Surface‐induced ordering in block copolymer melts

Long-Range Surface-Directed Polymerization-Induced Phase Separation: A Computational Study

The presence of a surface preferably attracting one component of a polymer mixture by the long-range van der Waals surface potential while the mixture undergoes phase separation by spinodal decomposition is called long-range surface-directed spinodal decomposition (SDSD). The morphology achieved under SDSD is an enrichment layer(s) close to the wall surface and a droplet-type structure in the bulk. In the current study of the long-range surface-directed polymerization-induced phase separation, the surface-directed spinodal decomposition of a monomer-solvent mixture undergoing self-condensation polymerization was theoretically simulated. The nonlinear Cahn-Hilliard and Flory-Huggins free energy theories were applied to investigate the phase separation phenomenon. The long-range surface potential led to the formation of a wetting layer on the surface. The thickness of the wetting layer was found proportional to time t*1/5 and surface potential parameter h 1 1/5. A larger diffusion coefficient led to the formation of smaller droplets in the bulk and a thinner depletion layer, while it did not affect the thickness of the enrichment layer close to the wall. A temperature gradient imposed in the same direction of long-range surface potential led to the formation of a stripe morphology near the wall, while imposing it in the opposite direction of surface potential led to the formation of large particles at the high-temperature side, the opposite side of the interacting wall.

Gelation Impairs Phase Separation and Small Molecule Migration in Polymer Mixtures

Surface segregation of the low molecular weight component of a polymeric mixture is a ubiquitous phenomenon that leads to degradation of industrial formulations. We report a simultaneous phase separation and surface migration phenomena in oligomer-polymer ( O P ) and oligomer-gel ( O G ) systems following a temperature quench that induces demixing of components. We compute equilibrium and time varying migrant (oligomer) density profiles and wetting layer thickness in these systems using coarse grained molecular dynamics (CGMD) and mesoscale hydrodynamics (MH) simulations. Such multiscale methods quantitatively describe the phenomena over a wide range of length and time scales. We show that surface migration in gel-oligomer systems is significantly reduced on account of network elasticity. Furthermore, the phase separation processes are significantly slowed in gels leading to the modification of the well known Lifshitz-Slyozov-Wagner (LSW) law ℓ ( τ ) ∼ τ 1 / 3 . Our work allows for rational design of polymer/gel-oligomer mixtures with predictable surface segregation characteristics that can be compared against experiments.

Impact of particle arrays on phase separation composition patterns

We examine the symmetry-breaking effect of fixed constellations of particles on the surface-directed spinodal decomposition of binary blends in the presence of particles whose surfaces have a preferential affinity for one of the components. Our phase-field simulations indicate that the phase separation morphology in the presence of particle arrays can be tuned to have a continuous, droplet, lamellar, or hybrid morphology depending on the interparticle spacing, blend composition, and time. In particular, when the interparticle spacing is large compared to the spinodal wavelength, a transient target pattern composed of alternate rings of preferred and non-preferred phases emerges at early times, tending to adopt the symmetry of the particle configuration. We reveal that such target patterns stabilize for certain characteristic length, time, and composition scales characteristic of the pure phase-separating mixture. To illustrate the general range of phenomena exhibited by mixture-particle systems, we simulate the effects of single-particle, multi-particle, and cluster-particle systems having multiple geometrical configurations of the particle characteristic of pattern substrates on phase separation. Our simulations show that tailoring the particle configuration, or substrate pattern configuration, a relative fluid-particle composition should allow the desirable control of the phase separation morphology as in block copolymer materials, but where the scales accessible to this approach of organizing phase-separated fluids usually are significantly larger. Limited experiments confirm the trends observed in our simulations, which should provide some guidance in engineering patterned blend and other mixtures of technological interest.

Pathways to equilibrium orientation fluctuations in finite stripe-forming systems

Small-angle orientation fluctuations in ordered stripe-forming systems free of topological defects can exhibit aging and anisotropic growth of two length scales. In infinitely extended systems, the stripe orientation field develops a dominant modulation length λ_{∥}^{*}(t) in the direction parallel to the stripes, which increases with time t as λ_{∥}^{*}(t)∼t^{1/4}. Simultaneously, the orientation correlation length ξ_{⊥}(t) in the direction perpendicular to the stripes increases as ξ_{⊥}(t)∼t^{1/2} [Riesch et al., Interface Focus 7, 20160146 (2017)2042-889810.1098/rsfs.2016.0146]. Here we show that finite systems of size L_{⊥}×L_{∥} with periodic boundary conditions reach equilibrium when the dominant modulation length λ_{∥}^{*}(t) reaches the system size L_{∥} in the stripe direction. The equilibration time τ_{eq}^{∥} is solely determined by L_{∥}, with τ_{eq}^{∥}∼L_{∥}^{4}. In systems with L_{⊥}<L_{∥}^{2}/2πλ_{p}, where λ_{p} is the undulation penetration length, the initial aging and coarsening dynamics changes at the crossover time τ_{C}^{⊥}∼L_{⊥}^{2} to an aging and coarsening dynamics described by the one-dimensional Mullins-Herring equation, before reaching equilibrium at τ_{∥}^{eq}. Our work reveals the two pathways to equilibrium in stripe phases with periodic boundary conditions, the finite-size scaling behavior of equilibrium orientation fluctuations, and the characteristic exponents associated with the influence of a finite system size.

Particles with selective wetting affect spinodal decomposition microstructures

We have used mesoscale simulations to study the effect of immobile particles on microstructure formation during spinodal decomposition in ternary mixtures such as polymer blends.

Influence of substrate interaction and confinement on electric-field-induced transition in symmetric block-copolymer thin films

In the present work, we study morphologies arising due to competing substrate interaction, electric field, and confinement effects on a symmetric diblock copolymer. We employ a coarse-grained nonlocal Cahn-Hilliard phenomenological model taking into account the appropriate contributions of substrate interaction and electrostatic field. The proposed model couples the Ohta-Kawasaki functional with Maxwell equation of electrostatics, thus alleviating the need for any approximate solution used in previous studies. We calculate the phase diagram in electric-field-substrate strength space for different film thicknesses. In addition to identifying the presence of parallel, perpendicular, and mixed lamellae phases similar to analytical calculations, we also find a region in the phase diagram where hybrid morphologies (combination of two phases) coexist. These hybrid morphologies arise either solely due to substrate affinity and confinement or are induced due to the applied electric field. The dependence of the critical fields for transition between the various phases on substrate strength, film thickness, and dielectric contrast is discussed. Some preliminary 3D results are also presented to corroborate the presence of hybrid morphologies.

Stability and orientation of lamellae in diblock copolymer films

The dynamics of microphase separation and the orientation of lamellae in diblock copolymers are 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 an efficient functional approach introduced with this work. The effects of the interaction of diblock copolymers with two confining substrates on the lamellae orientation are studied by an extensive analysis of the total free energy. By changing the wetting property at one boundary, a transition from a preferentially perpendicular to a parallel lamellar orientation with respect to the confining plates is found, which is rather independent of the distance between the boundaries. Simulations of the dynamics of microphase separation reveal that the time scale of the lamellar orientational order dynamics, which is quantitatively characterized in terms of an orientational order parameter and the structure factor, depends significantly on the properties of the confining boundaries as well as on the quench depth.

Thermal quenching sample chamber for grazing incidence small angle x-ray scattering studies of polymer films

The second generation of a sample chamber designed for in situ measurement of temperature- and time-dependent polymer film nanostructure using the method of grazing incidence small angle x-ray scattering is presented. An increased operating temperature limit (from 260 to 400 degrees C) with precise control (+/-0.1 degrees C) at fixed temperatures as well as a fourfold increase in maximum instantaneous cooling rate (up to 73 degrees C/s) relative to the first generation chamber [M. N. Groves et al, J. Appl. Crystallogr. 39, 120 (2006)] are reported. Thermal quenches from 220 to 90 degrees C are shown to be reproducible to within +/-1 degrees C of the final temperature. Experimental tests on spin-coated films of symmetric diblock styrene-butadiene copolymer demonstrate the ability to resolve the kinetics of orientation of lamellar domains parallel to the silicon substrate, distinct from the initial formation of randomly oriented lamellar domains immediately following the thermal quench.

Guided self-assembly of diblock copolymer thin films on chemically patterned substrates

We study the guided self-assembly of symmetric/asymmetric diblock copolymer (BCP) films on heterogeneous substrates with chemically patterned surface by using a coarse-grained phase-separation model. During the procedure, the free energy employed for the BCP films was modeled by the Ginzburg-Landau free energy with nonlocal interaction, and the flat, chemically patterned surface was considered as a heterogeneous surface with short-range interaction with the BCP molecules. The resulting Cahn-Hilliard equation was solved by means of an efficient semi-implicit Fourier-spectral algorithm. Effects of pattern scale, surface chemical potential, and BCP asymmetry on the self-assembly process were explored in detail and compared with those without chemically patterned substrate surfaces. It was found that the morphology of both symmetric and asymmetric BCP films is strongly influenced by the commensurability between the unconstrained natural period lambda* of the bulk BCP and the artificial pattern period. Simulation shows that patterned surface with period close to lambda* leads to highly ordered morphology after self-assembly for both symmetric and asymmetric BCP films, and it also dramatically accelerates the guided self-assembly process. The present simulation is in a very good agreement with the recent experimental observation in BCP nanolithography. Finally, the present study also expects an innovative nanomanufacturing method to produce highly ordered nanodots based on the guided self-assembly of asymmetric BCP films on chemically patterned substrates.

Simulated annealing study of asymmetric diblock copolymer thin films

We report a simulated annealing study of the morphology of asymmetric diblock copolymer thin films confined between two homogeneous and identical surfaces. We have focused on copolymers that form a gyroidal morphology in the bulk. The morphological dependence of the confined films on the film thickness and the surface-polymer interaction has been systematically investigated. From the simulations it is found that much richer morphologies can form for the gyroid-forming asymmetric diblock copolymer thin films, in contrast to the lamella-forming symmetric and cylinder-forming asymmetric diblock copolymer films. Multiple morphological transitions induced by changing the film thickness and polymer-surface interactions are observed.

Wetting-driven structure ordering of a copolymer/homopolymer/nanoparticle mixture in the presence of a modulated potential

We investigate pattern formation on a solid substrate of a diblock copolymer-homopolymer mixture containing doping wettable nanoparticles with a preferential attraction for one component of the copolymers, using a three-order-parameter model. The presence of doping nanoparticles under the surface-interaction modulation breaks the isotropy in the process of microphase-separation and macrophase-separation. This leads to the formation of orientational microphase and macrophase structures due to the interplay between the phase separation and wetting particle ordering under a modulated potential at the late stage. Simulations suggest that the microphase morphology and macrophase morphology can be changed through adjustment of the wetting strength, the amplitude as well as the period of the modulated potential. It provides some important insights for changing microphase and macrophase structures in polymer blends by wetting-driven spinodal decomposition.

Orientational order transition of the striped microphase structure of a copolymer-homopolymer mixture under oscillatory particles

Based on the three-order-parameter model, we investigate the orientational order transition of striped patterns in microphase structures of diblock copolymer-homopolymer mixtures in the presence of periodic oscillatory particles. Under suitable conditions, although the macrophase separation of a system is almost isotropic, the microphase separation of the system will be significantly perturbed by the oscillatory field, and composition fluctuations are suppressed anisotropically. The isotropy of the microphase will be broken up. By changing the oscillatory amplitude and frequency, we observe the orientational order transition of a striped microphase structure from the isotropic state to a state parallel to the oscillatory direction, and from the parallel state to a state perpendicular to the oscillatory direction. We examine, in detail, the microstructure and orientational order parameter as well as the domain size in the process of orientational order transition under the oscillatory field. We study also how the microphase structure changes with the composition ratio of homopolymers and copolymers in mixtures. The results suggest that our model system may provide a simple way to realize orientational order transition of soft materials.

Influence of confinement on the orientational phase transitions in the lamellar phase of a block-copolymer melt under shear flow

In this paper, 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. 62 1856 (1989) and G. H. Fredrickson, J. Rheol. 38, 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 the spinodal. We associate this transition with a crossover from the fluctuation to the mean-field behavior. At lower temperatures, the stability of the parallel orientation is restored. We find that the region of stability of the perpendicular orientation rapidly decreases as shear rate increases. This behavior might be misinterpreted as an additional perpendicular to parallel transition recently discussed in literature.

Cylindrical phase of block copolymers: stability of circular configuration to elliptical distortions and thin film morphologies

We study the cylindrical phase of a diblock copolymer melt in the strong segregation limit, and initially examine the stability of this morphology against elliptical perturbations. Surprisingly, we find that an elliptical conformation of the columns has lower free energy than a circular one. The size of the ellipse's eccentricity depends on f, the minority block fraction. We proceed to examine the morphology of the melt when placed between two hard, flat surfaces. The columns can either form with their axes in the plane of the bounding surfaces (denoted parallel) or with their axes perpendicular to the bounding surfaces. We determine when the parallel alignment is preferred over the perpendicular alignment.

Polymer adsorption-driven self-assembly of nanostructures

Driven by prospective applications, there is much interest in developing materials that can perform specific functions in response to external conditions. One way to design such materials is to create systems which, in response to external inputs, can self-assemble to form structures that are functionally useful. This review focuses on the principles that can be employed to design macromolecules that when presented with an appropriate two-dimensional surface, will self-assemble to form nanostructures that may be functionally useful. We discuss three specific examples: (a) biomimetic recognition between polymers and patterned surfaces. (b) control and manipulation of nanomechanical motion generated by biopolymer adsorption and binding, and (c) creation of patterned nanostructuctures by exposing molten diblock copolymers to patterned surfaces. The discussion serves to illustrate how polymer sequence can be manipulated to affect self-assembly characteristics near adsorbing surfaces. The focus of this review is on theoretical and computational work aimed toward elucidating the principles underlying the phenomena pertinent to the three topics noted above. However, synergistic experiments are also described in the appropriate context.

Density mismatch in thin diblock copolymer films

Thin films of diblock copolymer subject to gravitational field are simulated by means of a cell dynamical system model. The difference in density of the two sides of the molecule and the presence of the field causes the formation of lamellar patterns with orientation parallel to the confining walls even when they are neutral. The concentration profile of those films is analyzed in the weak segregation regime and a functional form for the profile is proposed.

Thin diblock copolymer films on patterned surfaces: computer simulations and the Frenkel-Kontorowa model

We study by direct numerical integration of the dynamical evolution equation the equilibrium configuration of a diblock copolymer thin film melt on a patterned surface. The surface has a large number of stripes and the mismatch between the bulk diblock spacing and the stripe width is small. We investigate primarily the formation of small discommensurations in the incommensurate phase and compare the results with the predictions of an analogous model of solid-state physics, the Frenkel-Kontorowa model.