Electric field versus surface alignment in confined films of a diblock copolymer melt

The dynamics of alignment of microstructure in confined films of diblock copolymer melts in the presence of an external electric field was studied numerically. We consider in detail a symmetric diblock copolymer melt, exhibiting a lamellar morphology. The method used is a dynamic mean-field density functional method, derived from the generalized time-dependent Ginzburg-Landau theory. The time evolution of concentration variables and therefore the alignment kinetics of the morphologies are described by a set of stochastic equations of a diffusion form with Gaussian noise. We investigated the effect of an electric field on block copolymers under the assumption that the long-range dipolar interaction induced by the fluctuations of composition pattern is a dominant mechanism of electric-field-induced domain alignment. The interactions with bounding electrode surfaces were taken into account as short-range interactions resulting in an additional term in the free energy of the sample. This term contributes only in the vicinity of the surfaces. The surfaces and the electric field compete with each other and align the microstructure in perpendicular directions. Depending on the ratio between electric field and interfacial interactions, parallel or perpendicular lamellar orientations were observed. The time scale of the electric-field-induced alignment is much larger than the time scale of the surface-induced alignment and microphase separation.     

Orthogonal fields: a path to long-range three-dimensional order in block copolymers

Large-scale computer simulations show that two orthogonal external fields can control the orientation of lamellar microdomains in diblock copolymers in three dimensions and lead to an enhanced long-range ordering.     

Macroscopic lamellae orientations of diblock copolymer induced by dynamic shear

Computer simulation based on the coupled map lattices has been carried out for morphologies of the diblock copolymeric system under applied periodic shear deformation.The main effort is concentrated on the influence of pre-annenling history on the lamellae orientations in dynamically sheared diblock copolymers.It is found that whatever the quenching temperature is,the perpendicular orientation (i.e.the lamellae normal is parallel to the vorticity axis) is always observed if the dynamic shear deformation with shear amplitude F=1.0 and reduced shear frequency=0.005 is applied during annealing.In contrast to that,the parallel orientation (i.e.the lamellae normal is parallel to the velocity gradient direction) is observed if the dynamic shear with the same amplitude and frequency is applied to a thoroughly annealed (with the annealing time t>4 000) diblock copolymer.Therefore,it is pointed out that the selection of lamellar orientations in dynamically sheared diblock copolymers is not solely dependent on th     

Coarse-grained molecular dynamics simulation on the placement of nanoparticles within symmetric diblock copolymers under shear flow

We present molecular dynamics simulations coupled with a dissipative particle dynamics thermostat to model and simulate the behavior of symmetric diblock copolymer/nanoparticle systems under simple shear flow. We consider two categories of nanoparticles, one with selective interactions toward one of the blocks of a model diblock copolymer and the other with nonselective interactions with both blocks. For the selective nanoparticles, we consider additional variants by changing the particle diameter and the particle-polymer interaction potential. The aim of our present study is to understand how the nanoparticles disperse in a block copolymer system under shear flow and how the presence of nanoparticles affects the rheology, structure, and flow behavior of block copolymer systems. We keep the volume fraction of nanoparticles low (0.1) to preserve lamellar morphology in the nanocomposite. Our results show that shear can have a pronounced effect on the location of nanoparticles in block copolymers and can therefore be used as another parameter to control nanocomposite self-assembly. In addition, we investigate the effect of nanoparticles on shear-induced lamellar transition from parallel to perpendicular orientation to further elucidate nanocomposite behavior under shear, which is an important tool to induce long-range order in self-assembling materials such as block copolymers.     

Mesoscopic dynamics of inhomogeneous polymers based on variable cell shape dynamic self-consistent field theory

In this paper, we combine variable cell shape method with dynamic self-consistent field theory and extend to study structure and dynamics under shear for triblock copolymer melts. Due to shear, the calculation cell shape is variable and no longer orthogonal. Pseudospectral method is employed to solve the diffusion equation for chain propagator on the nonorthogonal coordinate and the shear periodical condition can be easily designed in terms of the variable cell shape method. By using this strategy, the shear induced morphology evolution is investigated for topologically complex polymeric systems such as linear and star triblock copolymers; the morphology of linear ABC triblock copolymers is more shear sensitive than that of star triblocks. In particular, once the chain propagator is obtained, the microscopic elastic stress and spatial stress distribution can be derived and thus the dynamic mechanical property can be calculated under shear. By imitating the dynamic storage modulus G' corresponding to any given morphology in the oscillatory shear measurements, we explore the relationship between the morphology and the storage modulus G' and extend to study the mechanism of phase separation dynamics as well as order-disorder transition (ODT) for linear and star triblock copolymers. The results show that the chain architecture can be easily distinguished by investigating the ODT, though the systems such as AB symmetric diblock and ABA triblock copolymers by coupling AB precursors almost exhibit similar microstructures. In addition, the storage modulus G' and loss modulus G" can be simultaneously determined in frequency sweeps of oscillatory shear measurements and the dependence of the moduli on phase separated patterns and the chain topology is investigated. The simulation findings are in qualitatively agreement with the experimental results.     

嵌段共聚物和星型均聚物共混体系相行为的自洽场理论研究

用自洽场理论方法(Self-consistent field theory, SCFT)计算了嵌段共聚物AB和三等臂星型均聚物A共混体系的微相形态. 为了简化计算, 着重讨论了固定嵌段共聚物本体的相形态(如层状相)时, 所加入的均聚物的体积分数及均聚物与嵌段共聚物链长之比对体系相形态的影响; 并结合体系的熵和相互作用能的变化, 讨论了星型均聚物在体系微相结构中的分布.     

Coarse graining in block copolymer films

We present few ordering mechanisms in block copolymer melts in the coarse-graining approach. For chemically homogeneous or modulated confining surfaces, the surface ordering is investigated above and below the order–disorder temperature. In some cases, the copolymer deformation near the surface is similar to the copolymer morphology in bulk grain boundaries. Block copolymers in contact with rough surfaces are considered as well, and the transition from lamellae parallel to perpendicular to the surface is investigated as a function of surface roughness. Finally, we describe how external electric fields can be used to align block copolymer mesophases in a desired direction, or to induce an order–order phase transition, and dwell on the role of mobile dissociated ions on the transition. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2725–2739, 2006     

Long-range ordered thin films of block copolymers prepared by zone-casting and their thermal conversion into ordered nanostructured carbon

Large-scale alignment of lamellae in thin films of diblock copolymers containing polyacrylonitrile and poly(n-butyl acrylate) was achieved by casting copolymer solution on a silicon substrate moved away at a constant speed from the casting nozzle (zone-casting). Grazing incidence small-angle X-ray scattering revealed that the lamellae, which were perpendicular to the substrate, were also aligned over macroscopic scale in the direction perpendicular to the casting direction. Such long-range ordered block copolymer films were then converted by pyrolysis into nanostructured carbons, with excellent preservation of lamellar morphology and orientation.     

Influence of electric field on the phase transitions of the hexagonal cylinder phase of diblock copolymers.

We have used the cell dynamic simulations (CDS) method to study the evolution of asymmetric and symmetric diblock copolymers under electric fields. For symmetric diblock copolymers, long-range-ordered lamellar phases form readily under electric fields. For asymmetric diblock copolymers, sphere-to-cylinder phase transitions occur rapidly when strong electric fields are applied, but it takes longer for the system to form hexagonal cylinder structures. The results of these simulations suggest that the sphere phase is stable under weak electric fields, but a threshold electric intensity exists for the sphere-to-cylinder phase transition. In addition, we also studied the kinetic pathways of the transition of the lamellar phase to the hexagonal cylinder phase of the asymmetric diblock copolymers under electric fields. Hexagonal cylinder structures form when the lamellar phase is subjected to a sudden temperature jump. The scattering functions suggest that the hexagonal cylinder structures are very regular and possess very few flaws.     

Electric field manipulation of charged copolymer worm micelles

Manipulation of diblock copolymer worm micelles by external electric fields is visualized by fluorescence microscopy in dilute, aqueous solution. Hydrodynamic coupling of the poly(acrylic acid)-(1,4)-polybutadiene (PAA-PBD) worm motion to the electric field and the effective stiffening of the worms in an oscillating electric field are demonstrated. A brief discussion on using this technique to estimate the rheological properties of wormlike micelles is presented.     

多分散性对两亲性两嵌段共聚物在选择性溶剂中自组装行为影响的Monte Carlo模拟

采用Monte Carlo模拟方法研究了多分散性AB两亲性两嵌段共聚物在选择性溶剂中的自组装行为.模拟结果表明,嵌段共聚物的多分散性对体系在选择性溶剂中自组装所形成的胶束形貌结构有很大影响.当AB两嵌段共聚物的多分散系数由1.0增加至1.4时,体系中自组装所形成的胶束将会发生由囊泡到片层直至球状的一系列形态转变.通过统...     

Viscoplastic flow and shear thickening in concentrated diblock copolymer solutions

Concentrated (typically 6%) solutions of a polystyrene-polyisoprene diblock copolymer in low viscosity paraffinic solvents form a micelle system by precipitating the polystyrene blocks, whereas the polyisoprene blocks are in solution. Besides viscoplastic behavior without thixotropy, this system exhibits a pronounced shear thickening in steady-state shear flow. The micelles are stable up to shear rates of more than 10⁵ s^–1. The properties of the solutions, especially the shear-thickening behavior, depend on the thermal history of the samples as well as on the solvent properties and are sensitive to flow field disturbances occurring in rotational viscometer devices with a profiled surface structure as commonly used to avoid wall slip in dispersed materials. The shear thickening is found to be related to the formation of a long-range ordered structure which also gives rise to the yield point. This long-range order enables aggregate flow with less energy dissipation at low shear rates. Shear-induced break-up of the aggregates appears as a shear-thickening transition which is observed in different types of flow fields.     

Microphase separation of block copolymer solutions in a flow field

Films of polystyrene–polybutadiene–polystyrene (PS/PB/PS) triblock copolymer and polystyrene-poly(ethylene/propylene) (PS/PEP) diblock copolymer were cast from toluene solutions subjected to hydrodynamic flow at room temperature using a device based on a novel casting method we term ‘roll-casting.’ Polymer solutions were rolled between two corotating eccentric cylinders while at the same time the solvent was removed at a controlled rate. As the solvent evaporated, the block copolymers microphase separated into globally oriented structures. A discussion of the flow field that develops during roll-casting is presented and specific attention is given to the importance of the shear and elongation rates present. For the triblock and diblock, respectively, the processed structures consisted of polystyrene cylinders assembled on a hexagonal lattice in a polybutadiene matrix, and unidirectional lamellae of alternating polystyrene and polyethylene/propylene. Small-angle x-ray scattering (SAXS) and transmission electron microscopy (TEM) indicated the near single-crystal structure both types of films. SAXS also showed the styrene cylinders and the alternating lamellae to be packed closer together in roll-cast films than in simple quiescently cast films. A molecular orientation mechanism is proposed to describe both these results as well as the changes in packing and in macroscopic sample dimensions measured after complete solvent evaporation and after sample annealing. © 1993 John Wiley & Sons, Inc.     

Mesophase Separation of Diblock Copolymer Confined in a Cylindrical Tube Studied by Dissipative Particle Dynamics

Summary: The morphologies of diblock copolymers confined in a cylindrical tube have been investigated by the dissipative particle dynamics (DPD) method. Results indicate that the morphology depends on the volume ratio of the immiscible blocks, the diameter of the cylindrical tube and the interactions between the blocks and between the confinement wall and blocks. For symmetric diblock copolymers, when the tube wall is uniform toward the two blocks, perpendicular lamellae or a stacked disk morphology are generally formed except when the diameter of the cylindrical tube is very small; in that case, a special bi‐helix morphology forms because of the entropy effect. When the tube wall is non‐uniform, as the diameter of the tube increases, perpendicular lamellae are first formed, then changing to parallel lamellae and, finally, back to perpendicular lamellae again. An intermediate morphology characterizing the transition between perpendicular and parallel lamellae is observed. If the non‐uniformity of the wall is further enhanced, only parallel lamellae can be found. In the case of asymmetric diblock copolymers, more complex morphologies can be obtained. Multi‐cylindrical micro‐domains and a multilayer helical phase as well as other complex pictures are observed. Generally, the morphologies obtained could find their counterparts from experiments or Monte Carlo simulations; however, differences do exist, especially in some cases of asymmetric diblock copolymers.

Bi‐helix and stacked disks morphologies of A₅B₅ diblock copolymer confined in two different neutral nanocylinders.     

STRUCTURE EVOLUTION OF THE CYLINDRICAL PHASE OF DIBLOCK COPOLYMERS IN FILMS

In the weak segregation limit,the structure evolution of the hexagonal cylindrical phase of diblock copolymers in films was investigated.Employing the Landau-Brazovskii mean field theory,we obtained three amplitude parameters as functions of temperature,surface field strength and film thickness.By controlling confinement size and surface field strength, lamellae and undulated lamellae appear in the cylindrical bulk phase of diblock copolymers."Phase diagrams"of confinement-induced structures are construc...     

Application of power expansion in the thermodynamics of compressible Markovian copolymers

The problem of constructing phase diagrams for a compressible melt of a binary Markovian copolymer is reduced to a set of nonlinear differential equations in partial derivatives with transcendental relationships. Using power expansions, the closed set of nonlinear differential equations is derived. This set allows its further analytical study. Eigenvalues of a linearized system are analyzed, and the boundaries of the thermodynamic stability of melts are defined. Nonlinear equations in normal coordinates are obtained; for symmetric melts, these equations are reduced to a single equation by adiabatic elimination of small-scale variables. Binodal curves are calculated for such solutions of this equation, which correspond to the free energy minimum of melts. Corrections reflecting the effect of melt nonsymmetry are found. The results are applied for copolymers, whose composition is similar to that of homopolymers, diblock copolymers, and random and regularly alternating copolymers. Spinodals and binodals corresponding to microphase separation are constructed.     

Temperature-induced formation and contraction of micelle-like aggregates in aqueous solutions of thermoresponsive short-chain copolymers

A combination of turbidity, light scattering, and steady shear viscosity experiments has revealed that aqueous solutions of an amphiphilic diblock copolymer or a negatively charged triblock copolymer, both containing poly(N-isopropylacrylamide), can undergo a temperature-induced transition from loose intermicellar clusters to collapsed core-shell nanostructures. Turbidity, light scattering, and viscosity results of these short-chain copolymers disclose transition peaks at intermediate temperatures. At high temperatures, the compact core-shell particles from the diblock copolymer aggregate, whereas no renewed interpolymer association is observed for the triblock copolymer or for the solution of the diblock copolymer with added sodium dodecyl sulfate because the electrostatic repulsive interactions suppress the tendency of forming interpolymer clusters. The temperature-induced building up of intermicellar structures and the formation of large aggregates at high temperature in the solution of the diblock copolymer is significantly reduced under the influence of high shear rates.     

棒-棒二嵌段共聚物自组装行为的自洽场研究

利用格子自洽场模型, 模拟了棒-棒二嵌段共聚物熔体系统的自组装行为, 并与线-棒二嵌段共聚物系统性质进行了对比. 结果表明, 棒-棒二嵌段共聚物系统的有序无序转变临界点低于线-棒二嵌段共聚物系统的相变临界点. 通过模拟计算, 发现薄层交叠柱状相、柱状相、层状相和Z形层状相4种稳定的有序形貌. 薄层交叠柱状相和柱状相仅在有序无序转变曲线的边缘位置出现, 层状相也仅存在于有序无序转变临界点上面的一小块区域内, 而稳定的Z形层状结构则占据了相图中较强相互作用的大部分区域.     

Structural Changes in Block Copolymer Solutions under Shear Flow as Determined by Non‐Equilibrium Molecular Dynamics

Summary: A non‐equilibrium molecular dynamics computer simulation on microsegregated solutions of symmetrical diblock copolymers is reported. As the polymer concentration increases, the system undergoes phase transitions in the following order: body centered cubic (BCC) micelles, hexagonal (HEX) cylinders, gyroid (GYR) bicontinuous networks and lamellae (L), which are the same morphology reported for block copolymer melts. Structural classification is based on the patterns of the anisotropic static structure factor and characteristic 3‐dimensional images. The systems in the BCC micellar (ρσ³ = 0.3) and HEX cylindrical (ρσ³ = 0.4) phases were then subjected to a steady planar shear flow. In weak shear flow, the segregated domains in both systems tend to rearrange into sliding parallel close‐packed layers with their normal in the direction of the shear gradient. At higher shear rates, both systems adopt a perpendicular lamellar structure with the normal along the neutral direction. A further increase in the shear rate results in a decrease in lamellar spacing without any further structural transitions. Two critical shear rate values that correspond to the demarcation of different structural behaviors were found.

Shear‐induced BCC‐LAM phase transition.