Local and chain dynamics in miscible polymer blends: A Monte Carlo simulation study

Local chain structure and local environment play an important role in the dynamics of polymer chains in miscible blends. In general, the friction coefficients that describe the segmental dynamics of the two components in a blend differ from each other and from those of the pure melts. In this work, we investigate polymer blend dynamics with Monte Carlo simulations of a generalized bond fluctuation model, where differences in the interaction energies between nonbonded nearest neighbors distinguish the two components of a blend. Simulations employing only local moves and respecting a no bond crossing condition were carried out for blends with a range of compositions, densities, and chain lengths. The blends investigated here have long time dynamics in the crossover region between Rouse and entangled behavior. In order to investigate the scaling of the self-diffusion coefficients, characteristic chain lengths N(c) are calculated from the packing length of the chains. These are combined with a local mobility mu determined from the acceptance rate and the effective bond length to yield characteristic self-diffusion coefficients D(c)=muN(c). We find that the data for both melts and blends collapse onto a common line in a graph of reduced diffusion coefficients DD(c) as a function of reduced chain length NN(c). The composition dependence of dynamic properties is investigated in detail for melts and blends with chains of length N=20 at three different densities. For these blends, we calculate friction coefficients from the local mobilities and consider their composition and pressure dependence. The friction coefficients determined in this way show many of the characteristics observed in experiments on miscible blends.     

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 .     

Dynamic Monte Carlo simulation of chain growth polymerization and its concentration effect

Polymerization kinetics and chain configuration are two of lasting hotspots in Polymer Science. As these problems are concerned, computer experiment affords a very useful method besides theoretical and experi-mental investigations. The conventional Monte …     

Monte Carlo simulation on symmetric ABA/AB copolymer blends in confined thin films

The effects of blend composition on morphology, order-disorder transition (ODT), and chain conformation of symmetric ABA/AB copolymer blends confined between two neutral hard walls have been investigated by lattice Monte Carlo simulation. Only lamellar structure is observed in all the simulation morphologies under thermodynamic equilibrium state, which is supported by theoretical prediction. When the composition of AB diblock copolymer (phi) increases, both lamellar spacing and the corresponding ODT temperature increase, which can be attributed to the variation of conformation distribution of the diblock and the triblock copolymer chains. In addition, both diblock and triblock copolymer, chains with bridge conformation extend dramatically in the direction parallel to the surface when the system is in ordered state. Finally, the copolymer chain conformation depends strongly on both the blend composition and the incompatibility parameter chiN.     

A Monte Carlo simulation study of the effect of chain length on the hydrolysis of poly(lactic acid)

Abstract The intrinsic relationship between molecular chain length and the probability of chain reaction during poly(lactic acid)(PLA)hydrolysis was investigated by Monte Carlo simulation.The chain reaction rate was calculated by introducing a power function of different molecular chain lengths.The hydrolysis of both amorphous and extended-chain crystal PLA was selected as the model system.It is found that,the chain reaction probability was proportional to the chain length with a power of 0.4 for amorphous PLA and 0.7 1 for extended-chain crystal PLA,respectively.These results indicate that PLA with longer chain length usually exhibits larger reaction rate than that with shorter length.Comparing the hydrolysis of the two kinds of PLA,the competition between longer and shorter chains in the different condensed structures is different.     

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 study of droplet nucleation

A new rigorous Monte Carlo simulation approach is employed to study nucleation barriers for droplets in Lennard-Jones fluid. Using the gauge cell method we generate the excess isotherm of critical clusters in the size range from two to six molecular diameters. The ghost field method is employed to compute the cluster free energy and the nucleation barrier with desired precision of (1-2)kT. Based on quantitative results obtained by Monte Carlo simulations, we access the limits of applicability of the capillarity approximation of the classical nucleation theory and the Tolman equation. We show that the capillarity approximation corrected for vapor nonideality and liquid compressibility provides a reasonable assessment for the size of critical clusters in Lennard-Jones fluid; however, its accuracy is not sufficient to predict the nucleation barriers for making practical estimates of the rate of nucleation. The established dependence of the droplet surface tension on the droplet size cannot be approximated by the Tolman equation for small droplets of radius less than four molecular diameters. We confirm the conclusion of ten Wolde and Frenkel [J. Chem. Phys. 109, 9901 (1998)] that integration of the normal component of the Irving-Kirkwood pressure tensor severely underestimates the nucleation barriers for small clusters.     

Study on structure formation of short polyethylene chains via dynamic Monte Carlo simulation

Monte Carlo (MC) simulations of structure formation for short polyethylene chains at low temperature are performed based on a recent developed method that uses coarse-grained chains on a high coordination lattice. Local short-range interactions based on rotational isomeric state (RIS) model and long-range interactions obtained from Lennard–Jones (LJ) potential are introduced during the simulation. Properties evaluated from the simulations are the mean square dimensions, anisotropy of the radius of gyration tensor, local conformation determined by the occupancy of trans state and orientation correlation functions, energy of the system, and chain packing reflected by the pair correlation functions and structure factors. All of these parameters reveal an ordering process that produces an approximation to a hexagonal crystal phase. The hexagonal structure is imposed by the presence of a diamond lattice underlying the high coordination lattice on which the simulation is performed. Folding of the chains in the crystal is mandatory, because they have fully extended lengths in excess of the dimension of the simulated periodic box. Nevertheless, the simulations demonstrate that a high degree of crystallinity can be achieved in reasonable computer time. The simulation technique should be applicable to other choices of periodic boundary conditions that do not affect the results as strongly as in the present case.     

A Monte Carlo simulation study of branched polymers

Monte Carlo simulations are presented for the static properties of highly branched polymer molecules. The molecules consist of a semiflexible backbone of hard-sphere monomers with semiflexible side chains, also composed of hard-sphere monomers, attached to either every backbone bead or every other backbone bead. The conformational properties and structure factor of this model are investigated as a function of the stiffness of the backbone and side chains. The average conformations of the side chains are similar to self-avoiding random walks. The simulations show that there is a stiffening of the backbone as degree of crowding is increased, for example, if the branch spacing is decreased or side chain length is increased. The persistence length of the backbone is relatively insensitive to the stiffness of the side chains over the range investigated. The simulations reproduce most of the qualitative features of the structure factor observed in experiment, although the magnitude of the stiffening of the backbone is smaller than in experiment.     

Molecular origin of demixing, prior to crystallization, of atactic polypropylene/isotactic polypropylene blends upon cooling from the melt

An amorphous 50/50 atactic polypropylene (aPP)/isotactic polypropylene (iPP) mixture at 125 degrees C was simulated using a second nearest neighbor diamond lattice and a three states rotational isometric state model. The result suggests that at the liquidlike density that corresponds to the atmospheric pressure, aPP prefers to interact with other aPP chains rather than with iPP chains. The result is consistent with the inference of Keith and Padden [J. Appl. Phys. 35, 1286 (1964)] that aPP and iPP will tend to separate from one another in their melt at 125 degrees C, before the onset of crystallization of iPP. The tendency for immiscibility of the amorphous aPP/iPP blend is likely attributed to the presence of short syndiotactic sequences in the aPP chains adopting all-trans conformations. The attractive intermolecular interaction of pairs of such subchains at 125 degrees C promotes the separation of aPP from iPP. This interaction is weakened at higher temperature, where aPP and iPP become miscible. The result also shows that miscibility of the blend increases with increasing pressure. However, the origin of the pressure effect is not clear.     

Solvent effect on K to Na ion mutation: a Monte Carlo simulation study

Monte Carlo simulation studies of statistical perturbation theory (SPT) have been carried out to investigate the solvent effects on the relative free energies of solvation and the difference in partition coefficients (log P) for K⁺ to Na⁺ ion mutation in the several solvents. We compared the relative free energies for interconversion of K⁺ to Na⁺, in H₂O (TIP4P) in this study with those published works, that in H₂O (TIP4P) is −16.55 kcal/mol in this study, those of the published works are −17.6, −17.3 and −17.31 kcal/mol and that of the experiment is −17.6 kcal/mol, respectively. Comparing the relative free energies for interconversion of K⁺ to Na⁺, in CH₃OH in this study with those published works, that in CH₃OH is −18.08±0.28 kcal/mol in this study, that of molecular dynamic simulation is −19.6±0.4 kcal/mol and that of the experimental work is −17.3 kcal/mol, respectively. There is good agreement among the several studies if we consider both methods of obtaining the solvation (or hydration) free energies and the standard deviations. For the present K⁺ and Na⁺ ions, the relative free energies of solvation vs Born's function of solvents are decreased with increasing Born's function of solvent except for CH₃OH, THF and MEOME. There is also good agreement between the calculated structural properties in this study and the computer simulation, ab initio and experimental works.     

Monte Carlo simulation of phase separations of block copolymers and of corresponding blends

The Monte Carlo method has been used to simulate the phase separations of block copolymers and of corresponding blends with very high concentration (sum of volume fractions of blocks A and B: ϕ_A + ϕ_B = 0,9545). Our main findings are as follows: (1) The mixing is nonrandom even in the athermal limit. (2) The nonselective good solvent molecules (ϕ_V = 0,0455) are mostly located at the interface between A- and B-rich phases, thus, it is not true that solvent and monomeric units will remain mixed at all temperatures. (3) Even for the same microscopic A-B interaction energy, ε, and at the same temperature, the Flory-Huggins parameter χ of block copolymers is always higher than that of corresponding blends, and the χ values of block copolymers and corresponding blends have different ε-dependencies. (4) The critical values of χ both for block copolymer and corresponding blend are obtained and compared with the meanfield theoretical predictions. It is found that the ratio of χ_c (block)/χ_c (blend) is qualitatively compatible with the prediction of the Flory-Leibler theory.     

Solvent effect on La to Nd ion mutation: a Monte Carlo simulation study

A Monte Carlo simulation of statistical perturbation theory (SPT) has been applied to investigate solvent effects on the relative free energies of solvation of La³⁺ to Nd³⁺ ion mutation in several solvents. Comparing the relative free energies for interconversion of La³⁺ to Nd³⁺, in H₂O (TIP3P) from this Letter with computer simulation and experiments, there is good agreement among the three studies, There is also reasonable agreement between calculated structural properties from this Letter and other works. For these ion pairs, the Born's function of the solvents and the differences in solvation dominate the differences in the relative free energies of solvation and partition coefficients.     

Anomalous mixing behavior of polyisobutylene/polypropylene blends: molecular dynamics simulation study

The unusual mixing behavior of polyisobutylene (PIB) with head-to-head (hhPP) and head-to-tail polypropylene (PP) is studied using large-scale molecular dynamics (MD). The heats of mixing and Flory chi parameters were computed from MD simulations of both blends using a united atom model. The chi parameters from the simulations were estimated from the structure factors using the random phase approximation in analogy with neutron scattering (SANS) experiments. MD simulations for syndiotactic hhPP/PIB predicted a lower critical solution temperature with a chi parameter in very good agreement with SANS experiments on the atactic hhPP/PIB blend. MD simulations also predicted that the isotactic PP/PIB blend was immiscible at high molecular weight in qualitative agreement with cloud point measurements on atactic PP/PIB.     

Grand canonical Monte Carlo simulation study on the catenation effect on hydrogen adsorption onto the interpenetrating metal-organic frameworks

Among recently synthesized isoreticular metal-organic frameworks (IRMOFs), interpenetrating IRMOFs show high hydrogen adsorption capacities at low temperature and under ambient pressure. However, little is known about the molecular basis of their hydrogen binding properties. In this work, we performed grand canonical Monte Carlo (GCMC) simulations to investigate the effect of catenation on the interactions between hydrogen molecules and IRMOFs. We identified the adsorption sites and analyzed the adsorption energy distributions. The simulation results show that the small pores generated by catenation can play a role to confine the hydrogen molecules more densely, so that the capacity of the interpenetrating IRMOFs could be higher than that of the non-interpenetrating IRMOFs.     

Dynamics of polypropylene chains in their binary blends of different stereochemical sequences studied by Monte Carlo simulations

The conformational and dynamic properties of polypropylene （PP） for both pure melts and blends with different chain tacticity were investigated by Monte Carlo simulation of isotactic （iPP）, atactic （aPP） and syndiotactic （sPP） polypropylenes. The simulation of coarse-grained PP models was performed on a high coordination lattice incorporating short- and long-range intramolecular interactions from the rotational isomeric state （RIS） model and Lennard-Jones （LJ） potential function of propane pairs, respectively. The dynamics of chains in binary PP/PP mixture were investigated with the composition of C150H302 with different chain taciticity. The diffusion rates of PP with different stereochemistry are generally in the order as： iPP 〉 aPP 〉〉 sPP. For PP/PP blends with 50：50 wt% binary mixtures, immiscibility was observed when sPP was introduced into the mixtures. The diffusion rate of iPP and aPP became slower after mixing, while sPP diffuses significantly faster in the binary mixtures. The mobility of PP chains depends on both intramolecular （molecular size and chain stiffness） and intermolecular （chain packing） interactions. The effect of intramolecular contribution is greater than that of intermolecular contribution for iPP and aPP chains in binary mixtures. For sPP chain, intermolecular interaction has greater influence on the dynamics than intramolecular contribution.     

Morphological and structural features of heat-treated drawn polypropylene/high-density polyethylene blends

The ion etching technique has been applied to a morphological study of mechanically blended polypropylene (PP) with high-density polyethylene (HDPE). Samples blended to PP/HDPE compositions of 65/35 and 85/15 by weight were highly drawn and then heat treated for 30 min at selected temperatures up to 163°C. When these samples are carefully ion-etched several features are observed in electron micrographs, namely (i) crosshatched, and (ii) twisted or layered textured inclusions of HDPE crystals within arrays of lamellalike PP crystals situated perpendicular to the direction of drawing. X-ray diffraction measurements of the drawn samples heat treated in the range 145–163°C for 30 min shows that oriented HDPE crystallizes with b-axis orientation along the drawing direction. Supporting evidence is obtained from electron diffraction measurements. The molecular weight of the HDPE component is a major factor in the b-axis-oriented growth of HDPE crystals in PP/HDPE blends.