高分子构象模拟研究中的Monte Carlo方法

介绍了Monte Carlo方法及其特点,进而分析了Monte Carlo用于高分子模拟的优势,并描述了两类模拟模型。论文重点综述了近年来Monte Carlo方法在高分子构象模拟中的一些研究与应用,并展望了Monte Carlo方法在高分子构象模拟中的发展趋势和前景。     

Mechanical and gas transport properties of poly-ϵ-caprolactone model networks

The glass transition temperature increases with increasing crosslink densities in model networks formed by endlinking poly-?-caprolactone with a triisocyanate crosslinking agent. In the noncrystalline networks, the gas permeability decreases with increasing crosslink density. These results are consistent with an interpretation that the crosslinks reduce the main-chain molecular motions which are important to these processes. At the lowest crosslink density, where poly-?-caprolactone networks are crystalline, the gas permeability is lower than would be expected based on the volume fraction of amorphous polymer. The excess reduction in permeability is attributed to crystallization-induced enrichment of crosslink junction points in the amorphous fraction of the network. This reduces the permeability by creating an artificially high crosslink density in those regions of the network responsible for gas transport. Since crosslinking increases the stiffness and reduces the flexibility of the network polymer chains, it affects large penetrants more strongly than small ones. Therefore, increasing the crosslink density proves to be a useful method for increasing gas separation factors.     

Monte Carlo simulation of molecular motion and phase transition in poly(ethylene) crystal

Conformational properties of a chain and a phase transition in poly(ethylene) crystal are studied by extending a previous Monte Carlo calculation for a chain in a cylindrical crystalline potential. The crystalline potential is here estimated from van der Waals interactions between one CH₂ group of a chain and its six neighbouring chains. Firstly, conformational disorders of the chains of various chain length are examined, and a definite dependence of the chain conformation on its length is demonstrated. Secondly, the behaviour of the chain at atmospheric pressure is simulated, where the modes of molecular motions and the associated disorders in conformation are clarified as a function of temperature. Thirdly, the phase transition at high temperature and pressure, from orthorhombic phase to hexagonal one, is simulated by assuming a proper molecular field for the chain. All these calculations show the present Monte Carlo calculation to have a wide variety of applications in the studies of polymer crystals.     

Molecular structural evolution in crosslinking low density polyethylene–trimethylolpropane trimethacrylate systems

A Monte Carlo simulation algorithm for investigation the structural growth in a polymer‐polyfunctional monomer system and the method to obtain the required simulation parameters are proposed. Combining the Monte Carlo sampling technique and swell ratio experiments, the molecular structural evolution in crosslinking LDPE‐TMPTMA systems is explored. The crosslinking level can be effectively promoted at high TMPTMA concentrations and at high cure temperatures. With increasing overall crosslinking density, gelation occurs at lower degree of conversions; the gel corsslinking density, increases: the TMPTMA densities in both sol and gel fractions also increase; while the sol polymer molecular weights and the sol crosslinking density decrease. The implications of the simulated results to the processing of LDPE‐TMPTMA compounds are also discussed.     

Mechanistic investigation of the simultaneous addition and free-radical polymerization in batch miniemulsion droplets: Monte Carlo simulation versus experimental data in polyurethane/acrylic systems

A detailed kinetic Monte Carlo simulation was used to predict the characteristics of the batch miniemulsion polymerization of an isocyanate and an acrylic monomer mixture that contains a hydroxyl functional monomer (HEMA). The simulation takes into account the simultaneous polyaddition of the polyurethane prepolymer with the hydroxyl group of HEMA and the free radical polymerization of the acrylic monomers and all reactions in aqueous and polymer particle phases. The model has been assessed by batch miniemulsion polymerizations carried out using an aliphatic isocyanate prepolymer, n-butyl acrylate, 2-hydroxyethyl methacrylate monomers and potassium persulfate as an initiator. It was found that partitioning of water had a significant effect on both kinetics and microstructure of the resulting polymer. Evolution of different species of PU prepolymer produced in the reaction and the sol and gel fractions revealed that the terminal pendent double bond of the HEMA in polymer chains has significantly lower reactivity than that of the HEMA free monomer. Detailed information on gel microstructure has been derived in the model by both distribution of molecular weight between crosslinking points in acrylic chains and distribution of chain extension of PU prepolymers. These crosslinking density distributions can be related to mechanical and adhesive properties of the polymer.     

An application of Monte Carlo method to simulate disorders in polymer crystals

The Monte Carlo method is applied to polymer crystals of idealized linear chain molecules of 30 carbon atoms, and the unharmonic, large-amplitude, oscillations and the subsequent conformational disorders of the chains are investigated. A crystalline field that confines the chain is treated by the molecular field approximation, and assumed to be cylindrical in this work. A production type simulation is adopted taking into account rigorous statistical weights for each sample conformation. Both the rotational isomeric model and the continuous rotation model of chain conformation are considered. By averaging over 10⁴–8 × 10⁴ chains, mean-square end-to-end distance, fractions of gauche and trans states and a detailed distribution of internal rotation angle are obtained. The effects of temperature and pressure on the conformation of the chain in the crystals are also simulated.     

Prediction of Viscoelastic Properties of Enzymatically Crosslinkable Tyramine–Modified Hyaluronic Acid Solutions Using a Dynamic Monte Carlo Kinetic Approach

The present study deals with the mathematical modeling of crosslinking kinetics of polymer–phenol conjugates mediated by the Horseradish Peroxidase (HRP)-hydrogen peroxide (H₂O₂) initiation system. More specifically, a dynamic Monte Carlo (MC) kinetic model is developed to quantify the effects of crosslinking conditions (i.e., polymer concentration, degree of phenol substitution and HRP and H₂O₂ concentrations) on the gelation onset time; evolution of molecular weight distribution and number and weight average molecular weights of the crosslinkable polymer chains and gel fraction. It is shown that the MC kinetic model can faithfully describe the crosslinking kinetics of a finite sample of crosslinkable polymer chains with time, providing detailed molecular information for the crosslinkable system before and after the gelation point. The MC model is validated using experimental measurements on the crosslinking of a tyramine modified Hyaluronic Acid (HA-Tyr) polymer solution reported in the literature. Based on the rubber elasticity theory and the MC results, the dynamic evolution of hydrogel viscoelastic and molecular properties (i.e., number average molecular weight between crosslinks, M_c, and hydrogel mesh size, ξ) are calculated.     

Monte carlo approach to estimating the photodegradation of polymer coatings

The degradation of a polymer coating and predicting the coating lifetime based on physical properties and distribution within the coating of the polymer binder, pigments, and fillers are economically very important. As technologies advance and allow for control of coatings at the nanoscale level, methods such as Monte Carlo can be used not only to predict the behavior of a nanodesigned coating with time but also to design coatings, such as optimizing pigment particle distributions or optimum hard and soft phase distributions of the binders in multiphase systems for maintaining the desired property with time. Erosion of the coating surface was simulated using Monte Carlo techniques where terrestrial solar flux is the initiator for polymer segment cleavage and removal. The impact on the sensitivity of the polymer adjacent to the detached polymer segment can be increased or decreased in the model based on the chemistry and surface energy of the remaining polymer matrix. Multiple phases with varying sensitivity to degradation can be modeled. The Monte Carlo generates a statistically similar surface topography and chemistry of the coating. The results of the Monte Carlo model are compared to measurable properties such as gloss, fracture toughness, and wetting contact angle, using various published correlations of the property to the surface topology. The simulated properties change through the life-time of the coating in ways that are consistent with observed behavior. Apparently, complicated changes in many properties can be described by the repeated application of simple, random processes. Presented at the 79th Annual Meeting of the Federation of Societies for Coatings Technology, October 28–November 1, 2002, in New Orleans, LA.     

Blocked crystallization in capped ultrathin polymer films studied by molecular simulations

The crystallization of capped ultrathin polymer films is closely dependent on film thickness and interfacial interaction. Using dynamic Monte Carlo simulations, the crystallization behaviors of polymer films confined between two substrates were investigated. The crystallization rate of confined polymers is reduced with high interfacial interactions. Above a critical strength of interfacial interaction, polymer crystallization in the thin film is inhibited within the simulation time scales. An increase in film thickness leads to a rise in critical interfacial interaction. In thicker films, the chains have more space to change conformation to form crystal stems. In addition, there are fewer absorbed segments in confined chains for the thicker films, and thus the chains have stronger ability to adjust their conformation. Therefore an increase in film thickness can cause a reduction in the entropic barrier required for the formation of crystals and thus an increase in the critical interfacial interaction. © 2018 Society of Chemical Industry     

蒙特卡洛模拟高分子溶液在泊肃叶流场中的运动

研究流场中高分子溶液的行为具有非常重要的作用。运用格子链动态蒙特卡洛模拟研究泊肃叶流场中高分子溶液链的运动行为,考察了流场大小不同时对链的均方回转半径及取向度的影响。结果表明流场越大,链的变形越明显,且整条链沿着流场方向发生明显的取向。最后给出了高分子链在外加流场中的形态图,证实了流场中高分子链的变形及取向。     

Structure of polymers in the vicinity of convex impenetrable surfaces: the athermal case

The influence of the presence of a curved (convex) solid wall on the conformations of long, flexible polymer chains is studied in a dense polymer system and in the athermal limit by means of lattice Monte Carlo simulations. It is found that the chain conformation entropy drives a reduction of the density at the wall, similar to the flat wall case. The chain end density is higher next to the interface compared to the bulk polymer (segregation), with the difference increasing with chain length. The wall curvature does not significantly affect the segregation. The bonds are preferentially oriented in the direction tangential to the wall. The distance from the interface over which this effect is observed is about two bond lengths. Similar results are obtained when probing the preferential orientation of chain segments. In this case, the perturbed region has a thickness on the order of the considered probing chain segment length. This suggests that experimental results on the thickness of the ‘bonded layer’ next to a wall depend on the wavelength of the radiation employed for probing. The chains are ellipsoidal in the bulk and rotate close to the surface with the large semi-axis of the ellipsoid normal to the line connecting their center of mass with the filler center. Since there is no energetic interaction with the filler, no adsorption transition is observed, but the chains tend to wrap around the filler once the gyration radius becomes comparable to the filler radius.     

Monte Carlo simulation of radiation-induced solid state polymerization

A Monte Carlo method was used for a computer simulation of radiation-induced solid state polymerization. The propagation of polymer chains was simulated by means of self-avoiding random walks on a tetrahedral lattice. The initiation and termination of the chains were modelled by pseudorandom processes. The influence of conditions of the in-source process on the post-polymerization kinetics and on the degree of polymerization of the polymers was studied.     

Properties of branched polymer chains adsorbed on a patterned surface

The aim of this study was to investigate the properties of polymer chains strongly adsorbed on a planar surface. Model macromolecules were constructed of identical segments, the positions of which were restricted to nodes of a simple cubic lattice. The chains were in good solvent conditions, thus, the excluded volume was the only interaction between the polymer segments. The polymer model chain interacted via a simple contact potential with an impenetrable flat surface with two kinds of points: attractive and repulsive (the latter being arranged into narrow strips). The properties of the macromolecular system were determined by means of Monte Carlo simulations with a sampling algorithm based on the local conformational changes of the chain. The structure of adsorbed chains was found to be strongly dependent on the distance between the repulsive strips, whenever this distance was very short. The mobility of the chains was also studied and it was found that diffusion across repulsive strips was suppressed for large distances between the strips.     

Curing of styrene‐free unsaturated polyester alkyd: synthesis,characterization and simulation

Experimental and simulation studies of the crosslinking process of styrene‐free unsaturated polyester (UP) alkyd chains are presented. The thermal and mechanical properties of the crosslinked UP alkyd are studied as a function of the peroxide concentration. The characterized and simulated thermoset matrix properties are compared. Simulation of the crosslinking reaction is used to improve the understanding of the process and to define the species involved in it. The main experimental characterization tools used were differential scanning calorimetry and dynamic mechanical analysis. The main simulation tools used were a Monte Carlo procedure for the crosslinking process and a density functional theory‐based quantum code for the scission process. Good agreement between the experimental and simulation results was achieved. Copyright © 2010 Society of Chemical Industry     

Computer-Aided Design of Crosslinked Polymer Membrane Using Machine Learning and Molecular Dynamics

The formation of crosslinking network between polymer chains has significant influence on polymer properties. In particular, the crosslinked structure of ionic networks like proton exchange membrane affects the conductivity performance. To further develop in this area, a framework for polymer membrane design based on the developed quantitative prediction model of the properties of crosslinked polymer is proposed. First, polymers with different crosslinking degrees are constructed by a crosslinking algorithm. Next, molecular dynamics is used to calculate the properties of crosslinked polymers. Then, the quantitative relationship between crosslinked polymer structures and macroscopical properties is developed. Subsequently, computer-aided polymer design method is integrated with the developed quantitative predict model. The crosslinked polymer design problem is expressed as an optimization problem to obtain the optimal crosslinking degree. Bayesian optimization strategy is used to solve the established optimization model. Finally, two case studies of perfluoro sulfonic acid and perfluoro imide acid design are given to illustrate the application of the proposed polymer design framework.     

Silicone Rubber Tack I: Relation to Network Structure

The influence of the network structure on the poly(dimethyl siloxane) (PDMS) rubber is described. The telechelic polymers have crosslinking sites restricted to the ends of polymer chains only, giving well-defined networks. Rubber-rubber tack is related to the network structure, mostly to the amount of loose polymer chains not linked into the network, that can diffuse through the interface. The amount of mobile chains can be adjusted by varying crosslinker amount and functionality. By controlled variation of the degree of crosslinking of the telechelic silicone rubbers, various levels of tack are induced, which may be related to the network topology.     

Influence of confinement on conformational entropy of a polymer chain and structure of polymer-nanoparticles complexes

Behaviour of a polymer chain in the presence of fixed obstacles has been studied by the static Monte Carlo simulations. A modified self-avoiding walk on a cubic lattice has been used to model the polymer in an athermal solution. The statistical counting method has been applied to calculate the conformational entropy of the chain, assumed to be grafted to an obstacle. Different chain lengths and obstacle curvatures have been examined. Some implications of the confinement induced changes in the conformational entropy of polymer chains to the structure of complexes composed of long polymer chains and nanoparticles are discussed.     

Conformational properties and elastic behavior of protein-like lattice polymers

The interior conformations and elastic behaviors of protein-like lattice polymers in the process of tensile elongation are investigated by means of Monte Carlo method and the (310) hybrid lattice model. Here (HHPPHPP)_x sequence of protein-like polymer chains is adopted. It is found that three types of contacts, i.e. HH-, PP- and HP-contact, have different behavior in the process of elongation. Second structures of protein-like chains, i.e. helical, coil and expanded structures, have distinct characteristic in our simulation. The average energy, the Helmholtz free energy and elastic force are also investigated at different temperature. Moreover, and 〈δ^*〉 as a function of elongation ratio carefully reflect the shape change in the process of tensile elongation, and the snapshots of contact maps can directly explain the interior conformation change of protein-like chains, therefore, here we give some discussions about the shape and the snapshots of contact maps. These investigations may provide some insights into the elastic behavior of protein-like chains.     

Monte Carlo study of structure and kinetics of formation of end-linked polymer networks

The kinetics of formation and structural properties of end-linked polymer networks were studied by Monte Carlo simulations on a three-dimensional cubic lattice. Networks were generated from the solutions of linear polymer chains with functional end groups and tetrafunctional cross linkers. Systems of 10-, 20-mer precursor polymer chains with values of the ratio of cross linkers to polymer chains end groups r ranging from 0.9 to 1.4 were studied. Polymer volume fraction ? was varied from 0.1 to 0.5. Different ways of polymer network formation are possible, namely, gel creation process can proceed as homogeneous gelation as well as microgel separation. In addition to those limiting ways of polymerization process, intermediate cases were observed. All varied parameters (length of precursor polymer chains N, r and ?) influence the kinetics of the cross-linking. An algorithm to determine the soluble fraction in solution and the amount of loops and pendent structures in the polymer network was proposed. In agreement with experimental observations, simulations show that networks with lower soluble fractions which are more defect-free result from long precursor polymer chains (N=20) for approximately polymer melt densities (?≈0.4) at higher than stoichiometric r values (r≈1.2).