PerspectiveMaterials Science

Recasting Metal Alloy Phases with Block Copolymers

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Science  15 Oct 2010:
Vol. 330, Issue 6002, pp. 333-334
DOI: 10.1126/science.1196698

Crystalline order develops through a balance between short-range attractive and repulsive interactions (1) that not only operate on atoms but work at the nanoscale on supramolecular structures (2). Spherical particles often pack together into simple, high-symmetry arrangements, but more complex topologically close-packed structures, such as the Frank-Kasper σ phase (3, 4) first seen in metal alloys, have also been observed (see the figure, panel A). Spherical supramolecular aggregates formed from polymers and monodisperse branched macromolecules (57) can be used to mimic atoms and explore how these phases arise. On page 349 of this issue, Lee et al. (8) show that linear block copolymers that form spherical aggregates through microphase separation can crystallize into a Frank-Kasper σ phase. Relative to metal alloys, the volume of its crystalline repeating unit, the unit cell, is six orders of magnitude greater (see the figure, panel C). The scaling up of atomic lattices by using spherical supramolecular aggregates is also of practical interest because such structures could be used as photonic materials (9), nanoreactors (5), or drug delivery vehicles (10).

Understanding how spherical supramolecular aggregates organize into crystals remains a challenging task. In the ideal case of incompressible “hard” spheres—which are a good model for metal atoms—the most stable structures correspond to the hexagonal close-packed (hcp) and face-centered cubic (fcc) periodic close-packing configurations shown in panel A of the figure. These structures maximize the packing of atoms and fill 74% of their unit cell volume (versus 68% for the body-centered cubic, or bcc, packing). The stability of the packing derives from large numbers of nearest neighbors interactions that decrease free energy.

Spherical aggregates formed by soft macromolecules, including block copolymers, should follow the same principle and predominantly self-organize into hcp, fcc, and bcc structures (6). However, compared to atoms, such aggregates are more compressible—they have intrinsic “softness”—which can be expected to create slight deviations from spherical symmetry that can favor other complex three-dimensional organizations. Such deviations are driven not only by minimization of the free energy of the overall crystal structure but also by changes within the aggregate (11) that are neglected in the simplistic “hard sphere” model.

Preferences in packing spheres into crystals.

(A) Close-packed spheres can group together to fill space in many different arrangements. (B) An electron density distribution shows the σ phase formed from soft macromolecules (7). The overlaid squares and triangles mark the unusual periodic packing within the alternating layers (planes z = 1/2 and z = 1/4) formed by spherical assemblies with five nearest neighbors. (C) The dependence of the molecular weight of the building block and unit cell volume for the σ phase illustrating the scaling-up principle in soft matter. The large unit cells seen by Lee et al. result from the large spherical aggregates formed by hundreds of individual polymers. Data were calculated for metal alloys from (4), for self-assembling dendrons and dendrimers from (13, 1619), and for block copolymers from (8).

One notable example in soft materials is the ubiquitous A15 cubic phase (see the figure, panel A) that self-organizes from spherical and oblate spherical (12) or polyhedral (11) supramolecular dendrimers, which are formed by monodisperse branched macromolecules resembling covalent or noncovalent bonded fractal structures. This cubic packing seems to replace (13) the fcc and bcc structures because of the peculiar internal structure of the supramolecular dendrimers that form it. They consist of a “hard” aromatic core surrounded by a “soft” aliphatic shell. This combination was shown theoretically to favor the A15 cubic packing that minimizes the surface free energy better than fcc and bcc structures (14) and to increase the filling of the unit cell volume to higher fractions, in the range of 76 to 83% (12). Remarkably, a few soft spherical aggregates self-assembled from dendrons (partial wedges of dendrimers), and dendrimers occasionally form unexpected quasiperiodic structures that have rotational symmetry but no translation symmetry (1517) and σ phases (1619). The rare occurrence of the σ phase in soft macromolecules is correlated with the formation of alternating layers populated by spherical assemblies exhibiting the atypical five first nearest neighbors within the layer (see the figure, panel B).

The study of first-order phase transitions driven by heating or cooling can also provide insight into the structural parameters that control the formation of these phases. Such control is essential to the next step of the scaling-up of structure seen in atomic and small-molecule crystals in soft matter. For example, the σ phase was consistently observed to form before the bcc phase upon heating (8, 19). In this first example of the σ phase formed by block copolymers, Lee et al. attribute this order to the slightly lower surface area per unit volume in the σ phase compared to the bcc phase, which can account for a lower enthalpy (8). However, the similarity of the A15 and σ phases eluded a definitive assessment of their thermal order. Nevertheless, self-assembling dendrons and dendrimers exhibiting these two close-packing of spheres consistently reverse their thermal sequence from σ to A15, to A15 to σ, respectively, illustrating that the macromolecular topology (7) also plays an important role in selecting the type of close packing in soft matter.

The discovery of a new equilibrium phase in block copolymers, which have been studied for more than half a century, is truly rare. Their remarkable finding of the thermodynamically stable σ phase hints that block copolymers might also form quasiperiodic phases (8, 1517) and opens the door to the fabrication of other complex supramolecular organizations from soft nanomaterials.

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