Hybrid time-dependent Ginzburg-Landau simulations of block copolymer nanocomposites: nanoparticle anisotropy

Block copolymer melts are perfect candidates to template the position of colloidal nanoparticles in the nanoscale, on top of their well-known suitability for lithography applications. This is due to their ability to self-assemble into periodic ordered structures, in which nanoparticles can segregate depending on the polymer-particle interactions, size and shape. The resulting coassembled structure can be highly ordered as a combination of both the polymeric and colloidal properties. The time-dependent Ginzburg-Landau model for the block copolymer was combined with Brownian dynamics for nanoparticles, resulting in an efficient mesoscopic model to study the complex behaviour of block copolymer nanocomposites. This review covers recent developments of the time-dependent Ginzburg-Landau/Brownian dynamics scheme. This includes efforts to parallelise the numerical scheme and applications of the model. The validity of the model is studied by comparing simulation and experimental results for isotropic nanoparticles. Extensions to simulate nonspherical and inhomogeneous nanoparticles are discussed and simulation results are discussed. The time-dependent Ginzburg-Landau/Brownian dynamics scheme is shown to be a flexible method which can account for the relatively large system sizes required to study block copolymer nanocomposite systems, while being easily extensible to simulate nonspherical nanoparticles

Cell dynamics simulations of sphere-forming diblock copolymers in thin films on chemically patterned substrates

The morphology of sphere-forming block copolymers assembled in thin films on patterned surfaces is theoretically analyzed. The patterns on the lower surface are alternating bands of a given width distinctively attracting or repelling a given block. We find that long- range order can be achieved, and it depends on the commensurability of the characteristic length of the block domains with both band periodicity and slit thickness. The comparison of the simulation results with experimental data shows a very good agreement. Furthermore, we show that the proper selection of the band periodicity and, consequently, of the film thickness permits the system to switch from hexagonal packing to body-centered orthohedra. Therefore, we show that it exists a way to control the formation of long-range ordered structures of different types in this kind of system

Mechanisms of electric-field-induced alignment of block copolymer lamellae

We demonstrate that two mechanisms of lamellae reorientation observed experimentally under applied electric field [A. Böker H. Elbs, H. Hänsel, A. Knoll, S. Ludwigs, H. Zettl, V. Urban, V. Abetz, A. H. E. Müller and G. Krausch, Phys. Rev. Lett., 2002, 89, 135502] which have been previously described within dynamic self consistent field theory [A. V. Zvelindovsky and G. J. A. Sevink, Phys. Rev. Lett., 2003, 90, 049601] can be fully explained within a much more simple model using the Ginzburg–Landau Hamiltonian. A third alignment mechanism has been identified which was not previously reported. A more complete picture of reorientation under electric field emerges that clarifies the crucial role of structural defects

Parallel Hybrid Simulations of Block Copolymer Nanocomposites using Coarray Fortran

Computer simulations of experimentally comparable system sizes in soft matter often require considerable elapsed times. The use of many cores can reduce the needed time, ideally proportionally to the number of processors. In this paper a parallel computational method using coarray Fortran is implemented and tested for large systems of purely block copolymer melts, as well as block copolymer nanocomposites. A satisfactory strong scaling is shown up to 512 cores while a weak scaling with a drop in performance is achieved up to 4096 cores. The scaling of the parallel cell dynamic simulations scheme displays no drawbacks over MPI and provides an example of the simplicity of the coarray approach. The code has been tested on several architectures and compilers. The hybrid block copolymer/nanoparticle algorithm can achieve previously unavailable system sizes

Nonspherical Nanoparticles in Block Copolymer Composites: Nanosquares, Nanorods, and Diamonds

A hybrid two-dimensional block copolymer (BCP) nanocomposite computational model is proposed to study nanoparticles (NPs) with a generalized shape including square, rectangle, and rhombus. Simulations are used to study the role of anisotropy in the assembly of colloids within BCPs, ranging from NPs that are compatible with one phase to neutral NPs. The ordering of squarelike NPs into grid configurations within a minority BCP domain was investigated, as well as the alignment of nanorods in a lamellarforming BCP, comparing the simulation results with experiments of mixtures of nanoplates and polystyrene-b-poly- (methyl methacrylate) BCP. The assembly of rectangular NPs at the interface between domains resulted in alignment along the interface. The aspect ratio is found to play a key role in the aggregation of colloids at the interface, which leads to a distinct co-assembly behavior for low- and high-aspect-ratio NPs

Hybrid Time-Dependent Ginzburg–Landau Simulations of Block Copolymer Nanocomposites: Nanoparticle Anisotropy

Block copolymer melts are perfect candidates to template the position of colloidal nanoparticles in the nanoscale, on top of their well-known suitability for lithography applications. This is due to their ability to self-assemble into periodic ordered structures, in which nanoparticles can segregate depending on the polymer–particle interactions, size and shape. The resulting coassembled structure can be highly ordered as a combination of both the polymeric and colloidal properties. The time-dependent Ginzburg–Landau model for the block copolymer was combined with Brownian dynamics for nanoparticles, resulting in an efficient mesoscopic model to study the complex behaviour of block copolymer nanocomposites. This review covers recent developments of the time-dependent Ginzburg–Landau/Brownian dynamics scheme. This includes efforts to parallelise the numerical scheme and applications of the model. The validity of the model is studied by comparing simulation and experimental results for isotropic nanoparticles. Extensions to simulate nonspherical and inhomogeneous nanoparticles are discussed and simulation results are discussed. The time-dependent Ginzburg–Landau/Brownian dynamics scheme is shown to be a flexible method which can account for the relatively large system sizes required to study block copolymer nanocomposite systems, while being easily extensible to simulate non-spherical nanoparticles

Co-assembly of Janus nanoparticles in block copolymer systems

Block copolymer are ideal matrices to control the localisation of colloids. Furthermore, anisotropic nanoparticles such as Janus nanoparticles possess an additional orientational degree of freedom that can play a crucial role in the formation of highly ordered materials made of block copolymers. This work presents a mesoscopic simulation method to assert the co-assembly of Janus nanoparticles in a block copolymer mixture, finding numerous instances of aggregation and formation of ordered configurations. Comparison with chemically homogeneous neutral nanoparticles shows that Janus nanoparticles are less prone to induce bridging along lamellar domains, thus being a less destructive way to segregate nanoparticles at interfaces. The combination of asymmetric block copolymer and asymmetric Janus nanoparticles can result in assembly of colloids with an even number of layers within the minority domain

Nanoparticle anisotropy induces sphere-to-cylinder phase transition in block copolymer melts

Block copolymer nanocomposites including anisotropic nanoparticles have been previously found to co-assemble into complex structures with nanoparticle alignment. Anisotropic nanoparticles with large aspect ratios are found to modify the morphology of block copolymers at modest concentrations, inducing a sphere-tocylinder phase transition by breaking the local symmetry in the vicinity of a solid particle. This transition takes place over a wide range of NP lengths comparable with the BCP spacing. Controlling the orientation of uniaxial nanoparticles provides additional control over the global orientation of the block copolymer, as previously reported by experiments

Nematic Ordering of Anisotropic Nanoparticles in Block Copolymers

Block copolymer melts have been previously used to control the position and alignment of anisotropic nanoparticles. In this work, 2D and 3D mesoscopic simulations are used to explore the phase behavior of block copolymer/nanoparticle systems. The method combines a time-dependent Ginzburg-Landau for the polymer and Brownian dynamics for the anisotropic nanoparticles. Rhomboidal and spheroidal shaped particles are simulated in two and three dimensions, respectively. It is found that the nanoparticle nematic order aligned by the block copolymer domains enhances the lamellar phase of the block copolymer, due to an anisotropy-driven phase transition. Additionally, anisotropic nanoparticles within circular-forming block copolymer leads to a competition between the nematic colloidal ordering and the hexagonally ordered mesophase. At large concentrations, the nematic order dominates, deforming the block copolymer mesophase

Block Copolymer–Nanorod Co-assembly in Thin Films: Effects of Rod–Rod Interaction and Confinement

Simulations and experiments of nanorods (NRs) show that co-assembly with block copolymer (BCP) melts leads to the formation of a superstructure of side-to-side NRs perpendicular to the lamellar axis. A mesoscopic model is validated against scan- ning electron microscopy (SEM) images of CdSe NRs mixed with polystyrene-block- poly(methyl methacrylate). It is then used to study the co-assembly of anisotropic nanoparticles (NPs) with a length in the same order of magnitude as the lamellar spac- ing. The phase diagram of BCP/NP is explored as well as the time evolution of the NR. NRs that are slightly larger than the lamellar spacing are found to rotate and organise side-to-side with a tilted orientation with respect to the interface. Strongly interacting NPs are found to dominate the co-assembly while weakly interacting nanoparticles are less prone to form aggregates and tend to form well-ordered configurations