The tunnel effect

Bell, R.P., 1980, The Tunnel Effect in Chemistry (Chapman and Hall, London). 

It appears that the bending vibrations, which are ignored in the above discussion, may act to increase as can the tunneling effect, so it is possible for the... 

The percolation theory [5, 20-23] is the most adequate for the description of an abstract model of the CPCM. As the majority of polymers are typical insulators, the probability of transfer of current carriers between two conductive points isolated from each other by an interlayer of the polymer decreases exponentially with the growth of gap lg (the tunnel effect) and is other than zero only for lg < 100 A. For this reason, the transfer of current through macroscopic (compared to the sample size) distances can be effected via the contacting-particles chains. Calculation of the probability of the formation of such chains is the subject of the percolation theory. It should be noted that the concept of contact is not just for the particles in direct contact with each other but, apparently, implies convergence of the particles to distances at which the probability of transfer of current carriers between them becomes other than zero. 

Theoretically, the problem has been attacked by various approaches and on different levels. Simple derivations are connected with the theory of extrathermodynamic relationships and consider a single and simple mechanism of interaction to be a sufficient condition (2, 120). Alternative simple derivations depend on a plurality of mechanisms (4, 121, 122) or a complex mechanism of so called cooperative processes (113), or a particular form of temperature dependence (123). Fundamental studies in the framework of statistical mechanics have been done by Riietschi (96), Ritchie and Sager (124), and Thorn (125). Theories of more limited range of application have been advanced for heterogeneous catalysis (4, 5, 46-48, 122) and for solution enthalpies and entropies (126). However, most theories are concerned with reactions in the condensed phase (6, 127) and assume the controlling factors to be solvent effects (13, 21, 56, 109, 116, 128-130), hydrogen bonding (131), steric (13, 116, 132) and electrostatic (37, 133) effects, and the tunnel effect (4,... 

Hie possibility that a particle with energy Jess than the barrier height can penetrate is a quantum-mechanical phenomenon known as the tunnel effect. A number of examples are known in physics and chemistry. The problem illustrated here with a rectangular barrier was used by Eyring to estimate the rates of chemical reactions. ft forms the basis of what is known as the absolute reaction-rate theory. Another, more recent example is the inversion of the ammonia molecule, which was exploited in the ammonia maser - the fbiemnner of the laser (see Section 9.4,1). 

Many molecules have more than one well-defined structure - or even none. If there is more than one equilibrium structure the passage from one to another can take place because of the tunnel effect , although it may be impossible from a purely classical point of view. The best known example is certainly the ammonia molecule, NH3. 

This equation is referred to as the Marcus-Levich equation in which the tunneling effect is included. 

Figure 3. The trajectories of electron s motion in the area of the tunnel effect at change of value of its initial speed. 1 — the trajectories of electron s motion in an electric field, 2 and 3 — the trajectory of electron s motion in aggregate electrical and thermal fields, accordingly, under px = 0.25pe and pr = 0.5pe, 4 and 5 — the trajectory of electron s motion in aggregate electrical and thermal fields, accordingly, under px = —0.25pe and px = —0.5pe.

Quantum-mechanical tunnelling has been recognized as a possible contributor to the rate of a chemical reaction for many years. For instance, the theory of tunnelling for proton transfer reactions was developed by Bell (1959) in his famous book The Proton in Chemistry. Later, Bell (1980a) published a more thorough treatment of tunnelling in his book The Tunnel Effect in Chemistry. 

Bell, R. P. (1959). The Proton in Chemistry. Cornell University Press, Ithaca, NY Bell, R. P. (1980a). The Tunnel Effect in Chemistry, Chapman and Hall, London Bell, R. P. (1980b). The Tunnel Effect in Chemistry. Chapman and Hall, London, pp. 60-63... 

DR. EYRING Well, I think we are all conscious of the fact that Bell writes extensively on the subject of tunneling in connection with proton transfer. In fact, there is a recent book that was published within the last year that is on that particular topic [Bell, R. P. "The Tunnel Effect in Chemistry" Chapman and Hall London, 1980]. 

The polarization, or the van der Waals interaction, can be accounted for by a stationary-state perturbation theory, effectively and accurately. The exchange interaction or tunneling can be treated by time-dependent perturbation theory, following the method of Oppenheimer (1928) and Bardeen (1960). In this regime, the polarization interaction is still in effect. Therefore, to make an accurate description of the tunneling effect, both perturbations must be considered simultaneously. This is the essence of the MBA. 

If an electron rather than an atom tunnels, the transition probability for this particle is much larger in view of its smaller mass therefore the tunnel effect may account for the observed rates of such chemical reactions (22) in which an electron transition can be considered an essential step. Detailed calculations based on the tunneling theory have been... 

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