Tunneling in Chemistry: Quantum & Classical Phenomenon
Quantum tunnelling is a phenomenon which becomes relevant at the nanoscale and below. It is a paradox from the classical point of view as it enables elementary particles and atoms to permeate an energetic barrier without the need for sufficient energy to overcome it.
Tunneling might seem to be an exotic process only important for special physical effects and applications such as the Tunnel Diode, Scanning Tunnelling Microscopy (electron tunneling), or Near-field Optical Microscopy operating in photon tunneling mode. However, this review demonstrates that tunneling can do far more, being of vital importance for life.
WHAT IS QUANTUM TUNNELLING?
Quantum tunneling falls under the domain of quantum mechanics: the study of what happens at the quantum scale. Tunneling cannot be directly perceived. Much of its understanding is shaped by the microscopic world [Fig-1.1], which classical mechanics cannot explain.
To understand the phenomenon, particles attempting to travel across a potential barrier can be compared to a ball trying to roll over a hill. Quantum mechanics and classical mechanics differ in their treatment of this scenario [Fig-1.2].
Classical mechanics predicts that particles that do not have enough energy to classically surmount a barrier cannot reach the other side. Thus, a ball without sufficient energy to surmount the hill would roll back down. A ball that lacks the energy to penetrate a wall bounces back [Fig-1.4]. Alternatively, the ball might become part of the wall (absorption).
In quantum mechanics, these particles can, with a small probability [Fig-1.5], tunnel to the other side, thus crossing the barrier. The ball, in a sense, borrows energy from its surroundings to cross the wall. It then repays the energy by making the reflected electrons more energetic than they otherwise would have been.
The reason for this difference comes from treating matter as having properties of waves and particles. One interpretation of this duality [Fig-1.4] involves the Heisenberg uncertainty principle, which defines a limit on how precisely the position and the momentum of a particle can be simultaneously known. This implies that no solutions have a probability of exactly zero (or one), though it may approach infinity. If, for example, the calculation for its position was taken as a probability of 1, its speed, would have to be infinity (an impossibility). Hence, the probability of a given particle’s existence on the opposite side of an intervening barrier is non-zero, and such particles will appear on the ‘other’ (a semantically difficult word in this instance) side in proportion to this probability.
Quantum Tunneling:-
The phenomenon of tunneling, which has no counterpart in classical physics, is an important consequence of quantum mechanics. Consider a particle with energy E in the inner region of a one-dimensional potential well V(x). (A potential well is a potential that has a lower value in a certain region of space than in the neighbouring regions.) In classical mechanics, if E < V (the maximum height of the potential barrier), the particle remains in the well forever; if E > V , the particle escapes [Fig-1.6]. In quantum mechanics, the situation is not so simple. The particle can escape even if its energy E is below the height of the barrier V , although the probability of escape is small unless E is close to V [Fig-1.6]. In that case, the particle may tunnel through the potential barrier and emerge with the same energy E.
The phenomenon of tunneling has many important applications. For example, it describes a type of radioactive decay in which a nucleus emits an alpha particle (a helium nucleus). According to the quantum explanation given independently by George Gamow and by Ronald W. Gurney and Edward Condon in 1928, the alpha particle is confined before the decay by a potential. For a given nuclear species, it is possible to measure the energy E of the emitted alpha particle and the average lifetime of the nucleus before decay [Fig-1.7]. The lifetime of the nucleus is a measure of the probability of tunneling through the barrier — the shorter the lifetime, the higher the probability.
With plausible assumptions about the general form of the potential function, it is possible to calculate a relationship between and E that is applicable to all alpha emitters. This theory, which is borne out by experiment, shows that the probability of tunneling is extremely sensitive to the value of E. For all known alpha-particle emitters, the value of E varies from about 2 to 8 megaelectron volts, or MeV (1 MeV = 10 electron volts). Thus, the value of E varies only by a factor of 4, whereas the range of is from about 10¹¹ years down to about 1/10⁶ second, a factor of 10²⁴. It would be difficult to account for this sensitivity of to the value of E by any theory other than quantum mechanical tunneling.
Quantum tunneling refers to the non-zero probability that a particle in quantum mechanics can be measured to be in a state that is forbidden in classical mechanics. Quantum tunneling occurs because there exists a nontrivial solution to the Schrödinger equation in a classically forbidden region, which corresponds to the exponential decay of the magnitude of the wavefunction [Fig-1.8].
To illustrate the concept of tunneling, consider trying to confine an electron in a box. One could try to pin down the location of the particle by shrinking the walls of the box, which will result in the electron wavefunction acquiring greater momentum uncertainty by the Heisenberg uncertainty principle. As the box gets smaller and smaller, the probability of measuring the location of the electron to be outside the box increases towards one, despite the fact that classically the electron is confined inside the box.
HISTORY :
Quantum tunneling was developed from the study of radioactivity, which was discovered in 1896 by Henri Becquerel. Radioactivity was examined further by Marie Curie and Pierre Curie, for which they earned the Nobel Prize in Physics in 1903. Ernest Rutherford and Egon Schweidler studied its nature, which was later verified empirically by Friedrich Kohlrausch. The idea of half-life and the possibility of predicting decay was created from their work.
Quantum tunneling was first noticed in 1927 by Friedrich Hund while he was calculating the ground state of the double-well potential Leonid Mandelstam and Mikhail Leontovich discovered it independently in the same year. They were analyzing the implications of the then new Schrödinger wave equation.
Its first application was a mathematical explanation for alpha decay, which was developed in 1928 by George Gamow (who was aware of Mandelstam and Leontovich’s findings) and independently by Ronald Gurney and Edward Condon. The latter researchers simultaneously solved the Schrödinger equation for a model nuclear potential and derived a relationship between the half-life of the particle and the energy of emission that depended directly on the mathematical probability of tunneling.
https://medium.com/r/?url=https%3A%2F%2Fyoutu.be%2FK64Tv2mK5h4Is Not Quantum Tunneling Instantaneous??
Although it would not get you past a brick wall and onto Platform 9¾ to catch the Hogwarts Express, quantum tunneling — in which a particle “tunnels” through a seemingly insurmountable barrier — remains a confounding, intuition-defying phenomenon. Now Toronto-based experimental physicists using rubidium atoms to study this effect have measured, for the first time, just how long these atoms spend in transit through a barrier [Fig-1.9]. Their findings appeared in Nature on July 22.
The researchers have showed that quantum tunneling is not instantaneous — at least, in one way of thinking about the phenomenon — despite recent headlines that have suggested otherwise. “This is a beautiful experiment,” says Igor Litvinyuk of Griffith University in Australia, who works on quantum tunneling but was not part of this demonstration. “Just to do it is a heroic effort”.
To appreciate just how bizarre quantum tunneling is, consider a ball rolling on flat ground that encounters a small, rounded hillock. What happens next depends on the speed of the ball. Either it will reach the top and roll down the other side or it will climb partway uphill and slide back down, because it does not have enough energy to get over the top.
This situation, however, does not hold for particles in the quantum world. Even when a particle does not possess enough energy to go over the top of the hillock, sometimes it will still get to the opposite end. “It’s as though the particle dug a tunnel under the hill and appeared on the other side.” says study co-author Aephraim Steinberg of the University of Toronto.
Dynamical tunneling
The concept of quantum tunneling can be extended to situations where there exists a quantum transport between regions that are classically not connected even if there is no associated potential barrier. This phenomenon is known as dynamical tunneling
1. Tunneling in phase space
2. Chaos-assisted tunneling
3. Resonance-assisted tunneling
Advantages:
- Lower power assumption
- Good scalability
Disadvantages:
- Operated usually at low temperature
- High output impedance due to tunneling
- Vds has to be less than Vg to have get fully control the switch
Applications:-
1) Electronics
2) Cold emission
3) Tunnel junction
4) Quantum-dot cellular automat
5) Tunnel diode
6) Tunnel field-effect transistors
7) Nuclear fusion
8) Radioactive decay
9) Astrochemistry in interstellar clouds
10) Quantum biology
11) Quantum conductivity
12) Scanning tunneling microscope
13) Kinetic isotope effect
NOTE: Different types of quantum tunneling is available. Some of these I’m mentioning below —1.Dielectric barrier discharge
2. Field electron emission
3. Holstein–Herring method
4. Proton tunneling
5. Superconducting tunnel junction
6. Tunnel diode
7. Tunnel junction
8. Quantum cloning
9. White hole
10. Faster than light
Also, if you want to do full video lecture about quantum tunneling, you can consult these videos—
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References :
1)
https://www.chemistryworld.com/news/explainer-what-is-quantum-tunnelling/4012210.article2)
https://www.scientificamerican.com/article/quantum-tunneling-is-not-instantaneous-physicists-show/3)
https://medium.com/r/?url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FQuantum_tunnelling4) https://medium.com/r/url=https%3A%2F%2Fen.wikipedia.org%2Fwiki%2FQuantum_tunnelling5) http://ieeexplore.ieee.org/document/7405851/#:~:text=The%20developed%20detectors%20based%20on,support%20for%20intelligent%20transportation%20sy
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