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Materials science

Continuity through dispersity

By making polymers whose central blocks have a range of lengths, materials have been prepared that contain separate, intermeshed domains extending throughout the material — a highly desirable structure.

Ideas about nanometre-scale self-assembly — the phenomenon in which nanoscale objects organize themselves into arrays — are commonly underpinned by two assumptions. The first is that the higher the degree of regularity the array has, the better. The second is that obtaining a high degree of regularity requires the assembling objects to be as monodisperse (identical in shape and size) as possible. But these assumptions have recently come under intense scrutiny in the case of self-assembling block copolymers. The molecules in these materials consist of long runs (blocks) made from different monomer types, which can separate into distinct nanoscale domains. Writing in the Journal of the American Chemical Society, Mahanthappa and colleagues1 report that molecules of 'ABA' triblock copolymers (in which A and B represent different blocks) robustly generate desirable self-assembled structures containing separate A and B domains when the middle blocks have a broad range of lengths.

For many applications, it is preferable for the A and B domains of a block copolymer to be bicontinuous — that is, to interweave and extend throughout the material. For example, in photovoltaic films used in solar cells, excitons (electron–hole pairs, where holes are quasiparticles formed by the absence of electrons) generated by photon absorption could rapidly diffuse to interfaces between bicontinuous A and B domains, thus allowing the charges to separate, find their way out of the film and so generate a current2,3. Or consider the separator membranes in batteries, which divide the anode from the cathode but provide a medium through which ions can pass. A bicontinuous material could provide both a soft, rubbery domain that would facilitate ion diffusion, and a hard, glassy domain that would maintain the membrane's mechanical integrity and stiffness4.

Unfortunately, the regular bicontinuous structures (such as the gyroid phase; Fig. 1a) that form in conventional, near-monodisperse copolymers consisting of only two types of block occupy frustratingly narrow slices of 'composition space' — if the fraction of material occupied by A blocks is expressed as a percentage, then the range of values for which regular bicontinuous domains can form is only about 3%. But Mahanthappa and colleagues1 report that an irregular bicontinuous structure5 can be obtained over a broader composition window of about 10%, simply by introducing substantial polydispersity (a range of polymer chain lengths) into an ABA triblock copolymer. Previous studies have shown that AB diblocks6 and BAB triblocks7 that have polydisperse B blocks do not form such a bicontinuous structure, so it seems that the key to success is for the centre block to be polydisperse.

Figure 1: Self-assembly of copolymers.

ABA triblock copolymer chains consist of two A blocks (blue) separated by a B block (red), where the A and B blocks are formed from different monomers. a, In this case, all blocks of the same type are the same length, and the blocks are long enough to be incompatible — the different types don't mix. At certain ratios of the lengths of A and B, the molecules instead self-assemble into a regular bicontinuous structure (known as a gyroid) containing separate, intermeshed domains of A and B that span the whole material. b, Here, all blocks of the same type are again the same length, but the blocks are short enough to mix with each other. No separate A or B domains form. c, Mahanthappa and colleagues1 report that when the B blocks of the polymer have a range of lengths, an irregular bicontinuous structure forms robustly — even though the A blocks are the same length as in b, and the average length of the B blocks is shorter than in b. (Image in a courtesy Daniel C. Fredrickson; image in c courtesy Andrew L. Schmitt.)

Mahanthappa and co-workers found that the irregular bicontinuous structure is not the only morphology that their ABA triblock copolymers can adopt. At other compositions (A:B ratios), they form well-ordered lamellae or cylinders, again despite the chain-length variation. But the bicontinuous structure is especially stable. To explain what this means in more detail, we need to consider the factors that affect the formation of such domain structures.

In any block copolymer, when the blocks become too short, they no longer separate into domains. Instead, they simply mix (Fig. 1b). The driving force for block segregation is parameterized as the product χN, where χ is the Flory interaction parameter (a measure of the strength of repulsive interactions between the monomers that make up A and B blocks, independent of block length) and N is the total degree of polymerization of the block copolymer (a measure of the copolymer's length). For monodisperse ABA triblock copolymers, the minimum value of χN for domain formation8 is close to 18. But in Mahanthappa and colleagues' triblocks, which have near-monodisperse endblocks and a polydisperse midblock, the minimum χN value required to form the disordered bicontinuous structure is only about 5, an enormous reduction. In practice, this means that even polymers that have fairly low molar masses — an average of 12 kilograms per mole for the authors' ABA triblocks, in which A was polystyrene and B was polybutadiene — are sufficient to generate the sought-after bicontinuous domain structure.

Near-monodisperse block copolymers are conventionally synthesized using one of several controlled polymerization mechanisms. In these syntheses, the block sequence is dictated simply by the order in which different monomers are charged into the reaction mixture; each monomer is allowed to polymerize fully, or excess unreacted monomer is removed, before the next monomer is added. If a particular mechanism cannot polymerize a given monomer to sufficiently high average molar mass and/or if it cannot yield a product that has a sufficiently narrow distribution of molar masses, then it is generally discarded as a route to the target polymer. But Mahanthappa and co-workers' findings show that neither a narrow distribution nor a particularly high molar mass is required to make bicontinuous structures. Instead, all that seems necessary is that the polydisperse B blocks should be tethered at a minimum of two points, as they are in ABA triblock copolymers.

Less clear at present is whether asymmetric polydispersity is also required — that is, whether the lengths of the A blocks must be narrowly distributed, as they are in Mahanthappa and colleagues' polymers. A narrow distribution of A-block lengths causes asymmetric block mixing, which in turn affects the compositions over which different phases (cylinders, bicontinuous structures and lamellae) form. For example, if some of the B blocks in a sample of an ABA triblock copolymer are short, such as those depicted at the top of Fig. 1c, then they will readily dissolve in the A domains. But if all the A blocks are essentially the same length, then relatively few of them will dissolve in B domains. As a consequence, the fraction of the volume of the material that consists of B-rich domains will differ substantially from what one would expect assuming complete separation of A and B into pure domains.

It remains to be seen how the mixing of A and B blocks in Mahanthappa and colleagues' polydisperse polymers affects the physical properties of the materials — such as the glass transition temperature, which is important both for diffusion of small molecules or ions through rubbery domains and for the mechanical integrity of glassy domains. Another question is whether both domains are fully continuous (sample-spanning) across the entire composition range for which the irregular bicontinuous structure forms. Follow-up studies investigating these issues will surely come quickly. In the meantime, we should add mid-block polydispersity to the toolbox of macromolecular architecture variations9 that allows the synthesis of polymers that have predictable self-assembled structures and useful properties.


  1. 1

    Widin, J. M., Schmitt, A. K., Schmitt, A. L., Im, K. H. & Mahanthappa, M. K. J. Am. Chem. Soc. (2012).

  2. 2

    Crossland, E. J. W. et al. Nano Lett. 9, 2807–2812 (2009).

    CAS  ADS  Article  Google Scholar 

  3. 3

    Ho, V. et al. J. Am. Chem. Soc. 133, 9270–9273 (2011).

    CAS  Article  Google Scholar 

  4. 4

    Singh, M. et al. Macromolecules 40, 4578–4585 (2007).

    CAS  ADS  Article  Google Scholar 

  5. 5

    Widin, J. M., Schmitt, A. K., Im, K., Schmitt, A. L. & Mahanthappa, M. K. Macromolecules 43, 7913–7915 (2010).

    CAS  Article  Google Scholar 

  6. 6

    Lynd, N. A., Meuler, A. J. & Hillmyer, M. A. Prog. Polym. Sci. 33, 875–893 (2008).

    CAS  Article  Google Scholar 

  7. 7

    Ruzette, A.-V. et al. Macromolecules 39, 5804–5814 (2006).

    CAS  ADS  Article  Google Scholar 

  8. 8

    Mayes, A. M. & Olvera de la Cruz, M. J. Chem. Phys. 91, 7228–7235 (1989).

    CAS  ADS  Article  Google Scholar 

  9. 9

    Matyjaszewski, K. Science 333, 1104–1105 (2011).

    CAS  ADS  Article  Google Scholar 

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Correspondence to Richard A Register.

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Register, R. Continuity through dispersity. Nature 483, 167–168 (2012).

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