Asymmetric Barriers

Brinkman WF, Dynes RC, Rowell JM (1970) Tunneling conductance of asymmetrical barriers. J Appl Phys 41 1915-1921... 

X = Cl, Br), represent the rather few cases of intermediate size asymmetric barriers where the torsional potential has been determined from electron-diffraction data. In these investigations the mixture of two conformers has been determined at different temperatures. The gauche conformer is described as a rigid, staggered model. 

The tunnelling correction T is the transmission probability through the potential barrier averaged over all possible crossing points and potential energies69. An asymmetrical barrier of the Eckart type70 is assumed in the present model. 

The driving force for the processes being the generation of asymmetric barriers between the liquid-Ti02 and metal-Ti02 interfaces, as shown in Fig.4, which allows charge carriers to splitt and then to react with OH and H+ species. 

Also here, AR enhances the pumped current in case of symmetric tunnel barriers, while a reduction occurs for asymmetric barriers. Maximum enhancement of 7ns, peak/ N, peak 2.55 is reached for T jT2 1.292. This factor is less than 4, because the average over energy e from which the peak heights (13) are obtained also involves contributions of 7ns [Eq. (8)] further away from resonance, for which 7ns/7n is much less than 4 [consider, e.g., Eq. (11) for e — res = hv /Tf + /2], This results in lower maximal enhancement of... 

UF membranes are usually characterized as asymmetric barriers where the support layer gives an insignificant contribution to flow resistance, and where the skin layer gives the membrane its... 

The equation, analogous to equation 2.58, for the characteristic ratio for asymmetric barriers is modified to the form... 

For a strongly asymmetric barrier (e.g., of a triangular shape), one can analogously express the adsorption constants in the form... 

This problem has been solved for short linear alkane chains by Pitzer, who considered that the asymmetric barrier to rotation of the central bond in a structure such as n-butane in the trans form comprises a three-fold symmetric ethane type barrier together with a steric contribution from the two high energy gauche conformers. For a linear hydrocarbon containing N carbon atoms the number of hindered internal rotations will then be (A -3) and Cy can be expressed as two terms... 

Although unsynunetrically substituted amines are chiral, the configuration is not stable because of rapid inversion at nitrogen. The activation energy for pyramidal inversion at phosphorus is much higher than at nitrogen, and many optically active phosphines have been prepared. The barrier to inversion is usually in the range of 30-3S kcal/mol so that enantiomerically pure phosphines are stable at room temperature but racemize by inversion at elevated tempeiatuies. Asymmetrically substituted tetracoordinate phosphorus compounds such as phosphonium salts and phosphine oxides are also chiral. Scheme 2.1 includes some examples of chiral phosphorus compounds. 

The property of chirality is determined by overall molecular topology, and there are many molecules that are chiral even though they do not possess an asymmetrically substituted atom. The examples in Scheme 2.2 include allenes (entries 1 and 2) and spiranes (entries 7 and 8). Entries 3 and 4 are examples of separable chiral atropisomers in which the barrier to rotation results from steric restriction of rotation of the bond between the aiyl rings. The chirality of -cyclooctene and Z, -cyclooctadiene is also dependent on restricted rotation. Manipulation of a molecular model will illustrate that each of these molecules can be converted into its enantiomer by a rotational process by which the ring is turned inside-out. ... 

The thylakoid membrane is asymmetrically organized, or sided, like the mitochondrial membrane. It also shares the property of being a barrier to the passive diffusion of H ions. Photosynthetic electron transport thus establishes an electrochemical gradient, or proton-motive force, across the thylakoid membrane with the interior, or lumen, side accumulating H ions relative to the stroma of the chloroplast. Like oxidative phosphorylation, the mechanism of photophosphorylation is chemiosmotic. 

Schematic energy level diagrams of a metal/polymer/metal structure before and after the layers are in contact are shown in the top two drawings of Figure 11-6. Before contact, the metals and the polymer have relative energies determined by the metal work functions and the electron affinity and ionization potential of the polymer. After contact there is a built-in electric field in the structure due to the different Schottky energy barriers of the asymmetric metal contacts. Capacitance-voltage measurements demonstrate that the metal/polymer/metal structures are fully depleted and therefore the electric field is constant throughout the bulk of the structure [31, 35]. The built-in potential, Vhh i.e. the product of the constant built-in electric field and the layer thickness may be written...

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