NANOLAB – Educational Nanoscience - www.nanolab.unimore.it

Background reading

1

Polymeric conductive composites & Quantum Tunneling Composite

Polymeric conductive composites

The boundary between electrical conductors and insulators is not so clear-cut as it is traditionally thought of. Nowadays, thanks to modern technologies, the range of conductive materials is extremely varied. Research has developed lighter, less expensive, and more versatile conductive materials. Even glass, ceramics, polymers and polymeric composites can be made conductive with specific treatments. Glass, for instance, can be made conductive by coating it with a titanium dioxide thin film.

Plastic is typically considered an insulator. However, for many applications, plastic conductors are extremely useful. Antistatic footwear, for firemen must have conductive soles in order to avoid sparks, which could lead to devastating explosions in gas saturated environments. Delicate electronic instruments, which may be damaged by electrical discharge, are often packaged in conductive plastic.

Traditional electro-conductive rubber is typically produced with vulcanized rubber filled with a high percentage of carbon black. Conductive particles of carbon, metals, carbon fibers, graphite, pyrolitic carbons and carbon black (with different purity and morphology) have been used as filler in polymeric1 composites since the ‘50s.

1 Nowadays carbon nanotubes are widely used as filler too.

Version: 20/06/2013

All NANOLAB materials, this document included, belong to NANOLAB authors (www.nanolab.unimore.it) and are distributed under Creative Commons 3.0 not commercial share alike license.

Fig.1 Percolation: conductive paths

progressively form with the increase of filler concentration. Image courtesy: .T.Zimmerman, Pennsylvania State University, Altoona College.

NANOLAB – Educational Nanoscience - www.nanolab.unimore.it

Background reading

2

Percolation

The conduction mechanism of traditional polymeric composites is called percolation. Such materials are made of an insulator matrix (elastomer) in which micrometer-sized conductive particles are finely dispersed. For conductivity to work properly concentration, i.e. filler-polymeric matrix ratio, is fundamental.

Suppose you have different samples with increasing ratio of metallic filler. There’s a critical threshold for the filler (called pc in fig. 1) at which the sample suddenly becomes an excellent conductor, owing to the fact that there’s now at the very least one whole conductive path ensuring charge transport through the metallic particles, (fig.1). Beyond this threshold the sample conductivity σ increases further since new paths form by adding new metal filler but saturation will soon be reached .

Fig.2shows the dramatic change in conductivity at the percolation threshold for spherically shaped particles of different diameter. Near the threshold many other physical and chemical properties of the sample undergo dramatic changes as well. It’s also possible to engineer the percolation threshold since it also depends on the shape of the filler particles. For “needle” shaped particles the threshold is lower than 1%, and for spherical ones it is beyond 10%. Finally, it’s possible to lower the percolation threshold in anisotropic composites during manufacturing: particle chains can be forced to align by the application of either electrical or magnetic fields.

The percolation mechanism can be effectively studied with computer simulations. Imagine a chessboard whose squares are being blackened randomly. If the probability for each square to be painted is low, for instance 20%, then the ratio of painted squares

on the whole chessboard will be around 0.02 (Fig.3.1). If the probability for each square to be painted increases, then clusters of adjoining black squares begin to form (Fig.3.2). Further increases lead to an increase in cluster dimensions; in Fig.3.3, one of the clusters almost reaches across the whole chessboard. In Fig. 3.4, once p = pc = 0.5, the largest clusters form complete paths from one side to the opposite without interruption. The transition from none to at least one conductive path is called percolation transition, and can be considered as a real phase transition.

Fig.2 Percolation threshold and saturation for

particles of varying diameter. Image courtesy: D.T.Zimmerman, Pennsylvania State University, Altoona College.

Fig.3 Percolation threshold

simulation. Image courtesy:. T.Zimmerman, Pennsylvania State University, Altoona College.

NANOLAB – Educational Nanoscience - www.nanolab.unimore.it

Background reading

3

If the chessboard represents a real sample with both conductive (black) and insulating (white) particles then it is clear that it will behave as a good conductor when the larger clusters cross it. Researchers resort to computers to simulate different possibilities and investigate how cluster sizes change by increasing the value of p. Such simulations allow scientists to model the mechanism by which the properties of real materials change near the percolation threshold.

Usually electro-conductive percolation-based composites have a conductivity that changes with any mechanical interaction. For instance, upon compression the number of touching filler particles increases, therefore the number of conductive paths increases too owing to a higher relative concentration ratio. Under tension, on the other hand, particles are separated and experience a decrease in conductivity (with a few rare exceptions). This mechanism can be exploited to design highly sensitive sensors and transducers. However, electrical resistance R of these materials varies in a rather restricted range, typically between 103Ω and 102Ω for samples of a few mm2. R never goes to zero and at the same time never exceeds a maximum threshold variable with the specific material. However, the response to applied pressure is mostly linear. This fact limits the performance of traditional conductive polymeric composite as pressure sensors.

QTC©

The Quantum Tunneling Composites (QTC©) show similar behavior to traditional polymeric composites, but on the nanoscale they differ in a very special way. Their conductive mechanism is based on quantum effects, and this makes them particularly suitable for specific applications.

QTC©, inventor, David Lussey, was looking for a conductive adhesive to be used for PC antitheft labels, when an apparent mistake (1996) opened a very promising new research path. Lussey tested the adhesives by putting them between two metal plates and by subsequently separating them while measuring conductivity. Applying the same procedure to a newly made composite based on Nickel particles, he discovered that, when extended, the sample became more conductive instead of more insulating. The new material displayed properties that had been observed separately in other materials, but never all together in the same one! Undeformed QTC© is insulating (R almost infinite), while kind mechanical deformation (compression, traction or twisting) produces a decrease in resistance until the point of reaching metallic behavior.

The conductive mechanism

Fig.4 TEM images show the

dimensions of the particles

(0,5 ) and of the spikes (100

nm). Image courtesy D.Bloor

Durham Universiy, UK

NANOLAB – Educational Nanoscience - www.nanolab.unimore.it

Background reading

4

TEM (transmission electron microscopy) and SEM (scanning electron microscopy) images of the Nickel nanoparticles used in QTC© manufacturing were instrumental in guiding researchers to their understanding of the odd behavior of this new material. Two things clearly appear in the electron microscope pictures:

the presence of spikes: The surface of Nickel nanoparticles have a structure with many extremely thin spikes specifically designed to make the powder flow more easily in methallurgy applications (Fig. 4 );

the extreme wettability (adhesion) of the metal particles by the polymeric material: the nanoparticles thus result entirely coated and isolated.

In QTC© manufacturing, Nickel micrometer sized particles are mixed manually and randomly into the polymeric matrix (elastomer). Usually in similar materials, the mixing is a mechanical process leading to a collateral effect of “milling” which reduces the particles to a spherical shape. This did not happenduring QTC© manufacturing since the more delicate mixing preserved the nanostructured surface with the thin spikes. These spikes ultimately appear as one of the fundamental elements of the conductive mechanism. In fact, it has been shown that, if the spikes are intentionally damaged, the same type of composite is much less sensitive to the applied pressure. The particles morphology is clearly visible with TEM.

In SEM images (Fig.5) the coating hides the spikes, but thanks to an higher accelerating potential leading to a better electron penetration, it’s still possible to discern the presence of underlying spikes. The high filler concentration is also visible. Distances between the particles vary over a wide range, but many particles are less than 100 nm apart. Such a high concentration of the filler in the absence of a polymeric

insulating coating would produce many conductive paths by percolation. In QTC©, however, owing to the high wettability of the particles, such paths are cut off by the insulating elastomer barrier. As a consequence, “injected” charges in the composite are not able to flow freely. Instead, they stop on particles at the end of the paths, leading to the creation of local electrostatic fields that, at the spike tip, can reach extreme values. The spikes enhance the local electrostatic field up to 1000 times, therefore favoring Fowler Nordheim tunneling field assisted emission.

Fig.5 SEM pictures: the elastomer completely coats the Nickel

nanoparticles, totally separating them. Image courtesy: D.Bloor Durham

University,UK.

NANOLAB – Educational Nanoscience - www.nanolab.unimore.it

Background reading

5

Within QTC©, the conducting nanoparticles are never touching, even when their distances diminish on compression; classical conduction via percolation is not a possibility. However, the decreased distances and extreme voltages make the charge transfer possible through tunneling 2 at the spikes.

Experimental data

Different types of experimental data are consistent with the model of a conduction mechanism dominated by quantum tunneling.

First, the Resistance versus applied Pressure relationship is an exponential one. As explained previously, in QTC© a classical percolation mechanism is not available. In the normal state (zero compression) the material should be a perfect insulator, i.e. R should be infinite. Experimentally, resistance values for QTC© are very large, but finite (up to 1014 ). The resistance of carbon composites, on the other hand, normally does not exceed a few thousand Ω, since, even below the percolation threshold, a minimum conductivity is still there. The result is even more striking when you consider that

QTC© is an insulator at a metal/polymer weight ratio of 4-6:1, which is usually well beyond the percolation threshold.

The piezoresistive3 effect exhibited by QTC© is quite strong and the resistivity of the material is extremely responsive to deformation: under a very moderate compression, R can quickly go from 1012-1013Ω to less than 1 Ω. This is an exceptionally wide dynamic range for a property of a solid material at room temperature. This also agrees with a quantum tunneling hypothesis; if the deformation and the subsequent shortening of the interspaces between the metal particles is linear, the exponential decay of the electron wave function should lead to an exponentially higher probability of tunneling. If the applied voltage is constant this should cause an exponential decrease in resistance, which is exactly what is experimentally observed (Fig.6).4

2 See at the end of document “Quantum tunneling effect”

3 Piezoresistive materials resistances change according to the applied pressure.

4 In experiments, it is difficult to compress the QTC© in a perfectly linear way along the particles direction (owing to

larger thickness this is even more difficult in QTC© pills than in QTC© sheet). Invariably, the material deforms in a very complicated manner according to how the force is being applied. As a consequence, the ratio (compression percentage) / Force is not exactly linear, and resistance VS applied force can deviate from an exponential curve.

Fig. 6. Resistence VS applied load

NANOLAB – Educational Nanoscience - www.nanolab.unimore.it

Background reading

6

Another unusual characteristic of QTC© is that the resistance decreases exponentially upon extension, torsion, or bending. In traditional composites, R increases under extension: this is

intuitive if you consider the percolation mechanism. Since such a movement will increase the average separation of metal particles dispersed within the elastomer, fewer percolation pathways will exist. The fact that QTC© behaves differently suggests that the reduction in particle separation in the supposed percolation paths perpendicular to the stretching direction may dominate over increasing separation in the parallel direction. This is totally consistent with the hypothesis of field induced tunneling. The same hypothesis also means that carriers may be able to go across larger gaps than

in a conventional composite and this further counteracts the effect of the increasing particle separation in the parallel direction. The dependence of the conductivity on the applied voltage at a constant compression (fig.7) is also consistent with a quantum tunneling model. At very low voltage, the electrons will have very little energy, and not many of them will be able to tunnel through the insulating material barrier. Therefore, in the normal state (zero compression) a QTC© is an insulator. Even at a compression level allowing conduction, the current will be very low. By increasing voltage, that is increasing the energy given to the electrons, the probability of tunneling increases considerably and a higher current is observed. In order to better understand the charge transport mechanism in QTC©, it is convenient to investigate also the I-V curve, since its behavior is definitively anomalous. In our case the curve, appears ohmic at both nearly zero and extremely high applied pressure, while at intermediate pressures it exhibits a highly nonlinear behavior with regions of negative resistance and a pronounced hysteresis. In contrast, traditional carbon composites exhibit almost linear behavior, except when under the influence of a strong Joule effect (in this case it’s possible to record a slightly negative resistance).

Current increases, at first very quickly, reaching a maximum value Imax. As the voltage increases further however, current intensity decreases and the negative resistance regime is recorded with random current fluctuations. Then as voltage decreases, a pronounced hysteresis is observed. Current intensity slowly increases, but stays very low for a wide range of V and then suddenly increases within an extremely limited V range. As voltage is decreased further, the current decreases to zero nonlinearly.

However, the observed behavior is still clearly different from the one recorded with traditional composites.

Vo

ltag

e (V

)

Force (N) Fig.7 Effect of the varying applied

voltage

NANOLAB – Educational Nanoscience - www.nanolab.unimore.it

Background reading

7

From the slope of the graph, it is clear that the initial and final resistances are different. As a rule final resistance in case of low or intermediate compression (fig.8-a,b) is lower than the initial one, the reverse happens for initially high compression (fig.8-c)

Such a phenomenology can be interpreted consistently with the hypothesis of quantum tunneling. The negative resistance is due to electrical charge storage on the metal particles, mainly on the spikes, and to the subsequent current “pinch off”. At an applied voltage of 240 V, internal electrostatic fields in excess of 3*106 Vm-1 have been recorded. The disordered particle distribution, both in shape and number, creates a number of barriers with different potentials. This ultimately impairs charge transport. When conductivity begins to show, the charge flows through the elastomer barriers that can be easily overcome, till the charge reaches a state at which tunneling is no longer possible. As a consequence, charge accumulates and leads to the deformation of the surrounding electrostatic field. Interestingly enough, this redistribution of charge inhibits the tunneling in the nearby region: other conductive paths are “pinched off” and the charge flow stops. The charge distribution due to the increased voltage initially lasts even when the voltage decreases, leading to the observed hysteresis. However, in the end, the applied field is not strong enough to keep the charge trapped and the redistribution of charge is partially reversed. The redistribution shows up in the I-V curve as “current jumps”. The residual trapped charge at the end of the cycle is the cause of a final resistance R that differs from the initial one (which was measured in an electrically neutral condition)

In addition to what has been described above, the internal charge distribution generates electrostatic forces between the Nickel nanoparticles that, owing to the deformation of the matrix, bring a further mechanical response. This also contributes to the modification of the conductive paths determined within the sample with the varying voltage. The sample micro geometry varies with respect to the initial configuration and the continuous charge redistribution explains hysteresis and the difference between initial and final R. With a higher compression, conductivity increases and charge accumulation is inhibited. Actually compressing the sample to a low initial resistance charge accumulation is inhibited, the stored charge flows away and the sample again reaches the initial charge configuration.

Fig.8 I-V curves in QTC© for an initial R respectively of 100 kΩ, 900 Ω and10 Ω. Image courtesy D. Bloor

Durham University. The effect of changing voltage as the compression is kept constant. It’s possible to observe the

highly non-ohmic behavior. However, the observed behavior is ohmic under either very low or extremely high

compression..

NANOLAB – Educational Nanoscience - www.nanolab.unimore.it

Background reading

8

To summarize: I-V curves depend on initial deformation (i.e. initial resistance), maximum applied voltage, and sample history. Generally speaking, the behavior of any QTC© component is influenced by the following factors, each one can be easily controlled either at manufacturing or application stage in order to satisfy specific uses:

original distance between the metal nanoparticles (which is also connected to the filler concentration within the polymeric matrix);

geometry of the specific QTC© element;

elastomeric properties of the matrix polymer;

the way in which the deformation is applied;

applied voltage.

Traditional composites QTC

Shape of the filler particles

round with nanometric spikes

Filler concentration Lower than percolation threshold

Mechanism percolation Assisted tunnel effect

Matrix Intimately coating

Resistence at zero compression

≈103Ω Up to 1014Ω

QTC© applications

For its incredible sensitivity to deformation, together with its minimal thickness (approx. 75 micron or even less), a QTC© is suitable for many exciting applications, some of which are already on the market, from touch screens (clear QTC© – 2011) to integrated textile switches and printed electronics. It is particularly suitable for

safety switches: In traditional switches there is a spark just before the moment of contact between the two electrodes. In gas saturated environments, for instance on oil platforms, this can be extremely dangerous!

Impact or pressure sensor. Since QTC© is able to record minimal changes in pressure and tiny deformations, one of the most interesting applications is related to the use as tactile sensors in artificial hands (either prosthetic or robotic ones). It has been successfully used in the gloves covering the hands of Robonaut2 (the NASA humanoid robot sent to the International Space Station in 2011)

Tab.1 QTC and traditional composites comparison.

NANOLAB – Educational Nanoscience - www.nanolab.unimore.it

Background reading

9

Integrated into bandages in order to monitor whether they are too tight and impairing blood circulation.

Since it can easily stand the passage of high currents, up to a few Amperes, QTC© can be used for direct load control.

An intense reaction to many volatile compounds has been observed. Using this characteristic, a QTC© can be easily used in electronic noses. For such application, QTC© has been used in granular form with the granules trapped between two Nickel nets. The increase in resistance is due to the homogeneous expansion resulting from vapor absorption.

Quantum tunnel effect

Quantum tunneling is a typically quantum mechanical effect allowing the transition between two states that is forbidden according to the laws of classical mechanics. In classical mechanics, the energy conservation law dictates that a particle can’t overcome a potential barrier unless it has sufficient energy. Quantum mechanics predicts that a particle always has a finite, however small, probability to pass through an arbitrarily high barrier. In the well-known case of the one-dimensional potential barrier, the wave function is represented by an exponential function progressively decreasing as it crosses the barrier. When the barrier is finite, the wave function has a finite value on the far side of the barrier, and there is a probability that the particles will be observed on the other side of the barrier. Such a probability depends exponentially on the barrier width.

While counterintuitive, quantum tunneling is not an uncommon effect. Quantum tunneling is based on a large quantity of experimental evidence, and there are many applications that rely on the effect. Just to cite the most important ones, the operating principles of an STM (Scanning

Fig.9 According to classical physics, when the electron (particle) does not have enough energy to overcome an insulating barrier, it will never be found on the other side of the barrier. On the contrary, according to a quantum model, the electron as a wave has a finite probability to emerge beyond the barrier thanks to the tunnel effect.

NANOLAB – Educational Nanoscience - www.nanolab.unimore.it

Background reading

10

Tunneling Microscope) and of many modern electronic devices such as tunnel diodes and flash memory are based on tunneling.

In the specific case of QTC©, the elastomeric coating wetting the Nickel particles and separating them from each other, serves as a very high potential barrier confining charges the Nickel particles. When the electron reaches this barrier of the insulating material, a classical model requires that the electron “bounce back” abruptly, or at the very least stop (Fig.9 - left). In a quantum model however, the electron wave extends into the barrier. Though it decays exponentially inside the barrier, it has a will emerge on the other side with reduced amplitude. In other words there is a probability to find the electron on the other side of the barrier, i.e. a probability that the electron will tunnel through it (Fig.9 - right).

Electronic field emission

Electronic field emission was explained using electron quantum tunneling in 1920, indeed, it represented one of the first successes of the newly developed quantum mechanics. The theory of metal field emission has been proposed by Fowler and Nordheim, and consists of the idea that electrostatic fields induce electron emission. The most common example is the emission from a solid free surface in a vacuum, but there are also emission examples from both solid and liquid surfaces in a vacuum, in air, in fluids, or in non-conductive or slightly conductive dielectrics. In

metals, the field emission takes place in presence of high electric fields (typically in the presence of spikes): gradients are normally higher than 1 GV/m and strongly depend on work function.

In some cases, such electronic emission is considered a negative phenomenon, since it it’s the first and main cause of electric discharge in vacuum systems. On other occasions, however, such an emission produced deliberately, such as in discharge systems of stored electrostatic charge on the surfaces of planes. This limits charge induced interference and disturbance of radio transmissions.

Electronic sources, based on field emission, have multiple applications, such as “bright” electron sources in high-resolution electron microscopes. Nowadays, it is possible to build emitters with the dimensions of a single atom. Ordered arrays of such emitters, each of them with a spike diameter smaller than 100 nm (Fig. 11 e 12), are being produced as thin films and used, for instance, in the new generations of touchscreens.

Fig.10 Discharge systems of the accumulated electrostatic charge on the external of the wing. Imagine Wikipedia

NANOLAB – Educational Nanoscience - www.nanolab.unimore.it

Background reading

11

Further research

Outreach materials on QTC© and traditional conductive polymeric composites

o Percolative phenomena in polymeric composites http://www.aa.psu.edu/physics/Materials_group.html

o QTC© manufacturer http://www.peratech.com/qtcapplications.php

o “QTC© a remarkable new material to control electricity” - SEP publication o “QTC©– Making the Most of a Novel Material” –free article o www.msa.ac.uk/~fraser/wiringpg/files/integration-guide.pdf technical guide to qtc use

Research papers from Durham University UK:

o “Metal–polymer composite with nanostructured filler particles and amplified physical properties ”D. Bloor, A. Graham, and E. J. Williams 2006 Appl. Phys. Lett. 88, 102103

o “A metal-polymer composite with unusual properties” D Bloor et al 2005 J. Phys. D: Appl. Phys. 38 2851-2860

o Bloor, D., et al, Metal–polymer composite sensors for volatile organic compounds: Part 1. Flow-through chemi-resistors, Sensors and Actuators B: Chemical, 2011 162, Issue 1: p. 400-408

o Robonaut2 NASA http://www.nasa.gov/mission_pages/station/main/robonaut.html

Fig.12 Field emitters obtained with the “focused ion beam milling” technique. The diameter of the spikes is less than 100 nm. Image courtesy of FEI & captured by Alexey Kolomiytsev on an FEI Nova DualBeam

Fig.11 Electron field emission in auto organized matrices of emitters - boron nitride films. Immagine http://www.nanonet.go.jp

NANOLAB – Educational Nanoscience - www.nanolab.unimore.it

Background reading

12

On tunnel effect and electron field emission

o VIDEO: How Quantum tunneling works Ivar Giaevar, Edison Tech Center http://www.youtube.com/watch?v=AJY8farPqdI

o SIMULATIONS : o http://concord.org/activities/quantum-tunneling a Java free application to

research tunnel effect through different types of barriers with an eye to applications. Registering in the project website it’s also possible to save data..

o http://phet.colorado.edu/en/simulation/quantum-tunneling o web.phys.ksu.edu/vqm/vqmnextgen/qmbasics/ e

http://web.phys.ksu.edu/vqm/software/online/vqm/html/qtunneling.html It is part of Visual quantum mechanics project: the software is sold by Ztek but the accompanying materials are freely downloadable.

o http://www.nanoscience.com/education/STM.html focusing on scanning tunneling microscope

o http://en.wikipedia.org/wiki/Field_electron_emission

o Electron field emission from self-organized micro emitters of new-type boron nitride films http://www.nanonet.go.jp/english/mailmag/2006/067b.html