Science -- Your Future, Scotland's Future
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A nanogear
This snowflake is an end-on view of a slightly stylised nanometre-scale gear, with the ellipses representing individual atoms. A 'real' simulation of a nanogear assembly is shown opposite, taken from the NASA Nanotechnology Team video page, which includes many short films of running gears. (There are also some nice films of a benzene molecule running full tilt into a buckyball...)
A nanogear

On 29th December 1959, Physicist and Nobel Laureate Richard Feynman gave a talk at the annual meeting of the American Physical Society, called "There's Plenty of Room at the Bottom". (Click here for an online transcript.) It's generally accepted that Feynman's sparkling discussion of the problems and promise of miniaturisation was the starting point for the original definition of nanotechnology (or molecular manufacturing): the use of nanoscale machines to build complex products (including, of course, other nanomachines).

In recent years the term has increasingly been used to describe any nanoscale products, from thin coatings to tiny particles, and any tiny objects in general. Whole areas of materials-science, biotechnology and chemistry are labeled (and, of course, marketed) as nanotechnology. Public perceptions have also been both raised and alarmed, by inaccurate news stories and exaggerated claims.

Of course, true nano-scale mechanisms do exist, all around us. Cells and other biological processes operate at the multi-atom level, and the evolution of life has involved the 'solving' of many of the problems we face when dealing with the new ways materials behave at these distance scales. (Viscosity, magnetic and electrical differences, thermal and quantum effects, Van der Waals forces, and others.)

An interesting paragraph from the Wikipedia article on nanotechnology is below, summarising issues of safety:

An often cited worst-case scenario is the so-called "grey goo", a substance into which the surface objects of the earth might be transformed by amok-running, self-replicating nano-robots, a process which has been termed global ecophagy. Defenders point out that smaller objects are more susceptible to damage from radiation and heat (due to greater surface area-to-volume ratios): nanomachines would quickly fail when exposed to harsh climates. More realistic are criticisms that point to the potential toxicity of new classes of nanosubstances that could adversely affect the stability of cell walls or disturb the immune system when inhaled or digested [4] ( Objective risk assessment can profit from the bulk of experience with long-known microscopic materials like carbon soot or asbestos fibres.

Excellent starting points for web browsing are Ralph Merkle's Nanotechnology site, and Eric Drexler's Both have in-depth information on current issues, and extensive links to other pages.

The Nanomedicine Book Site has entire online copies of the first two volumes of work in the field, the second of which goes into detail on the potential toxicity of nanoscale compounds.

An origami snowflake
The Instruction Sheet for the Origami Snowflake
The snowflake opposite is folded from a single hexagonal sheet of paper. This technique of paper-folding is called origami (from the Japanese oru: to fold, and kami: paper).

Click on the image on the right for a snowflake instruction sheet. [Hint from Peter: when you come to crimp the final bits on each leg, the sheet makes it look as though these regions stick up out of the snowflake. (At least, it did to me, for about an hour's frustrating folding, until I ended up like the angry man in Chewin' the Fat.) In fact, as you can see from the photograph on the right, they're actually cavities.]

There's another, more complex, origami snowflake design, the PDF instructions file for which I discovered on the diagrams page of Joseph Wu's origami website. (It's well worth browsing through his site, especially the gallery.)

The purist form of origami involves using a single square sheet of paper (white on one side, and self-coloured on the other) with no cutting or extra colouring. Given those limitations, the number of models one can build is extraordinary.

Koch Snowflakes
Koch Snowflakes
Koch snowflakes are an example of a fractal curve, one which exhibits a variety of unusual properties. (For example, taken to its limit the snowflake has an infinite perimeter, yet surrounds a finite area.)

We have a page describing the mathematics behind the Koch snowflake, as well as giving information on other fractals, which you can get to by clicking on the image opposite, or here.

Graphite Crystals
A Graphite crystal
Layers of carbon atoms in graphite
This flake is an image of a graphite crystal. (See the page with the original here.)

The hexagonal nature of the crystal arises because graphite is a form of carbon which exists as a stack of 'sheets' of carbon atoms, each sheet having a hexagonal arrangement of atoms, as shown opposite. As the crystal grows, it adds carbon atoms to its growth faces, but in some cases, defects called screw dislocations in the crystal structure cause the atoms to be added, not in flat planes, but in a spiralling structure (a bit like adding extra steps to a spiral staircase). An animation showing the growth of a spiral is shown here. (You'll need the Flash plug-in for your browser, but there are static and SWF versions too.)

The crystal image was produced using differential interference contrast microscopy, a method by which differences in thickness or refractive index of a specimen can be enhanced, the colours in the image arising from interference effects. The result is as if the specimen is being lit from one side (in this case from top-right), and for this image lets us see the microtopography (the tiny surface bumps :-) of the growth spiral of the crystal.

The graphite image is used with the kind permission of Dr John Jaszczak of the Department of Physics at Michigan Technological University.

Minimal Honeycombs
A bee's hive honeycomb cell
This is part of the honeycomb from a beehive. (Click on the image to see the full picture.) The cells are used both for the storage of honey and for the developing larvae.

The hexagonal structure in the hive is a wonderful example of the ways in which minimum-material or energy solutions tend to evolve in nature: in this case the hexagonal lattice requires the minimum of wax to surround the largest area. Only triangles, squares and hexagons can be used to fill a space without gaps, but for a given circumference of material, the hexagon surrounds the largest area. (In terms of a single unit, of course, it's the circle that's best (as a polygonal limit), but they leave gaps when packed.)

There's an overarching property of physical systems: they tend to seek states of minimum energy. (A ball rolling in a saucer will end up at the base, where its potential energy is least, after it's lost its kinetic energy to sound and heat; a bubble forms a sphere, because the total strain energy of all the molecular links is least; molecules tend to pack in structures which exhibit overall minimum energy; and so on.)

In evolution, time and time again we see cases where minimum materials are used, which of course amounts to the same thing, since an organism has only a limited energy budget to move around, build internal structure, build offspring, acquire/construct food, or more generally interact with its environment. There's survival merit in making the best use of available materials, so it's no surprise that there's a tendency towards the most efficient organisms.

Incidentally, bees don't actually make hexagonal cells! If you film the construction of a honeycomb, you see that each bee makes a tubular structure; it's the presence of the surrounding cells that causes each cell to have a hexagonal shape. This is also the way in which we tend to group circular objects. (Imagine packing a lot of tins of cat food as close as possible on a table.) I'd argue that the 'choice' of hexagon is nothing of the sort: the evolutionary mechanisms operating here are to do with the way in which each bee decides where to build the next tube, and "as near as possible to another two" will result in the packing we see, given that the least time/material/energy spent on this task means more time/material/energy for others, and thus a fractionally better chance of survival. Complex systems out of simple rules...

A hexagonal arrangement of circles is another minimum energy form. As an example, take a couple of handfuls of circular cross-section pencils and put them on a shelf between two books, so you can see the ends. If you shake the bundle around, it'll have an overall tendency to end up in an arrangement where the centres of the pencils form a hexagonal matrix.

For some more examples of hexagonal packing in nature, have a look at the wonderful page Hexagons in a Packed World.

A molecular anaglyph of Benzene
The image opposite is a 3D red-green anaglyph of a benzene molecule, shown in the traditional ball-and-stick form: a ring of six carbon atoms linked to six outer hydrogen atoms.

The discovery of this structure is interesting, as it illustrates the ways in which inspiration can come from the oddest situations.

The German chemist Friedrich August Kekule, who proposed for the first time the existence of complex carbon molecular structures, also proposed a solution for the unusual properties of benzene, when it didn't at first seem to fit with the theory of long-chain carbon molecules. (There are other structures for a molecule with six carbons and hydrogens, but they aren't as stable (or common) as benzene.)

The following comes from Kekule's diary, describing his dream: "…. I was sitting writing on my textbook, but the work did not progress; my thoughts were elsewhere. I turned my chair to the fire and dozed. Again the atoms were jumbling before my eyes. This time the smaller groups kept modestly in the background. My mental eye, rendered more acute by the repeated visions of the kind, could now distinguish larger structures of manifold conformation; long rows sometimes more closely fitted together all twining and twisting in snake-like motion. But look! What was that? One of the snakes had seized hold of its own tail, and the form whirled mockingly before my eyes. As if by a flash of lightning I awoke...".

Benzene's Transform
The diffraction pattern of benzene molecules
When waves pass an object, they are diffracted: the path of the wave is disrupted by the object's shape (in particular the edges).

The degree of diffraction is related to the size of the object and the wavelength of the incident waves. Small water waves in a tank can be visibly diffracted, while light wave diffraction starts to become obvious on the sub-millimetre scale.

At the molecular (or crystalline) level, light waves are too large to be diffracted (they simply pass around the objects), and we need radiation with a much shorter wavelength: X-rays.

The image above is actually a visible-light diffraction pattern of a mockup of a benzene molecule: in particular the model is hexagonal arrangement of holes, which cause the incident (laser) light to diffract in the highly symmetrical pattern shown.

From the overall structure of the pattern, and the distances between the component blobs, it's possible to reconstruct the diffracting object: the mathematics of Fourier Transforms lets us associate spatial properties of the image above with the structure of the original body.

Franklin's X-ray diffraction pattern of DNA
With highly complex molecules it is of course much more difficult to work out the original structure. Perhaps the most famous molecular diffraction pattern in history is the one shown opposite: the key B-form X-ray diffraction photograph of DNA produced by Dr Rosalind Franklin in 1952, which led to the discovery of the helical structure of the molecule by Crick and Watson (when Watson briefly saw the image, before it had been published).

Using various mathematical techniques, it's possible to work out the parameters of the molecule from the photograph. For example, the equal-intensity crossed pattern of dots, with empty space in the diamond-shaped regions above and below, tells us that the structure is helical (though not the number of helical chains). The vertical distance between the dots gives us the number of nucleotide units (making up the 'rungs' of the ladder) in one pitch of the helix, and the number of layers in the diamond pattern (up to the first reflection) tells you the pitch (or the repeat pattern, in this case) of the molecule.

The final impetus for Crick and Watson's model-building efforts came from seeing this photograph with the clearest indication yet of DNA's helical structure, and then using helical diffraction theory (much of which was due to Crick) to analyse the measurements within it. They announced their proposed model in this article, in 1953 (with a somewhat guilty recognition of "the knowledge of the general nature of the unpublished experimental results and ideas" at the bottom of the page...)

It's one of the tragedies of science that Franklin never received widespread recognition for her work. She died in 1958, and the Nobel Prize for Chemistry in 1963 was awarded to Crick, Watson and Franklin's colleague at King's College, Maurice Wilkins. (The rules of the Nobel committee do not allow prizes to be awarded posthumously, although, since one prize is never given to more than three recipients, it's interesting to speculate as to what would have happened had Franklin lived.) Indeed, Franklin almost single-handedly discovered the helical structure: her MRC report gives tantalising clues to its form, but she just missed it.

More Fractals
Some more fractal snowflakes
Text is coming! (And so is Christmas...)

Something will be written here this year!! – Peter

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