Monte Carlo Simulations of Nano-Confined Block Copolymers

Block copolymers consist of chemically distinct polymer chains (blocks) covalently bonded together. Unlike polymer blends exhibiting phase separation on a macroscopic scale, block copolymers spontaneously self-assemble into ordered microdomains on the length scale of tens of nanometers, a phenomenon known as microphase separation [1, 2]. Due to the uniformity and periodicity of these microdomains, block copolymers have great potential applications in nanotechnology (e.g., templates for nanolithography, nanowires, high-density storage devices, quantum dots, photonic crystals, nanostructured membranes, etc.) [3-5], where the size, shape and spatial arrangement of the microdomains (morphology) are utilized. Understanding, predicting and controlling the selfassembled morphology of block copolymers are therefore of paramount interest. For the simplest architecture of linear diblock copolymers AB, four morphologies have been determined to be thermodynamically stable in the bulk, depending on the temperature and the volume fractions of the two blocks: lamellae of alternating A-rich and B-rich layers, hexagonally packed cylinders of the minority component (A) in the matrix of the other component (B), A-spheres packed on a body-centered cubic lattice in the B-matrix, and bicontinuous gyroid phase [6,7]. For more complex molecular architectures such as linear triblock copolymers ABC, many other morphologies have been observed in experiments and their bulk phase behavior is not fully understood yet [2, 8]. In many applications, a solution of block copolymers is spin-coated on a supporting substrate (e.g., silicon wafer) to form a thin film of tens to hundreds of nanometers thick, and the copolymers microphase separate in the film upon solvent evaporation and/or annealing. Under such nano-confinement, the tendency to resemble the bulk morphology with its characteristic period L0, the surface-block interactions (surface preference) and the surface con- finement all have important effects on the self-assembled morphology of block copolymers, thereby making it radically different from its bulk counterpart. One can therefore use the confining surface(s) to generate much more complex and fascinating morphologies, desirable for a broad array of applications [3-5]. The influence of confinement on the microphase separation and morphology of block copolymers is also of fundamental interest in polymer science. The self-assembled morphology of block copolymers under nano-confinement has been extensively studied by experiments, Monte Carlo (MC) simulations and various theories in the past decade. MC simulations are relatively easy to implement, and can give the exact solution (apart from statistical errors, which are controllable) to the model system studied. In addition to the selfassembled morphology, one can also access molecular details such as chain conformations and segmental distributions in MC. In this chapter, we focus on three-dimensional (3D) MC simulations of confined block copolymers, and compare the simulation results with experiments and theories when available.