Simulated annealing study of morphological transitions of diblock copolymers in solution

The mechanism underlying the transitions between stripes, helices, and stacked toroids in the cylindrical shell formed by AB diblock copolymers on a long nanocylinder

The self-assembly of block copolymers on nanocylinders has attracted a lot of interest due to its potential application in biomedicine and other fields. In this study, the self-assembly phase behavior of AB diblock copolymers on long nanocylinders in soft confinement has been studied by using a simulated annealing method. A square phase diagram of the morphology was constructed by increasing the number of chains of copolymers (cn) and the cylindrical diameter (D). As a result, morphological transitions from striped to helical and axially stacked toroids, as well as reversible transitions, started to appear. By analyzing the chain packing in a fan-shaped region and calculating the mean-square end-to-end distance (DEE2) of the copolymers and number of AB contacts, both types of transitions were found to be driven by the competition between conformational entropy and AB interfacial energy. The number of stripes increased and the helical angle decreased with the increase in cylinder diameter. The chirality of the helix was found to be random.

Polymersomes in Drug Delivery─From Experiment to Computational Modeling

Polymersomes, composed of amphiphilic block copolymers, are self-assembled vesicles that have gained attention as potential drug delivery systems due to their good biocompatibility, stability, and versatility. Various experimental techniques have been employed to characterize the self-assembly behaviors and properties of polymersomes. However, they have limitations in revealing molecular details and underlying mechanisms. Computational modeling techniques have emerged as powerful tools to complement experimental studies and enabled researchers to examine drug delivery mechanisms at molecular resolution. This review aims to provide a comprehensive overview of the state of the art in the field of polymersome-based drug delivery systems, with an emphasis on insights gained from both experimental and computational studies. Specifically, we focus on polymersome morphologies, self-assembly kinetics, fusion and fission, behaviors in flow, as well as drug encapsulation and release mechanisms. Furthermore, we also identify existing challenges and limitations in this rapidly evolving field and suggest possible directions for future research.

Asymmetric block copolymer membrane fabrication mechanism through self-assembly and non-solvent induced phase separation (SNIPS) process

In this paper, the concept of the functional mechanism of copolymer membrane formation is explained and analyzed from the theoretical and experimental points of view. To understand the phase inversion process and control the final membrane morphology, styrene-acrylonitrile copolymer (SAN) membrane morphology through the self-assembly phenomena is investigated. Since the analysis of the membrane morphology requires the study of both thermodynamic and kinetic parameters, the effect of different membrane formation conditions is investigated experimentally; In order to perceive the formation mechanism of the extraordinary structure membrane, a thermodynamic hypothesis is also developed based on the hydrophilic coil migration to the membrane surface. This hypothesis is analyzed according to Hansen Solubility Parameters and proved using EDX, SAXS, and contact angle analysis of SAN25. Moreover, the SAN30 membrane is fabricated under different operating conditions to evaluate the possibility of morphological prediction based on the developed hypothesis.

DPD simulations on morphologies and structures of blank PLGA-b-PEG-b-PLGA polymeric micelles and docetaxel-loaded PLGA-b-PEG-b-PLGA polymeric micelles

Dissipative particle dynamics (DPD) simulation was used to study the morphologies and structures of blank (no drug) poly(lactic-co-glycolic acid)-b-poly(ethylene glycol)-b-poly(lactic-co-glycolic acid) (PLGA-b-PEG-b-PLGA) polymeric micelles and the docetaxel (Dtx)-loaded PLGA-b-PEG-b-PLGA polymeric micelles. We focused on the influences of PLGA-b-PEG-b-PLGA copolymer concentration, composition, Dtx drug content and the shear rate on morphologies and structures of the micelles. Our simulations show that the PLGA-b-PEG-b-PLGA copolymers in the aqueous solutions could aggregate and form blank micelles while Dtx drug and PLGA-b-PEG-b-PLGA could aggregate and form drug-loaded micelles. Under different PLGA-b-PEG-b-PLGA concentrations and drug content, the blank and drug-loaded micelles are observed as spherical, onionlike, columnar, and lamellar structures. The onionlike structures are comprised of the PEG hydrophilic core, the PLGA hydrophobic middle layer, and the PEG hydrophilic shell. As the structure of micelles varies from a spherical core–shell structure to a core–middle layer–shell onionlike structure, the distribution of the Dtx drugs diffuses from the core to the PLGA middle layer of the aggregate. In addition, the drug release process of the Dtx-loaded micelles under shear flow is also simulated. And the results show that the spherical micelles turn into a columnar structure under a shear rate from 0.2 to 3.4. When the shear rate increases to 3.5, the Dtx drugs released gradually increase until all are released with time evolution. These findings illustrate the dependence of the structural morphologies on the detailed molecular parameters of PLGA-b-PEG-b-PLGA and Dtx.

Dissipative particle dynamics simulation was used to study the morphologies and structures of blank (no drug) poly(lactic-co-glycolic acid)-b-poly(ethylene glycol)-b-poly(lactic-co-glycolic acid) polymeric micelles and the docetaxel-loaded polymeric micelles.

Solvent-induced morphological transitions in methacrylate-based block-copolymer aggregates

Poly(ethylene oxide)-b-poly(butylmethacrylate) (PEO-b-PBMA) copolymers have recently been identified as excellent building blocks for the synthesis of hierarchical nanoporous materials. Nevertheless, while experiments have unveiled their potential to form bicontinuous phases and vesicles, a general picture of their phase and aggregation behavior is still missing. By performing Molecular Dynamics simulations, we here apply our recent coarse-grained model of PEO-b-PBMA to investigate its self-assembly in water and tetrahydrofuran (THF) and unveil the occurrence of a wide spectrum of mesophases. In particular, we find that the morphological phase diagram of this ternary system incorporates bicontinuous and lamellar phases at high copolymer concentrations, and finite-size aggregates, such as dispersed sheets or disk-like aggregates, spherical vesicles and rod-like vesicles, at low copolymer concentrations. The morphology of these mesophases can be controlled by tuning the THF/water relative content, which has a striking effect on the kinetics of self-assembly as well as on the resulting equilibrium structures. Our results disclose the fascinating potential of PEO-b-PBMA copolymers for the templated synthesis of nanostructured materials and offer a guideline to fine-tune their properties by accurately selecting the THF/water ratio.

Formation and Regulation of Multicompartment Vesicles from Cyclic Diblock Copolymer Solutions: A Simulation Study

The self-assembly of a cyclic AB copolymer system with relatively long A blocks and short B blocks in B-selective solvents is investigated using a simulated annealing method. By investigating the effect of the lengths and solubilities of A and B blocks (N A and N B, εAS and εBS), the incompatibility between A and B blocks (εAB), as well as the polymer concentration (C p) and the conditions for the formation of multicompartment vesicles in cyclic diblock copolymer solutions, is predicted. The phase diagrams in terms of N B, εAS, and C p are constructed. The mechanism of the morphological transition is elucidated. It is shown that for cyclic copolymers the change in the above factors relating to the polymer and solvent properties all can lead to the transition from simple vesicles to multicompartment vesicles, but two different transition mechanisms are revealed. In addition, our simulations demonstrate that the self-assembly of cyclic copolymers could provide a powerful strategy for regulating the compartment number and the wall thickness of the multicompartment vesicles by adjusting the block solubilities and block lengths, respectively. These findings will facilitate the application of multicompartment architectures in cell mimicry, drug delivery, and nanoreactors.

Phase behavior of ABC cyclic terpolymer melts: a simulation study

The phase behavior of ABC cyclic terpolymer melts is investigated using a simulated annealing technique. A ternary phase diagram is constructed by tuning the volume fractions of the three blocks (f_A, f_B, and f_C) in the case of symmetric interactions. 11 phases are predicted, including lamellae with spheres at the interfaces, lamellae with spheres inside a domain, lamellae with spheres inside domains, cylinders in perforated lamellae, [6.6.6] tiling patterns, lamella + cylinder, hierarchical double-gyroid, columnar piled disk, patched spheres, cylinders with spheres at the interfaces and double gyroid with spheres at the interfaces. In these structures, the end segments of the three blocks tend to distribute uniformly on the A/B, B/C, or A/C interfaces, which may result in superior mechanical properties of the structures in cyclic terpolymer systems than those of the same structures formed in star or linear terpolymer systems. The physical reason for the similarities and differences between the phases formed in ABC cyclic and star terpolymer systems is investigated. Our simulation results are compared with related experimental observations and theoretical calculations.

Shape Transformations of Vesicles Self-Assembled from Amphiphilic Hyperbranched Multiarm Copolymers via Simulation

The understanding of shape transformations of vesicles is of fundamental importance in biological and clinical sciences. Hyperbranched polymer vesicles (branched polymersomes) are newly emerging polymer vesicles with special structure and property. They have also been regarded as a good model for biomembranes. However, the shape transformations of hyperbranched polymer vesicles have not been studied from either an experimental or theoretical level. Herein, the shape transformations of vesicles self-assembled from amphiphilic hyperbranched multiarm copolymers (HMCs) in response to the interaction parameters between the hydrophobic core and hydrophilic arms and the polymer concentrations are investigated carefully through dissipative particle dynamics (DPD) simulations. In the morphological phase diagram, two types of vesicles are obtained: one type corresponds to vesicles without holes formed at low concentrations including unilamellar vesicles, double-lamellar vesicles, discocyte-shaped vesicles, and tubular vesicles, and the other type corresponds to vesicles with holes formed at high concentrations including stomatocyte-shaped vesicles, toroidal vesicles, genus-3 (G-3) toroidal vesicles with three holes, and genus-4 (G-4) toroidal vesicles with four holes. In addition, both the self-assembly mechanisms and the dynamics for the formation of these vesicles have been systematically studied. The current work will offer theoretical support for fabricating novel vesicles with various shapes from hyperbranched polymers.

Formation Mechanisms of Porous Particles from Self-Assembly of Amphiphilic Diblock Copolymers inside an Oil-in-Water Emulsion Droplet upon Solvent Evaporation

The formation mechanisms of porous particles from self-assembly of amphiphilic diblock copolymers inside an oil-in-water emulsion droplet upon evaporation of the organic solvent are investigated based on Monte Carlo simulations for the first time. A morphological diagram of particles is constructed as a function of the surfactant concentration (φ) and the copolymer composition characterized by the volume fraction of the hydrophilic B block ( f_B). Particles with various morphologies are predicted. Morphological sequences from non-porosity to closed-porosity to capsules and finally to open-porosity particles are usually observed with increasing φ when f_B ≤ 1/2, with the only exception that capsules do not occur when f_B = 1/6. Furthermore, the critical φ value for a given morphological transition usually decreases with increasing f_B. Micelles are always observed at higher φ regions when f_B > 1/2. It is found that the specific surface area falls on almost the same regime for particles with the same kind of morphology, indicating that the morphology of a particle largely determines its specific surface area. The chain stretching varies with the particle morphology. It is the presence of the surfactant that makes the formation of porous particles possible, while when φ > 0, multiple morphological transitions can be induced by changing f_B. In the process of organic solvent removal, the value of f_B may affect the shape of pores inside the droplet and hence leads to the f_B dependence of the morphological sequences. When the solvent evaporation is not too fast, the resulting morphological sequence does not depend on the evaporation rate. Our results are compared with related experiments.

Effect of Chain Architecture on Self-Assembled Aggregates from Cyclic AB Diblock and Linear ABA Triblock Copolymers in Solution

The self-assembly behaviors of two block copolymers with the same chain length but different chain architectures (cyclic AB, linear ABA) in B-selective solvents are investigated using Monte Carlo simulations. A morphological transition sequence, from spherical micelles to cylindrical micelles, to vesicles and then to multicompartment vesicles, is observed for both copolymer systems when the interaction between the solvophobic A-block and the solvent is increased. In particular, toroidal micelles could be formed in triblock systems due to the presence of the bridging chains at the parameter region between cylindrical micelles and vesicles whereas disklike micelles are formed in cyclic systems. The simulation results demonstrated that the architecture of block copolymers could be used to regulate the structural characteristics and thermal stability of these self-assembled aggregates.

Synthesis and self-assembly behavior of polyhedral oligomeric silsesquioxane-based triblock copolymers in selective solvents by dissipative particle dynamics simulation

Self-assembly behaviors of POSS-based triblock copolymers were studied by DPD, and the results were in qualitative agreement with the experimental data.

Influence of Grafting Point Distribution on the Surface Structures of Y-Shaped Polymer Brushes in Solution

We report a simulated annealing study of surface structures of the Y-shaped copolymers grafted onto a planar substrate in nonselective solvents. The influences of the lateral size of the grafting surface and the distribution manner of the grafting point on the order degree of the ripple structures are investigated. Under uniformly distribution conditions, it is found that the well-defined ripple structures can be formed when the lateral size less than a threshold which depends on the solvent quality and grafting density. However, introducing a density fluctuation into the uniformly distribution grafting points in different ways, the defects with different degrees are observed in the ripple structures. The influence of the density fluctuations on the ripple phase are studied quantitatively. Furthermore, the possibility of the formation of surface structures with long-range order induced by directed self-assembly is investigated. The findings provide guidelines for fabricating patterned surfaces with highly ordered structures.

Single Step Process for Self-Assembled Block Copolymer Patterns via in Situ Annealing during Spin-Casting

We demonstrated a simple and time-efficient processing method for facilitating a microphase separation of block copolymers (BCPs) based on a single step of spin-casting with low volatile solvent and in situ annealing. Well-ordered lamellar patterns of poly(styrene-b-methyl methacrylate) BCP films having wide range of molecular weights (51-235 kg/mol) were fabricated by a single 3 min process of spin-casting, even without the conventional pretreatment of substrate neutralization. The formation of this well-ordered lamellar structure is attributed to a synergetic effect between slow solvent evaporation and thermal energy that may provide an efficient cooling profile for the BCP film during the spin-casting process.

Simulation methods for solvent vapor annealing of block copolymer thin films

Recent progress in modelling the solvent vapor annealing of thin film block copolymers is examined in the context of a self-consistent field theory framework. Key control variables in determining the final microdomain morphologies include swelling ratio or swollen film solvent volume fraction, swollen film thickness, substrate and vapor atmosphere surface energies, effective volume fraction, and effective Flory-Huggins interaction parameter. The regime of solvent vapor annealing studied is where the block copolymer has a high enough Flory-Huggins parameter that ordered structures form during swelling and are then trapped in the system through quenching. Both implicit and explicit consideration of the solvent vapor is considered to distinguish the cases in which solvent vapor leads to a non-bulk morphology. Block-selective solvents are considered based on the experimental systems of polystyrene-b-polydimethylsiloxane annealed with toluene and heptane. The results of these simulations are compared with these experiments.

Monte Carlo study of the micelles constructed by ABCA tetrablock copolymers and their formation in A-selective solvents

Micelles with hamburger-type and Janus-type solvophobic parts, asymmetric vesicles with multicompartment outer surface formed by ABCA tetrablock copolymers in A-selective solvent.

Finite-length effects on the coil-globule transition of a strongly charged polyelectrolyte chain in a salt-free solvent

The nature of coil-globule transition and scaling behavior of a strongly charged polyelectrolyte chain in a solution system with explicit neutralizing counterions and solvent molecules are studied using replica-exchange Monte Carlo simulations, focusing on the effects of finite chain length. The results reveal that at the thermodynamic limit of infinitely long chain length, the coil-globule transition may remain first order. Phase transition temperatures at various ion concentrations are obtained by extrapolating the values obtained at finite chain lengths. Furthermore, it is found that the exponent ν of the radius of gyration, <R(g)(2)> ~ N(2ν), can be slightly larger than 1 under some conditions.

Highly symmetric patchy multicompartment nanoparticles from the self-assembly of ABC linear terpolymers in C-selective solvents

Multicompartment micelles, especially those with highly symmetric surfaces such as patchy-like, patchy, and Janus micelles, have tremendous potential as building blocks of hierarchical multifunctional nanomaterials. One of the most versatile and powerful methods to obtain patchy multicompartment micelles is by the solution-state self-assembly of linear triblock copolymers. In this article, we applied the simulated annealing method to study the self-assembly of ABC linear terpolymers in C-selective solvents. Simulations predict a variety of patchy and patchy-like multicompartment micelles with high symmetry and also yield a detailed phase diagram to reveal how to control the patchy multicompartment micelle morphologies precisely. The phase diagram demonstrates that the internal segregated micellar structure depends on the ratio between the volume fractions of the two solvophobic blocks and their incompatibility, whereas the overall micellar shape depends on the copolymer concentration. The relationship between the interfacial energy, stretching energy of chains and the micellar morphology, micellar morphological transition are elucidated by computing the average contact number among the species, the mean square end-to-end distances of the whole terpolymers, the AB blocks in the terpolymers, the AB diblock copolymers, and angle distribution of terpolymers. The anchoring effect of the solvophilic C block on micellar structures is also examined by comparing the morphologies formed from ABC terpolymers and AB diblock copolymers.

ORDERED MICROPHASES OF SYMMETRIC DIBLOCK COPOLYMER IN SELECTIVE SOLVENT: DISSIPATIVE PARTICLE DYNAMICS SIMULATION AND RADIAL DISTRIBUTION FUNCTION ANALYSIS

The self-assembly process of a symmetric diblock copolymer A5B5 in a selective solvent is studied using the dissipative particle dynamics method. Four types of morphologies can form, including lamellae, perforated lamellae, cylinders and spheres. Three phase diagrams are presented to demonstrate the effect of the concentration and interaction parameters on the ordered microstructures. Radial distribution function (RDF) characterizing the spatial correlations of the blocks is calculated. RDF not only confirms the morphological observations, but also provides more quantitative details. The evolution process of hexagonally packed cylinder and lamellae is also illustrated.

Soft confinement-induced morphologies of diblock copolymers

The self-assembly of diblock copolymers under soft confinement is studied systematically using a simulated annealing method applied to a lattice model of polymers. The soft confinement is realized by the formation of polymer droplets in a poor solvent environment. Multiple sequences of soft confinement-induced copolymer aggregates with different shapes and self-assembled internal morphologies are predicted as functions of solvent-polymer interaction and the monomer concentration. It is discovered that the self-assembled internal morphology of the aggregates is largely controlled by a competition between the bulk morphology of the copolymer and the solvent-polymer interaction, and the shape of the aggregates can be non-spherical when the internal morphology is anisotropic and the solvent-polymer interaction is weak. These results demonstrate that droplets of diblock copolymers formed in poor solvents can be used as a model system to study the self-assembly of copolymers under soft confinement.

Complex micelles from self-assembly of ABA triblock copolymers in B-selective solvents

We report an extensive simulation study of the self-assembly of amphiphilic ABA triblock copolymers dissolved in solvents selective for the middle B-block. The effects of copolymer composition, copolymer concentration, and A-solvent interactions on the morphologies and morphological transitions of the aggregates are examined systematically. The simulations reveal that a rich variety of aggregates, ranging from spherical and rodlike micelles and vesicles to toroidal and net-cage micelles, can be formed spontaneously from a randomly generated initial state. Phase diagrams are constructed and rich morphological transitions are predicted. Chain packing in different micelles is investigated. The simulation results are compared with previous observations or predictions for related copolymer systems.

Self-assembly of diblock copolymers confined in cylindrical nanopores

Self-assembly of AB diblock copolymers confined in cylindrical nanopores is studied using a simulated annealing technique. The pore diameter and surface preference are systematically varied to examine their effects on the self-assembled morphologies and the chain conformations. For bulk lamella-forming and cylinder-forming diblock copolymers, novel structures such as helices and concentric (perforated) lamellae spontaneously form when the copolymers are confined in cylindrical pores. The observed equilibrium morphologies are compared with that obtained from experiments, theory, and other simulations. A simple model is proposed for symmetric diblock copolymers, which gives a reasonable description of the layer thickness for the concentric lamellae. It is found that chains near the pore surfaces are compressed relative to the bulk chains, which can be attributed to the existence of the surfaces. The dependence of the chain conformation on the degree of confinement and strength of the surface preference are reasonably explained. The energetics is discussed qualitatively and used to account for the appearance of the complex phase behavior observed for certain intermediate conditions.

Self-assembled morphologies of diblock copolymers confined in nanochannels: Effects of confinement geometry

The self-assembly of diblock copolymers confined in channels of various shaped cross sections is studied using a simulated annealing technique with the "single-site bond fluctuation" model. In the bulk, the asymmetric diblock copolymers used in this study form hexagonally packed cylinders with period L0. The cross sections of the confining channels are of different shapes including regular triangles, rectangles, squares, regular hexagons, regular octagons, and ellipses. For a given geometry, the channel size (characterized by one or two lengths) is varied from very small to several times of L0. It is found that the geometry and size of the confining channels have a large effect on the structure and symmetry of the self-assembled morphologies. Multiple packed cylinders with the symmetry of the confining channels are the major morphologies for low-symmetry cross sections such as triangle, rectangle, and square. More complex structures such as helices or stacked toroids spontaneously form when the confining channels are shaped such as a regular hexagon, a regular octagon, or an ellipse. The domain spacing of the self-assembled structures can be altered by the shape and size of the confining channels. Our results are consistent with available experiments. These results indicate that the self-assembled structures of block copolymers can be manipulated by the shape of the confining channels.

Study of Controllable Aggregation Morphology of ABA Amphiphilic Triblock Copolymer in Dilute Solution by Changing the Solvent Property

We have studied, both experimentally and theoretically, the aggregation morphology of the ABA amphiphilic triblock copolymer in dilute solution by changing the solvent property. Experimental results showed that the micellar morphology changed from spheres to rods and then to vesicles by changing the common solvent from N-N-dimethylformamide (DMF) to dioxane and then to tetrahydrofuran (THF). These controllable aggregates were also obtained by Monte Carlo simulation. The simulative results showed that the solvent property is a key factor that determines the copolymer aggregation morphology. The morphology changed from spheres to rods and then to vesicles by increasing the solvent solubility, corresponding to the change of stretched of the copolymer chains in the micellar cores. This result is in good agreement with the experimental one. Moreover, the simulative results revealed that the end-to-end distant of the ABA triblock copolymer in the vesicle was larger than that in the spheres and rods, indicating that the copolymer chains were more stretched in vesicles than in the spheres and rods. Furthermore, we gave the distribution of the fraction of the chain number with the end-to-end distance. The results indicated that the amount of folded chains is almost the same as that of stretched chains in the vesicle. Although most chains were folded, stretched chains could be found in the rod and sphere micelles.

Monte Carlo Simulations of Cylinder-Forming ABC Triblock Terpolymer Thin Films

We systematically study the cylinder-forming ABC triblock terpolymer thin films using canonical ensemble Monte Carlo simulations. The simulated annealing procedure is applied to the self-assembling process. By judicious choice of the system dimensions, we elaborately investigate the effect of film thickness on the orientation of the cylinders. This confined triblock terpolymer system exhibits different phase behavior under the weak and strong surface fields. In addition, we also investigate the ensemble-averaged chain orientations and relative density profiles.

Simulated annealing study of asymmetric diblock copolymer thin films

We report a simulated annealing study of the morphology of asymmetric diblock copolymer thin films confined between two homogeneous and identical surfaces. We have focused on copolymers that form a gyroidal morphology in the bulk. The morphological dependence of the confined films on the film thickness and the surface-polymer interaction has been systematically investigated. From the simulations it is found that much richer morphologies can form for the gyroid-forming asymmetric diblock copolymer thin films, in contrast to the lamella-forming symmetric and cylinder-forming asymmetric diblock copolymer films. Multiple morphological transitions induced by changing the film thickness and polymer-surface interactions are observed.

Confinement-induced novel morphologies of block copolymers

Self-assembly of block copolymers confined in cylindrical nanopores is studied systematically using a simulated annealing technique. For diblock copolymers which form two-dimensional hexagonally packed cylinders with period L0 in the bulk, novel structures such as helices and stacked toroids spontaneously form inside the cylindrical pores. These confinement-induced morphologies have no counterpart in the bulk system and they depend on the pore diameter (D) and the surface-polymer interactions, reflecting the importance of structural frustration and interfacial interactions. On tightening the degree of confinement, transitions from helices to toroids to spheres are observed. Mechanisms of the morphological transitions can be understood based on the degree of structural frustration parametrized by the ratio D/L0.

Cylinder-gyroid-lamella transitions in diblock copolymer solutions: A simulated annealing study

The morphological transition of an asymmetric diblock copolymer [A3-b-B9] in A-selective solvents is investigated using a simulated annealing technique. The study was carried out at high copolymer concentrations. Phase-transitions among hexagonally packed cylinders (C), gyroid (G), and lamellae (L) are observed. The phase transition sequence, C-->G-->L, was obtained with decreasing copolymer concentration and/or increasing B-solvent interaction. The predicted phase-transition sequence is consistent with experiments of diblock copolymers with similar volume fractions in selective solvents of different selectivity. The morphological transitions were further analyzed in terms of the average contact numbers for A or B monomers with other molecules and the total surface area of the core or matrix in each structure. It is found that these quantities correlate with the structures, providing an understanding of the phase-transition mechanisms.

Simulated annealing study of gyroid formation in diblock copolymer solutions

Conditions for the formation of gyroid structures in diblock copolymer solutions are examined using a simulated annealing technique. The simulations were performed on diblock copolymer systems of A(NA)-b-B(NB) (with NA<NB) in solvents that are selective to the A blocks. It is shown that gyroid structures form in a narrow range of block copolymer concentrations between the hexagonally packed cylindrical and the lamellar phases and at an almost constant B-monomer concentration. It is also shown that the gyroid structure is especially sensitive to the B-solvent interaction (epsilonBS) and the length of the B block (NB). Phase diagrams for the diblock copolymer solutions are constructed. These predicted results are consistent with previous experimental observations. The three-dimensional isosurface contour plots of the simulated gyroid structure shows two interpenetrating strut networks. The projection along the [111] direction of the simulated gyroid structure and the spherically averaged structure factor are in good agreement with previous experimental results.