Need help modelling Quantum Tunnelling Composites

In summary, a 17 year old British student recently completed a disappointing month-long placement at Newcastle University researching quantum tunnelling. The placement lacked interaction with physics professionals and the opportunity to conduct experiments. The student is now working on a theoretical research project and writing a report on the mathematical description of electrical current in relation to compressive strain in Quantum Tunnelling Composites. The student is seeking help to find an equation that links the change in current to the strain of the elastomer, and is currently using assumptions and approximations based on electron density, cross sectional area, and tunnelling probability coefficient. The student acknowledges their lack of expertise in quantum mechanics and is seeking suggestions and corrections.
  • #1
willfarquhar96
7
0
Hi all,

This is my first post on PF so forgive any rookie errors. I'm a 17 year old British student. I have just finished a month long placement at Newcastle University researching my chosen topic of quantum tunnelling. The placement itself was very disappointing and I had no interaction with a single physics professional, so I had no one to rely on if I had specific questions to ask. There was also no chance to perform any experiments.

I am now finishing my theoretical research and writing up a report. The aim of my brief project was to obtain a mathematical description of electrical current in relation to compressive strain in Quantum Tunnelling Composites. These components are fairly simple: a silicon rubber elastomer containing conductive filler particles sandwiched by two conductive plates as part of a circuit. In its rest state the elastomer acts as a near perfect insulator. When compressively strained its conductivity increases by many orders of magnitude as a result of Quantum Tunnelling occurring between the filler particles. This means the component may be used to calculate strain by measuring the change in current elsewhere in the circuit, acting as an effective pressure sensor, or as a switch.

There is little more information available on the components as they trademarked by PeratechTM, a UK firm. Their website specifies that they will not reply to academic correspondence and true to their word I have not received a reply.

I really only need help finding an equation which will link the change in current to the strain on the elastomer. Here are the assumptions/approximations I am currently using:

The current entering the elastomer at any time may be calculated using the electron density of the conductor and the cross sectional area of the interface (and possibly the equation linking drift velocity to electron mobility and electric field strength - I have less knowledge of this so some suggestions would be helpful)

The percentage of filler particles in the elastomer may be used to obtain an average distribution and hence an average distance between each conductive particle.

An individual electron entering the elastomer would tunnel from one filler particle to the next with a probability coeffecient which is a function of the distance to the next particle, the energy of the electron (presumably found by its velocity) and and the magnitude of the potential energy barrier created by the elastomer. Again I would appreciate any suggestions regarding this approach.

No time passes during the 'tunnelling' but the probability of an electron which enters the elastomer leaving the elastomer is Tn where T is the tunnelling probability coefficient, a function of the electrons energy, the barrier height and the barrier width, and n is the number of particles it must tunnel between to reach the other conducting plate. I've a feeling this is most likely an over simplification as plugging in a high probability coefficient with a relatively low n gives a seemingly low number. But then again it is only a single electron.

The decrease in the width of the elastomer (the compressive strain) will be proportional to average decrease in distance between the metal filler particles, with some constant of proportionality which is beyond my knowledge, so again suggestions are appreciated.

I understand this is a long post and my thoughts are somewhat scattered so please help me by pointing out any glaring mistakes and offering any suggestions you may have. I am most definitely not any sort of expert in quantum mechanics so I imagine I am guilty of approaching this problem too classically.

Thanks in advance,
Will Farquhar
 
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  • #2
No one has anything to contribute regarding quantum tunnelling? I'm surprised
 
  • #3
I'm not sure, but it seems you need data to help you. Are there any published papers on the material you are modelling?
 

Related to Need help modelling Quantum Tunnelling Composites

1. What are Quantum Tunnelling Composites (QTCs)?

Quantum Tunnelling Composites, also known as QTCs, are a type of smart material that can change their electrical conductivity based on applied pressure or mechanical stress. They consist of a matrix material, such as an insulator, filled with conductive particles that are separated by a small distance. When pressure is applied, the particles come closer together, allowing electrons to tunnel through the insulating matrix and create an electrical current.

2. How are QTCs used in modelling?

QTCs can be modelled using various methods, such as finite element analysis or molecular dynamics simulations. These models help to predict the behavior and performance of QTCs under different conditions, such as varying pressure or temperature. They also aid in the design of QTC-based devices and systems.

3. What are the key factors to consider when modelling QTCs?

Some of the key factors to consider when modelling QTCs include the type and properties of the matrix material, the size and distribution of conductive particles, the applied pressure or stress, and the temperature. These factors can greatly affect the electrical conductivity and performance of QTCs.

4. What are the challenges in modelling QTCs?

One of the main challenges in modelling QTCs is accurately representing the behavior of the conductive particles and their interaction with the matrix material under different conditions. The size and distribution of these particles can also be difficult to control, which can affect the overall performance of QTCs. Additionally, modelling the effects of multiple layers or complex geometries can be challenging.

5. How are QTC models validated?

QTC models are typically validated by comparing the predicted behavior of the material with experimental data. This can involve measuring the electrical conductivity of QTCs under different pressure or stress levels and comparing it with the model predictions. Other methods of validation may include using imaging techniques to visualize the distribution of conductive particles within the matrix material.

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