Discovering ordered phases of block copolymers: new results from a generic Fourier-space approach

A generic Fourier-space approach to solve the self-consistent field theory of block copolymers is developed. This approach is based on the fact that, for any computational box with periodic boundary conditions, all spatially varying functions are spanned by the Fourier series determined by the size and shape of the box. The method reproduces all known diblock copolymer phases. The application of this method to a model "frustrated" triblock copolymer leads to a phase diagram with a number of new phases. Furthermore, the capability of the method to reproduce experimentally observed structures is demonstrated using the knitting pattern of triblock copolymers.     

Probing the two-stage transition upon crossing the glass transition of polystyrene by solid-state NMR

A two-stage transition upon crossing the glass transition of polystyrene with increasing temperature was precisely determined and interpreted by using solid-state nuclear magnetic resonance(SSNMR), ~1H-~1H dipolar couplings based double quantum-filtered(DQF) and dipolar filter(DF) experiments and ~(13)C chemical shift anisotropy(CSA) based centerband-only detection of exchange(CODEX) experiment are used to fully characterize the time scale of molecular motions during the glass transition. While differential scanning calorimetry(DSC) and CODEX experiment predicted the first stage of glass transiton, DQF and DF experiments provided the evidence for the second stage transition during which the time scale of molecular motions changed from very slow(t ms) to very fast(t μs). The first stage of glass transition begins with the occurrence of remarkable slow re-orientation motions of the polymer backbone segments and ends when the degree of slow motion reaches maximum. The onset and endpoint of the conventional calorimetric glass transition of polystyrene can be quantitatively determined at the molecular level by SSNMR. In the second stage, a subsequent dramatic transition associated with the melting of the glassy components was observed. In this stage liquid-like NMR signals appeared and rapidly increased in intensity after a characteristic temperature T_f(~1.1T_g). The signals associated with the glassy components completely disappeared at another characteristic temperature T_c(~1.2T_g).     

Simulated annealing study of morphological transitions of diblock copolymers in solution

The simulated annealing method was applied to study the self-assembling process of diblock copolymers in selective solvents for one block. The simulation results illustrated that the morphologies of the copolymer aggregates strongly depend on the interactions between the core-forming blocks and the solvents and on the length of the corona-forming blocks. Multiple morphological transitions were observed in one system. The transition sequence (disordered state-spherical micelles-short rodlike micelles-long rodlike micelles-onionlike aggregates) was observed for copolymers with increasing core-solvent interaction. Similar transitions were observed with the decrease of the length of the corona-forming blocks. The mechanisms of these transitions are investigated. The simulation results are compared with experiments and other simulations.     

The influence of volume fractions on the phase behaviors of linear A(BC)(n)BA' multiblock terpolymers

The phase behaviors of A(BC)(n)BA' linear multiblock terpolymers are investigated using the pseudo-spectral method of self-consistent field theory by varying the volume fractions of different blocks. The relative stability among the lamellae-in-lamellae structures with different BC internal layers is tuned by the volume fraction of the two long tails. A larger A volume fraction favors the formation of structures with fewer BC thin layers. When the volume fraction of A is increased further, a hierarchical cylinder phase can be formed because of the effect of the spontaneous curvature and vice versa. The separation between B and C significantly reduces the phase regime of the cylinder, especially for the case of small A volume fraction.     

Soft confinement-induced morphologies of diblock copolymers

The self-assembly of diblock copolymers under soft confinement is studied systematically using a simulated annealing method applied to a lattice model of polymers. The soft confinement is realized by the formation of polymer droplets in a poor solvent environment. Multiple sequences of soft confinement-induced copolymer aggregates with different shapes and self-assembled internal morphologies are predicted as functions of solvent-polymer interaction and the monomer concentration. It is discovered that the self-assembled internal morphology of the aggregates is largely controlled by a competition between the bulk morphology of the copolymer and the solvent-polymer interaction, and the shape of the aggregates can be non-spherical when the internal morphology is anisotropic and the solvent-polymer interaction is weak. These results demonstrate that droplets of diblock copolymers formed in poor solvents can be used as a model system to study the self-assembly of copolymers under soft confinement.     

A numerical method for the study of nucleation of ordered phases

A numerical approach based on the string method is developed to study nucleation of ordered phases in first-order phase transitions. Among other things, this method allows an efficient computation of the minimum energy path (MEP) during the nucleation process. The MEP provides information about the size, shape and free energy barrier of the critical nucleus. To improve the efficiency of the string method, a special initialization process is proposed. Constraints from physical models are treated using two methods, a generalized coordinates method and a projection method. Strategies for choosing the computational domain and defining the nucleus boundary are also introduced. The validity of our approach is illustrated by two nontrivial examples from soft condensed matter physics, namely the nematic–isotropic transition of liquid crystals and the ordered-to-ordered phase transition of diblock copolymers.     

Cylinder-gyroid-lamella transitions in diblock copolymer solutions: a simulated annealing study

The morphological transition of an asymmetric diblock copolymer [A3-b-B9] in A-selective solvents is investigated using a simulated annealing technique. The study was carried out at high copolymer concentrations. Phase-transitions among hexagonally packed cylinders (C), gyroid (G), and lamellae (L) are observed. The phase transition sequence, C-->G-->L, was obtained with decreasing copolymer concentration and/or increasing B-solvent interaction. The predicted phase-transition sequence is consistent with experiments of diblock copolymers with similar volume fractions in selective solvents of different selectivity. The morphological transitions were further analyzed in terms of the average contact numbers for A or B monomers with other molecules and the total surface area of the core or matrix in each structure. It is found that these quantities correlate with the structures, providing an understanding of the phase-transition mechanisms.     

Simulated annealing study of diblock copolymer thin films confined between two homogeneous surfaces.

Thin films of symmetric diblock copolymers confined between two parallel surfaces have been systematically investigated by means of simulated annealing on a simple cubic lattice. The study was carried out for systems with different film thicknesses and surface-polymer interactions. Very regular equilibrium morphologies of lamella are formed in almost all cases. The dependence of lamellar orientations, total energy, chain-conformation entropy, and free energy of the confined films on the film thickness and the strength of surface-polymer interactions has been studied systematically. The influence of packing frustration on morphology is observed and the mechanisms of lamellar orientations are investigated.     

Phase behavior of binary blends of diblock copolymer/homopolymer confined in spherical nanopores

Binary blends of a diblock copolymer (AB) and an incompatible homopolymer (C) confined in spherical cavities are studied using a simulated annealing technique. The phase behavior of the blends is examined for four typical cases, representing the different selectivity of the pore surface to the A, B, and C species. The internal morphology of the spherical polymeric particles is controlled by the homopolymer volume fraction, the degree of confinement, and the composition of the copolymer. Inside a particle, the homopolymers segregate to form one or, under some conditions, two domains; thus, the homopolymers may act as an additional controlling parameter of the shape and symmetry of the copolymer domain. A rich array of confinement-induced novel diblock copolymer morphologies is predicted. In particular, core-shell particles with the copolymers as the shell wrapping around a homopolymer core or a copolymer-homopolymer combined core and Janus-like particles with the copolymers and the homopolymers on different sides are obtained.