Comparison of Monte Carlo and quasi-Monte Carlo technique in structure and relaxing dynamics of polymer in dilute solution

Structure and dynamics of polymer in solvent solution is an important area of research since the functional properties of polymer are largely dependent on the morphology of the polymers in solution. This structure related properties are especially important in case of surface science where the phase-separated morphology in the micro/nano scale dictates the properties of the product. Modeling polymers in solution is an efficient way to determine the morphology and thus the properties of the products. It saves time as well as helps to design novel materials with desired properties. Polymers in solution systems are generally modeled with bead spring model and Monte Carlo or importance sampling Monte Carlo simulations is used to find the optimal configuration where the energy of the system is minimized. Often in these simulations, random numbers are used in the Monte Carlo steps. Normally random numbers try to form clusters and do not cover the entire dimension of the system. Thus the minimum energy structures obtained from simulations with random numbers are not optimal configuration of the system. In the present work a lattice-based model is used for polymer solution system and importance sampling Monte Carlo is used for simulation. Quasi-random numbers generated from Hammersley sequence sampling (HSS) are used in the simulation steps for stochastic selection polymers and its movements. Quasi-random numbers obtained from HSS are random in nature and they have n-dimensional uniformity. They do not form clusters and the structural configuration obtained using quasi-random numbers are optimal in nature. The optimal configurations of the polymers as obtained from random number and quasi-random number are compared. The result shows that simulation with HSS attains a lower energy state after initial quench. At the late stage of spinodal decomposition, the structure factor decrease-showing Ostwald ripening which is not observed from simulation with random numbers.     

Dynamic Monte Carlo study on the permeation of polymer chains through small holes

The permeation of polymer chains through a small hole is simulated using dynamic Monte Carlo method. The dependence of the permeation velocity v on concentration C of polymer chain, chain length n and hole size s is investigated. The velocity v increases non-linearly with C, differing from linear dependence of hard sphere system, indicating that inter-chain interaction plays an important role in the permeation process. At the same concentration, the velocity decreases with the chain length n via a relation v=a+bn^−?, where the exponent ? increases linearly with C. Such a behavior is different from a single chain system. The possible physical reason is addressed. The velocity is proportional to hole size when the chain size is smaller than the hole size, but it decreases obviously if the chain size is much larger than the hole size.     

Study of the kinetics of mushroom-to-brush transition of charged polymer chains

The grafting of thiol-terminated poly[(2-dimethylamino)ethyl methacrylate] (HS-PDMEM) chains to a gold surface from a solution was investigated with quartz crystal microbalance with dissipation (QCM-D) in real time. The frequency and energy dissipation responses revealed a three-regime-kinetics of the grafting. The chains are quickly grafted in regime I forming a random mushroom. In regime II, the grafted chains have a rearrangement and form an ordered mushroom structure. The grafting is accelerated in regime III. As the grafting density increases, the chains form brushes. From regime II to III, the mushroom-to-brush transition occurs. The results were further supported by atomic force microscopy (AFM) imagines.     

Polyurethane-poly(methyl methacrylate) interpenetrating polymer networks: 1. Early steps and kinetics of network formation; intersystem grafting

Several side-reactions occurring during the early stages of the formation of polyurethane-poly(methyl methacrylate) interpenetrating polymer networks (PUR/PAc IPNs) have been examined. Thus, the PUR catalyst, stannous octoate, is able to initiate the polymerization of the methacrylic monomers, or to accelerate it in the presence of the proper initiator of the system, azo-bisisobutyronitrile. Nevertheless, this effect does not influence the overall reaction process. On the other hand, light has to be excluded in order to obtain transparent IPNs. The kinetics of formation of the individual networks have been investigated in experimental conditions as close as possible to the actual preparation of the corresponding IPNs. Intersystem grafting, if any, is very limited and its influence on the mechanical properties may therefore be neglected.     

Monte Carlo simulation of two interpenetrating polymer networks: Structure, swelling, and mechanical properties

The swelling and mechanical properties of various interpenetrating polymer networks (IPNs) were studied. Six networks made from permutations of a moderately crosslinked polyelectrolyte network (ref), a moderately crosslinked neutral polymer network (net1), and a highly crosslinked polyelectrolyte network (net2) were first swollen in water and structural properties such as end-to-end chain lengths and radial distribution functions were compared with the component networks' equilibrium properties. The swelling of composite IPNs was discussed in terms of a balance between the osmotic pressure due to mobile counterions and the restoring force of the network chains, which act in parallel to counteract the osmotic swelling. For the ref-net2 system, the strong stretching of net2 chains increases the network restoring force and the further swelling due to the counterions is suppressed. The swollen networks were then uniaxially stretched, and equilibrium stress-strain plots were obtained up to high extension ratios. The equilibrium volume decreased upon uniaxial extension, and the elastic moduli of IPNs of the A-A type were slightly greater than that of their respective single networks.     

Dynamic Monte Carlo study on the polymer chain in random media filled with nanoparticles

The effect of nanoparticles on the dynamic and configurational properties of a single polymer chain has been studied by using dynamic Monte Carlo simulation. An attractive potential, ε, is considered between fixed nanoparticles and polymer beads. The diffusion coefficient of the polymer D remains constant for weak interactions, i.e. small β=−ε/k_BT, and then gradually drops to zero at a critical value . However, the mean square end-to-end distance 〈R²〉 shows a different behavior with an increase in the attractive interaction. 〈R²〉 decreases at small β and reaches a minimum at , then goes up slowly and at last saturates at strong interaction. The values and scale with the concentration of nanoparticles. Interesting findings are: (1) a chain has its minimum size before the chain stops its diffusion, and (2) a chain continues its configuration adjustment even for .     

Low-field NMR studies of polymer crystallization kinetics: Changes in the melt dynamics

The free induction decay in ¹H NMR experiments carried out for crystallizing polymers can be directly decomposed in contributions from crystals, melt-like regions and amorphous regions with a reduced mobility. Here, the results of time-dependent experiments conducted with the aid of a cost-efficient low-field NMR instrument are presented, obtained for sPP, P?CL and P(EcO). Crystallization isotherms are compared with those obtained by X-ray scattering and dilatometry. There are some minor systematic deviations which can be explained and accounted for. For all systems, a large fraction of amorphous chain parts in regions with a reduced mobility is found.     

氰酸酯/聚甲基丙烯酸甲酯互穿聚合物网络的探究

用同步法合成了氰酸酯/聚甲基丙烯酸甲酯(CE/PMMA)互穿聚合物网络(IPN),研究了甲基丙烯酸甲酯(MMA)含量对CE/PMMA-IPN体系力学性能及密度的影响。结果表明CE/PMMA-IPN体系的性能比单一树脂的优异。     

含氮磷高分子肥料的制备和结构研究

水溶性合成高分子聚合物能被微生物分解,是一种优良的土壤改良剂,并对土壤营养元素有良好的吸附作用,可减少元素流失,提高肥效。合成了一种营养元素高分子缓释化肥,将含氮磷的降解水溶性高分子材料引入到化肥领域,并通过实验研究不同的反应工艺条件对高分子肥料结构和含氮磷肥效的影响。     

Synthesis of novel bis- and tris-(cyclic carbonate)s and their use in preparation of polymer networks

Novel six-membered bis- and tris-(cyclic carbonate)s that are useful as cross-linking agents in the synthesis of structurally stable yet biodegradable polycarbonates and polyesters have been synthesized in good to moderate yield (85-45%). Cross-linked aliphatic polycarbonates, and polyesters were prepared by copolymerization of the bis-cyclic carbonate (3f) with trimethylene carbonate, and ε-caprolactone. The polymers swelled in a wide variety of organic solvents, including CHCl₃, CH₂Cl₂, ethyl acetate, acetone, DMSO, and DMF but not in protic polar solvents, such as methanol, ethanol, and water. Swelling ratios of trimethylene carbonate/3f and ε-caprolactone/3f networks at different feed ratios were investigated in dichloromethane. The glass transition temperature of the TMC/3f networks increased with increasing cross-link density.     

Adsorption of a weakly charged polymer on an oppositely charged colloidal particle: Monte Carlo simulations investigation

Monte Carlo simulations were used to investigate the conformational and electrical properties of isolated weak polyelectrolytes in the presence of an oppositely charged particle. Titrations curves were calculated to get an insight into the role of pH on the degree of ionization and conformation of isolated chains. The effect of ionic concentration and polyelectrolyte length on the titration curves was also investigated. The complex formation between the isolated polyelectrolyte and the oppositely charged particle was considered at different pH and ionic concentration values. The adsorption/desorption limit was calculated and the effect of the polyelectrolyte adsorption on the titration curves investigated. In particular, it was demonstrated that the presence of an oppositely charged particle clearly increases the degree of ionization of the weak polyelectrolyte and that ionic concentration plays a subtle role by increasing/reducing both the attractive energy between the polyelectrolyte and the particle and the polyelectrolyte degree of ionization.     

Recent advances in polymer reaction engineering: Modeling and control of polymer properties

Complex reaction kinetics and mechanisms, physical changes and transport effects, non-ideal mixing, and strong process nonlinearity characterize polymerization processes. Polymer reaction engineering is a discipline that deals with various problems concerning the fundamental nature of chemical and physical phenomena in polymerization processes. Mathematical modeling is a powerful tool for the development of process understanding and advanced reactor technology in the polymer industry. This review discusses recent developments in modeling techniques for the calculation of polymer properties including molecular weight distribution, copolymer composition distribution, sequence length distribution and long chain branching. The application of process models to the design of model-based reactor optimizations and controls is also discussed with some examples. This paper is dedicated to Professor Hyun-Ku Rhee on the occasion of his retirement from Seoul National University.     

Solid polymer electrolytes V: microstructure and ionic conductivity of epoxide-crosslinked polyether networks doped with LiClO4

A crosslinked polyether network was prepared from poly(ethylene glycol) diglycidyl ether (PEGDE) cured with poly(propylene oxide) polyamine. Significant interactions between ions and polymer host have been observed for the crosslinked polyether network in the presence of LiClO₄ by means of FT-IR, DSC, TGA, and ⁷Li MAS solid-state NMR. Thermal stability and ionic conductivity of these complexes were also investigated by TGA and AC impedance measurements. The results of FT-IR, DSC, TGA and ⁷Li MAS solid-state NMR measurements indicate the formation of different types of complexes through the interaction of ions with different coordination sites of polymer electrolyte networks. The dependence of ionic conductivity was investigated as a function of temperature, LiClO₄ concentration and the molecular weight of polyether curing agents. It is observed that the behavior of ion transport follows the empirical Vogel-Tamman-Fulcher (VTF) type relationship for all the samples, implying the diffusion of charge carrier is assisted by the segmental motions of polymer chains. Moreover, the conductivity is also correlated with the interactions between ions and polymer host, and the maximum ionic conductivity occurs at the LiClO₄ concentration of [O]/[Li⁺]=15.     

Calculation of the effect of macromolecular architecture on structure and thermodynamic properties of linear-tri-arm polyethylene blends from Monte Carlo simulation

A Monte Carlo simulation formalism proposed recently [Peristeras et al. Macromolecules 2007;40:2904-14] is applied here to linear-tri-arm polyethylene blends using atomistic models. Elementary Monte Carlo moves for long chain and branched molecules are used and shown to result in efficient relaxation of long chains. The effect of chain and arm molecular weight and of temperature on the structure and thermodynamic properties of blends is examined. Chemical potential versus composition diagrams are drawn in order to assess the non-ideality of mixing that may lead to phase separation. All of the blends examined are shown to be fully miscible. The microscopic blend structure is examined by calculating the radial distribution function. Finally, the radii of gyration of linear and branched chains are calculated and scaling exponents are evaluated.     

Diffusion of polymer chains in porous media. A Monte Carlo study

In order to determine the structure and the dynamical properties of branched polymers in a random environment an idealized model was developed and studied by means of the Monte Carlo method. All atomic details were suppressed and the chain was represented as a sequence of identical beads. The model chains were star-branched with three arms of equal length. The chains were embedded to a simple cubic lattice and the polymer systems were confined between two parallel surfaces. The confining surfaces were attractive for polymer segments. A set of irregular obstacles was also introduced into the slit which can be viewed as a model of porous media. A Metropolis sampling algorithm employing local changes of chain conformation was used to sample the conformational space. It was shown that the mean dimensions of the chain depend strongly on the strength of surface's attraction and the concentration of obstacles. It was found that the size of the chains scales with the exponent close to the 2-dimensional case rather than to the 3-dimensional system. The long-time (diffusion) dynamic properties of the system were studied. The differences in the mobility of chains depending on the confinement, on the filling of the slit and on the internal macromolecular architectures were shown and discussed. The possible mechanism of chain's motion was shown: during the migration of the chain in the obstacles dense environment it can be trapped in the region of local lower density of obstacles (a ‘cavity’) and after some time it can leave the place moving into another cavity.     

Confinement effects on the kinetics of formation of sequential semi-interpenetrating polymer networks

Summary Peculiarities of formation kinetics of sequential semi-interpenetrating polymer networks based on crosslinked polyurethane with different cross-linking density and linear polystyrene and polybutylmethacrylate have been studied. Polyurethane networks were synthesized differing in molecular mass M_c of the chains between cross-links. Monomeric styrene and butyl methacrylate were introduced into these networks by swelling them in monomers up to equilibrium. The kinetics of polymerization of monomers in swollen networks was investigated. The experimental data show the dependence of the kinetic parameters of polymerization on M_c, this dependence being different for various monomers. Sharp discrepancy in molecular mass distribution of polymers formed in various matrices has been observed. The differences in dependencies of reaction kinetics and molecular mass distribution are supposed to be connected to various dependence of the chain growth and termination of various monomers on the density of network, i.e. on the confinements imposed by the intranetwork space.     

The effect of interpenetrating polymer network formation on polymerization kinetics in an epoxy‐acrylate system

The kinetics of thermally initiated cationic epoxy polymerization and free radical acrylate photopolymerization were studied using photo-differential scanning calorimetry. The reactions of the neat monomers and diluted monomers as well as interpenetrating polymer networks (IPNs) were studied as a function of dilution by the other monomer and temperature. The reaction sequence was also varied to study its effect on the kinetics of formation of the simultaneous IPN's. Both reactions quickly become diffusion controlled. The effects of increasing temperature and dilution on the acrylate polymerization rate profiles are similar, leading to reduced polymerization rate and longer polymerization times. The dilution effect on the epoxy polymerization is similar to that of the acrylate. However, unlike the acrylate reaction the epoxy polymerization rate increases strongly with temperature. The preexistence of one polymer has a significant effect on the polymerization of the second monomer. This effect is larger for the acrylate than for the epoxy polymerization. New kinetic models are needed to capture these complex behaviors.     

Experimental and modeling study of the kinetics of methane hydrate formation and dissociation

In this work, several experiments were conducted at isobaric and isothermal condition in a CSTR reactor to study the kinetics of methane hydrate formation and dissociation. Experiments were performed at five temperatures and three pressure levels (corresponding to equilibrium pressure). Methane hydrate formation and dissociation rates were modeled using mass transfer limited kinetic models and mass transfer coefficients for both formation and dissociation were calculated. Comparison of results, shows that mass transfer coefficients for methane hydrate dissociation are one order greater than formation conditions. Mass transfer coefficients were correlated by polynomials as relations of pressure and temperature. The results and the method can be applied for prediction of methane production from naturally occurring methane hydrate deposits.