Formation and Structure of Ramified Transportation Networks in an

Report
Synthetic Atoms: High Energy Density and a Record Power Density
Alfred Hubler, Department of Physics, University of Illinois at Urbana-Champaign
CNLS Seminar, Los Alamos National Lab, July 30th, 2013
We study the dielectric strength of nanocapacitors
experimentally.
We designed theoretically a new type of nanocaps:
Synthetic atoms are nanocapacitors which mimic the
geometry of atoms and simple molecules, but are a
factor 10 factor larger.
Synthetic atoms are a potentially important
new technology for storing energy:
Measured Energy Density
Nano capacitor arrays with high energy density
- In synthetic atoms energy is stored by moving electrons, instead of ions. Since electrons have much less
mass, the power density of synthetic atoms is much higher than in Li-ion batteries.
- In chemical batteries the energy density is limited by the energy density of the molecular bonds, which is
typically around 1GJ/m3. The theoretical limit for energy density in synthetic atoms is more than 100
times larger if the electrode material has a particularly high tensile strength, such as graphene, carbon
nano tubes, or boron-nitrate nano-wires.
- Arrays of synthetic atoms can be recharged, and discharged with minimal losses millions of times and
operate in a large temperature range.
- The combustion front in explosives propagates roughly with the speed of sound. Arrays synthetic atoms
have a similar energy density, but the energy-release front propagates with the speed of light and creates an
EMP. A second failure mode propagates roughly with the speed sound and creates a pressure wave.
Energy storage in capacitors
vs. energy storage in chemical batteries,
hydrogen fuel cells, and gasoline
Energy stored in chemical systems is due to the interaction of positive and negative charges.
Energy stored in
capacitors is due to the interaction of positive and negative charges.
=> Energy storage in chemical systems and capacitors are the same, except for their dimensions.
But, in chemicals such as hydrogen, the limiting electric fields are more than 10,000 times larger:
Quantization phenomena on the nano-scale suppress charge recombination
=> Quantization suppresses sparks in nano-gaps
Example: Atomic hydrogen
w = 13.6eV / (volume of hydrogen atom) = 3.3 x 1013J / m3 (1.31 x 1012J/kg)
i.e. nine orders of magnitude above the maximum energy density in a
conventional capacitor.
Energy storage in synthetic atoms:
The geometry matters
Synthetic Atoms are
- spherical nanocapacitors
- cylindrical nanocapacitors
- planar double layer nanocapacitors
Synthetic atoms have the geometry of an atom or a simple molecule,
but are 10 times larger.
In the gap is vacuum, or a low density gas, or a dielectric.
Electrons are stored on the cathode surface and on quantum levels in
the gap.
Thin wires are attached to the electrodes to add/remove charges.
The energy density of nanocapacitors with sharp anodes (nano vacuum
tubes) can be 5-10 times higher than that for planar double layer capacitors.
The energy density in Faradic systems and synthetic atoms is limited by
the energy density in ionic bonds (about 1GJ/m3 ). The energy density in
nanocapacitors and synthetic atoms is limited by the energy density in
covalent bonds (tensile strength of the electrodes, i.e. 1.5TJ/m3 for doped
boron nitrate). Faradic systems have a smaller power density, lower
efficiency, and shorter life time.
Cylindrical nano-capacitor,
where a = 1nm and b = 10nm
Leak currents in nanocapacitors
Fowler-Nordheim field emission current:
where I is the tunnel current, Ar is the effective field emitting area, a and b are the Fowler-Nordheim
constants, v(f) is the Schottky barrier correction factor, E is the electric field at the cathode, φ is the work
function of the cathode material, and β is the field enhancement factor.
The scaling of the field enhancement factor
The field enhancement factor versus the gap size d. The
circles indicate experimental values measured by Alpert,
Lee, Lyman, and Tomaschke on tungsten electrodes.
The squares indicate experimental values measured by
Boyle, Kisliuk, and Germer on tungsten electrodes. The
diamond indicates the theoretical value on an atomic
scale.
Break down occurs when the field emission
current exceeds 105A/cm2.
Small β => Small field emission current => High electric fields at break down
 Miniaturization increases the energy density
The scaling of the field enhancement factor
on the nano-scale
Measured Field Enhancement β
Versus Gap Size d
6
5
4
Measured β
UHV-STM with a
tungsten tip of radius
R=15nm is used at room
temperature at
4 × 10−11 Torr in
constant current mode at
I=10pA.
The cathode is Au (111).
3
2
1
0
0
10
20
30
40
50
60
Gap Size d (nm)
=> Miniaturization increases the energy density (electric fields ~ 1V/nm)
70
80
The scaling of the energy density at break down
measured with a STM
Measured Energy density, U, with a
15nm tungsten tip and flat gold cathode
is found to scale with gap size d as:
U=(26 GJ/m3)*(1nm / d)1.5
(empirical power law)
The experimental data deviate from the
power law for d < 5nm, because electrons
begin to tunnel directly from the cathode to
the anode tip. The largest measured energy
density is U=3.2 GJ/m3 (25V/nm).
=> Miniaturization increases the energy density
The scaling of the self-discharge time
due to field emission currents
Charge stored in a vacuum
nanocapacitor with gap size d and
a pointed anode of radius R:
Q = 2 πε0 E (d + R)2
Charge density in the center:
q= 2 π E (d + R)2
Field emission current density (β=1):
j= a E2 / φ exp(-b φ 3/2 /E)
Self discharge time:
τself = q / j = 2 π (d + R)2 φ exp(b φ 3/2 /E) / (a E )
Preliminary experimental results with dielectric nanocapacitors have self-discharge times greater
than one day at 1V/nm (10MJ/m3).
Field emission current is a potential problem = > Use electrode thickness, coatings, gases,
and quantization phenomena to suppress leak current
Modeling quantized space charge in synthetic atoms =>
Leak currents are suppressed because electrons in the gap are governed
by Fermi statistics and block field emission (Coulomb-blockade).
No current
Field Emission / STM style tunneling
Field Emission, Coulomb blockade, Quantum cap.
Diagram of potential energy function. Wc is the work function of the 2 cathodes. Wa is the work function of the anode. The occupied levels of
the conduction bands are shown in gray. The Fermi energy and occupied energy levels in the gap are shown in red. Thin red lines are unoccupied energy levels in the gap.
We consider problem of a confined particle in this linear potential, U = F q∣ x∣ which is described
by the following Schrodinger equation:
Modeling quantized space charge in synthetic atoms =>
Leak currents are suppressed because electrons in the gap are governed
by Fermi statistics and block field emission (Coulomb-blockade).
The quantized energy levels are added into the potential energy function in a double layer capacitor with gap size 10 nm. The work function of
the 2 tungsten cathodes is about Wc = 4.55eV ≈7.29×10−19J. The work function of a graphene anode is about Wa=4.56eV ≈7.31×10−19 J . There
are 69 bound states. 28 bound states are below the Fermi energy of the cathode. The largest energy spacing is between the ground and the first
excited state, which is E2 - E1  7.12  10-20 J; the smallest energy spacing is between the highest two energy levels, which is E69 - E68  1.56 
10-20 J. Thermal activation is rare at room temperature, because kbT ≈ 4.0 10-21J is about a factor of 10 smaller.
Modeling quantized space charge in synthetic atoms =>
Leak currents are suppressed because electrons in the gap are governed
by Fermi statistics and block field emission (Coulomb-blockade).
Allowed energies En for a confined particle with charge q and mass m in the potential U (x)=F q∣x∣:
where
and n=1,2,3… . For typical system parameters the energy difference between ground and first excited state is about 10 times larger than kbT at
room temperature. We computed the corresponding wave functions numerically. The spontaneous transition rate from the n-th to the m-th state
(n > m ) is:
In this case, the spontaneous emission rate of the first excited state is about T= 470ns.
Quantized space charge in the gap increases the capacity beyond the geometric capacity. The number of states per unit area and per eigenstate
below the Fermi energy of the cathode is:
Modeling quantized space charge in synthetic atoms =>
Leak currents are suppressed because electrons in the gap are governed
by Fermi statistics and block field emission (Coulomb-blockade).
The quantized energy levels are added into the potential energy function in a double layer capacitor with gap size 4 nm. The work function of the
2 tungsten cathodes is about Wc = 4.55eV ≈7.29×10−19J. The work function of a graphene anode is about Wa=4.56eV ≈7.31×10−19 J . There are
17 bound states. All bound states are above the Fermi energy of the cathode. The largest energy spacing is between the ground and the first
excited state, which is E2 - E1  7.12  10-20 J; the smallest energy spacing is between the highest two energy levels, which is E69 - E68  1.56 
10-20 J. Thermal activation is rare at room temperature, because kbT ≈ 4.0 10-21J is about a factor of 10 smaller.
Modeling quantized space charge in synthetic atoms =>
Leak currents are suppressed because electrons in the gap are governed
by Fermi statistics and block field emission (Coulomb-blockade).
The quantized energy levels are added into the potential energy function in a double layer capacitor with gap size 4 nm. The work function of the
2 tungsten cathodes is about Wc = 4.55eV ≈7.29×10−19J. The work function of a graphene anode is about Wa=4.56eV ≈7.31×10−19 J . There are
54 bound states. 45 bound states are below the Fermi energy of the cathode. The largest energy spacing is between the ground and the first
excited state, which is E2 - E1  3.32  10-19 J; the smallest energy spacing is between the highest two energy levels, which is E54 – E53  7.88 
10-20 J. Thermal activation is rare at room temperature, because kbT ≈ 4.0 10-21J is more than a factor of 10 smaller.
Power density of synthetic atoms:
We observed very bright flashes of light
and sub-nano-second EMPs
from a nm-sized spot.
The power density is related to the energy density by a characteristic external discharge time τe = sqrt(L C)
of the system. For example, a 1 square cm capacitor discharging through 1cm long wires has τe = 10-9s .
Locally, is limited by the plasmon period of the metal, the time it takes for electrons
oscillate in the atomic lattice. The plasmon period of silver, for example, is τp = 10-15s.
Formation of the plasma channel: τc = (gap size) / (speed of light) = 10-17s
Max. power density: From p = (1 GJ/m3) / τe = 1018 W/m3
to p = (1 GJ/m3) / τp = 1024 W/m3
Rocket engines have a power density of 105 W/m3
Before break down
Sub micron trench
Trench with MWCNT
After break down
When an nano wire across a nano-scale trench is purposely charged to twice its operating voltage until it
fails, the power density is high enough to melt the gold at each capacitor site, even though the melting point
of gold is 1000C.
=> A record power density?
A simple method for fabricating synthetic atoms:
Angled vapor deposition creates a Spindt ridge in a trench.
In this experiment, the anode is a gold ridge with apex
radius 30 nanometers sitting in a 300 nanometer trench.
The cathode is placed to lie flat across the top of the
trench. The gap size between electrodes is 75 nanometers
A simple method for fabricating synthetic atoms:
Angled vapor deposition creates a Spindt ridge in a trench.
Current-voltage curve of a 100 nm
trench as shown in the top Figure,
on a linear scale (left) and on a
log-log scale (right). Even at 100V
there is no arcing.
Easier to fabricate: Dielectric nanocapacitors.
The dielectric strength
of silicon oxide nanocapacitors.
Figure. The leak current (left) and the resistance (right) versus the applied voltage of a 300 nm layer of
SiO2 with a thin gold electrode (1mm2).
Easier to fabricate: Dielectric nanocapacitors.
The dielectric strength
of silicon oxide nanocapacitors.
Figure. The break down voltage Vb versus the thickness of the silicon oxide layer.
The limiting dielectric strength of silicon oxide nanocapacitors is about 1 V/nm = 1GV/m.
This is 3 orders of magnitude larger than the dielectric strength of macroscopic vacuum gaps and
conventional capacitors (about 1 MV/m).
The dielectric strength household aluminum oxide layers
Figure. The dielectric strength of aluminum foil (aluminum metal with a 4nm layer of aluminum oxide) is
about 1V/nm. The Blue “Star” points are from the dull side and the other colors/shapes are from the shiny
side. Aluminum oxide has a large dielectric constant of about 10 ε0
The dielectric strength of household aluminum oxide layers
at low temperatures
R (Ohm)
1E13
1E12
1E11
1E10
R (Ohm)
1E9
1E8
-667.34V
667.285V
1E7
1000000
100000
-10 degrees Celsius
10000
1000
100
-1000
-500
0
500
1000
Voltage (V)
The resistance of a two 4nm aluminum oxide layers versus the
applied voltage at -10 degrees Celsius, after being treated with
liquid nitrogen. A few samples appear to have a dielectric
strength above 80V/nm.
Other materials might have an even larger dielectric strength.
The dielectric strength of household aluminum oxide layers
at low temperatures
The resistance of two 4nm aluminum oxide layers versus the
applied voltage in liquid nitrogen. In a few samples the
dielectric strength appeared to be above 80V/nm.
Other materials might have an even larger dielectric strength.
Applications: General purpose rechargeable battery
An array of four nanocapacitors
(cross section, side view).
The cathode (− − −) is
planar. The anode (+ + +) is a
nano tip on a flat electrode. The
thin curved lines indicate the
electric field lines. The cathode
is a conducting solid with high
work function, such as gold or
platinum. The flat part of the
anode needs to have a high
tensile strength, such as steel. The
nano tip is a conducting solid with extremely high tensile strength, such as a carbon nanotube clamped to
the steel electrode, or a tungsten Spindt tip. The design of the electrodes is similar to a tunneling microscope,
except that tunneling microscopes have one movable tip, whereas the vacuum tube arrays have many
stationary tips. The insulating walls (dots) are solids with a high compressive strength, such as silicon oxides.
The electrodes and the walls create a vacuum tube. The electric field is in the vacuum tube between the anode
tip and the cathode.
Potential failure modes: mechanical (speed of sound) , thermal (speed of sound), electrical (speed of light) –
very similar to stimulated emission in a LASER (70V EMP on open BNC connector 20cm from source)
Applications: General purpose rechargeable battery
- Safety issues
Propagating dielectric break down
Applications: Explosive work
with synchronized energy release of synthetic atoms
Specific Energy
[MJ/kg]
Min. Energy
Release Time [s]
Peak Power-to-Weight Ratio
[kW/kg]
Typical electrostatic capacitor
0.000036
General Atomics high voltage capacitor
0.0023
6.8  10 3
Saft VL 6Ah Li-ion battery
0.004
2.1  10 1
Nesccap Electric double-layer capacitor
0.005
5  10 0
10nm SiO2 nanocapacitor (0.8V/nm, soft )
0.005
3 10 -17
2  10 17
4nm Al2O3 nanocapacitor (1V/nm, soft )
0.011
1.2  10 -17
1  10 18
Typical Li-ion battery
0.8
10 4
1  10 -1
10 nm synthetic atom (vac. gap., 25V/nm, soft )
1
3  10 -17
3  10 20
TNT
4.6
10 -5
5  10 8
Kerosene
42
10 4
4  10 0
4nm Al2O3 nanocapacitor (l N2, 80V/nm, soft )
75?
1.2  10 -17
5  10 21
Weapon grade Uranium (hard )
144,000,000
10 -5 ?
1  10 16
[1] https://en.wikipedia.org/wiki/Energy_density
1 kWh = 3.6 MJ
[2] http://en.wikipedia.org/wiki/Power-to-weight_ratio
[3] Alfred Hubler, Synthetic atoms: Large energy density and record power density, Complexity 18(4), 12-14 (2013)
Applications: Explosive work
with synchronized energy release of synthetic atoms
Synthetic atoms have potentially a record power density, more than 20 orders of magnitude larger than
Li-ion batteries and almost 1 million times larger than nuclear devices. This means 50 milligram (3
table spoon) of charged synthetic atoms can deliver the same power as a nuclear chain reaction of 50kg
(100 pounds) of highly enriched nuclear material. Currently, 50 milligrams of synthetic atoms can
store roughly the same as amount of energy as a digital camera battery, but can potentially store 1001000 times more energy.
Application: Harvesting energy in particle radiation
with synthetic atoms (stacks of graphene NCs)
-
Efficiency of conventional nuclear power plants (heat engines): 35 percent.
Here: The kinetic energy of nuclear reaction products is directly converted into electric energy in a stack of charged capacitors with a gap size of
500 nm and graphene electrodes.
Graphene is expected to be chemically and mechanically stable in high radiation environments because it's tensile strength of 130 GPa is
very large, about 100 times larger than most metals.
The dielectric strength of nanocapacitors is very large, above 1 GV/m.
In a 1 GV/m electric field charged nuclear reaction products, such as 5.6 MeV alpha particles, come to rest in of a stack with 5000
nanocapacitors.
We show that during the deceleration more than 90 percent of kinetic energy of charged nuclear reaction products is stored as electric energy in
the stack. Each stack is 2.5mm thick and produces a high voltage DC current. A device with a 1 Ci - 241Am source generates 22 mW of
electric power.
Similar reactors with a 200nm Am-242(m) foil and beryllium / beryllium oxide sheets to act as both neutron moderators and reflectors are
critical [1]. 72 percent of kinetic energy of charged nuclear reaction products is stored as electric energy in a stack of 8000 sheets of
graphene.
[1] Y. Ronen, A. Hatav, N. Hazenshprung, Nucl. Instr. and Meth. A 531, 639 (2004).
[2] E. Shinn, A. Hubler, D. Lyon, M. Grosse-Perdekamp, A. Bezryadin, A. Belkin, Complexity 18(3), 24–27(2013).
Application: Harvesting energy in particle radiation with
synthetic atoms (stacks of dielectric NCs)
Conclusion: Nuclear radiation (Co-60 10.5mCi gamma source,
8.51 mC Am 241 alpha source at a distance of 1cm from the
NC) reduces the dielectric strength only by 25%.
Application: Synthetic atom as a nano scale particle
accelerator
If the polarization
is reversed this
design can be used
as a nano-accelerator for
propulsion,
X-ray source for lithography,
medical applications.
Application: Nuclear protection suits made of synthetic atoms
- Fabric with 16mm thick, 1cm2-plates which reflect nuclear
radiation
Conclusion: Nuclear radiation suits are
electrically neutral and can reflect charged
particle radiation with energies up to
100MeV/charge,
and efficiently scatter gamma radiation.
Synthetic atoms: High power density
and a record power density
A.Hubler, Physics, UIUC
We study tunnel currents and electric break down in nanocapacitors and synthetic atoms (double layer
capacitors). We find:
(1)
(2)
(3)
Miniaturization reduces the tunnel currents by several orders of magnitude. Dielectric nanocapacitors
have a large dielectric strength and small leak currents.
In nanocapacitors the electric field at the cathode is limited by the work function of the cathode surface
material (280 MJ/m3 for platinum) and the tensile strength of the anode (150 GJ/m3 - 360 GJ/m3 for
MWNVTs, 1.5TG/m3 for boron nitrate). Synthetic atoms with quantized space charges are not limited
by the work function of the cathode and have an increased capacity.
In synthetic atoms leak currents are suppressed because the population of the electrons in the gap is
governed by the Fermi statistics and because of Coulomb blockade.
Recent Publications:
[1] A. Hubler, Digital batteries. Complexity 14(3), 7-9 (2008).
[2] A. Hubler and O. Osuagwu, Digital quantum batteries: Energy and information storage in nano vacuum
tube arrays, Complexity 15(5), 48-55 (2010).
[3] A. Hubler and D. Lyon, Gap Size Dependence of the Dielectric Strength in Nano Vacuum Gaps, IEEE
Transactions on Dielectrics and Electrical Insulation, 20(4), 1467-1471 (2013).
[4] E. Shinn, A. Hubler, D. Lyon, M. Grosse-Perdekamp, A. Bezryadin, and A. Belkin, Nuclear Energy
Conversion with Stacks of Graphene Nano-capacitors, Complexity 18(3), 24–27(2013)
This paper won a DOE innovation award.
[5] Alfred Hubler, Synthetic Atoms: Large energy density and record power density, Complexity 18(4), 1214(2013)
Synthetic Atoms: High energy density and a record power density
A.Hubler, Physics, UIUC
Synthetic Atoms are nano-capacitors which mimic the geometry of atoms and simple molecules.
(1) In chemical batteries the energy density is limited by the energy density of ionic bonds, which is typically
around 1GJ/m3. The theoretical limit for energy density in synthetic atoms is more than 1000 times larger
if the electrode material has a particularly strong covalent bonds and therefore high tensile strength, such
as graphene, carbon nano tubes, or boron nitrate nano tubes.
(2) In synthetic atoms electric energy is stored by moving electrons, instead of ions. Since electrons have much
less mass, the power density arrays of synthetic atoms is much higher than in Li-ion batteries. Because
the response times are extremely short (10-17 s) and the electric fields more than 1000 times larger than in
macroscopic capacitors power densities exceed 1024 W/kg. Arrays of synthetic atoms can be used as
conventional capacitors.
(3) Arrays of synthetic atoms require no maintenance, are low cost, and are fully operational in a large
temperature range and under extreme conditions, such as strong nuclear radiation.
Broader Impact: Potential applications include general purpose rechargeable batteries for advanced
electronics (i.e. batteries integrated in CPUs & memory) power sources for electric cars and airplanes,
temporary power storage for utilities, force actuators, robust and resilient power grids with digital
wires, thin insulation for high-voltage power lines, propulsive and explosive work, EMP sources, nanoX-ray sources for nano lithography, medical micro accelerators, nuclear protection suits (alpha,
beta, gamma) for people and equipment, harvesting energy from solar wind and nuclear chain
reactions in very small distributed nuclear batteries (1 milligram and up, 90% efficient).
Synthetic Atoms: High energy density and a record power density
A.Hubler, Physics, UIUC
IP Protection:
[1] H. Higuraskh, A. Toriumi, F. Yamaguchi, K. Kawamura, and A. Hübler. Correlation tunnel device. Unites States Patent # 5,679,961 (1997).
[2] A. Hubler and O. Osuagwu, Digital Quantum Batteries, provisional patent filed by the University of Illinois (2009)
[3] A. Hubler, D. Lyon, M. Grosse-Perdekamp, A. Bezryadin, A. Belkin, A. Friedl, Nanocapacitor Arrays for Energy Storage using Native
Aluminum Oxide Layers and Other Ultra-Thin Dielectrics, provisional patent filed by the University of Illinois, TF12200 (2013)
[4] A. Hubler, E. Shinn, D. Lyon, M. Grosse-Perdekamp, A. Bezryadin, A. Belkin, A. Friedl, Energy Conversion with Stacks of Nanocapacitors,
provisional patent filed by the University of Illinois, TF12206 (2013)
Trend lines for the energy density of commercial
energy storage devices by Chris Magee, “Towards
qualifications of the role of materials innovation in
overall technological development “, Complexity
18(1), 10–25 (2012)
Thank you.
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