Theoretical Predictions
of Nanometer Phenomena
R.J. Heaston* and D.F. Van der Werken, Jr.
Dr. Robert J. Heastona
Daniel F. Van Der Werken, Jr.b
This is an abstract
for a poster to be presented at the
Fifth
Foresight Conference on Molecular Nanotechnology.
There will be a link from here to the full article when it is
available on the web.
Summary. Phenomena taking place at nanometer dimensions
may be theoretically described with a relatively obscure
relationship that has been known for at least 40 years. The paper
will describe the derivations in detail and relate experimental
measurements of forces and dimensions to predicted bands.
Boundary conditions for nanotechnology will be defined.
Theory. The classical radiius of an electron, r0,
is related to the Compton wavelength, r2, and the Bohr
radius, r4, by the formula rn = r0/ n/2,
where n = 0, 1, 2, 3, 4..., and is the fine structure
constant. It appears that no one has looked at the significance
of n>4. This paper looks at relationships from n = 0 to n =
12, which actually separates natural phenomena into a series of
unique bands. Calculations of rn from n = 0 to n = 12
are summarized in Table 1.
The various bands, when related to the Coulomb force, leads to
a series of stairsteps between the Coulomb force and some
hypothetical new force, Fh. The Coulomb force, Fe,
at rn is equal to to Fh at rn+1.
For example, Fe at r2 is equal to Fh
at r3, or Fe at r10 is equal to
Fh at r11. Note this recurring relationship
in Table 1 between the Coulomb force and the hypothetical force.
It is relatively easy to show that this hypothetical force has a
surprisingly simple force law of Fh = hc/2 r2.
Observations. The last column in Table 1 summarizes
some of the observations about the different dimensions and
forces. When n = 0, r0 is the classical radius, which
has more theoretical value than any physical significance. The
case of n = 1, or r1, has not been observed. As
already stated, when n = 2, r2 defines the Compton
wavelength and the region where the scattering of particles by
waves has been observed. Another non-observed region is at n = 3
and r3. Bohr derived the result at n = 4, and r4,
which has been observed as the minimum orbit of electrons around
nuclei. It would appear, from what has already been stated, that
even magnitudes of n = 0, 2, 4 are favored; however a transition
may take place at n = 5 and r5. Nothing appears to be
prominent about n = 5 and r5, except that this is the
beginning of the region of nanotechnology. Experimental
measurements with atomic force microscopy/spectroscopy fall in
the band between n = 5 and n = 6. The much used Rydberg number
plays a role at n = 6 and r6. Experimental
measurements have been made at n = 7 and r7 of the
zero point radiation force, or the so-called Casimir effect,
between two very close, neutral plates. The hypothetical force
derived above, Fh, is very similar to the empirical
formula for the zero point radiation force. A very interesting
phenomenological pattern emerges from n = 7 to n = 11. The
average feature sizes of various electronic devices fall in the
middle of different bands rather than at specific rn
magnitudes. Consequently, the following bands exist: Very Large
Scale Integrated circuits (VLSIC) between r7 and r8;
Large Scale Integrated Circuits (LSIC) between r8 and
r9; Small Scale Integrated Circuits (SSIC) between r9
and r10; and, transistors between r10 and r11.
One last observation should be noted: the hypothetical force in
Table 1 has an observed range from 10-16 to 10-6
m. This force is exactly equal in magnitude to the
measured strong-color force (7.14 x 105 N) when Fh
is calculated at the Compton wavelength of a proton, r = 2.11 x
10-16 m.
Predictions. One nanometer falls approximately in the
middle, near n = 5 and r5, in Table 1. This region is
at the boundary of atomic structure and the beginning of
molecular structure. The hypothetical force (zero point radiation
force) should have a major effect on phenomena in this region.
The Rdyberg length at n = 6 and r6 may be the maximum
Bohr orbit. Large atoms may force nanotechnology explorations
above r6. Measurements of forces should all fall
between the Coulomb force and the hypothetical force for the
dimensions indicated in Table 1. In other words, phenomena are
bounded between Fe and Fh. Different
thresholds may exist for nanotechnology. The pattern set by
electronic devices indicates that it may be easier to develop
nanotechnology devices within the bands of r5 to r6
and r6 to r7, not specifically at r5,
r6, or r7, although r6 might be
preferred. The odd levels, n = 1, 3, 5, 7, 9, should be examined
for any unique experimental transitions.
Table 1.
Various bands of phenomena are defined theoretically starting
with the classical radius of the electron. Calculations are
based upon the mass of the electron using the equation rn
= r0/n/2.
Band
n |
Dimensions ..
rn, meters .. |
Coulomb ..
Force, N .. |
Hypothetical ..
Force, N .. |
Phenomena .. .. ..
.. ..
.. ..
.. ..
.. |
| 0 |
2.82 x 10-15 |
2.91 x 101. . |
3.98 x 103 . . |
Classical radius of electron, r0
|
| 1 |
3.30 x 10-14 |
2.12 x 10-1.. |
2.91 x 10-1
.. |
Particle structure, r0 to
r1 |
| 2 |
3.86 x 10-13 |
1.55 x 10-3.. |
2.12 x 10-1
.. |
Compton wavelength, r2 |
| 3 |
4.52 x 10-12 |
1.13 x 10-5.. |
1.55 x 10-3
.. |
Particle interactions, r2
to r3 |
| 4 |
5.29 x 10-11 |
8.25 x 10-8. |
1.13 x 10-5
.. |
Bohr radius, r4 |
| 5 |
6.19 x 10-10 |
6.03 x 10-10 |
8.25 x 10-8
. |
Nanotechnology, r5 to r7
|
| 6 |
7.25 x 10-9.. |
4.39 x 10-12 |
6.03 x 10-10 |
Maximum atomic orbit, r6 |
| 7 |
8.49 x 10-8.. |
3.20 x 10-14 |
4.39 x 10-12 |
Molecular structure, r5 to
r7 |
| 8 |
9.94 x 10-7.. |
2.34 x 10-16 |
3.20 x 10-14 |
VLSIC, r7 to r8
|
| 9 |
1.16 x 10-5.. |
1.72 x 10-18 |
2.34 x 10-16 |
LSIC, r8 to r9 |
| 10 |
1.36 x 10-4.. |
1.25 x 10-20 |
1.72 x 10-18 |
SSIC, r9 to r10
|
| 11 |
1.59 x 10-3.. |
9.14 x 10-23 |
1.25 x 10-20 |
Transistors, r10 to r11
|
| 12 |
2.00 x 10-2.. |
5.78 x 10-25 |
9.14 x 10-23 |
Macroscopic |
*Corresponding Address:
Dr. Robert J. Heaston, 220 Arlington Avenue, Naperville, IL
60565, ph: 630-416-8338, fax: 630-416-9203, email:
[email protected]
aDR. ROBERT J. HEASTON (principal author) has a BS
and MS from the University of Arkansas and a Ph.D. from Ohio
State University, all in chemical engineering. He is retired from
the Department of Defense (DOD), where he organized the DOD
Microwave and Millimeter Wave Monolithic Integrated Circuit
(MIMIC) program and assisted witht he organization of the Very
High Speed Integrated Circuit (VHSIC) program. Dr. Heaston is
currently a member of the Board of Army Science and Technology
under the National Research Council.
bDANIEL F. VAN DER WERKEN, JR., has a BS from
Virginia Tech and an MS from the Air FOrce Institute of
Technology, both in electrical engineering. Microsoft employs him
as an Escalation Engineer.
4625 Highcroft Lane, Charlotte, NC 28269, Bus. ph: (704)
582-8290, Home ph: (704) 548-8333, fax: (704) 357-1170, email: [email protected]
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