U.S. patent application number 12/098890 was filed with the patent office on 2009-03-19 for composite materials.
This patent application is currently assigned to QINETIQ LIMITED. Invention is credited to Ian John Youngs.
Application Number | 20090073548 12/098890 |
Document ID | / |
Family ID | 33568268 |
Filed Date | 2009-03-19 |
United States Patent
Application |
20090073548 |
Kind Code |
A1 |
Youngs; Ian John |
March 19, 2009 |
Composite Materials
Abstract
A composite material having a plasma frequency comprising a
random mixture of conductive and non-conductive particles. A
material having smaller conductive than non-conductive particles
and a concentration of conductive particles approximately at, close
to or above the percolation threshold for mixtures of the
conducting and non-conducting particles may show a plasma frequency
well below plasma frequencies for conventional bulk materials.
Inventors: |
Youngs; Ian John;
(Wiltshire, GB) |
Correspondence
Address: |
MCDONNELL BOEHNEN HULBERT & BERGHOFF LLP
300 S. WACKER DRIVE, 32ND FLOOR
CHICAGO
IL
60606
US
|
Assignee: |
QINETIQ LIMITED
|
Family ID: |
33568268 |
Appl. No.: |
12/098890 |
Filed: |
April 7, 2008 |
Related U.S. Patent Documents
|
|
|
|
|
|
Application
Number |
Filing Date |
Patent Number |
|
|
10995303 |
Nov 24, 2004 |
|
|
|
12098890 |
|
|
|
|
Current U.S.
Class: |
359/321 ;
428/323 |
Current CPC
Class: |
Y10T 428/24942 20150115;
H01B 1/22 20130101; Y10T 428/25 20150115 |
Class at
Publication: |
359/321 ;
428/323 |
International
Class: |
G02F 1/00 20060101
G02F001/00; B32B 5/16 20060101 B32B005/16 |
Foreign Application Data
Date |
Code |
Application Number |
Nov 25, 2003 |
GB |
0327412 |
Jun 7, 2004 |
GB |
0412665 |
Jun 8, 2004 |
GB |
0412771 |
Claims
1. A composite material comprising a proportion of a electrically
non-conductive material and a proportion of a randomly distributed
electrically conductive material, and wherein: a) the electrically
conductive material is particulate with an average particle size
which is not more than 1 .mu.m; b) the electrically non-conductive
material is not particulate; c) the electrically conductive
material proportion is sufficiently large to provide for the
composite material to exhibit a plasma-like response corresponding
to at least an onset of a percolation threshold; and d) the
composite material has a plasma frequency which is below the plasma
frequencies of conventional bulk metals.
2. A composite material according to claim 1 wherein the
electrically conductive material comprises gold or silver particles
with average particle size in the range 1 .mu.m to 1 nm.
3. A composite material according to claim 1 wherein the
electrically conductive material has an average particle size of
100 nm.
4. A composite material according to claim 1 wherein the plasma
frequency is not greater than 10.sup.12 Hz.
5. A method of influencing propagation of electromagnetic radiation
having a radiation frequency by arranging for the radiation to be
incident upon a composite material, and wherein: a) the composite
material comprises an electrically non-conductive material and an
electrically conductive material; b) the electrically conductive
material is randomly distributed in the composite material; c) the
composite material exhibits a plasma-like response and has a plasma
frequency which is below conventional bulk metals' plasma
frequencies; and d) the plasma frequency is located relative to the
radiation frequency such that radiation propagation at the
radiation frequency in the composite material Is affected by the
plasma-like response.
6. A method according to claim 5 wherein the radiation and plasma
frequencies are in at least one of the ranges 10.sup.3 to 10.sup.15
Hz, 10.sup.8 to 10.sup.15 Hz and 10.sup.8 to 10.sup.12 Hz.
7. A method according to claim 5 wherein the radiation and plasma
frequencies are microwave frequencies.
8. A method according to claim 5 wherein: a) the electrically
non-conductive and conductive materials are both particulate; b)
the electrically conductive material has a particle size which is
less than one tenth that of the electrically non-conductive
material; c) the electrically non-conductive material has an
average particle size which is not more than 100 .mu.m; and d) the
electrically conductive material is a proportion of the composite
material which is sufficiently large for the composite material to
exhibit a plasma-like response indicating that it is at least at an
onset of a percolation threshold.
9. A method according to claim 5 wherein: a) the electrically
conductive material is particulate; b) the electrically
non-conductive material is not particulate; c) the electrically
conductive material has an average particle size which is not more
than 1 .mu.m; and d) the electrically conductive material
proportion is sufficiently large to provide for the composite
material to exhibit a plasma-like response indicating that it is at
least at an onset of a percolation threshold.
10. A method according to claim 5 wherein the electrically
conductive material has an average particle size of substantially
100 nm.
11. A method according to claim 5 wherein the electrically
conductive material exhibits no long range order.
12. A method according to claim 11 wherein the electrically
conductive material exhibits no long range order over a region
having a dimension in the range 3 mm to 3 m.
13. A method according to claim 12 wherein the region's dimension
is substantially 3 cm.
14. A method according to claim 5 wherein the electrically
conductive material exhibits no long range order over a region
having a dimension of the order of a wavelength in the material
corresponding to the plasma frequency.
15. A method according to claim 5 wherein the composite material
contains sufficient electrically conductive material to form
therein at least one electrically conductive network extending
between opposite sides of the composite material.
16. A method according to claim 5 wherein the electrically
non-conductive and conductive materials are both particulate and
have larger and smaller average particle sizes respectively
relative to one another, and a ratio of the average particle sizes
being greater than or equal to 100 or 1000.
17. A method according to claim 16 wherein the electrically
conductive material comprises one of an oxidation resistant metal,
a metallic alloy, an electrically conductive coating on
electrically non-conductive particles and a conducting ceramic, and
the average particle size of the electrically conducting material
is in the range 1 nm to 1 .mu.m.
18. A method according to claim 17 wherein the electrically
conductive material has a conductivity greater than 1 S/m.
19. A method according to claim 17 wherein the electrically
conductive material comprises gold or silver particles.
20. A method according to claim 5 wherein the electrically
non-conductive material comprises either one of, or alternatively a
mixture of at least two of, PTFE, paraffin wax, a thermosetting
material, a thermoplastic material, a polymer, air, an insulating
ceramic material and glass.
21. A method according to claim 20 wherein the electrically
non-conductive material is PTFE with an average particle size of
substantially 100 .mu.m, and the electrically conductive material
is gold or silver with an average particle size of substantially
100 nm.
22. A method according to claim 5 wherein the electrically
conductive material comprises either one of, or alternatively a
mixture of at least two of, a metal, metal alloy, an oxidation
resistant metal, a conductive coating on non-conductive particles,
an electrically conductive metal oxide, an intrinsically conductive
polymer, an ionic conductive material, and a conducting
ceramic.
23. A method according to claim 5 wherein the composite material
has an effective conductivity exceeding at least one of 10 S/m, 30
S/m and 100 S/m.
24. A method according to claim 5 including switching the composite
material between radiation propagating and attenuating states by
altering its plasma frequency.
25. A method according to claim 5 wherein the electrically
conductive material comprises regions of electrically conductive
particles and the electrically non-conductive material comprises
regions of electrically non-conductive particles, and the composite
material has a degree of electrical connectivity between the
regions of electrically conductive particles determining electrical
properties, and the method includes applying a stimulus to the
composite material to change the degree of connectivity.
26. A method according to claim 25 wherein the stimulus is
pressure, temperature, chemical absorption, electric field or
electric current, and applying the stimulus switches the composite
material between radiation propagating and attenuating states.
27. A method according to claim 5 wherein the composite material is
in the form of any one of a directional coupler lens, filter,
transparent electrode, absorbing electrode, capacitor, inductor,
waveguide, sensor, remote interrogation sensor package, active
electromagnetic shutter, radome, switch, shield, fuse and anechoic
chamber.
28. A method according to claim 5 wherein the composite material is
one of a series of composite materials with differing
concentrations of electrically conductive and non-conductive
materials, and wherein for the series a graph of conductivity
against electrically conductive material concentration on
logarithmic axes has a slope which is less than 100 for an
insulator to metal transition.
Description
[0001] The present invention is concerned with composite materials.
In particular, preferred embodiments are concerned with
metal/insulator composites having plasma frequencies below the
plasma frequencies of conventional bulk metals.
[0002] Many applications, devices and/or methods rely on the
control of electromagnetic radiation. For example, enclosures
(radomes) are necessary to provide environmental protection for
antenna systems. In mobile communications and other similar
applications, there is a need to separate electromagnetic signals
of different frequency. There is also a need to dissipate
electromagnetic energy at the walls of anechoic chambers used in
radio and microwave measurements, and to confine, within specific
bounds, unintentionally emitted electromagnetic energy to meet
electromagnetic compliance regulations and prevent electromagnetic
interference between electrical and electronic equipment.
[0003] Materials are used to provide the means of control, either
in bulk form, as coatings or as components in devices. For example,
radomes tend to be fabricated from bulk materials such as plastics
and fibre-reinforced polymer composites; frequency separation can
be achieved at a component level in guided wave communications or
by using coatings (for example on radomes) for free-field
propagation; dissipation tends to be achieved by coating an
existing structure (e.g. the walls and floor of an anechoic
chamber); and electromagnetic shielding can be achieved either
through coating an equipment enclosure or by fabricating the
enclosure from an appropriate material.
[0004] At the simplest level, the role of the material can be to
modify the propagation characteristics of incident radiation.
Modification could include transmitting, filtering, absorbing or
reflecting incident electromagnetic radiation as in radomes,
frequency separation, coatings for anechoic chambers and equipment
enclosures for electromagnetic compatibility.
[0005] Advances have also led to materials and devices that amplify
or change the frequency or polarisation of incident electromagnetic
radiation (consider, for example, lasers, second harmonic
generation using non-linear optical materials, or the use of
Faraday rotation in ferromagnetic ceramics).
[0006] Materials and devices also exist whose influence on incident
electromagnetic radiation can be changed as a function of an
extrinsic (or external) stimulus. These are known as smart, dynamic
or adaptive electromagnetic materials and include ferroelectrics,
whose permittivity is a function of applied electric field
strength, and chromogenic materials (photo-, thermo-, or
electro-chromic) whose optical colour and often electrical
conductivity varies with light intensity, temperature or electrical
current.
[0007] The thesis, "Electrical Percolation and the Design of
Functional Electromagnetic Materials" by Ian J, Youngs, published
in December 2001, and available from the library of the University
of London includes a comprehensive discussion of the background to
and physics surrounding this invention.
[0008] The influence exerted by a material on an electromagnetic
wave is determined by two intrinsic material properties. These are
the permittivity (.di-elect cons.) and magnetic permeability
(.mu.). The permittivity (.di-elect cons.) characterises the
response of a material to an applied electric field, and is a
measure of the extent to which a material can resist the flow of
charge in an electric field. The magnetic permeability (.mu.)
characterises the response of a material to a magnetic field, and
is equal to the ratio of the magnetic flux density to the magnetic
field strength measured in the material.
[0009] It is usual to relate (or normalise) the absolute properties
of permittivity and magnetic permeability to those of a vacuum
(.di-elect cons..sub.o=8.854.times.10.sup.-12 Fm.sup.-1;
.mu..sub.o=1.257.times.10.sup.-6 Hm.sup.-1) so that one then
discusses the relative permittivity (.di-elect
cons..sub.r=.di-elect cons./.di-elect cons..sub.0) and relative
permeability (.mu..sub.r=.mu./.mu..sub.0) of a material. For
example, the relative permittivity and relative permeability of a
vacuum equal unity.
[0010] The present invention is primarily concerned with responses
to an applied electric field (i.e. permittivity) and the manner in
which they govern the propagation of an electromagnetic wave
through the bulk of a material. For the purposes of a general
introduction, only the behaviour of non-magnetic materials is
considered below. This is a reasonable assumption to make, since
materials exhibiting diamagnetic or paramagnetic behaviour have a
relative magnetic susceptibility (.chi..sub.m, a ratio of the
magnetic moment per unit volume of material to the magnetic field
strength) of |.chi..sub.m|<10.sup.-5 and so are treated as
having a value of .mu..sub.r of 1.
[0011] In the case of ferromagnetic and ferromagnetic materials,
where |.chi..sub.m| is significantly greater then 0, the analogous
case to that outlined below will be apparent to those skilled in
the art.
[0012] Materials can either support (or allow) the propagation of
an electromagnetic wave through their bulk or they cannot. All
materials contain electronic charges and so respond, to varying
degrees, to the application of an electric field.
[0013] Metals contain significant numbers of electronic charges
that are free to move through the bulk of the material (the
conduction band electrons). An electric field applied to a metal
therefore induces a macroscopic transport current in the
material.
[0014] The frequency response of the permittivity of metals is
determined by the weakly-bound ("free") electrons in the conduction
band. At low frequencies, the electrons oscillate in phase with an
applied electric field. However, at a certain characteristic
frequency, oscillation in phase with the applied field can no
longer be supported, and resonance occurs.
[0015] The weakly bound electrons within the metal can be
considered to act as a plasma--a gas consisting either wholly or
partly of charged particles. A simple example is to consider such
an electron gas as being in two dimensions and held between two
opposing electrodes, one at the top of the plasma and one at the
bottom. When an electric field is applied to this plasma, the
electrons will receive enough momentum to move in the opposite
direction to that in which the field is applied, and will continue
to move after the field is turned off.
[0016] After time t, N electrons of charge e will have moved a
distance, x, producing a sheet of unbalanced charge -Nex at the top
of the plasma. Consequently, a region of opposite charge, Nex is
left at the bottom of the plasma. This results in an electric
field, E in the upward direction, of magnitude E=(Ne/.di-elect
cons..sub.0)x acting within the plasma. This produces a restoring
force on the electrons, creating an equation of motion
2 x t 2 + N 2 m e 0 = 0 ( 1 ) ##EQU00001##
where m.sub.e is the mass of our electron.
[0017] The electrons therefore vibrate at the plasma frequency,
.omega..sub.p, where
.omega..sub.p.sup.2=(e.sup.2/m.sub.e.di-elect cons..sub.0)N (2)
[0018] For metals, this characteristic frequency is in the
ultraviolet region of the electromagnetic spectrum. For frequencies
above .omega..sub.p, metals can be considered to act like
dielectrics, i.e. they have a positive permittivity and support a
propagating electromagnetic wave.
[0019] The oscillation of a plasma may be quantised: a plasmon is
the unit of quantisation. Plasmons have a profound impact on the
properties of the metal, especially on the effect of incident
electromagnetic waves. The action of the plasmons produces a
complex dielectric function (or permittivity) of the form
( .omega. ) = 1 - .omega. p 2 .omega. ( .omega. + .gamma. ) ( 3 )
##EQU00002##
[0020] The imaginary component arises through the damping term
.gamma., which represents the amount of plasmon energy dissipated
into the system, generally as heat. The real permittivity is
essentially negative below the plasma frequency, .omega..sub.p, at
least down to frequencies of the order of .gamma..
[0021] For frequencies below .omega..sub.p, metals therefore
exhibit a negative permittivity. In this case, an electromagnetic
wave cannot propagate through the material, and decays
exponentially within a characteristic distance determined by the
attenuation coefficient, .alpha.=2.omega.n.sub.i/c. In a sense, the
metal acts as a high-pass filter for the frequency range spanning
the plasma frequency.
[0022] For metals, where the frequency of the electromagnetic
radiation is below the ultraviolet end of the spectrum most of the
radiation is reflected and the remainder is attenuated by the
metal.
[0023] Dielectrics are classed as non-magnetic materials, and
contain charges which are mostly bound and whose motion is
therefore localised to distances much smaller than the wavelength
of the incident electromagnetic radiation. The relative
permittivity of a dielectric material will be positive and greater
than that of a vacuum.
[0024] Bound electric charges can exist on many scales within a
material, from electrons orbiting atomic nuclei to charges residing
at interfaces between phases of dissimilar chemical composition
within a material. At low frequencies, all charges will oscillate
in phase with an applied electric field. This contributes to the
maximum value of the permittivity exhibited by the material. This
is shown in a dynamic permittivity resulting from an applied AC
field, rather than the dielectric constant which is representative
of an applied DC (or static) field. Under these conditions and in
the absence of free electric charges, the material exhibits no
significant loss. Again, at certain characteristic frequencies, the
individual types of charge carriers no longer oscillate in phase
with the applied field. Maxima in the loss (or absorption) spectrum
occur at these frequencies.
[0025] When an E-field is applied to a dielectric material,
polarisation of the charges within the material occurs. The force
exerted on an electron by the electric field, E(t) of a harmonic
wave of frequency .omega., gives an equation of motion for an
electron of
m e 2 x t 2 + m e .gamma. x t + m e .omega. 0 2 x - e E 0 cos
.omega. t = 0 ( 4 ) ##EQU00003##
where m.sub.e is the electron mass, E.sub.0 is the magnitude of the
applied electric field, .omega..sub.0 is the characteristic (or
resonance) frequency, .omega. is the frequency of the applied
electric field, e is the electronic charge and x is the distance
moved by an electron under the influence of the applied electric
field. m.sub.e.gamma.dx/dt is a damping term representing the delay
between the application of the external field and the time after
which an equilibrium in the polarisation is established. The
polarisation of the material in this field is caused by N
contributing electrons and is given by P=exN, which is related to
the permittivity of the material, .di-elect cons. by
.di-elect cons.=.di-elect cons..sub.0+P(t)/E(t) (5)
Hence the permittivity of the material is given by
= 0 + 2 N m e 1 ( .omega. 0 2 - .omega. 2 - .gamma. .omega. ) ( 6 )
##EQU00004##
[0026] Furthermore, there is a relationship between the real
(.di-elect cons.') and imaginary (.di-elect cons.'') parts of the
permittivity of a material, given by the Kramers-Kronig
relations:
' ( .omega. ) = 0 + 2 .pi. .intg. 0 .infin. .omega. ' '' ( .omega.
' ) .omega. ' ( .omega. '2 - .omega. 2 ) ( 7 a ) '' ( .omega. ) = -
2 .omega. .pi. .intg. 0 .infin. [ ' ( .omega. ' ) - 0 ] .omega. '
.omega. '2 - .omega. 2 ( 7 b ) ##EQU00005##
[0027] These characteristic frequencies (.omega..sub.0) are found
experimentally by a maximum in the imaginary permittivity component
and represent a region of absorption over which incident
electromagnetic energy is converted to heat through electron-phonon
interactions within the material. A phonon is an elastic wave
caused by harmonic vibrations within the crystal lattice.
[0028] Over the frequency range containing the absorption band, the
real permittivity component will also be frequency
dependent--through the Kramers-Kronig relationships. The nature of
this frequency dependence is related to the level of damping. At
high frequencies, generally well above the microwave region, the
damping effects are greatly reduced and the polarisation mechanisms
are related to the creation of dipoles at electronic and atomic
scales. In this case the real polarisability component is of a
resonant nature centred on the characteristic frequency as shown in
FIG. 1. At lower frequencies, including the microwave region, the
damping effects are larger and the polarisation mechanisms are
related to molecular through to macroscopic scales. The response
about the characteristic frequencies tends to that of a critically
damped system and the real polarisability component decays
monotonically with increasing frequency, as shown in FIG. 2. This
is known as dielectric relaxation. These effects can be used to
absorb the energy of incident electromagnetic radiation in a
frequency range centred on the characteristic frequency, rather
than transmitting it or reflecting it back to its source.
[0029] The ratio of the imaginary to real components represents the
phase lag of the electric component of an incident electromagnetic
wave inside the material, compared to the electric field component
of the incident electromagnetic wave outside the material.
[0030] At an interface, such as that shown in FIG. 3, it is the
relative permittivity that determines the proportion of incident
radiation that is reflected, shown as r, and the proportion which
is transmitted, shown as t. This is given by the Fresnel equations,
(where .zeta. and * indicate components when the incident electric
field is perpendicular and parallel to the plane of incidence
respectively)
r.sub..zeta.=[Z.sub.2 cos(.theta..sub.i)-Z.sub.1
cos(.theta..sub.t)]/[(Z.sub.2 cos(.theta..sub.i)+Z.sub.1
cos(.theta..sub.t)] (8a)
r.sub.*=[Z.sub.1 cos(.theta..sub.i)-Z.sub.2
cos(.theta..sub.t)]/[(Z.sub.1 cos(.theta..sub.i)+Z.sub.2
cos(.theta..sub.t)] (8b)
t.sub..zeta.=2Z.sub.2 cos(.theta..sub.i)/[Z.sub.2
cos(.theta..sub.i)+Z.sub.1 cos(.theta..sub.t)] (8c)
t.sub.*=2Z.sub.2 cos(.theta..sub.i)/[Z.sub.1
cos(.theta..sub.i)+Z.sub.2 cos(.theta..sub.t)] (8d)
where Z.sub.2=.mu..sub.r/.di-elect cons..sub.r and the subscripts 1
and 2 refer to the materials either side of the interface, with
material 1 containing the incident electromagnetic wave. Material 1
is often air in which case Z.sub.1=.mu..sub.r1=.di-elect
cons..sub.r1=1. If material 2 is non-magnetic then .mu..sub.r2=1,
also.
[0031] For example, for metals in air, most of the incident
radiation in the microwave and visible regions of the spectrum
(frequencies in the region of approximately 10.sup.8 to 10.sup.15
Hz) is reflected. For example, the reflectivity of freshly
deposited aluminium, in air, is around 94% to 99% for wavelengths
between 10 and 30 .mu.m.
[0032] The angles of incidence (.theta..sub.i) and refraction
(.theta..sub.t) in these equations are given by Snell's law,
n.sub.1 sin .theta..sub.i=n.sub.2 sin .theta..sub.t (9)
where n.sub.2=.di-elect cons..sub.r.mu..sub.r and the subscripts 1
and 2 are as defined for Z in the Fresnel equations.
[0033] It is clear then that identifying materials with different
permittivities can enable the design of components and devices with
different electromagnetic functionality (for example, different
levels of reflection, transmission and absorption) operating over
specific regions of the electromagnetic spectrum. However, the
range of naturally occurring permittivities has become restrictive
to the design engineer. For example, either because the desired
real permittivity value is not available or absorption mechanisms
do not exist at a required frequency, or in a material that has the
required processibility, mechanical, environmental or visual
properties. For these reasons, engineers have sought to form
composite media with tailored complex permittivity. For example,
and for many years, high permittivity materials and metals have
been added, in powdered forms, to polymers and other low
permittivity host materials (matrices) (e.g. ceramics and glasses)
to raise the base permittivity of the host or to engineer
absorption (e.g. through electrical resistance or the
Maxwell-Wagner-Sillars effect). The permittivity of these composite
media is now considered an `effective` permittivity. For this to be
valid, and the composite medium to be treated as a homogeneous
material for design purposes, the size of the inclusions must be
smaller (and ideally) much smaller than the wavelength of
interest.
[0034] Work has also been done on trying to design solid materials
that have a plasma frequency at lower frequencies than naturally
occur in metals.
[0035] It has been known for some time [Bracewell R, Wireless
Engineer, p. 320, 1954], that periodic arrays of metal elements can
be used to form composite media with low plasma frequencies. More
recently [Pendry J et al, Physical Review Letters, vol. 76, p.
4773, 1996] it was demonstrated that a periodic lattice of thin
metallic wires could exhibit a plasma frequency given by;
.omega..sub.p.apprxeq.2.pi.c.sup.2/(d.sup.2 ln(d/r)) (10)
in the microwave region when the wire radius (r) is much smaller
than the wire spacing (d), and c is the speed of light in vacuum.
For example, when the wire radius is 20 .mu.m and the wire spacing
is 5 mm, the plasma frequency is approximately 10 GHz.
[0036] There have been no other experimental observations of plasma
resonances at microwave frequencies in naturally occurring
materials or artificial composites other than in the fine wire
system discussed above. However, there is evidence of low frequency
plasmons in the infrared region of the electromagnetic spectrum.
For example, low frequency plasmons have been observed in
intrinsically conducting polymers (Kohlman R et al, Chapter 3,
Handbook of Conducting Polymers, Second Ed., Ed. Skotheim,
Elsenbaumer and Reynolds, Marcel Dekker, New York 1998 ISBN
0-8247-0050-3), in coupled metallic island structures (Govorov et
al, Physics of the Solid State, vol. 40, p 499, 1998) and in
metallic photonic bandgap crystals (Zakhidov et al. Synthetic
Metals, vol. 116, p 419, 2001).
[0037] It is also known how to create artificial dielectric
structures, for example, for use as radar antennas (see Skolnik,
Introduction to Radar Systems, McGraw-Hill, London, 1981,
Martindale, J. Brit. IRE, vol. 13, p 243, 1953, Stuetzer, Proc.
IRE, 38, p 1053, 1950, and Harvey, Proc. IRE, vol. 106 Part B, p
141, 1959). An artificial dielectric comprises discrete metallic
particles of a macroscopic size. For example, these particles may
be spheres, disks, strips or rods embedded within a material of low
dielectric constant, such as polystyrene foam. These particles are
arranged in a three dimensional lattice configuration, with the
dimensions of the particles in the direction parallel to the
applied electric field, as well as the spacing between the
particles, being of an order comparable with the incident
wavelength. For a small concentration of metallic spheres of radius
r and spacing d, and assuming there is no interaction between the
spheres, the dielectric constant of an artificial dielectric is
approximately
.kappa.=1+4.pi.r.sup.3/d.sup.3 (11)
(The symbol .kappa. has been used here to represent the dielectric
constant to avoid confusion with the use of the symbol .di-elect
cons. to represent permittivity.)
[0038] An artificial dielectric may also be constructed using a
solid dielectric material that comprises a controlled arrangement
of spherical or cylindrical voids.
[0039] Leaving behind the assumption of non-magnetic materials
taken above, and following on from wire arrays, it is also possible
to produce alternative periodic arrangements of metallic elements
which exhibit negative magnetic permeability also at microwave
frequencies (Pendry J et al., IEEE Transactions on Microwave Theory
and Techniques, vol. 47, p 2075, 1999). A combination of these two
techniques has also led to real materials exhibiting "left-handed"
electromagnetic behaviour or a negative angle of refraction (Smith
D R et al., Phys. Rev. Lett., vol. 84(18), p 4184, 2000.).
[0040] Very recently a theoretical model has led to speculation
[Holloway et al, IEEE Transactions on Antennas and Propagation, Vol
51, No. 10, October 2003] that it may be possible to produce double
negative media (i.e. having effective permeability and permittivity
simultaneously negative) by producing a composite material
consisting of insulating magnetodielectric spherical particles
embedded in an insulating background matrix.
[0041] The advantages of producing a material with a negative
magnetic permeability are similar to those found on producing a
negative permittivity. So far, we have only considered the electric
component of an applied electromagnetic field, but any material
which produces a loss when exposed to an applied electromagnetic
field can do so via the electric or the magnetic component of that
field, or both. The best materials which exhibit losses via the
magnetic field component are ferrites. These materials show
ferromagnetism, where saturation magnetisation does not correspond
to parallel alignment of the magnetic moments within the material.
Such materials also tend to have a spinel crystal structure,
comprising 8 occupied tetrahedral sites and 16 occupied octahedral
sites within a unit cell. For example, magnetite, Fe.sub.3O.sub.4
or FeO.Fe.sub.2O.sub.3 comprises both ferric (Fe.sup.3+) and
ferrous (Fe.sup.2+) ions. At saturation, the moments of all of the
Fe.sup.3+ ions on the tetrahedral sites and of the Fe.sup.3+ ions
filling 8 of the octahedral sites are aligned antiparallel, thus
cancelling each other out. The residual magnetic moment is
therefore only contributed to by the Fe.sup.2+ ions on the
remaining octahedral sites. Such a material has a complex
permeability,
.mu.=.mu.'+i.mu.'' (12)
where .mu.' is the real component and .mu.'' the imaginary
component.
[0042] Consequently, it is also desirable to find materials with a
negative permeability, since in these the magnetic component of the
electromagnetic wave will die away exponentially within the
material.
[0043] Although a single period of a fine wire array of the type
proposed by Pendry J. et al in Physical review letters, 76, 9773,
1996 is smaller than the incident wavelength (0.03 m at 10 GHz,
with .lamda./d.apprxeq.6) it is not much smaller (an order of
magnitude) than the wavelength. In practice, more than one period
of such a structure may be required in the direction of propagation
of an electromagnetic wave for the effective permittivity of such a
composite medium to be a valid representation of the
electromagnetic response of that medium. Consequently, this could
not be considered to be "thin" in comparison with the wavelength at
the plasma frequency. This may be a limiting factor to the use of
such media in practical applications. Media of the type proposed by
Pendry J. et al would also be difficult and expensive to
produce.
[0044] A further benefit to the design engineer would be realised
if it were possible to produce composite media with a tailored
plasma frequency. Particularly, if in a solid material, the plasma
frequency could be tailored to exist at lower frequencies than
naturally occur in metals. For example, work has recently been
reported in the scientific literature where this has been achieved
in the microwave or even radio frequency regions of the
electromagnetic spectrum.
[0045] There is, therefore, a need to develop alternative composite
media which exhibit metallic-like permittivity spectra with a
plasma frequency well below that of conventional bulk metals, which
do not depend on the use of components and spacings of the
components with dimensions related to the wavelength of interest,
whose effective permittivity is realisable on a scale much smaller
than the wavelength of interest, and which may be more easily
manufactured than the wire structures discussed above.
[0046] The present invention, in its various aspects, provides a
composite material, use of a composite material product, device or
apparatus, or a method as defined in one or more of the attached
independent claims to which reference should now be made.
[0047] Further preferred features of the invention are set out in
the dependent claims to which reference should also be made.
[0048] The invention in a first aspect provides a composite
material according to claim 1.
[0049] It is known to make composites comprising mixtures of
electrically conductive and non-electrically conductive particles
(see, for example, EP 779,629 or U.S. Pat. No. 4,997,708). However,
such known composites would not exhibit a plasma frequency. The
known composites of this nature are mostly reflective to incident
radiation below optical wavelengths. Composites embodying the
present invention could be reflective, absorbing or exhibit
filtering characteristics similar to electromagnetic bandgap
structures.
[0050] In the claims and description, the term random is intended
to mean without order. The electrically conductive material need
not be uniformly dispersed and there could be portions of the
material in which there is localized order of the electrically
conductive material.
[0051] In a preferred embodiment, the electrically conductive
material has no long range order within the composite material. By
long range order, it is intended that there is no regularity of
structure (crystal or otherwise) for the electrically conductive
material. Consequently there is no regularity of crystal structure,
or periodic lattice structure present of the conductive material
within the composite material.
[0052] As discussed in more detail below an alternative definition
of what is meant by no long range order is no order at or above the
dimensions corresponding to the effective wavelength of
electromagnetic radiation propagating in the material.
[0053] The invention in another aspect provides a composite
material comprising an electrically conductive material and a
non-electrically conducting material, wherein the concentration of
electrically conductive material is approximately at, close to or
above its percolation threshold.
[0054] A discussion of how to achieve percolation threshold is set
out in a paper by the inventor (Ian J. Youngs) "A geometric
percolation model for non-spherical excluded volumes"--Journal of
Physics D: Applied Physics 36 (2003) p. 738-747.
[0055] The inventor has appreciated that the existing theoretical
models of the behaviour of composite material comprising mixtures
of conductive and non-conductive or insulating materials are wrong.
The inventor is the first to establish that such materials may have
a plasma frequency below that of conventional bulk materials.
[0056] Preferably the composite material comprises particles of
electrically conductive and non-electrically conductive materials.
Such materials are easy to make.
[0057] Preferably, the particles are randomly distributed. The
inventor is the first to appreciate that composite materials need
not have a regular structure of the type previously thought
necessary (see, for example, Physical Review Letters, vol. 76, p.
4773, 1996] Pendry et al) to control or alter the plasma
frequency.
[0058] Preferably, the particles are small, with the conductive
particles being smaller than the non-electrically conductive
particles. The reasons for the behaviour of the composites of the
investigation are as yet not fully understood and investigations
are ongoing. However, it appears that composites in which spaces of
insulating material (e.g. a non-conductive particle or area) are
surrounded by conductive particles (e.g. a coating of conductive
particles on an insulating or non-conductive particle) are
particularly advantageous.
[0059] Preferably the conductive particles are resistant to
oxidation and passivation. Small particles are more reactive than
larger particles and it is therefore advantageous to have particles
whose surface will not react so as to try and ensure that the
conductive particles' behaviour (e.g. conductivity) is not altered
or affected by surface effects such as oxidation.
[0060] Preferably the oxidation resistant particles are noble
metals, conducting ceramics or metallic alloys.
[0061] Preferred embodiments of the present invention will be
described, by way of example only, with reference to the attached
figures. The figures are only for the purposes of illustrating one
or more preferred embodiments of the invention and are not to be
construed as unifying the invention or limiting the invention or
limiting the appendent claims. The skilled man will readily and
easily envisage alternative embodiments of the invention in its
various aspects.
[0062] In the figures:
[0063] FIG. 1 illustrates the high-frequency permittivity of a
typical dielectric material centred on a resonance frequency;
[0064] FIG. 2 illustrates the low-frequency permittivity component
of a typical dielectric material centred on a relaxation
frequency;
[0065] FIG. 3 shows an interface between two media for illustrating
the Fresnel equations;
[0066] FIG. 4 shows the theoretical electromagnetic properties of a
composite material with a filler conductivity of 1.times.10.sup.7
S/m in a matrix with a permittivity of 2.1-j0.001 at 1 GHz
predicted using Maxwell-Garnett mixture law;
[0067] FIG. 5 shows the theoretical electromagnetic properties for
the composite material of FIG. 4, but with a filler volume fraction
or concentration of 99.9 vol % predicted using Maxwell-Garnett
mixture law;
[0068] FIG. 6 shows the theoretical variation of composite
permittivity and conductivity with filler volume fraction or
concentration predicted using the Bruggeman model;
[0069] FIG. 7 illustrates the theoretical variation in permittivity
and conductivity under percolation theory using the Bruggeman
model;
[0070] FIG. 8 shows the theoretical variation in permittivity and
conductivity for a composite with a filler volume fraction or
concentration of 33.3 vol %, using the Bruggeman model;
[0071] FIGS. 9a to 9f illustrate, respectively, the theoretical
variations in the real permittivity, imaginary permittivity,
conductivity, dielectric loss tangent, real electric modulus and
imaginary electric modulus for composites with filler
concentrations above and below the percolation threshold predicted
using the Bruggeman model;
[0072] FIGS. 10a-10d illustrate, respectively, the experimentally
determined variation in the real permittivity, conductivity,
dielectric loss tangent and imaginary electric modulus respectively
of nano-aluminium in PTFE composites;
[0073] FIGS. 11a-11d illustrate, respectively, the experimentally
determined variation in the real permittivity, conductivity,
dielectric loss tangent and imaginary electric modulus respectively
of nano-silver in 100 .mu.m PTFE composites
[0074] FIGS. 12a-12d illustrate, respectively, the experimentally
determined variation in the real permittivity, conductivity,
dielectric loss tangent and imaginary electric modulus respectively
of nano-silver in 1 .mu.m PTFE composites
[0075] FIGS. 13a to 13d illustrate the experimentally determined
variation of the real permittivities in the microwave region for
different nano-silver in 100 .mu.m PTFE composites;
[0076] FIGS. 13e, 13f and 13g illustrate the experimentally
determined variation in conductivity, real permeability and
imaginary permeability, respectively, for different nano-silver in
100:m PTFE;
[0077] FIGS. 14a to 14d illustrate the experimentally determined
variation of permittivity in the microwave region for different
nano-silver in 1 .mu.m PTFE composites;
[0078] FIGS. 14e, 14f and 14g illustrate the experimentally
determined variation in conductivity, real permeability and
imaginary permeability, respectively, for different nano-silver in
1:m PTFE composites;
[0079] FIG. 14h is a comparison of the filler concentration
dependence of conductivity for different silver-filled composites,
highlighting variations in the gradient of the percolation
(insulator-conductor) transition (solid data points and data points
with a background represent samples exhibiting a plasma-like
response).
[0080] FIGS. 15a and 15b illustrate the experimental complex
permittivity spectrum of a titanium diboride PTFE composite;
[0081] FIGS. 16a to 16d illustrate the experimentally determined
dielectric response of nano-copper PTFE composites;
[0082] FIGS. 17a to 17d illustrate the experimentally determined
dielectric response of nano-cobalt PTFE composites;
[0083] FIGS. 18a to 18d illustrate the experimentally determined
microwave magnetic permeability spectra of cobalt PTFE and cobalt
wax composites;
[0084] FIGS. 19a to 19d illustrate the fit between experimental
data and modelled or theoretical data using the fitting parameters
given in Table 3;
[0085] FIGS. 20a to 20d illustrate the fit between experimental
data and modelled or theoretical data using the fitting parameters
given in Table 4;
[0086] FIGS. 21a to 21h show SEM (scanning electron microscope)
images of PTFE and nano-silver particles composites;
[0087] FIGS. 22a to 22d show a further fit between experimental
data and modelling or theoretical data using the fitting parameters
given in Table 5;
[0088] FIG. 23a shows low frequency conductivity measurements for
nano-silver compositions; and
[0089] FIG. 23b shows low frequency real permittivity measurements
for the nano-silver samples of FIG. 23a.
[0090] FIG. 24 is a schematic graph of the insulator-to-metal
transition for compositions with matrix particle sizes of 1 .mu.m
and 100 .mu.m;
[0091] FIG. 25 is a graph comparing the concentration dependence of
the conductivity of four silver-based compositions at 0.5 GHz;
[0092] FIG. 26 is a graph showing scaling of the real permittivity
of a sample of 100 nm Ag/100 .mu.m PTFE composite;
[0093] FIG. 27 is a graph showing scaling of the conductivity of a
sample of 100 nm Ag/100 .mu.m PTFE composite;
[0094] FIG. 28 is a graph showing scaling of the real permittivity
of a sample of 100 nm Ag/1 .mu.m PTFE composite;
[0095] FIG. 29 is a graph showing scaling of the conductivity of a
sample of 100 nm Ag/1 .mu.m PTFE composite;
[0096] FIG. 30 is a graph of frequency dependent conductivity of a
2 vol % 100 nm Ag/100 .mu.m PTFE composite over the range 1 Hz to 1
MHz and power law analysis;
[0097] FIG. 31 is a graph of frequency dependent real permittivity
of a 2 vol % 100 nm Ag/100 .mu.m PTFE composite over the range 1 Hz
to 1 MHz and power law analysis;
[0098] FIG. 32 is a graph of frequency dependent conductivity of a
8 vol % 100 nm Ag/1 .mu.m PTFE composite over the range 1 Hz to 1
MHz and power law analysis
[0099] FIG. 33 is a graph of frequency dependent real permittivity
of a 8 vol % 100 nm Ag/1 .mu.m PTFE composite over the range 1 Hz
to 1 MHz and power law analysis;
[0100] FIG. 34 illustrates dielectric response;
[0101] FIG. 35 is a summary of experimental results in terms of
measured conductivity at 0.5 GHz;
[0102] FIG. 36 is a graph showing the temperature dependence of the
conductivity of samples of 1 vol % 100 nm Ag/100 .mu.m PTFE
composite (2 samples);
[0103] FIG. 37 is a graph showing the temperature dependence of the
conductivity of samples of 2 vol % 100 nm Ag/100 .mu.m PTFE
composite (3 samples);
[0104] FIG. 38 is a graph showing the temperature dependence of the
conductivity of samples of 3 vol % 100 nm Ag/100 .mu.m PTFE
composite (3 samples);
[0105] FIG. 39 is a graph showing the temperature dependence of the
conductivity of samples of 5 vol % 100 nm Ag/100 .mu.m PTFE
composite (2 samples);
[0106] FIG. 40 is a graph showing the temperature dependence of the
conductivity of samples of 2 vol % 100 nm Ag/1 .mu.m PTFE composite
(1 sample);
[0107] FIG. 41 is a graph showing the temperature dependence of the
conductivity of samples of 8 vol % 100 nm Ag/1 .mu.m PTFE composite
(2 sample);
[0108] FIG. 42 is a graph showing the temperature dependence of the
conductivity of samples of 10 vol % 100 nm Ag/1 .mu.m PTFE
composite (2 samples);
[0109] FIG. 43 shows graphs of ln(conductivity)v 1/T and
ln(conductivity) v ln(temperature) for the samples of FIG. 37;
[0110] FIG. 44 shows graphs of ln(conductivity)v 1/T and
ln(conductivity) v ln(temperature) for the samples of FIG. 38;
and
[0111] FIG. 45 shows graphs of ln(conductivity)v 1/T and
ln(conductivity) v ln(temperature) for the samples of FIG. 42.
[0112] FIG. 46 illustrates the percolation threshold for a
composite material,
[0113] FIGS. 47a to 47c illustrate three different conductive
patterns made up of circular conductive elements for placing on a
dielectric substrate.
[0114] FIG. 48 illustrates an alternative conductive pattern made
up of crossed dipoles or crosses; and
[0115] FIGS. 49 and 50 illustrate two possible methods of making a
two-dimensional composite material using conductive patterns of the
type shown in FIGS. 47 and 48.
[0116] The inventor of the subject invention is the first to
appreciate, after extensive research and investigation, that it is
possible to produce a material having a plasma frequency below the
plasma frequencies of conventional bulk metals. The inventor is the
first to establish that materials comprising electrically
conductive particles within an insulating host medium can have a
plasma frequency below that of conventional bulk metals.
[0117] Although it is known (See Kiesow et al, Journal of Applied
Physics, Vol. 94, number 10-15 Nov. 2003) that plasma polymer films
with embedded silver nanoparticles can exhibit a reversible
electronic switching effect, the inventor of the subject
application is the first to realise that it is possible to create
materials having a plasma frequency below that for conventional
bulk metals using composite metals comprising a mixture of
electrically conductive and electrically non-conductive particles
in the manner set out in the claims of the subject application.
[0118] Some embodiments of the present invention are developed from
a non-periodic and generally random distribution of conducting
particles within an insulating host medium. The conducting
particles may be a metal, metal alloy, conductive metal oxide,
intrinsically conductive polymer, ionic conductive material,
conductive ceramic material or a mixture of any of these. In
preferred embodiments the conducting particles are stable against
oxidation and passivation and are, for example, noble metals such
as silver or gold, metallic alloys or conducting ceramics (titanium
diboride).
[0119] The insulating material may be particles of
polytetrafluoroethylene (PTFE), paraffin wax, a thermosetting
material, a thermoplastic material, a polymer, an insulating
ceramic material, glass or a mixture of insulating materials. The
insulating material could also be air, or contain trapped air.
[0120] Investigations into the performance of different composites
are ongoing. Presently, the inventor has determined that composite
materials comprising a mixture at approximately its percolation
threshold of conductive particles in the size range 1 nm to 1 .mu.m
and larger non-conductive particles (preferably at least 10 times
as large as conductive particles) have particularly desirable
properties. For example and as discussed in more detail below,
silver particles having an average size of 100 nm (as determined
using specific surface area measurements (BET)) randomly
distributed in a PTFE host made up of PTFE particles having an
average size of 100 .mu.m. (Aldrich 468811-8).
[0121] The nano silver in PTFE composite may be made by mixing
particles of the two constituent elements to form a mix, forming
the mix to produce a preform and recovering the composite
material.
[0122] The composite may be made by the methods described below in
connection with the experiments carried out by the inventors (see
experiments 1 to 3). In these methods powders are mixed and then
die-pressed at a pressure in the range 130-260 MPa for a period in
the range 80-300 second.
[0123] Although in the experiments the powder mixtures were
die-pressed at room temperature, the temperature used to press the
medium may be varied according to the polymer used, and should be
sufficient to allow preferable conductive particle coating of
non-conductive matrix by inducing mechanically or thermally induced
flow. Pressure and time may also be varied accordingly. Other
methods of consolidating a powder feedstock include extrusion and
flame-spraying.
[0124] Alternatively, the conducting powder could be dispersed by
stirring into a carrier material such as a thermoplastic at a
temperature above its melting point, or after the thermoplastic has
been dissolved in a suitable solvent, or paraffin wax. The
conducting particles could be mixed with a thermosetting polymer
prior to curing (by chemical or other means). The conducting
particles could be formed in situ within a polymer phase by
chemically or electrochemically reducing an appropriate precursor.
The conducting powder could be mixed with insulating ceramic or
glass powder, compacted and then sintered to form a consolidated
ceramic or glass component.
[0125] It is possible that any of these systems could be formed
into a foam (blown or syntactic or a hybrid of both), in which case
the conducting particles would reside in the cell walls. The foam
may be blown using air or an inert gas (for example, Argon). In
ceramic systems it could be possible to form the conducting phase
during the sintering reactions and for the conducting phase to
reside at grain boundaries within the resulting ceramic. A further
possibility is to form a metallic foam in which case the insulating
phase could be air. Again this could be achieved by blowing or
syntactically by the addition of hollow particles above the melting
point of the metal or a hybrid combination of the two methods. In
addition, it may be beneficial to influence the connectivity of the
conducting phase through the application of an external stimulus
such as an electric or magnetic field during the consolidation or
solidification process.
[0126] By connectivity, it is intended to mean any form of
connection between particles or other constituents which forms an
electrical connection. It is not necessary therefore that the
particles or constituents should be in physical contact, but an
electrical connection could be made even if there was a distance of
the order of a few nanometers between the particles or
constituents. This would increase the probability of electron
tunneling or hopping between particles or constituents, resulting
in charge transfer. In particular, any electrical conductivity
between particles in the form of a network, must extend over a
distance greater than the order of the wavelength corresponding to
the plasma frequency in the material.
[0127] Although the preparation of the samples is described in the
experiments on a laboratory scale, it would be possible to use
various known methods of materials processing on an industrial
scale, including, but not limited to, injection moulding,
extrusion, spraying or casting.
[0128] The results of experiments 1 to 3 (see below) show that it
is possible to produce composite materials exhibiting a plasma-like
response by dispersing silver nano-particles with micron-sized or
larger PTFE particles, or micron sized titanium diboride particles
with larger PTFE particles. The effect appears to be more
reproducible when the conducting particle size is significantly
smaller than the insulating particle size. This may be because it
is easier and more reproducible to form conductive networks around
and between larger non-conductive particles if the conductive
particles forming this network are small in comparison.
[0129] A further benefit of using conducting particles that are
much smaller than the insulating particles would appear to be a
significant reduction in the critical conducting particle
concentration--the percolation threshold--and more reproducible
control of insulator/conductor morphology.
[0130] However, particle size per se does not appear to be a first
order cause of the observed effects, but it is the nature of the
inter-particle contacts and formation of a percolated
microstructure which are critical, as illustrated by the particle
size difference effects discussed above and in connection with the
experiments discussed below. However, the ratio of sizes of
conductive to non-conductive particles may be less than, equal to
or greater than unity.
[0131] Further materials systems that may be of use are excluded
volume systems (which utilise small filler concentrations),
conductor coated particles and impregnated ceramic materials. Foams
and other well known insulating matrices may also be of use. Other
ceramic materials, including those where a second phase (for
example a conducting phase) is included at grain boundaries may
also be suitable for use with the invention, for example, Zinc
Oxide (ZnO) thin films. Metal-matrix composites may also be of
use.
[0132] In addition, it is proposed that the combination of the
current invention with a component that exhibits negative magnetic
permeability over a frequency range where the permittivity is also
negative (i.e. below the plasma frequency) would result in a
material with a negative refractive index over the same frequency
range. A suitable magnetic material would be a ferromagnetic
substance: For example the replacement of the purely conductive
filler particles discussed above with ferromagnetic metal particles
such as cobalt, iron or nickel or their alloys. Such a material
would exhibit a negative permeability if inherent damping
mechanisms were sufficiently suppressed or excluded.
[0133] The ferromagnetic material could be added to the insulator
phase prior to the formation of the negative permittivity composite
as shown by way of example in Experiments 1 and 2. Alternatively,
if the ferromagnetic component has sufficient electrical
conductivity then it could be used in place of the silver or
titanium diboride to form a composite with simultaneous negative
permittivity and permeability.
[0134] The effective properties of composites comprising a random
distribution of conductively particles in an insulating host medium
may be predicted using mixture laws (also referred to as effective
medium theories), of which there are many (Priou A Dielectric
Properties of Heterogeneous Materials, Elsevier, New York, 1992;
Neelakanta P Handbook of Electromagnetic Materials, CRC Press, New
York, 1995; Youngs I Electrical Percolation and the Design of
Functional Electromagnetic Materials, PhD Thesis, University of
London, 2001). In the majority of cases, selection of an
appropriate mixture law is achieved empirically. It is possible to
relate different mixture laws to specific combinations of particle
shape, orientation and microstructural arrangement. However, it can
be difficult to pre-determine the microstructural arrangement that
will result from a particular combination of components because the
particle arrangement will be influenced by surface chemistry and
processing conditions.
[0135] Bearing in mind the above limitations, it is possible to
select a small number of mixture laws that enable the engineer to
explore the qualitative nature of the filler concentration and
frequency dependence of complex permittivity that can be expected
for these composites, even if the laws may be quantitatively
incorrect.
[0136] It will become clear in the following analysis that one of
the existing mixture laws suggests that metals of the type claimed
would result in plasma frequencies lower than that of conventional
bulk metals. The inventor is the first to appreciate the
advantageous properties of the claimed materials. The following
discussion of the existing mixture laws clearly demonstrates how
no-one would have considered creating or using materials as claimed
in this application.
[0137] The earliest mixture laws were developed on the assumption
of dilute filler concentrations, with the separation between filler
particles being large compared to their radius. A good example is
that due to Maxwell-Garnett (Maxwell-Garnett J. `Colours in metal
glasses and in metal films`. Philosophical Transactions of the
Royal Society, CCIII, pp. 385, 1904.)
[0138] The Maxwell-Garnett model or mixture law defines how the
overall permittivity .di-elect cons. of the composite material is
related to the permittivity of the filler .di-elect cons..sub.f,
the permittivity of the matrix .di-elect cons..sub.m, and the
filler volume fraction V:
= m + 3 m V .DELTA. f + 2 m 1 - V .DELTA. f + 2 m ( 13 )
##EQU00006##
with .DELTA..di-elect cons.=.di-elect cons..sub.f-.di-elect
cons..sub.m. If the filler is a metal then its permittivity may be
approximated using the low frequency form of the Drude model
f = 1 - .sigma. f 2 .pi. f o ( 14 ) ##EQU00007##
[0139] Where .sigma..sub.f is the filler conductivity.
[0140] The filler volume fraction dependence of the relevant
effective electromagnetic properties (real and imaginary components
of permittivity, and conductivity) for a representative theoretical
composite with a filler conductivity (.sigma..sub.f) of
1.times.10.sup.7 S/m and a matrix permittivity of 2.1-j0.001 is
illustrated in FIG. 4 (using the Maxwell-Garnett model) for a
frequency of 1 GHz.
[0141] It is observed that both components of permittivity and
conductivity increase with increasing filler volume fraction from
those of the matrix to those of filler. In particular, it is
observed that the composite has properties close to those of the
filler phase when the filler volume fraction or concentration is
very close to 100%. Intuitively, this is incorrect for a composite
containing mono-disperse filler particles, especially in terms of
the composite conductivity, because it is to be expected that the
composite conductivity would approach that of the filler component
as soon as the particles touch--i.e. at close-packing, which occurs
for filler concentrations in the range 52 to 74 vol. % for
spherical particles. Nevertheless, it is recalled that the
Maxwell-Garnett model was developed under the assumption of dilute
filler concentrations.
[0142] The frequency dependence of the effective electromagnetic
properties for the same composite at a filler concentration of 99.9
vol. %, derived using Maxwell-Garnet theory, is illustrated in FIG.
5. A relaxation-type dielectric response similar to that shown in
FIG. 2 is observed. The relaxation frequency is at approximately 10
THz (10.times.10.sup.12--i.e. above the microwave range, which is
approximately 10.sup.8 to 10.sup.12 Hz).
[0143] An important advance was made by Bruggeman (Bruggeman D.
"Annalen der Physik Leipzig", vol 24, p 636, 1935.sub.e). Bruggeman
sought to overcome the dilute approximation by treating the filler
particles as being dispersed within a background medium that had
the permittivity of the mixture rather than the permittivity of the
insulating phase. This led to the following equation, known as the
Bruggeman symmetric mixture law or effective medium theory.
( 1 - V ) - m 2 + m + V - f 2 + f = 0 ( 15 ) ##EQU00008##
[0144] FIG. 6 illustrates the theoretical filler volume fraction
concentration dependence of the real (.di-elect cons.',
.sigma..sub.f') and imaginary (.di-elect cons.'',.sigma..sub.f'')
components of permittivity and conductivity for the same
representative composite (i.e. with a filler conductivity
.sigma..sub.f of 1.times.10.sup.7 S/m, a matrix permittivity
.di-elect cons..sub.m of 2.1-j0.001 and for a frequency of 1 GHz).
This figure may be compared directly to FIG. 4.
[0145] The Bruggeman model predicts that the properties of the
mixture increase dramatically at a critical filler concentration
that is much smaller than the concentration for close packing. This
critical concentration is generally referred to as the percolation
threshold (Vc). The Bruggeman model predicts (see FIG. 6) for
spherical particles randomly filling a cubic lattice, percolation
is predicted to occur at a filler volume fraction of approximately
35%. In fact, for real composite materials comprising spherical
particles randomly filling a cubic lattice, percolation is reached
at the much lower volume fraction of approximately 16%. The
Bruggeman theory is therefore quantitatively wrong insofar as
prediction of the critical threshold volume filler fraction V.sub.c
is concerned. It is however qualitatively correct in that the
percolation threshold of the material is important, since it
represents the filler volume fraction at which the composite system
will undergo an insulator-to-conductor transition. It is expected
that the composite material would exhibit insulator-like properties
for filler concentrations below the percolation threshold and
potentially metal-like properties for filler concentrations above
it.
[0146] Percolation theory is a way of describing the processes,
properties and phenomena in a random or disordered system. The
amount of disorder is defined by the degree of connectivity between
particles. If p is a parameter that defines the degree of
connectivity between various particles in a material, then if p=0,
none of the particles are connected, and if p=1, all the particles
are connected to the maximum number of neighbouring particles.
There is a point, p.sub.c (the percolation threshold), where each
of the particles is connected to the minimum number of neighbouring
particles, such that there is a sufficiently long unbroken path of
that type of particle for current to flow in the material.
[0147] In a metal matrix composite, where, e.g. aluminium particles
are dispersed in a ceramic matrix, the percolation threshold for
applied D.C. (Direct Current) is reached when there is at least one
continuous path of aluminium from one side of the matrix to the
other. In a similar metal matrix composite the percolation
threshold for applied A.C. (Alternating Current) is reached when
there are sufficiently long paths around particles at the ends of
the matrix, for electrons to move as far as is possible in each
direction of cycle of applied current before the direction of
applied current is reversed. In other words, the paths are
sufficiently long for electrons to move as far as the phase of the
applied alternating current allows them. At this point, the
material may begin to exhibit metallic characteristics; for
example, an electric current may flow.
[0148] The behaviour of random materials, for example those showing
no form of ordering or periodic structure, such as powder systems,
near their percolation threshold has been widely studied, both
experimentally and theoretically. It is apparent that, for
perfectly random systems, there are a number of features associated
with their behaviour over a narrow concentration range about the
percolation threshold.
[0149] Many of these features are related to the power-law response
observed in systems exhibiting percolative behaviour and the fact
that the exponents in these power-laws appear independent of the
precise nature of the material, except for the dimensionality of
the connectivity between particles. A macroscopic example of this
is the filler volume fraction or concentration dependence of the
real permittivity and conductivity for a conductor-insulator
composite near the percolation threshold. Percolation theory
suggests the following power-laws:
' .varies. ( V - Vc ) - s , .sigma. .varies. ( V - Vc ) t and '' =
.sigma. .omega. o ( 16 ) ##EQU00009##
[0150] Where .di-elect cons.' is real permittivity, V is the volume
fraction of the filler, Vc is the critical filler volume fraction
corresponding to the percolation threshold and .sigma. is
conductivity.
[0151] FIG. 7 illustrates this point using the data presented in
FIG. 6 and calculated using the Bruggeman mixture law. The
logarithm of each property is plotted against the logarithm of a
normalised filler volume fraction (V-Vc)/Vc. The data for real
permittivity .di-elect cons.' is for filler volume fractions
leading up to the percolation threshold. The data for the imaginary
permittivity .di-elect cons.'', and conductivity .sigma. are for
filler volume fractions above the percolation threshold filler
volume fraction Vc. The gradients in FIG. 7 provide the values for
the exponents set out in equation (16) above. It is deduced that
the Bruggeman mixture law predicts that both s and t equal unity.
It is at this point that the Bruggeman model deviates from
percolation theory on a quantitative level. Percolation theory
predicts that for particles connected on a three-dimensional
network, the exponents should have the following values: s=0.73 and
t=1.9.
[0152] FIG. 8 illustrates the frequency dependence of the effective
electromagnetic properties for the same composite at a filler
volume fraction V of 33.3 vol. %, calculated using the Bruggeman
mixture law. In terms of the normalised filler concentration
(V-Vc)/Vc defined previously, this concentration is equivalent to
that presented in FIG. 5 for the Maxwell-Garnett mixture law. It is
observed that the Bruggeman mixture law predicts a much broader and
non-Debye relaxation peak for this filler concentration which is
close to but below the percolation threshold. This peak may be
characterised by two characteristic frequencies .omega..sub..xi.
and .omega..sub.MWS that mark the clear changes in gradient visible
in all three parameters shown in FIG. 8. In addition, since the
data is already plotted on log-log scales, it is observed that the
data covering the central frequency range, defined by these two
characteristic frequencies, also obeys a distinct power-law
response. In this case, the gradients all equal one half.
[0153] Percolation theory predicts such a power-law response, with
the relationships:
.di-elect cons.'(.omega.,V=Vc)).varies..omega..sup.-.gamma. and
.sigma.(.omega.,V=Vc)).varies..omega..sup.x (17)
[0154] furthermore, that these exponents x, y are related to the
exponents s, t (see above) for the concentration dependence by:
x + y = 1 , x = t s + t .apprxeq. 0.72 , y = s s + t .apprxeq. 0.28
( 18 ) ##EQU00010##
[0155] Again, it is noted that the Bruggeman model is
quantitatively incorrect, yet self-consistent.
[0156] The loss angle .delta. (where tan(.delta.)=.di-elect
cons.''/.di-elect cons.', and .di-elect cons.'' is the imaginary
part of the permittivity, and .di-elect cons.' is the real part)
attains a constant value given by y.pi./2 for the frequency range
between the two characteristic frequencies, which may be specified
as
( V - Vc ) s + t .sigma. f o m .apprxeq. .omega. .xi. .ltoreq.
.omega. .ltoreq. .omega. MWS .apprxeq. .sigma. f o m ( 19 )
##EQU00011##
[0157] The term (V-V.sub.c).sup.s+t is a weighting to indicate how
close a composition is the percolation threshold. The frequencies
occurring between .omega..sub..xi. and .omega..sub.MWS indicate the
parallel nature of the behaviour of the real and imaginary
permittivity components, as shown, for example, in FIG. 8.
[0158] Thus, as the percolation threshold is approached, the lower
characteristic frequency .omega..sub..xi. tends to zero.
[0159] This discussion highlights the importance of an accurate
quantitative description of the electromagnetic response of
materials near the percolation threshold to the design of composite
materials for electromagnetic applications. The inventor has
appreciated that the existing theoretical models are wrong. The
Maxwell-Garnet model (see FIGS. 4 and 5) is both quantitatively and
qualitatively wrong in that it entirely fails to predict
percolation threshold effects. The Bruggeman model (see FIGS. 6 to
9) is quantitatively wrong as although it predicts percolation
effects it predicts values for the percolation threshold which
differ widely from actual measured values.
[0160] FIGS. 9a to 9f present the generic regimes according to the
Bruggeman model for the frequency dependence of the electromagnetic
properties of composites for filler volume fractions below, at and
above the percolation threshold. The concentrations used are
(V.sub.c-0.70), (V.sub.c-0.01), Vc, (V.sub.c+0.01) and
(V.sub.c+0.70), (all volume concentrations) where V.sub.c is the
critical filler volume fraction corresponding to the percolation
threshold. FIG. 9a shows the real permittivity, FIG. 9b the
imaginary permittivity, FIG. 9c the conductivity, FIG. 9d the
dielectric loss tangent, FIG. 9e the real electric modulus and FIG.
9f the imaginary electric modulus. It is observed that a metallic
or plasma-like dielectric response is not predicted even for filler
concentrations well above the percolation threshold.
[0161] As discussed above, the inventor has however appreciated
that the existing theoretical models are flawed. The inventor is
the first to appreciate that mixtures of conductive and
non-conductive parties can exhibit a dielectric response at
conductive filler concentrations from near to and above the
percolation threshold.
[0162] In the light of the inventor's realisation, a series of
experiments to determine the feasibility of producing composite
materials which exhibit a plasma frequency and a negative
permittivity to incident radiation of selected frequencies or
ranges or frequencies were carried out.
[0163] Initially, experiments were carried out to determine the
percolation threshold of each type of conductor-insulator composite
(defined by a unique choice of conducting filler and insulating
host medium) and to determine the level of conductivity achieved in
composites with filler concentrations above the percolation
threshold. Such experiments would also determine whether the
percolation threshold and the dielectric properties of the
materials were influenced by any particle size effects (for example
the ratio of the conducting particle size to the insulating
particle size).
[0164] For these experiments, composites comprising mixtures of
small (relative to the effective wavelength of electromagnetic
waves in the composite) particles of conductive materials such as
metals or conductive ceramics and small particles of insulating
materials such as insulating polymers are made up by mixing
controlled quantities of the conductive and insulating particles to
form a loose powder mixture. The materials may be mixed using a
shaker mixer and the particles may be of any suitable average size
or size distribution, although particle sizes that are small (less
than one tenth) of the wavelength of interest are preferred.
[0165] In particular, where the selected frequencies are in the
range 0.1 to 100 GHz (i.e. wavelength in the range 3 m to 3 mm),
suitable particle size distributions are from 1 nm to 250 nm for
the conductive particles (for example, nano-silver, having an
average particle size of 10 nm) and 1 .mu.m to 100 .mu.m for the
non-conductive particles. The powder mixture was then die pressed
at room temperature to provide a consolidated composite medium, for
example using a pressure in the range of 130-260 MPa applied for a
period in the range 60-300 seconds.
[0166] The plasma frequencies determined in the following
experiments give rise to a range of effective wavelengths within
the actual material. The values of these effective wavelengths are
determined using the equations:
C = f .lamda. ; C = ( 1 r .mu. r ) ( 1 o .mu. o ) ( 20 )
##EQU00012##
[0167] where .di-elect cons..sub.r and .mu..sub.r are the relative
permittivity and relative permeability respectively, .di-elect
cons..sub.o and .mu..sub.o are the permittivity and permeability in
a vacuum and c is the speed of light.
[0168] Initially, experiments were carried out to study the
dielectric properties of composite materials comprising various
fillers and conductive components. In each of these experiments,
the conductive components are in the form of particles. The
non-conductive components may also be composed of particles.
[0169] Size measurements for very small particles are dependent on
the form of measurement used to analyse the particles. This is
because of both morphology effects being important and the fact
that the particles will be polydisperse (not all of the same size).
In the following experiments (and elsewhere in this patent
application), sizes are average sizes determined by specific
surface area measurements (BET).
Experiment 1 (See FIGS. 10a to 10d)
[0170] Initially, four nano-aluminium PTFE
(polytetrafluoroethylene) mixtures were prepared, with two
different PTFE average particle sizes used to investigate particle
size effects, as shown in Table 1 below. The nano-aluminium had an
average size of 100 nm as measured using specific surface area
measurements (BET). The two other experiments and the preferred
embodiments of the invention described above PTFE particle sizes
used in this, were 1 micron powder (Aldrich 43093-5) and 100 micron
powder (Aldrich 46811-8).
TABLE-US-00001 TABLE 1 nano-aluminium and PTFE particle sizes in
initial experiment nano-aluminium PTFE particle size concentration
(vol. %) (.mu.m) 1.7 100 8.1 100 8.1 1 15.6 1
[0171] For each composition, appropriate quantities of the
different materials were measured into a container. The container
was then placed in a dry argon atmosphere (less than 50 ppm air)
for at least 12 hours to remove any residual moisture so as to
reduce particle agglomeration during mixing. The container was then
sealed under the argon atmosphere before placing on a shaker mixer
that was then operated for approximately 60 minutes to thoroughly
mix the particles. The argon atmosphere minimises any further
oxidation of the particles during mixing. The resulting powder was
then die-pressed at room temperature at a pressure of 260 MPa for
300 seconds to produce test samples.
[0172] For the measurements of complex permittivity over the
frequency range 10 mHz to 1 GHz the sample geometry was a disc with
a diameter of 10 mm and a uniform thickness in the range 0.5 to 5.0
mm. The top and bottom faces of the sample were coated with a
conducting paint to improve electrode contact. For measurements of
complex permittivity and permeability over the frequency range 0.5
to 18 GHz the sample geometry was a toroid with an outer diameter
of 6.995 mm and an inner diameter of 3.045 mm (designed to fit
standard 7 mm coaxial microwave transmission line). The samples
again had a uniform thickness in the range 0.5 to 5.0 mm.
[0173] The resulting composite was then subjected to a number of
experiments to determine its frequency dependent dielectric
properties and its structure.
[0174] Electrical properties of the composites of experiment 1 are
shown in FIGS. 10a to 10d. FIG. 10a illustrates the real
permittivity, FIG. 10b the conductivity, FIG. 10c the dielectric
loss tangent and FIG. 10d the imaginary electric modulus for
nano-aluminium dispersed in PTFE. These measurements were
undertaken at room temperature using a Novocontrol broadband
dielectric spectrometer, comprising a Novocontrol Alpha dielectric
analyser for the frequency range up to 1 MHz and an Agilent 4291 RF
Impedance analyser for the frequency range 1 MHz to 1 GHz.
[0175] A comparison of FIG. 10 to FIG. 9, suggests that the highest
aluminium concentration for each PTFE particle size is above the
percolation threshold, as the trends in FIG. 10 in real
permittivity, conductivity, dielectric loss and electric modulus
are similar to those for compositions in FIG. 9 which are above
V.sub.c. In addition, it is feasible that the percolation threshold
for the larger PTFE particle size is lower. Therefore, it is
surprising that the increase in conductivity at 10 mHz from the
lowest to highest aluminium concentration for a given PTFE particle
size is less than three orders of magnitude. Normally, for
composites containing metal filler particles, it is expected that
the percolation transition would result in at least ten orders of
magnitude increase in composite conductivity at such a frequency.
Moreover, for filler concentrations above the percolation
threshold, the composite conductivity would exceed 1 S/m. In
addition, the upper limiting frequency, .omega..sub.MWS, for
maximum dielectric loss appears several orders of magnitude below
the microwave frequency range, (for comparison, conventional metal
particles yield values several orders of magnitude above 1 GHz).
This reduction in .omega..sub.MWS suggests that there has been a
significant reduction in the conductivity of the conducting phase,
below that of bulk aluminium. This may be due to appreciable
surface oxidation of the aluminium nano-particles. This oxidation
may be due in part to the particles being supplied under air,
rather than under hexane, which is known to prevent or at least
reduce surface oxidation effects. Because the resulting composite
conductivity was so low and the upper characteristic frequency for
critical behaviour associated with percolation theory was deduced
to be below the microwave region, microwave measurements of the
complex permittivity and permeability were not undertaken.
Experiment 2 (See FIGS. 11a to 14g)
[0176] Eight different silver/PTFE composites were prepared. Silver
particles with a mean size of approximately 100 nm were dry-mixed
with PTFE (polytetrafluoroethylene) particles as shown in Table
2:
TABLE-US-00002 TABLE 2 nano-silver and PTFE particle sizes in
initial experiment PTFE average size PTFE average size 100 .mu.m 1
.mu.m nano-silver 0.5 1 concentration 1 2 (vol. %) 5 10 15 20
[0177] Composites were prepared as described for Experiment 1. The
resulting composite was then subjected to a number of experiments
to determine its frequency dependent dielectric properties and its
structure.
[0178] The electrical properties of the composites resulting from
different concentrations or fractions of silver in 100 .mu.m PTFE
are shown in FIGS. 11a to 11d. FIG. 11a illustrates the real
permittivity, FIG. 11b the conductivity, FIG. 11c the dielectric
loss tangent and FIG. 11d the imaginary electric modulus for
nano-silver dispersed in 100 .mu.m PTFE.
[0179] The electrical properties of the composites resulting from
different fractions of silver in 1:m PTFE are shown in FIG. 12a to
12d. FIG. 12a illustrates the real permittivity, FIG. 12b the
conductivity, FIG. 12c the dielectric loss tangent and FIG. 12d the
imaginary electric modulus for nano-silver dispersed in 1 .mu.m
PTFE. The measurements shown in FIGS. 11a-11d were undertaken at
room temperature using a Novocontrol broadband dielectric
spectrometer, comprising a Novocontrol Alpha dielectric analyser
for the frequency range up to 1 MHz and an Agilent 4291 RF
Impedance analyser for the frequency range 1 MHz to 1 GHz.
[0180] The nano-silver composites exhibited a more obvious
percolative response than the nano-aluminium composite, with the
higher silver concentrations resulting in composites with
significant conductivity for both PTFE particle sizes. There is
also greater qualitative evidence that the percolation threshold is
lower for a larger PTFE particle size, with the percolation
threshold lying between 1.0 and 5.0 vol % for 100 .mu.m PTFE, and
between 2.0 and 10.0 vol. % for 1 .mu.m PTFE. Given that the
results for 1.0 and 2.0 vol. % for 1 .mu.m PTFE are quantitatively
very similar, it would appear that the percolation threshold will
be significantly above 2.0 vol. %.
[0181] FIGS. 13 and 14a to g show the microwave response for the
samples prepared in Experiment 2. These measurements were made
using an Agilent 8510 Vector Network Analyser with an S-parameter
Test Set and 7 mm Coaxial Transmission Line according to the method
of Nicolson, Ross (IEEE Trans Instrum. And Meas., vol 19, p 377,
1970) and Weir (Proc. IEEE, vol 62, p 33, 1974).
[0182] It is observed that for silver concentrations above the
percolation threshold, some samples have a real permittivity whose
frequency dependence is unlike that expected from the Bruggeman
model (through comparison to FIG. 9a, see samples XC02379 and
XC02380 at concentrations of 5% and 15% in FIGS. 13c and 13d). The
measured frequency dependence closely resembles that expected for a
plasma. Some test samples exhibit a plasma frequency in the
measured frequency range. Other test samples have a plasma
frequency above the measured frequency range. For the 1 .mu.m PTFE
samples, some samples only have a real positive permittivity, which
is a typical response for conductive composite materials. The
plasma-like response is most consistently observed for the 100
.mu.m PTFE samples. The conductivity highlights the percolation
transition, as shown in FIGS. 13e and 14e. These microwave response
results indicate that the material would be reflective to incident
electromagnetic radiation at frequencies below the plasma
frequency, but strongly absorbing above it.
[0183] These measurements also indicate a diamagnetic effect for
silver concentrations above the percolation threshold, with a
maximum magnetic loss associated with this effect. This is
consistent with the Kramers-Kronig relations. Visual inspection of
the composite material highlighted a significant optical
reflectivity and a silvery appearance.
[0184] FIG. 14h compares the filler concentration dependence of the
conductivity for different silver particle filled composites at an
arbitrary frequency of 0.5 GHz. Composites formed from nano-silver
particles dispersed with 100 .mu.m and 1 .mu.m PTFE particles are
compared to previously obtained silver coated microspheres
dispersed in paraffin wax [see Youngs I. Dielectric measurements
and analysis for the design of conductor/insulator artificial
dielectrics. IEE Proc., Sci. Meas. & Tech., 147(4), p 202, July
2000; Youngs I. Electrical percolation and the design of functional
electromagnetic materials. PhD Thesis, University College, London.
2001]. It is observed that the gradient of the percolation
transition for the nano-silver/1 .mu.m PTFE composite is similar to
that for the microsphere/wax composites although the latter has a
higher percolation threshold. In contrast, the gradient of the
percolation transition for the nano-silver/100 .mu.m PTFE
composites is much reduced. This difference is consistent with the
relative positions of the composites on the particle size ratio
scale. The microsphere/wax system exhibits a perfectly random
microstructure and because the particle size ratio of the
nano-silver/1 .mu.m PTFE system is relatively close to unity its
microstructure should be similarly random, whereas the
nano-silver/100 .mu.m PTFE system exhibits a clear excluded-volume
microstructure. This striking difference serves to explain the
increased repeatability observed in the properties of nominally
identical samples of nano-silver/100 .mu.m PTFE prepared at filler
concentrations spanning the transition region.
[0185] As can be seen in FIG. 14h (which shows samples exhibiting a
plasma-like response as solid data points and/or data points with a
background) the plasma like response is exhibited for samples above
the percolation threshold and on or approaching the upper plateau
of the conductivity against concentration plot. The experiments
suggest that the composite must have a conductivity of greater than
10 S/m and preferably about 30 S/m for a plasma-like response to be
exhibited.
Experiment 3 (See FIGS. 15a and 15b)
[0186] Titanium diboride powder, of a maximum particle size of 45
.mu.m was dry-mixed with PTFE particles having an average size of 1
.mu.m at a titanium diboride fraction of 50 vol. %, and processed
as described above for Experiment 1. The titanium diboride powder
was 45 micron powder purchased from Goodfellow Cambridge
Limited.
[0187] FIGS. 15a and 15b, respectively, show the experimental
complex permittivity and permeability spectrum of the resulting
composite, over a frequency range of 0.5 to 18 GHz (measured using
the same method used in Experiment 2.
[0188] Titanium diboride was selected because it is an oxidation
resistant ceramic conductor.
[0189] The plasma resonance .omega..sub.p is clearly visible at
approximately 3 GHz. There are additional zero-points in the real
permittivity (at approximately 5 and 10 GHz), unlike the silver
samples discussed above. The highest (3rd) zero crossing (shown as
.omega..sub.p1) is a plasma frequency that may be associated with a
group of charge carriers that are more localised (which cannot
cross the sample and so are probably part of finite clusters
unconnected with the percolating cluster). Reference can be made to
the Handbook of Conducting Polymers (Kohlman R et al ISBN
0-8247-0050-3). The ratio of .omega..sub.p to .omega..sub.p1 is
associated with the ratio of free electrons to the full conduction
electron density.
[0190] There were difficulties in replicating the results of
Experiment 3. The inventor believes that these difficulties may
result from the fact that the conductive titanium diboride
particles are larger than the non-conductive PTFE particles.
[0191] Experiments 4 and 5 (See FIGS. 16 to 18)
[0192] Following the results of experiments 1 to 3, the inventor
has appreciated that it is also possible to produce composite
materials utilising copper and cobalt nano-particles. Three
composite materials were made: a nano copper in PTFE composite
comprising copper particles having an average size of 90 nm and
PTFE particles having an average size of 100 .mu.m; a nano cobalt
in PTFE composite with cobalt particles having an average size of
20 nm and PTFE particles having an average size of 100 .mu.m; and a
nano cobalt in wax composite with cobalt particles having an
average size of 20 nm. The materials were produced as including
PTFE and all the experiments carried out as described above for
Experiment 1. The cobalt-wax composites were prepared by first
dissolving the required quantity of paraffin wax (paraffin wax
flakes--Aldrich 41166-3) using hexane and then stirring-in the
required quantity of nano-cobalt powder. Stirring was continued
until the solvent evaporated and a solid mixture remains. Test
samples were prepared by die-pressing as described for Experiment
1.
[0193] FIGS. 16 and 17 show the measured dielectric responses for
the copper and cobalt composites, respectively, the experiments 4
and 5. Although the dielectric responses of copper and cobalt are
similar to that of aluminium, as shown in FIGS. 16 and 17, of these
three fillers, cobalt composites produce the highest conductivity,
subject to the accuracy of filler concentration. FIGS. 16a and 17a
show real permittivity, FIGS. 16b and 17b show imaginary
permittivity, FIGS. 16c and 17c show conductivity, FIGS. 16d and
17d show dielectric loss tangent, FIGS. 16e and 17e show real
electric modulus and FIGS. 16f and 17f show imaginary electric
modulus.
[0194] FIG. 18 shows that negative real permeability has not been
observed in either cobalt-PTFE or cobalt-wax composites, but that a
ferromagnetic contribution (the reduction in real permeability with
increasing frequency) inherent to the cobalt particles is
observed.
[0195] Cobalt is a transition metal with unpaired electrons in the
outer d-orbitals. These unpaired electrons give rise to domains of
aligned magnetic dipoles and a net magnetisation which may be
represented by a vector precessing about a preferred
crystallographic axis. The precession frequency is determined by
specific material parameters which relate to the magnetic
anisotropy field inherent to the material. An incident
electromagnetic wave can couple to this precession and at a
critical frequency at which the incident frequency approaches the
natural precession frequency resonant absorption will occur. For
the transition metals and many ferrites (transition metal oxides)
this occurs at microwave frequencies. The features observed in the
experimental data are evidence of this process and moreover,
demonstrate that damping processes are present resulting in
features that are closer to the relaxation form (discussed for
dielectric response) rather than a sharp resonance.
[0196] This ferromagnetic contribution increases with filler
fraction, although the dependence of the magnetic properties on the
filler fraction is not dependent on the percolation threshold.
Consequently, it is possible to maximise the magnetic properties by
simply increasing the filler fraction or concentration.
[0197] In composites embodying the present invention (including
those discussed in relation to the experiments FIGS. 10-18 above);
the electrically conductive material exhibits no long range order
over a distance of the order of the wavelength of radiation
propagating in the material, and for frequencies close to the
plasma frequencies (where the permittivity would be close to zero
and there is a singularity), the effective wavelength of
electromagnetic radiation in the material diverges. Waves
travelling through a material have an effective wavelength which is
governed by the permittivity of the material. As the material's
permittivity drops, the effective wavelength increases. However,
there is a singularity because at the plasma frequency the
permittivity is zero which would give an effective wavelength of
infinity.
[0198] This should not be taken to mean that amongst the conductive
component there is no regular ordering of individual particles, but
merely that clusters and networks are formed. In the composites,
the conductive material is randomly dispersed although not
necessarily uniformly dispersed. There is no form of periodicity in
the dispersion of the conductive component. The amount of
electrically conductive material is preferably sufficient to form a
conductive network, extending over a distance of the order of the
effective wavelength of radiation travelling through the material.
There is therefore also no long range order of particles forming
the network or within the network.
[0199] A single conductive network may be formed, which extends
from one face of the material to another, preferably an opposite
face, or a plurality of linked networks (i.e. linked by clusters)
may be formed.
[0200] The network may be in one, two or three dimensions. This
merely reflects the dimensionality of the connectivity between the
individual elements forming the network. However, this does not
place any form of limitation on the structure or design of the
material in which the network exists. For example, it may be
possible to have a three-dimensional material, which contains a
two-dimensional network. Other forms of material, such as sheets or
hollow bodies manufactured from sheets or other materials may also
contain one-dimensional, two-dimensional or three-dimensional
networks.
[0201] Although only materials which are designed to exhibit a
negative permittivity with a plasma frequency in the microwave
regions of the electromagnetic spectrum have been described here,
it will be understood by those skilled in the art that the same
techniques of materials design and production can be applied to
produce a composite material which exhibits a small positive
permittivity, resulting in a material with a small (less than
unity) positive refractive index. Such materials are of interest as
if their refractive index is less than that of air, total internal
reflection could be achieved easily for radiation incident from air
onto such a material.
[0202] The physics underlying the effects described above is
complicated and not yet fully understood. As is clear from the
experiments carried out by the inventor the existing models fail to
accurately predict the behaviour of composite materials having
conductive material in an insulating host. The inventor was the
first to appreciate how such materials would behave and how they
have a plasma frequency which may be affected by the nature of the
electrically conductive and non-conductive materials making up a
composite material. The inventor's analysis suggests that there are
a number of theoretical models which when modified, the inventor
believes have the potential to fit the experimental evidence and
explain the dependence of the plasma frequency on material
parameters such as particle shape, size, conductivity,
microstructure and concentration to aid composite design.
[0203] The candidate models identified by the inventor as having
the potential, when modified, to fit the measured microwave
plasma-like response include:
[0204] 1) The model for the infra-red dielectric response of
intrinsically conducting polymers discussed in Kohlman R, Epstein
A. Insulator-metal transition and inhomogeneous metallic state in
conducting polymers. Chapter 3 (pages 100-110 in particular) in
Handbook of Conducting Polymers, 2.sup.nd Ed., Marcel Dekker, New
York, 1998;
[0205] 2) The model for metallic patches joined by narrow
connections discussed in Govorov A, Studenikin S, Frank W. Low
frequency plasmons in coupled electronic microstructures. Physics
of the Solid State, 40(3), p 499, 1998; and
[0206] 3) The effective medium model discussed in Sarychev &
Shalaev. EM properties of metal-dielectric composites beyond the
Quasi-static approximation. Physics Reports, 335, p 275 371
2000.
[0207] A comparison of the inventor's experimental results
described herein, appears to indicate that a modified version of
the Sarychev and Shalaev model provides a qualitative match to the
experimental data. This is an effective medium model that goes
beyond the quasi-static approximation by including a skin-depth
component (to determine the extent to which applied fields die away
within the material)
( 1 - V ) - m 2 + m + V - ~ f 2 + ~ f = 0 with ( 21 a ) ~ f = f 2 F
( k f a ) 1 - F ( k f a ) ( 21 b ) F ( x ) = 1 x 2 - cot ( x ) x
and ( 21 c ) k f = 2 .pi. f c f .mu. f ( 21 d ) ##EQU00013##
[0208] By inspection, it is deduced that this model is an extension
of the symmetric Bruggeman model given earlier. McLachlan
(McLachlan D, Heiss W, Chiteme C and Wu J. Physical Review B,
58(20), p 13558, 1998.) has previously modified the Bruggeman model
to introduce the features of percolation theory in a more
quantitative fashion. Specifically, McLachlan introduces the
percolation threshold and the power law exponents
( 1 - V ) 1 / s - m 1 / s ( 1 - V c V c ) 1 / s + m 1 / s + V 1 / t
- f 1 / t ( 1 - V c V c ) 1 / t + f 1 / t = 0 ( 22 )
##EQU00014##
[0209] The similarity of these models leads to the application, by
the inventor, of McLachlan's phenomenological modifications to the
Sarychev-Shalaev model,
( 1 - V ) 1 / s - m 1 / s ( 1 - V c V c ) 1 / s + m 1 / s + V 1 / t
- ~ f 1 / t ( 1 - V c V c ) 1 / t + ~ f 1 / t = 0 ( 23 )
##EQU00015##
[0210] Analogous equations can be set out for the magnetic
permeability.
[0211] The real benefit of the new model is that it can be used to
simultaneously predict or fit both the complex permittivity and
permeability of a conductor-insulator composite. The parameters in
the model are: [0212] matrix and filler permeability and
permittivity, complex if required; [0213] filler concentration or
fraction; [0214] percolation threshold; [0215] percolation
exponents; [0216] filler particle size; and [0217] frequency of the
applied electromagnetic field.
[0218] FIG. 19 illustrates an attempt to fit representative
experimental data, in the form of the complex permittivity and
permeability for 5 vol. % silver nano-particles (the average size
100 nm) mixed with 100 .mu.m PTFE particles, over the frequency
range 0.5 to 18 GHz using the Sarychev-Shalaev-McLachlan model. In
this case, the percolation exponents were set at unity,
representing the situation for the Sarychev-Shalaev model. All
other parameters were set to values representative of the measured
composite as shown in Table 3:
TABLE-US-00003 TABLE 3 Parameters for FIG. 19 Parameter Value
Matrix permittivity 2.1-j0.001 Matrix permeability 1 Filler
conductivity (S/m) 1E7 Filler permeability 1 Percolation threshold
0.04469, 0.04470 Filler volume fraction 0.05 Percolation exponent,
s 1.0 Percolation exponent, t 1.0 Filler particle radius (nm)
50
[0219] It is observed that the diamagnetic effect in the magnetic
permeability is not predicted, the conductivity of the composite is
over estimated and no minimum is predicted, but most significantly
a plasma frequency is not predicted even with control of the
percolation threshold to a tolerance of 0.001 vol. %.
[0220] If the values of the percolation exponents are set to the
universal values for a three-dimensionally connected network, then
it becomes possible to predict a plasma-like response. This is
illustrated in FIG. 20. However, the gradient of the real
permittivity at the plasma frequency remains poorly predicted, as
does the composite conductivity and the magnetic permeability. The
parameters used in this calculation are shown in Table 4:
TABLE-US-00004 TABLE 4 Parameters for FIG. 20 Parameter Value
Matrix permittivity 2.1-j0.001 Matrix permeability 1 Filler
conductivity (s/m) 1E7 Filler permeability 1 Percolation threshold
0.04 Filler volume fraction 0.05 Percolation exponent, s 0.73
Percolation exponent, t 1.9 Filler particle radius (nm) 50
[0221] A much better qualitative fit to all four parameters is
obtained by re-considering the structure of the composite. In the
case of the nano-silver particles mixed with 100 .mu.m PTFE
particles, concentrations above the percolation threshold resembled
a close-packed arrangement of approximately 100 .mu.m diameter
pseudo-conducting particles. The pseudo-conducting particles are
taken to have a PTFE core with semi-continuous or continuous silver
coating created by the silver nano-particles. This is shown in the
SEM (scanning electron microscope) images of FIG. 21.
[0222] FIGS. 21a, 21b, 21c and 21d show backscattered images of
compositions comprising 0.5 vol %, 1.0 vol %, 5.0 vol % and 15 vol
% nano-silver particles and 100 .mu.m PTFE particles respectively.
In FIGS. 21a and 21b, it is clear that individual silver particles
form some clusters on the surface of the PTFE particles, but not
enough to form a conductive network. Consequently these particular
samples do not conduct, or exhibit a plasma frequency.
[0223] FIGS. 21c and 21d show compositions with a higher
nano-silver concentration. In FIG. 21c, the nano-silver
concentration is high enough that some clusters have begun to form
networks, one of which is shown stretching from the left-hand side
of the image to the right-hand side. In FIG. 21d, the silver
concentration is high enough to form a coating of approximately
three silver particles deep over each PTFE particle. Both of the
samples shown in FIGS. 21c and 21d conduct, and exhibit a plasma
frequency.
[0224] FIGS. 21e and 21f show materials with identical nano-silver
concentrations (5.0 vol %) with PTFE particles of 100 .mu.m and 1
.mu.m size, respectively. The nano-silver distribution in FIG. 21f
is fairly regular across the entire sample, whereas that in FIG.
21e clearly forms a network.
[0225] FIGS. 21g and 21h show backscattered images of two nominally
identical compositions with 10 vol % nano-silver particles and 1
.mu.m PTFE particles. The sample in FIG. 21g exhibited a plasma
frequency, whereas that in FIG. 21h, did not, but exhibited a
"conventional" positive permittivity.
[0226] It is necessary to determine how the model parameters relate
to the materials tested, which is determined by the behaviour of
the insulator phase, the PTFE particles. Taking a case where the
PTFE particles have a nominal radius of 50 .mu.m, the silver
particles have a tendency to coat the surface of the PTFE
particles. Ultimately, this leads to the creation of
pseudo-conducting particles once there is a percolating network of
silver particles over the PTFE particle surface. This has occurred
in the samples tested because the results demonstrate a significant
DC conductivity. These conductor-coated particles are also
close-packed. Close-packing occurs for concentrations of the order
of 60 vol %.
[0227] A second explanation is that the properties are driven by
two-dimensional percolation over the sample surface because the
theoretical percolation threshold for two-dimensional systems is 50
vol %. These points are emphasised by the backscatter scanning
electron micrographs presented in FIGS. 21a to 21d.
[0228] It is also of interest to compare the microstructures of the
composites formed using 100 .mu.m and 1 .mu.m PTFE, and to consider
why the properties of the latter have a much lower sample to sample
repeatability, as shown in FIGS. 21e and 21f. The excluded volume
microstructure is much less evident for the smaller PTFE particle
size. In fact, in this case, the distribution of silver particles
appears much closer to a distribution that might be formed if the
silver particles are allowed to occupy space in the composite on a
perfectly random basis. The issue of repeatability can be explained
as follows. When the conducting filler particles are able to fill
space on a perfectly random basis, then a composite sample will
only become conductive when there is a connected network of
conducting particles across the bulk of the sample. However, when
the insulating matrix particles are much larger than the filler
particles, the bulk sample will conduct when there is a percolated
layer of particles surrounding individual matrix particles.
Simplistically, the scale of control is reduced to an individual
particle surface rather than the bulk dimensions of the object. At
present, the gradient of the transition from the excluded-volume
dominated behaviour to the random filling behaviour, as a function
of particle size ratio, is not known. The steeper this transition,
the smaller the matrix particles can be without reducing
repeatability. This would lead to the prospect of thinner coatings
or smaller components.
[0229] Since the conducting filler distribution is critical to the
phenomenon, it is also interesting to compare the microstructures
for two nominally identical samples, but which give quite different
dielectric response. For example, FIGS. 21g and 21h compare two
samples, which are nominally 10 vol % concentrations of silver
nano-particles dispersed with 1 .mu.m PTFE particles. The sample
shown in FIG. 21g exhibited a microwave plasma frequency, whereas
that shown in FIG. 21h had a conventional positive dielectric
response. The micrographs reveal a subtle difference in silver
particle distribution. There is an indication that the silver
particles are more uniformly dispersed in the sample shown in FIG.
21g. In the context of the model, a uniform dispersion of
sufficient filler particles to form a percolation path around a
matrix particle should more readily enable percolation over the
bulk and a higher composite conductivity. This is consistent with
the experimental conductivity data. The conductivity for high
silver concentrations in the 100 .mu.m PTFE composites is much more
repeatable and at the higher end of the spread in the equivalent
data for the 1 .mu.m PTFE composites. It is the 1 .mu.m PTFE
samples with highest conductivity that exhibit the plasma response.
This observation further supports the hypothesis that there is a
critical conductivity that must also be surpassed to achieve the
plasma response. This critical conductivity could be associated
with a conducting material being classed as `truly metallic`.
Indeed, the critical conductivity deduced from the available data
is close to Mott's limiting value for metals (approximately
10.sup.4 S/m). To further put this into context, the conductivity
of bulk copper is approximately 10.sup.8 S/m.
[0230] Consequently, it may be relevant to re-assign different
values to the conducting filler concentration, the percolation
threshold and the filler particle size. The resulting fit is
illustrated in FIG. 22. The parameters used in this calculation are
given in Table 5 below:
TABLE-US-00005 TABLE 5 Parameters for FIG. 22 Parameter Value
Matrix permittivity 2.1-j0.001 Matrix permeability 1 Filler
conductivity (S/m) 1E7 Filler permeability 1 Percolation threshold
0.6 Filler volume fraction 0.6025 Percolation exponent, s 0.73
Percolation exponent, t 1.9 Filler particle radius (nm) 50,000
[0231] As can be seen from the modelling results (in FIGS. 19, 20
and 22), although a good qualitative fit is obtained, there are
some discrepancies where differing sizes of PTFE filler are used.
The experiments show that there is little difference in the
magnitude of the diamagnetic effect for samples with 100 .mu.m PTFE
particles or 1 .mu.m PTFE particles. In the model, diamagnetic
effect is partly compensated for by adjusting particle size.
Consequently, the predicted properties for small particle
composites differ somewhat from those observed in experiments.
However, it may be possible to overcome this by modelling the
diamagnetic effect by including a macroscopic toroidal field
component, or alternatively using Mie theory, although other
factors such as sample geometry must be taken into account.
[0232] FIG. 22 demonstrates that a good qualitative fit can be
obtained using the modified Sarychev-Shalaev-McLachlan model for
the 5 vol. % silver nano-particles mixed with 100 .mu.m PTFE
particles, albeit after some re-assignment of certain parameters
including the filler particle size, filler fraction and percolation
threshold. For such modifications to be truly permissible, then
they should hold for related cases. An important example, is the 10
vol % silver nano-particles mixed with 1 .mu.m PTFE particles.
Here, the adjusted filler particle radius would need to be 500 nm.
This would have the effect of significantly reducing the
diamagnetic effect in the microwave range.
[0233] However, comparison of FIGS. 13 f and g to FIGS. 14 f and g
indicate that the diamagnetic effect is largely unaffected by the
change in PTFE particle size. Thus, greater understanding is
required before the modified Sarychev-Shalaev-McLachlan model can
be used to quantitatively design materials of this type.
[0234] The inventor has also observed plasma-like frequencies at
much lower frequencies, as shown in FIGS. 23a and 23b. Materials
with a nano-silver concentration of 5 vol %, and a PTFE particle
size of 100 .mu.m demonstrate a conductivity change at 10.sup.4 Hz
(FIG. 23a), and a negative real permittivity at around 10.sup.3 Hz
(FIG. 23b). These materials were prepared in the manner discussed
above for Experiment 1. In each case, the samples were cooled to
-60.degree. C. and -10.degree. C. or heated to 30.degree. C. This
gave fairly consistent results, with one sample exhibiting
repeatability.
[0235] The issues of particle size, particle packing and contact
areas of the particles in the composite material have been explored
further by the inventors in order to understand the mechanism by
which the conductivity gradient changes, and to enable the
production of materials of uniform and repeatable compositions
having tailored dielectric and conductive properties. The materials
comprise regions of electrically conductive and non-electrically
conductive materials, where the conductivity of each material is
determined by the degree of connectivity between the electrically
conductive regions.
[0236] FIG. 25 compares the concentration dependence of the
conductivity of four compositions at 0.5 GHz:
Ag (100 nm particle size) and PTFE (1 .mu.m particle size); Ag (100
nm particle size) and PTFE (1 .mu.m particle size); Ag (100 nm
particle size) and paraffin wax; and Ag (15 .mu.m diameter spheres)
and paraffin wax.
[0237] For each composition, appropriate quantities of the
different materials were measured into a container. The container
was then placed in a dry argon atmosphere (less than 50 ppm air)
for at least 12 hours to remove any residual moisture to reduce
particle agglomeration during mixing. The container was then sealed
under the argon atmosphere before placing on a shaker mixer that
was then operated for approximately 60 minutes to thoroughly mix
the particles. The argon atmosphere minimises any further oxidation
of the particles during mixing. The resulting powder was then
die-pressed at room temperature at a pressure of 260 MPa for 300
seconds to produce test samples.
[0238] The behaviour of these materials in the region of the
percolation threshold may be determined by either 3D percolation
only at close packing concentrations, or by 2D percolation over the
surface of the insulating particle. A distinction between these two
types of behaviour can be identified using the percolative power
law exponents.
[0239] Although the gradients of the percolation transition for the
100 nm Ag/1 .mu.m PTFE composites is similar to that of
microsphere/wax composites, the percolation threshold of the
microsphere/wax composites is higher. The gradient of the
percolation transition of the 100 nm Ag/100 .mu.m PTFE compositions
is reduced, which is consistent with the relative positions of the
materials on a particle size ratio scale. The gradient (on a
log-log scale) for the 1 .mu.m PTFE material is approximately 30,
whereas that for the 100 .mu.m PTFE material is approximately
7.
[0240] The microsphere/wax system exhibits a perfectly random
microstructure, and the particle size ratio of the 100 nm Ag/1
.mu.m PTFE is relatively close to unity (1:10), the microstructure
is also similarly random. However, the 100 nm Ag/100 .mu.m PTFE
system has a particle size ratio of 1:1000, and exhibits the
properties of an excluded volume microstructure, whose physical
properties arise from the use of a small filler concentration
within a composite material. In an excluded volume microstructure,
the regions of electrically conductive material will be excluded
from certain areas (the non-electrically conductive matrix), which
means that in order for the material to exhibit an electrical
conductivity, the conductive regions need to be connected somehow
across the non-electrically conductive regions. By increasing the
number of and/or volume of the excluded regions of the
microstructure, the rate at which connections are formed for
increasing concentrations of conductive material will drop, as it
requires more material to connect over the excluded regions than if
there were few or smaller excluded regions present. This then
produces the flattened gradient observed in the experiments. It is
also possible to use an electrically conductive matrix, such as a
foam to produce a network around gas-filled pockets. This would
also act as an excluded volume microstructure.
[0241] The power law exponents for the percolation transition can
be determined by scaling analysis of the real permittivity and
conductivity of the composites discussed above for filler
concentrations in the region of the percolation threshold. FIGS. 26
and 27 show the scaling of real permittivity and conductivity
respectively for 100 nm Ag/100 .mu.m PTFE compositions, and FIGS.
28 and 29 the scaling of real permittivity and conductivity
respectively for 100 nm Ag.1 .mu.m PTFE compositions.
[0242] According to percolation theory, these exponents should
adopt universal values that only depend on the dimensionality of
the percolation process. As the percolation threshold is approached
from below, the real permittivity should vary according to equation
24:
.di-elect cons..varies.|v-v.sub.c|.sup.-s (24)
with the exponent s taking the value of .apprxeq.0.73 for 3D
systems and 1.33 for 2D systems. Similarly, as the percolation
threshold is approached from above, the conductivity should vary in
accordance with equation 25:
.sigma..varies.|v-v.sub.c|.sup.t (25)
with the exponent t taking the value .apprxeq.1.9 for 3D systems
and 1.33 for 2D systems. Table 6 below summarises the percolation
threshold and exponent values obtained from this analysis, and
includes the values determined for microsphere/wax composites,
using the same technique, for comparison.
TABLE-US-00006 TABLE 6 Composite type v.sub.c s t Microsphere/wax
0.18 0.70 1.97 100 nm Ag/1 .mu.m PTFE 0.075 0.72 1.85 100 nm Ag/100
.mu.m 0.0141 0.73 2.38 PTFE
[0243] The values of the exponents most closely resemble the
universal values for 3D systems, although the value of t for the
100 nm Ag/100 .mu.m PTFE system is much larger than that of the 3D
system. This is indicative of a broader percolation transition.
[0244] According to percolation theory, power-law behaviour in the
frequency dependence of the permittivity and conductivity is also
expected for filler concentrations near/in the transition region.
The appropriate power laws are given by equations 26 and 27:
.di-elect cons.'.varies..omega..sup.-.gamma.(26)
.sigma..varies..omega..sup.x (27)
[0245] In the strictest sense, these power laws only apply at the
percolation threshold, but are often applied for filler
concentrations near the threshold. The values of these exponents
are related to the exponents s and t within the context of a
polarisation-based model. The actual relationships are given in
equations 28 and 29:
x = t s + t ( 28 ) y = s s + t ( 29 ) ##EQU00016##
The relationship for both real and imaginary components is the
same. For 3D systems it is expected that x=0.72, y=0.28, and for 2D
systems, that x=y=0.5.
[0246] FIG. 30 presents the frequency dependent conductivity for a
2 vol % 100 nm Ag/100 .mu.m PTFE composite material over the
frequency range 1 Hz to 1 MHz. For composites well below the
percolation threshold, the conductivity will be dominated by the
capacitance between the conducting filler particles and is
therefore inversely proportional to frequency (having a gradient of
-1). For composites well above the percolation threshold and at low
frequencies, the conductivity becomes dominated by conduction
through connected conducting particles. The conductivity therefore
becomes frequency independent (having a gradient of zero). The data
in FIG. 30 clearly shows an intermediate behaviour that is
represented by a power law over the frequency range 1 kHz to 1 MHz
(as shown by the trend line). The power-law exponent is shown to be
0.71, which is in good agreement with the expected value for a 3D
system. However, this is not perfectly consistent with the
non-universal value of t derived from the concentration
dependence.
[0247] FIG. 31 presents the corresponding data and power-law
analysis for the real and imaginary components of permittivity. The
power-law exponent for the imaginary permittivity is consistent.
However, the power-law component for the real permittivity is not,
which may indicate that the material tested had not quite reached
the percolation threshold. If the percolation threshold has been
reached, the dielectric loss tangent (the ratio of the real and
imaginary permittivity components) is frequency independent, as
predicted by percolation theory.
[0248] FIGS. 32 and 33 present an equivalent power law analysis of
the frequency dependence of the conductivity and permittivity of an
8 vol % 100 nm Ag/1 .mu.m PTFE material. This is a sample that has
a filler concentration similarly related to the relevant
percolation threshold, compared with the 2 vol % 100 nm Ag/100
.mu.m PTFE sample discussed above. The data of FIG. 32 indicates
that two distinct power-laws can be used to describe the trend
within the measured frequency range of 1 Hz to 1 MHz. Over the
frequency range 1 Hz to 1 kHz, the power-law exponent is in
reasonable agreement with the expected value for a 3D system, as
before. Again, the real component of the permittivity is not
consistent with the predicted and expected values.
[0249] The percolation behaviour therefore appears to be that of a
3D system, regardless of the particle size ratio of the conducting
and non-conducting components.
[0250] The frequency dependent dielectric properties of the
composite material examined may also be interpreted using the
"Universal Dielectric Response Theory" of Jonscher (Jonscher A.,
"The universal dielectric response and its physical significance",
IEEE Trans. Electrical Insulation, 27(3), p 407, 1992, Jonscher A.,
"Dielectric relaxation in solids", J. Phys. D: Appl. Phys., 32,
pR57, 1999).
[0251] In materials in which the polarisation is dominated by
slowly mobile charge carriers, such as those whose mobility is
dominated by hopping, the loss peaks due to relaxation of such a
polarisation process are replaced by a fractional power-law or
constant phase angle response given by equation 30 and illustrated
in FIG. 34:
.di-elect cons.''(.omega.)/.di-elect cons.'(.omega.)=cot(n.pi./2)
(30)
[0252] The extreme low frequency dispersion (LFD) is due to the
fact that the charges are relatively unbound and can move over
large distances compared to more conventional dipoles that give
rise to a dielectric response due to polarisation effects.
Moreover, whilst these charges are relatively free to move, a dc
conductivity, indicated by a frequency independent real
permittivity is not observed. The general response shown in FIG. 34
can be compared to the experimental data in FIGS. 31 and 33. There
is a clear correspondence between FIGS. 31 and 34, including the
crossover of the real and imaginary traces. This comparison may
provide an explanation for the inconsistency between the power-law
exponents derived from the data in FIGS. 31 and 33. In both
figures, there is no constant ratio between the real and imaginary
components. This is indicative of the crossover region. The
crossover range therefore occurs at frequencies outside of those
measured.
[0253] The repeatability of the observed properties of the above
composite materials was also investigated by the inventors. In
particular, the repeatability of a plasma-like response (where the
material acts as if it is a metal, exhibiting a plasma frequency)
when the particle size ratio increases, was investigated.
[0254] FIG. 35 summarises the experimental results in terms of the
measured conductivity at 0.5 GHz, with the error bars representing
the spread of results from 3 nominally identical samples. Although
there is no clear indication that the reproducibility varies with
size ratio, there is an indication that the size ratio affects the
gradient of the percolation transition. This is important for
ensuring the reliability of compositions prepared within or
sufficiently near the transition region.
[0255] Inter-particle contact resistance and therefore contact area
are important factors in determining the overall conductivity of
the composites. Dielectric measurements were taken to examine the
conduction mechanism. These measurements were undertaken using a
Novocontrol Alpha Dielectric Spectrometer and Novocontrol Quatro
Cryosystem. Dielectric spectra over the frequency range 1-10.sup.7
Hz were collected for temperatures over the range -150 to
50.degree. C. at 10.degree. C. intervals. Some further measurements
were repeated over the temperature range -100.degree. C. to
100.degree. C. at 5.degree. C. intervals.
The following samples were tested: FIG. 36: 1 vol % 100 nm Ag in
100 .mu.m PTFE (samples B, C); FIG. 37: 2 vol % 100 nm Ag in 100
.mu.m PTFE (samples A-C); FIG. 38: 3 vol % 100 nm Ag in 100 .mu.m
PTFE (samples A-C); FIG. 39: 5 vol % 100 nm Ag in 100 .mu.m PTFE
(samples A, D); FIG. 40: 2 vol % 100 nm Ag in 1 .mu.m PTFE (sample
A); FIG. 41: 8 vol % 100 nm Ag in 1 .mu.m PTFE (sample A); and FIG.
42: 10 vol % 100 nm Ag in 1 .mu.m PTFE (samples B, C).
[0256] The experimental data is presented as a function of
temperature for three representative frequencies of approximately
10 Hz, 1 kHz and 0.1 MHz, spanning the tested range. The data from
100 nm Ag/100 .mu.m PTFE composites (FIGS. 37 to 39) demonstrate
that the temperature dependence of the conductivity varies markedly
as the concentration of the 100 nm Ag component is increased
through the percolation transition. This is the same, in general,
for repeat tests. In some cases, at the lowest frequencies, the
real permittivity can become very noisy. This is usually for
composites that are developing into conductive materials, such that
the dielectric loss tangent diverges with decreasing frequency, and
exceeds the operational range of the measurement equipment.
[0257] A high conductivity that is inversely proportional to
temperature, for temperatures above the Debye temperature (215K for
Ag), may be representative of the temperature dependence expected
for a metal.
[0258] For 1 vol % 100 nm Ag/100 .mu.m PTFE (FIG. 37), the
conductivity and permittivity is observed to be frequency dependent
and to increase with temperature above a particular temperature.
This trend is most obvious at lower frequencies, and potentially
marks the onset of the percolation transition. The temperature
dependence above this transition temperature may be due to
"hopping" conduction mechanisms, discussed below.
[0259] For 3 vol % 100 nm Ag/100 .mu.m PTFE (FIG. 38), the
conductivity is observed to be frequency independent,
characteristic of being above the percolation threshold. The
conductivity initially decreases slowly with increasing
temperature, but then undergoes a further increase in negative
gradient before rapidly increasing. As the data is presented on a
logarithmic scale, these trends cover a small magnitude range.
[0260] For 5 vol % 100 nm Ag/100 .mu.m PTFE (FIG. 39), the
temperature dependence of the conductivity is similarly complex.
Both samples tested show two turning points.
[0261] It was expected that samples near the percolation threshold
could undergo a rapid thermally induced insulator-metal transition
during the measurement, although this was not observed in the 1, 3
or 5 vol % samples. Therefore samples with 2 vol % 100 nm Ag in 100
.mu.m PTFE were tested (FIG. 37).
[0262] It was observed that, in contrast to the other compositions
tested, the properties of individual samples for 2 vol % 100 nm Ag
varied dramatically, and were not at all consistent. For example,
sample A was somewhat anomalous in that the conductivity was
frequency independent, as if above the percolation threshold.
Furthermore, the conductivity exhibited a maximum before rapidly
decreasing at higher temperatures. This may be due to the
percolation network being broken as the temperature increases in
the higher temperature range due to the expansion of the matrix
PTFE particles.
[0263] The conductivity of sample B exhibited comparable frequency
and temperature dependence to that of the 1 vol % 100 nm Ag
samples, and so also potentially provides evidence for hopping
conductivity. However, a maximum conductivity is also found at an
elevated temperature.
[0264] The conductivity of sample C exhibited several
discontinuities, indicative of the sample undergoing repeated
insulator/metal transitions during the measurements, although these
inconsistencies were not observed on the repeat tests.
[0265] A possible explanation for the changes in the direction of
the conductivity gradient is that the percolating networks of
silver particles are disrupted or reinforced as the PTFE matrix
particles expand. Negative gradients would be consistent with
disruption of the network, and positive gradients with
reinforcement of the network. Conventionally, for particles
dispersed in a continuum matrix, with a particle size ratio,
r.sub.filler/r.sub.matrix.fwdarw..infin., it would be expected that
the network would be disrupted as the matrix phase expands.
However, in the opposite limit, r.sub.filler/r.sub.matrix.fwdarw.0,
for excluded volume systems, it may be possible for both behaviours
to exist. For filler particles dispersed over the surface of a
matrix particle, the filler particles may tend to be separated as
the particle expands and the surface area increases. However, this
action might also tend to force filler particles distributed over
the surface of one matrix particle to come into greater contact
with another matrix particle on the surface of an adjoining matrix
particle. This may reform the network or change the contact
resistance. For the more highly loaded composites, in which the
matrix particles are densely covered, the latter effect may
dominate. Such a reinforcing mechanism would be completely absent
in the silver coated microsphere paraffin wax composites, and
should be less apparent in the 1 .mu.m PTFE composites.
[0266] 100 nm Ag/1 .mu.m PTFE composites were also tested to enable
a comparison that would reveal any differences that could
potentially be associated with the difference in silver particle
contact between the two systems. Representative experimental data
is shown in FIGS. 17-19. The experimental data for the 1 .mu.m PTFE
composites is broadly consistent with that for the 100 .mu.m PTFE
composites.
[0267] The data for the 2 vol % 100 nm Ag/1 .mu.m PTFE (FIG. 40) is
indicative of being further below the percolation threshold than
that for 2 vol % 100 nm Ag/100 .mu.m PTFE (FIG. 14) due to the
absence of a temperature above which the conductivity and
permittivity are seen to increase.
[0268] The data for 8 vol % 100 nm Ag/1 .mu.m PTFE composites (FIG.
41) is perhaps more closely comparable to that for the 1 vol % 100
nm Ag/100 .mu.m PTFE composites (FIG. 36) as a temperature above
which the conductivity and permittivity increases is obvious. The
conductivity is also close to a maximum at the highest temperature
tested, a feature that was observed in the 2 vol % 100 nm Ag/100
.mu.m PTFE samples (FIG. 37). It is of some concern that the
turning points observed in the temperature dependence closely match
the phase transition temperatures for water (freezing and boiling
points), but no step discontinuities are observed. The samples were
dry blended under an inert atmosphere before moulding and
testing.
[0269] The data from 10 vol % 100 nm Ag/1 .mu.m PTFE composites
(FIG. 19) is similar to the 5 vol % 100 nm Ag/100 .mu.m PTFE
composites (FIG. 16). Interestingly a broad peak is observed in the
conductivity for sample C for this composition.
[0270] The various 100 nm Ag-based composites tested therefore show
a difference in conductivity to the Ag-coated 15 .mu.m spheres and
paraffin wax composition tested in FIG. 2. The temperature
dependence of the conductivity for the composites identified above
as being driven by a hopping mechanism were analysed in the context
of the Austin-Mott Activated Polaron Hopping (APH) and
Variable-Range-Hopping (VRH) models. The temperature dependence for
each model is given by equations (31) and (32):
.sigma. a c ( .omega. , T ) .varies. .omega. s ( - W ( 1 - s ) k b
T ) ( A P H ) ( 31 ) .sigma. a c ( .omega. , T ) .varies. .omega. s
T '' ( V R H ) ( 32 ) ##EQU00017##
[0271] The data from a selected portion of the temperature range,
from FIGS. 36, 37 and 41 is re-plotted in FIGS. 43-45,
respectively, as ln(conductivity) against the reciprocal of
temperature, and ln(temperature) to determine the activation energy
W and the temperature exponent n as defined in equations 31 and 32
(Menon R, Yoon C, Moses D and Heeger A, Chapter 12 "Metal-insulator
transition in doped conducting polymers" in Handbook of Conducting
Polymers, 2.sup.nd Edition, Ed. Skotheim T et al, Marcel Dekker,
New York 1998). The values obtained at 10 Hz are summarised in
Table 7.
TABLE-US-00007 TABLE 7 Composite -W(1 - s)/k.sub.B n 1 vol % 100 nm
Ag/100 .mu.m -2200 6.9 PTFE 2 vol % 100 nm Ag/100 .mu.m -1283 4.4
PTFE 8 vol % 100 nm Ag/1 .mu.m -3395 10.9 PTFE
[0272] The activation energy and temperature exponent appear to
decrease with increasing filler concentration, which is consistent
with a decreasing inter-particle separation and hence a reduced
barrier to hopping. Depending on the value of s (defined in
equation 24 above), the values obtained are in reasonable agreement
with values reported for intrinsically conducting polymers. The
activation energy and temperature exponent are large for composites
comprising 1 .mu.m PTFE particles, suggesting that the large
particle size ratio in the 100 .mu.m PFTE composites promotes
tunneling, allowing the hopping conduction mechanism to occur more
easily. Low frequency dispersion is also observed, which causes
difficulties with the extraction of dc data to determined the
dimensionality of the hopping mechanism.
[0273] The gradient of the percolation transition can therefore be
altered by choosing filler and matrix particles with a large size
ratio. By altering the gradient, it is possible to reliably produce
composite materials that have a particular conductivity range. As
the gradient of the transition is relatively flat, the conductivity
will not be influenced, or influenced to a small extent, by
compositional variations resulting from the production process used
to make the materials, for example, weighing errors. The reliable
temperature dependence of the measured conductivity of the samples
is also useful in situations where non-ambient temperatures need to
be measured. Such tailored composite materials are therefore of use
in a wide variety of applications, such as sensors for measuring
temperature, pressure or concentration of absorbed chemicals. The
external stimulus could also be electric field or current (which
may cause heating).
[0274] For example, as the degree of connectivity between the
electrically conductive regions is increased when an external
stimulus is applied to the composite material. Such materials could
then be used as sensors, actuators or switches, if the stimulus is
applied dynamically. Alternatively in a passive form, the material
could realise a conductivity that enables antistatic, electrostatic
discharge, electromagnetic shielding products.
[0275] Although the materials discussed above have comprised silver
or silver-based conductive components, other suitable materials,
could be used. For example, the electrically conductive material
could be one of metal, metal alloy, conductive metal oxide,
intrinsically conductive polymer, ionic conductive material,
conductive ceramic material or a mixture including one or more of
any of these. Alternatively, an oxidation resistant metal, a
metallic alloy, a conducting ceramic or a mixture including one or
more of any of these could be used. The non-electrically conductive
material could be PTFE, paraffin wax, a thermosetting material, a
thermoplastic material, a polymer, air, an insulating ceramic
material, glass or a mixture including one or more of any of
these.
[0276] The theories developed by Maxwell-Garnett and Bruggeman and
discussed above with reference to FIGS. 5 to 8 can generally be
considered as concerning the forming of three-dimensionally
connected networks. The composite production described above can
also result in three dimensional materials. However it is only
necessary for an incident electromagnetic wave to have an electric
field component in a direction of connectivity for the effect to be
observed. Hence, anisotropic composites with connectivity in two
dimensions or even one dimension could suffice. Composites with
two-dimensional or one-dimensional connectivity in the plane
perpendicular to the plane of incidence would be particularly
useful. In this context, printing, etching and lithographic
techniques, such as photolithography could be employed to produce
two-dimensional connectivity rather than the three dimensional
connectivity which the methods described would produce. Printed
layers could then be laminated to form a bulk composite.
[0277] FIG. 46 is a schematic graph of conductivity in relation to
conductive filler concentration for a composite material comprising
conductive particles in an insulating or non-conductive filler. The
graph illustrates that the conductivity of the samples falls into 3
distinct regions, marked A, B and C.
[0278] In region A, the filler concentration level is low, and the
material does not conduct any electrical current. There are no
connected pathways of conducting elements in the composite.
[0279] In region B, an insulator-conductor transition occurs. This
transition is prompted by the formation of the first network of
conducting elements within the material. For dc use, this network
must span the entire material. For ac use, the network need only
span a region of the material. The steepness of the gradient in
region B is determined by the difference in conductivity between
the constituent materials, the concentration of the conducting
elements at which the first network forms and the concentration of
the conductivity elements at which the overall conductivity becomes
limited by the contact resistance between adjacent conductive
elements.
[0280] The gradient of the insulator/conductor transition (region
B) can be influenced by the degree of randomness in the
distribution of the conducting elements and the nature of
electrical charge transport across the contact interface. For
example, the gradient can be influenced if the electrical charge
transport is dominated by charge hopping or tunneling rather than
essentially free-electron movement.
[0281] In the transition region B, the conductivity continues to
increase rapidly as additional parallel paths of conducting
elements are created in the principal network through the
successive addition of conducting elements. This is the percolation
region.
[0282] Eventually, the gradient reduces to a plateau or saturation
region C in which the further addition of conducting elements does
not significantly increase the conductivity of the composite. In
region C, the filler concentration is high enough for the composite
to conduct electricity at a level similar to that at the
conductivity elements. Typically, in this region the composite is
useful as an electrical conductor.
[0283] A composite material is produced by printing or placing a
pattern of conductive elements onto an insulating film substrate.
The conducting elements could be formed from any conductive
material, including metals, conducting metal oxides, graphitic
material, fullerenes, organic conductors or ionic conductors. The
insulating film substrate could be formed from any insulating
material including natural or synthetic papers, cloth, fabrics or
thin polymer films.
[0284] The pattern of conductive elements or particles may be
printed or placed using any pattern transfer mechanism or method
whereby a thin layer of the conducting material can be placed in a
controlled manner on a surface to form a user defined pattern. The
possible methods involve inkjet printing, screen printing,
block-foil patterning or autocatalytic deposition such as described
in WO 02/099162 and WO 02/099163, or physical or chemical
disposition methods. In the case of printing methods, conducting
particles would be dispersed in a low viscosity binder to enable
deposition on the substrate. Alternatively, conducting material
could be removed from an initially complete conducting film to
produce a similar pattern of conducting material. The possible
removing methods include etching or hole punching.
[0285] The size of the conducting elements making up the pattern is
of secondary importance and would be chosen to be smaller than the
area of the substrate or area over which the composite is to be
used, whichever is the smaller. Typically, the element size would
be less than one tenth of this size limit, and preferably less than
one hundredth.
[0286] A pre-determined pattern representing a selected
concentration of conductive material is stored as part of a library
of pre-determined patterns each representing selected
concentrations of conductive materials. These pre-determined
patterns may be determined either empirically or theoretically. A
combination of both theory and experience in which a basic pattern
is generated theoretically before being empirically checked is a
possible way of generating pre-determined patterns.
[0287] The pre-determined patterns are chosen or selected so as
have particular properties in particular circumstances. For
example, the library of patterns may include patterns which when
used to print or place an ink comprising elements of a particular
conductor (e.g. copper) of a particular size and shape (e.g. discs
of diameter 1.6 mm--see FIG. 2a) on a particular substrate (e.g.
synthetic paper) have a conductivity falling within a particular
small range .DELTA.S (see FIG. 1).
[0288] There are likely even with the method of the present
invention to be statistical variations from one sample to the next
but they will be significantly smaller than the variations in the
properties of the materials made by the known mixing methods. In
other words the standard deviation of the conductivity of sample
composite materials of a particular conductor concentration
produced by the method of this application will be significantly
smaller than the standard deviation of the same apparent composite
material produced by the known methods. This means that the
behaviour of different samples will be closer and therefore
materials can be made with more confidence that properties will be
repeatable.
[0289] FIGS. 47a to 47c illustrate a number of pre-determined
patterns made up of a 100.times.100 array including discs 1 of
circular material, corresponding to, respectively, 20%, 50% and 70%
loadings of conductive elements.
[0290] FIG. 48 illustrates a pre-determined pattern made up of
crossed dipoles 2 and corresponding to a loading concentration of
50%. The aspect ratio of the crosses could be used, for example, to
control the percolation threshold of a composite.
[0291] FIGS. 49 and 50 illustrate the three stage autocatalytic
deposition methods described in WO 02/099162 and WO 02/099163 to
which reference should be made. The contents of these two
publications are herein incorporated by way of reference and as
illustrations of how the preferred embodiments of invention might
be implemented or created.
[0292] Turning to FIG. 49, an ink jet printing system 3 coats a
substrate 4 with an ink formulation containing a deposition
promoting material in a user determined pattern 5. The treated
substrate 4, 5 is then immersed in an autocatalytic deposition
solution 6 to produce a user determined metalised pattern 7.
[0293] Ink jet printers operate using a range of solvents normally
in the viscosity range 1 to 50 centipoise.
[0294] Turning to FIG. 50, a screen printing system 8 coats a
substrate 4, with an ink formulation containing a deposition
promoting material in a user determined pattern 5 (like numerals
being used to denote like features between FIGS. 4 and 5). The
treated substrate 4,5 is once again immersed in an autocatalytic
deposition solution 6 to produce a user determined metalised
pattern 7.
[0295] A range of ink formulations are possible. Criteria suitable
for printing may include the following: [0296] 1) They contain
materials that are able to pass through the chosen printing
mechanism (for example, either an Epson 850 inkjet system or a Dek
screen printer); [0297] 2) They contain liquids with the correct
properties for the printing process, for example suitable
viscosity, boiling point, vapour pressure and surface wetting;
[0298] 3) Where suitable they contain binders and fillers affecting
either the viscosity or physical printing properties of the printed
ink.
[0299] The patterns of conductive material may also be transferred
onto a non-conductive substrate using a straightforward printing
technique such as that described by Messrs Schwartz and Ludwena in
"An experimental method for studying two-dimensional percolation".
[Am. J. Phys 72(3), March 2004 .COPYRGT. 2004 American Association
of Physics Teachers] Messrs Schwartz and Ludwena describe an
experimental technique for analysing a range of two-dimensional
problems. The method is based on the printing of computer generated
patterns using conducting ink. The metal-insulator transition is
measured from the print out of the conductive patterns, and the
conductivity critical component and the percolation threshold are
calculated from these measurements.
[0300] Three-dimensional composite materials may be made by placing
a second layer of insulating material over the material of FIG. 49c
or 59c and then repeating the printing process. The process may be
repeated as many times as are necessary to achieve the desired
material thickness or properties. Such a material will,
essentially, be three dimensional in terms of its physical shape
but as the insulating layers are continuous it will only be
two-dimensional in so far as its electrical properties are
concerned. Materials being three-dimensional insofar as their
electrical properties are concerned may be created by connecting
the metalised pattern of adjacent coated substrate layers 4, 5. The
connection could be done using conductive vias through the
insulating material separating adjacent metalised or conductive
patterns.
[0301] The present invention allows for increased confidence in the
manufacturing of composites having particular properties. This has
a number of clear advantages including the reduction of scrap.
[0302] Embodiments of the invention can, as discussed above, be
used to engineer composites having, inter alia, desirable
electrical, magnetic, thermal and/or physical properties. Possible
applications of composites including active materials (e.g. photo
sensitive, piezoelectric, chemical sensitive, thermally sensitive)
include sensors, actuators or switches. Composites embodying the
invention could also be used as reference materials (for e.g.
absorbing) in metrology in support of national and/or international
traceability claims. The ability to produce something having a
known and pre-determined property or behaviour could also be used
in support of security and anti-counterfeiting measures.
[0303] For example, WO02/099163 and WO02/009162 (both assigned to
QinetiQ Limited) disclose methods of autocatalytic coating and
patterning respectively. This is a form of electroless plating in
which metals, for example, cobalt, nickel, gold, silver or copper
are deposited onto a substrate via a chemical reduction process.
Non-metallic surfaces may be coated following suitable
sensitisation of the substrate. Pre-determined areas of the
substrate may be prepared for coating, allowing various patterns to
be formed. Such patterns are printed onto the substrate using
pattern transfer mechanisms such as printing using autocatalytic
inks. This would enable a number of random or non-periodic patterns
to be printed on single sheets, formed into a composite material by
laminating, and which would then exhibit a plasma frequency,
similar to those described below for 3-dimensional composite
materials. Suitable substrate materials include insulating sheet
materials, such as paper, card, polymer film or cloth.
[0304] The composite materials of the embodiments of the invention
may be used in various applications. One important use would be to
combine the composite material with another material which has a
magnetic permeability of less than 0, to produce a material with a
refractive index of less than 0. Using the composite material to
produce a material with a refractive index between 0 and 1 (less
than air) would also be of use, since this would allow the
formation of components exhibiting total internal reflection.
[0305] The composite material is also suitable for filtering
applications, including those which require a tuneable filter. Such
filter behaviour may be coupled with various DC frequency
applications. This may be used to produce transparent or absorbing
electrodes, capacitors or inductors. Transparent electrodes would
be of particular use in microwave chemistry applications.
[0306] The fact that composite materials of the type embodying the
invention can demonstrate D.C. conductivity comparable with
conventional metals whilst remaining microwave transparent
(behaving like a normal dielectric) is of potential usefulness.
These potential useful properties can be engineered into materials
using the processing described. The advantageous behaviour arises
from the percolating networks of conducting particle being arranged
in a suitable geometry. Consequently if this geometry can be
altered by physical, thermal or electrical deformation then these
properties can be tuned or switched on and off depending on the
desired application. Possible applications of the composite
materials therefore include tunable high pass filters, commercial
microwaveable food packaging, mechanically, thermally or
electrically switchable microwave filters for use in radomes or
other applications requiring microwave spectrum selectively (e.g.
telecommunications). Details of how to make products or devices for
acting on or processing electro-magnetic waves are well known to
those skilled in the art and easily found in relevant textbooks
such as "The Electrical Engineering Handbook", (Editor-in-Chief,
Richard C. Dorf; Publisher CRC Press Inc of Boca Raton, Fla.).
Examples of possible products which might use the composite
material include: [0307] a) a written directional coupler lens--a
negative permittivity in concert with a negative permeability would
lead to a negative refractive index material. Such a `left handed`
material would possess unique refraction properties allowing, for
example, a flat lens that would allow perfect image projection with
no aberrations due to geometrical shape as in a conventional lens.
Such effects are, of course, highly dispersive limiting the device
to monochromatic operation. [0308] b) filter--simple variation of
the conductor/insulator morphology within the composite can raise
or lower the plasma frequency of the material by several orders of
magnitude. Therefore the cut-off frequency where radiation can
propagate through the medium (where the permittivity crosses from
negative to positive across the plasma frequency) can be varied
thus allowing easy fabrication of a tuneable high pass filter
device. [0309] c) transparent electrode--in electrically
addressable devices such as frequency agile sensors, the ability to
apply an electric field across such a device without any wavelength
feature related artefacts or attenuation occurring is very
desirable. Thus, the high conductivity conventional dielectric
behaviour (positive permittivity) above the plasma frequency allows
the application of .about.kHz driving electric field across a
metal-like conductor whilst allowing transmission of .about.GHz
microwave radiation through a conventional dielectric. [0310] d)
absorbing electrode--as above, optimisation of the plasma frequency
allows fine control over the sign and magnitude of the complex
permittivity of the composite device to provide easily customizable
dielectric properties. [0311] e) capacitor or inductor--as above,
straightforward permittivity/impedance/admittance manipulation can
realise such devices. [0312] f) waveguide--the low permittivity
behaviour frequency regime behaviour of these composite materials
above the plasma frequency allows microwave propagation through a
slab of such material with total internal reflection occurring off
the composite/air interface exploiting the positive, sub-unity
value of permittivity close to but just above the plasma frequency.
Such behaviour is highly dispersive but this is not a problem in
monochromatic telecommunications frequency applications. [0313] g)
sensor--the transition from insulating to conducting behaviour via
the percolating region of interest in this patent can be tuned to
be very sharp or a much gentler process. By careful choice of
insulator conductor concentration and processing conditions, a
composite can be achieved where the width of the percolating region
is very sensitive to electrical, mechanical or thermal
perturbation. Thus, relatively small changes in driving field,
force or temperature can induce relatively large changes in plasma
frequency and related dielectric properties. Hence, a high Q-factor
sensor can be fabricated. [0314] h) remote interrogation sensor
package--as above, a switchable filter device could be incorporated
into a potential quantum cryptography application. [0315] i)
radome--typically, a radome needs to have durable physical
properties to house the microwave device within. In addition to
this, radar absorbing material (RAM) is included--often as a
backing applique. If the electrical properties (complex
permittivity and admittance) of the composite used in the
structural part of the radome could also be used in the RAM, then
substantial weight and complexity savings could be achieved. [0316]
j) switch or shield--as above, tuning of the width of the insulator
to conductor transition could be exploited to make the device
sensitive to electrical, mechanical or thermal perturbations thus
realising a switchable device. [0317] k) fuse--as above,
manipulation of the insulator/conductor transition would enable a
thermal or electrical (or mechanical) solid state switch. [0318] l)
anechoic chamber--as above, precise tuning of the electrical
properties (permittivity, admittance) of a material allows
stringent absorption and reflection design criteria to be met
cheaply and easily.
[0319] The composite material may also be used as a sensor,
possibly as a remote interrogation sensor, where the plasma
frequency is monitored by interrogation by microwaves, in order to
determine the state of the sensor.
[0320] As mentioned above, uses include materials for use in the
food industry, for example, to aid heating or to provide packaging
for microwaveable foods.
[0321] Various other modifications are possible and will occur to
those skilled in the art without departing from the scope of the
invention which is defined by the appended claims.
* * * * *