Profile shape

Figure 9.2 Pressure-driven (a) and electrodriven (b) flow profiles. Laminar flow in pressure-driven systems results in a bullet-shaped profile, wliile the profile of electroosmotic flow is plug-shaped, wliich reduces band broadening.

Figure 5. Development of U concentration profiles during a leaching scenario, D/R=10. Here diffusive uptake occurs for 10 ky at a relative groundwater concentration of 10 after which the concentration is dropped to 1. U is lost initially from the outer portions of the bone, leading to distinctive M- and n-shaped profiles. [Used by permission of Elsevier Science, from Pike et al. (2002), Geochim Cosmochim Acta, Vol. 66, Fig. 3f, p. 4276.]...

Figure 4. Scheme of lipophilicity profile of zwitterionic compounds. The line drawn represents the case where the neutral tautomer predominates or the zwitterion is rather hydrophobic, resulting in a bell-shaped profile. The dashed line represents the case where the zwitterion predominates and intramolecular interactions are not possible, resulting in a U-shaped profile. Adapted with permission from [133] Pagliara, A. et al. (1997). Lipophilicity profiles of ampholytes , Chem. Rev., 97, 3385-3400 copyright (1997) American Chemical Society... 

Under certain circumstances it is possible to represent concentration profiles encountered in titrations as linear combinations of the typical S-shaped profiles known from equilibrium studies. 

Cyclic voltammetry at spherical electrodes. As discussed in Chapter 1, Section 4.2.3, diffusion laws at a spherical electrode must take into account the curvature r0 of the electrode. The mathematical treatment of diffusion at a spherical electrode becomes somewhat more complicated6 with respect to the preceding one for planar diffusion and we will not dwell on it. On the basis of what we will see in Chapter 11, Section 2, it is important to consider that, under radial diffusion, the cyclic voltammogram loses its peak-shaped profile to assume a sigmoidal profile, see Figure 6. 

The full curve of Fig. 1.12 is drawn in accordance with (1.207). Considering limits, we find k = when [H + ] > and k = k/ with [H + ] < The full S-shaped profile will be observed in reactions of acid/base pairs where both forms are attainable and show different reactivities. Examples are hydroxy and aqua complexes as typified by the example shown in (1.199), O2 and CN- and HCN, Au(NH3)5+ and Au(NH3)3NHi+,and others. 

Observation of the semblance of an S-shaped profile has been used to estimate the pAT n value for an acid/base pair which may be difficult to obtain directly. This may be as the result of one of the pairs being unstable (polynuclear formation or hydrolysis, for example). 

Because the local pressure distribution depends on the surface shape, and the evolution of the surface shape depends on the local pressure distribution, a discretization in space of the shape profile combined with a time-step approach can be used to predict the progress of the polish process. 

Partial results of the calculation are cited in Table 2, which shows that the work of adhesion is expressed as a bell-shape curve. In other words, the maximal adsorption of protein takes place on polymer surface having intermediate hydrophilicity. Ikada et al. confirmed this by the results of BSA adsorption on 8 polymer surfaces [12], and also by those of albumin and fibronectin adsorption on 13 polymer surfaces [14]. L-Cell attachment also showed a bell-shape profile [15],... 

The bell-shape-profile concept for protein adsorption may be a useful guideline for researchers when they consider the adsorptive behavior of proteins on polymers with different degrees of hydrophilicity. As will be discussed in later Sect. (2.3), when material surfaces carry ionic groups, the contribution from... 

As Peppas pointed out, however, the values of the interaction parameter g23 reveal that protein dislike hydrophobic materials more than they dislike hydrophilic ones. It is anticipated that a similar result to the bell-shape profile may be obtained from the ternary systems where influence of parameter g13 becomes less significant, as will be discussed in connection with the results illustrated in Fig. 3. 

From an analysis of the Cooper results the present author found that the surface concentrations of FGN, FN and VN at 120 min. correlate with the contact angles of the five polymer surfaces, to give a bell-shape profile with a maximum at the PTMO-PU surface. Under the experimental conditions of Fig. 3, the final quantity of adsorption (T) is probably determined by the g23 term, but not by the g13 term (see Sect. 2.1). 

In the plot of the first components (Fig. 5), the difference between the wet granulation and the direct compression profiles is confirmed. The first component discriminates between the shape profiles. The second component discriminates between the initial slopes of the release profiles. Then, it is possible to differentiate between the separate compaction and the other processes, because it has the highest initial slope. This is also observed in Fig. 3. 

In the presence of a large excess of EtO ion, the bimetallic catalyst is fully saturated with EtO as shown by structure I in Scheme 5.3. Incremental additions of a carboxylate substrate would cause the gradual conversion of I into the 1 1 productive complex II, but further additions would yield the unproductive complex III. As expected from this mechanism a bell-shaped profile is observed in a plot of initial rate versus substrate concentration related to the catalyzed ethanolysis of 16 (Figure 5.5). The fairly good quality of the fit supports the validity of Scheme 5.3. Further confirmation comes from the finding that benzoate anions behave as competitive inhibitors of the reaction. Since the reaction product of the ethanolysis of 16 is also a benzoate anion, product inhibition is expected. Indeed, only four to five turnovers are seen in the ethanolysis of 16 before product inhibition shuts down the reaction. The first two turnovers are shown graphically in Figure 5.6. 

U. Buontempo, S Cunsolo, P. Dore, and P. Maselli. Analysis of the translational band measured in Ne-Ar mixtures with a new line-shape profile. Can. J. Phys., 59 1499, 1981. 

Figs. 25 to 28 show that the metal deposition in CoMo/A1203 hydrotreating catalysts is a function of the radial position within the catalyst and the axial location of the catalyst sample within the fixed-bed reactor. Nickel and vanadium both exhibit radial profiles with internal maxima, termed M-shaped profiles, at the reactor entrance. These maxima shift to the pellets edge at the reactor outlet, generating the classic U-shaped profile. 

As the table and Fig. 30 indicate, reaction of Ni-T3MPP in the presence of basic additives (Cs, Na) is characterized by small Thiele moduli and uniform profiles (0m — 1), indicative of kinetic-controlled reactions. Acidic components (S, I, Cl) result in larger Thiele moduli (smaller 6m) and more sharp, U-shaped profiles, signaling strong diffusion-limited reactions. 

Hydrodemetallation reactions are revealed to be diffusion limited by examination of metal deposition profiles in catalysts obtained from commercial hydroprocessing reactors. Intrapellet radial metal profiles measured by scanning electron x-ray microanalysis show that vanadium tends to be deposited in sharp, U-shaped profiles (Inoguchi et al, 1971 Oxenrei-ter etal., 1972 Sato et al., 1971 Todo et al., 1971) whereas nickel has been observed in both U-shaped (Inoguchi et al., 1971 Todo et al., 1971) and... 

It is possible to use cyclic voltammetry in the presence of ferrocene carboxylic acid to confirm the presence of micro-electrodes due to the typical sigmoidal-shaped profile produced [2] (Fig. 24.3). Twenty different sensors comprising micro-electrode arrays formed by this technique were analysed for reproducibility. This analysis can be performed by holding the sensors at a potential of +100 mV for 60s and recording the... 

Fjord A deep glacially carved channel partially submerged by seawater. Fjords typically have U-shaped profiles and are common in Alaska and Scandinavia. 

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