Block Copolymers Under Shear Flow

Shear-induced microstructures and dynamics processes of phospholipid cylinders in solutions

Shear-induced microstructures and their corresponding dynamic processes are investigated for phospholipid cylinders in aqueous solution by dissipative particle dynamic simulation. Various phospholipid cylinders with cross-sections, which are formed under shear-free flow, are selected to examine the effects of shear flow on their structures and dynamic processes. Shear flow induces the transition from cylinders into vesicles at weak rate and the transition into vesicle–lamella mixtures with increased shear rate and lamella structures at the strong shear rate. Then, the average radius of gyration and shape factors of the polymer chains in the dynamic processes are discussed in detail. Results show that shear flow causes the structure of the polymer chains to be elongated along the shear direction, and the configuration of the polymer chain can be rapidly transformed into an ellipsoid structure under strong shear.

Shear-induced parallel and transverse alignments of cylinders in thin films of diblock copolymers

Coarse-grained Langevin dynamics simulations were performed to investigate the alignment behavior of monolayer films of cylinder-forming diblock copolymers under steady shear, a structure of significant importance for many technical applications such as nanopatterning. The influences of shear conditions, the interactions involved in the films, and the initial morphology of the cylinder-forming phase were examined. Our results showed that above a critical shear rate, the cylinders can align either along the shearing direction or transverse (log-rolling) to the shearing direction depending on the relative strength between the interchain attraction in the cylinders (εAA) and the surface attraction of the confining walls with the film (εBW). To understand the underlying mechanism, the microscopic properties of the films under shear were systematically investigated. It was found that at low εAA/εBW, the majority blocks of the diblock polymer that are adsorbed on the confining walls prefer to move synchronously with the walls, inducing the cylinder-forming blocks to align along the flow direction. When εAA/εBW is above a threshold value, a strong attraction between the cylinder-forming blocks restrains their movement during shear, leading to the log-rolling motions of the cylinders. To predict the threshold εAA/εBW, we developed an approach based on equilibrium thermodynamics data and found good agreement with our shear simulations.

Diblock-copolymer thin films under shear

The behavior of lamellae forming diblock-copolymer melts confined by two non-selective substrates under shear is studied by means of molecular dynamics simulations. Since the substrate/copolymer preferential interaction is absent, the vertically oriented lamellae (L_⊥) are formed. The response of L_⊥ phase under transverse and perpendicular modes of shear is studied for a wide range of shear rates, γ̇. In particular, shear deformation and reorientation transition, flow behavior, and difference in the macroscopic response under the two modes of shear are discussed. We show that an inclined lamellae state observed for transverse shear below a critical shear rate γ̇^* is stabilized by a cyclic motion of chains close to the substrates. The value of γ̇^*, at which lamellae dissolve and reorient along the flow field during transverse shear, coincides with the onset of shear-thinning. For γ̇<γ̇^*, the shear viscosity for transverse shear is much larger compared to that observed in perpendicular shear, while there is no difference for γ̇>γ̇^*.

Rapid ordering of block copolymer thin films

Block-copolymers self-assemble into diverse morphologies, where nanoscale order can be finely tuned via block architecture and processing conditions. However, the ultimate usage of these materials in real-world applications may be hampered by the extremely long thermal annealing times-hours or days-required to achieve good order. Here, we provide an overview of the fundamentals of block-copolymer self-assembly kinetics, and review the techniques that have been demonstrated to influence, and enhance, these ordering kinetics. We discuss the inherent tradeoffs between oven annealing, solvent annealing, microwave annealing, zone annealing, and other directed self-assembly methods; including an assessment of spatial and temporal characteristics. We also review both real-space and reciprocal-space analysis techniques for quantifying order in these systems.

Thin films of homopolymers and cylinder-forming diblock copolymers under shear

We study thin films of homopolymers (PS) and monolayers of cylinder-forming diblock copolymers (PS–PHMA) under shear. To this end, we employed both experiments and computer simulations that correctly take into account hydrodynamic interactions and chain entanglements. Excellent quantitative agreement for static as well as dynamic properties in both the homopolymer and diblock copolymer cases was achieved. In particular, we found that the homopolymer thin films exhibit a distinct shear thinning behavior, which is strongly correlated with the disentanglement and shear alignment of the constituent polymer chains. For the PS–PHMA films, we show that shear can be employed to induce long-range ordering to the spontaneously self-assembled microdomains, which is required for many applications such as the fabrication of nanowire arrays. We found that the impact of chemical incompatibility on the viscosity is only minor in shear-aligned films. Once the domains were aligned, the films exhibited an almost Newtonian response to shear because the cylindrical microdomains acted as guide rails, along which the constituent copolymer chains could simply slide. Furthermore, we developed a model for predicting the onset of shear alignment based on equilibrium dynamics data, and found good agreement with our shear simulations. The employed computational method holds promise for a faster and more cost-effective route for developing custom tailored materials.

Phase-field modeling of the formation of lamellar nanostructures in diblock copolymer thin films under inplanar electric fields

Recent experiments show that external inplanar electric field can be employed to guide the molecular self-assembly in diblock copolymer (BCP) thin films to form lamellar nanostructures with potential applications in nanotechnology. We study this self-assembly process through a detailed coarse-grained phase-separation modeling. During the process, the free energy of the BCP films is modeled as the Ginzburg-Landau free energy with nonlocal interaction and electrostatic coupling. The resulting Cahn-Hilliard (CH) equation is solved using an efficient semi-implicit Fourier-spectral algorithm. Numerical results show that the morphology of order parameter formed in either symmetric or asymmetric BCP thin films is strongly influenced by the electric field. For symmetrical BCPs, highly ordered lamellar nanostructures evolved along the direction of the electric field. Phase nucleation and dislocation climbing in the BCP films predicted by the numerical simulation are in a good agreement with those observed in recent BCP electronanolithography. For asymmetrical BCPs, numerical simulation shows that nanodots are guided to align to the electric field. Furthermore, in the case of high electric field, nanodots formed in asymmetrical BCPs may further convert into highly ordered lamellar nanostructures (sphere-to-cylinder transition) parallel to the electric field. Effects of the magnitude of electric field, BCP asymmetry, and molecular interaction of BCPs on the self-assembly process are examined in detail using the numerical scheme developed in this study. The present study can be used for the prediction of the formation of nanostructures in BCP thin films and the quality control of BCP-based nanomanufacturing through optimizing the external electric fields.

Kinetic pathways of gyroid-to-cylinder transitions in diblock copolymers under external fields: cell dynamics simulation

Using cell dynamics simulation we investigate the cubic gyroid morphology of block copolymer melts under simple shear flow and electric field. The electric field should be stronger than a certain critical value to induce transition to a cylindrical phase. In the case of simple steady shear the gyroid-to-cylinder transition was observed even for a very weak shear. Quantitative analysis of pathways of gyroid-to-cylinder transition is performed by means of Minkowski functionals. We found that the kinetics of the gyroid-to-cylinder transition are different under electric field and shear flow. Moreover, the gyroid structure under different strengths of electric field shows different pathways. Different types of intermediates such as five-, four-fold connections and "winding" cylinders are found for different pathways.

Alignment of lamellar diblock copolymer phases under shear: insight from dissipative particle dynamics simulations

Sheared self-assembled lamellar phases formed by symmetrical diblock copolymers are investigated through dissipative particle dynamics simulations. Our intent is to provide insight into the experimental observations that the lamellar phases adopt parallel alignment at low shear rates and perpendicular alignment at high shear rates and that it is possible to use shear to induce a transition from the parallel to perpendicular alignment. Simulations are initiated either from lamellar structures prepared under zero shear where lamellae are aligned into parallel, perpendicular, or transverse orientations with respect to the shear direction or from a disordered melt obtained by energy minimization of a random structure. We first consider the relative stability of the parallel and perpendicular phases by applying shear to lamellar structures initially aligned parallel and perpendicular to the shear direction, respectively. The perpendicular lamellar phase persists for all shear rates investigated, whereas the parallel lamellar phase is only stable at low shear rates, and it becomes unstable at high shear rates. At the high shear rates, the parallel lamellar phase first transforms into an unstable diagonal lamellar phase; and upon further increase of the shear rate, the parallel lamellar phase reorients into a perpendicular alignment. We further determine the preferential alignment of the lamellar phases at low shear rate by performing the simulations starting from either the initial transverse lamellar structure or the disordered melt. Since the low shear-rate simulations are plagued by the unstable diagonal lamellar phases, we vary the system size to achieve the natural spacing of the lamellae in the simulation box. In such cases, the unstable diagonal lamellar phases disappear and lamellar phases adopt the preferential alignment, either parallel or perpendicular. In agreement with the experimental observations, the simulations show that the lamellar phase preferentially adopts the parallel orientation at low shear rates and the perpendicular orientation at high shear rates. The simulations further reveal that the perpendicular lamellar phase has lower internal energy than the parallel lamellar phase, whereas the entropy production of the perpendicular lamellar phase is higher with respect to the parallel lamellar phase. Values of the internal energy and entropy production for the unstable diagonal lamellar phases lie between the corresponding values for the parallel and perpendicular lamellar phases. These simulation results suggest that the relative stability of the parallel and perpendicular lamellar phases at low shear rates is a result of the interplay between competing driving forces in the system: (a) the system's drive to adopt a structure with the lowest internal energy and (b) the system's drive to stay in a stationary nonequilibrium state with the lowest entropy production.

Icosahedral packing of polymer-tethered nanospheres and stabilization of the gyroid phase

We present results of simulations that predict the phases formed by the self-assembly of model nanospheres functionalized with a single polymer "tether," including double gyroid, perforated lamella, and crystalline bilayer phases. We show that microphase separation of the immiscible tethers and nanospheres causes confinement of the nanoparticles, which promotes local icosahedral packing that in turn stabilizes the gyroid. We present a new metric for determining the local arrangement of particles based on spherical harmonic "fingerprints," which we use to quantify the extent of icosahedral ordering.

Cubic phases of block copolymers under shear and electric fields by cell dynamics simulation. I. Spherical phase

Cell dynamics simulation is used to investigate pathways of sphere-to-cylinder transition in block copolymer melt under applied simple shear flow and electric field. Both fields can induce the transition when their strength is above some critical value. At weak fields the spherical phase is preserved, with spheres being deformed into ellipsoids. Weak shear flow is found to improve order in the spherical phase. Observed sliding of layers of spheres under shear is very similar to the experimental finding by Hamley et al. [J. Chem. Phys. 108, 6929 (1998)]. The kinetic pathways are sensitive to the degree of microphase separation in the system and hence affected by temperature. The details of the pathways are described by means of Minkowski functionals.

Simulation of the gyroid phase in off-lattice models of pure diblock copolymer melts

Particle-based molecular simulations of pure diblock copolymer (DBC) systems were performed in continuum space via dissipative particle dynamics and Monte Carlo methods for a bead-spring chain model. This model consisted of chains of soft repulsive particles often used with dissipative particle dynamics. The gyroid phase was successfully simulated in DBC melts at selected conditions provided that the simulation box size was commensurate with the gyroid lattice spacing. Simulations were concentrated at conditions where the gyroid phase is expected to be stable which allowed us to outline approximate phase boundaries. When more than one phase was observed by varying simulation box size, thermodynamic stability was discerned by comparing the Helmholtz free energy of the competing phases. For this purpose, chemical potentials were efficiently simulated via an expanded ensemble that gradually inserts/deletes a target chain to/from the system. These simulations employed a novel combination of Bennett's [J. Comput. Phys. 22, 245 (1976)] acceptance-ratio method to estimate free-energy differences and a recently proposed method to get biasing weights that maximize the number of times that the target chain is regrown. The analysis of the gyroid nodes revealed clear evidence of packing frustration in the form of an (entropically) unfavorably overstretching of chains, a phenomenon that has been suggested to provide the structural basis for the limited region of stability of the gyroid phase in the DBC phase diagram. Finally, the G phase and nodal chain stretching were also found in simulations with a completely different DBC particle-based model.

Dissipative particle dynamics study on the morphology changes of diblock copolymer lamellar microdomains due to steady shear

The morphology changes of linear diblock copolymer lamellar microdomains under uniform simple shear are studied via the dissipative particle dynamics technique. The parallel and perpendicular reorientations of the lamellae are observed in the simulations, and two different reorientation mechanisms, under small and large shear rates respectively, are proposed. The parallel-to-perpendicular transition is also observed and the kinetics is discussed. Sinusoidal and chevron instabilities due to the shear are found. After relaxation the peculiar "bidirectionally undulating" instability is obtained.