Lattice Boltzmann method for multiscale self-consistent field theory simulations of block copolymers

Efficient Langevin and Monte Carlo sampling algorithms: The case of field-theoretic simulations

We introduce Langevin sampling algorithms to field-theoretic simulations (FTSs) of polymers that, for the same accuracy, are ∼10× more efficient than a previously used Brownian dynamics algorithm that used predictor corrector for such simulations, over 10× more efficient than the smart Monte Carlo (SMC) algorithm, and typically over 1000× more efficient than a simple Monte Carlo (MC) algorithm. These algorithms are known as the Leimkuhler-Matthews (the BAOAB-limited) method and the BAOAB method. Furthermore, the FTS allows for an improved MC algorithm based on the Ornstein-Uhlenbeck process (OU MC), which is 2× more efficient than SMC. The system-size dependence of the efficiency for the sampling algorithms is presented, and it is shown that the aforementioned MC algorithms do not scale well with system sizes. Hence, for larger sizes, the efficiency difference between the Langevin and MC algorithms is even greater, although, for SMC and OU MC, the scaling is less unfavorable than for the simple MC.

Simulation and Fabrication of Nanoscale Spirals Based on Dual-Scale Self-Assemblies

Archimedean spirals in nanometer scale have shown remarkable plasmonic responses derived from their linear and rotational asymmetry. Despite the unique optical properties of nanoscale spirals, their applications have been limited due to the difficulty in fabricating large-scale arrays with uniform and systematic control of the morphology. Here, we report simulation results of spiral morphologies, which are used to design a scalable fabrication process for nanoscale spirals and predict their plasmonic responses. First, self-consistent field theory (SCFT) simulations were performed to design optimal templates to guide self-assembly into spiral morphologies. Using the SCFT results, we developed a scalable fabrication process, which is based on the micron-scale assembly of microspheres combined with glancing angle deposition and nanoscale assembly of block copolymers, to induce the formation of uniform nanospirals with diverse size, handedness, orientation, and winding number. Finally, finite-difference time-domain simulation results show linear dichroism and electric field intensity enhancement effects of these nanospirals, which are highly dependent on the winding number of the spirals, indicating the importance of precise control of the structural parameters.

Interfacial Energy-Controlled Top Coats for Gyroid/Cylinder Phase Transitions of Polystyrene-block-polydimethylsiloxane Block Copolymer Thin Films

Block copolymers (BCPs) with a high Flory-Huggins interaction parameter (χ) can form well-defined sub-10 nm periodic structures and can be used as a template for fabrication of various functional nanostructures. However, the large difference of surface energy between the blocks commonly found in high-χ BCPs makes it challenging to stabilize a useful gyroid morphology in thin film form. Here, we used an interfacial-energy-tailored top-coat on a blended film of a polystyrene-block-polydimethylsiloxane (PS-b-PDMS) BCP and a low-molecular-weight PDMS homopolymer with a hydrophilic end functional group. The top coat consisted of a random mixture of 40% hydrolyzed poly(vinyl acetate)-random-poly(vinly alcohol) (PVA-r-PVAc, PVA40) and PVAc homopolymer. At the optimized top-coat composition, gyroid nanostructures with sub-10 nm strut width were achieved down to ∼125 nm film thickness, which is only 3 times the lattice parameter of the gyroid structure. This is in marked contrast with a mixed morphology of gyroid and cylinders obtained for other compositions of the top coat. Self-consistent field theoretic simulations were used to understand the effect of the interfacial energy between the top coat and BCP/homopolymer blends on the phase transition behavior of the BCP/homopolymer films.

In Situ Nanolithography with Sub-10 nm Resolution Realized by Thermally Assisted Spin-Casting of a Self-Assembling Polymer

In situ nanolithography is realized based on warm spin-casting of block copolymer solutions. This advancement is based on Si-containing block copolymers with an appropriate thermodynamic driving force for spontaneous phase-separation combined with the thermal assistance provided by slight temperature elevations during the spin-casting. Sub-10 nm half-pitch nanoscale patterns are produced within 30 s without a separate annealing process.

Free energy landscape and localization of nanoparticles at block copolymer model defects

Nanoparticle localization in block copolymer model defects is studied using self-consistent field theory simulations. In particular we study the nanoparticle free energy landscape for three different model defects: X, T, Y shape defects. Our results indicate that nanoparticles can be strongly bound to certain locations in these defects. The symmetry of the defects affects in a non-trivial fashion the "stiffness of the trap", with the X shape defect displaying the deepest energy well. The T and Y defects exhibit orientations along which the potential energy well is rather shallow. Furthermore, we find that the free energy well is tunable by the size of the nanoparticles. Our results help to explain recent experimental observations in block copolymer templated assembly of nanoparticles. Furthermore, they may open new avenues to assemble arbitrary heterogeneous patterns with precise nanoparticle positions by carefully controlling the morphology of a block copolymer system by using directed self-assembly techniques.

Host-guest self-assembly in block copolymer blends

Ultrafine, uniform nanostructures with excellent functionalities can be formed by self-assembly of block copolymer (BCP) thin films. However, extension of their geometric variability is not straightforward due to their limited thin film morphologies. Here, we report that unusual and spontaneous positioning between host and guest BCP microdomains, even in the absence of H-bond linkages, can create hybridized morphologies that cannot be formed from a neat BCP. Our self-consistent field theory (SCFT) simulation results theoretically support that the precise registration of a spherical BCP microdomain (guest, B-b-C) at the center of a perforated lamellar BCP nanostructure (host, A-b-B) can energetically stabilize the blended morphology. As an exemplary application of the hybrid nanotemplate, a nanoring-type Ge2Sb2Te5 (GST) phase-change memory device with an extremely low switching current is demonstrated. These results suggest the possibility of a new pathway to construct more diverse and complex nanostructures using controlled blending of various BCPs.