(89b) Parameterization of Coarse-Grained Models for Block Copolymers: Approaches to Simulating Real Polymer Systems

Block copolymers have received significant attention due to their ability to naturally self-assemble into a variety of complex nano- and micro-structured phases. The ability to form structure via thermodynamic driving forces rather than by requiring external manipulation has made them an interesting and potentially critically important material in a variety of applications including organic photovoltaics, semiconductors, optical coatings, and catalysts. In understanding and designing such block copolymer systems, polymer simulation techniques including self-consistent field theory (SCFT), Monte Carlo, and molecular dynamics methods have proven extremely useful. For example, coarse-grained models of block copolymers and the simulation of their microphase separation have provided valuable insight into the design and understanding of materials and processes for directed self-assembly (DSA) in the semiconductor lithography field. However, the majority of polymer models used in these simulation studies are relatively simple, which limits their utility and ability to represent real polymer systems. For example, many such studies have used the simple Flory-Huggins interaction parameter (χ) to describe the inter-block interactions. This approach fails to account for realistic polymer complexities such as asymmetry in block cohesive energy density. As a result, in many cases no attempt is even made to connect the modeling work to real polymer systems.

As the applications for block copolymers continue to progress and the need arises to utilize modeling and simulation methods to go beyond a qualitative understanding of phenomena to the design and simulation of real polymer systems, there is a critical need to develop models and methods for parameterizing them that can reproduce the behavior of real polymer systems. For example, while much has been learned about the DSA of block copolymers like poly(styrene-b-methyl methacrylate) from simulation studies utilizing the simplistic Flory-Huggins interaction model, the field is moving to higher χ polymers which possess differences in physiochemical properties such as block density and block cohesive energy density; unfortunately, such simple models fail to reproduce the proper behavior. While atomistically detailed molecular dynamics simulations provide an approach to more faithfully represent the important physiochemical behavior that would allow for the proper modeling of such systems, the general simulation size required to represent microphase-separated systems such as these block copolymers prohibits this approach in a practical sense due to the speed and memory limitations of current computational systems. Coarse-grained analogs instead offer a solution to permit simulation at the large length and time scales required, but this technique also requires the development of such coarse-grained models that can faithfully represent the important chemistry and physics of the real polymer systems of interest. In general, there is still no single widely accepted method for parameterizing such course-grained block copolymer models to reflect the atomic details and physical property behavior of a given specific polymer. As a result, in this work a systematic procedure to parameterize course-grained molecular dynamics models has been developed that utilizes data from a combination of experimental property measurements and detailed atomistic simulations. The resulting coarse-grained models include energetic parameters that go beyond the overly simplistic Flory-Huggins χ parameter to allow for the representation of polymers whose behavior is complicated by effects such as disparities in the cohesive energy density of the copolymer constituent blocks. This energetic interaction asymmetry between blocks is common among high-χ BCPs, and in particular it can explain some of the unique process behaviors such as the rotation of lamellae to be parallel to an interface and the resulting need for topcoat layers to prevent such rotation in DSA processes being explored for semiconductor device fabrication.

In this work, the methodology developed for coarse-graining and model parameterization has been applied to producing a coarse-grained model for the relatively high-χ poly(styrene-b-isoprene) system due to both: (1) the extensive body of available data on its phase behavior and other physiochemical properties and (2) the aforementioned block density and cohesive energy density differences in the PS-b-PI system. The ability of the coarse-grained model to reproduce important results such as the phase diagram for this system will be shown as one validation of this approach.