Effect of Sinusoidal Surface Roughness and Energy on the Orientation of Cylinder-Forming Block Copolymer Thin Films

We explore the relative stability of three possible orientations of cylinder-forming di-block copolymer on a sinusoidally corrugated substrate. The cylinders can be aligned either parallel to the substrate, with their long axis being oriented along or orthogonal to the corrugation trenches, or perpendicular to the substrate. Using self-consistent field theory, we investigate the influence of substrate roughness and surface preference on the phase transition between the three orientations. When the substrate preference, $u$, towards one of components is small, increasing the substrate roughness induces a phase transition from parallel to perpendicular cylindrical phase. However, when $u$ is large, the parallel orientation is more stable than the perpendicular one. Within this parallel phase, increasing the substrate roughness leads to a transition of cylinder orientation changing from being orthogonal to parallel to the trench long axis. Increasing the substrate preference leads to an opposite transition from parallel to orthogonal to the trenches. Furthermore, we predict that the perpendicular cylinder phase is easier to be obtained when the unidirectional corrugation is along the longer unit vector of the hexagonal packing than when it is along the shorter unit vector. Our results qualitatively agree with previous experiments, and contribute towards applications of the cylinder-forming block copolymer in nanotechnology.Comment: 9 pages, 7 figure

Enhanced electro-actuation in dielectric elastomers: the non-linear effect of free ions

Plasticized poly(vinyl chloride) (PVC) is a jelly-like soft dielectric material that attracted substantial interest recently as a new type of electro-active polymers. Under electric fields of several hundred Volt/mm, PVC gels undergo large deformations. These gels can be used as artificial muscles and other soft robotic devices, with striking deformation behavior that is quite different from conventional dielectric elastomers. Here, we present a simple model for the electro-activity of PVC gels, and show a non-linear effect of free ions on its dielectric behaviors. It is found that their particular deformation behavior is due to an electro-wetting effect and to a change in their interfacial tension. In addition, we derive analytical expressions for the surface tension as well as for the apparent dielectric constant of the gel. The theory indicates that the size of the mobile free ions has a crucial role in determining the electro-induced deformation, opening up the way to novel and innovative designs of electro-active gel actuators

The Chain Flexibility Effects on the Self-assembly of Diblock Copolymer in Thin Film

We investigate the effects of chain flexibility on the self-assembly behavior of symmetric diblock copolymers (BCPs) when they are confined as a thin film between two surfaces. Employing worm-like chain (WLC) self-consistent field theory, we study the relative stability of parallel (L$_{\parallel}$) and perpendicular (L$_{\perp}$) orientations of BCP lamellar phases, ranging in chain flexibility from flexible Gaussian chains to semi-flexible and rigid chains. For flat and neutral bounding surfaces (no surface preference for one of the two BCP components), the stability of the L$_{\perp}$ lamellae increases with chain rigidity. When the top surface is flat and the bottom substrate is corrugated, increasing the surface roughness enhances the stability of the L$_{\perp}$ lamellae for flexible Gaussian chains. However, an opposite behavior is observed for rigid chains, where the L$_{\perp}$ stability decreases as the substrate roughness increases. We further show that as the substrate roughness increases, the critical value of the substrate preference, $u^{*}$, corresponding to an L$_{\perp}$-to-L$_{\parallel}$ transition, decreases for rigid chains, while it increases for flexible Gaussian chains. Our results highlight the physical mechanism of tailoring the orientation of lamellar phases in thin-film setups. This is of importance, in particular, for short (semi-flexible or rigid) chains that are in high demand in emerging nanolithography and other industrial applications

Kinetic Paths of Block Copolymer Particles: Dynamic Self-Consistent Field Theory Studies

We explore the kinetic paths of structural evolution and formation of block copolymer (BCP) particles using dynamic self-consistent field theory (DSCFT). We show that the process-directed self-assembly of BCP immersed in a poor solvent leads to the formation of striped ellipsoids, onion-like particles and double-spiral lamellar particles. The theory predicts a reversible path of shape transition between onion-like particles and striped ellipsoidal ones by regulating the temperature (related to the Flory-Huggins parameter between the two components of BCP, $\chi_{\rm{AB}}$) and the selectivity of solvent towards one of the two BCP components. Furthermore, a kinetic path of shape transition from onion-like particles to double-spiral lamellar particles, and then back to onion-like particles is demonstrated. By investigating the inner-structural evolution of a BCP particle, we identify that changing the intermediate bi-continuous structure into a layered one is crucial for the formation of striped ellipsoidal particles. Another interesting finding is that the formation of onion-like particles is characterized by a two-stage microphase separation. The first is induced by the solvent preference, and the second is controlled by the thermodynamics. Our findings lead to an effective way of tailoring nanostructure of BCP particles for various industrial applications, ranging from sensors to smart coating to drug delivery

Coherent States Formulation of Polymer Field Theory

We introduce a stable and efficient complex Langevin (CL) scheme to enable the first numerical simulations of the coherent-states (CS) formulation of polymer field theory. In contrast with Edwards' well known auxiliary-field (AF) framework, the CS formulation does not contain an embedded non-linear, non-local functional of the auxiliary fields, and the action of the field theory has a fully explicit, finite-order and semi-local polynomial character. In the context of a polymer solution model, we demonstrate that the new CS-CL dynamical scheme for sampling fluctuations in the space of coherent states yields results in good agreement with now-standard AF simulations. The formalism is potentially applicable to a broad range of polymer architectures and may facilitate systematic generation of trial actions for use in coarse-graining and numerical renormalization-group studies.Comment: 14pages 8 figure