A mean-field phase diagram for conformationally symmetric diblock melts using the standard Gaussian polymer model is presented. Our calculation, which traverses the weak- to strong-segregation regimes, is free of traditional approximations. Regions of stability are determined for disordered (DIS) melts and for ordered structures including lamellae (L), hexagonally packed cylinders (H), body-centered cubic spheres (QIm3m), close-packed spheres (CPS), and the bicontinuous cubic network with Ia3d symmetry (QIa3d). The CPS phase exists in narrow regions along the order−disorder transition for χN ≥ 17.67. Results suggest that the QIa3d phase is not stable above χN ∼ 60. Along the L/QIa3d phase boundaries, a hexagonally perforated lamellar (HPL) phase is found to be nearly stable. Our results for the bicontinuous Pn3m cubic (QPn3m) phase, known as the OBDD, indicate that it is an unstable structure in diblock melts. Earlier approximation schemes used to examine mean-field behavior are reviewed, and compa...

Unifying Weak- and Strong-Segregation Block Copolymer Theories

Enabling nanotechnology with self assembled block copolymer patterns

Directing the self-assembly of block copolymers

The nanometer-scale architectures in thin films of self-assembling block copolymers have inspired a variety of new applications. For example, the uniformly sized and shaped nanodomains formed in the films have been used for nanolithography, nanoparticle synthesis, and high-density information storage media. Imperative to all of these applications, however, is a high degree of control over orientation of the nanodomains relative to the surface of the film as well as control over order in the plane of the film. Induced fields including electric, shear, and surface fields have been demonstrated to influence orientation. Both heteroepitaxy and graphoepitaxy can induce positional order on the nanodomains in the plane of the film. This article will briefly review a variety of mechanisms for gaining control over block copolymer order as well as many of the applications of these materials. Particular attention is paid to the potential of perfecting long-range two-dimensional order over a broader range of length scales and the extension of these concepts to functional materials and more complex architectures.

/pdf/patterning-with-block-copolymer-thin-films-5gldelhkf5.pdf

Patterning with block copolymer thin films

https://www.cell.com/biophysj/pdf/S0006-3495(01)75737-2.pdf

Mesoscopic Simulation of Cell Membrane Damage, Morphology Change and Rupture by Nonionic Surfactants

Two intermediate phases have been observed upon heating an asymmetric poly(ethylenepropylene)-poly(ethylethylene) diblock copolymer between lamellar and hexagonal cylinder phases near the order-disorder transition. Phase transitions betwen ordered morphologies are indicated by the temperature dependence of the dynamic shear moduli, and SANS experiments are used to identify these structures as hexagonally modulated lamellae and layered hexagonal packed channels. The observed wavevectors associated with the interlayer scattering for these structures are incommensurate, leading to an a periodic structure in which the long range translational order of the layers is destroyed

Hexagonal mesophases between lamellae and cylinders in a diblock copolymer melt

Reciprocating shear is found to increase the isotropic-to-lamellar transition temperature in a symmetric diblock copolymer melt. The temperature at which the isotropic state becomes unstable rapidly approaches the ordering transition as the shear rate increases. Shear-induced ordering results in lamellae orientation with wave vectors directed normal to the shear and velocity gradient directions. These results are anticipated by a recent theory that accounts for the suppression of fluctuations by a symmetry breaking field in this class of weakly first-order phase transitions.

Shear-induced isotropic-to-lamellar transition.

Two poly(ethylenepropylene)–poly(ethylethylene) (PEP‐PEE) diblock copolymer melts, containing 25% and 83% by volume PEP, were investigated using small‐angle neutron scattering (SANS) and rheological measurements. The SANS measurements were performed with the aid of an in situ shearing device operated directly in the neutron beam. Each sample was observed to possess three equilibrium phases: two ordered phases at low temperature and a disordered phase at elevated temperatures. The low and high temperature ordered phases have been evaluated to be hexagonally packed (hex) cylinders and body centered cubic (bcc) spheres, respectively. Application of a large amplitude dynamic shear deformation to the hex phase leads to well‐aligned cylinders, with a specific crystallographic orientation relative to the shear plane. Upon heating through the cylinder‐to‐sphere transition, the bcc phase grows epitaxially, with the [111] direction coincident with the original cylinder axis, leading to a well‐defined twinned micros...

Epitaxial growth and shearing of the body centered cubic phase in diblock copolymer melts

Two distinct lamellae orientations have been identified by small-angle neutron scattering (SANS) in dynamically sheared poly(ethylene-propylene)-poly(ethylethylene) (PEP-pEE) diblock copolymer melts. Near the order-disorder transition temperature, T→T ODT , and at low shear frequencies, the lamellae arrange with unit normal perpendicular to the flow direction and parallel to the velocity gradient direction (parallel orientation). Higher frequency processing leads to lamellae with unit normal perpendicular to both the flow and velocity gradient directions (perpendicular orientation). The crossover from low to high frequency behavior occurs at ω≃τ -1 where τ is the relaxation time for local doamin deformations. At temperatures further from the ODT, T<<T ODT , the parallel orientation is obtained at all shearing frequencies. Based on dynamic and steady rheological measurements we propose two mechanisms to account for these results. The perpendicular orientation is proposed to arise from shear-induced disordering, followed by reordering in the perpendicular direction due to the effect of vorticity. Parallel lamellae are believed to be a manifestation of defect mediated stress relaxation. These findings are supported by additional experiments on various other shear-oriented polyolefin diblock copolymers

Lamellae orientation in dynamically sheared diblock copolymer melts

A poly(ethylenepropylene)-poly(ethylethylene) (PEP-PEE) diblock copolymer conctaining 65 vol% PEP was studied by SANS and rheological measurements. Four distinct phases were identified as a function of temperature: three ordered phase at low temperatures and a disordered phase at high temperatures. The order-disorder and disorder-order transitions were determined to be first-order.

Kurt A. Koppi

Papers

Hexagonal mesophases between lamellae and cylinders in a diblock copolymer melt

Shear-induced isotropic-to-lamellar transition.

Epitaxial growth and shearing of the body centered cubic phase in diblock copolymer melts

Lamellae orientation in dynamically sheared diblock copolymer melts

Multiple ordered phases in a block copolymer melt