A Monte Carlo simulation for the micellization of ABC 3-miktoarm star terpolymers in a selective solvent

We have used Monte Carlo simulation to study the micellization of ABC 3-miktoarm star terpolymers in a selective solvent (good to A segment, bad to B and C segments). The simulation results reveal that the self-assembled morphology is determined by the block length, molecular architecture, terpolymer concentration and insolubility of insoluble block in the solvent. In dilute solution, symmetric terpolymers (N-B = N-C = 30) tend to aggregate into a novel wormlike pearl-necklace structure linked by an alternating arrangement of B and C spheres, whereas the asymmetric terpolymers (NB = 10, NC = 50) are likely to aggregate into spherical or cylindrical micelles (formed by C blocks) connected with some small B spheres, when the concentration of terpolymer is relatively low (chain number is 100). However, when the concentration of terpolymer is relatively high (chain number is 250), the symmetric terpolymers tend to aggregate into a netlike structure linked by an alternation of B and C spheres, whereas the asymmetric terpolymers are likely to aggregate into wormlike micelles (formed by C blocks) connected with some of small spheres (formed by B blocks). Moreover, when the insolubility of insoluble block in the solvent is weak, the insoluble blocks aggregate into some incompact micelles.

Monte Carlo simulation of the aggregation of rod-flexible triblock copolymers in a thin film

The aggregation of rod-flexible ABA and BAB triblock (A was rod block and repulsive with block B) copolymers in a thin film was studied as a function of varying the rigidity (eta) and the length of the rod block by Monte Carlo simulation. The rigidity of block A was defined as eta = R-c/R-max in this study. R-c, was the end-to-end distance below which the conformation of the block was not allowed, whereas R-max, was the longest end-to-end distance that the block could be. If eta = 0 the block was flexible, whereas if eta = 1 the block was a straight rod. The simulation results showed that the ABA triblock copolymer film were likely to form lamella structure with increasing the rigidity (eta) of block A. The lamellas were parallel each other and perpendicular to the film surface. However, the aggregation of BAB triblock copolymers tended to change from lamella to cylinder structure with increasing the rigidity (eta) of block A. Typical lamella and cylinder co-exist structure was obtained at eta = 0.504 for the BAB copolymer film. On the other hand, the simulation results indicated that the film changed from disorder to order, then to disorder structure with increasing the relative length of B block for both ABA and BAB copolymer films.

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 ((ε) over bar (AB)) 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 ((h) over bar) in different systems indicates that the copolymer chains tend to coil with the decrease Of (ε) over bar (AB) whereas the (h) over bar of the homopolymer chains depends on the chain structure of the copolymers.

Monte Carlo simulation of the grafting of maleic anhydride onto polypropylene at higher temperature

The graft of maleic anhydride (MAH) onto isotactic polypropylene (iPP) initiated by dicumyl peroxide (DCP) at 190 degreesC was studied by means of the Monte Carlo method. The ceiling temperature theory, i.e., no possibility for the homopolymerization of MA-H to occur at higher temperatures, was used in this study. The simulation results show that most MAH monomers were grafted onto the radical chain ends arising from beta scission at a lower MAH concentration, whereas the amount of MAH monomers attached to the tertiary carbons was much larger than that grafted onto the radical chain ends at a higher MAH concentration for various DCP concentrations. This conclusion gives a good interpretation for the disagreement on the grafting sites along a PP chain. Moreover, it was found that the grafting degree increased considerably up to a peak value; thereafter, it decreased continuously with increasing MA-H concentration. The peak shifted in the lower MAH concentration direction and became lower and lower with increasing DCP concentration. When the DCP concentration was below 0.1 wt %, the peak was hardly observed. Those results are in good agreement with the experiments.

Monte Carlo simulation of pulsed-laser polymerization in emulsion

The pulsed-laser polymerization in emulsions has been simulated by the Monte Carlo method. Our simulation shows that the best measure of the propagation rate coefficients K-p is the peak maximum of molecular weight distribution for microemulsions when the droplets are small. However, the inflection point at the low-molecular-weight side of the peaks provides the best measure of K-p of bigger droplets. (C) 2000 Elsevier Science Ltd. All rights reserved.

Monte Carlo simulation for the modification of polymer via grafting

Monte Carlo method has been applied to investigate the kinetic of grafting reaction in free radical copolymerization. The simulation is quits in agreement with that of theoretical and experimental results. It proves that the Monte Carlo simulation is an effective method for investigating the grafting reaction of free radical copolymerization. (C) 2000 Elsevier Science Ltd. All rights reserved.

Monte Carlo simulation of phase behavior of polymer blends with special interactions

Full Paper: The phase, behavior of A-B-random copolymer/C-homopolymer, blends with special interaction was studied by a. Monte, Carlo simulation in two dimensions. The interaction between I segment A and segment C was repulsive, whereas it was attractive between segment B and segment C. The simulation results showed that the blend became two large co-continuous phase domains at lower segment-B component compositions, indicating that the blend showed spinodal decomposition. With an increase of the segment-B component, the miscibility between the copolymer,and the polymer was gradually improved up to being miscible. In addition, it was found that segment B tended to move to the surface of the copolymer phase in the case of a lower component of segment B. On the other hand, if was observed that the average, end-to-end distances ((h) over bar) for both copolymer and polymer changed slowly with increasing segment-B component of the copolymer up to 40%, thereafter they increased considerably with increasing segment B component. Moreover, it was found that the (h) over bar of the copolymer was obviously shorter than that of the homopolymer for the segment-B composition, region from 0% to 80%. Finally, a, phase diagram showing I phase and - II phase regions under the condition of constant-temperature is presented.

Monte Carlo simulation of phase separation of A/B/A-B ternary mixtures

Monte Carlo simulations were used to model A/B/A-B ternary mixtures with different AB diblock copolymer volume fractions for which both the dispersed and continuous phase volume fractions were kept constant. For concentrations of the diblock copolymer below a critical value, the domain size increment of the dispersed phase decreases linearly with the copolymer concentration. This is in agreement with the predictions of Noolandi and Hong. The dependence of the domain size as a function of the copolymer volume fraction can also be fitted by the equation of Tang and Huang. Our simulations indicate, for the first time, that the micelles form before saturation of the interface occurs. This means that the formation of the micelles is not a result of the saturation of the interface.

Ukryty punkt krytyczny w mieszaninach binarnych – badania metodami symulacji Monte – Carlo

Wydział Fizyki

Quantum Monte Carlo in the Interaction Representation --- Application to a Spin-Peierls Model

A quantum Monte Carlo algorithm is constructed starting from the standard perturbation expansion in the interaction representation. The resulting configuration space is strongly related to that of the Stochastic Series Expansion (SSE) method, which is based on a direct power series expansion of exp(-beta*H). Sampling procedures previously developed for the SSE method can therefore be used also in the interaction representation formulation. The new method is first tested on the S=1/2 Heisenberg chain. Then, as an application to a model of great current interest, a Heisenberg chain including phonon degrees of freedom is studied. Einstein phonons are coupled to the spins via a linear modulation of the nearest-neighbor exchange. The simulation algorithm is implemented in the phonon occupation number basis, without Hilbert space truncations, and is exact. Results are presented for the magnetic properties of the system in a wide temperature regime, including the T-->0 limit where the chain undergoes a spin-Peierls transition. Some aspects of the phonon dynamics are also discussed. The results suggest that the effects of dynamic phonons in spin-Peierls compounds such as GeCuO3 and NaV2O5 must be included in order to obtain a correct quantitative description of their magnetic properties, both above and below the dimerization temperature.

Conductance of quantum impurity models from quantum monte carlo

The conductance of two Anderson impurity models, one with twofold and another with fourfold degeneracy, representing two types of quantum dots, is calculated using a world-line quantum Monte Carlo (QMC) method. Extrapolation of the imaginary time QMC data to zero frequency yields the linear conductance, which is then compared to numerical renormalization-group results in order to assess its accuracy. We find that the method gives excellent results at low temperature (T TK) throughout the mixed-valence and Kondo regimes but it is unreliable for higher temperature. © 2010 The American Physical Society.