Experimentally Determined Surfaces

General hydrodynamic theory for liquid penetrant testing (PT) has been worked out in [1], Basic principles of the theory were described in details in [2,3], This theory enables, for example, to calculate the minimum crack s width that can be detected by prescribed product family (penetrant, excess penetrant remover and developer), when dry powder is used as the developer. One needs for that such characteristics as surface tension of penetrant a and some characteristics of developer s layer, thickness h, effective radius of pores and porosity TI. One more characteristic is the residual depth of defect s filling with penetrant before the application of a developer. The methods for experimental determination of these characteristics were worked out in [4]. 

Now consider some examples of the influence of sedimentation process upon PT sensitivity. Let us consider the application of fine-dispersed magnesia oxide powder as the developer. Using the methods described in [4] we experimentally determined the next characteristics of the developer s layer IT s 0,5, Re s 0,25 pm. We used dye sensitive penetrant Pion , which has been worked out in the Institute of Applied Physics of National Academy of Sciences of Belarus. Its surface tension ct = 2,5 10 N m V It can be shown that minimum width of an indication of magnesia powder zone, imbibed by Pion , which can be registered, is about W s 50 pm. Assume that n = 1. 

A quite different means for the experimental determination of surface excess quantities is ellipsometry. The technique is discussed in Section IV-3D, and it is sufficient to note here that the method allows the calculation of the thickness of an adsorbed film from the ellipticity produced in light reflected from the film covered surface. If this thickness, t, is known, F may be calculated from the relationship F = t/V, where V is the molecular volume. This last may be estimated either from molecular models or from the bulk liquid density. 

As pointed out in Section XVII-8, agreement of a theoretical isotherm equation with data at one temperature is a necessary but quite insufficient test of the validity of the premises on which it was derived. Quite differently based models may yield equations that are experimentally indistinguishable and even algebraically identical. In the multilayer region, it turns out that in a number of cases the isotherm shape is relatively independent of the nature of the solid and that any equation fitting it can be used to obtain essentially the same relative surface areas for different solids, so that consistency of surface area determination does not provide a sensitive criterion either. 

It can be seen from Table 2 that the intrinsic values of the pK s are close to the model compound value that we use for Cys(8.3), and that interactions with surrounding titratable residues are responsible for the final apparent values of the ionization constants. It can also be seen that the best agreement with the experimental value is obtained for the YPT structure suplemented with the 27 N-terminal amino acids, although both the original YPT structure and the one with the crystal water molecule give values close to the experimentally determined one. Minimization, however, makes the agreement worse, probably because it w s done without the presence of any solvent molecules, which are important for the residues on the surface of the protein. For the YTS structure, which refers to the protein crystallized with an SO4 ion, the results with and without the ion included in the calculations, arc far from the experimental value. This may indicate that con-... 

The size of the droplets formed in an aerosol has been examined for a range of conditions important in ICP/MS and can be predicted from an experimentally determined empirical formula (Figure 19.6). Of the two terms in the formula, the first is most important, except at very low relative flow rates. At low relative velocity of liquid and gas, simple droplet formation is observed, but as the relative velocity increases, the stream of liquid begins to flutter and to break apart into long thinner streamlets, which then break into droplets. At even higher relative velocity, the liquid surface is stripped off, and the thin films so-formed are broken down into... 

The above inequality implies that the surface roughness enhances wetting whenever A/( 1) > 0 and is quite consistent with the experimentally determined Wenzel law [203]... 

Lobo et al. [47] proposed the packing factor, F, and experimentally determined that it better represented the data than the calculated a/e term. Values calculated using surface area per cubic foot and percent free gas space from manufacturer s tables can be as much as 40% off. The ralues are dependent upon the method of packing the tower, i.e., dry dumped, wet dumped, or wet dumped and shaken. The latter condition may approximate the situation after a tower has been running a while and the packing settled. 

Great care must, therefore, be exercised in attaching theoretical significance to experimentally determined values of A and E. The identification of an activation energy with a particular slow surface reaction requires perhaps greater knowledge of the specialized conditions prevailing at the interface than is often available or assumptions that cannot be demonstrated. 

TABLE 6.2. Experimental Determination of the Energies (in kcal/mol) at the Asymptotic Points of the Potential Surface of the General Acid Catalysis Reaction16... 

Emerson, S., Quay, P., Karl, D. et al. (1997). Experimental determination of the organic carbon flux from open-ocean surface waters. Nature 389, 951-954. 

The determination of the laser-generated populations rij t) is infinitely more delicate. Computer simulations can certainly be applied to study population relaxation times of different electronic states. However, such simulations are no longer completely classical. Semiclassical simulations have been invented for that purpose, and the methods such as surface hopping were proposed. Unfortunately, they have not yet been employed in the present context. Laser spectroscopic data are used instead the decay of the excited state populations is written n (t) = exp(—t/r ), where Xj is the experimentally determined population relaxation time. The laws of chemical kinetics may also be used when necessary. Proceeding in this way, the rapidly varying component of AS q, t) can be determined. 

By applying the machinery of statistical thermodynamics we have derived expressions for the adsorption, reaction, and desorption of molecules on and from a surface. The rate constants can in each case be described as a ratio between partition functions of the transition state and the reactants. Below, we summarize the most important results for elementary surface reactions. In principle, all the important constants involved (prefactors and activation energies) can be calculated from the partitions functions. These are, however, not easily obtainable and, where possible, experimentally determined values are used. 

Given a certain metal, what can we do to alter its reactivity First there is the structure of the surface. More open surfaces expose atoms of lower coordination. This narrows the d band, and shifts its position (up if it is more than half filled, down if the d band is less than half filled). To illustrate the point Tab. 6.2 shows experimentally determined activation energies of NO dissociation on the (111) and (100) surfaces of rhodium. 

Experimental determination of the surface composition in nonideal systems, in which the gradients extend over several layers inwards the crystal is as difficult as the exact calculations. Therefore, one has to make again rather unpleasant assumptions. 

Apparatus and Procedure. The apparatus and procedure were identical to those outlined in ref. Surface composition measurements were based on an O2-CO titration technique described by Miura and Gonzalez (5-6). The ratio of surface metal/02/CO was 1/1/T on Ru-sllica, 1/0.5/1.75 on Rh-sllica, 1/0.5/2.0 on Pt-silica and 1/0.5/1.6 on Ir-silica. These titration ratios were found to be independent of surface composition. Surface compositions determined by the O2-CO titration method have been verified using a variety of experimental techniques (2,5-6). 

Accessibility to Cu sites was determined by temperature programmed desorption of NO (NO TPD), using an experimental setup similar to that used for TPR, except the detector was a quadrupole mass spectrometer (Balzers QMS421) calibrated on standard mixtures. The samples were first activated in air at 673 K, cooled to room temperature in air, and saturated with NO (NO/He 1/99, vol/vol). They were then flushed with He until no NO could be detected in the effluent, and TPD was started up to 873 K at a heating rate of 10 K/min with an helium flow of 50 cm min. The amount of NO held on the surface was determined from the peak area of the TPD curves. 

Since experimental determination of intestinal absorption is quite demanding, Caco-2 cell monolayers have been successfully used to model passive drug absorption. Several models for the prediction of Caco-2 permeability using PSA were developed, including those of van de Waterbeemd et al. [5] and Palm et al. [22] who found that relationships between Caco-2 permeability and PSA is stronger than with Clog D, Krarup et al. [23] who used dynamic PSA calculated for water accessible molecular surface and Bergstrom et al. [24]. 

For this last stage, the one-at-a-time procedure may be a very poor choice. At Union Carbide, use of the one-at-a-time method increased the yield in one plant from 80 to 83% in 3 years. When one of the techniques, to be discussed later, was used in just 15 runs the yield was increased to 94%. To see why this might happen, consider a plug flow reactor where the only variables that can be manipulated are temperature and pressure. A possible response surface for this reactor is given in Figure 14-1. The response is the yield, which is also the objective function. It is plotted as a function of the two independent variables, temperature and pressure. The designer does not know the response surface. Often all he knows is the yield at point A. He wants to determine the optimum yield. The only way he usually has to obtain more information is to pick some combinations of temperature and pressure and then have a laboratory or pilot plant experimentally determine the yields at those conditions. 

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