Surface relaxivity

The amount of material deposited and the effective temperature of the substrate during deposition were systematically varied, while deposition rale was held constant. A set of about 50 samples has been generated. Tfl films are stable over time, due to the large energy barriers for surface relaxation and reoiganization, and the topographical features remain unaltered over a time span of several months. 

Actually, the scheme has only a quahtative character, because it does not take into consideration that the aocro angle can vary in a wide interval, as discussed above. Furthermore, we have to consider that the adsorption of molecules is always associated with a surface relaxation phenomenon. The relaxation may occur starting from an increment of the Cr-L distance to a complete displacement of the ligand L, as we will discuss. 

FIGURE 27.8 Specular reflectivity for a clean Au(lOO) surface in vacuum at 310 K ( ). The solid line is calculated for an ideally terminated lattice. The dashed line is a fit to the data with a reconstmcted surface with a 25% increase in the surface density combined with a surface relaxation that increases the space between the top and next layers by 19%. In addition, the data indicate that the top layer is buckled or cormgated with a buckling amplitude of 20%. (From Gibbs et al., 1988, with permission from the American Physical Society.)... 

Surface reconstmction and relaxation can be understood as a deviation from the bulk-truncated stmcture on the atomic level, by which the surface minimizes its free energy [Kolb, 1996]. In particular, surface reconstruction usually involves a change in the periodicity of the surface and in some cases a change in symmetry as well, whereas surface relaxation is a (small) rearrangement of surface layers. 

Lucas CA, Markovic NM, Ross NM. 1999. The adsorption and oxidation of carbon monoxide at the Pt(lll)/electiol3de interface atontic structure and surface relaxation. Surf Sci 425 L381-L386. 

The T) and T2 dependence is described by Eqs. (3.4.3) and (3.4.4) [34] where Qi and q2 are spin-lattice and spin-spin surface relaxivity constants, and S/ Vis the surface-to-volume ratio of the pore. These equations provide the basis of a methodology for crack detection in cement paste specimens [13]. 

NMR relaxation of liquids such as water in porous solids has been studied extensively. In the fast exchange regime, the spin-lattice relaxation rate of water in pores is known to increase due to interactions with the solid matrix (so-called surface relaxation ). In this case, T) can be described by Eq. (3.5.6) ... 

The first possibility is that the attractive potential associated with the solid surface leads to an increased gaseous molecular number density and molecular velocity. The resulting increase in both gas-gas and gas-wall collision frequencies increases the T1. The second possibility is that although the measurements were obtained at a temperature significantly above the critical temperature of the bulk CF4 gas, it is possible that gas molecules are adsorbed onto the surface of the silica. The surface relaxation is expected to be very slow compared with spin-rotation interactions in the gas phase. We can therefore account for the effect of adsorption by assuming that relaxation effectively stops while the gas molecules adhere to the wall, which will then act to increase the relaxation time by the fraction of molecules on the surface. Both models are in accord with a measurable increase in density above that of the bulk gas. 

Whereas in CF4 we can ignore the surface relaxation term, this term is significant for c-C4F8 at 291 K, with the relative weighting becoming increasingly important as we add additional molecular layers, as shown below. This is equivalent to Eq. (3.5.6), with the bulk fluid term set to the spin-rotation relaxation of the bulk gas. It is clear that in such a system, in comparison with CF4 at 294 K, the effect of liquid phase surface relaxation cannot be ignored. 

Surface Relaxation and Pore Size Distribution 3.6.6.1 Fast Diffusion Limit... 

The key to obtaining pore size information from the NMR response is to have the response dominated by the surface relaxation rate [19-26]. Two steps are involved in surface relaxation. The first is the relaxation of the spin while in the proximity of the pore wall and the other is the diffusional exchange of molecules between the pore wall and the interior of the pore. These two processes are in series and when the latter dominates, the kinetics of the relaxation process is analogous to that of a stirred-tank reactor with first-order surface and bulk reactions. This condition is called the fast-diffusion limit [19] and the kinetics of relaxation are described by Eq. (3.6.3) ... 

Temperature and measured surface relaxivity have shown only a weak dependence [21, 27] in some cases, whereas the opposite temperature dependence between silicate and carbonate surfaces has been shown in others [28]. 

Natural rocks seldom have a single pore size but rather a distribution of pore sizes. If all pores are in the fast-diffusion limit, have the same surface relaxivity and have no diffirsional coupling, then the pores will relax in parallel with a distribution of relaxation times that corresponds to the distribution of the pore sizes. The magnetization will decay as a sum of the exponentials as described by Eq. (3.6.4). 

The relaxation time for each pore will still be expressed by Eq. (3.6.3) where each pore has a different surface/volume ratio. Calibration to estimate the surface relaxivity is more challenging because now a measurement is needed for a rock sample with a distribution of pore sizes or a distribution of surface/volume ratios. The mercury-air or water-air capillary pressure curve is usually used as an estimator of the cumulative pore size distribution. Assuming that all pores have the same surface relaxivity and ratio of pore body/pore throat radius, the surface relaxivity is estimated by overlaying the normalized cumulative relaxation time distribution on the capillary pressure curve [18, 25], An example of this process is illustrated in Figure 3.6.5. The relationship between the capillary pressure curve and the relaxation time distribution with the pore radii, assuming cylindrical pores is expressed by Eq. (3.6.5). 

R. L. Kleinberg 1996, (Utility of NMR T2 distributions, connections with capillary pressure, day effect, and determination of the surface relaxivity parameter n >). Magn. Reson. Imaging 14 (7/8), 761—767. 

M. D. Hurlimann, K. G. Helmer, L. L. Lator, C. H. Sotak 1994, (Restricted diffusion in sedimentary rocks. Determination of surface-area-to-volume ratio and surface relaxivity),/. Magn. Reson., Ser. A 111, 169-178. 

S. Godefroy, M. Fleury, F. Deflandre, J.-P. Korb 2002, (Temperature effect on NMR surface relaxation in rocks for well logging applications),/. Phys. Chem. B 106, 11183-11190. 

Poisoning is caused by chemisorption of compounds in the process stream these compounds block or modify active sites on the catalyst. The poison may cause changes in the surface morphology of the catalyst, either by surface reconstruction or surface relaxation, or may modify the bond between the metal catalyst and the support. The toxicity of a poison (P) depends upon the enthalpy of adsorption for the poison, and the free energy for the adsorption process, which controls the equilibrium constant for chemisorption of the poison (KP). The fraction of sites blocked by a reversibly adsorbed poison (0P) can be calculated using a Langmuir isotherm (equation 8.4-23a) ... 

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