The chief scientist from IBM Almaden gave a talk on manipulation of individual cesium atoms on a planar copper substrate at the Institute for Advanced Study (Princeton) in the Spring of 1997. After the talk, I suggested that one could move from 2D to 3D patterns at the nanoscale in the same way as machinists moved from planar milling machines (2D) to the lathe (3D). A few days later I disclosed the details of my "nanolathe" to the IBM folks in the following email, but they never wrote back!

The main idea is to think of replacing the 111 copper plane with graphite, and then replace graphite with a (multilayer) carbon nanotube. Just as one sputtered cesium onto copper, so one can sputter atoms onto the graphite plane or nanotube. And just as one used an atomic force microscope (AFM) stylus to manipulate the atoms in the planar setting, so will the AFM stylus serve as the "cutting" edge in the nanolathe. The trick is to mount the nanotube axis so that it can be turned like a lathe....

Please contact me for further infomation.

From: Robert B Kusner
Date: Sun, 25 May 1997 10:28:25 -0400

Paul and Pete,
The other day Don Eigler of IBM Almaden gave a talk here at the IAS. I don't know much about the frontier of scanning tunneling or atomic force microscopy, but during his talk, had the idea of this "micro-lathe" (see below).

Have you ever heard of a z-theta (cylindrical coordinate) based STM or AFM? If these exist, it should be easy to modify what Eigler and company are doing with x-y (planar) STMs to manipulate atoms on copper planar surfaces to make my micro-lathe (perhaps someone already has?! ;-)
The relevant chemistry questions I wanted to check with you involve:
1) how true is the assumption that a graphite plane is electronocally like the (1,1,1) plane in metallic copper, i.e. that the electron density is quite smooth (and almost constant) even at the C-C covalent bond scale?
2) how true is this for a graphitic tubule of circumference 30-75 (say) C-C bonds (i.e 20-50 A in diameter)? of course, there are differing "helicity" bond patterns for a tubule which might affect this, but it would be nice to do some modelling to see how close one gets to cylindrical symmetry?
3) how reasonable is my suggestion of "stuffing" the tubule with metal atoms, such as copper, to smooth out the electron density, and perhaps to stiffen the turning axis of the micro-lathe as well?
4) it would be nice to "terminate" such a tubule with a negatively curved "trumpet" at each end, so that it could be grafted into parallel graphite sheets:

graphite----------------- | -----------------------
\ | /
\ | /
^ |||
| |||
| ->|||<- 20-50 A
. ...
>10,000 A
| ||| tubule (axial section)
| |||
v |||
/ | \
/ | \
graphite----------------- | -----------------------

P.S. Here is what I wrote to him:

From: Robert B Kusner
Date: Sat, 24 May 1997 13:50:03 -0400
Subject: curved substrates and 3D designer molecules

Dear Don Eigler,

I wanted to follow up on our conversation at the IAS yesterday and ask if you could send me some of your reports and (p)reprints on this topic. (I am the fellow who asked about curved substrates and mentioned how such might lead to some simple 3D constructions.)
The "back-of-the-envelope" thoughts I had were that graphite might provide a (rough) approximation to the (1,1,1) copper plane. Electronically, I am not sure how valid this is, but I had presumed the high conductivity of graphite means that it looks rather flat even below scale (about 1.4 A) of its covalent bonds - comments?

My idea, then, is to make a "micro-lathe". Utilize long, cylindrical graphitic tublules (say, 20-50 A in diameter, and many microns in length) to approximate a curved substrate with the geometry of a cylinder as the axis of the lathe. Perhaps the tubule could be filled with copper atoms to make the electron surface even smoother at small scales. Such filling is analogous to filling fullerenes with metal atoms (and that has been done years ago). The STM (or AFM or "molecular manipulator") would be the "cutting edge" of the lathe, pushing around stuff deposited on the cylinder....

I gather from what you said that such a lathe does not yet exist. Now that "I have invented it", how big a challenge would it be to construct? In principle, z-theta coordinates are just as easy as x-y coordinates. In fact, if the analogy of a lathe seems too indelicate, recall that the first phonograph records were cylindrcal drums and pickup the needle travelled along a line parallel to the axis: the idea would be to have the STM or AFM travel in the z direction, while arranging for the tubule to spin.

Let me just close by adding that my own work is mainly in "pure mathematics" (differential geometry of surfaces). Occasionally I have dabbled in designer chemistry and molecular modeling (see, for example, "New surface allotropes of carbon", Chem. Phys. Lett. 241 (1995) 522-527) and would be interested to engage in further collaborative work with materials scientists. I may be visiting MSRI (in Berkeley) and Stanford next month, and would enjoy talking with you further.

Keep in touch,

Rob Kusner School of Mathematics Institute for Advanced Study Princeton, NJ 08540

Professor of Mathematics Director, Center for Geometry, Analysis, Numerics & Graphics University of Massachusetts Amherst, MA 01003
____________________________________________________________________________ ____________________________________________________________________________

To: Robert B Kusner
From: "Don Eigler/Almaden/IBM"
Date: 31 May 97 12:47:11
Subject: Re: curved substrates and 3D designer molecules
Mime-Version: 1.0
Content-Type: Text/Plain

Thanks for your e-mail. I will be away until June 10 and will not be able to
respond until then.