Attraction of Nanoparticles to Tilt Grain Boundaries in Block Copolymers

Equilibrium Field Theoretic Study of Nanoparticle Interactions in Diblock Copolymer Melts

Block copolymer matrices are often used to control nanoparticle (NP) dispersion behavior, but the effects of diblock domain interfaces on particle-particle interactions have not been well characterized. In this paper, polymer field theoretic simulations are used to quantify interactions between both bare and grafted spherical NPs in microphase-separated A-B diblock copolymers. It is shown that for bare NPs that have an athermal interaction with and a diameter similar to the B domain, the presence of an A-B interface leads to an effective interaction between the particles with multiple minima separated by a free energy barrier. It is further shown that these effects primarily result from chain stretching and compression near the A-B interface induced by particle-particle interactions as opposed to increases in A-B contact at the interfaces. Grafted chains largely prevent these effects and reduce particle-particle interaction strength. When confined by diblock domain interfaces, grafted chains have a reduced extension compared to what is expected for de-wetted brush chains, as commonly described in homopolymer results. Finally, these studies indicate a new route toward linking spherical NPs in a controlled fashion, allowing for tunable plasmonic properties in the case of metallic NPs.

Customizing topographical templates for aperiodic nanostructures of block copolymers via inverse design

The limited complexity of self-assembled nanostructures of block copolymers seriously impedes their potential utility in the semiconductor industry. Therefore, the customizability of complex nanostructures has been a long-standing goal for the utilization of directed self-assembly in nanolithography. Herein, we integrated an advanced inverse design algorithm with a well-developed theoretical model to deduce inverse solutions of topographical templates to direct the self-assembly of block copolymers into reproducible target structures. The deduced templates were optimized by finely tuning the input parameters of the inverse design algorithm and through symmetric operation as well as nanopost elimination. More importantly, our developed algorithm has the capability to search inverse solutions of topographical templates for aperiodic nanostructures over exceptionally large areas. These results reveal design rules for guiding templates for the device-oriented nanostructures of block copolymers with prospective applications in nanolithography.

Field-Theoretic Simulations of the Distribution of Nanorods in Diblock Copolymer Thin Films

Using block copolymer microphases to guide the self-assembly of nanorods in thin films can give rise to polymeric materials with unique optical, thermal, and mechanical properties beyond those found in neat block copolymers. Often the design and manufacture of these materials require exquisite control of the nanorod distribution, which is experimentally challenging due to the large parameter space spanned by this class of materials. Simulation approaches, on the other hand, can access the thermodynamics that contribute to the nanorod distribution and hence offer valuable guidance toward the design and manufacture of the materials. In this work, we employ complex Langevin field-theoretic simulations to examine the thermodynamic forces that govern the assembly of nanorods in thin films of block copolymers with a particular focus on vertically oriented cylindrical and lamellar domains. Our simulations show that the nanorod geometry, the substrate selectivity for the distinct blocks of the copolymer, and the film thickness all play important roles in engineering both the nanorod orientation and spatial distribution in diblock copolymer thin films. In addition, we employ thermodynamic integration to examine how the nanorods alter the stability of vertical and horizontal domains in thin films, where we find that the tendency of the nanorods to stabilize a vertical orientation depends on both the film thickness and the nanorod concentration.

Solvent vapor annealing in block copolymer nanocomposite films: a dynamic mean field approach

Polymer nanocomposites are an important class of materials due to the nanoparticles' ability to impart functionality not commonly found in a polymer matrix, such as electrical conductivity or tunable optical properties. While the equilibrium properties of polymer nanocomposites can be treated using numerous theoretical and simulation approaches, in experiments the effects of processing and kinetic traps are significant and thus critical for understanding the structure and the functionality of polymer nanocomposites. However, simulation methods that can efficiently predict kinetically trapped and metastable structures of polymer nanocomposites are currently not common. This is particularly important in inhomogeneous polymers such as block copolymers, where techniques such as solvent vapor annealing are commonly employed to improve the long-range order. In this work, we introduce a dynamic mean field theory that is capable of predicting the result of processing the structure of polymer nanocomposites, and we demonstrate that our method accurately predicts the equilibrium properties of a model system more efficiently than a particle-based model. We subsequently use our method to predict the structure of block copolymer thin films with grafted nanoparticles after solvent annealing, where we find that the final distribution of the grafted nanoparticles can be controlled by varying the solvent evaporation rate. The extent to which the solvent evaporation rate can affect the final nanoparticle distribution in the film depends on the grafting density and the length of the grafted chains. Furthermore, the effects of the solvent evaporation rate can be anticipated from the equilibrium nanoparticle distribution in the swollen and dry states.

Recent Developments in Fully Fluctuating Field-Theoretic Simulations of Polymer Melts and Solutions

We review the latest developments in computational methods for direct simulation of fully fluctuating field theories of polymeric assemblies. In this context, we describe a newly developed theoretical and computational framework for accurately computing fluctuation-corrected phase diagrams of mesostructured polymer systems and report the first such complete phase diagram for a diblock copolymer melt. The method is based on complex Langevin sampling of a UV regularized field-theoretic model, with Helmholtz free energies computed using thermodynamic integration. UV regularization ensures that the free energies do not have an arbitrary reference; they can be compared between incommensurate phases, permitting for the first time the computation of order-order transitions with fluctuation corrections. We further demonstrate that computed free energies are accurate in the disordered phase by comparison to perturbation theory on the one-loop level. Importantly, we note that our method uses no uncontrolled approximations beyond the initial definition of a coarse-grained molecular model for the polymer melt or solution. The method can be applied straightforwardly to melts and solutions containing multiple species with diverse polymer architectures.