Block copolymers are all around us, found in such products as upholstery foam, adhesive tape and asphalt additives. This class of macromolecules is produced by joining two or more chemically distinct polymer blocks, each a linear series of identical monomers, that may be thermodynamically incompatible (like oil and vinegar). Segregation of these blocks on the molecular scale (5–100 nm) can produce astonishingly complex nanostructures, such as the “knitting pattern” shown on the cover of this issue of PHYSICS TODAY. This striking pattern, discovered by Reimund Stadler and his coworkers, reflects a delicate free‐energy minimization that is common to all block copolymer materials.

Block Copolymers—Designer Soft Materials

The observation by transmission electron microscopy of six different stable aggregate morphologies is reported for the same family of highly asymmetric polystyrene-poly-(acrylic acid) block copolymers prepared in a low molecular weight solvent system. Four of the morphologies consist of spheres, rods, lamellae, and vesicles in aqueous solution, whereas the fifth consists of simple reverse micelle-like aggregates. The sixth consists of up to micrometer-size spheres in aqueous solution that have hydrophilic surfaces and are filled with the reverse micelle-like aggregates. In addition, a needle-like solid, which is highly birefringent, is obtained on drying of aqueous solutions of the spherical micelles. This range of morphologies is believed to be unprecedented for a block copolymer system.

https://science.sciencemag.org/content/sci/268/5218/1728.full.pdf

Multiple Morphologies of "Crew-Cut" Aggregates of Polystyrene-b-poly(acrylic acid) Block Copolymers.

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

Different polymers can be combined into a single material in many ways, which can lead to a wide range of phase behaviors that directly influence the associated physical properties and ultimate applications. Four factors control polymer-polymer phase behavior: choice of monomers, molecular architecture, composition, and molecular size. Current theories and experiments that deal with the equilibrium thermodynamics and non-equilibrium dynamics of polymer mixtures are described in terms of these experimentally accessible parameters. Two representative molecular architectures, binary linear homopolymer mixtures and diblock copolymers, exhibiting macrophase separation and microphase segregation, respectively, are examined in some detail. Although these model systems are fairly well understood, a myriad of mixing scenarios, with both existing and unrealized materials applications, remain unexplored at a fundamental level.

https://science.sciencemag.org/content/sci/251/4996/898.full.pdf

Polymer-polymer phase behavior.

Description du modele. Tendances generales et comparaison avec l'experience. Concentration micellaire critique

Theory of micelle formation in block copolymer-homopolymer blends

Using self-consistent mean field theory, we have investigated the effects of conformational asymmetry on the phase diagram of diblock copolymers, considering spherical, cylindrical and lamellar microphases. This asymmetry, which reflects the mismatch of the pure component densities and Kuhn statistical lengths for the two blocks, is characterized by a single additional parameter. We calculated one phase diagram for systems with asymmetry corresponding approximately to copolymers such as PS-b-PI or PS-b-PBD, and a second one for a system with high asymmetry. In addition to shifting the microphase boundaries, it opens up direct windows from the disordered phase to the lamellar and cylindrical phases on one side of the phase diagram

Self-consistent field theory of block copolymers with conformational asymmetry

Using self-consistent mean field theory, the phase behavior of diblock copolymers was examinedfrom the weak to the strong segregation regimes, considering spherical, cylindrical, and lamellar microphases. It was shown that the phase diagram depends on three quantities: χrc where rc is an effective degree of polymerization, the relative volume fractions of each block, and e= (ρ 0B b B 2 )/(ρ 0A b A 2 ) where ρ 0P and b p are the pure component density and Kuhn length for each block. The phase diagram, domain sizes and density profiles were calculated for e= 1.

Self-consistent mean field theory of the microphases of diblock copolymers

Calcul de l'energie libre de copolymeres bisequences dont l'un des blocs est cristallisable et l'autre amorphe

Theory of crystallizable block copolymer blends

Melange de copolymeres bisequences et d'homopolymeres ayant la meme composition chimique que l'une des sequences du copolymere

Mark D. Whitmore

Papers

Theory of micelle formation in block copolymer-homopolymer blends

Self-consistent field theory of block copolymers with conformational asymmetry

Self-consistent mean field theory of the microphases of diblock copolymers

Theory of crystallizable block copolymer blends

Theory of phase equilibria in block copolymer-homopolymer blends