Nanomachines, Nanomaterials, and Klm

by Eric Drexler on 2009/02/20

Toward Advanced Nanotechnology: Nanomaterials (5)

My previous post in this series, Nanostructures, Nanomaterials, and Lattice-Scaled Stiffness, explains why the lattice-scaled modulus, Klm, is an important figure of merit: For a set of machines made of different materials, but with similar structures (similar numbers and arrangements of lattice cells), the Klm parameter determines the energy required for a thermal fluctuation to cause an error when the critical distances are scaled by the lattice size. Error rates decline exponentially with increasing energy, and hence with increasing Klm.

Lattice-based scaling is appropriate both for internal machine motions (parts slipping, etc.) and for operations performed on external structures made of the same material — for example, when using a machine to direct the fabrication of machine parts. One might think that stiffer materials are always better, but this is mistaken: The size of the lattice cells matters, and more than one might expect. To review,

Klm = Ea3r2err,

where E = Young’s modulus, a = the lattice parameter (this is a simplification, since not all crystals have cubic symmetry), and r2err accounts for the ratio of the minimum error displacement to the lattice parameter; rerr = (1/2)1/2 is a common value.

The following graphic compares several materials by Young’s modulus and by the lattice-scaled modulus:

Materials compared by lattice-scaled stiffness vs. Young’s modulus
Young’s modulus and the lattice-scaled stiffness
for selected materials

Modulus and lattice geometry data from multiple sources. Klm values for “keratin” represent building blocks of protein (or other folded polymers) with a keratin-like Young’s modulus, showing the effect of differing block sizes.

All the materials shown above are found in nature (ignoring the thorium in cerianite, which is mostly cerium dioxide). All but one, diamond, can be synthesized in water, at atmospheric pressure, near room temperature. Pyrite (“fool’s gold”) is often a product of biomineralization, and bacteria can synthesize magnetite as nanocrystals of controlled size and shape. Polymeric blocks with mechanical properties comparable to keratin could consist of any of a wide range of engineered proteins or other foldamers, and as can be seen, the value of Klm shifts from worst to best with a factor of 3 increase in block size.

As we explore implementation pathways that lead toward advanced nanotechologies, it’s important to keep in mind that conditions for forming pyrite (and a range of other hard, inorganic materials) are compatible with soft-material technologies; these include macromolecular templates, crystal-growth promoters and inhibitors, and surface-binding molecules with diverse functions. Continued progress in engineering interfaces between macromolecules and inorganic crystals will be of critical importance.

Are soft and hard machines at odds with each other? Surely not. Soft biomolecules and hard inorganic solids have worked together since a bacterium first succeeded in gluing itself to a mineral grain, and perhaps long before, at the origin of life itself. There is no gap between soft and hard nanomachines: The technologies form a continuum, and working together, they can form a bridge.

Updated 25 Aug 2009: Corrected graph label and some ambiguous text.

{ 3 comments… read them below or add one }

Erin February 26, 2009 at 3:48 am UTC

Research scientists have discovered a material called WURTZITE BORON NITRIDE that is 18 times harder or stress resistant than diamond! Also a carbon material called Londeseite that is 58 times harder or more stress resistant than diamond, I am not so familiar with exactly how the stress tests go, but I find this very interesting. Here is the reference:

Eric Drexler February 26, 2009 at 11:43 pm UTC

That’s an interesting reference, but it doesn’t report the discovery of materials with huge improvements, just theoretical calculations that predict 18% and 58% improvements. These improvements are small enough to be plausible, but I’d want to see the basis for the calculations before deciding what to think of them. The materials are both hexagonal-symmetry relatives of more common cubic-symmetry forms; the local bonding is the same in the cubic and hexagonal forms. I wouldn’t expect differences in hardness to be very large.

Cubic and hexagonal boron nitride are interesting materials; they resemble the analogous carbon structures (diamond and lonsdaleite) in many ways, yet have quite different chemical behaviors. For example, B–N bonds of this kind (dative bonds) cleave asymmetrically rather than forming unstable radicals.

Erin February 27, 2009 at 4:46 am UTC

Thank you for this appreciated insight, Mr Drexler! Question about this: Would such materials be able to fit into the overall category of
“diamondoid” even if they do not contain carbon?

Some time back I was involved in a discussion about carbyne chains and a related material, cumulene, and the question that arose was this: Could we, using nanomechanisms, assemble stable macroscopic structures from carbyne rods, or not? The consensus seemed to be no, you could not have a stable macroscopic carbyne structure (say a fabric of woven carbyne strands) at room temperature, but, they have great utility in nanoscale mechanisms. Would you say this is basically correct?

One reason I bring this up has to do with this article I read some time ago:

From that article, are they claiming a new form of carbon that rivals even fullerene nanotubes when it comes to strength?

One material that greatly interested me was that H6 carbon metal (correct formula?) you mention in Nanosystems.

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