Spinodal decomposition in a Hele-Shaw cell

Phase transition of a symmetric diblock copolymer induced by nanorods with different surface chemistry

We investigate the phase transition of a symmetric diblock copolymer induced by nanorods with different surface chemistry. The results demonstrate that the system occurs the phase transition from a disordered structure to ordered parallel lamellae and then to the tilted layered structure as the number of rods increases. The dynamic evolution of the domain size and the order parameter of the microstructure are also examined. Furthermore, the influence of rod property, rod-phase interaction, rod-rod interaction, rod length, and polymerization degree on the behavior of the polymer system is also investigated systematically. Moreover, longer amphiphilic nanorods tend to make the polymer system form the hexagonal structure. It transforms into a perpendicular lamellar structure as the polymerization degree increases. Our simulations provide an efficient method for determining how to obtain the ordered structure on the nanometer scales and design the functional materials with optical, electronic, and magnetic properties.

Domain patterns in a diblock copolymer-diblock copolymer mixture with oscillatory particles

We investigate the orientational order transition of striped patterns in microphase structures of diblock copolymer-diblock copolymer mixtures in the presence of periodic oscillatory particles. Under certain conditions, although the macrophase separation of a system is almost isotropic, microphase separation of one diblock copolymer takes place and becomes anisotropic gradually. By changing the oscillatory frequency and amplitude, the orientational order transition of a striped microphase structure from the state parallel to the oscillatory direction to the state perpendicular to the oscillatory direction is observed. We also find that the order transition occurs when we change the initial composition ratio. Furthermore, we examine the domain size and the orientational order parameter of microstructure in the process of orientational order transition. The results may provide guidance for experimentalists. This model system can also give a simple way to realize orientational order transition of soft materials by changing the oscillatory field.

Nucleation, growth, and coarsening of crystalline domains in order-order transitions between lamellar and hexagonal phases

Using the numerical solution of the time-dependent Ginzburg-Landau equation, we study the entire process of transformation between the lamellar and the hexagonal phases from the early-stage nucleation and growth to the late-stage coarsening regime. The metastable crystalline structure that nucleates first is identified in terms of the mean-field theory under the single-wave-number approximation. This has been borne out by the numerically efficient preparation of single-crystal structure developed via the noise-induced self-organization. We also present results for the scaling of the late-time domain growth, which is quantified by two measures: the structure factor and the orientational correlation function. In particular, the growth exponent is shown to be robust and indifferent to conservation of the order parameter.

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.

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.

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.

Phase separation of a polymer blend driven by oscillating particles

We study the possible formation of ordered structures of a binary polymer blend by introducing mobile particles in a periodically oscillating driving field. The particles which have a preferential attraction to one of the immiscible phases, will significantly perturb the phase separation of the system and breakup the isotropy of the system, so that some interesting structures such as lamellar and cylinder phases are observed by appropriate selection of the simulation parameters. We examine in detail the dependence of formed morphology and domain size on the oscillating fields, the relative composition of mixtures, the diffusion coefficient, and quench depth, and then discuss how to realize stable and highly ordered structures.

Crossover from the hydrodynamic regime to the thermal fluctuation regime in a two-dimensional phase-separating binary fluid containing surfactants

Extensive simulations were carried out to investigate the crossover between the hydrodynamic regime at intermediate stage and the thermal fluctuation regime at late stage in a phase-separating binary fluid/surfactant system in two dimensions. The existence of the crossover and its dependence on the surfactant concentration were analyzed using Kawasaki and Ohta's interface kinetic equation [Physica A 118, 175 (1983)]. The analysis showed that there should exist a critical surfactant concentration, above which thermal fluctuations dominate phase separation at all times. Simulations suggested that the crossover exists and the hydrodynamic regime shrinks when surfactant concentration increases. Simulations also demonstrated that the trapped surfactants seen in a previous study [Phys. Rev. E 59, 2109 (1999)] can remain trapped for a time much longer than the time needed to form well segregated domains, in spite of the presence of significant thermal fluctuations.