Perpendicular Lamellar Phases Research Articles

Orientation control of the hexagonal and lamellar phases in thin block copolymer films using in-plane AC electric field

Lamellar and hexagonal pattern rearrangements in thin films of polystyrene–block–poly(2-vinyl pyridine) and polystyrene–block–poly(4-vinyl pyridine) copolymers simultaneously exposed to an in-plane AC electric field and saturated chloroform vapor are studied with atomic force microscopy and analyzed via the numerical solution of the self-consistent field theory equations. It is demonstrated that the use of AC field with the root-mean-square strength higher than 8 V⋅μm−1 allows one to effectively orient microphase-separated domains along the field direction on the tens of microns scale. At the same time, the AC field considerably lowers the risk of breakdown and eliminates effects related to ionic transport in the presence of solvent vapor. The role of such factors as the exposure time, field strength and frequency is investigated. Theoretical considerations prove the equivalent effect of AC and DC fields on the structure of the copolymer film in a wide frequency range. Self-consistent field theory calculations of the free energy as a function of film thickness make it possible to exactly identify which phase dominates in the film. In particular, an apparent transformation of standing cylinders into long threads aligned in the field direction should be interpreted as the phase transition from the perpendicular to parallel hexagonal phase, which can take place in a certain range of film thicknesses, provided the electric field strength exceeds a certain threshold value. In the case of a perpendicular lamellar phase, the domain orientation along the direction of the electric field is always profitable. The observed morphological rearrangements under an in-plane field, which preserve connectivity between the film surfaces through the domains of the minor copolymer block, can be important for practical applications.

Defect-Free Perpendicular Diblock Copolymer Films: The Synergy Effect of Surface Topography and Chemistry

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 the desired perpendicular lamellar phase with perfect inplane ordering. Defect-free BCP lamellar phases are reproducible for several random initial states, and are obtained for a range of substrate roughness and chemical characteristics, even for a uni-directional multi-mode substrate roughness. Our theoretical study suggests possible experiments that will explore the interplay between uni-directional substrate corrugation and chemical surface treatment. It may lead to viable and economical ways of obtaining BCP films with defect-free lateral alignment.

In‐plane and out‐of‐plane defectivity in thin films of lamellar block copolymers

ABSTRACTWe investigate the ordering of poly(styrene‐b‐methyl methacrylate) (PS‐PMMA) lamellar copolymers (periodicityL0 = 46 nm) confined between a free surface and brushed poly(styrene‐r‐methyl methacrylate) silicon substrate. The processing temperature was selected to eliminate wetting layers at the top and bottom interfaces, producing approximately neutral boundaries that stabilize perpendicular domain orientations. The PS‐PMMA film thickness (t = 0.5L0 − 2.5L0) and brush grafting density (Σ = 0.2–0.6 nm−2) were systematically varied to examine their impacts on in‐plane and out‐of‐plane ordering. Samples were characterized with a combination of high‐resolution microscopy, X‐ray reflectivity, and grazing‐incidence small‐angle X‐ray scattering. In‐plane order at the top of the film (quantified through calculation of orientational correlation lengths) improved withtn, where the exponentnincreased from 0.75 to 1 as Σ decreased from 0.6 to 0.2 nm−2. Out‐of‐plane defects such as tilted domains were detected in all films, and the distribution of domain tilt angles was nearly independent oftand Σ. These studies demonstrate that defectivity in perpendicular lamellar phases is three‐dimensional, comprised of in‐plane topological defects and out‐of‐plane domain tilt, with little or no correlation between these two types of disorder. Strong interactions between the block copolymer and underlying substrate may trap both kinds of thermally generated defects. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016, 54, 339–352

Complex microstructures of ABC triblock copolymer thin films directed by polymer brushes based on self-consistent field theory.

The morphology and the phase diagram of ABC triblock copolymer thin film directed by polymer brushes are investigated by the self-consistent field theory in three dimensions. The polymer brushes coated on the substrate can be used as a good soft template to tailor the morphology of the block copolymer thin films compared with those on the hard substrates. The polymer brush is identical with the middle block B. By continuously changing the composition of the block copolymer, the phase diagrams are constructed for three cases with the fixed film thickness and the brush density: identical interaction parameters, frustrated and non-frustrated cases. Some ordered complex morphologies are observed: parallel lamellar phase with hexagonally packed pores at surfaces (LAM3 ll -HFs), perpendicular lamellar phase with cylinders at the interface (LAM⊥-CI), and perpendicular hexagonally packed cylinders phase with rings at the interface (C2⊥-RI). A desired direction (perpendicular or parallel to the coated surfaces) of lamellar phases or cylindrical phases can be obtained by varying the composition and the interactions between different blocks. The phase diagram of ABC triblock copolymer thin film wetted between the polymer brush-coated surfaces is very useful in designing the directed pattern of ABC triblock copolymer thin film.

Self-Assembly of Lamellar- and Cylinder-Forming Diblock Copolymers in Planar Slits: Insight from Dissipative Particle Dynamics Simulations

We present a dissipative particle dynamics simulation study on nanostructure formation of symmetric and asymmetric diblock copolymers confined between planar surfaces. We consider symmetric and slightly asymmetric diblock copolymers that form lamellar nanostructures in the bulk, and highly asymmetric diblock copolymers that form cylindrical nanostructures in the bulk. The formation of the diblock copolymer nanostructures confined between the planar surfaces is investigated and characterized by varying the separation width and the strength of the interaction between the surfaces and the diblock copolymers. Both the slit width and the surface interaction strongly influence the phase diagram, especially for the asymmetric systems. For the symmetric and slightly asymmetric diblock copolymer systems, the confinement primarily affects the orientation of the lamellar domains and only marginally influences the domain morphologies. These systems form parallel lamellar phases with different number of lamellae, and perpendicular and mixed lamellar phases. In a narrow portion of the phase diagram, these systems exhibit a parallel perforated lamellar phase, where further insight into the appearance of this phase is provided through free-energy calculations. The confined highly asymmetric diblock copolymer system shows, in addition to nanostructures with parallel and perpendicular cylinders, noncylindrical structures such as parallel lamellae and parallel perforated lamellae. The formation of the various confined nanostructures is further analyzed by calculating structural characteristics such as the mean square end-to-end distance of the diblock copolymers and the nematic order parameter.

Self-Assembly of Symmetric Diblock Copolymers in Planar Slits with and without Nanopatterns: Insight from Dissipative Particle Dynamics Simulations

We present a dissipative particle dynamics simulation study on the formation of nanostructures of symmetric diblock copolymers confined between planar surfaces with and without nanopatterns. The nanopatterned surface is mimicked by alternating portions of the surface that interact differently with the diblock copolymers. The formation of the diblock-copolymer nanostructures confined between the planar surfaces is investigated and characterized by varying the separation width and the strength of the interaction between the surfaces and the diblock copolymers. For surfaces with nanopatterns, we also vary both the mutual area and location of the nanopatterns, where we consider nanopatterns on the opposing surfaces that are vertically (a) aligned, (b) staggered, and (c) partially staggered. In the case of planar slits without nanopatterns, we observe the formation of perpendicular and parallel lamellar phases with different numbers of lamellae. In addition, the symmetric diblock copolymers self-assemble into adsorbed layer and adsorbed layer-parallel lamellar phases and a mixed lamellar phase when the opposing surfaces of the planar slits are modeled by different types of wall beads. In the case of nanopatterned planar slits, we observe novel nanostructures and attempt to rationalize the diblock copolymer self-assembly on the basis of the behavior that we observed in the planar slits without nanopatterns. In particular, we investigate the applicability of predicting the structures formed in the nanopatterned slits by a superposition of the observed structures in slits without nanopatterns.

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.

Shear-induced parallel-to-perpendicular orientation transition in the amphiphilic lamellar phase: A nonequilibrium molecular-dynamics simulation study

The present work is devoted to a study of the shear-induced parallel-to-perpendicular orientation transition in the lamellar system by the large-scale nonequilibrium molecular-dynamics (NEMD) simulation. An effective generic model-A2B2 tetramer for amphiphilies is used. The NEMD simulation produces unambiguous evidence that undulation instability along the vorticity direction sets in well above a critical shear rate and grows in magnitude as the shear rate is further increased. At a certain high shear rate, the coherent undulation instability grows so large that defects are nucleated and the global lamellar monodomain breaks into several aligned lamellar domains. Subsequently layers in these domains rotate into the perpendicular orientation with the rotation of chains towards the y direction, merge into a global perpendicular-aligned lamellar monodomain, and organize into a perfect well-aligned perpendicular lamellar phase by the migration and annihilation of edge dislocations and disclinations. The macroscopic observable viscosity as a function of time or shear rate is correlated with the structural response such as the mesoscopic domain morphology and the microscopic chain conformation. The onset of undulation instability concurs with the start-up of shear-thinning behavior. During the orientation transformation at the high shear rate, the complex time-dependent thixotropic behavior is observed. The smaller viscosity in the perpendicular lamellar phase gives an energetic reason for the shear-induced orientation transition.

Orientational Transitions in Symmetric Diblock Copolymers on Rough Surfaces

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.

Parallel and perpendicular lamellar phases in copolymer–nanoparticle multilayer structures

Recent results in developing novel nanocomposite multilayer structures are presented. We used symmetric polystryrene–block–polymethylmethacrylate (deuterated) P(S–b–MMAd) lamellar thin films as a self-assembling matrix for the lamellar arrangement of Fe 3O 4 nanoparticles. Pure copolymer films showed an unusual structure with a perpendicular to the surface orientation of the lamellae, in the part of the film towards the free surface. This is a new phenomenon because up to now this orientation was obtained only on specially prepared substrates. After the incorporation of nanoparticles into the copolymer matrix, the system switched to a lamellar structure parallel to the surface. Further increasing of the nanoparticles concentration led to a more perfect lamellar structure, which shows that the limit for a high concentration of nanoparticles, important for nanotechnology has not yet been reached.

Diblock copolymer thin films: Parallel and perpendicular lamellar phases in the weak segregation limit

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 that a surface interaction, which is quadratic in the monomer concentration, favors the perpendicular lamellar phase. In particular, the degeneracy between perpendicular and unfrustrated parallel lamellar phases for walls without a preferential adsorption is removed.

Thin films of block copolymer

We develop a numerical method for examining complex morphologies in thin films of block copolymer using self-consistent field theory. Applying the method to confined films of symmetric diblock copolymer, we evaluate the stability of parallel, perpendicular, and mixed lamellar phases. In general, lamellar domains formed by the diblocks are oriented parallel to the film by surface fields. However, their orientation can flip to perpendicular when the natural period of the lamellae is incommensurate with the film thickness. Experiments and Monte Carlo simulations have indicated that mixed lamellar phases may also occur, but for symmetric diblocks, we find these phases to be slightly unstable relative to perpendicular lamellae. Nevertheless, just a small asymmetry in the molecule stabilizes a mixed lamellar phase. Although our work focuses on confined films, we do discuss the behavior that results when films are unconfined.