Extrapolation distance linear

Figure 7.4 Change In peak width at half height as a function of nigration distance for a typical test nixture on a high perfomance TLC plate. The values for b, and bf are calculated by extrapolation using linear regression.

Figure 1. No-slip condition and slip condition with slip length, for one-dimensional shear flow. The slip length b is the extrapolation distance into the solid, to obtain the no-slip point. The slope of the linear velocity profile near the wall is the shear rate y.

A possible explanation for the lack of electron-transfer characteristics in the trimer 9d is derived when extrapolating the linear relationship in Fig. 9.8 to the distance of the trimer. As a matter of fact, the charge-separation would not be able to compete with the intrinsic singlet lifetime of C6o (i.e. dashed line). This, in turn, explains the lack of fullerene emission quenching in 9d. Nevertheless, the photophysical assays clearly established that oPPE bridges effectively mediate electron-transfer processes over distances up to 20 A. These findings were further corroborated by quantum mechanical calculations. 

Fig. 3.7. Definition of linear extrapolation distance d. This is obtained by a linear extrapolation of the neutron flux into the region outside the reactor, using the flux gradient at the boundary.

Fig. 2. Distance classes j = 0,1, 2,... (left) are defined for an atom (central dot) by a set of radii Rj+i the right cnrves sketch the temporal evolntion of the tot il force acting on the selected atom originating from cill atoms in distance class j shown are the exact forces (solid line), their exact valnes to be computed within the multiple time step scheme (filled squares), linear force extrapolations (dotted lines), and resulting force estimates (open sqnares).

The wavenumbers of the MMCT transition between Pt(II) and Pt(IV) are related to the Pt(II)-Pt(IV) distance in the chain, as follows from a study of these compounds using different types of ligands. This relation is hnear [97]. ff the linear curve is extrapolated to a MMCT transition energy of zero, we obtain a distance equal to twice the Pt(IV)-ligand distance. This is the situation in which the Ugand, for example Cl or Br , is placed in between the two platinum ions, i.e. in which the difference between the platinum ions vanishes. 

Next we estimate the contribution from correlations of valence electrons with outercore ones (which also account for correlations between outercore electrons) as the difference between the results of the corresponding 10- and 30-electron GRECP/RCC calculations (see also [136] where this correction is applied to the Pb atom). We designate such correlations in Table 5 as outercore correlations . When taking into account outercore contributions at the point R = 4.0 a.u. we used the results of the RCC calculation at the point R = 3.8 a.u. Since these contributions are relatively small and because the correlations with the outercore electrons are more stable than correlations in the valence region when the internuclear distance is changed, this approximation seems reasonable. Finally, we have linearly extrapolated the results of the calculations to the experimental equilibrium distances. Re = 4.06 a.u. for a(l) [137] and Re = 3.91 a.u. for B 1) [119]. The final results are Ay = —3826 MHz, W = —6.1-10 Hz/(e cm) for a(l) and A = 4887 MHz, W = —8.0-10 Hz/(e cm) for H(l). The estimated error for the final W value is 20% for the B 1) state. For a(l) the estimated error... 

Now, in general, this concentration profile is such that there is a linear variation of concentration over small distances from the interface and then the concentration asymptotically approaches the bulk value. In this context, Nernst put forward a simplifying suggestion. One might extrapolate (Fig. 7.95) the linear part of the concentration vs. distance curve until it intersects the bulk value of the concentration at some distance 8 from the interface. Then the gradient of the concentration at x = 0, i.e., (dc/cbc), can be replaced by (c° - c /8 to give [from 7201]... 

A linear dependence with pore diameter is observed. The intermolecular distance, directly dependent on the curvature of the pores, i.e. the average pore diameter, is linearly related to the activation energy for dehydroxylation. Extrapolation to smaller pores suggests activation energies of approximately 100 kJ mol 1 for dehydroxylation of hydroxyl groups in e.g. zeolite channels, if the hydroxyls are of a comparable type. Rees published corresponding activation energies for water desorption in dealuminated Y-zeolites.34... 

Consider the process of plating copper on a plane electrode. Near the electrode, copper ions are being discharged on the surface and their concentration decreases near the surface. At some point away from the electrode, the copper ion concentration reaches its bulk level, and we obtain a picture of the copper ion concentration distribution, shown in Fig. 6. The actual concentration profile resembles the curved line, but to simplify computations, we assume that the concentration profile is linear, as indicated by the dashed line. The distance from the electrode where the extrapolated initial slope meets the bulk concentration line is called the Nernst diffusion-layer thickness S. For order of magnitude estimates, S is approximately 0.05 cm in unstirred aqueous solution and 0.01 cm in lightly stirred solution. 

Calculation Calculate the linear equation of the graph using a least-squares fit, and derive from it the concentration of nickel in the Test Preparation. Alternatively, plot on a graph the mean of the readings against the added quantity of nickel. Extrapolate the line joining the points on the graph until it meets the concentration axis. The distance between this point and the intersection of the axes represents the concentration of nickel in the Test Preparation. 

---