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A self-consistent field (SCF) theory and a Monte Carlo (MC) simulation technique have been developed for block copolymer systems. Calculations were carried out using both SCF theory (with a simple mean-field potential) and MC simulation for an AB diblock copolymer chain for a wide range of solvent conditions. Fairly good agreement between these two methods was found. For an ABA triblock copolymer,...
An efficient algorithm is presented for numerically evaluating a self-consistent field theoretic (SCFT) model of block copolymer structure. This algorithm is implemented on a distributed memory parallel cluster in order to solve the SCFT equations on large computational grids. Simulation results are presented for a two-component molten mixture of a symmetric ABA triblock copolymer with an A homopolymer...
The order to disorder transition of comb copolymers A m+1 B m is investigated by the self-consistent field theory. Although there are only two components in a molecule, the side chain number m affects the phase diagram largely due to the fact that the architecture of a comb copolymer is not invariant under the interchange of A- with B-monomers. With the increase of the side chain number,...
A two-gradient self-consistent-field theory using the discretisation scheme of Scheutjens and Fleer is applied to predict the structure in the lateral direction of the free surface of a microphase-separated compressible polymeric melt. A fluorinated block copolymer system is described in which parameters are chosen such that the fluorinated units preferentially segregate at the free surface. As soon...
Recasting a many-particle problem in a field-theoretic formalism is nowadays a well-established theoretical tool used by scientists across a wide spectrum of research areas, ranging from polymer physics to molecular electronic structure theory. It has shown to provide useful results in many complex situations, where the physics of the system involves many degrees of freedom and a multitude of different...
Numerical self-consistent field theory is used to study the structural characteristics of a polydisperse polymer brush. We consider the relevant case of a Schulz–Zimm distribution and find that even a small degree of polydispersity completely destroys the parabolic density profile. The first moment (average height) of the brush increases with polydispersity, while the average stretching in the brush...
The self-assembly of symmetric diblock copolymers confined films with embedded nanorods is investigated by the self-consistent field (SCF) theory. We obtain some phase diagrams as a function of film thickness H and nanorod diameter D. The increase in preferential nanorod diameter D can promote the formation of incomplete cylindrical and spherical structures near the film surfaces, and can also induce...
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...
The microstructures of lamellae-forming diblock copolymer melts confined in nanorod arrays are investigated using the real-space self-consistent field theory. The nanorod array leads to the incomplete confinement at each direction so that the confinement-dimension is fractional between zero and two. This incomplete confinement can yield a rich variety of mixture microstructures by varying its fractional...
Here we report the results of a three dimensional hybrid self-consistent field theoretic (HSCFT) model describing the equilibrium particle distribution of spherical nanoparticles within symmetric AB diblock copolymer melts. Holding the polymer composition and morphology fixed, we consider a comprehensive parameter space comprised of the Flory interaction parameter describing interactions between B...
Self-consistent field theory is used to make direct predictions for the maximum possible cell densities for model polymer foam systems without recourse to classical nucleation theory or activation barrier kinetic arguments. Maximum possible cell density predictions are also made subject to constraining the systems to have maximal possible internal interface and to have well formed bubbles (no deviation...
Using the continuum self-consistent field theory (SCFT), the adsorption of flexible homo-polymers onto the surfaces of two identical cylinders immersed in a neutral polymer solution is studied. The effects of various system parameters (the chain length, the radius of the cylinders, the number density of objects, the intensity of short-region field, etc.) on the bridging chain conformation and the...
We used three-dimensional self-consistent field theory to investigate the micellization behavior of A-b-(B-alt-C) n multiblock terpolymers in the presence of a solvent that is selective to the terminal A-block. In particular, we focused on the effects of the incompatibility parameter between B and C, χ BC , and the composition of the solvophilic A-block, f A , on the formation...
Thermodynamic upper bounds for polymer foam cell densities are predicted using compressible self-consistent field theory. It is found that the incompressible limit always gives the highest, and therefore ultimate, upper bound. Qualitative comparisons between the compressible and incompressible cases agree, indicating that low temperatures and high blowing agent content should be used to achieve high...
The synthesis via anionic polymerization of six linear triblock terpolymers with various sequences of blocks such as PS (polystyrene), PB [poly(butadiene)], PI [(poly(isoprene)] and PCHD [poly(1,3-cyclohexadiene)] is reported. The synthesis of the terpolymers was carried out by the use of anionic polymerization with high-vacuum techniques and sequential monomer addition. Molecular characterization...
The phase behavior of coil-comb copolymers A–(B m+1 C m ) (side chain number m = 1–5) is investigated by real-space self-consistent field theory (SCFT). Depending on the copolymer composition and architecture, eight two-dimensional ordered phases are observed, including two-color lamellae (LAM 2 ), three-color lamellae (LAM 3 ), hexagonal cylinders (HEX), core–shell...
The self-consistent field theory (SCFT) is employed to numerically study the scaling laws of brush height and the amount of counter-ions trapped inside a spherical polyelectrolyte (PE) brush immersed in a good solvent with no added salt ions. In particular, the curvature effect of the grafting substrate on the brush height and the amount of counter-ions trapped inside the PE brush is carefully examined...
We extended self-consistent field theory to study the phase behavior of supramolecular blends of diblock copolymers with hydrogen-bonding interactions. The hydrogen-bonding interactions are described by Yukawa potentials. The hydrogen-bonding donors and acceptors were modeled as two blocks smeared with opposite screened charges. Hierarchical microstructures such as parallel and perpendicular lamellae-in-lamellae...
A systematical calculation is performed to explore the equilibrium phase behaviors of linear-dendritic triblock copolymer AB(2g+1−2)C2g+1 (g is the generation number of the block B, and Gg is short for AB(2g+1−2)C2g+1) from G1 to G5 by using self-consistent field theory. Eight phases are found: two-colored lamellar phase, three-colored lamellar phase, hexagonal phase, core shell hexagonal phase, tetragonal...
The development of nanoscale morphologies for a molten compressible polymeric surfactant is investigated by using a recently formulated self-consistent field theory. A linear ABC block copolymer is taken as our model system that allows a disparity in the propensities for curved interfaces and in pressure responses of ij-pairs. The interplay of those features leads the copolymer to new morphologies...
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