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Morphology of symmetric ABCD tetrablock quaterpolymers in melt was studied by the Monte Carlo (MC) simulation, where the volume fractions of the block chains, f, kept the relationships of fA = fD and fB = fC, and the volume fraction of the two mid-blocks φ was defined as φ = fB + fC. Previous self-consistent field theory for ABCD reported morphological change including several structures; however, the scope was limited within a two-dimensional system. To the contrary, in this paper, MC simulations were carried out in three dimensions with changing the φ value finely, which resulted in finding a tetracontinuous structure in the range of 0.625 ⩽ φ ⩽ 0.75. Moreover the tetracontinuous structure has been found to be the gyroid structure, and the mean curvature of the B/C interface is nearly zero. We concluded that the B/C interface must be the Schoen gyroid surface, one of three-dimensional periodic minimal surfaces. The geometrical nature of the A/B interface should be equivalent to that of the C/D interface, and they stand as level surfaces to the Schoen gyroid surface. [ABSTRACT FROM AUTHOR]

This paper investigates the conformational and scaling properties of long linear polymer chains. These investigations are done with the aid of Monte Carlo (MC) and molecular dynamics (MD) simulations. Chain lengths that comprise several orders of magnitude to reduce errors of finite size scaling, including the effect of solvent quality, ranging from the athermal limit over the θ-transition to the collapsed state of chains are investigated. Also the effect of polydispersity on linear chains is included which is an important issue in the real fabrication of polymers. A detailed account of the hybrid MD and MC simulation model and the exploited numerical methods is given. Many results of chain properties in the extrapolated limit of infinite chain lengths are documented and universal properties of the chains within their universality class are given. An example of the difference between scaling exponents observed in actual solvents and those observed in the extremes of “good solvents” and “θ-solvents” in simulations is provided by comparing simulation results with experimental data on low density polyethylene. This paper is concluded with an outlook on the extension of this study to branched chain systems of many different branching types. [ABSTRACT FROM AUTHOR]

We use the bond fluctuation model (BFM) to study the pore-blockade times of a translocating polymer of length N in two dimensions, in the absence of external forces on the polymer (i.e., unbiased translocation) and hydrodynamic interactions (i.e., the polymer is a Rouse polymer), through a narrow pore. Earlier studies using the BFM concluded that the pore-blockade time scales with polymer length as τd∼Nβ, with β=1+2ν, whereas some recent studies using different polymer models produce results consistent with β=2+ν, originally predicted by us. Here ν is the Flory exponent of the polymer; ν=0.75 in 2D. In this paper we show that for the BFM if the simulations are extended to longer polymers, the purported scaling τd∼N1+2ν ceases to hold. We characterize the finite-size effects, and study the mobility of individual monomers in the BFM. In particular, we find that in the BFM, in the vicinity of the pore the individual monomeric mobilities are heavily suppressed in the direction perpendicular to the membrane. After a modification of the BFM which counters this suppression (but possibly introduces other artifacts in the dynamics), the apparent exponent β increases significantly. Our conclusion is that BFM simulations do not rule out our theoretical prediction for unbiased translocation, namely, β=2+ν. [ABSTRACT FROM AUTHOR]

In this paper, we construct an effective model for the dynamics of an excluded-volume chain under confinement by extending the formalism of Rouse modes. We make specific predictions about the behavior of the modes for a single polymer confined to a tube. The results are tested against Monte Carlo simulations using the bond-fluctuation algorithm which uses a lattice representation of the polymer chain with excluded-volume effects. [ABSTRACT FROM AUTHOR]

Molecular mechanisms of crystal growth and homogeneous nucleation from the melt of polyethylene-like linear polymer are investigated by molecular dynamics simulations. The present paper is aimed at extending our previous work with respect to the system size and the boundary condition, thereby enabling detailed studies on the structures of sufficiently large lamellae and fully equilibrated melt. Lamellae of uniform thickness but with marked tapered edges are found to grow at constant velocity from the substrate. Three-dimensional shape of the growing lamellae exhibits peculiar undulation at the growth front, the origin of which is suggested to be the inhomogeneous thickness distribution within the lamellae. Trajectories of chains crystallizing onto the growth front reveal an unexpected pathway for chain folding, where a partially attached chain stem forms a new fold by plunging its head back into a neighboring stem position through slithering snake motions of the chain. Detailed statistics of folds and cilia show that the folds are rather neat and mostly make re-entries into the nearest or the second or third nearest neighboring stem positions, whereas the cilia are generally short but with a small number of longer cilia forming thick amorphous layers. Structure of supercooled melt investigated versus temperature reveals that, at moderate degree of supercooling, the overall chain conformation remains Gaussian random coil but the persistent length of chains increases monotonically with increasing supercooling. Exceptions are at the largest supercooling where homogeneous nucleation takes place; usual melt structure becomes rapidly unstable and emerges many crystallites of random orientations. During early 10–20 ns after the quench, density of melt, radius of gyration of chains, and fraction of kinked bonds show marked alterations. These structural changes are highly cooperative and are considered simply due to the emergence of many embryonic crystals in the melt. Conformations of the chains forming nuclei are also traced to reveal that the homogeneous nuclei are fringed micelle like aggregates of chains, but the chains as a whole have folded conformations, which are similar to those reported in previous simulations on a single polyethylene in a vacuum. [ABSTRACT FROM AUTHOR]

We present a computer simulation model of polymer melts representing each chain as one single particle. Besides the position coordinate of each particle, we introduce a parameter nij for each pair of particles i and j within a specified distance from each other. These numbers, called entanglement numbers, describe the deviation of the system of ignored coordinates from its equilibrium state for the given configuration of the centers of mass of the polymers. The deviations of the entanglement numbers from their equilibrium values give rise to transient forces, which, together with the conservative forces derived from the potential of mean force, govern the displacements of the particles. We have applied our model to a melt of C800H1602 chains at 450 K and have found good agreement with experiments and more detailed simulations. Properties addressed in this paper are radial distribution functions, dynamic structure factors, and linear as well as nonlinear rheological properties. [ABSTRACT FROM AUTHOR]

It is the purpose of this paper to establish a bottom-up multiscale approach for dendronized polymers. Based on our understanding of the phenomenology of an atomistic model for this class of polymers, we introduce a “Janus chain” (JC) model which adds a vectorial degree of freedom (Janus vector)—related to the sectorial amphiphilicity—to each segment of the linear backbone of a (classical) uncharged, semiflexible, and multibead chain representation of a polymer. The JC features induced polymeric curvature and ultimately triggers complexation. JC parameters related to the topology and chemical details are obtained from the atomistic level. Available experimental observations including the formation of superstructures and double helical conformations are well reproduced by the JC model. JC is efficiently solved via Brownian dynamics simulation and can be seen as a member of a universality class which is one (two) level(s) above the magnetic (semiflexible) chain model. It therefore should allow to model not only dendronized polymers but also structures belonging to the same class—exhibiting induced (or spontaneous) curvature—such as single stranded DNA and actin filaments. [ABSTRACT FROM AUTHOR]

This paper is aimed to develop a Brownian dynamics simulation method for strongly confined semiflexible polymers where numerical simulation plays an indispensable role in complementing theory and experiments. A wormlike chain under strong confinement is modeled as a string of virtual spherical beads connected by inextensible rods with length varying according to the confinement intensity of the chain measured by the Odijk deflection length. The model takes hydrodynamic interactions into account. The geometrical constraints associated with the inextensible rods are realized by the so-called linear constraint solver. The model parameters are studied by quantitatively comparing the simulated properties of a double-stranded DNA chain with available experimental data and theoretical predictions. [ABSTRACT FROM AUTHOR]

It has been suggested that, due to topological constraints, rings in the melt may assume a more compact shape than Gaussian chains. In this paper, we exploit the availability of narrow fractions of perdeuterated linear and cyclic polydimethylsiloxane (PDMS) and, through the analysis of the small angle neutron scattering (SANS) profiles, demonstrate the difference in scattering properties of linear and cyclic PDMS molecules. As expected for Gaussian chains, for the H/D linear PDMS samples, log-log plots of the scattered intensity versus scattering vector Q display a Q(-2) dependence. However, for H/D cyclic blends, the scaling exponent is higher than 2, as predicted by computer simulations reported in the literature. We show that cyclic molecules in bulk display the characteristic maximum in plots of scattered intensity versus Q(-2) that is expected on the basis of Monte Carlo calculations and from the Casassa equation [E. F. Casassa, J. Polym. Sci. A 3, 605 (1965)]. It is also shown that, for rings, the Debye equation [P. Debye, J. Appl. Phys. 15, 338 (1944)] is no longer appropriate to describe the SANS profiles of H/D cyclic blends, at least up to Mw≈10 000. For these samples, the Casassa form factor gives a better representation of the SANS data and we show that this function which was developed for monodisperse cyclics is still adequate to describe our slightly polydisperse samples. Deviations from all above observations are noted for Mw>11 000 and are attributed to partial contamination of cyclic samples with linear chains. The failure of both the Debye and the Casassa form factors could be due to contamination of the cyclic fractions by linear polymers or to a real conformational change. [ABSTRACT FROM AUTHOR]

Using methods adapted from the simulation of suspension dynamics, we have developed a Brownian dynamics algorithm with multibody hydrodynamic interactions for simulating the dynamics of polymer molecules. The polymer molecule is modeled as a chain composed of a series of inextensible, rigid rods with constraints at each joint to ensure continuity of the chain. The linear and rotational velocities of each segment of the polymer chain are described by the slender-body theory of Batchelor [J. Fluid Mech. 44, 419 (1970)]. To include hydrodynamic interactions between the segments of the chain, the line distribution of forces on each segment is approximated by making a Legendre polynomial expansion of the disturbance velocity on the segment, where the first two terms of the expansion are retained in the calculation. Thus, the resulting linear force distribution is specified by a center of mass force, couple, and stresslet on each segment. This method for calculating the hydrodynamic interactions has been successfully used to simulate the dynamics of noncolloidal suspensions of rigid fibers [O. G. Harlen, R. R. Sundararajakumar, and D. L. Koch, J. Fluid Mech. 388, 355 (1999); J. E. Butler and E. S. G. Shaqfeh, J. Fluid Mech. 468, 204 (2002)]. The longest relaxation time and center of mass diffusivity are among the quantities calculated with the simulation technique. Comparisons are made for different levels of approximation of the hydrodynamic interactions, including multibody interactions, two-body interactions, and the “freely draining” case with no interactions. For the short polymer chains studied in this paper, the results indicate a difference in the apparent scaling of diffusivity with polymer length for the multibody versus two-body level of approximation for the hydrodynamic interactions.© 2005 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We present the results of numerical simulations of the irreversible aggregation process for self-avoiding flexible polymers in three dimensions. We have paid special attention to two experimentally interesting systems: telechelic ionomers and reverse micelles. The dynamics used in this paper to simulate the clustering process is based on Eden’s method. This dynamics was previously introduced by us for two-dimensional systems. We find a scaling relation between the radius of gyration of the cluster Rg, the chain length n and the number of chains N in the cluster in the form Rg∼nαNβ. The values of the exponents α and β calculated from the numerical simulations are somewhat lower than those predicted by Flory’s classical theory. We argue that the lower values of the exponents are possibly due to the finite size of the clusters and the presence of higher order interaction terms not considered in Flory’s theory. [ABSTRACT FROM AUTHOR]

The scanning simulation method is applied to a model of polymer adsorption in which a single self-avoiding walk is terminally attached to an attracting impenetrable surface on a simple cubic lattice. Relatively long chains are studied, of up to 1000 steps, which enable us to obtain new estimates for the reciprocal transition temperature |ε|/kBTa=θa =0.291±0.001 (ε is the interaction energy of a monomer with the surface), the crossover exponent [lowercase_phi_synonym]=0.530±0.007 and the free energy exponents at Ta, γ1SB =1.304±0.006 and γ11SB =0.805±0.015. At T=∞ we obtain, γ1=0.687±0.005, γ11=-0.38±0.02, and the effective coordination number q=4.6839±0.0001, which are in good agreement with estimates obtained by other methods. At T>Ta we demonstrate the existence of strong correction to scaling for the perpendicular part of the mean-square end-to-end distance ⊥ and for the monomer concentration profile ρ(z) (z is the distance from the surface). At T=∞ the leading correction to scaling term for ⊥ is c/Nψ, where c≊-0.9 and ψ≊0.4 is close to 0.5 obtained for the random walk model in the preceding paper. This means that the asymptotic regime, in which these corrections become negligible, corresponds to a large polymer length that is not realized experimentally. Close enough to Ta we demonstrate for our lattice model the validity of various scaling forms predicted by Eisenriegler, Kremer, and Binder [J. Chem. Phys. 77, 6296 (1982)] for a continuum model on the basis of the n-vector model. [ABSTRACT FROM AUTHOR]

The effective diffusivity in a polymer matrix modified with inclusions is usually calculated based on Kalnin-Kotomin's model [J. R. Kalnin, E. A. Kotomin, and J. Maier, J. Phys. Chem. Solids 63, 449-456 (2002)], which extends the well known Maxwell-Garnett formula. Kalnin-Kotomin's model correctly predicts effective diffusivity for stationary diffusion or for infinite media. In the present paper diffusion in composite media is studied for finite systems under transient conditions. The process of diffusion is modeled numerically and effective diffusion coefficient in the transient state is estimated, which, under certain conditions, is different from the predictions of the Kalnin-Kotomin's model. An analytical model is proposed to explain deviations of the transient effective coefficient of diffusion from the stationary case. [ABSTRACT FROM AUTHOR]

By employing the Massieu formalism presented in the preceding paper, Monte Carlo methods and extrapolation techniques are combined to simulate polymers with chain-length polydispersity. Semigrand canonical and grand canonical ensembles supplemented by identity exchange moves and expanded-ensemble moves have been tailored to simulate both thermodynamic properties and the structure of various coarse-grained model systems. It is demonstrated that the proposed methods can be used to simulate systems with arbitrary molecular weight distribution (e.g., to match experimental data), bulk-pore partitioning of polymer solutions, and liquid–liquid equilibrium of polydisperse polymer melts. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]