Tunneling barrier plot

Figure 7.12 Plot of the survival probability 5(t) as a function of time for the quadruple tunneling barrier system discussed in the text that exhibits decaying nonexponential Rabi oscillations. The inset shows S(t) in a wider time interval that includes the exponential-postexponential transition at long times.

Figure 10.10 shows an example of a measurement of the energy gap by a tunneling experiment The measurement gives the tunnel resistance between two crystals of /S-(BEDT-TTF)2 13 in the superconducting state. The tunnel barrier here is the vacuum between the two minimally separated crystals [7]. The plot of d V/dl, the dif-... 

Here is the tip-enhanced electric field that is, the increased electric field surrounding the sharp emitter. The sharper the emitter is the greater the enhancement factor and the steeper the potential profile gradient, which narrows the corresponding tunnel barrier. The field enhancement factor is a standard performance metric that is empirically evaluated by measuring the I V characteristics and plotting the so-called Fowler-Nordheim (FN) curve according to... 

Fig. 8. Arrhenius plot of dissipative tunneling rate in a cubic potential with Vq = Sficoo and r jlto = 0, 0.25 and 0.5 for curves 1-3, respectively. The cross-over temperatures are indicated by asterisks. The dashed line shows k(T) for the parabolic barrier with the same CO and Va-...

Fig. 17. Contour plots for a

When the electric field-induced tunneling currents are analyzed in a log WE1) versus ME plot, a straight line should be obtained. The height of the potential barrier can be derived from the slope of this straight line using Eq. (9.12). 

Relationships between reaction rate and temperature can thus be used to detect non-classical behaviour in enzymes. Non-classical values of the preexponential factor ratio (H D i 1) and difference in apparent activation energy (>5.4kJmoRi) have been the criteria used to demonstrate hydrogen tunnelling in the enzymes mentioned above. A major prediction from this static barrier (transition state theory-like) plot is that tunnelling becomes more prominent as the apparent activation energy decreases. This holds for the enzymes listed above, but the correlation breaks down for enzymes... 

The value of log rn for the Fe(H20) 2+ - Fe(H20)6 + exchange (which features a relatively large inner-sphere barrier) is plotted as a function of 1/T in Figure 5. The nuclear tunneling factors are close to unity at room temperature but become very large at low temperatures. As a consequence of nuclear tunneling, the electron transfer rates at low temperatures will be much faster than those calculated from the classical model. 

Fig. 19 Resistance-area product (a) and magnetoresistance (b) plotted as a function of Alqa barrier thickness in MgO/Alq3 magnetic tunnel junctions. The solid line is the fit to a (8), with parallel tunelling and hopping channels. The line in (b) is a guide to the eye. Taken Irom [23] with permission...

When NMA+ reacts with phenyl-substituted N-phenyldihydronicotin-amides, X-PhNAH, also in anhydrous acetonitrile (Powell and Bruice, 1983b), rate and equilibrium data yield a Bronsted plot with a slope of 0.51, consistent with a centrally located transition state. The primary k.i.e. s h2/ d2, increase from 3.98 for X = />-methoxy to 4.77 for X = m-trifluoro-methyl at 50° and may indicate a trend to a more symmetrical transition state. Marcus treatment of the substituent dependence of the k.i.e. s yields an intrinsic barrier AG = 22.2 kJ mol - L. The temperature dependence of the k.i.e. for reduction by X-PhNAH with X = / -methyl gives [A ] = 7.68 kJ mol-1, but AJA = 4.3 is unusually large. A tunnelling correction of ca. 2 was estimated so that the semi-classical k.i.e. was in the range 2 to 3. 

---