On the orientation of lamellar block copolymer phases under shear

Self-assembled lamellar structures composed of block copolymers are simulated by molecular dynamics. The response of a bulk system to external shear is investigated, in particular, the average energy, the entropy production, and the stability of the lamellae's orientation. We distinguish two orientations, a parallel orientation in which the normal to the lamellae sheets lies in the direction of the shear gradient, and a perpendicular orientation in which the normal lies perpendicular to the shear gradient and shear direction. The perpendicular phase is stable throughout all shear rates. The parallel phase has higher internal energy and larger entropy production than the perpendicular phase and moreover becomes unstable at relatively small shear rates. The perpendicular orientation should therefore be more stable at any finite shear rate. Surface effects are probably responsible for the stability of the parallel phase observed experimentally at small shear rates.     

Mesoscopic Simulations of Lamellar Orientation in Block Copolymers

Mesoscopic simulation techniques are employed to investigate lamellar orientation in block copolymers subjected to oscillatory shear. Dynamic mean‐field density functional theory (MesoDyn) is able to capture parallel lamellar and perpendicular lamellar states at low and higher shear rates. At higher shear rates a third orientation state is identified from cell dynamics and MesoDyn simulations, and corresponds to predominantly parallel‐aligned lamellae. This is explained on the basis of partial shear‐melting at higher shear rates. The results are compared to the lamellar alignment diagram obtained experimentally for polystyrene/polyisoprene block copolymers.     

Diffusion,elasticity, and shear flow in self-assembled block copolymers: A molecular dynamics study

Self-assembled ordered structures composed of block copolymers are simulated by molecular dynamics under stress-free conditions and under shear. We address several methodological points. The system must be allowed to adjust its size to accommodate natural periods of self-assembled structures. In addition, these structures need to be capable of rotating freely under shear. An examination of the diffusion of polymer molecules in the lamellar phase reveals subdiffusion along translationally invariant directions between the ballistic and diffusive regime. The diffused distance d increases with time t as d ∝ t^1/3. We also examine the possibility of mapping structures such as cylindrical phases onto particle–field types of models. Using measurements of the wavevector-dependent dynamic matrix, we show that this cannot be done with only two-body potentials. We then examine the molecular origin of shear alignment of lamellar phases. Lamellae oriented parallel to the shear direction become unstable at high shear rates when the major axis of the tensor of gyration of individual polymers forms an average angle of 45° with the lamellae. This instability can be understood in analogy to similar transitions in liquid crystals. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 970–982, 2005     

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.     

受限于两平行板间的对称星形共聚物Am Bm熔体相行为的格子自洽场理论研究

采用格子自洽场理论计算研究了受限于2个平行板间的对称星形共聚物AmBm(m=1,2,3,4,5)熔体形成的层状相结构.在给定的相互作用下(χNAB不变,χ为Flory-Huggins相互作用参数,NAB=(N?1)/m为单个聚合物分子中一对AB臂的总链节数目),针对平行板间距为体相周期的情况,系统考察了共聚物链长N和单个聚合物分子中A(或B)臂数目m对受限层结构细节及层取向的影响.由计算结果,当N或NAB不变时,受限层的归一化界面宽度随m的增大而减小.受限板为中性时,垂直层结构的单链自由能比平行层结构的低.随着板对共聚物中一种嵌段的选择作用Λ的增大,体系发生垂直层到平行层的转变,该转变为一阶相变.当m不变时,N越小,上述转变出现在越大的Λ值处,体系越容易保持垂直层结构.并且N越小,层状结构周期越小.当N或NAB不变时,m越大体系越容易保持垂直层结构.总之,星形共聚物的链长越短、臂数越多时,垂直层稳定的Λ区间越大、层状结构的界面宽度越小.这些结论可以指导刻蚀应用中对体系参数的选择.     

Nonequilibrium molecular dynamics simulation study on the orientation transition in the amphiphilic lamellar phase under shear flow

By the extensive large-scale nonequilibrium molecular dynamics simulation on an effective generic model-A2B2 tetramer for amphiphiles, we investigate the shear-induced parallel to perpendicular orientation transition in the lamellar phase as a function of segregation degree and shear rate. Under low rate shear flow the evolution of parallel lamellar configurations at different segregation strengths shows a similar kinetic pathway independent of the segregation degree. While under high rate shear flow in which the lifetime of undulation instability exceeds the characteristic time of the applied shear flow, the kinetic pathway of the shear-induced parallel-to-perpendicular orientation transition in lamellar systems is the segregation degree dependent. Comparing the temporal mesoscopic domain morphology, the microscopic chain conformation, and macroscopic observable-viscosity changes with the experimentally proposed mechanisms, we find that the undulation instability, partial breakup of monodomain, grain rotation, and recombination combined with defect migration and annihilation are the kinetic pathway for the parallel-to-perpendicular orientation transition in the lamellar phase in or near the intermediate segregation limit, and that the undulation instability, domain dissolution, and reformation along the preferred direction combined with defect migration and annihilation are the kinetic pathway for the parallel-to-perpendicular orientation transition in the lamellar phase close to the order-to-disorder phase transition point. A detailed underlying microscopic picture of the alignment process illustrates that the orientation transition is driven by the alignment of molecules with shear flow. The orientation diagram that characterizes the steady-state orientations as a function of shear rate and attractive potential depth is built, in which the attractive potential depth takes the role of an inverse temperature, somewhat like the Flory-Huggins interaction parameter. The microscopic mechanism of the critical orientation transition condition is discussed.     

Lamellar lyomesophases under shear as studied by deuterium nuclear magnetic resonance

The lamellar phases of two aqueous ethylene oxide surfactants, tetra(ethylene oxide) dodecyl ether and hexa(ethylene oxide) dodecyl ether, have been investigated by deuterium nuclear magnetic resonance spectroscopy during shear. The evolution of the shear-induced NMR line shapes and their dependence on surfactant concentration, shear geometry and shear history is analyzed. Two of three previously described shear-induced states (Diat O, Roux D, Nallet F (1993) J Phys II France 3: 1427–1452), namely the state of aligned lamellae with the layer normal parallel to the velocity gradient, which occurs at low shear rates, and the vesicular state at intermediate shear rates are found and identified by their characteristics NMR line shapes.     

Effect of shear on vesicle and lamellar phases of DDAB/lecithin ternary systems

The influence of shear flow on bilayer structures (vesicle and planar lamellar phases, L(α)), formed in DDAB/lecithin ternary systems, is studied by means of conventional rheology, Rheo NMR, and optical microscopy. The vesicles in the diluted (Lam(1)) phase are polydisperse multilamellae which turn into smaller monodisperse vesicles under shear. The concentrated (Lam(2)) phase is formed by non-oriented lamellae that do not surprisingly exhibit any pronounced shear-induced alignment prior to the transition into giant multilamellar vesicles. The biphasic region (Lam(1)+Lam(2)) shows a mosaic texture with a powder pattern indicating the prevalence of lamellae that transform into onions under shear.     

Simulations of Electric Field Induced Lamellar Alignment in Block Copolymers in the Presence of Selective Electrodes

Computer simulations have been performed for electric field induced parallel‐perpendicular lamellar phase transition in the presence of electrodes. The simulations are based on the dynamic density functional theory. Here we provide the extension of earlier work in two dimensions (2D) to three dimensions (3D). The result is a vivid picture of the transitions through defect creation and collision.

Observed change in lamellar alignment with applied electric field.     

Kinetics of the shear-induced isotropic-to-lamellar transition of an amphiphilic model system: a nonequilibrium molecular dynamics simulation study

The shear-induced isotropic-to-lamellar phase transition in the amphiphilic systems in the vicinity of the quiescent order-to-disorder transition point is investigated by the large-scale parallel nonequilibrium molecular dynamics simulations of simple amphiphilic model systems. There is a shear-induced upward shift of the ordering temperature. The initial isotropic phase orders into a lamellar phase perpendicular to the shear vorticity. The phase diagram as a function of temperature and shear rate is established. The dependency of the ordering transition on interaction strength and shear rate is rationalized by the competition between shear rate and chain relaxation. The time evolution of morphology reveals that the shear-induced ordering proceeds via nucleation and growth, a signature of a first-order phase transition. At low shear rate, a single ordered domain grows after an incubation period. With increasing shear rate ordering speeds up, but eventually develops in a lamellar system with disordered shear bands. The time dependence of the order parameter follows that of the mean-squared end-to-end distance, shear viscosity, and bulk pressure, and follows an Avrami scheme with an Avrami exponent between 2 and 4.     

Morphology of drawn syndiotactic polypropylene films

Morphological studies were conducted to investigate the drawability of melt-quenched (MQ) and slowly cooled (MSC) films of syndiotactic polypropylene (sPP) with a high syndiotactic pentad fraction. Transmission electron microscopy (TEM) using the ruthenium tetraoxide staining and ultrathin sectioning method revealed that amorphous chains as the matrix of MQ film played a role in drawability of the film by their alignment to machine direction (MD) and partial crystallizations into nanofibrils. On the other hand, the initial strain induced, rotations of clusters of long lamellar crystals as the major entity of MSC film accompanying breaks of long lamellae and formation of crazes and microvoids at the cluster boundary. Compared with a homogeneous thinning of MQ film by drawing, ca. 100 nm-thick layer slips along MD and parallel to the film surface took place in MSC film. This gave rise to the formation of V-shaped bent lamellar morphology and their further break into a smaller cluster of stacked lamellae which were aligned oblique by ca. 35° from MD. With elongation, some nanofibrils formed from chains generated by the partial breaks of lamellae are aligned perpendicular to the remained oblique lamellae and others parallel to MD in region where lamellar morphology almost disappeared. No chain slips in the nanofibrils can be related to a low elongation at break, i.e. a low ductility of sPP films. The lower elongation at break for MSC film than for MQ one can be interpreted by microvoids initially formed in the neck region and later moved to the fully drawn part, the microvoids initiating the break of the drawn film.     

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     

Memory effects across surfactant mesophases

We report a detailed analysis of deuteron NMR spectra of micellar, lamellar, cubic, and hexagonal mesophases in the aqueous non-ionic surfactant system C(12)E(6)/water. Samples are prepared with and without shear. Particular attention is paid to an interesting temperature-driven phase sequence that includes all of the above phases that are studied before and after shear parallel or perpendicular to the magnetic field direction. Surprising memory effects are found across mesophase transitions. These memory effects provide clues to the structure of the various phases.     

Quiescent and strain-induced crystallization of poly(p-phenylene terephthalamide) from sulfuric acid solution

Quiescent and strain-induced crystallization of poly(p-phenylene terephthalamide) (PPTA) from sulfuric acid solution has been studied. Negative spherulites (SA-PPTA spherulites) are formed from hot concentrated solutions by cooling. The spherulite consists of radiating fibrous lamellae several hundred angstroms wide. The electron diffraction pattern indicates that PPTA molecules are oriented perpendicular to the long axes of the fibrous lamellae and that the [010] or [110] direction of the modification I crystal and [010] direction of the modification II crystal are parallel to the long axes of the fibrous lamellae. The width of the lamellae is much smaller than the chain length of the starting PPTA. It appears that hydrolysis of PPTA during melting crystallization determines the chain length, i.e., the width of the fibrous lamella. Stacked, lamellar structures like “row structures” are formed under shear. The longer axes of the fibrous lamellae are oriented perpendicular to the shear direction. It is confirmed by electron diffraction studies that the PPTA molecules are oriented parallel to the shear direction. Well-developed fibrils with the PPTA molecules oriented to the fibril axis, are formed by adding the SA-PPTA spherulites to water with vigorous stirring.     

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.     

Studies of translational diffusion in the smectic A phase of a Gay-Berne mesogen using molecular dynamics computer simulation

Molecular dynamics computer simulations are used to determine the self-diffusion coefficients for a Gay-Berne model mesogen GB (4.4,20,1,1) in the isotropic, nematic and smectic A phases along two isobars. The values of the parallel and perpendicular diffusion coefficients, D(parallel) and D(perpendicular), are calculated and compared in the different phases. For the phase sequence isotropic-smectic A, D(perpendicular)*> or =D(parallel)* over the whole smectic A range with the ratio D(parallel)*/D(perpendicular)* decreasing with decreasing temperature. At a higher pressure, a nematic phase is observed between these two phases and we find that D(parallel)*>D(perpendicular)* throughout the nematic region and the inequality D(parallel)*>D(perpendicular)* remains on entering the smectic A phase. However, the ratio D(parallel)*/D(perpendicular)* decreases with decreasing temperature within the smectic A range and eventually this ratio inverts such that D(perpendicular)*>D(parallel)* at low temperatures. The temperature dependence of the parallel diffusion coefficient in the smectic A phase for this model mesogen is compared to that predicted by a theoretical model for diffusion subject to a cosine potential.     

Preparation of Oriented Liquid‐Crystalline/Isotropic Block Copolymer Films with Parallel or Perpendicular Arrangement of Smectic Layers and Lamellar Microdomains

Films of a symmetric liquid‐crystalline/isotropic block copolymer consisting of a smectic LC side‐chain polymer and polystyrene were prepared by solvent casting from solution and from the isotropic melt. By annealing the solvent‐cast film in the S_A phase an oriented microphase‐separated film of lamellar morphology was obtained in which both the lamellae of the block copolymer and the smectic layers of the LC block were oriented parallel to the film surface. A lamellar morphology with perpendicular orientation of lamellae and smectic layers was generated by cooling the block copolymer from the melt.     

Phase segregation of a symmetric diblock copolymer in constrained space with a square-pillar array

In this study, we apply a self-consistent field theory of polymers to study the structures of a symmetric diblock copolymer in parallel substrates filled with square-pillar arrays in which the substrates and pillars exhibit a weak preference for one block of the copolymer. Three classes of structures, i.e., lamellae, perpendicular cylinders, and bicontinuous structures, are achieved by varying the polymer film thickness, the pillar pitch (the distance between two centers of the nearest neighboring pillars), the gap and rotation of the pillars. Because of the confinement along horizontal directions imposed by the pillar array, eight novel types of perpendicular lamellar structures and eight novel types of cylindrical structures with various shapes and distributions occur. In the hybridization states of the parallel and perpendicular lamellar structures, several novel bicontinuous structures such as the double-cylinder network, pseudo-lamellae, and perforated lamellar structure are also found. By comparing the free energies of the various possible structures, the antisymmetric parallel lamellae are observed to be stable with the larger pillar gap at a certain film thickness. The structural transformations between the alternating cylindrical structures (alternating cross-shaped, square-shaped, and octagonal perpendicular cylinders) and parallel lamellae with increasing film thickness or pillar gap are well explained by the modified strong separation theory. Our results indicate that array confinement can be an effective method to prepare novel polymeric nanopattern structures.     

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.     

Preliminary Communications. Micellar phases formed by a solution of l-serine hydrochloride decylester and orthophosphoric acid

Polarizing microscope studies showed that the isotropic solution composed of l-serine hydrochloride decylester and orthophosphoric acid forms micellar cholesteric, nematic and lamellar phases, whereas the solution of the optically inactive ester gives micellar nematic and lamellar phases. The phase transitions were tentatively assigned as the result of two concurrent reactions at which ortho-phosphoserine hydrochloride decylester and orthophosphoric acid monodecylester are produced. Dilution of the optically active and the optically inactive lamellar phases with water gave a cholesteric and a nematic phase, respectively. The nematic director is aligned perpendicular to the glass plate, whereas that of the cholesteric phase is aligned parallel.