particles to periodicity and anisotropy of ordered structures. Our method requires fewer efforts for preliminary simulations prior to production runs, compared with the other advanced simulation techniques such as multicanonical method. A free energy measurement method, suitable for the system with the three reservoirs, is also discussed, based on Euler equation of thermodynamics. This measurement method needs fewer computational efforts than other free energy measurement methods do., Comment: 15 pages, 10 figures

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 Letters

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 EPL