Monte Carlo simulations of the exchange kinetics of polymers adsorbed on a solid surface

The exchange kinetics of polymers adsorbing on a solid surface is extensively studied by dynamic Monte Carlo simulations. A model employed simulates a semidilute polymer solution placed in contact with a solid surface that attracts polymer segments by the adsorption interaction (χ_s). The exchange process of polymer chains, between the solution and the adsorbed polymer layer, is examined under various conditions. The exchange kinetics shows two characteristic regimes with increasing chain length. One is the diffusion‐controlled regime found with a small χ_s , and the other the detachment‐controlled regime with a large χ_s . These two regimes are well described by a kinetic theory. Various dynamic quantities show that the diffusion‐controlled regime is not due to sluggish dynamics near the surface, but rather to bulk diffusion of chains. The diffusion‐controlled regime found in this study is considered to appear at the high temperature limit.     

Monte Carlo simulations of polymer dynamics: Recent advances

A brief review is given of applications of Monte Carlo simulations to study the dynamical properties of coarse-grained models of polymer melts, emphasizing the crossover from the Rouse model toward reptation, and the glass transition. The extent to which Monte Carlo algorithms can mimic the actual chain dynamics is critically examined, and the need for the use of coarse-grained rather than fully atomistic models for such simulations is explained. It is shown that various lattice and continuum models yield qualitatively similar results, and the behavior agrees with the findings of corresponding molecular dynamics simulations and experiments, where available. It is argued that these simulations significantly enhance our understanding of the theoretical concepts on the dynamics of dense macromolecular systems. © 1997 John Wiley & Sons, Inc.     

Monte Carlo simulations of single crystals from polymer solutions

A novel "anisotropic aggregation" model is proposed to simulate nucleation and growth of polymer single crystals as functions of temperature and polymer concentration in dilute solutions. Prefolded chains in a dilute solution are assumed to aggregate at a seed nucleus with an anisotropic interaction by a reversible adsorption/desorption mechanism, with temperature, concentration, and seed size being the control variables. The Monte Carlo results of this model resolve the long-standing dilemma regarding the kinetic and thermal roughenings, by producing a rough-flat-rough transition in the crystal morphology with increasing temperature. It is found that the crystal growth rate varies nonlinearly with temperature and concentration without any marked transitions among any regimes of polymer crystallization kinetics. The induction time increases with decreasing the seed nucleus size, increasing temperature, or decreasing concentration. The apparent critical nucleus size is found to increase exponentially with increasing temperature or decreasing concentration, leading to a critical nucleus diagram composed in the temperature-concentration plane with three regions of different nucleation barriers: no growth, nucleation and growth, and spontaneous growth. Melting temperatures as functions of the crystal size, heating rate, and concentration are also reported. The present model, falling in the same category of small molecular crystallization with anisotropic interactions, captures most of the phenomenology of polymer crystallization in dilute solutions.     

Monte Carlo simulations of radioactive waste embedded into polymer

Radioactive waste is generated from the nuclear applications and it should properly be managed according to the regulations set by the regulatory authority. Poly(carbonate urethane) and poly(bisphenol a-co-epichlorohydrin) are radiation-resistant polymers and they are possible candidate materials that can be used in the radioactive waste management. In this study, maximum allowable waste activity that can be embedded into these polymers and dose rate distribution of the waste drum (containing waste and the polymer matrix) were found via Monte Carlo simulations. The change of mechanical properties of above-mentioned polymers was simulated and their variations within the waste drum were determined for 15, 30 and 300 years after embedding.     

Lattice Monte Carlo simulations of three-dimensional charged polymer chains

The configurational properties of strongly charged polyelectrolytes accompanied by neutralizing counterions in dilute solutions are simulated using the cooperative motion algorithm on the face-centered-cubic lattice. The full Coulomb potential and the excluded volume condition between different ions/beads are taken into account and the reduced temperature T* is considered the main, variable parameter. The calculations that have been carried out for solutions of both single and several chains indicate a few regions of their behavior: (1) for T*--> infinity, it corresponds to that of neutral, self-avoiding polymers under good solvent conditions; (2) for T* approximately 1, due to the electrostatic interactions being effectively stronger, the chains are more outstretched compared to their size at other temperatures; (3) for T* well below one, the counterion condensation becomes more and more dominant, which gradually leads to strongly collapsed chains; and (4) at the lowest temperatures the chains and counterions assume low-energy configurations in the form of neutral, compact aggregates.     

Monte Carlo simulations of a liquid crystal copolymer in the solid state

The condensed phase of the alternating copolyester of p-hydroxybenzoic acid (HBA) and 2-hydroxy-6-naphthoic acid (HNA) is investigated by studying the room temperature packing arrangement of the copolymer chains. A molecular modeling methodology is employed with a Monte Carlo sampling of the configurational phase space. Realistic poly(HBA-alt-HNA) polymer chains are represented by an explicit atom representation of the HBA/HNA dimers. States are sampled from the NVT ensemble using a sampling scheme consisting of (1) valence and torsional variations, (2) rigid body rotations of the chain about the chain axis, and (3) rigid body translations of the chain. The effect of chain packing on the conformation of chains, as well as the relative intra- and intermolecular orientations of aromatic rings, is investigated. Correlation of chain positioning along the chain axis is dominated by aromatic rings maintaining a center-to-center plane of registry. These layers of aromatic units pack with a preference for edge-to-face orientations in a herringbone-type pattern and have an intermolecular ring angle between the pairs of aromatic rings in the unit cell that is ca. 68°. The aromatic rings, on average, are rotated 38° out from the b–c plane. The phenylene rings of these copolyesters are less restricted in their relative orientation in comparison to the naphthalene rings. Intramolecular orientational probability density distributions indicate a preference for staggering the successive aromatic rings along the chain, with a staggering angle of ca. 66°. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 727–741, 1998     

Direct observation of nanoparticle embedding into the surface of a polymer melt

Direct embedding of metal nanoparticles (NPs) into the surface of a polymer melt is observed by TEM and a new embedding mechanism proposed. Upon annealing above the glass transition temperature of polystyrene (PS), NPs (20 nm gold) are rapidly covered by a thin PS wetting layer, h* approximately 1.3-1.8 nm (i.e., about two or three monomers). Because it creates capillary pressure on a NP, this "universal" wetting layer is proposed to be responsible for NP embedding. The value of h* is independent of the molecular weight of PS and constant during the embedding process. The value of h* is found to be similar to the equilibrium wetting layer thickness of a polymer melt spreading on a metal substrate. Using a model that includes the spreading coefficient, long-range van der Waals interactions, and a chain-stretching penalty, h* is shown to be independent of the molecular weight of the polymer. Using this model and the measured value of h*, the interfacial energy between Au NP and PS is estimated to be 8.7 J/m2.     

Monte Carlo simulations of phase transitions and adsorption isotherm discontinuities on surface compression

Low temperature, Grand Canonical Monte Carlo simulations were used to study the adsorption of fluid layers on cubic, hexagonal, and atomically smooth substrates to determine the effects of registry and surface compression on the system. The size of the fluid molecules was fixed to be 20% larger than the substrate molecules in order to observe the transition from an expanded to commensurate and finally to an incommensurate monolayer. For relatively weak fluid-substrate interactions, the cubic system underwent a first-order phase transition. As the strength of the fluid-substrate interactions increased, the molecules became fixed at commensurate locations and the transition from low density to commensurate packing became continuous. The strong fluid-substrate interactions lead to the development of a kink in the adsorption isotherm that showed the increased stability of the commensurate phase. This kink became more pronounced as the system temperature was decreased. The hexagonal system showed less dramatic results due to a decrease in the substrate well depth of the relative to the cubic system. The system did experience a first-order phase transition for a weak fluid-substrate interactions and the transition became much more gradual as the fluid-substrate interaction increased. The molecules became fixed to commensurate substrate locations, but the surface was not corrugated sufficiently to have a stable commensurate phase. The atomically smooth substrate showed the first-order phase transition expected of a low temperature system with no effects of registry.     

A multiple chain Monte Carlo method for atomistic simulation of high molecular weight polymer melts

A new Monte Carlo method is proposed for the simulation of bulk systems of atomistically detailed polymers. Each move consists of a configurational rearrangement of the atoms in a specified region of the material, rather than a specified molecule. Thus atoms within different chains may be displaced cooperatively in each Monte Carlo move. Here, the method is implemented for the case of melts of linear chains, where the bond lengths and bond angles are held constant during the move. The performance of the algorithm is examined for linear polyethylene systems with chain lengths of 100 and 1000 backbone atoms, under a range of conditions. The method shows a considerable potential as a very general and flexible tool for simulating realistic polymer materials, subject to a number of performances limiting factors which are described in detail.     

Supramolecular polymer formation by metal-ligand complexation: Monte Carlo simulations and analytical modeling

Equilibrium metal-ligand complexation leading to formation of linear or ringlike supramolecular polymers is studied by means of Monte Carlo (MC) simulations and theoretical analysis. We found that in most of the cases high-molecular-weight polymers are formed over a rather narrow composition range (near the 2:1 ligand-metal ratio). Besides the imbalance in the number of metals and ligands, the molecular weight decrease in the metal-rich area is caused by an increase in 1:1 ligand-metal complex formation. The results of simulations and theoretical modeling show that the fraction of 1:1 complexes considerably decreases for metal-ligand pairs with a high cooperativity of complexation. On the basis of our analytical model, we suggest a simple criterion for choosing the metal/ligand pair to achieve high molecular weight complexes in a broad range of metal-rich compositions. Dilution of a solution of metallosupramolecular polymers is found to decrease the average molecular weight and to enhance ring formation, which otherwise is very limited.     

Monte Carlo simulations and analysis of scattering from neutral and polyelectrolyte polymer and polymer-like systems

Methods for analyzing small-angle scattering data from complex liquids with particles with many internal degrees of freedom have progressed substantially during the past years. This is mainly due to the use of Monte Carlo simulation techniques for obtaining scattering functions and the use of an approach in which the obtained scattering functions are subsequently parameterized, so that they can be used for data fitting. The present paper reviews recent applications of the Monte Carlo technique for obtaining parameterized scattering functions, and the application of these with emphasis on semiflexible polymers and wormlike micelle systems with and without electrostatic interactions.     

Reactive Monte Carlo and grand-canonical Monte Carlo simulations of the propene metathesis reaction system

The influence of silicalite-1 pores on the reaction equilibria and the selectivity of the propene metathesis reaction system in the temperature range between 300 and 600 K and the pressure range from 0.5 to 7 bars has been investigated with molecular simulations. The reactive Monte Carlo (RxMC) technique was applied for bulk-phase simulations in the isobaric-isothermal ensemble and for two phase systems in the Gibbs ensemble. Additionally, Monte Carlo simulations in the grand-canonical ensemble (GCMC) have been carried out with and without using the RxMC technique. The various simulation procedures were combined with the configurational-bias Monte Carlo approach. It was found that the GCMC simulations are superior to the Gibbs ensemble simulations for reactions where the bulk-phase equilibrium can be calculated in advance and does not have to be simulated simultaneously with the molecules inside the pore. The confined environment can increase the conversion significantly. A large change in selectivity between the bulk phase and the pore phase is observed. Pressure and temperature have strong influences on both conversion and selectivity. At low pressure and temperature both conversion and selectivity have the highest values. The effect of confinement decreases as the temperature increases.     

Monte Carlo simulations of chains confined inside a cube

Self-avoiding walks (SAWs) and random-flight walks (RFWs) of various lengths embedded on a simple cubic lattice have been computer generated inside cubes of varying side. If B is the side of the confining cube, we define the reduced cube side size B₀ as B₀ = (B − 1)/<r²>^1/2, where <r²>^1/2 is the root-mean-square end-to-end distance of the non-confined chains. Dimensionless diagrams are then given of the Monte Carlo estimates for the dimensions, the entropy, and the compressibility parameter PV/(kT) of the confined chains as a function of B₀. The comparative behaviour of the confined SAWs and RFWs is established, scaling properties are examined, and the Monte Carlo estimates compared with theory when such theory is available.     

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.     

Lattice Monte Carlo simulations of three-dimensional charged polymer chains. II. Added salt

The configurational properties of strongly charged polyelectrolytes accompanied by counterions and salt ions in dilute solutions are simulated using the cooperative motion algorithm on the face-centered-cubic lattice. The calculations indicate that both positive and negative ions condense on the chains at sufficiently low temperatures and their amount depends on the concentration of added salt. As the temperature decreases from high to low, the chains undergo conformational changes from neutral-like, self-avoiding polymers by more outstretched forms to compact globules. The observed extension of the chains at intermediate temperatures is also affected by the amount of salt. Furthermore, configurations with the lowest energies recorded at the lowest temperatures are aggregates of single or more entangled chains and ions of both types.     

Monte Carlo simulations of low background detectors

An implementation of the Electron Gamma Shower 4 code (EGS4) has been developed to allow convenient simulation of typical gamma ray measurement systems. Coincidence gamma rays, beta spectra, and angular correlations have been added to adequately simulate a complete nuclear decay and provide corrections to experimentally determined detector efficiencies. This code has been used to strip certain low-background spectra for the purpose of extremely low-level assay. Monte Carlo calculations of this sort can be extremely successful since low background detectors are usually free of significant contributions from poorly localized radiation sources, such as cosmic muons, secondary cosmic neutrons, and radioactive construction or shielding materials. Previously, validation of this code has been obtained from a series of comparisons between measurements and blind calculations. An example of the application of this code to an exceedingly low background spectrum stripping will be presented.Pacific Northwest Laboratory is operated by Battelle Memorial Institute for the US Department of Energy under Contract DE-AC06-76RLO 1830.     

Dynamic Monte Carlo simulations of anisotropic colloids

We put forward a simple procedure for extracting dynamical information from Monte Carlo simulations, by appropriate matching of the short-time diffusion tensor with its infinite-dilution limit counterpart, which is supposed to be known. This approach - discarding hydrodynamics interactions - first allows us to improve the efficiency of previous dynamic Monte Carlo algorithms for spherical Brownian particles. In the second step, we address the case of anisotropic colloids with orientational degrees of freedom. As an illustration, we present a detailed study of the dynamics of thin platelets, with emphasis on long-time diffusion and orientational correlations.     

Cluster algorithm to perform parallel Monte Carlo simulation of atomistic systems

We propose an efficient algorithm to perform Monte Carlo simulations of dense systems using multiple particle moves. The method is intended to be used in the atomistic simulation of complex systems, where the computing requirements for a single simulation run make advisable the use of parallel computing. The algorithm is based on the use of steps in which all the particle positions of the system are perturbed simultaneously. A division of the system in clusters of particles is performed, using a bonding criterion which makes feasible that the acceptance or rejection of the new particle coordinates can be carried out independently for each cluster.