Within ordered poly(styrene-b-methyl methacrylate) (PSb-PMMA) block copolymer (BCP) lamellae, oriented nanoplates [gadolinium trifluoride doped with ytterbium and erbium, GdF 3 :Yb/Er (20/2 mol %)] grafted with polyethylene glycol assemble into aligned strings at small interparticle separations. Herein, we investigate the origin of these aligned assemblies using X-ray scattering, electron microscopy, and hybrid particle/self-consistent field theory simulations. From previous reports, the insertion of a nanoplate in a BCP microdomain is expected to perturb the polymer chains and produce a local domain bulge as the PS/PMMA interface distorts to optimize conformational entropy. While experimental techniques are unable to directly resolve this small distortion, the two-dimensional simulations of the equilibrium BCP nanocomposite structure clearly show bulge formation around the nanoplates. As a function of particle separation, the potential of mean force (PMF) calculation reveals a global minimum corresponding to an equilibrium interparticle spacing of 7.0 nm, which agrees well with a mean experimental value of 6.4 nm. Furthermore, the PMF calculation exhibits a small activation barrier due to the high curvature penalty between two nanoplates at a separation distance of 21.7 nm. Ultimately, nanoplate strings form to fulfill the criteria where the energy benefit of decreasing interfacial area and minimizing chain stretching outweighs the energy penalty associated with reducing the translational entropy affiliated with evenly distributing the nanoplates. The simulations also illustrate a narrow tolerance for orientation angles, supporting the high degree of nanoplate alignment observed experimentally. We anticipate that the ability to align and couple anisotropic nanoparticles in BCPs presents opportunities to create functional polymer nanocomposites with orientation-dependent properties.
In this paper, we announce the public release of a massively parallel, graphics processing unit (GPU)-accelerated software, which is the first to combine both coarse-grained particle simulations and field-theoretic simulations in one simulation package. MATILDA.FT (Mesoscale, Accelerated, Theoretically Informed, Langevin, Dissipative particle dynamics, and Field Theory) was designed from the ground-up to run on CUDA-enabled GPUs with Thrust library acceleration, enabling it to harness the possibility of massive parallelism to efficiently simulate systems on a mesoscopic scale. It has been used to model a variety of systems, from polymer solutions and nanoparticle-polymer interfaces to coarse-grained peptide models and liquid crystals. MATILDA.FT is written in CUDA/C++ and is object oriented, making its source-code easy to understand and extend. Here, we present an overview of the currently available features, and the logic of parallel algorithms and methods. We provide the necessary theoretical background and present examples of systems simulated using MATILDA.FT as the simulation engine. The source code, along with the documentation, additional tools, and examples, can be found on the GitHub MATILDA.FT repository.
Grafted nanoparticle polymer composites have been used to create a highly bespoke class of materials, with spherical nanoparticles serving as the gateway design into this class. Grafted nanoplates (nanoparticles where the radius is longer than the height of the particle) provide opportunities and pathways to control overall system properties through their anisotropic properties. Current research on addressing the challenges associated with assembly is quite limited and unexplored. Using hybrid particle/self-consistent field theory (hSCFT) simulations, we build upon our previous work examining polyethylene glycol (PEG) grafted nanoplates within a nearly symmetric (f ≈ 0.5) lamellar poly(styrene-b-methyl methacrylate) (PS-b-PMMA) block copolymer (BCP) matrix. We examine the interplay between the nanoplate graft length and matrix molecular weight and their effect on the potential of mean force (PMF). Ultimately, we discover that the location and depth of both the energetic well (local minimum) and the energetic barrier (local maxima) of the PMF, as well as the existence of the local maxima, are dependent on the relative width of the nanoplates to the lamellar domain, with the longer grafts experiencing deeper energetic wells and further interplate separation distances. The results are driven by the interfacial tension due to the local domain bulging effects caused by the insertion of the nanoplates into the lamellar system. With experimental separation distances of a PEG-grafted gadolinium trifluoride doped with ytterbium and erbium, GdF3:Yb/Er (20/2 mol %) nanoplates corroborate the correlation found in the simulations between larger matrix domains and a widening of the energetic well. Additionally, the average separation distance follows a trend similar to the hSCFT data. We anticipate these results to help in the development and design of anisotropic nanoparticles within BCPs to create nanocomposites tailored for specific applications and properties.
In this paper we announce the public release of a massively-parallel, GPU-accelerated software, which is the first to combine both coarse-grained molecular dynamics and field-theoretical simulations in one simulation package. MATILDA.FT (Mesoscale, Accelerated, Theoretically-Informed, Langevin, Dissipative particle dynamics, and Field Theory) was designed from the ground-up to run on CUDA-enabled GPUs, with the Thrust library acceleration, enabling it to harness the possibility of massive parallelism to efficiently simulate systems on a mesoscopic scale. MATILDA.FT is a versatile software, enabling the users to use either Langevin dynamics or Field Theory to model their systems -all within the same software. It has been used to model a variety of systems, from polymer solutions, and nanoparticle-polymer interfaces, to coarse-grained peptide models, and liquid crystals. MATILDA.FT is written in CUDA/C++ and is object oriented, making its source-code easy to understand and extend. The software comes with dedicated post-processing and analysis tools, as well as the detailed documentation and relevant examples. Below, we present an overview of currently available features. We explain in detail the logic of parallel algorithms and methods. We provide necessary theoretical background, and present examples of recent research projects which utilized MATILDA.FT as the simulation engine. We also demonstrate how the code can be easily extended, and present the plan for the future development. The source code, along with the documentation, additional tools and examples can be found on GitHub MATILDA.FT repository.
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