Molecular theory of the tilting transition and computer simulations of the tilted lamellar phase of rod-coil diblock copolymers

General weak segregation theory with an application to monodisperse semi-flexible diblock copolymers

A general theory has been developed for a polydisperse semi-flexible multi-block copolymer melt. Using the Bawendi-Freed approach to model semi-flexible chains, an expression for the Landau free energy is derived in the weak segregation regime, which includes density and orientation order-parameters. The orientation order-parameter is described in the smectic phase and in more complicated structures, such as the hexagonal phase. The Landau free energy contains contributions of two kinds of interactions. The first kind is the Flory-Huggins interaction, which describes the incompatibility of chemically different blocks and may induce microphase separation. The second kind is the Maier-Saupe interaction, which may induce nematic ordering. In the framework of the weak segregation limit, the Landau theory allows us to predict phase structures in the melt as a function of the composition, persistence length, and the strength of the Flory-Huggins and Maier-Saupe interaction. The general theory is applied to a simple system of monodisperse semi-flexible diblock copolymers. In several phase diagrams, a number of possible phase structures are predicted, such as the bcc, hexagonal, smectic-A, smectic-C, and nematic phase. The influence of the Maier-Saupe interaction on the microphase structure is thoroughly discussed.

Liquid-Crystal Ordering and Microphase Separation in the Lamellar Phase of Rod-Coil-Rod Triblock Copolymers. Molecular Theory and Computer Simulations

A molecular model of the orientationally ordered lamellar phase exhibited by asymmetric rod-coil-rod triblock copolymers has been developed using the density-functional approach and generalizing the molecular-statistical theory of rod-coil diblock copolymers. An approximate expression for the free energy of the lamellar phase has been obtained in terms of the direct correlation functions of the system, the Flory-Huggins parameter and the Maier-Saupe orientational interaction potential between rods. A detailed derivation of several rod-rod and rod-coil density-density correlation functions required to evaluate the free energy is presented. The orientational and translational order parameters of rod and coil segments depending on the temperature and triblock asymmetry have been calculated numerically by direct minimization of the free energy. Different structure and ordering of the lamellar phase at high and low values of the triblock asymmetry is revealed and analyzed in detail. Asymmetric rod-coil-rod triblock copolymers have been simulated using the method of dissipative particle dynamics in the broad range of the Flory-Huggins parameter and for several values of the triblock asymmetry. It has been found that the lamellar phase appears to be the most stable one at strong segregation. The density distribution of the coil segments and the segments of the two different rods have been determined for different values of the segregation strength. The simulations confirm the existence of a weakly ordered lamellar phase predicted by the density-functional theory, in which the short rods separate from the long ones and are characterized by weak positional ordering.

Different Mechanisms of Translational Symmetry Breaking in Liquid-Crystal Coil–Rod–Coil Triblock Copolymers

A molecular-statistical theory of coil-rod–coil triblock copolymers with orientationally ordered rod-like fragments has been developed using the density functional approach. An explicit expression for the free energy has been obtained in terms of the direct correlation functions of the reference disordered phase, the Flory–Huggins parameter and the potential of anisotropic interaction between rigid rods. The theory has been used to derive several phase diagrams and to calculate numerically orientational and translational order parameter profiles for different polymer architecture as a function of the Flory–Huggins parameter, which specifies the short-range repulsion and as functions of temperature. In triblock copolymers, the nematic–lamellar transition is accompanied by the translational symmetry breaking, which can be caused by two different microscopic mechanisms. The first mechanism resembles a low dimensional crystallization and is typical for conventional smectic liquid crystals. The second mechanism is related to the repulsion between rod and coil segments and is typical for block copolymers. Both mechanisms are analyzed in detail as well as the effects of temperature, coil fraction and the triblock asymmetry on the transition into the lamellar phase.

Microphase separation in helix-coil block copolymer melts: computer simulation

By means of molecular dynamics simulation, the process of the microphase separation in the melts of diblock helix-coil copolymers comprising a flexible and a helical block was studied. The resulting microstructures were examined, and the spatial distribution of the blocks and molecular packing were investigated. The phase diagram was built in terms of the fraction of the helical block and the incompatibility parameter of the blocks. The comparison of the diagrams for helix-coil and the classic coil-coil copolymer blends was carried out. It was shown that the total region where the ordering into distinctive microstructures takes place is similar for both diagrams. But for the helix-coil copolymers the area of the cylinders splits into the region of those with circular and elliptical cross-sections; the bicontinuous phase area is much wider; in the lamellar phases, the helical blocks were oriented precisely perpendicular to the lamellar interface, forming a cohesive interlocked structure of densely packed helices.

Bending Behavior and Directed Self-Assembly of Rod-Coil Block Copolymers

The formation of zigzags, chevrons, Y-junctions, and line segments is demonstrated in thin films formed from cylindrical morphology silicon-containing conformationally asymmetric rod-coil diblock copolymers and triblock terpolymers under solvent annealing. Directed self-assembly of the block copolymers within trenches yields well-ordered cylindrical microdomains oriented either parallel or transverse to the sidewalls depending on the chemical functionalization of the sidewalls, and the location and structure of concentric bends in the cylinders is determined by the shape of the trenches. The innate etching contrast, the spontaneous sharp bends and junctions, and the range of demonstrated periodicity and line/space ratios make these conformationally asymmetric rod-coil polymers attractive for nanoscale pattern generation.