New fast SCFT algorithm applied to binary diblock copolymer/homopolymer blends

We present an efficient strategy for mapping out the classical phase behavior of block copolymer systems using self-consistent field theory (SCFT). With our new algorithm, the complete solution of a classical block copolymer phase can be evaluated typically in a fraction of a second on a single-processor computer, even for highly segregated melts. This is accomplished by implementing the standard unit-cell approximation (UCA) for the cylindrical and spherical phases, and solving the resulting equations using a Bessel function expansion. Here the method is used to investigate blends of AB diblock copolymer and A homopolymer, concentrating on the situation where the two molecules are of similar size.

Improving polymeric microemulsions with block copolymer polydispersity

Recent experiments have demonstrated that block copolymers are capable of stabilizing immiscible homopolymer blends producing bicontinuous microemulsion. The stability of these polymeric alloys requires the copolymer to form flexible, nonattractive monolayers along the homopolymer interfaces. We predict that copolymer polydispersity can substantially and simultaneously improve the monolayers in both of these respects. Furthermore, polydispersity should provide similar improvements in systems, such as colloidal suspensions and polymer/clay composites, that utilize polymer brushes to suppress attractive interactions.

Effective interaction between monolayers of block copolymer compatiblizer in a polymer blend

The stability of ternary blends of two immiscible homopolymers and a block copolymer compatiblizer depends crucially on the effective interaction between the copolymermonolayers that form between the unlike homopolymer domains. Here, the interaction is calculated for blends involving A and B homopolymers of equal size with ABABdiblock copolymers of symmetric composition using both self-consistent field theory (SCFT) and strong-segregation theory (SST). If the homopolymers are larger than the copolymer molecules, an attractive interaction is predicted which would destroy the blend. This conclusion coupled with considerations regarding the elastic properties of the monolayer suggests that the optimum size of the homopolymer molecules is about 80% that of the copolymer molecule. A detailed examination of the theory demonstrates that the attraction results from the configurational entropy loss of the homopolymer molecules trapped between the copolymermonolayers. We conclude by suggesting how the monolayers can be altered in order to suppress this attraction and thus improve compatiblization.

Polydispersity-induced macrophase separation in diblock copolymer melts

The effect of A-block polydispersity on the phase behavior of AB diblock copolymer melts is examined using a complete self-consistent field theory treatment that allows for fractionation of the parent molecular-weight distribution. In addition to observing the established shift in phase boundaries, we find the emergence of significant two-phase coexistence regions causing, for instance, the disappearance of the complex phase window. Furthermore, we find evidence that polydispersity relieves packing frustration, which will reduce the tendency for long-range order.

Monte Carlo phase diagram for diblock copolymer melts

A partial phase diagram is constructed for diblock copolymer melts using lattice-based Monte Carlo simulations. This is done by locating the order-disorder transition (ODT) with the aid of a recently proposed order parameter and identifying the ordered phase over a wide range of copolymer compositions (0.2 <= f <= 0.8). Consistent with experiments, the disordered phase is found to exhibit direct first-order transitions to each of the ordered morphologies. This includes the spontaneous formation of a perforated-lamellar phase, which presumably forms in place of the gyroid morphology due to finite-size and/or nonequilibrium effects. Also included in our study is a detailed examination of disordered cylinder-forming (f=0.3) diblock copolymers, revealing a substantial degree of pretransitional chain stretching and short-range order that set in well before the ODT, as observed previously in analogous studies on lamellar-forming (f=0.5) molecules. (c) 2006 American Institute of Physics.

Converting the nanodomains of a diblock-copolymer thin film from spheres to cylinders with an external electric field

We investigate the ability of an applied electric field to convert the morphology of a diblock-copolymer thin film from a monolayer of spherical domains embedded in the matrix to cylindrical domains that penetrate through the matrix. As expected, the applied field increases the relative stability of cylindrical domains, while simultaneously reducing the energy barrier that impedes the transition to cylinders. The effectiveness of the field is enhanced by a large dielectric contrast between the two block-copolymer components, particularly when the low-dielectric contrast component forms the matrix. Furthermore, the energy barrier is minimized by selecting sphere-forming diblock copolymers that are as compositionally symmetric as possible. Our calculations, which are the most quantitatively reliable to date, are performed using a numerically precise spectral algorithm based on self-consistent-field theory supplemented with an exact treatment for linear dielectric materials.

Electric field alignment in thin films of cylinder-forming diblock copolymer

We investigate thin films of cylinder-forming diblock copolymer confined between electrically charged parallel plates, using self-consistent-field theory ( SCFT) combined with an exact treatment for linear dielectric materials. Our study focuses on the competition between the surface interactions, which tend to orient cylinder domains parallel to the plates, and the electric field, which favors a perpendicular orientation. The effect of the electric field on the relative stability of the competing morphologies is demonstrated with equilibrium phase diagrams, calculated with the aid of a weak-field approximation. As hoped, modest electric fields are shown to have a significant stabilizing effect on perpendicular cylinders, particularly for thicker films. Our improved SCFT-based treatment removes most of the approximations implemented by previous approaches, thereby managing to resolve outstanding qualitative inconsistencies among different approximation schemes.

Undulation instability in block-copolymer lamellae subjected to a perpendicular electric field

We examine the stability of lamellar stacks in the presence of an electric field, E-0, applied normal to the lamellae. Calculations are performed with self-consistent field theory (SCFT) supplemented by an exact treatment of the electrostatic energy for linear dielectric materials. The calculations identify a critical electric field, E-0*, beyond which the lamellar stack becomes unstable with respect to undulations. This E-0* rapidly decreases towards zero as the number of lamellae in the stack diverges. Our quantitative predictions for E-0* are consistent with previous experimental measurements by Xu and co-workers.