Self-assembly of diblock copolymer mixtures in confined states: A Monte Carlo study

The self-assembly of diblock copolymer mixtures (A-b-B/A-b-C or A-b-B/B-b-C mixtures) subjected to cylindrical confinement (two-dimensional confinement) was investigated using a Monte Carlo method. In this study, the boundary surfaces were configured to attract blocks A but repel blocks B and C. Relative to the structures of the individual components, the self-assembled structures of mixtures of the diblock copolymers were more complex and interesting. Under cylindrical confinement, with varying cylinder diameters and interaction energies between the boundary surfaces and the blocks, we observed a variety of interesting morphologies. Upon decreasing the cylinder's diameter, the self-assembled structures of the A(15)B(15)/A(15)C(15) mixtures changed from double-helix/cylinder structures (blocks B and C formed double helices, whereas blocks A formed the outer barrel and inner core) to stacked disk/cylinder structures (blocks B and C formed the stacked disk core, blocks A formed the outer cylindrical barrel), whereas the self-assembled structures of the A(15)B(7)/B7C15 mixtures changed from concentric cylindrical barrel structures to screw/cylinder structures (blocks C formed an inside core winding with helical stripes, whereas blocks A and B formed the outer cylindrical barrels) and then finally to the stacked disk/cylinder structures.

Monte Carlo simulation of the compatibility of graft copolymer compatibilized two incompatible homopolymer blends: Effect of graft structure

Compatibility of graft copolymer compatibilized two incompatible homopolymer A and B blends was simulated by using Monte Carlo method in a two-dimensional lattice model. The copolymers with various graft structures were introduced in order to study the effect of graft structure on the compatibility. Simulation results showed that incorporation of both A-g-B (A was backbone) and B-g-A (B was backbone) copolymers could much improve the compatibility of the blends. However, A-g-B copolymer was more effective to compatibilize the blend if homopolymer A formed dispersed phase. Furthermore, simulation results indicated that A-g-B copolymers tended to locate at the interface and anchor two immiscible components when the side chain is relatively long. However, most of A-g-B copolymers were likely to be dispersed into the dispersed homopolymer A phase domains if the side chains were relatively short. On the other hand, B-g-A copolymers tended to be dispersed into the matrix formed by homopolymer B. Moreover, it was found that more and more B-g-A copolymers were likely to form thin layers at the phase interface with decreasing the length of side chain.

A Monte Carlo simulation of morphology and structure for thin films of symmetric triblock copolymer after quenching and annealing

Self-assembly thin films of symmetric triblock copolymer after annealing and quenching were examined by an effective Monte Carlo simulation method. The defects in the ordered lamellae of the thin films after quenching, which were dependent on the initialization of copolymer melts, are removed in the thin films after annealing. The mean-square gyration radius and end-to-end distance of copolymer chains in the thin films after annealing are smaller than those in the thin films after quenching because of the complete relaxation of polymer during annealing. We also find that the density of A block in the region near to the surface is higher than that in the interior of the thin films. As a result, it is different from the thin films of symmetric A(n)B(n) diblock copolymer, in which surface ordering forms before the interior, that ordering phenomena occurs first in the interior region in the thin films of symmetric A(n)B(m)A(n). triblocl copolymer.

Grafting of maleic anhydride onto linear polyethylene: A Monte Carlo study

Monte Carlo simulation was used to study the graft of maleic anhydride (MAH) onto linear polyethylene (PE-g-MAH) initiated by dicumyl peroxide (DCP). Simulation results revealed that major MAH monomers attached onto PE chains as branched graft at higher MAH content. However, at extremely low MAH content, the fraction of bridged graft was very close to that of branched graft. This conclusion was somewhat different from the conventional viewpoint, namely, the fraction of bridged graft was always much lower than that of branched graft under any condition. Moreover, the results indicated that the grafting degree increased almost linearly to MAH and DCP concentrations. On the other hand, it was found that the amount of grafted MAH dropped sharply with increasing the length of grafted MAH, indicating that MAH monomers were mainly attached onto the PE chain as single MAH groups or very short oligomers. With respect to the crosslink of PE, the results showed that the fraction of PE-(MAH)(n)-PE crosslink structure increased continuously, and hence the fraction of PE-PE crosslink decreased with increasing MAH concentration.

Effects of chain flexibility on polymer conformation in dilute solution studied by lattice Monte Carlo simulation

Effects of chain flexibility on the conformation of homopolymers in good solvents have been investigated by Monte Carlo simulation. Bond angle constraint coupled with persistence length of polymer chains has been introduced in the modified eight-site bond fluctuation simulation model. The study about the effects of chain flexibility on polymer sizes reveals that the orientation of polymer chains under confinement is driven by the loss of conformation entropy. The conformation of polymer chains undergoing a gradual change from spherical iso-diametric ellipsoid to rodlike iso-diametric ellipsoid with the decrease of polymer chain flexibility in a wide region has been clearly illustrated from several aspects. Furthermore, a comparison of the freely jointed chain (FJC) model and the wormlike chain (WLC) model has also been made to describe the polymer sizes in terms of chain flexibility and quasi-quantitative boundary toward the suitability of the models.

Investigation of sol-gel transition in Pluronic F127/D2O solutions using a combination of small-angle neutron scattering and Monte Carlo simulation

Physical gelation in the concentrated Pluronic F127/D2O solution has been studied by a combination of small-angle neutron scattering (SANS) and Monte Carlo simulation. A 15% F127/D2O solution exhibits a sol-gel transition at low temperature and a gel-sol transition at the higher temperature, as evidenced by SANS and Monte Carlo simulation studies. Our SANS and simulation results also suggest that the sol-gel transition is dominated by the formation of a percolated polymer network, while the gel-sol transition is determined by the loss of bound solvent. Furthermore, different diffusion behaviors of different bound solvents and free solvent are observed. We expect that this approach can be further extended to study phase behaviors of other systems with similar sol-gel phase diagrams.

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.