Prediction of Conformational and Mixing Properties of Polymers relevant to Lithographic Applications through Atomistic Simulations

Abstract

In Directed Self-Assembly (DSA) lithography, atomistic simulations can provide valuable information about the structure, thermodynamics, and dynamics of the polymer systems employed. Essential parameters, such as the density, the solubility parameter, the diffusivity and the chain dimensions of polymeric materials used in DSA can be estimated from atomistic simulations and fed as input to DSA coarse-grained simulations. Furthermore, the Flory-Huggins parameter, χ, is estimable from polymer blend simulations, allowing the identification of high-χ materials for use in DSA lithography. In this thesis we first describe the molecular dynamics (MD) simulations applied for equilibration of four pure oligomeric materials: polystyrene (PS), poly(methyl methacrylate) (PMMA), polylactic acid (PLA) and polydimethylsiloxane (PDMS) and estimation of the diffusivity, the longest relaxation time, and a variety of physical properties. Then, based on Flory-Huggins theory we present our predictions, via MD, for the Flory-Huggins interaction parameter, χ, of three atomistically generated oligomeric blends: PS/PMMA, PS/PLA, and PDMS/PLA. The development of a general methodology for predicting the Gibbs energy of mixing is also of great importance in many applications of polymer blends and block copolymers. For example, beginning from the Gibbs energy of mixing and applying Flory-Huggins theory one can estimate the well-known Flory-Huggins interaction parameter, χ, including its entropic component. The latter is key to any process involving self-organization of block copolymers, such as Directed Self-Assembly (DSA). The χ parameter is the most important input to coarse-grained simulations of DSA. Unfortunately, methods based on particle insertion or deletion of molecules are not practical for the calculation of the Gibbs energy of mixing in polymer blends. Kirkwood-Buff theory of solutions allows the estimation of thermodynamic properties which cannot be directly extracted from atomistic simulations, such as the Gibbs energy of mixing (ΔmixG). In our work we present a methodology, based on Kirkwood-Buff theory, which allows us to perform a full thermodynamic analysis of n-hexane/ethanol binary mixtures in the liquid state under two temperature-pressure conditions and at various mole fractions in order to calculate the Kirkwood-Buff (KB) integrals in the isothermal-isobaric (NpT) ensemble. Then we extract the activity coefficients, excess Gibbs energy, excess enthalpy, and excess entropy, and by comparing our results against predictions of vapor-liquid equilibria obtained in a previous simulation work using the same force field, as well as with experimental data, we find very good agreement. The Kuhn length is also a key parameter in many coarse-grained models and theories, a notable example being field theory of inhomogeneous polymers. In Directed Self Assembly (DSA) lithography of block copolymers, the Kuhn length, or, equivalently, the mean square end-to-end distance for given chain length, is a very important input parameter to single chain in mean field calculations of the ordered structures expected under given conditions and of the thermodynamics and the kinetics of defect formation and annihilation. We have developed a general methodology for predicting the chain dimensions of any polymer chain in the unperturbed state starting from its detailed atomistic structure. The methodology is based on performing Metropolis Monte Carlo (MC) simulation, leading to equilibration of the conformational distribution of a single unperturbed polymer chain, subject only to local interactions along its backbone. Based on our methodology we have predicted the characteristic ratios for a series of polymers against the corresponding values estimated from MC simulations and reported experimental values of the same polymers in the melt state. Τhe miscibility of various polymer blends is determined by the tacticity of the mixed chains. Furthermore, the effect of tacticity on polymer chain miscibility is also reflected in the different micro-phases in which block copolymers usually self-organize. Different tacticities can lead to the formation of different micro-phases such as lamellae, cylindrical, hexagonal etc. out of copolymers of the same composition. Therefore, tacticity of the blocks is a very important design parameter in block copolymer applications, such as Directed Self-Assembly (DSA) Lithography. Using our general methodology for predicting the chain dimensions of unperturbed polymer chains, we focus on tacticity effects on the conformations and more specifically on the unperturbed dimensions of single polypropylene (PP) homopolymer and both block and random poly(ethylene-propylene) copolymer chains. We find that tacticity has a significant effect on the stiffness of PP homopolymer. The characteristic ratio exhibits a non-monotonic dependence on the fraction of meso dyads along the PP chains, which results from two competing mechanisms, revealed by analysis of the torsional states of the PP chain backbones. A simple theoretical model is developed to describe the dependence of the stiffness of poly(ethylene-block-propylene) copolymer on its propylene content and on the tacticity of its PP block. Finally, the effect of both tacticity and propylene content on the stiffness of poly(ethylene-random-propylene) chains, used to model ethylene propylene monomer (EPM) materials, is found to be in very good qualitative agreement with available Rotational Isomeric State (RIS) model predictions.