Computer simulation of rod-coil block copolymers and tetrapod,polymer mixtures

In this thesis I present a new coarse-grained model suitable to investigate the phase behavior of rod-coil block copolymers on mesoscopic length scales. In this model the rods are represented by hard spherocylinders, whereas the coil block consists of interconnected beads. The interactions between the constituents are based on local densities. This facilitates an efficient Monte-Carlo sampling of the phase space. I verify the applicability of the model and the simulation approach by means of several examples. I treat pure rod systems and mixtures of rod and coil polymers. Then I append coils to the rods and investigate the role of the different model parameters. Furthermore, I compare different implementations of the model. I prove the capability of the rod-coil block copolymers in our model to exhibit typical micro-phase separated configurations as well as extraordinary phases, such as the wavy lamellar state, percolating structuresrnand clusters. Additionally, I demonstrate the metastability of the observed zigzag phase in our model. A central point of this thesis is the examination of the phase behavior of the rod-coil block copolymers in dependence of different chain lengths and interaction strengths between rods and coil. The observations of these studies are summarized in a phase diagram for rod-coil block copolymers. Furthermore, I validate a stabilization of the smectic phase with increasing coil fraction.rnIn the second part of this work I present a side project in which I derive a model permitting the simulation of tetrapods with and without grafted semiconducting block copolymers. The effect of these polymers is added in an implicit manner by effective interactions between the tetrapods. While the depletion interaction is described in an approximate manner within the Asakura-Oosawa model, the free energy penalty for the brush compression is calculated within the Alexander-de Gennes model. Recent experiments with CdSe tetrapods show that grafted tetrapods are clearly much better dispersed in the polymer matrix than bare tetrapods. My simulations confirm that bare tetrapods tend to aggregate in the matrix of excess polymers, while clustering is significantly reduced after grafting polymer chains to the tetrapods. Finally, I propose a possible extension enabling the simulation of a system with fluctuating volume and demonstrate its basic functionality. This study is originated in a cooperation with an experimental group with the goal to analyze the morphology of these systems in order to find the ideal morphology for hybrid solar cells.

Self-assembly of T-shaped rod-coil block copolymer melts

Self-assembled behavior of T-shaped rod-coil block copolymer melts is studied by applying self-consistent-field lattice techniques in three-dimensional space. Compared with rod-coil diblock copolymers with the anchor point positioned at one end, the copolymers with the anchor point at the middle of the rod exhibit significantly different phase behaviors. When the rod volume fraction is low, the steric hindrance of the lateral coils prevents the rods stacking into strip or micelle as that in rod-coil diblock copolymers. The competition between interfacial energy and entropy results in the formation of lamellar structures and the increasing thickness of the lamellar layer with increasing rod volume fraction.

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.

Rigidity effect on phase behavior of symmetric ABA triblock copolymers: A Monte Carlo simulation

The phase behavior of symmetric ABA triblock copolymers containing a semiflexible midblock is studied by lattice Monte Carlo simulation. As the midblock evolves from a fully flexible state to a semiflexible state in terms of increase in its persistence length, different phase behaviors are observed while cooling the system from an infinite high temperature to a temperature below T-ODT (order-disorder transition temperature). Within the midblock flexibility range we studied (l(p)/N-c <= 0.105), a lamellar structure is formed at equilibrium state as the situation for fully flexible chains. The fraction of bridge chain is evaluated for the lamellar structures. We find that the increase in midblock rigidity indeed results in the increase in bridge chain fraction within the range from 44.9% to 51.8%.

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 chi N.

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.

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.

Self-Assembly of Rod-Terminally Tethered Three-Armed Star-Shaped Coil Block Copolymer: Investigation of the Presence of the Branching in the Coil to the Self-Assembled Behavior

Self-assembled behavior of rod-terminally tethered three-armed star-shaped coil block copolymer melts was studied by applying self-consistent-field lattice techniques in three-dimensional (3D) space. Similar to rod-coil diblock copolymers, five morphologies were observed, i.e., lamellar, perforated lamellar, gyroidlike, cylindrical and sphericallike structures, while the distribution of the morphologies in the phase diagram was dramatically changed with respect to that Of rod-coil diblock copolymers.

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.

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.

"Sandglass"-shaped self-assembly of coil-rod-coil triblock copolymer containing rigid aniline-pentamer

The amphiphilic PEG1 500-b-EM AP-b-PEG1 500 (EM PAP) triblock copolymer of poly(ethylene glycol) (PEG) and emeraldine aniline-pentamer (EM AP) in its concentrated solution can self-assemble into a special shape like "sandglass", as observed by transmission electron microscopy (TEM), field emission scanning electron microscopy (ESEM) and atomic force microscopy (AFM). This "sandglass"- shaped assembly is composed of several "rods" aggregated in the middle, with every "rod" being about 8 VLrn in length and 300 nm in diameter.

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 hard spherocylinders under confinement

When a liquid crystal is confined to a cavity its director field becomes subject to competing forces: on the one hand, the surface of the cavity orients the director field (``surface anchoring''), on the other hand deformations of the director field cost elastic energy. Hence the equilibrium director field is determined by a compromise between surface anchoring and elasticity. One example of a confined liquid crystal that has attracted particular interest from physicists is the nematic droplet. In this thesis a system of hard rods is considered as the simplest model for nematic liquid crystals consisting of elongated molecules. First, systems of hard spherocylinders in a spherical geometry are investigated by means of canonical Monte Carlo simulations. In contrast to previous simulation work on this problem, a continuum model is used. In particular, the effects of ordering near hard curved walls are studied for the low-density regime. With increasing density, first a uniaxial surface film forms and then a biaxial surface film, which eventually fills the entire cavity. We study how the surface order, the adsorption and the shape of the director field depend on the curvature of the wall. We find that orientational ordering at a curved wall in a cavity is stronger than at a flat wall, while adsorption is weaker. For densities above the isotropic-nematic transition, we always find bipolar configurations. As a next step, an extension of the Asakura-Oosawa-Vrij model for colloid-polymer mixtures to anisotropic colloids is considered. By means of computer simulations we study how droplets of hard, rod-like particles optimize their shape and structure under the influence of the osmotic compression caused by the presence of spherical particles that act as depletion agents. At sufficiently high osmotic pressures the rods that make up the drops spontaneously align to turn them into uniaxial nematic liquid crystalline droplets. The nematic droplets or ``tactoids'' that so form are not spherical but elongated, resulting from the competition between the anisotropic surface tension and the elastic deformation of the director field. In agreement with recent theoretical predictions we find that sufficiently small tactoids have a uniform director field, whilst large ones are characterized by a bipolar director field. From the shape and director-field transformation of the droplets we estimate the surface anchoring strength.