The Concentration Gap

As we shall see in Chapter 4 the anticipated concentration of explosive molecules in many search situation, such as for buried landmines, may be very low, perhaps 1 pg/L (or 100 ppq, or 1 in 1013 molecules). Most sensing systems are not capable of detecting such low concentrations directly. Hence there usually exists a gap between the available sensitivity of existing systems and our perceived needed sensitivity. 

10ag/L 10fg/L 10pg/L 10 ng/L 10 fxg/L 1 part in 1018 io15 io12 109 106 

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The concentric gap is c = r2 — r, and clearly a < c. The gap is very small, and locally we can assume flow between parallel plates. Thus we define a rectangular coordinate system X, YfZ located on the surface of the journal such that X is tangential to the journal, as indicated in Fig. E2.9a. The gap between the journal and bearing is denoted as B ) and is well approximated as a function of angle 6 by the following expression ... 

The phase transitions of liquid crystals in solutions occur normally through two mechanisms, i.e. lyotropic and thermotropic transitions. The lyotropic liquid crystal occurs upon addition of solvent into the crystalline phase, while the thermotropic liquid crystal occurs upon heating the crystalline phase, as illustrated by the two arrows in Fig. 10.3, respectively. The phase diagrams for the transition from the homogeneous solution to the liquid crystal are formed by two almost parallel curves, reflecting the concentration gap between the two coexisting phases. 

One procedure makes use of a box on whose silk screen bottom powdered desiccant has been placed, usually lithium chloride. The box is positioned 1-2 mm above the surface, and the rate of gain in weight is measured for the film-free and the film-covered surface. The rate of water uptake is reported as u = m/fA, or in g/sec cm. This is taken to be proportional to - Cd)/R, where Ch, and Cd are the concentrations of water vapor in equilibrium with water and with the desiccant, respectively, and R is the diffusional resistance across the gap between the surface and the screen. Qualitatively, R can be regarded as actually being the sum of a series of resistances corresponding to the various diffusion gradients present ... 

Therefore, the locus of the values ( ) with a vanishing second derivative of A delimits the region of the miscibility gap in which spinodal decomposition occurs. This locus is referred to as the spinodal (figure C2.1.10 (bl). The length scale of the concentration fluctuations at the beginning of the separation process is controlled by... 

The miscibility gap becomes progressively more lopsided as n increases. This means that c occurs at lower concentrations and that the tie line coordinates—particularly for the more dilute phase-are lower for large n. 

The equihbtium lever relation, np = can be regarded from a chemical kinetics perspective as the result of a balance between the generation and recombination of electrons and holes (21). In extrinsic semiconductors recombination is assisted by chemical defects, such as transition metals, which introduce new energy levels in the energy gap. The recombination rate in extrinsic semiconductors is limited by the lifetime of minority carriers which, according to the equihbtium lever relation, have much lower concentrations than majority carriers. Thus, for a -type semiconductor where electrons are the minority carrier, the recombination rate is /S n/z. An = n — is the increase of the electron concentration over its value in thermal equihbtium, and... 

Ordinarily, the energy gap (Eg) between the filled and empty bands is appreciably greater than kT. The concentration of conduction electrons n in the pure stoichiometric material is equal to the concentration of holes p and is given by... 

FIG. 22-58 Concentration profile of electrolyte across an operating ED cell. Ion passage through the membrane is much faster than in solution, so ions are enriched or depleted at the cell-solution interface, d is the concentration boundary layer. The cell gap, A should he small. The ion concentration in the membrane proper will he much higher than shown. (Couttesij Elsevier.)... 

In Modulation Spectroscopy, which is mosdy used to characterize semiconductor materials, the peak positions, intensities and widths of features in the absorption spectrum are monitored. The positions, particularly the band edge (which defines the band gap)> are the most useful, allowing determination of alloy concentration. 

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