Study of morphology and phase diagram of the H-shaped (AC)B(CA) ternary block copolymers using self-consistent field theory

By using a combinatorial screening method based on the self-consistent field theory (SCFT) for polymer systems, the micro-phase morphologies of the H-shaped (AC)B(CA) ternary block copolymer system are studied in three-dimensional (3D) space. By systematically varying the volume fractions of the components A, B, and C, six triangle phase diagrams of this H-shaped (AC)B(CA) ternary block copolymer system with equal interaction energies among the three components are constructed from the weaker segregation regime to the strong segregation regime, In this study, thirteen 3D micro-phase morphologies for this H-shaped ternary block copolymer system are identified to be stable and seven 3D microphase morphologies are found to be metastable.

Simulation Study of Aggregate Morphologies Formed by ABC Linear Triblock Copolymers in a Selective Solvent Through the Self-Consistent Field Theory

The effect of the hydrophobic properties of blocks B and C on the aggregate morphologies formed by ABC linear triblock copolymers in selective solvent was studied through the self-consistent field theory. Five typical micelles, such as core-shell-corona, hamburger-like, segmented-wormlike, were obtained by changing the hydrophobic properties of blocks B and C. The simulation results indicate that the shape and size of micelle are basically controlled by the hydrophobic degree of the middle block B, whereas the type of micelle is mainly determined by the hydrophobic degree of the end block C.

A self-consistent field theory study on the morphologies of linear ABCBA and H-shaped (AB)(2)C(BA)(2) block copolymers

By using a combinatorial screening method based on the self-consistent field theory, we investigate the equilibrium morphologies of linear ABCBA and H-shaped (AB)(2)C(BA)(2) block copolymers in two dimensions. The triangle phase diagrams of both block copolymers are constructed by systematically varying the volume fractions of blocks A, B, and C. In this study, the interaction energies between species A, B, and C are set to be equal. Four different equilibrium morphologies are identified, i.e., the lamellar phase (LAM), the hexagonal lattice phase (HEX), the core-shell hexagonal lattice phase (CSH), and the two interpenetrating tetragonal lattice phase (TET2). For the linear ABCBA block copolymer, the reflection symmetry is observed in the phase diagram except for some special grid points, and most of grid points are occupied by LAM morphology. However, for the H-shaped (AB)(2)C(BA)(2) block copolymer, most of the grid points in the triangle phase diagram are occupied by CSH morphology, which is ascribed to the different chain architectures of the two block copolymers. These results may help in the design of block copolymers with different microstructures.

Compression of polymer brushes: quantitative comparison of self-consistent field theory with experiment

The self-consistent field theory (SCFT) prediction for the compression force between two semi-dilute polymer brushes is compared to the benchmark experiments of Taunton et al. [Nature, 1988, 332, 712]. The comparison is done with previously established parameters, and without any fitting parameters whatsoever. The SCFT provides a significant quantitative improvement over the classical strong-stretching theory (SST), yielding excellent quantitative agreement with the experiment. Contrary to earlier suggestions, chain fluctuations cannot be ignored for normal experimental conditions. Although the analytical expressions of SST provide invaluable aids to understanding the qualitative behavior of polymeric brushes, the numerical SCFT is necessary in order to provide quantitatively accurate predictions.

Strong-segregation limit of the self-consistent field theory for diblock copolymer melts

The self-consistent field theory (SCFT) introduced by Helfand for diblock copolymer melts is expected to converge to the strong-segregation theory (SST) of Semenov in the asymptotic limit, $\chi N \rightarrow \infty$. However, past extrapolations of the lamellar/cylinder and cylinder/sphere phase boundaries, within the standard unit-cell approximation, have cast some doubts on whether or not this is actually true. Here we push the comparison further by extending the SCFT calculations to $\chi N = 512,000$, by accounting for exclusion zones in the coronae of the cylindrical and spherical unit cells, and by examining finite-segregation corrections to SST. In doing so, we provide the first compelling evidence that SCFT does indeed reduce to SST.

Self-consistent field theory for diblock copolymers grafted to a sphere

An efficient numerical self-consistent field theory (SCFT) algorithm is developed for treating structured polymers on spherical surfaces. The method solves the diffusion equations of SCFT with a pseudospectral approach that combines a spherical-harmonics expansion for the angular coordinates with a modified real-space Crank–Nicolson method for the radial direction. The self-consistent field equations are solved with Anderson-mixing iterations using dynamical parameters and an alignment procedure to prevent angular drift of the solution. A demonstration of the algorithm is provided for thin films of diblock copolymer grafted to the surface of a spherical core, in which the sequence of equilibrium morphologies is predicted as a function of diblock composition. The study reveals an array of interesting behaviors as the block copolymer pattern is forced to adapt to the finite surface area of the sphere.

A new efficient approach to the direct restricted active space self-consistent field method

An implicitly parallel method for integral-block driven restricted active space self-consistent field (RASSCF) algorithms is presented. The approach is based on a model space representation of the RAS active orbitals with an efficient expansion of the model subspaces. The applicability of the method is demonstrated with a RASSCF investigation of the first two excited states of indole

Accelerating self-consistent field convergence with the augmented Roothaan-Hall energy function.

Based on Pulay's direct inversion iterative subspace (DIIS) approach, we present a method to accelerate self-consistent field (SCF) convergence. In this method, the quadratic augmented Roothaan-Hall (ARH) energy function, proposed recently by Høst and co-workers [J. Chem. Phys. 129, 124106 (2008)], is used as the object of minimization for obtaining the linear coefficients of Fock matrices within DIIS. This differs from the traditional DIIS of Pulay, which uses an object function derived from the commutator of the density and Fock matrices. Our results show that the present algorithm, abbreviated ADIIS, is more robust and efficient than the energy-DIIS (EDIIS) approach. In particular, several examples demonstrate that the combination of ADIIS and DIIS ("ADIIS+DIIS") is highly reliable and efficient in accelerating SCF convergence.

Study of self-assembly of symmetric coil-rod-coil ABA-type triblock copolymers by self-consistent field lattice method

The self-assembly of symmetric coil-rod-coil ABA-type triblock copolymer melts is studied by applying self-consistent field lattice techniques in a three-dimensional space. The self-assembled ordered structures differ significantly with the variation of the volume fraction of the rod component, which include lamellar, wave lamellar, gyroid, perforated lamellar, cylindrical, and spherical-like phases. To understand the physical essence of these phases and the regimes of occurrence, we construct the phase diagram, which matches qualitatively with the existing experimental results. Compared with the coil-rod AB diblock copolymer, our results revealed that the interfacial grafting density of the separating rod and coil segments shows important influence on the self-assembly behaviors of symmetric coil-rod-coil ABA triblock copolymer melts. We found that the order-disorder transition point changes from f(rod)=0.5 for AB diblock copolymers to f(rod)=0.6 for ABA triblock copolymers. Our results also show that the spherical-like and cylindrical phases occupy most of the region in the phase diagram, and the lamellar phase is found stable only at the high volume fraction of the rod.

A novel self-consistent-field lattice model for block copolymers

We develop a self-consistent-field lattice model for block copolymers and propose a novel and general method to solve the self-consistent-field equations. The approach involves describing the polymer chains in a lattice and employing a two-stage relaxation procedure to evolve a system as rapidly as possible to a free-energy minimum. In order to test the validity of this approach, we use the method to study the microphases of rod-coil diblock copolymers. In addition to the lamellar and cylindrical morphologies, micellar, perforated lamellar, gyroid, and zigzag structures have been identified without any prior assumption of the microphase symmetry. Furthermore, this approach can also give the possible orientation of the rods in different structures.