Monte Carlo simulation of the structure of mono- and bidisperse polyethylene nanocomposites

The structure of bidisperse polyethylene(PE) nanocomposite mixtures of 50:50(by mole) of long and short chains of C160H322/C80H162 and C160H322/C40H82 filled with spherical nanoparticles were investigated by a coarse-grained, on lattice Monte Carlo method using rotational isomeric state theory for short-range and Lennard-Jones for long-range energetic interactions. Simulations were performed to evaluate the effect of wall-to-wall distance between fillers(D), polymer-filler interaction(w) and polydispersity(number of short chains in the mixture) on the behavior of the long PE chains. The results indicate that long chain conformation statistics remain Gaussian regardless of the effects of confinement, interaction strength and polydispersity. The various long PE subchain structures(bridges, dangling ends, trains, and loops) are influenced strongly by confinement whereas monomer-filler interaction and polydispersity did not have any impact. In addition, the average number of subchain segments per filler in bidisperse PE nanocomposites decreased by about 50% compared to the nanocomposite system with monodisperse PE chains. The presence of short PE chains in the polymer matrix leads to a reduction of the repeat unit density of long PE chains at the interface suggesting that the interface is preferentially populated by short chains.     

Monte Carlo simulation of polymer adsorption

We developed and employed the incremental gauge cell method to calculate the chemical potential (and thus free energies) of long, flexible homopolymer chains of Lennard-Jones beads with harmonic bonds. The free energy of these chains was calculated with respect to three external conditions: in the zero-density bulk limit, confined in a spherical pore with hard walls, and confined in a spherical pore with attractive pores, the latter case being an analog of adsorption. Using the incremental gauge cell method, we calculated the incremental chemical potential of free polymer chains before and after the globual-random coil transitions. We also found that chains confined in attractive pores exhibit behaviors typical of low temperature physisorption isotherms, such as layering followed by capillary condensation.     

Monte Carlo simulation of polymer welding

Monte Carlo Modelling of random polymer chains, course grained onto a cubic F lattice, provides the ability to monitor the long range relaxation processes and the dynamic parameters of chains up to 400 units long. The model, described and verified by Haire et al. (Haire KR, Carver TJ, Windle AH. A Monte Carlo model for dense polymer systems and its interlocking with molecular dynamics simulation. Computational and Theoretical Polymer Science 2000; in press), is here applied to the study of molecular parameters in the vicinity of different types of surface and also to the process of polymer welding, whereby adhesion between two adjacent surfaces is achieved by the interpenetration of chains which are across the surface.The model demonstrates that a surface distorts the conformation of chains adjacent to it to give an oblate molecular envelope, that the concentration of vacant sites and chain ends increases near to the surface and that the density of points representing the centres of mass of the chains increases in the sub-surface regions. These results confirm earlier predictions and provide additional confidence in the model.Modelling of the welding process leads to the parameter intrinsic weld time, t_w, which is the time from initial perfect contact of the surfaces to the achievement of a weld within which the chain conformation is indistinguishable from the bulk. After the initial period in which the mating surfaces roughen, the welding proceeds according to the t^1/4 law predicted by reptation theory. The time to a given level of interdiffusion across the boundary is proportional to the chain length l, a comparatively weak dependence, while t_w is proportional to l³, a strong dependence. This is the same dependence on length as for the relaxation time of the chain end-to-end vectors. In fact, the agreement between the relaxation time, measured on the model of the bulk, and t_w is surprisingly close, at least for the monodisperse polymers investigated here.     

Monte Carlo simulation of miscibility of polymer blends with repulsive interactions: effect of chain structure

The effects of the chain structure and the intramolecular interaction energy of an A/B copolymer on the miscibility of the binary blends of the copolymer and homopolymer C have been studied by means of a Monte Carlo simulation. In the system, the interactions between segments A, B and C are more repulsive than those between themselves. In order to study the effect of the chain structure of the A/B copolymer on the miscibility, the alternating, random and block copolymers were introduced in the simulations, respectively. The simulation results show that the miscibility of the binary blends strongly depends on the intramolecular interaction energy () between segments A and B within the A/B copolymers. The higher the repulsive interaction energy, the more miscible the A/B copolymer and homopolymer C are. For the diblock copolymer/homopolymer blends, they tend to form micro phase domains. However, the phase domains become so small that the blend can be considered as a homogeneous phase for the alternating copolymer/homopolymer blends. Furthermore, the investigation of the average end-to-end distance () in different systems indicates that the copolymer chains tend to coil with the decrease of whereas the of the homopolymer chains depends on the chain structure of the copolymers. As for the system containing the alternating or the random copolymers, the homopolymer chains also tend to coil with the decrease of . However, for the systems including the block copolymers, there is a slight difference in the of the homopolymer chains with the variation of .     

Monte Carlo simulation studies of polymer systems

Polymers molecules in solution or melt are more or less flexible and continuously change their shape and size. Thus, characteristic properties of the system fluctuate around statistical mean values which are dependent on the concentration of the solution, on the quality of the solvent used, and on the specific structure of the molecules, e.g. linear or star-branched. The most direct approach to these quantities on a molecular level are computer simulations. Due to restrictions of computer power fully atomistic simulations of macromolecules are presently still at the beginning but several arguments justify the use of simplified models. The most efficient way dealing with polymer systems are Monte Carlo simulations based on lattice chains, at least as long as static properties are of interest only. In the present paper a short introduction to the field is given and selected examples are presented in order to demonstrate the usefulness of these methods.     

Monte Carlo simulation on polymer translocation in crowded environment

The effect of crowded environment with static obstacles on the translocation of a three-dimensional self-avoiding polymer through a small pore is studied using dynamic Monte Carlo simulation. The translocation time τ is dependent on polymer-obstacle interaction and obstacle concentration. The influence of obstacles on the polymer translocation is explained qualitatively by the free energy landscape. There exists a special polymer-obstacle interaction at which the translocation time is roughly independent of the obstacle concentration at low obstacle concentration, and the strength of the special interaction is roughly independent of chain length N. Scaling relation τ ~ N(1.25) is observed for strong driving translocations. The diffusion property of polymer chain is also influenced by obstacles. Normal diffusion is only observed in dilute solution without obstacles or in a crowded environment with weak polymer-obstacle attraction. Otherwise, subdiffusion behavior of polymer is observed.     

Monte Carlo simulation of polymer mixtures: recent progress

The phase diagram of symmetrical polymer blends (A,B) confined into thin films is studied, considering both the effect of finite film thickness D and of surface forces at the confining walls that either prefer both the same species, or different species. In the case of <“>neutral<”> walls confinement enhances the compatibility of the blend. The critical temperature is depressed, the coexistence curve gets flattened (reflecting a crossover from 3‐dimensional to 2‐dimensional critical behavior). But if both walls preferentially attract species A, then also the critical composition of the blend is shifted to the A‐rich side of the phase diagram, and the coexistence curve exhibits a bulge just above the wetting transition temperature. If one wall attracts A and the other B, lateral phase separation sets in via a first order transition. Above this transition, an interface parallel to the walls is stabilized in the system.     

Monte Carlo simulation in polymer physics: Some recent developments

The computer simulation of macromolecular materials has to deal with phenomena on length scales from 1Å to 100Å, as well as with time scales ranging over many orders of magnitude, and thus still presents a challenge. With suitably coarse-grained models which disregard detailed information on chemical structure nevertheless collective phenomena can be described, such as unmixing of polymer blends, mesophase ordering of block-copolymer melts, “blob formation” in semidilute solutions, etc. Simulations of such models provide a sensitive test of approximate theories and give valuable hints for experiments.     

Biomolecule-directed assembly of nanoscale building blocks studied via lattice Monte Carlo simulation

We perform lattice Monte Carlo simulations to study the self-assembly of functionalized inorganic nanoscale building blocks using recognitive biomolecule linkers. We develop a minimal coarse-grained lattice model for the nanoscale building block (NBB) and the recognitive linkers. Using this model, we explore the influence of the size ratio of linker length to NBB diameter on the assembly process and the structural properties of the resulting aggregates, including the spatial distribution of NBBs and aggregate topology. We find the constant-kernel Smoluchowski theory of diffusion-limited cluster-cluster aggregation describes the aggregation kinetics for certain size ratios.     

Monte Carlo liquid water simulation with four-body interactions included

A four-body interaction potential for water molecules is derived. The new terms are combined with previously developed two- and three-body potential terms and applied in a Metropolis—Monte Carlo simulation at 298 K for an (N, V, T) ensemble with 512 water molecules. Improvements, relative to the results using only two-body, or two- and three-body interactions, are reported for the correlation function g(OO), for the X-ray and neutron-beam scattering intensities, and for the enthalpy.     

Monte Carlo simulation of a polymer-analogous reaction in a polymer blend

The autocatalytic polymer-analogous reaction A → B in a blend composed of two contacting layers of compatible homopolymers A and B is studied by numerical simulation using the dynamic continuum Monte Carlo method. The evolution of the numerical density of units A and units initially belonged to the chains of homopolymer A is investigated in the course of the reaction and interdiffusion. Local characteristics of the distribution of the homopolymer with respect to its composition and blocks A and B with respect to their length are calculated at different times. The dispersions of the above distributions are appreciably higher than the corresponding dispersion of the Bernoullian copolymer of the same average composition, despite the random character of the reaction. This effect can be provided by changes in the composition of the blend on the scale of the reacting chain as well as by the diffusive mixing of the above chains. For the products of the polymer-analogous reaction, the broadening of the compositional distribution is predicted also by the theoretical model, which describes interdiffusion in the reacting system on scales that are markedly greater than the size of a polymer chain.     

Monte Carlo simulation of polarization reversal of ferroelectric polymer polyvinylidene fluoride

We consider a system composed of planar zigzag chain molecules of ferroelectric polymer PVDF. Taking the Lennard–Jones potential and the dipole–dipole interaction into consideration and assuming restrictions on molecular degrees of freedom, we have performed a Monte Carlo simulation which enables us to discuss the polarization reversal of PVDF under constant external electric field. Our simulation shows that the phenomenon is accompanied by nucleation and expansion of reversed domains. It also indicates that the dipole–dipole interaction between molecules causes growth anisotropy of the reversed domains.     

Monte Carlo simulation of phase separation kinetics in a concentrated polymer solution

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Monte Carlo simulation of a lattice model for ternary polymer mixtures

Monte Carlo studies of symmetrical polymer mixturesAB, modelled by selfavoiding walks withN _A =N _B =N steps on a simple cubic lattice, are presented for arbitrary concentrations of vacancies _v in the range from _v =0.2 to _v =0.8 and chain lengthsN64. We obtained the phase diagrams and the equation of state for three choices of the ratio / _AB ( being the energy between monomers of the same kind, _AB being the energy between different monomers). Flory-Huggins theory provides only a qualitative understanding of these results. If the equation of state is fitted with an effective Flory-Huggins parameter _eff , the latter turns out to be strongly dependent on both concentration and temperature.Contributed paper delivered at the Tagung der Deutschen Physikalischen Gesellschaft, Fachausschuß Polymerphysik, Berlin, March 30–April 3, 1987.     

Biopolymer structure simulation and optimization via fragment regrowth Monte Carlo

An efficient exploration of the configuration space of a biopolymer is essential for its structure modeling and prediction. In this study, the authors propose a new Monte Carlo method, fragment regrowth via energy-guided sequential sampling (FRESS), which incorporates the idea of multigrid Monte Carlo into the framework of configurational-bias Monte Carlo and is suitable for chain polymer simulations. As a by-product, the authors also found a novel extension of the Metropolis Monte Carlo framework applicable to all Monte Carlo computations. They tested FRESS on hydrophobic-hydrophilic (HP) protein folding models in both two and three dimensions. For the benchmark sequences, FRESS not only found all the minimum energies obtained by previous studies with substantially less computation time but also found new lower energies for all the three-dimensional HP models with sequence length longer than 80 residues.     

Properties of simple models of polymer networks. A Monte Carlo simulation

A model polymer network was constructed from branched chains. Each chain was built on a simple cubic lattice forming a star-branched polymer consisting of f = 3 arms of equal lengths. The fragment of network under consideration consisted of 1, 2 and 3 star polymers with different topology of connections. The only potential used was excluded volume (athermal chains). The properties of the network were determined by the means of computer simulations using the classical Metropolis sampling algorithm (local micromodifications of chain conformation). The behaviour of linear chains of the same molecular weight was also studied as a state of reference. The influence of attaching the next star-branched chain to the network on its static and dynamic properties was studied. The short-time dynamic behaviour of chain fragments was determined and discussed.     

Critical phenomena in polymer mixtures: Monte Carlo simulation of a lattice model

A lattice model of a symmetrical binary (AB) polymer mixture is studied, modelling the polymer chains by self-avoiding walks withN _A =N _B =N steps on a simple cubic lattice. If a pair of nearest neighbour sites is taken by different monomersAB orBA, an energy _ab is won; if the pair of sites is taken by anAA or aBB pair, an energy is won, while the energy is reduced to zero if at least one of the sites of the pair is vacant. To allow enough chain mobility, 20% of the lattice sites are vacancies. In addition to local motions of the chain segments we use a novel grand-canonical simulation technique:A chains are transformed intoB chains and vice versa, keeping the chemical potential difference fixed. The phase diagram is obtained forN=4, 8,16 and 32; the critical behaviour is analysed by finite-size scaling methods. It is shown that the critical exponents are those of the Ising model (=0.32,=0.63) rather than those of the Flory-Huggins meanfield theory (==1/2). Implications of these results for real polymers are briefly discussed.Paper presented at the Frühjahrstagung 1986, Polymerphysik, der Deutschen Physikalischen Gesellschaft, Kaiserslautern, March 12–14, 1986.     

Lattice Monte Carlo simulation of polymer adsorption at an interface, 1. Monodisperse polymer

Adsorption of a monodisperse polymer at a solid-liquid interface is comprehensively studied by Monte Carlo simulation. The distributions of total segment density and different adsorption configurations including trains, loops and tails are obtained. Effects of reduced exchange interaction energies $ \tilde \varepsilon $, bulk concentrations ϕ^*, reduced adsorption energies $ \tilde \varepsilon_a $ and chain lengths r on those distributions are studied. Comparisons with predictions of the Scheutjens-Fleer (SF) theory are also provided. Generally, the chain molecules are more easily adsorbed at an interface in non-solvents than in good solvents. Longer chains are more likely to be adsorbed than shorter ones. The reduced adsorption energy and the bulk concentration have shown strong effects on the segment-density distributions. In addition, the thickness of the adsorption layer is mainly determined by the extension of tails into the bulk solution, which are in turn determined by the chain length. The trains, loops and tails are overwhelmingly short. On the other hand, the amounts of trains and loops are usually much greater than that of tails. Though not perfect, satisfactory agreement is found in comparison with the theoretical predictions of the SF theory.     

Histogram Monte Carlo simulation on phase transitions in single‐polymer systems

Applying the histogram Monte Carlo simulation method and the bond‐fluctuation model, various phase transitions in single‐polymer systems were investigated. The critical transition temperature (Θ point) in the coil‐globule collapse transition of a macromolecular chain is accurately determined. Finite‐size scaling results near the transition point are verified. The first‐order transition associated with the freezing/crystallization of a polymer at a temperature below the Θ point is also observed. The free energy profiles associated with these two transitions are explicitly computed. Furthermore, the unfolding phase transition associated with stretching a collapsed polymer chain is investigated. The free energy profile associated with the transition is explicitly computed. Results on the energy cumulants and free energy profiles provide direct evidences for the first‐order nature of the unfolding phase transition.