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

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.

Design of polymer nanocomposites in solution by polymer functionalization

Polymer nanocomposites, materials combining polymers and inorganic components such as nanosized crystallites or nanoparticles have attracted significant attention in recent years. A successful strategy for designing polymer nanocomposites is polymer functionalization via attaching functional groups with specific affinity for the inorganic component. In this paper, a systematic investigation by molecular dynamics of polymer functionalization for design of composites combining nanosize crystallites with multiblock polymers in solution is presented. It is shown that functionalization is an example of active self-assembly, where the resulting polymer nanocomposite exhibits a different type of order than the original pure polymer system (without inorganic components). Optimal polymer architectures and concentrations are identified appropriate for different applications, alongside an in-depth analysis on the origin and stability of the resulting phases as well as its experimental implications.

Monte Carlo phase diagram for diblock copolymer melts

The phase diagram for diblock copolymer melts is evaluated from lattice-based Monte Carlo simulations using parallel tempering, improving upon earlier simulations that used sequential temperature scans. This new approach locates the order-disorder transition (ODT) far more accurately by the occurrence of a sharp spike in the heat capacity. The present study also performs a more thorough investigation of finite-size effects, which reveals that the gyroid (G) morphology spontaneously forms in place of the perforated-lamellar (PL) phase identified in the earlier study. Nevertheless, there still remains a small region where the PL phase appears to be stable. Interestingly, the lamellar (L) phase next to this region exhibits a small population of transient perforations, which may explain previous scattering experiments suggesting a modulated-lamellar (ML) phase.

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.

Optimized expanded ensembles for simulations involving molecular insertions and deletions. II. Open systems

In the Grand Canonical, osmotic, and Gibbs ensembles, chemical potential equilibrium is attained via transfers of molecules between the system and either a reservoir or another subsystem. In this work, the expanded ensemble (EXE) methods described in part I [F. A. Escobedo and F. J. Martinez-Veracoechea, J. Chem. Phys. 127, 174103 (2007)] of this series are extended to these ensembles to overcome the difficulties associated with implementing such whole-molecule transfers. In EXE, such moves occur via a target molecule that undergoes transitions through a number of intermediate coupling states. To minimize the tunneling time between the fully coupled and fully decoupled states, the intermediate states could be either: (i) sampled with an optimal frequency distribution (the sampling problem) or (ii) selected with an optimal spacing distribution (staging problem). The sampling issue is addressed by determining the biasing weights that would allow generating an optimal ensemble; discretized versions of this algorithm (well suited for small number of coupling stages) are also presented. The staging problem is addressed by selecting the intermediate stages in such a way that a flat histogram is the optimized ensemble. The validity of the advocated methods is demonstrated by their application to two model problems, the solvation of large hard spheres into a fluid of small and large spheres, and the vapor-liquid equilibrium of a chain system.

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.