Pattern multiplication by template-guided self-assembly of cylinder-forming copolymers: Field-theoretic and particle-based simulations

Template Design for Complex Block Copolymer Patterns Using a Machine Learning Method

This study represents the first attempt to address the inverse design problem of the guiding template for directed self-assembly (DSA) patterns using solely machine learning methods. By formulating the problem as a multi-label classification task, the study shows that it is possible to predict templates without requiring any forward simulations. A series of neural network (NN) models, ranging from the basic two-layer convolutional neural network (CNN) to the large NN models (32-layer CNN with 8 residual blocks), have been trained using simulated pattern samples generated by thousands of self-consistent field theory (SCFT) calculations; a number of augmentation techniques, especially suitable for predicting morphologies, have been also proposed to enhance the performance of the NN model. The exact match accuracy of the model in predicting the template of simulated patterns was significantly improved from 59.8% for the baseline model to 97.1% for the best model of this study. The best model also demonstrates an excellent generalization ability in predicting the template for human-designed DSA patterns, while the simplest baseline model is ineffective in this task.

Direct calculation of the functional inverse of realistic interatomic potentials in field-theoretic simulations

We discuss the functional inverse problem in field-theoretic simulations for realistic pairwise potentials such as the Morse potential (widely used in particle simulations as an alternative to the 12-6 Lennard-Jones one), and we propose the following two solutions: (a) a numerical one based on direct inversion on a regular grid or deconvolution and (b) an analytical one by expressing attractive and repulsive contributions to the Morse potential as higher-order derivatives of the Dirac delta function; the resulting system of ordinary differential equations in the saddle-point approximation is solved numerically with appropriate model-consistent boundary conditions using a Newton-Raphson method. For the first time, exponential-like, physically realistic pair interactions are analytically treated and incorporated into a field-theoretic framework. The advantages and disadvantages of the two approaches are discussed in detail in connection with numerical findings from test simulations for the radial distribution function of a monatomic fluid at realistic densities providing direct evidence for the capability of the analytical method to resolve structural features down to the Angstrom scale.

Optimizing topographical templates for directed self-assembly of block copolymers via inverse design simulations

An inverse design algorithm has been developed that predicts the necessary topographical template needed to direct the self-assembly of a diblock copolymer to produce a given complex target structure. The approach is optimized by varying the number of topographical posts, post size, and block copolymer volume fraction to yield a template solution that generates the target structure in a reproducible manner. The inverse algorithm is implemented computationally to predict post arrangements that will template two different target structures and the predicted templates are tested experimentally with a polydimethylsiloxane-b-polystyrene block copolymer. Simulated and experimental results show overall very good agreement despite the complexity of the patterns. The templates determined from the model can be used in developing simpler design rules for block copolymer directed self-assembly.

Inverse Design of Topographical Templates for Directed Self-Assembly of Block Copolymers

A computational inverse design algorithm is presented that predicts the necessary topographical template to direct the self-assembly of a diblock copolymer thin film into a desired complex morphology. This topographical template is determined from the spatial configuration of a template that results in an energy minimum for the system. Degenerate solutions are accounted for by performing multiple simulations with random starting configurations of the topographical template and making a statistically weighted template that is tested using self-consistent field theory simulations. The final template is, thus, the inverse design solution of the desired block copolymer morphology. The results also yield nonintuitive post-configuration design principles.

Surface induced self-organization of comb-like macromolecules

We present a review of the theoretical and experimental evidence for the peculiar properties of comb copolymers, demonstrating the uniqueness of these materials among other polymer architectures. These special properties include an increase in stiffness upon increasing side-chain length, the spontaneous curvature of adsorbed combs, rod-globule transition, and specific intramolecular self-assembly. We also propose a theory of chemically heterogeneous surface nanopattern formation in ultrathin films of comblike macromolecules containing two different types (A and B) of incompatible side chains (so-called binary combs). Side chains of the binary combs are strongly adsorbed on a surface and segregated with respect to the backbone. The thickness of surface domains formed by the B side chains is controlled by the interaction with the substrate. We predict the stability of direct and inverse disc-, torus- and stripelike nanostructures. Phase diagrams of the film are constructed.