U.S. patent application number 11/230354 was filed with the patent office on 2007-03-22 for ultra-low friction configuration.
Invention is credited to Federico Capasso, Davide Iannuzzi, Jeremy Munday.
Application Number | 20070066494 11/230354 |
Document ID | / |
Family ID | 37884985 |
Filed Date | 2007-03-22 |
United States Patent
Application |
20070066494 |
Kind Code |
A1 |
Iannuzzi; Davide ; et
al. |
March 22, 2007 |
Ultra-low friction configuration
Abstract
Briefly, embodiments of a configuration for ultra-low friction
is disclosed
Inventors: |
Iannuzzi; Davide;
(Hilversum, NL) ; Munday; Jeremy; (Somerville,
MA) ; Capasso; Federico; (Cambridge, MA) |
Correspondence
Address: |
BERKELEY LAW & TECHNOLOGY GROUP
1700NW 167TH PLACE
SUITE 240
BEAVERTON
OR
97006
US
|
Family ID: |
37884985 |
Appl. No.: |
11/230354 |
Filed: |
September 19, 2005 |
Current U.S.
Class: |
508/150 |
Current CPC
Class: |
B81B 3/0078 20130101;
F16C 39/00 20130101; C10N 2030/06 20130101; F16C 32/00 20130101;
F16C 33/10 20130101 |
Class at
Publication: |
508/150 |
International
Class: |
C10M 125/04 20060101
C10M125/04 |
Claims
1. An apparatus comprising: a device exhibiting ultra-low
friction.
2. The apparatus of claim 1, wherein said device comprises a device
exhibiting ultra-low dynamic friction.
3. The apparatus of claim 2, wherein said device exhibits ultra-low
dynamic friction at least in part by substantially counterbalancing
net weight of a first object with van der Waals repulsion between
the first object and a second object.
4. The apparatus of claim 2, wherein said device comprises a device
exhibiting ultra-low static friction.
5. The apparatus of claim 4, wherein said device exhibits static
friction below a value, wherein said value is ultra-low.
6. The apparatus of claim 4, wherein said device exhibits ultra-low
static friction at least in part by substantially counterbalancing
net weight of a first object with van der Waals repulsion between
the first object and a second object.
7. The apparatus of claim 6, wherein the spatial relationship
between the first object and the second object is not necessarily
perfectly vertically oriented.
8. The apparatus of claim 6, wherein said objects comprise metallic
material.
9. The apparatus of claim 6, wherein said objects comprise at least
partially birefringent material.
10. The apparatus of claim 9, wherein one of said objects comprises
a disk and the other of said objects comprises a plate.
11. The apparatus of claim 10, wherein said disk is around 20
microns thick.
12. The apparatus of claim 10, wherein said disk has a diameter of
around 40 microns.
13. The apparatus of claim 10, wherein said objects are separated
by a fluid.
14. The apparatus of claim 13, wherein said fluid comprises
ethanol.
15. The apparatus of claim 10, wherein said disk is substantially
free to rotate.
16. The apparatus of claim 6, wherein said objects are separated by
a relatively small distance sufficient to maintain the
counterbalancing.
17. The apparatus of claim 16, wherein said distance is
sufficiently small so that van der Waals forces between said
objects are not negligible.
18. The apparatus of claim 16, wherein said distance is
sub-micron.
19. The apparatus of claim 1, wherein said device is incorporated
into at least one of the following: an actuator; an accelerometer;
a gyroscope; a compass and/or a high sensitivity sensor.
20. An apparatus comprising: a device made of materials selected so
that van der Waals forces between at least some of said materials
are repulsive.
21. The apparatus of claim 20, wherein said materials have a
respective dielectric function, .epsilon..sub.N, in which N is 1,
2, 3 such that for imaginary frequencies
.epsilon..sub.1<.epsilon..sub.3<.epsilon..sub.2; and the
material corresponding to dielectric function .epsilon..sub.3
corresponds to a fluid separating the other materials.
22. The apparatus of claim 20, wherein said materials have a
respective dielectric function, .epsilon..sub.N, in which N is 1,
2, 3 such that for imaginary frequencies
.epsilon..sub.2<.epsilon..sub.3<.epsilon..sub.1; and, the
material corresponding to dielectric function .epsilon..sub.3
corresponds to a fluid separating the other materials.
23. The apparatus of claim 20, wherein said repulsive van der Waals
forces substantially counterbalance one or more other forces in
said device.
24. The apparatus of claim 23, wherein said one or more forces
comprise net weight of a portion of solid material.
25. The apparatus of claim 20, wherein said materials include at
least one of the following: quartz; calcite; and/or barium
titanate.
26. A method of producing ultra-low friction comprising: combining
materials so that van der Waals forces between at least some of
said materials are repulsive.
27. The method of claim 26, wherein said materials have a
respective dielectric function, .epsilon..sub.N, in which N is 1,
2, 3 such that for imaginary frequencies
.epsilon..sub.1<.epsilon..sub.3<.epsilon..sub.2; and the
material corresponding to dielectric function .epsilon..sub.3
corresponds to a fluid separating the other materials.
28. The method of claim 26, wherein said materials have a
respective dielectric function, .epsilon..sub.N, in which N is 1,
2, 3 such that for imaginary frequencies
.epsilon..sub.2<.epsilon..sub.3<.epsilon..sub.1; and, the
material corresponding to dielectric function .epsilon..sub.3
corresponds to a liquid separating the other materials.
29. The method of claim 26, wherein said repulsive van der Waals
forces substantially counterbalance one or more other forces in
said device.
30. The method of claim 29, wherein said one or more forces
comprise net weight of a portion of solid material.
31. An apparatus comprising means for producing ultra-low static
friction and a sensor to sense said ultra-low static friction.
32. The apparatus of claim 31, wherein said means for producing
ultra-low static friction comprises means for substantially
counterbalancing net weight of a first object with van der Waals
repulsion between the first object and a second object.
33. The apparatus of claim 32, wherein said objects comprise
metallic material.
Description
BACKGROUND
[0001] This disclosure is related to ultra-low friction, such as,
to a configuration that exhibits such friction.
[0002] Micro-electromechanical systems are sometimes referred to as
MEMS. Such devices, apparatuses and/or systems, for example,
typically include parts or one or more portions that move or
otherwise function on a scale of size that is around a micron. This
type of technology is currently receiving commercial attention. The
small size of such devices is at least one advantage. Likewise,
work is also being pursued with devices and/or the like on a
relatively larger scale or a relatively smaller scale, such as the
sub-micron and/or the nanometer scale level, for example. Whether
the size of such devices is around several microns, larger, or
smaller, it may be advantageous to have the capability to reduce
friction that may typically be present.
BRIEF DESCRIPTION OF THE DRAWINGS
[0003] Subject matter is particularly pointed out and distinctly
claimed in the concluding portion of the specification. Claimed
subject matter, however, such as with respect to organization
and/or method of operation, for example, together with objects,
features, and/or advantages thereof, may be understood by reference
to the following detailed description if read with the following
accompanying drawings in which:
[0004] FIGS. 1-4 are plots illustrating particular examples of
force plots of dielectric functions associated with a particular
embodiment of a device having ultra-low friction, the particular
embodiment being made from particular materials;
[0005] FIG. 5 is a schematic diagram of an embodiment of a micro-
or nano-compass exhibiting ultra-low friction;
[0006] FIG. 6 is a schematic diagram of another embodiment of a
device exhibiting ultra-low friction;
[0007] FIG. 7 is a plot of dielectric functions for various
birefringent materials;
[0008] FIG. 8 is a schematic diagram of an embodiment of a system
exhibiting ultra-low friction;
[0009] FIG. 9 is a table of parameters for various materials that
may be employed to compute a dielectric function of those
materials; and
[0010] FIG. 10 is another table of parameters for various materials
that may be employed to compute a dielectric function of those
materials.
DETAILED DESCRIPTION
[0011] In the following detailed description, numerous specific
details are set forth to provide a thorough understanding of
claimed subject matter. However, it will be understood by those
skilled in the art that claimed subject matter may be practiced
without these specific details. In other instances, well-known
methods, procedures, components and/or circuits have not been
described in detail so as not to obscure claimed subject
matter.
[0012] According to quantum electrodynamics, quantum fluctuations
of electric and magnetic fields may give rise to zero-point energy
that may remain, even in the absence of electromagnetic sources.
See, for example, P. W. Milonni, The Quantum Vacuum: An
Introduction to Quantum Electrodynamics (Academic Press, San Diego,
1993). In 1948, H. B. G. Casimir predicted, for example, that two
electrically neutral metallic parallel plates in a vacuum, assumed
to be perfect conductors, should attract each other with a force
inversely proportional to the fourth power of separation. The
plates act as a cavity for electromagnetic modes having nodes on
both walls. Zero-point energy, per unit area, in this example, if
such plates are kept at close proximity to each other, is smaller
than if the plates are at infinite separation. The plates thus
should mutually attract to reduce energy associated with
electromagnetic field fluctuations. This led to a generalized
theory regarding isotropic dielectrics by E. M. Lifshitz, I. E.
Dzyaloshinskii, and L. P. Pitaevskii (referred to hereinafter as
"Lifshitz's theory" or "Lifshitz's equation") from Casimir's
theory. In this latter theory, a force between two uncharged
parallel plates with arbitrary dielectric functions may be derived
according to an analytical formula that relates the Helmholtz free
energy associated with electromagnetic field fluctuations to the
dielectric functions of interacting materials and of the medium in
which they are immersed. At relatively short distances, such as
smaller than a few nanometers, for example, this theory provides a
complete description of the non-retarded van der Waals force. At
larger separations, however, retardation effects associated with a
finite speed of light value may give rise to a long-range
interaction that, in the case of two ideal metals in a vacuum,
reduces to Casimir's result. Lifshitz's equation also shows that
two plates made out of the same material will attract. For slabs of
different materials, on the contrary, the sign of the force depends
at least in part on dielectric properties of the medium in which
they are immersed. While the force is attractive in a vacuum, there
may be situations for which a properly chosen liquid or fluid may
result in two plates that mutually repel. See, for example, J.
Mahanty and B. W. Ninham, Dispersion Forces (Academic Press,
London, 1976); J. N. Isrealachvilli, Intermolecular and Surface
Forces (Academic Press, London, 1991).
[0013] This so-called Casimir-Lifshitz force between dielectrics is
now receiving considerable attention. The theory has been verified
in several high-precision experiments mainly focused on the
interaction between metallic surfaces in a vacuum. Less precise
measurements in liquids have also been reported, and experimental
evidence for a repulsive van der Waals force between dielectric
surfaces in different fluids has also been reported. See, for
example, A. Milling, P. Mulvaney, and I. Larson, J. Colloid
Interface Sci. 180, 460 1996; A. Meurk, P. F. Luckham, and L.
Bergstrom, Langmuir 13, 3896 1997; S. Lee and W. M. Sigmund, J.
Colloid Interface Sci. 243, 365 2001. It has also been pointed out
that the Casimir-Lifshitz force might be a potentially relevant
issue for development of micro- and nano-electromechanical systems.
See, for example, H. B. Chan, V. A. Aksyuk, R. N. Kleiman, D. J
Bishop, and F. Capasso, Phys. Rev. Lett. 87, 211801 (2001).
[0014] As shall be explained in more detail hereinafter, in a
suitable environment, it may be possible to employ such a force to
reduce friction for systems, devices, apparatuses and/or the like
having a size of several microns or smaller, for example. In this
context, this type of friction shall be referred to as ultra-low
friction. Of course, as is well-understood, typically there is
static friction and dynamic friction. It is noted that claimed
subject matter includes both ultra-low static friction and
ultra-low dynamic friction. As shall be explained in more detail
hereinafter, ultra-low static friction refers to static friction
that may be reduced to such a relatively small amount that it
exceeds the sensitivity of conventional or state-of-the-art
sensors. Although claimed subject matter is not limited in scope in
this respect, in an embodiment, as described in more detail
hereinafter, it is believed that static friction may, in theory, be
made arbitrarily small. This would appear to involve a value that
is at least smaller than the feasible sensitivity of a sensor
employed to measure such friction. For example, in the embodiment
described in more detail later, a vertical force, such as weight,
is suppressed or counterbalanced. While, theoretically at least,
substantially no static friction should be present, practically
speaking there may be some small, albeit not feasibly measurable,
surface roughness and/or contamination, for example. Likewise,
embodiments within the scope of claimed subject matter, such as
described in more detail below, also reduce dynamic friction
between surfaces. This reduced dynamic friction in this context is
also referred to as ultra-low.
[0015] From Lifshitz's theory, it is possible to show that the
force between two plates with dielectric functions .epsilon..sub.1
and .epsilon..sub.2 immersed in a medium with dielectric function
.epsilon..sub.3 is repulsive if, for imaginary frequencies, we have
.epsilon..sub.1<.epsilon..sub.3<.epsilon..sub.2 or
.epsilon..sub.2<.epsilon..sub.3<.epsilon..sub.1 over a range
of frequencies which, at a given distance, substantially dominate
the force contribution; likewise, the force is attractive
otherwise. See, for example, J. Mahanty and B. W. Ninham,
Dispersion Forces, Academic, London, 1976; J. N. Israelachvilli,
Intermolecular and Surface Forces, Academic, London, 1991. It is
noted that at different distances, different frequencies contribute
different amounts to the force.
[0016] By way of example, without limiting the scope of claimed
subject matter, consider a common combination of materials:
Silica-Ethanol-Gold. For example, consider plates made of Silica
and Gold separated by Ethanol. As may be seen in FIG. 1,
.epsilon..sub.Silica<.epsilon..sub.Ethanol<.epsilon..sub.Gold
over a frequency range that, at a particular distance relevant to
micro- and nano-devices, for example, substantially dominates the
force contribution, which should give a repulsive interaction
between Silica and Gold, in this example. Here, E may be determined
from optical/spectral experiments; however, for convenience, we
also note that dielectric properties of a variety of materials may
be described reasonably well by a multiple oscillator model, such
as, for example, the so-called Ninham-Parsegian representation;
see, for example, the previously cited text, Dispersion Forces. In
this example, this representation may be written as follows:
.epsilon. .function. ( i .times. .times. .xi. ) = 1 + j = 1 N
.times. C j 1 + ( .xi. .omega. j ) 2 + g i .times. .times. .xi.
.omega. j . ##EQU1## in which C.sub.j is given by
(2f.sub.j)/(.pi..omega..sub.j), f.sub.j is the oscillator strength,
.omega..sub.j is the relaxation frequency multiplied by 2.pi., and
g.sub.i is the damping coefficient of the oscillator. For a variety
of inorganic materials, two un-damped oscillators, referred to
hereinafter as "the two oscillator model," may be employed with
satisfactory results to describe dielectric properties of
particular materials, as follows: .epsilon. .function. ( i .times.
.times. .xi. ) = 1 + C IR 1 + ( .xi. .omega. IR ) 2 + C UV 1 + (
.xi. .omega. UV ) 2 , ##EQU2## in which .omega..sub.IR and
.omega..sub.UV are the characteristic absorption angular
frequencies in the infrared and ultraviolet ranges, respectively,
and C.sub.IR and C.sub.UV are the corresponding absorption
strengths, for particular materials and for this particular
embodiment or example.
[0017] However, claimed subject matter is not limited to employing
the two oscillator model. For example, the two oscillator model
does not always provide a complete description of the dielectric
properties of materials; however, in spite of its simplicity, if
applied to dispersion effects, it often provides reasonably precise
results. Without limiting the scope of claimed subject matter,
applying this model to perform calculations allows one to determine
the force between these two plates using Lifshitz's theory, as
described in more detail hereinafter.
[0018] Of course, other models may also be employed. For example,
again, without limiting the scope of claimed subject matter, in
another embodiment, the so-called Drude model may be employed. This
latter model, for example, may be employed to describe dielectric
properties of metals, although, again, claimed subject matter is
not limited in scope in this respect. FIG. 10 is a table that
provides optical parameters found using a Drude Model fit of
experimental dielectric functions for a variety of metals. In this
context, more optical properties of dielectrics may be found in,
for example: Hough and White, Advances in Colloid and Interface
Science, 14 3-41 (1980) and Lennart Bergstrom, Advances in Colloid
and Interface Science, 70 125-169 (1997), and references therein.
Likewise, properties of many metals may be found in the following:
M. A. Ordal, et al papers: Applied Optics 22, 1099 (1983); Applied
Optics 26, 7449 (1987); Applied Optics 27, 1203 (1988).
[0019] Applying for this embodiment the two oscillator model
provides the force between the plates as: F .function. ( d , T ) =
.differential. .differential. d .times. k B .times. .times. T 8
.times. .times. .pi. .times. .times. d 2 .times. n = 0 .infin.
.times. .intg. r .infin. .times. x .times. .times. d x .times. { ln
.function. ( 1 - .DELTA. 31 R .times. .times. .DELTA. 32 R .times.
.times. e - x ) + ln .function. ( 1 - .DELTA. 31 R _ .times.
.times. .DELTA. 32 R _ .times. .times. e - x ) } ##EQU3## where
.DELTA. .times. jk .times. R = .times. s .times. k .times. .times.
.times. j .times. - .times. s .times. j .times. .times. .times. k
.times. s .times. k .times. .times. .times. j .times. + .times. s
.times. j .times. .times. .times. k , .times. .DELTA. .times. jk
.times. R _ = .times. s .times. k .times. - .times. s .times. j
.times. s .times. k .times. + .times. s .times. j , .times. s
.times. k = .times. p .times. 2 .times. - .times. 1 .times. +
.times. .times. k / .times. .times. 3 ##EQU4## r = 2 .times.
.times. d .times. .times. 3 .times. .times. .xi. n / c , .times.
.xi. n = 2 .times. .times. .pi. .times. .times. n .times. .times. k
B .times. .times. T / , .times. = .function. ( i .times. .times.
.xi. n ) , ##EQU4.2## k.sub.B=1.381.times.10.sup.-23 J/K, T=300 K,
c=2.998.times.10.sup.8 m/s, =1.055.times.10.sup.-34 Js, and where d
is the plate separation. The subscripts 1 and 2 refer to plates,
while subscript 3 refers to an intervening liquid or fluid for this
example. It is noted that here the force in this example or
embodiment is between the outer layers or plates.
[0020] The force between the plates per unit area is plotted in
FIG. 2, and is repulsive as expected, from these calculations. Note
here that by convention a repulsive force is indicated as positive,
although claimed subject matter is, of course, not limited in scope
to this convention.
[0021] Without limiting the scope of claimed subject matter,
another example is provided to illustrate that the sign of the
force may, at least in part, depend on a variety of factors,
including, here, distance or separation. Consider, for example, the
combination LiNbO3-Ethanol-Gold. Dielectric functions from
calculation using the two oscillator model are graphed in FIG. 3.
It can be seen that
.epsilon..sub.LiNbO3<.epsilon..sub.Ethanol<.epsilon..sub.Gold
for low frequencies, suggesting repulsive behavior between the
plates at larger separations, but we have
.epsilon..sub.Ethanol<.epsilon..sub.LiNbO3<.epsilon..sub.Gold
for higher frequencies, suggesting attractive behavior between the
plates at closer distances. The force is plotted in FIG. 4 and
confirms the above discussion.
[0022] In this system, as illustrated in the FIGs, there is a
crossover from
.epsilon..sub.1<.epsilon..sub.3<.epsilon..sub.2 to
.epsilon..sub.3<.epsilon..sub.1<.epsilon..sub.2. The force is
thus repulsive at large distances, where low imaginary frequencies
provide the dominant contribution to the force. Likewise, the force
is attractive for smaller separations, where higher frequencies
provide the dominant contribution. The zero-point energy here is
due at least in part to electromagnetic quantum fluctuations that
depend at least in part on the distance between the two interacting
plates. If the condition
.epsilon..sub.1<.epsilon..sub.3<.epsilon..sub.2 or
.epsilon..sub.2<.epsilon..sub.3<.epsilon..sub.1 is satisfied,
the zero-point energy per unit area is smaller at larger
separation, which means that it is energetically more favorable for
a liquid or a fluid, such as Ethanol, for example, to stay inside a
gap, such as between LiNbO3 and Gold or between Silica and Gold,
rather than outside it. As a consequence, the net force between
plates of such materials, for example, is repulsive. It is likewise
noted that designing a system, device or the like to at least
approximately exhibit a cross-over point, such as previously
described, for example, may be a desirable feature of a particular
embodiment, depending at least in part on the particular
embodiment, for example.
[0023] Note that it may be desirable to have surface roughness less
than the desired separation distance to avoid contact between
surfaces of the plates, for example. Surface roughness may be
reduced, for example, by use of polishing, etching techniques
(reactive ion etching (RIE), chemical, etc.), ion milling, cleaving
along crystal axes, etc. Use of such techniques may be employed to
reduce surface roughness to nanometer and/or sub-nanometer scales,
for example, if desired.
[0024] Although claimed subject matter is not limited in scope in
this respect, for an embodiment of a device exhibiting ultra-low
static friction, for example, movement may be detected and
amplified by employing a variety of different sensors, such as, for
example, an actuator, an accelerometer, a gyroscope, a compass
and/or a high sensitivity motion sensing device, for example. As
simply one example, without limitation, a micro- or a nano-bearing
may be used to measure static forces or torques and may find
application in situations in which ultra-low static friction is
desirable among micro- or nanofabricated mechanical parts. In such
devices, forces and torques (e.g. electric, magnetic,
gravitational, photon induced, etc.) may be detected that are much
smaller than may be identified using traditional sensors, such as
sensors which may provide one or more measurements by overcoming
static friction at least in part, for example. Thus, embodiments of
devices and/or the like employing ultra-low static friction, as
previously described, for example, may result in high measurement
sensitivity.
[0025] FIG. 5 depicts one potential embodiment of a nano- or
micro-compass, for example. Of course, claimed subject matter is
not limited in scope to this particular embodiment. This can be
made, for example, by coating a silica sample with a ferromagnetic
material, such as, for example, iron, and putting it, such as 510,
silica side down, above a gold surface, such as 520, in which the
device is submerged in ethanol. A silica/ethanol/gold combination
may lead to a repulsive force between silica and gold and, hence,
ultra-low static behavior. A small magnetic field, such as smaller
than may be detected from current devices which have static
friction, may be applied. Here, this may result in disk rotation
due at least in part to ferromagnetic material on the disk.
Similarly, a silica/ethanol/gold combination without ferromagnetic
material could be used as an accelerometer. A slight change in
velocity may allow the disk to slide as a result of ultra-low
static friction, for example. Thus, a high sensitivity measurement
may be obtained based at least in part on such sliding.
[0026] Further, in a variety of possible embodiments, mechanical
and/or electromechanical components may be moved or set into motion
by extremely small forces. Thus, different devices may be created
including, for example, actuators, accelerometers, gyroscopes,
compasses, low power MEMS; low power NEMS devices, piezo-like
devices, fluidic devices; valves, etc. Many of these devices could
be constructed in a similar fashion to their traditional
counterparts but be made with materials that lead to a repulsive
force, such as previously described. Any material combinations that
have dielectric functions which obey the relationship given earlier
will display a repulsive dispersion force between outer layers over
some distance range and will thus lead to ultra-low static friction
behavior. Simple examples include (but are not limited to) any low
dielectric function material, e.g. Silicon-dioxide, Calcite,
Teflon.RTM. or PTFE, etc., submerged in a fluid, e.g. Ethanol,
Methanol, Bromobenzene, Cyclohexene, Water, etc., and a metal, e.g.
Gold, Silver, Aluminum, Palladium, Platinum etc., or semiconductor,
e.g. Silicon, Germanium, GaAs, AlGaAs, etc.
[0027] Manufacturing such devices and structures on a relatively
small scale, such as, for example, a micron or nano-level scale,
may be done using techniques now known or to be later developed,
including: Lithography (electron, photon, etc.), Reactive Ion
Etching, Chemical Etching, Focused Ion Beams, Crystal Ion Slicing,
Silicon-On-Oxide and/or CMOS methods, etc. After structures are
created, they may be coated with materials whose dielectric
properties are chosen to satisfy conditions for repulsion, as
previously discussed, for example. Such techniques include:
Evaporation (thermal or otherwise), Sputtering, Spin Coating,
Molding, Stamping, Molecular Beam Epitaxy, etc. The devices may
likewise be packaged (e.g. PDMS enclosure, Lab On Chip devices,
etc.) for transportation and/or use.
[0028] In another embodiment of a device within the scope of
claimed subject matter, such as one that exhibits ultra-low
friction, a small birefringent disk, here, one having a diameter of
40 microns and a thickness of 20 microns, may be employed. Of
course, claimed subject matter is not limited in scope to these
particular dimensions. However, in this particular embodiment, this
disk, illustrated in FIG. 6 as 620, may be made out of quartz or
calcite, for example, and placed parallel to a birefringent
BariumTitanate (BaTiO3) plate, illustrated in FIG. 6 as 630. In one
potential embodiment, as described in more detail later, plate 630
may be immersed in ethanol and disk 620 may be placed on top. In
such an embodiment, as a result, a retarded van der Waals force
between the two birefringent slabs should be repulsive. Disk 620
may, in this embodiment, float on top of plate 630 at a distance of
approximately 100 nm, for example. Weight of disk 620 in this
embodiment may therefore be substantially counterbalanced by van
der Waals force repulsion. Likewise, in this embodiment, disk 620
is substantially free to rotate, as explained in more detail
hereinafter. Likewise, it is noted that this is one particular
embodiment and claimed subject matter is not intended to be limited
to this particular embodiment. As previously explained, a variety
of approaches and techniques may be employed to provide ultra-low
friction and this is merely one example embodiment. For example,
while in this particular embodiment, the spatial orientation
between the plates is illustrated as vertical, this is not
necessary and other spatial orientations may be employed. A
repulsive force may also be produced in a horizontal orientation,
as simply one example.
[0029] Continuing with the embodiment mentioned above, however,
consider two plates made of uniaxial birefringent materials, the
plates being kept substantially parallel at a distance d and
immersed inside a medium with dielectric function .epsilon..sub.3,
as explained in more detail hereinafter. For sake of simplicity,
for this particular embodiment, it is assumed that the two plates
are oriented as in FIG. 6, although, of course, claimed subject
matter is not limited in scope in this respect. Thus, for this
embodiment having this reference system, the z-axis is chosen to be
orthogonal to the plates. The optical axis of one of the two
crystals, such as the three fold, four fold, or six fold axis of
symmetry for rhombohedral, tetragonal, or hexagonal crystals, are
aligned with the x-axis. The optical axis of the second crystal is
also in the x-y plane, but rotated by an angle with respect to the
other, as illustrated in FIG. 6.
[0030] For illustrative purposes, if the distance between plates is
small enough that the force between them is non-retarded, that is,
of van der Waals type, torque may be demonstrated to be inversely
proportional to the second power of d and proportional to sin
(2.theta.), as follows: M = - .times. .times. .omega. _ .times.
.times. S 64 .times. .times. .pi. 2 .times. .times. d 2 .times. sin
.function. ( 2 .times. .theta. ) ##EQU5## where S is the surface
area and {overscore (.omega.)} is .omega. _ = .intg. 0 .infin.
.times. d .xi. .times. .times. .intg. 0 .infin. .times. d x .times.
x .times. .times. ( .epsilon. 2 .parallel. - .epsilon. 2 .perp. )
.times. ( .epsilon. 1 .parallel. - .epsilon. 1 .perp. ) .times.
.epsilon. 3 2 .times. e - x [ ( .epsilon. 1 .perp. + .epsilon. 3 )
.times. ( .epsilon. 2 .perp. + .epsilon. 3 ) - ( .epsilon. 1 .perp.
- .epsilon. 3 ) .times. ( .epsilon. 2 .perp. - .epsilon. 3 )
.times. e - x ] 2 ##EQU6## In a theory which includes retardation
effects, as described, for example, in Y. Barash, Ivestiya vuzov,
Radiofizika, 12 (1978) 1637, however, it may be difficult to reduce
the expression for torque to an analytically solvable expression.
Nonetheless, these expressions may be solved numerically. As
described in more detail hereinafter, this may be applied to the
previously described embodiment, such as the embodiment in which
disk 620 and plate 630 are separated by a vacuum.
[0031] In such an embodiment, as previously, consider a 20 micron
thick, 40 micron diameter disk made out of either quartz or
calcite, kept in vacuum substantially parallel to a large BaTiO3
plate at a distance d. To perform a numerical computation of torque
experienced by such a disk as a function of .theta. and d, one may
apply dielectric functions of the two plates at imaginary angular
frequencies, as previously described. Likewise, the previously
described two oscillator model may be applied, although claimed
subject matter is not limited in scope in this respect. For this
embodiment, parameters that determine the dielectric properties of
quartz, calcite, and BaTiO3 in the limit of the two oscillator
model are listed in table I of FIG. 9. FIG. 7 is a graph or plot
showing calculated dielectric functions at imaginary angular
frequencies. Using these functions, the torque was calculated for
different angles at d=100 nm, both in a quartz-BaTiO3 and in a
calcite-BaTiO3 configuration. Results were obtained for T=300 K,
but calculations for smaller temperatures give rise to nearly
identical values: at this distance, torque is primarily generated
by fluctuations of the electromagnetic field associated with
zero-point energy. Materials with less pronounced birefringent
properties, such as quartz with respect to calcite, may give rise
to a smaller torque and materials with more pronounced birefringent
properties may give rise to a larger torque. In this example, the
sign of the torque obtained for the quartz-BaTiO3 configuration is
opposite to the one obtained for calcite-BaTiO3. This behavior may
be understood from FIG. 7, for example. A dominant contribution to
torque comes from angular frequencies in the region where the
dielectric tensor perpendicular to the optical axis is greater than
the dielectric tensor parallel to the optical axis. The minimum
zero-point energy corresponds to the situation in which the axes of
the dielectric tensors with larger values of the dielectric
function are aligned.
[0032] As previously discussed, in an embodiment in which a quartz
or calcite disk is above a BaTiO3 plate immersed in ethanol, the
retarded van der Waals force between the disk and the plate is
repulsive; thus, if the disk is placed on top of the plate, this
repulsion may be used to substantially counterbalance the weight of
the disk, for example. In liquid ethanol, therefore, the disk would
float substantially parallel on top of the plate at a small
distance. The static friction between the two birefringent plates
in this particular embodiment would be ultra-low, and the disk
would be free to rotate suspended in bulk liquid. Likewise, the
dynamic friction should also be ultra-low for this particular
embodiment. Furthermore, viscous drag may also be reduced in other
embodiments by choosing a less viscous fluid or by modifying the
surface geometry of the interacting bodies, for example, although
claimed subject matter is not limited in scope in this respect.
[0033] For distances shorter than a few nanometers, the force is
attractive. However, at larger distances, where retardation effects
are non-negligible, the force becomes repulsive. From Lifshitz's
theory for isotropic materials, it is possible to show that the
force between two plates with dielectric functions .epsilon..sub.1
and .epsilon..sub.2 immersed in a medium with dielectric function
.epsilon..sub.3 is repulsive if, for imaginary frequencies,
.epsilon..sub.1<.epsilon..sub.3<.epsilon..sub.2 or
.epsilon..sub.2<.epsilon..sub.3<.epsilon..sub.1, and it is
attractive in other cases. In this particular embodiment, there is
a crossover from
.epsilon..sub.1<.epsilon..sub.1<.epsilon..sub.2 to
.epsilon..sub.3<.epsilon..sub.1<.epsilon..sub.2 at about
5.times.10.sup.15 rad/s. The force is thus repulsive at large
distances, where low imaginary frequencies primarily contribution
to the force, and attractive for smaller separations, where higher
frequencies are more relevant, as described in a previous
embodiment. Zero-point energy from electromagnetic quantum
fluctuations depends at least in part on the distance between
interacting plates. Assuming, for example, one of the relationships
just described applies, zero-point energy per unit area is smaller
at larger separation, which means, as also previously described,
that it is energetically more favorable for a liquid or fluid to
stay inside a gap, such as between a plate and disk, for example.
As a consequence, the net force is repulsive.
[0034] For this particular embodiment, the net weight of the disk
immersed in ethanol may be given by:
F.sub.gr=-Sh(.rho..sub.disk-.rho..sub.ethanol)g in which S is the
surface of the disk, h is its thickness, .rho..sub.disk is the mass
density of either quartz (2643 kg/m3) or calcite (2760 kg/m3),
.rho..sub.ethanol is the mass density of ethanol (789 kg/m3), and g
is 9.81 m/s.sup.2. In these particular embodiments, the equilibrium
separation is about 100 nm. Of course, claimed subject matter is
not limited in scope to this particular separation or to this
particular configuration. Likewise, this distance may be tailored
by a variety of techniques, such as by changing the thickness of
the disk to provide one simple example of one possible change. As
suggested previously, while some embodiments may not necessarily
exhibit a cross-over; likewise, in some embodiments, it may be
desirable to have a cross-over and/or have the capability to affect
at least somewhat its location.
[0035] A schematic view of one embodiment, as previously described,
is shown in FIG. 8. A 40 micron diameter, 20 micron thick disk made
out of quartz or calcite is placed on top of a BaTiO3 plate
immersed in ethanol. The optical axes of birefringent crystals are
oriented as in FIG. 6. A disk should levitate approximately 100 nm
above the plate and should be free to rotate. For example, a 100 mW
laser beam may be collimated onto the disk to rotate it by a
transfer of angular momentum of light, although claimed subject
matter is, of course, not limited in scope to the laser or power of
the laser employed. A shutter may block the beam to interrupt the
light-induced rotation. Using a laser, for example, one may rotate
the disk. After the laser beam is shuttered, the disk may be free
to rotate back towards the configuration of reduced energy.
[0036] Likewise, disks with different dimensions and geometries may
be constructed to rotate faster. Suitably engineered samples could
also result in additional configurations. For example, a thick
layer of lead could be deposited on a portion of a disk to make it
heavier: the disk may float at a smaller distance, where the
magnitude of the driving torque would be larger, for example.
Furthermore, use of a different liquid with optical properties
similar to ethanol but with a smaller viscosity may increase the
angular velocity of the disk, as another example.
[0037] It will, of course, be understood that, although particular
embodiments have just been described, claimed subject matter is not
limited in scope to a particular embodiment or implementation. For
example, one embodiment may be in hardware, such as implemented to
operate on a device or combination of devices, for example, whereas
another embodiment may be in software. Likewise, an embodiment may
be implemented in firmware, or as any combination of hardware,
software, and/or firmware, for example. Likewise, although claimed
subject matter is not limited in scope in this respect, one
embodiment may comprise one or more articles, such as a storage
medium or storage media. This storage media, such as, one or more
CD-ROMs and/or disks, for example, may have stored thereon
instructions, that when executed by a system, such as a computer
system, computing platform, or other system, for example, may
result in an embodiment of a method in accordance with claimed
subject matter being executed, such as one of the embodiments
previously described, for example. As one potential example, a
computing platform may include one or more processing units or
processors, one or more input/output devices, such as a display, a
keyboard and/or a mouse, and/or one or more memories, such as
static random access memory, dynamic random access memory, flash
memory, and/or a hard drive.
[0038] In the preceding description, various aspects of claimed
subject matter have been described. For purposes of explanation,
specific numbers, systems and/or configurations were set forth to
provide a thorough understanding of claimed subject matter.
However, it should be apparent to one skilled in the art having the
benefit of this disclosure that claimed subject matter may be
practiced without the specific details. In other instances,
well-known features were omitted and/or simplified so as not to
obscure claimed subject matter. While certain features have been
illustrated and/or described herein, many modifications,
substitutions, changes and/or equivalents will now occur to those
skilled in the art. It is, therefore, to be understood that the
appended claims are intended to cover all such modifications and/or
changes as fall within the true spirit of claimed subject
matter.
* * * * *