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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

The phase behavior of polystyrene (PS) brushes in cyclohexane (CHX) was investigated, for the first time, by environmental atomic force microscopy as a function of the graft density and temperature. The polystyrene brushes of three different graft densities exhibited island-, bicontinuous-, and hole-shape microdomains in the direction parallel to the substrate. The size of such “in-plane” microdomains is close to the end-to-end distance of PS brush chain due to the anchoring of one of the chain ends of PS brushes to the substrate. The microdomain structure disappeared as the temperature increased, and new structure with same morphological features reappeared by lowering temperature. This reversible temperature response corresponds to the in-plane phase separation of the PS brush/CHX system. The UCST type binodal line shifted toward slightly lower temperature in the PS brush/CHX system compared to that of the corresponding nongrafted polymer solution, i.e., PS/CHX system, in excellent agreement with our pr...

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

Recently, directed self-assembly (DSA) method is focused on as a next generation lithography technique. We performed the DPD simulations to analyze the self-assembling process of block copolymer in DSA using OCTA (in detail, see http://octa.jp) system. Using DPD simulation, we can obtain the phase separated structures at each moment consisted by block copolymer chains. As those structures are consisted by polymer chains, an analysis can be done on those structures. In this paper, we study the dynamics of end particles in the defect annihilation process to understand the dynamics of self-assembling of block copolymer in DSA. From our analysis, the end particles moves in advance than the change of domain structure in the defect annihilation process.

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

We simulate structural phase behavior of polymer-grafted colloidal particles by molecular Monte Carlo technique. The 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 two and three 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.

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

Using computer simulation of a solvent-free, coarse-grained model for amphiphilic membranes, we study the excess free energy of hourglass-shaped connections (i.e., stalks) between two apposed bilayer membranes. In order to calculate the free energy by simulation in the canonical ensemble, we reversibly transfer two apposed bilayers into a configuration with a stalk in three steps. First, we gradually replace the intermolecular interactions by an external, ordering field. The latter is chosen such that the structure of the non-interacting system in this field closely resembles the structure of the original, interacting system in the absence of the external field. The absence of structural changes along this path suggests that it is reversible; a fact which is confirmed by expanded-ensemble simulations. Second, the external, ordering field is changed as to transform the non-interacting system from the apposed bilayer structure to two-bilayers connected by a stalk. The final external field is chosen such that the structure of the non-interacting system resembles the structure of the stalk in the interacting system without a field. On the third branch of the transformation path, we reversibly replace the external, ordering field by non-bonded interactions. Using expanded-ensemble techniques, the free energy change along this reversible path can be obtained with an accuracy of 10(-3)k(B)T per molecule in the n VT-ensemble. Calculating the chemical potential, we obtain the free energy of a stalk in the grandcanonical ensemble, and employing semi-grandcanonical techniques, we calculate the change of the excess free energy upon altering the molecular architecture. This computational strategy can be applied to compute the free energy of self-assembled phases in lipid and copolymer systems, and the excess free energy of defects or interfaces.

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

Using molecular simulation of a coarse-grained model for a symmetric diblock copolymer melt, we calculate the free energy of interfaces between lamellar morphologies with different orientations. Two examples are considered: (a) a T-junction between two lamellar structures with perpendicular orientation and (b) a surface reconstruction that arises when lamella-forming diblock copolymers assemble on a stripe-patterned surface, where the pattern period is significantly larger than the lamellar spacing in the bulk. The computational scheme relies on reversibly relating the defect structure to a reference state by an external ordering field. Free energy differences are accurately obtained by using a combination of expanded-ensemble and replica-exchange Monte Carlo techniques.