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The authors present a hybrid Brownian dynamics/Monte Carlo algorithm for simulating solutions of highly entangled semiflexible polymers or filaments. The algorithm combines a Brownian dynamics time-stepping approach with an efficient scheme for rejecting moves that cause chains to cross or that lead to excluded volume overlaps. The algorithm allows simulation of the limit of infinitely thin but uncrossable threads, and is suitable for simulating the conditions obtained in experiments on solutions of long actin protein filaments. [ABSTRACT FROM AUTHOR]

It is well known that mass-metric tensor determinants det(Gs) influence the equilibrium statistics and the rates of conformational transitions for polymers with constrained bond lengths and bond angles. It is now standard practice to include a Fixman-style compensating potential of the form Uc(qs)∝(-kBT/2)ln[det(Gs)] as part of algorithms for torsional space molecular dynamics. This elegant strategy helps eliminate unwarranted biases that arise due to the imposition of holonomic constraints. However, the precise nature and extent of variation of det(Gs) and hence ln[det(Gs)] with chain conformation and chain length has never been quantified. This type of analysis is crucial for understanding the nature of the conformational bias that the introduction of a Fixman potential aims to eliminate. Additionally, a detailed analysis of the conformational dependence of det(Gs) will help resolve ambiguities regarding suggestions for incorporating terms related to det(Gs) in the design of move sets in torsional space Monte Carlo simulations. In this work, we present results from a systematic study of the variation of det(Gs) for a serial polymer with fixed bond lengths and bond angles as a function of chain conformation and chain length. This analysis requires an algorithm designed for rapid computation of det(Gs) which simultaneously allows for a physical/geometric interpretation of the conformational dependence of det(Gs). Consequently, we provide a detailed discussion of our adaptation of an O(n) algorithm from the robotics literature, which leads to simple recursion relations for direct evaluation of det(Gs). Our analysis of the conformational dependence of det(Gs) yields the following insights. (1) det(Gs) is maximized for spatial conformers and minimized for planar conformations. (2) Previous work suggests that it is logical to expect that the conformational dependence of det(Gs) becomes more pronounced with increase in chain length. Confirming this expectation, we provide systematic quantification of the nature of this dependency and show that the difference in det(Gs) between spatial and planar conformers, i.e., between the maxima and minima of det(Gs) grows systematically with chain length. Finally, we provide a brief discussion of implications of our analysis for the design of move sets in Monte Carlo simulations. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A computational strategy to model the amorphous phase of comblike polymers is presented. The strategy, denoted SuSi/CB (CB—configurational bias), combines the strength of an algorithm recently developed to generate reliable microstructures of dense amorphous polymers, which is based on a random search of energy minima, and configurational bias Monte Carlo method. The influence of different parameters used to define the characteristics of SuSi/CB on both the reliability of the generated structures and the computational effort has been examined in detail. Finally, we have modeled and characterized the supramolecular organization of poly(octadecyl acrylate) in the amorphous state. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The equilibrium thermodynamics of confined linear homopolymers between two impenetrable walls was investigated by means of Monte Carlo simulations in the canonical ensemble with the parallel tempering algorithm. The influence of confinement and chain size on the potential energy, heat capacity, radius of gyration, and the end-to-end distance was investigated as a function of temperature. A bead–spring model was used to simulate the chains. Two conformational changes were observed regardless of the differences in confinement of chain size: The coil-to-globule transition that resembles the gas to liquid transition and the liquidlike to solidlike transition. An additional transition between solid states was also observed for the smallest chain size studied (16 beads). Results indicate a shift of the coil-to-globule transition temperature to lower values as the slit width approaches the two-dimensional case (wall separation equal to bead diameter), and to higher temperature regions as the chain length increases. For separations greater than five bead diameters, the thermodynamic behavior was similar to the behavior in unconfined space. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We present results on the profiles of the first- and second-rank bond-order parameters, 〈P[sub 1](cos θ)〉 and 〈P[sub 2](cos θ)〉, of the grafted polymer melts simulated in atomistic detail in Part I of this work, with the end-bridging Monte Carlo (EBMC) algorithm. The 〈P[sub 1](cos θ)〉 and 〈P[sub 2](cos θ)〉 profiles are discussed in terms of bond distance from the grafting surface and bond coordinate along chain contour. A methodology is also presented for calculating the deuterium (²H) nuclear magnetic resonance (NMR) spectrum of the simulated grafted melts by analyzing the atomistic configurations accumulated in the course of the EBMC simulations. The calculation of the deuterium NMR spectrum is found to be very sensitive to the details of the profile of the second-rank bond-order parameter. For the systems simulated in the present work (melts of linear C[sub 78] and C[sub 156] polyethylene melts at grafting densities σ ranging from 1.31 to 2.62 nm[sup -2]), calculated ²H NMR splittings are on the order of a few kilohertz, in agreement with experimentally measured values through deuterium NMR spectroscopy. [ABSTRACT FROM AUTHOR]

We are reporting results of dynamic Monte Carlo simulations on the irreversible adsorption of single polymer chains. We find that the irreversibility of the surface-segment interaction results in trapping of segments exclusively in trains and loops but no tails. Such nonequilibrium effects are also observed in reversible adsorption simulations for large adsorption energies per segment (≥2kT). [ABSTRACT FROM AUTHOR]

The shape of isolated two-dimensional linear and star polymers, with and without excluded volume, have been determined by Monte Carlo simulations using a pivot algorithm. Stars with 3, 4, 5, and 6 arms are studied. The high efficiency of the pivot algorithm has allowed us to obtain accurate data for long chains. Good agreement is found with existing analytical expressions for nonexcluded volume chains and with other computer simulations for excluded volume chains. [ABSTRACT FROM AUTHOR]

We develop the hybrid Monte Carlo method for simulations of single off-lattice polymer chains. We discuss implementation and choice of simulation parameters in some detail. The performance of the algorithm is tested on models for homopolymers with short- or long-range self-repulsion, using chains with 16≤N≤512 monomers. Without excessive fine tuning, we find that the computational cost grows as N2+z’ with 0.64

The equation of state of associative polymer networks has been studied by Monte Carlo simulation. To describe the associations, an algorithm is introduced which for dilute monatomic systems reduces to the well-known mass action law. For the polymers, the simple bead spring model was employed. The incorporation of a finite volume of the beads is essential to prevent phase separation once the associative interaction is turned on, and the system is quenched into the gel state. The excess pressure of this quenched state is well described by two exponents of the density ρ. The repulsive part of the excess pressure scales proportional to ρα, the attractive part is proportional to ρβ. For the nonassociating polymers we measured the first exponent as α=2.339±0.006, and for associating polymers far away from the critical point we found β=2.06±0.05. For certain values of the density and the association constant the measured pressure was negative, in these cases we find microphase separated configurations. The simulations also enabled the establishment of the percolation transition. The association constant at the gel point has been obtained as a function of density and polymer length. Together with the equation of state this resulted in a phase diagram for polymer gels. [ABSTRACT FROM AUTHOR]

Using the pruned-enriched Rosenbluth Monte Carlo algorithm, the scattering functions of semiflexible macromolecules in dilute solution under good solvent conditions are estimated both in d = 2 and d = 3 dimensions, considering also the effect of stretching forces. Using self-avoiding walks of up to N = 25 600 steps on the square and simple cubic lattices, variable chain stiffness is modeled by introducing an energy penalty [variant_greek_epsilon]b for chain bending; varying qb = exp (-[variant_greek_epsilon]b/kBT) from qb = 1 (completely flexible chains) to qb = 0.005, the persistence length can be varied over two orders of magnitude. For unstretched semiflexible chains, we test the applicability of the Kratky-Porod worm-like chain model to describe the scattering function and discuss methods for extracting persistence length estimates from scattering. While in d = 2 the direct crossover from rod-like chains to self-avoiding walks invalidates the Kratky-Porod description, it holds in d = 3 for stiff chains if the number of Kuhn segments nK does not exceed a limiting value nK* (which depends on the persistence length). For stretched chains, the Pincus blob size enters as a further characteristic length scale. The anisotropy of the scattering is well described by the modified Debye function, if the actual observed chain extension (end-to-end distance in the direction of the force) as well as the corresponding longitudinal and transverse linear dimensions - 2, g,⊥2> are used. [ABSTRACT FROM AUTHOR]

We develop and test a new elementary Monte Carlo move for use in the off-lattice simulation of polymer systems. This novel Parallel-Rotation algorithm (ParRot) permits moving very efficiently torsion angles that are deeply inside long chains in melts. The parallel-rotation move is extremely simple and is also demonstrated to be computationally efficient and appropriate for Monte Carlo simulation. The ParRot move does not affect the orientation of those parts of the chain outside the moving unit. The move consists of a concerted rotation around four adjacent skeletal bonds. No assumption is made concerning the backbone geometry other than that bond lengths and bond angles are held constant during the elementary move. Properly weighted sampling techniques are needed for ensuring detailed balance because the new move involves a correlated change in four degrees of freedom along the chain backbone. The ParRot move is supplemented with the classical Metropolis Monte Carlo, the Continuum-Configurational-Bias, and Reptation techniques in an isothermal-isobaric Monte Carlo simulation of melts of short and long chains. Comparisons are made with the capabilities of other Monte Carlo techniques to move the torsion angles in the middle of the chains. We demonstrate that ParRot constitutes a highly promising Monte Carlo move for the treatment of long polymer chains in the off-lattice simulation of realistic models of dense polymer systems. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A special biased Monte Carlo algorithm is used to study flow of homopolymer melts between neutral, hard walls on a fcc lattice at full occupancy (φ=1). A random number biasing technique is developed to mimic slot flow of a melt; the biasing method preferentially moves the chains in the direction of flow. System properties including velocity profiles, chain-end density distributions, average radii of gyration, and end-to-end vector order parameters are investigated as functions of chain length and biasing parameter. Chain connectivity leads to non-Newtonian flow behavior evidenced as velocity profile blunting. Observation suggests a relationship between the logarithm of the biasing parameter and the pressure drop. Based on the prescribed biasing profile, it is shown that flow causes greater chain deformation for longer chains (N=64,256) than for smaller chains (N=16). Findings also include the ordering of chains with end-to-end vectors aligned with respect to the flow direction. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]