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We consider polymer structures which are known in the mathematical literature as 'cospectral.' Their graphs have (in spite of the different architectures) exactly the same Laplacian spectra. Now, these spectra determine in Gaussian (Rouse-type) approaches many static as well as dynamical polymer characteristics. Hence, in such approaches for cospectral graphs many mesoscopic quantities are predicted to be indistinguishable. Here we show that the introduction of semiflexibility into the generalized Gaussian structure scheme leads to different spectra and hence to distinct macroscopic patterns. Moreover, particular semiflexible situations allow us to distinguish well between cospectral structures. We confirm our theoretical results through Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

The absorption of free linear chains in a polymer brush was studied with respect to chain size L and compatibility ψ with the brush by means of Monte Carlo (MC) simulations and density functional theory (DFT)/self-consistent field theory (SCFT) at both moderate, σg=0.25, and high, σg=1.00, grafting densities using a bead-spring model. Different concentrations of the free chains 0.0625≤[lowercase_phi_synonym]o≤0.375 are examined. Contrary to the case of ψ=0 when all species are almost completely ejected by the polymer brush irrespective of their length L, for ψ<0 we find that the degree of absorption (absorbed amount) Γ(L) undergoes a sharp crossover from weak to strong (≈100%) absorption, discriminating between oligomers, 1≤L≤8, and longer chains. For a moderately dense brush, σg=0.25, the longer species, L>8, populate predominantly the deep inner part of the brush, whereas in a dense brush σg=1.00 they penetrate into the “fluffy” tail of the dense brush only. Gyration radius Rg and end-to-end distance Re of absorbed chains thereby scale with length L as free polymers in the bulk. Using both MC and DFT/SCFT methods for brushes of different chain length 32≤N≤256, we demonstrate the existence of unique critical value of compatibility ψ=ψc<0. For ψc([lowercase_phi_synonym]o) the energy of free chains attains the same value, irrespective of length L whereas the entropy of free chain displays a pronounced minimum. At ψc all density profiles of absorbing chains with different L intersect at the same distance from the grafting plane. The penetration/expulsion kinetics of free chains into the polymer brush after an instantaneous change in their compatibility ψ displays a rather rich behavior. We find three distinct regimes of penetration kinetics of free chains regarding the length L: I (1≤L≤8), II (8≤L≤N), and III (L>N), in which the time of absorption τ grows with L at a different rate. During the initial stages of penetration into the brush one observes a power-law increase of Γ∝tα with power α∝-ln [lowercase_phi_synonym]o, whereby penetration of the free chains into the brush gets slower as their concentration rises. [ABSTRACT FROM AUTHOR]

Mesopores present in inorganic barrier films have a unique structure since the bottom sides are blocked by underlying polymer substrates. Characterization of pore blockage by water condensation is important in understanding gas transport mechanisms because the pore blockage changes the transmission behavior of water vapor itself as well as other gases. In this study a water condensation behavior inside mesopores is investigated analytically and numerically. Appropriate modifications from the classical Kelvin equation-based solution are suggested to account for local and discrete molecular interactions and submolecular meniscus tip geometry. Grand canonical Monte Carlo simulations are also conducted to simulate the present problem and the result is compared with the analytical solutions. [ABSTRACT FROM AUTHOR]

A hybrid modeling approach is proposed for inhomogeneous polymer solutions. The method is illustrated for the depletion problem with polymer chains up to N=103 segments in semidilute solutions and good solvent conditions. In a three-dimensional volume, a set of freely jointed chains is considered for which the translational degrees of freedom are sampled using a coarse grained Monte Carlo simulation and the conformational degrees of freedom of the chains are computed using a modified self-consistent field theory. As a result, both intramolecular and intermolecular excluded volume effects are accounted for, not only for chains near the surface, but in the bulk as well. Results are consistent with computer simulations and scaling considerations. More specifically, the depletion thickness, which is a measure for the bulk correlation length, scales as δ∝φ-0.75 and converges to the mean field result in the concentrated regime. [ABSTRACT FROM AUTHOR]

Using a lattice-based Monte Carlo code for simulating self-avoiding flexible polymers in three dimensions in the absence of explicit hydrodynamics, we study their Rouse modes. For self-avoiding polymers, the Rouse modes are not expected to be statistically independent; nevertheless, we demonstrate that numerically these modes maintain a high degree of statistical independence. Based on high-precision simulation data we put forward an approximate analytical expression for the mode amplitude correlation functions for long polymers. From this, we derive analytically and confirm numerically several scaling properties for self-avoiding flexible polymers, such as (i) the real-space end-to-end distance, (ii) the end-to-end vector correlation function, (iii) the correlation function of the small spatial vector connecting two nearby monomers at the middle of a polymer, and (iv) the anomalous dynamics of the middle monomer. Importantly, expanding on our recent work on the theory of polymer translocation, we also demonstrate that the anomalous dynamics of the middle monomer can be obtained from the forces it experiences, by the use of the fluctuation-dissipation theorem. [ABSTRACT FROM AUTHOR]

We studied equilibrium conformations of ring polymers in melt over the wide range of segment number N of up to 4096 with Monte-Carlo simulation and obtained N dependence of radius of gyration of chains Rg. The simulation model used is bond fluctuation model (BFM), where polymer segments bear excluded volume; however, the excluded volume effect vanishes at N→∞, and linear polymer can be regarded as an ideal chain. Simulation for ring polymers in melt was performed, and the ν value in the relationship Rg∝Nν is decreased gradually with increasing N, and finally it reaches the limiting value, 1/3, in the range of N≥1536, i.e., Rg∝N1/3. We confirmed that the simulation result is consistent with that of the self-consistent theory including the topological effect and the osmotic pressure of ring polymers. Moreover, the averaged chain conformation of ring polymers in equilibrium state was given in the BFM. In small N region, the segment density of each molecule near the center of mass of the molecule is decreased with increasing N. In large N region the decrease is suppressed, and the density is found to be kept constant without showing N dependence. This means that ring polymer molecules do not segregate from the other molecules even if ring polymers in melt have the relationship ν=1/3. Considerably smaller dimensions of ring polymers at high molecular weight are due to their inherent nature of having no chain ends, and hence they have less-entangled conformations. [ABSTRACT FROM AUTHOR]

We present an extensive numerical study on the behavior of spherical brushes confined into a spherical cavity. Self-consistent field (SCF) and off-lattice Monte Carlo (MC) techniques are used in order to determine the monomer and end-chain density profiles and the cavity pressure as a function of the brush properties. A comparison of the results obtained via SCF, MC, and the Flory theory for polymer solutions reveals SCF calculations to be a valuable alternative to MC simulations in the case of free and softly compressed brushes, while the Flory’s theory accounts remarkably well for the pressure in the strongly compressed regime. In the range of high compressions, we have found the cavity pressure P to follow a scale relationship with the monomer volume fraction v, P∼vα. SCF calculations give α=2.15±0.05, whereas MC simulations lead to α=2.73±0.04. The underestimation of α by the SCF method is explained in terms of the inappropriate account of the monomer density correlations when a mean field approach is used. [ABSTRACT FROM AUTHOR]

We propose a new coarse-grained model for the description of liquid-vapor phase separation of colloid-polymer mixtures. The hard-sphere repulsion between colloids, and between colloids and polymers, which is used in the well-known Asakura–Oosawa (AO) model, is replaced with Weeks–Chandler–Andersen potentials. Similarly, a soft potential of height comparable to thermal energy is used for the polymer-polymer interaction, rather than treating polymers as ideal gas particles. It is shown by grand-canonical Monte Carlo simulations that this model leads to a coexistence curve that almost coincides with that of the AO model and that the Ising critical behavior of static quantities is reproduced. Then the main advantage of the model is exploited—its suitability for Molecular Dynamics simulations—to study the dynamics of mean square displacements of the particles, transport coefficients such as the self-diffusion and interdiffusion coefficients, and dynamic structure factors. While the self-diffusion of polymers increases slightly when the critical point is approached, the self-diffusion of colloids decreases and at criticality the colloid self-diffusion coefficient is about a factor of 10 smaller than that of the polymers. Critical slowing down of interdiffusion is observed, which is qualitatively similar to symmetric binary Lennard-Jones mixtures, for which no dynamic asymmetry of self-diffusion coefficients occurs. [ABSTRACT FROM AUTHOR]

The effect of attractive polymer-pore interaction on the translocation of polymer chain through a nanopore under electric field is studied by using dynamical Monte Carlo method. The translocation dynamics is remarkably influenced by the interaction. The translocation time for chain moving through nanopore is strongly dependent on the interaction. It reaches minimum at a moderate interaction which is found to be roughly independent of electric field as well as chain length. At weak interaction region, chain spends long time to overcome the barrier of the pore entrance, i.e., the chain is trapped at the entrance. While at strong interaction region, chain is difficult to leave the nanopore, that is, the chain is trapped at the exit of nanopore. The phenomenon is discussed from the view of free energy landscape. [ABSTRACT FROM AUTHOR]

Extensive Monte Carlo results are presented for the structure of a bottle-brush polymer under good solvent or theta solvent conditions. Varying the side chain length, backbone length, and the grafting density for a rigid straight backbone, both radial density profiles of monomers and side chain ends are obtained as well as structure factors describing the scattering from a single side chain and from the total bottle-brush polymer. To describe the structure in the interior of a very long bottle brush, a periodic boundary condition in the direction along the backbone is used, and to describe effects due to the finiteness of the backbone length, a second set of simulations with free ends of the backbone is performed. In the latter case, the inhomogeneity of the structure in the direction along the backbone is carefully investigated. We use these results to test various phenomenological models that have been proposed to interpret experimental scattering data for bottle-brush macromolecules. These models aim to extract information on the radial density profile of a bottle brush from the total scattering via suitable convolution approximations. Limitations of this approach and the optimal way to perform the analysis of the scattering data within this approach are discussed. [ABSTRACT FROM AUTHOR]

Macromolecular crowding is thought to be a significant factor driving DNA condensation in prokaryotic cells. Whereas DNA in prokaryotes is supercoiled, studies on crowding-induced DNA condensation have so far focused on linear DNA. Here we compare DNA condensation by poly(ethylene oxide) for supercoiled and linearized pUC18 plasmid DNA. It is found that supercoiling has only a limited influence on the critical amount of PEO needed to condense plasmid DNA. In order to pack DNA supercoils in condensates, it seems inevitable that they must be deformed in one way or another, to facilitate dense packing of DNA. Analytical estimates and Monte Carlo simulations indicate that packing of DNA supercoils in condensates is most likely facilitated by a decrease of the superhelical diameter rather than by unwinding of the supercoils. [ABSTRACT FROM AUTHOR]

A Monte Carlo study is made of the mean-square radius of gyration ≤S2≥ and second virial coefficient A2 for the two freely rotating chains with the Lennard-Jones (LJ) 6-12 potential and the hard-sphere (HS) one in the range of the bond angle θ from 109° (typical flexible chain) to 175° (typical semiflexible or stiff chain) and in the range of the number n of bonds from 6 to 1000. It is shown that a value may be properly assigned to the collision diameter of the HS potential so that ≤S2≥ of the chain with the HS potential agrees well with that of the chain with the LJ one whose parameter values correspond to a good-solvent condition irrespective of the chain stiffness. It is then found that A2 of the latter chain becomes remarkably smaller than that of the former as the chain stiffness is increased. The result implies that the binary-cluster approximation does not seem to work well for typical semiflexible and stiff polymers [ABSTRACT FROM AUTHOR]

We examine how the fluid-fluid phase behavior of a model colloid-polymer mixture evolves with variation of polymer size and/or interaction strength. Polymer-polymer interactions are approximated through Gaussian-core potentials while colloid-colloid and colloid-polymer interactions are assumed purely hard. Grand canonical transition matrix Monte Carlo simulation is used to construct binary liquid-liquid phase diagrams for a wide range of polymer sizes and interaction strengths. Overall, our results indicate that independently decreasing the polymer size or increasing the strength of repulsion between polymers have similar effects; these variations lead to an increase in the critical colloid concentration and decrease in the critical polymer concentration. An examination of the phase diagrams collected in this study reduced by their critical reservoir polymer concentration and critical colloid concentration reveals a single common phase envelope that is quantitatively similar to that for common models used to describe simple fluids. Finally, evaluation of the osmotic second virial coefficient in the vicinity of the critical point suggests that this quantity cannot be used as a reliable predictor for the conditions under which colloid-polymer mixtures phase separate. [ABSTRACT FROM AUTHOR]

The phase behavior of symmetric ABA triblock copolymers containing a semiflexible midblock is studied by lattice Monte Carlo simulation. As the midblock evolves from a fully flexible state to a semiflexible state in terms of increase in its persistence length, different phase behaviors are observed while cooling the system from an infinite high temperature to a temperature below TODT (order-disorder transition temperature). Within the midblock flexibility range we studied (lp/Nc≤=0.105), a lamellar structure is formed at equilibrium state as the situation for fully flexible chains. The fraction of bridge chain is evaluated for the lamellar structures. We find that the increase in midblock rigidity indeed results in the increase in bridge chain fraction within the range from 44.9% to 51.8%. In order to elucidate phase behavior evolution observed in our simulation, a detailed conformation distribution analysis is also given. Our results bridge a gap of different phase behaviors between rod-coil block copolymer and coil-coil block copolymer and show a necessity to investigate rigidity influence on phase diagram. [ABSTRACT FROM AUTHOR]

By using a recently developed Monte Carlo algorithm and an exact numerical method, we calculate the translocation probability and the average translocation time for charged heterogeneous polymers driven through a nanopore by an external electric field. The heteropolymer chains are composed of two types of monomers (A and B) which differ only in terms of their electric charge. We present an exhaustive study of chains composed of eight monomers by calculating the average translocation time associated with the 256 possible arrangements for various ratios of the monomer charges (λA/λB) and electric field intensities E. We find that each sequence leads to a unique value of the translocation probability and time. We also show that the distribution of translocation times is strongly dependent on the two forces felt by the monomers (∼λAE and ∼λBE). Finally, we present results that highlight the effect of having repetitive patterns by studying the translocation times of various block copolymer structures for a very long chain composed of N=218 monomers (all with the same number of A and B monomers). [ABSTRACT FROM AUTHOR]

In this study, we investigated the process of random sequential adsorption of stiff and flexible polymer chains on a two-dimensional square lattice. The polymer chains were represented by sequence of lattice points forming needles, T shapes, and crosses as well as flexible linear chains and star-branched chains consisted of three and four arms. The Monte Carlo method was employed to generate the model systems. The percolation threshold and the jamming threshold were determined for all systems under consideration. The influence of the chain length and the chain architecture on both thresholds was calculated and discussed. The changes in the ordering of the system were also studied. [ABSTRACT FROM AUTHOR]

It has been revealed by mean-field theories and computer simulations that the nature of the collapse transition of a polymer is influenced by its bending stiffness εb. In two dimensions, a recent analytical work demonstrated that the collapse transition of a partially directed lattice polymer is always first order as long as εb is positive [H. Zhou et al., Phys. Rev. Lett. 97, 158302 (2006)]. Here we employ Monte Carlo simulation to investigate systematically the effect of bending stiffness on the static properties of a two-dimensional lattice polymer. The system’s phase diagram at zero force is obtained. Depending on εb and the temperature T, the polymer can be in one of the three phases: crystal, disordered globule, or swollen coil. The crystal-globule transition is discontinuous and the globule-coil transition is continuous. At moderate or high values of εb the intermediate globular phase disappears and the polymer has only a discontinuous crystal-coil transition. When an external force is applied, the force-induced collapse transition will either be continuous or discontinuous, depending on whether the polymer is originally in the globular or the crystal phase at zero force. The simulation results also demonstrate an interesting scaling behavior of the polymer at the force-induced globule-coil transition. [ABSTRACT FROM AUTHOR]

Monte Carlo simulations were performed on semiflexible polymer chains with the goal of delineating their isotropic-nematic (IN) and gas-liquid coexistence envelopes. The chain monomers are spherical beads that interact via a square-well potential with all other beads. Bonded beads are connected by strings chosen so that bond length varies between 1.01σ and 1.05σ (where σ is the hard sphere diameter). The stiffness of the molecules is controlled via a potential between beads separated by two bonds; this potential restricts the distance between these beads to be between 2.02σ and 2.1σ. The vapor-liquid coexistence and IN coexistence curves are obtained using computer simulations. An IN transition is found for 10≤=Nb≤30. Both the density at which the IN transition occurs and the location of the gas-liquid coexistence go through a maximum with increasing Nb. For longer chains, behavior expected from theory is found and both of these coexisting densities decrease with increasing length. [ABSTRACT FROM AUTHOR]

Sorption and diffusion of binary mixtures of small molecules in model polymer networks is studied via computer simulation. Three types of molecules identical in volume but different in shape and flexibility (compact, linear stiff, and linear flexible) are combined into binary mixtures (compact/linear stiff) and (linear stiff/linear flexible). The relative effects of shape and flexibility on separation factor and diffusion coefficient inside random polymer networks are studied using a molecular dynamics/Gibbs-ensemble Monte Carlo hybrid technique. In addition the effects of temperature, pressure, and network strand length are considered. We find that the compact molecules are preferentially absorbed into the network at all strand lengths and temperatures considered here. Flexibility only leads to minor preferential sorption under most conditions. Diffusion coefficients of the competing species inside the network are found to agree within the error bars. [ABSTRACT FROM AUTHOR]

We report a numerical study of equilibrium phase diagrams and interfacial properties of bulk and confined colloid-polymer mixtures using grand canonical Monte Carlo simulations. Colloidal particles are treated as hard spheres, while the polymer chains are described as soft repulsive spheres. The polymer-polymer, colloid-polymer, and wall-polymer interactions are described by density-dependent potentials derived by Bolhuis and Louis [Macromolecules 35, 1860 (2002)]. We compared our results with those of the Asakura-Oosawa-Vrij model [J. Chem. Phys. 22, 1255 (1954); J. Polym Sci 33, 183 (1958); Pure Appl. Chem. 48, 471 (1976)] that treats the polymers as ideal particles. We find that the number of polymers needed to drive the demixing transition is larger for the interacting polymers, and that the gas-liquid interfacial tension is smaller. When the system is confined between two parallel hard plates, we find capillary condensation. Compared with the Asakura-Oosawa-Vrij model, we find that the excluded volume interactions between the polymers suppress the capillary condensation. In order to induce capillary condensation, smaller undersaturations and smaller plate separations are needed in comparison with ideal polymers. [ABSTRACT FROM AUTHOR]

Monte Carlo simulation methods that involve the insertion-deletion of molecules are of wide spread use for the study of thermophysical behavior of complex systems; e.g., for the estimation of chemical potentials in closed-system ensembles. In this work, efficient expanded ensemble methods are described to overcome the lack of ergodicity that often plagues such molecular moves, wherein an arbitrary physical parameter Λ is used to gradually couple and decouple a partial molecule to and from the system. In particular, we describe the use of (1) acceptance ratio methods for the robust estimation of free-energy changes associated with transitions between Λ states of the partial molecule, (2) non-Boltzmann sampling of the probability density of Λ states so that one can achieve either a flat histogram or an optimized histogram based on the maximization of round trips between the Λ bounds, and (3) an approach to select suitable intermediate stages of the Λ parameter that maximizes such round trips. The validity of the advocated methods is demonstrated by their application to two model systems, namely, the solvation of large hard spheres into a fluid of small spheres, and the mesophase formation of a block copolymer-homopolymer mixture. [ABSTRACT FROM AUTHOR]

The shielding effect of surrounding arms and chains on the encounter probability of reactive sites located both at the end of a linear chain and at several positions along the arms of star-branched chains with up to six arms is calculated by means of exact enumeration of samples prepared by Monte Carlo simulation. The changes of parameters that characterize the size and the shape of chain configurations during the approach of reactive centers located at the end of the linear chain and at the center of the star are evaluated. In addition to this specific case, which represents the central reaction step in reversible addition-fragmentation chain transfer star polymerization following the Z-group approach, a general discussion is given on the chain-length dependence of shielding factors associated with distinct segment positions. [ABSTRACT FROM AUTHOR]

We consider a lattice model of a mixture of repulsive, attractive, or neutral monodisperse linear polymers of two species, A and B, with a third monomeric species C, which may be taken to represent free volume. The mixture is confined between two hard, parallel plates of variable separation whose interactions with A and C may be attractive, repulsive, or neutral, and may be different from each other. The interactions with A and C are all that are required to completely specify the effect of each surface on all three components. We numerically study various density profiles as we move away from the surface, by using the recursive method of Gujrati and Chhajer [J. Chem. Phys. 106, 5599 (1997)] that has already been previously applied to study polydisperse solutions and blends next to surfaces. The resulting density profiles show the oscillations that are seen in Monte Carlo simulations and the enrichment of the smaller species at a neutral surface. The method is computationally ultrafast and can be carried out on a personal computer (PC), even in the incompressible case, when Monte Carlo simulations are not feasible. The calculations of density profiles usually take less than 20 min on a PC. [ABSTRACT FROM AUTHOR]

The authors numerically study a simple fluid composed of particles having a hard-core repulsion, complemented by two short-ranged attractive (sticky) spots at the particle poles, which provides a simple model for equilibrium polymerization of linear chains. The simplicity of the model allows for a close comparison, with no fitting parameters, between simulations and theoretical predictions based on the Wertheim perturbation theory. This comparison offers a unique framework for the analytic prediction of the properties of self-assembling particle systems in terms of molecular parameters and liquid state correlation functions. The Wertheim theory has not been previously subjected to stringent tests against simulation data for ordering across the polymerization transition. The authors numerically determine many of the thermodynamic properties governing this basic form of self-assembly (energy per particle, order parameter or average fraction of particles in the associated state, average chain length, chain length distribution, average end-to-end distance of the chains, and the static structure factor) and find that predictions of the Wertheim theory accord remarkably well with the simulation results. [ABSTRACT FROM AUTHOR]

The driven translocation kinetics of a single strand polynucleotide chain through a nanopore is studied using off-lattice Monte Carlo simulations, by which the authors demonstrate a novel method in controlling the driven polymer transport through a nanopore by a rotating electric field. The recorded time series of blockade current from the driven polynucleotide transport are used to determine the sequence of polynucleotides by implementing a modified Monte Carlo algorithm, in which the energy landscape paving technique is incorporated to avoid trapping at deep local minima. It is found that only six-time series of block current are required to completely determine the polynucleotide sequence if the average missing rate (AMR) of current signals in these time series is smaller than 20%. For those time series with AMR greater than 20%, the error rate in sequencing an unknown polynucleotide decreases rapidly by increasing the number of time series. To find the most appropriate experimental conditions, the authors have investigated the dependence of AMR of current signals and qualified rate of measured time series of blockade current on various controllable experimental variables. [ABSTRACT FROM AUTHOR]

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]

The authors investigate equilibrium properties of a simple model of hydrophobic polymer in aqueous solution by means of dynamic Monte Carlo simulations. The solvent is described by a simplified two-dimensional model, defined on a triangular lattice, which has been previously shown to account for most thermodynamic anomalies of pure water and of hydrophobic solvation for monomeric solutes. The polymer is modeled as a self-avoiding walk on the same lattice. In this framework, the degrees of freedom of water are taken into account explicitly, and in principle there is no need to introduce effective self-contact interactions for the polymer in order to mimic the hydrophobic effect. In certain conditions, the authors observe low-temperature-induced swelling, i.e., expansion of the polymer globule upon decreasing temperature. The authors discuss the relationship between this phenomenon and the anomalous properties of the solvent. [ABSTRACT FROM AUTHOR]

Four temperatures to characterize the gel transition in reversible associating polymers have been calculated in a novel mixed molecular dynamics/Monte Carlo model. (1) The temperature below which relaxation times no longer show Arrhenius dependence on temperature; (2) the Vogel-Fulcher temperature at which the structural relaxation time extrapolates to infinity; (3) the micelle formation temperature at which the number of reversible bonds sharply increases; and (4) a crossover temperature at which the viscosity exhibits a power law divergence as predicted by mode coupling theory. These specific temperatures are obtained from measurements of diffusivity, specific heat, and network topology. [ABSTRACT FROM AUTHOR]

The description of fluctuations by single chain in mean field (SCMF) simulations is discussed and the results of this particle-based self-consistent field technique are quantitatively compared to Monte Carlo simulations of the same discretized Edwards-Hamiltonian providing exact reference data. In SCMF simulations one studies a large ensemble of noninteracting molecules subjected to real, external fields by Monte Carlo simulations. The external fields approximate nonbonded, instantaneous interactions between molecules. In the self-consistent mean field theory the external fields are static and fluctuation effects are ignored. In SCMF simulations, the external fields fluctuate since they are frequently recalculated from the instantaneous density distribution of the ensemble of molecules. In the limit of infinitely high density or instantaneous update of the external fields, the SCMF simulation method accurately describes long-wavelength fluctuations. At high but finite updating frequency the accuracy depends on the discretization of the model. The accuracy is illustrated by studying the single chain structure and intermolecular correlations in polymer melts, and fluctuation effects on the order-disorder transition of symmetric diblock copolymers. [ABSTRACT FROM AUTHOR]

We present a mesoscale simulation technique, called the reaction ensemble dissipative particle dynamics (RxDPD) method, for studying reaction equilibrium of polymer systems. The RxDPD method combines elements of dissipative particle dynamics (DPD) and reaction ensemble Monte Carlo (RxMC), allowing for the determination of both static and dynamical properties of a polymer system. The RxDPD method is demonstrated by considering several simple polydispersed homopolymer systems. RxDPD can be used to predict the polydispersity due to various effects, including solvents, additives, temperature, pressure, shear, and confinement. Extensions of the method to other polymer systems are straightforward, including grafted, cross-linked polymers, and block copolymers. To simulate polydispersity, the system contains full polymer chains and a single fractional polymer chain, i.e., a polymer chain with a single fractional DPD particle. The fractional particle is coupled to the system via a coupling parameter that varies between zero (no interaction between the fractional particle and the other particles in the system) and one (full interaction between the fractional particle and the other particles in the system). The time evolution of the system is governed by the DPD equations of motion, accompanied by changes in the coupling parameter. The coupling-parameter changes are either accepted with a probability derived from the grand canonical partition function or governed by an equation of motion derived from the extended Lagrangian. The coupling-parameter changes mimic forward and reverse reaction steps, as in RxMC simulations. [ABSTRACT FROM AUTHOR]

We study the equilibrium properties of flexible polymer chains confined in a soft tube by means of extensive Monte Carlo simulations. The tube wall is that of a single sheet six-coordinated self-avoiding tethered membrane. Our study assumes that there is no adsorption of the chain on the wall. By varying the length N of the polymer and the tube diameter D we examine the variation of the polymer gyration radius Rg and diffusion coefficient Ddiff in soft and rigid tubes of identical diameter and compare them to scaling theory predictions. We find that the swollen region of the soft tube surrounding the chain exhibits a cigarlike cylindrical shape for sufficiently narrow tubes with D≤Rg. The observed scaling of static conformational properties with chain length N and tube diameter D follows the predictions of scaling theory and displays no significant difference between soft and rigid tubes. The Brownian dynamics of the polymer diffusion in a rigid tube is found to slow down in a tube with soft walls by an amount which depends on the Rg/D ratio albeit the relaxation time τ∥ for diffusive motion along the tube still scales as τ∥∝N3. [ABSTRACT FROM AUTHOR]

In solutions of star-branched polyelectrolytes, electrostatic interactions between charged arms on neighboring stars can compete with intrastar interactions and rotational entropy to induce anisotropy in the orientational distribution of arms. We explore the influence of arm orientational anisotropy on effective star-star interactions for model stars comprising rigid rodlike arms with evenly spaced charged monomers interacting via an effective screened-Coulomb (Yukawa) potential. Monte Carlo simulation and density-functional theory are used to compute the arm orientational distributions and effective pair potentials between weakly charged stars. For comparison, a torque balance analysis is performed to obtain the configuration and energy of the ground state, in which the torque vanishes on each arm of the two-star system. The degree of anisotropy is found to increase with the strength of electrostatic interactions and proximity of the stars. As two stars begin to overlap, the forward arms are pushed back by interstar arm-arm repulsion, but partially interdigitate due to rotational entropy. At center-center separations approaching complete overlap, the arms relax to an isotropic distribution. For nonoverlapping stars, anisotropy-induced changes in the intra- and interstar arm-arm interactions largely cancel and the effective pair interactions are then well approximated by a simple Yukawa potential, as predicted by linear-response theory for a continuum model of isotropic stars [A. R. Denton, Phys. Rev. E 67, 11804 (2003)]. For overlapping stars, the effective pair interactions in the simple rigid-arm-Yukawa model agree closely with simulations of a molecular model that includes flexible arms and explicit counterions [A. Jusufi et al., Phys. Rev. Lett. 88, 018301 (2002); J. Chem. Phys. 116, 11011 (2002)]. [ABSTRACT FROM AUTHOR]

We study polymer-polymer phase separation in a common good solvent by means of Monte Carlo simulations of the bond-fluctuation model. Below a critical, chain-length-dependent concentration, no phase separation occurs. For higher concentrations, the critical demixing temperature scales nonlinearly with the total monomer concentration, with a power law relatively close to a renormalization-group prediction based on “blob” scaling arguments. We point out that earlier simulations and experiments have tested this power-law dependence at concentrations outside the validity regime of the scaling arguments. The critical amplitudes of the order parameter and the zero-angle scattering intensity also exhibit chain-length dependences that differ from the conventional predictions but are in excellent agreement with the renormalization-group results. In addition, we characterize the variation of the average coil shape upon phase separation. [ABSTRACT FROM AUTHOR]

The conformational properties and static structure of freely jointed hard-sphere chains in matrices composed of stationary hard spheres are studied using Monte Carlo simulations and integral equation theory. The simulations show that the chain size is a nonmonotonic function of the matrix density when the matrix spheres are the same size as the monomers. When the matrix spheres are of the order of the chain size the chain size decreases monotonically with increasing matrix volume fraction. The simulations are used to test the replica-symmetric polymer reference interaction site model (RSP) integral equation theory. When the simulation results for the intramolecular correlation functions are input into the theory, the agreement between theoretical predictions and simulation results for the pair-correlation functions is quantitative only at the highest fluid volume fractions and for small matrix sphere sizes. The RSP theory is also implemented in a self-consistent fashion, i.e., the intramolecular and intermolecular correlation functions are calculated self-consistently by combining a field theory with the integral equations. The theory captures qualitative trends observed in the simulations, such as the nonmonotonic dependence of the chain size on media fraction. [ABSTRACT FROM AUTHOR]

We have performed Monte Carlo simulations to study the effect of cyclic architecture on the behavior of homopolymer chains under several conditions of confinement. The collapse of the rings in two stages, a coil-to-globule and a liquidlike-to-solidlike transition, was observed even at extreme confinement. Both transitions were observed at lower temperatures than for linear chains of the same length, 2%–5% lower for unconfined systems, and 10%–15% lower for wall separations below three bond lengths due to the effect of confinement. When the plates separation approached the two-dimensional regime, the coil-to-globule transition shifted to lower temperatures. The inverse trend was observed when the chain length was increased. In the collapsed state, the average size and conformations of linear and cyclic molecules of same length were similar independently of confinement. At temperatures near the coil-to-globule transition, the radius of gyration of unconfined linear chains, (R2g)linear, became larger than for the cyclic chains, (R2g)cyclic, and this difference increased considerably with confinement. The radius of gyration ratio (Rg2)linear/(Rg2)cyclic in this region decreased rapidly. The decrease was more pronounced and occurred at lower temperatures for slit width confinements. At higher temperatures, in the coil state, the radius of gyration ratio became nearly constant for a given separation, and varied from 0.56 for unconfined systems to 0.47 when the chain was completely confined between the walls. This reduction was attributed to the higher increase in the average size of linear chains with confinement when compared with cyclic chains, due to architectural restrictions. [ABSTRACT FROM AUTHOR]

The structure and phase behavior of oppositely charged macroions in solution have been studied with Monte Carlo simulations using the primitive model where the macroions and small ions are described as charged hard spheres. Size and charge symmetric, size asymmetric, and charge asymmetric macroions at different electrostatic coupling strengths are considered, and the properties of the solutions have been examined using cluster size distribution functions, structure factors, and radial distribution functions. At increasing electrostatic coupling, the macroions form clusters and eventually the system displays a phase instability, in analogy to that of simple electrolyte solutions. The relation to the similar cluster formation and phase instability occurring in solutions containing oppositely charged polymers is also discussed. [ABSTRACT FROM AUTHOR]

The effect of chain stiffness and entanglements on the elastic behavior and microscopic structure of cross-linked polymer networks was studied using Monte Carlo simulations. We investigated the behavior of entangled and entanglement-free networks at various degrees of chain stiffness and densities. Based on previous results that indicated that trapped entanglements prevent strain-induced order-disorder transitions in semiflexible chain networks, we prepared the entangled networks by end-linking the chains in very dilute conditions so as to minimize the extent of trapped entanglements. We also considered the entanglement-free case by using a “diamond” structure. We found that the presence of even a very small amount of trapped entanglements is enough to prevent a discontinuous strain-induced transition to an ordered phase. In these mildly entangled networks, a nematiclike order is eventually attained at high extensions but the elastic response remains continuous and the cross-links remain uniformly distributed through the simulation box. The entanglement-free diamond networks on the other hand show discontinuities in their stress-strain data. Networks at higher densities exhibit a more stable ordered phase and show an unusual staircaselike stress-strain curve. This is the result of a stepwise extension mechanism in which the chains form ordered domains that exclude the cross-links. Extension is achieved by increasing the number of these ordered domains in the strain direction. Cross-links aggregate in the spaces between these ordered domains and form periodic bands. Each vertical upturn in the stress-strain data corresponds to the existence of an integer number of ordered domains. This stepwise elastic behavior is found to be similar to that exhibited by some tough natural materials. [ABSTRACT FROM AUTHOR]

A density-functional theory is presented to study the structure of polymers, having attractive interactions, confined between attractive surfaces. The theory treats the ideal-gas free-energy functional exactly and uses weighted density approximation for the hard-chain contribution to the excess free-energy functional. The bulk interactions of freely jointed hard spheres are obtained from generalized Flory equation of state and the attractive interactions are calculated using the direct correlation function obtained from the polymer reference interaction site model theory along with the mean spherical approximation closure. The theoretical predictions are found to be in quite good agreement with the Monte Carlo simulation results for varying densities, chain lengths, and different interaction potentials. The results confirm important implications of using different approximations for the hard-sphere and attractive interactions. [ABSTRACT FROM AUTHOR]

We study a system of grafted polymers in a poor solvent by self-consistent-field methods as well as Monte-Carlo simulation methods. We observe a number of different morphological structures including an inverted solvent micelle or hole in the polymer layer, a lamella-like micelle structure, and fused, spherical micelle structures. These structures can be obtained by either varying the grafting density or chain length. We also develop a scaling theory for the existence of these structures and find reasonable agreement between this theory and our numerical calculations. [ABSTRACT FROM AUTHOR]

The gelation of physically associating triblock copolymers in a good solvent was investigated by Monte Carlo simulation, and the effect of the solvent size on the gelation was discussed in detail. The solvent size can greatly affect the conformation distribution of the polymer chains, the size distribution of the micelle, and the mechanism of the gelation on microscale, mesoscale, and macroscale. Our results indicate that the effect of the solvent size on the physical gelation exhibits three distinct regions. The gelation closely couples to the chain conformation transition when the solvent size is normal or quasinormal; the gelation occurs simultaneously with phase separation when the solvent size approaches the ideal end-to-end distance of the polymer chains; the gelation follows a glass transition mechanism upon increasing the solvent size to much larger than the ideal end-to-end distance of polymer chains. We also found that the volume fraction of the gel point can shift from 0.20 to 0.06, a range much broader than that reported in the literature. [ABSTRACT FROM AUTHOR]

Counterion condensation and release in micellar solutions are investigated by direct measurement of counterion concentration with ion-selective electrode. Monte Carlo simulations based on the cell model are also performed to analyze the experimental results. The degree of counterion condensation is indicated by the concentration ratio of counterions in the bulk to the total ionic surfactant added, α≤1. The ionic surfactant is completely dissociated below the critical micelle concentration (cmc). However, as cmc is exceeded, the free counterion ratio α declines with increasing the surfactant concentration and approaches an asymptotic value owing to counterion condensation to the surface of the highly charged micelles. Micelle formation leads to much stronger electrostatic attraction between the counterion and the highly charged sphere in comparison to the attraction of single surfactant ion with its counterion. A simple model is developed to obtain the true degree of ionization, which agrees with our Monte Carlo results. Upon addition of neutral polymer or monovalent salts, some of the surfactant counterions are released to the bulk. The former is due to the decrease of the intrinsic charge (smaller aggregation number) and the degree of ionization is increased. The latter is attributed to competitive counterion condensation, which follows the Hefmeister series. This consequence indicates that the specific ion effect plays an important role next to the electrostatic attraction. [ABSTRACT FROM AUTHOR]

The structure and the statistical fluctuations of interfaces between coexisting phases in the Asakura–Oosawa model [J. Chem. Phys. 22, 1255 (1954)] for a colloid-polymer mixture are analyzed by extensive Monte Carlo simulations. We make use of a recently developed grand canonical cluster move with an additional constraint stabilizing the existence of two interfaces in the (rectangular) box that is simulated. Choosing very large systems, of size L×L×D with L=60 and D=120, measured in units of the colloid radius, the spectrum of capillary wave-type interfacial excitations is analyzed in detail. The local position of the interface is defined in terms of a (local) Gibbs surface concept. For small wave vectors capillary wave theory is verified quantitatively, while for larger wave vectors pronounced deviations show up. When one analyzes the data in terms of the concept of a wave vector–dependent interfacial tension, a monotonous decrease of this quantity with increasing wave vector is found. Limitations of our analysis are critically discussed. [ABSTRACT FROM AUTHOR]

We exploit known properties of universal ratios, involving the radius of gyration Rg, the second and third virial coefficients B2 and B3, and the effective pair potential between the centers of mass of self-avoiding polymer chains with nearest-neighbor attraction, as well as Monte Carlo simulations, to investigate the crossover from good- to θ-solvent regimes of polymers of finite length L. The scaling limit and finite-L corrections to scaling are investigated in the good-solvent case and close to the θ temperature. Detailed interpolation formulas are derived from Monte Carlo data and results for the Edwards two-parameter model, providing estimates of universal ratios as functions of the observable ratio A2=B2/Rg3 over the whole temperature range, from the θ point to the good-solvent regime. The convergence with L (L≤8000) is found to be satisfactory under good-solvent conditions, but longer chains would be required to match theoretical predictions near the θ point, due to logarithmic corrections. A quantitative estimate of the universal ratio A3=B3/Rg6 as a function of temperature shows that the third virial coefficient remains positive throughout, and goes through a pronounced minimum at the θ temperature, which goes to zero as 1/ln L in the scaling limit. [ABSTRACT FROM AUTHOR]

The configurational properties of a single polyelectrolyte chain accompanied by counterions and added salt are simulated using the cooperative motion algorithm on the face-centered cubic lattice. In particular, a greater emphasis is put on the effect of valence zs and concentration of the added positive (negative) salt ions ns on the polymer behavior. This is achieved by inspecting two families of systems with widely varying numbers ns of monovalent (zs=1) or multivalent (zs=4) salt ions at two fixed reduced temperatures T*=0.5, 1. The calculations indicate that especially at the lower temperature the addition of some amount of multivalent salt has a tremendous impact on chain conformations compared to the situation with monovalent salt. Even for relatively low concentrations of the former, the mean radius of gyration 〈s2〉1/2 and the mean end-to-end distance 〈R2〉1/2 decrease sharply, i.e., the polymer exists in strongly collapsed forms. This reduction of polymer size is also accompanied by a drop in the system inner energy e* and the effective mean charge per monomer q*. The analysis of various pair-correlation functions gab(r) indicates that the latter effect—caused by condensation of ions onto the chain—is dominated by the multivalent ones. Furthermore, it is found that for zs=4, the uncondensed salt ions tend to group themselves into small clusters. [ABSTRACT FROM AUTHOR]

The conformation and titration curves of weak (or annealed) hydrophobic polyelectrolytes have been examined using Monte Carlo simulations with screened Coulomb potentials in the grand canonical ensemble. The influence of the ionic concentration pH and presence of hydrophobic interactions has been systematically investigated. A large number of conformations such as extended, pearl-necklace, cigar-shape, and collapsed structures resulting from the subtle balance of short-range hydrophobic attractive interactions and long-range electrostatic repulsive interactions between the monomers have been observed. Titration curves were calculated by adjusting the pH-pK0 values (pK0 represents the intrinsic dissociation constant of an isolated monomer) and then calculating the ionization degree α of the polyelectrolyte. Important transitions related to cascades of conformational changes were observed in the titration curves, mainly at low ionic concentration and with the presence of strong hydrophobic interactions. We demonstrated that the presence of hydrophobic interactions plays an important role in the acid-base properties of a polyelectrolyte in promoting the formation of compact conformations and hence decreasing the polyelectrolyte degree of ionization for a given pH-pK0 value. [ABSTRACT FROM AUTHOR]

The collapse behavior of a single comblike copolymer chain has been studied by Monte Carlo simulations. It has been supposed that the solvent is good for the side chains but the solvent quality for the backbone chain changes. It has been shown that depending on the structural parameters of the comb copolymer (the lengths of the backbone and side chains, grafting density of the side chains) various thermodynamically stable morphologies of the collapsed backbone chain can be realized. In addition to ordinary spherical globule we have observed elongated structures as well as necklacelike conformations. The proposed model can be used to describe conformational behavior of stoichiometric complexes between block copolymers with a polyelectrolyte short block and oppositely charged linear homopolymers. [ABSTRACT FROM AUTHOR]

A statistical mechanical model is presented which explicitly accounts for the fluctuations, the electrostatic, and the excluded volume correlations for ions bound to a polyelectrolyte such as DNA. The method can be employed to treat a wide range of ionic conditions including multivalent ions. The microscopic framework of the theory permits the use of realistic finite length and grooved structural model for the polyelectrolyte and modeling of the finite size of the bound ions. Test against Monte Carlo simulations suggests that the theory can give accurate predictions for the ion distribution and the thermodynamic properties. For multivalent ions, the theory makes improved predictions as compared with the mean-field approach. Moreover, for long polyelectrolyte and dilute salt concentration, the theory predicts ion binding properties that agree with the counterion condensation theory.© 2005 American Institute of Physics. [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]

Filamentous viruses such as fd and M13 are highly charged rodlike polyelectrolytes. In this study, we employ fd virus to test the recent prediction of charge inversion [Nguyen, Rouzina, and Shklovskii, J. Chem. Phys. 112, 2562 (2000)]. Light scattering measurements show bundle formation and resolubilization of fd viruses when MgCl2 was added from 0 to 600 mM. The effective charge of fd was studied by measuring their electrophoretic mobility using a filament tracking method uniquely suited for the system. Monte Carlo simulations were performed under canonical ensemble to predict the charge distribution around the rodlike virus. Charge inversion, which has been suggested theoretically to accompany with bundle resolubilization, was not observed in either experiments or simulations. A modified analysis of force balance is called upon to account for these new findings. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Monte Carlo simulations with a coarse-grained model were performed to study the microstructure of a semifluoroalkane C20 diblock oligomer [F(CF2)10(CH2)10H]. The coarse-grained model adopted is based on previously reported united-atom force fields for alkanes and perfluoroalkanes and was first validated by simulating the phase behavior of a mixture of hexane and perfluorohexane. These preliminary simulations established the need of a significant correction factor in the Berthelot mixing rule between alkane and perfluoroalkane groups. Using such a force field, the semifluorinated C20 oligomer liquid was simulated using efficient Monte Carlo moves to sample different molecular arrangements and box dimensions so as to allow different layering structures to form. In qualitative agreement with experimental observations, a smectic-to-isotropic phase transition occurs as temperature is increased but the transition point and the structure of the smectic phase depend on the stiffness of the torsional potential and the model of van der Waals interactions adopted. We identify two smectic phases LC1′ and LC2′, whose structures do not agree with those that have been postulated before to explain x-ray diffraction data, namely, LC1 and LC2. LC1′ has a layer spacing similar to LC1 but the antiparallel packing is not observed with individual chains but with groups of chains producing a checkerboard pattern. LC2′ has fully microsegregated blocks such as LC2 but the alkyl tails are not fully stretched or interdigitated. Despite these inconsistencies, and considering that reported experimental data also reveal the presence of mixed phases, the simulated structures suggest other plausible ways how the semifluorinated chains could pack and microsegregate to best negotiate energetic and entropic constraints. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]