Twist grain boundaries are widely observed in lamellar phases of block copolymers. A mesoscopic model of the copolymer is used to obtain stationary configurations that include a twist grain boundary, and to analyze their stability against long wavelength perturbations. The analysis presented is valid in the weak segregation regime, and includes direct numerical solution of the governing equations as well as a multiple scale analysis. We find that a twist boundary configuration with arbitrary misorientation angle can be well described by two modes, and obtain the equations for their slowly varying amplitudes. The width of the boundary region is seen to scale as $ε^{-1/4}$, with $ε$ being the dimensionless distance to the order-disorder transition. We finally present the results of the linear stability analysis of the planar boundary.
Diffusion of symmetric diblock copolymer chains in macroscopically oriented lamellar block copolymers are studied in a molecular dynamics simulation. Results for diffusion constant both parallel $D_\parallel$ and perpendicular $D_\perp$ to the lamellar planes are compared to results in the disordered one phase region. For diblocks of length N=40 (1.1 N_e) and $100 (3N_e)$, where $N_e$ is the entanglement length of a homopolymer melt at the same density, $D_\parallel$ is nearly independent of $χ$, while $D_\perp$ is strongly suppressed as $χ$ is increased. These results are in agreement with th…
We study morphologies of thin-film diblock copolymers between two flat and parallel walls. The study is restricted to the weak segregation regime below the order-disorder transition temperature. The deviation from perfect lamellar shape is calculated for phases which are perpendicular and parallel to the walls. We examine the undulations of the inter material dividing surface and its angle with the walls, and find that the deviation from its unperturbed position can be much larger than in the strong segregation case. Evaluating the weak segregation stability of the lamellar phases, it is shown…
The nucleation of a droplet of stable cylinder phase from a metastable lamellar phase is examined within the single-mode approximation to the Brazovskii model for diblock copolymer melts. By employing a variational ansatz for the droplet interfacial profile, an analytic expression for the interfacial free-energy of an interface of arbitrary orientation between cylinders and lamellae is found. The interfacial free-energy is anisotropic, and is lower when the cylinder axis is perpendicular to the interface than when the cylinders lie along the interface. Consequently, the droplet shape computed …
We develop a theory to describe the reorientation phenomena in the lamellar phase of block copolymer melt under reciprocating shear flow. We show that similar to the steady-shear, the oscillating flow anisotropically suppresses fluctuations and gives rise to the parallel-perpendicular orientation transition. The experimentally observed high-frequency reverse transition is explained in terms of interaction between the melt and the shear-cell walls.
We examined the kinetics of the transformation from the lamellar (LAM) to the hexagonally packed cylinder (HEX) phase for the triblock copolymer, polystyrene-b-poly (ethylene-co-butylene)-b-polystyrene (SEBS) in dibutyl phthalate (DBP), a selective solvent for polystyrene (PS), using time-resolved small angle x-ray scattering (SAXS). We observe the HEX phase with the EB block in the cores at a lower temperature than the LAM phase due to the solvent selectivity of DBP for the PS block. Analysis of the SAXS data for a deep temperature quench well below the LAM-HEX transition shows that the trans…
We present a model addressing the orientation transition of symmetric block copolymers such as PS/PMMA on smooth and rough surfaces. The distortion free energy of parallel and perpendicular lamellar phases in contact with a rough solid surface is calculated as function of the surface roughness amplitude and wavelength, as well as the polymer lamellar periodicity (molecular weight). We find an analytical expression for the orientation transition. This expression is compared and agrees well with recent experiments done with six different polymer molecular weights and surface preparations.
We investigate the effect of chemically patterned surfaces on the morphology of diblock copolymers below the order-disorder transition. Profiles for lamellar phases in contact with one surface, or confined between two surfaces are obtained in the weak segregation limit using a Ginzburg-Landau expansion of the free energy, and treating it with mean-field theory. The periodically patterned surface induces a tilt of the lamellae in order to match the surface periodicity. The lamellae relax from the constrained periodicity close to the surface to the bulk periodicity far from it. The phases we inv…
Using coarse-grained molecular-dynamics simulations, a generic styrene-(block)-butadiene-(block)-styrene (SBS) triblock copolymer under lamellar conformation is used in order to investigate the mutual entanglement evolution when a structure of alternating glassy (S)/rubbery (B) layers is submitted to an imposed deformation. By varying the amount of loop chains between each phase, i.e. noncrossing chains, it is possible to generate different types of S/B interface definitions. A specific boundary driven tensile strain protocol has been developed in order to mimic "real" experiments and measure …
We consider the effects of anisotropic diffusion and hydrodynamic flows on the relaxation time scales of the lamellar phase of a diblock copolymer. We first extend the two-fluid model of a polymer solution to a block copolymer, and include a tensor mobility for the diffusive relaxation of monomer composition which is consistent with the uniaxial symmetry of the lamellar phase. The resulting equation is coupled to the momentum conservation equation, allowing also for a dissipative stress tensor for a uniaxial fluid. We then study the linear relaxation of weakly perturbed lamellae, and the motio…
We introduce a model constitutive law for the dissipative stress tensor of lamellar phases to account for low frequency and long wavelength flows. Given the uniaxial symmetry of these phases, we argue that the stress tensor must be the same as that of a nematic but with the local order parameter being the slowly varying lamellar wavevector. This assumption leads to a dependence of the effective dynamic viscosity on orientation of the lamellar phase. We then consider a model configuration comprising a domain boundary separating laterally unbounded domains of so called parallel and perpendicular…
The phase behaviour of blends of ABC triblock and ac diblock copolymers is examined using self-consistent field theory. Several equilibrium lamellar structures are observed, depending on the volume fraction of the diblocks, phi_2, the monomer interactions, and the degrees of polymerization of the copolymers. For segregations just above the order-disorder transition the triblocks and diblocks mix together to form centrosymmetric lamellae. As the segregation is increased the triblocks and diblocks spatially separate either by macrophase-separating, or by forming a non-centrosymmetric (NCS) phase…
A mesoscopic model of a diblock copolymer is used to study the stability of a lamellar structure under a uniform shear flow. We first obtain the nonlinear lamellar solutions under both steady and oscillatory shear flows. Regions of existence of these solutions are determined as a function of the parameters of the model and of the flow. Finally, we address the stability of the lamellar solution against long wavelength perturbations.
The mesoscale rheology of a lamellar phase of a block copolymer is modeled as a structured fluid of uniaxial symmetry. The model predicts a viscoelastic response that depends on the angle between the the local lamellar planes and velocity gradients. We focus on the stability under oscillatory shear of a two layer configuration comprising a parallel and a perpendicularly oriented domain, so that the two layers have a different viscoelastic modulus $G^{*}(ω)$. A long wave, low Reynolds number expansion is introduced to analytically obtain the region of stability. When the response of the two lay…
Solvent vapor annealing (SVA) is known to be a simple, low-cost and highly efficient technique to produce defect-free diblock copolymer (BCP) thin films. Not only can the solvent weaken the BCP segmental interactions, but it can vary the characteristic spacing of the BCP microstructures. We carry out systematic theoretical studies on the effect of adding solvent into lamellar BCP thin films on the defect removal close to the BCP order-disorder transition. We find that the increase of the lamellar spacing, as is induced by addition of solvent, facilitates more efficient removal of defects. The …
We present numerical calculations of lamellar phases of di-block copolymers (BCP) confined between two surfaces, where the top surface is flat and the bottom one is corrugated. The corrugated substrate is assumed to have a single $q$-mode of lateral undulations with a wavenumber q_s and amplitude R. We focus on the effects of substrate roughness, parameterized by the dimensionless quantity, q_sR, on the relative stability between parallel and perpendicular orientations of the lamellar phase. The competition between film confinement, energy cost of elastic deformation and gain in surface energy…
We study thin films of A/B diblock copolymer in a lamellar phase confined between two parallel plates (electrodes) that impose a constant voltage across the film. The weak-segregation limit is explored via a Ginzburg-Landau-like free-energy expansion. We focus on the relative stability of parallel and perpendicular orientations of the lamellar phase, and how they are affected by variation of four experimental controllable parameters: addition of free ions, the difference in ionic solubilities between the A and B blocks, the dielectric contrast between the A/B blocks, and the preferential inter…
A mesoscopic model of a diblock copolymer is used to study the stability of a uniform lamellar phase under a reciprocating shear flow. Approximate viscosity contrast between the microphases is allowed through a linear dependence of the (Newtonian) shear viscosity on monomer composition. We first show that viscosity contrast does not affect the composition of the base lamellar phase in an unbounded geometry, and that it only couples weakly to long wavelength perturbations. A perturbative analysis is then presented to address the stability of uniform lamellar structures under long wavelength per…
Particle-Mediated Tuning of Defect Stability in Lamellar Block Copolymer Systems
Institute of Physics, Johannes Gutenberg University Mainz（美因茨约翰内斯·古腾堡大学物理研究所）；Instituto de Física del Sur (IFISUR), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Universidad Nacional del Sur（南方物理研究所（IFISUR），阿根廷国家科学研究委员会（CONICET），南方国立大学）
We present numerical calculations of lamellar phases of block copolymers at patterned surfaces. We model symmetric di-block copolymer films forming lamellar phases and the effect of geometrical and chemical surface patterning on the alignment and orientation of lamellar phases. The calculations are done within self-consistent field theory (SCFT), where the semi-implicit relaxation scheme is used to solve the diffusion equation. Two specific set-ups, motivated by recent experiments, are investigated. In the first, the film is placed on top of a surface imprinted with long chemical stripes. The …
In this work we incorporate some real-system effects into the theory of orientational phase transitions under shear flow (M. E. Cates and S. T. Milner, Phys. Rev. Lett. v.62, p.1856 (1989) and G. H. Fredrickson, J. Rheol. v.38, p.1045 (1994)). In particular, we study the influence of the shear-cell boundaries on the orientation of the lamellar phase. We predict that at low shear rates the parallel orientation appears to be stable. We show that there is a critical value of the shear rate at which the parallel orientation loses its stability and the perpendicular one appears immediately below th…
We present NanoImprint lithography experiments and modeling of thin films of block copolymers (BCP). The NanoImprint lithography is used to align perpendicularly lamellar phases, over distances much larger than the natural lamellar periodicity. The modeling relies on self-consistent field calculations done in two- and three-dimensions. We get a good agreement with the NanoImprint lithography setups. We find that, at thermodynamical equilibrium, the ordered BCP lamellae are much better aligned than when the films are deposited on uniform planar surfaces.
Simulations and experiments of nanorods (NRs) show that co-assembly with block copolymer (BCP) melts leads to the formation of a superstructure of side-to-side NRs perpendicular to the lamellar axis. A mesoscopic model is validated against scanning electron microscopy (SEM) images of CdSe NRs mixed with polystyrene-block-poly(methyl methacrylate). It is then used to study the co-assembly of anisotropic nanoparticles (NPs) with a length in the same order of magnitude as the lamellar spacing. The phase diagram of BCP/NP is explored as well as the time evolution of the NR. NRs that are slightly l…
Oriented block copolymers exhibit a buckling instability when submitted to a tensile test perpendicular to the lamellae direction. In this paper we study this behavior using a coarse grained molecular dynamics simulation approach. Coarse grained models of lamellar copolymers with alternate glassy rubbery layers are generated using the Radical Like Polymerization method, and their mechanical response is studied. For large enough systems, uniaxial tensile tests perpendicular to the direction of the lamellae reveal the occurrence of the buckling instability at low strain. The results that emerge …
The dynamics of microphase separation and the orientation of lamellae in diblock copolymers is investigated in terms of a mean-field model. The formation of lamellar structures and their stable states are explored and it is shown that lamellae are stable not only for the period of the structure corresponding to the minimum of the free energy. The range of wavelengths of stable lamellae is determined by a functional approach, introduced with this work, which is in agreement with the results of a linear stability analysis. The effects of the interaction of block copolymers with confining plane b…
We compare two theoretical approaches to dielectric diblock copolymer melts in an external electric field. The first is a relatively simple analytic expansion in the relative copolymer concentration, and includes the full electrostatic contribution consistent with that expansion. It is valid close to the order-disorder transition point, the weak segregation limit. The second employs self-consistent field (SCF) theory and includes the full electrostatic contribution to the free energy at any copolymer segregation. It is more accurate but computationally more intensive. Motivated by recent exper…
We propose a direct self-assembly mechanism towards obtaining defect-free perpendicular lamellar phases of diblock copolymer (BCP) thin films. In our numerical study, a thin BCP film having a flat top surface is casted on a uni-directional corrugated solid substrate. The substrate is treated chemically and has a weak preference toward one of the two BCP components. Employing self-consistent field theory (SCFT), we find that there is an enhanced synergy between two substrate characteristics: its topography (geometrical roughness) combined with a weak surface preference. This synergy produces th…
We study a model of flexible block copolymers (BCPs) in which there is an enlthalpic preference for local alignment, among like-block segments. We describe a generalization of the self-consistent field theory (SCFT) of flexible BCPs to include inter-segment orientational interactions via a Landau-DeGennes free energy associated with a polar or nematic order parameter for segments of one component of a diblock copolymer. We study the equilibrium states of this model numerically, using a pseudo-spectral approach to solve for chain conformation statistics in the presence of a self-consistent torq…
We study AB$_n$ miktoarm star block copolymers in the strong segregation limit, focussing on the role that the AB interface plays in determining the phase behavior. We develop an extension of the kinked-path approach which allows us to explore the energetic dependence on interfacial shape. We consider a one-parameter family of interfaces to study the columnar to lamellar transition in asymmetric stars. We compare with recent experimental results. We discuss the stability of the A15 lattice of sphere-like micelles in the context of interfacial energy minimization. We corroborate our theory by i…
Diblock copolymers blended with homopolymer may self-assemble into spherical, cylindrical or lamellar aggregates. Transitions between these structures may be driven by varying the homopolymer molecular weight or the molecular weight or composition of the diblock. Using self-consistent field theory (SCFT), we reproduce these effects. Our results are compared with X-ray scattering and transmission electron microscopy measurements by Kinning, Winey and Thomas and good agreement is found, although the tendency to form cylindrical and lamellar structures is sometimes overestimated due to our neglec…
The Leibler weak segregation theory in molten diblock copolymers is generalized with due regard for the 2nd shell harmonics contributions defined in the paper and the phase diagrams are built for the linear and miktoarm ternary ABC triblock copolymers. The symmetric linear copolymers with the middle block non-selective with respect to the side ones are shown to undergo the continuous ODT not only into the lamellar phase but also into various non-conventional cubic phases (depending on the middle block composition it could be the simple cubic, face-centered cubic or non-centrosymmetric phase re…
The phase behavior of a melt of monodisperse rod-coil diblocks is studied. We derive a Landau free energy functional for both a compositional and a nematic order parameter. The excluded volume interaction between the rod blocks is modeled by an attractive Maier-Saupe interaction. The incompatibility between rod- and coil blocks is modeled by the usual Flory-Huggins interaction. For a large volume fraction of the rods, a transition from isotropic to nematic to smectic C is observed upon decreasing the temperature, whereas for small rod volume fraction, spherical, hexagonal, and lamellar structu…
A nonequilibrium 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 morphologies that have been 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 micella…
We consider orientational transitions of lamellar phases under the influence of a spatially nonuniform electric field. The transition between parallel and perpendicular lamellar stackings with respect to the substrate is investigated as a function of the system parameters. The dielectrophoretic energy and the energy penalty for having dielectric interfaces perpendicular to the field's direction are identified as linear and quadratic terms in a free energy expansion in the dielectric constant mismatch. We find that if the dielectric constant mismatch $Δ\eps$ is smaller than some critical value …
In order to address the selection mechanism that is responsible for the unique lamellar orientation observed in block copolymers under oscillatory shears, we use a constitutive law for the dissipative part of the stress tensor that respects the uniaxial symmetry of a lamellar phase. An interface separating two domains oriented parallel and perpendicular to the shear is shown to be hydrodynamically unstable, a situation analogous to the thin layer instability of stratified fluids under shear. The resulting secondary flows break the degeneracy between parallel and perpendicular lamellar orientat…
We consider the relative stability of parallel and perpendicular lamellar layers on corrugated surfaces. The model can be applied to smectic phases of liquid crystals, to lamellar phases of short-chain amphiphiles and to lamellar phases of long-chain block copolymers. The corrugated surface is modelled by having a single $q$-mode lateral corrugation of a certain height. The lamellae deform close to the surface as a result of chemical interaction with it. The competition between the energetic cost of elastic deformations and the gain in surface energy determines whether parallel or perpendicula…
We inquire about the possible coexistence of macroscopic and microstructured phases in random Q-block copolymers built of incompatible monomer types A and B with equal average concentrations. In our microscopic model, one block comprises M identical monomers. The block-type sequence distribution is Markovian and characterized by the correlation λ. Upon increasing the incompatibility χ (by decreasing temperature) in the disordered state, the known ordered phases form: for λ > λ_c, two coexisting macroscopic A- and B-rich phases, for λ < λ_c, a microstructured (lamellar) phase with wave number k…
We study the effect of a random Flory-Huggins parameter in a symmetric diblock copolymer melt which is expected to occur in a copolymer where one block is near its structural glass transition. In the clean limit the microphase segregation between the two blocks causes a weak, fluctuation induced first order transition to a lamellar state. Using a renormalization group approach combined with the replica trick to treat the quenched disorder, we show that beyond a critical disorder strength, that depends on the length of the polymer chain, the character of the transition is changed. The system be…
We demonstrate the possibility of a stable equilibrium multi-lamellar (``onion'') phase in pure lamellar systems (no excess solvent) due to a sufficiently negative Gaussian curvature modulus. The onion phase is stabilized by non-linear elastic moduli coupled to a polydisperse size distribution (Apollonian packing) to allow space-filling without appreciable elastic distortion. This model is compared to experiments on copolymer-decorated lamellar surfactant systems, with reasonable qualitative agreement.
In this work we investigated the phase behavior of melts of block-copolymers with one charged block by means of dissipative particle dynamics with explicit electrostatic interactions. We assumed that all the Flory-Huggins \c{hi} parameters were equal to 0 and showed that the charge correlation attraction solely can cause microphase separation with long-range order; a phase diagram was constructed by varying the volume fraction of the uncharged block and the electrostatic interaction parameter λ. The obtained phase diagram was compared to the phase diagram of corresponding neutral diblock-copol…
We numerically investigate local defectiveness control of self-assembled diblock copolymer patterns through appropriate substrate design. We use a nonlocal Cahn-Hilliard (CH) equation for the phase separation dynamics of diblock copolymers. We discretize the nonlocal CH equation by an unconditionally stable finite difference scheme on a tapered trench design and, in particular, we use Dirichlet, Neumann, and periodic boundary conditions. The value at the Dirichlet boundary comes from an energy-minimizing equilibrium lamellar profile. We solve the resulting discrete equations using a Gauss-Seid…
Block copolymer are ideal matrices to control the localisation of colloids. Furthermore, anisotropic nanoparticles such as Janus nanoparticles possess an additional orientational degree of freedom that can play a crucial role in the formation of highly ordered materials made of block copolymers. This work presents a mesoscopic simulation method to assert the co-assembly of Janus nanoparticles in a block copolymer mixture, finding numerous instances of aggregation and formation of ordered configurations which can be related to dispersions of pure Janus colloids. Comparison with chemically homog…
We present an analysis of the structure of the fluctuation-induced microemulsion phase in a ternary blend of balanced AB diblock copolymers with equal amounts of A and B homopolymers. To this end, graphical analysis methods are employed to characterize two-dimensional configuration snapshots obtained with the recently introduced Field-Theoretic Monte Carlo (FTMC) method. We find that a microemulsion forms when the mean curvature diameter of the lamellar phase coincides roughly with the periodicity of the lamellar phase. Further, we provide evidence to the effect of a subclassification of the m…
Simulations of five different coarse-grained models of symmetric diblock copolymer melts are compared to demonstrate a universal (i.e., model-independent) dependence of the free energy on the invariant degree of polymerization $\overline{N}$, and to study universal properties of the order-disorder transition (ODT). The ODT appears to exhibit two regimes: Systems of very long chains ($\overline{N} \gtrsim 10^{4}$) are well described by the Fredrickson-Helfand theory, which assumes weak segregation near the ODT. Systems of smaller but experimentally relevant values, $\overline{N} \lesssim 10^4$,…
We study the effects of chirality at the segment scale on the thermodynamics of block copolymer melts using self consistent field theory. In linear diblock melts where segments of one block prefer a twisted, or cholesteric, texture, we show that melt assembly is critically sensitive to the ratio of random coil size to the preferred pitch of cholesteric twist. For weakly-chiral melts (large pitch), mesophases remain achiral, while below a critical value of pitch, two mesocopically chiral phases are stable: an undulated lamellar phase; and a phase of hexagonally-ordered helices. We show that the…
The ordering of block copolymers into lamellar microstructures is an attractive route for creating nanopatterns on scales too small to be constructed by current photolithography techniques. This utilises a technique known as graphoepitaxy where topography is used to define the alignment of the pattern for precise placement of pattern features. One problem with this approach is the failure of lamellae to maintain continuity around corners, due to geometrical frustration. We report simulation results using the extended Cahn-Hilliard equation which suggest that this problem could be solved by usi…
We examine the role of intrinsic chain susceptibility anisotropy in magnetic field directed self-assembly of a block copolymer using \textit{in situ} X-ray scattering. Alignment of a lamellar mesophase is observed on cooling across the disorder-order transition with the resulting orientational order inversely proportional to the cooling rate. We discuss the origin of the susceptibility anisotropy, $Δχ$, that drives alignment, and calculate its magnitude using coarse-grained molecular dynamics to sample conformations of surface-tethered chains, finding $Δχ\approx 2\times10^{-8}$. From field-dep…
We apply self consistent field theory to twist grain boundaries of block copolymer melts. The distribution of monomers throughout the grain boundary is obtained as well as the grain boundary free energy per unit area as a function of twist angle. We define an intermaterial dividing surface in order to compare it with minimal surfaces which have been proposed. Our calculation shows that the dividing surface is not a minimal one, but the linear stack of dislocations seems to be a better representation of it for most angles than is Scherck's first surface.
We present a generalized theory of microphase separation for charged-neutral diblock copolymer melt. Stability limit of the disordered phase for salt-free melt has been calculated using Random Phase Approximation (RPA) and self-consistent field theory (SCFT). Explicit analytical free energy expressions for different classical ordered microstructures (lamellar, cylinder and sphere) are presented. We demonstrate that chemical mismatch required for the onset of microphase separation ($χ^{\star} N$) in charged-neutral diblock melt is higher and the period of ordered microstructures is lower than t…
Numerically minimizing a continuous free-energy functional which yields several modulated phases, we obtain the order-parameter profiles and interfacial free energies of symmetric and non-symmetric tilt boundaries within the lamellar phase, and of interfaces between coexisting lamellar, hexagonal, and disordered phases. Our findings agree well with chevron, omega, and T-junction tilt-boundary morphologies observed in diblock copolymers and magnetic garnet films.
Cell dynamics simulation is used to investigate the phase behavior of block copolymer/homopolymer mixture subjected to a steady shear flow. Phase transitions occur from transverse to parallel and then to perpendicular lamellar structure with an increase of shear rate and this is the result of interaction between the shear flow and the concentration fluctuation. Rheological properties, such as normal stress differences and shear viscosity, are all closely related with the direction of the lamellae. Furthermore, we specifically explore the phase behavior and the order parameter under weak and st…
Poly(ethylene oxide)-$\textit{b}$-poly(butylmethacrylate) (PEO-$\textit{b}$-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-$\textit{b}$-PBMA to investigate its self-assembly in water and tetrahydrofuran (THF) and unveil the occurrence o…
We study block copolymers (BCP) on patterned substrates, where the top polymer film surface is not constrained but is a free interface that adapts its shape self-consistently. In particular, we investigate the combined effect of the free interface undulations with the wetting of the BCP film as induced by nano-patterned substrates. For a finite volume of BCP material, we find equilibrium droplets composed of coexisting perpendicular and parallel lamellar domains. The self-assembly of BCP on topographic patterned substrates was also investigated and it was found that the free interface induces …
Structural Relaxation and Anisotropic Elasticity of Ordered Block Copolymer Melts
Department of Chemistry, Texas A\&M University, College Station, TX 77843, USA；Department of Materials Science；Engineering, Texas A\&M University, College Station, TX 77843, USA
We study the effect of an externally imposed oscillatory shear on the motion of a grain boundary that separates differently oriented domains of the lamellar phase of a diblock copolymer. A direct numerical solution of the Swift-Hohenberg equation in shear flow is used for the case of a transverse/parallel grain boundary in the limits of weak nonlinearity and low shear frequency. We focus on the region of parameters in which both transverse and parallel lamellae are linearly stable. Shearing leads to excess free energy in the transverse region relative to the parallel region, which is in turn d…
Triply-periodic networks are among the most complex and functionally valuable self-assembled morphologies, yet they form in nearly every class of biological and synthetic soft matter building blocks. In contrast to simpler assembly motifs -- spheres, cylinders, layers -- TPN assemblies require molecules to occupy variable local domain shapes, confounding attempts to understand their formation. Here, we examine the double-gyroid (DG) network phase of block copolymer (BCP) melts, a prototypical soft self-assembly system, by using a geometric formulation of the strong stretching theory (SST) of B…
