Z-dependence

The potential energy 0(z) depends not only on the distance z hut also on the position of the gas molecule in the xy plane parallel to the surface of the solid and distant z from it. For any given position, the adsorption energy will be equal to the value of 0 = 0o minimum of the potential curve (cf. Fig. 1.2), which of course represents the equilibrium position. 

One consequence of the Z dependence is that the higher energy density per volume may be used to advantage by emulsification of the dispersed phase into a reduced amount of the continuous phase, followed by dilution. A reduced amount of the continuous phase means an increased value of Z, because the energy input is dissipated into a smaller volume. An exception to this rule is found if the continuous phase contains soHd particles. In such a case forces acting through the Hquid medium are not efficient for obvious reasons, and mechanical means such as a roUer mill should be used. 

The ratio to z depends only on (gag-, zjx, = 2/3 tga.g, and the ratio of x, /Xq has a constant value equal to 0.578. To clarify the trajectory equation of inclined jets for the cases of air supply through different types of nozzles and grills, a series of experiments were conducted. The trajectory coordinates were defined as the points where the mean values of the temperatures and velocities reached their maximum in the vertical cross-sections of the jet. It is important to mention that, in such experiments, one meets with a number of problems, such as deformation of temperature and velocity profiles and fluctuation of the air jet trajectory, which reduce the accuracy in the results. The mean value of the coefficient E obtained from experimental data (Fig. 7.25) is 0.47 0.06. Thus the trajectory of the nonisothermal jet supplied through different types of outlets can be calculated from... 

Eq z) is a laterally averaged contribution, which has only a z dependence (z is the distance from the surface). E z)fl x,y) depends on the position parallel to the surface. 

The z dependence has disappeared The reactor is well mixed and behaves like a CSTR with respect to component A. Noting that Qout = qL gives... 

The sphere-plane capacitor model gives a useful approximate expression for the function f(Rlz). Equation [13] shows that in the region 0 < z/R < I, which is typical in SPFM imaging, / can be approximated by a 1/z dependence. The planar lever adds a nearly constant term. Thus for the range 0 < z < f , we have the following approximate function... 

A Z depends on the identity of the material. For instance, 50 J of heat increases the temperature of 1 mol of gold more than it increases the temperature of 1 mol of water. The dependence of AT on the identity of the material is expressed by the molar heat capacity (C, units J moP ° C ). The molar heat capacity is the amount of heat needed to raise the temperature of 1 mol of substance by 1 °C. Eveiy substance has a different value for C. The molar heat capacities of several chemical substances are listed in Table 6-1. 

The weights Xf(z) are cut-off z-dependent, and are determined as solutions of a linear system ( ) In fact, the indicator estimators used for the case-study underlying Figures 3 were obtained by a- slightly more elaborate technique called probability kriging or PK (9, 10) ... 

Now we express this curvature in terms of the gravitational field and potential. Since the coordinate z depends on v, differentiation of U with respect to v gives at the point p... 

By using a simple model in which an electron in the surface atom of a polyanion is transferred to a solvent molecule, the effect of z on Alf through is considered as follows if the ionic radius r is much larger than the CT distance d and the radius of the surface atom yq, the z-dependence of can be expressed in terms of the surface field strength E of the polyanion as... 

From the above analysis, it is found that both and IFqi are linear functions of the surface electric field strength E, so that A W obtained from Eq. (9) is also a function of E. The important point is that the z-dependence of the matrix element can be expressed only through E. By actually solving the secular equation (9), it has been found that the E-dependence of A IF is well represented by a quadratic equation ... 

Since Jo and C are proportional to the diffusion coefficient (D) and activation free energy for formation of a critical nucleus (AG ), respectively, it is concluded that the Z dependence of J is mainly determined by the diffusion process of the polymer chain and not by the formation process of a critical nucleus. 

The structures shown in Fig. 4-1 are for B-form DNA, the usual form of the molecule in solution. Different double-helical DNA structures can be formed by rotating various bonds that connect the structure. These are termed different conformations. The A and B conformations are both right-handed helices that differ in pitch (how much the helix rises per turn) and other molecular properties. Z-DNA is a left-handed helical form of DNA in which the phosphate backbones of the two antiparallel DNA strands are still arranged in a helix but with a more irregular appearance. The conformation of DNA (A, B, or Z) depends on the temperature and salt concentration as well as the base composition of the DNA. Z-DNA appears to be favored in certain regions of DNA in which the sequence is rich in G and C base pairs. 

Performance Parameters. Typical resolving power for the commercial instrument is up to about 130,000 (FWHM) for m/z 400 Th. The mass resolving power is m/z dependent it decreases with fmfz (see the FTICR, described in Section 2.2.6, which decreases linearly with m/z). 

Image current detection is (currently) the only nondestructive detection method in MS. The two mass analyzers that employ image current detection are the FTICR and the orbi-trap. In the FTICR ions are trapped in a magnetic field and move in a circular motion with a frequency that depends on their m/z. Correspondingly, in the orbitrap ions move in harmonic oscillations in the z-direction with a frequency that is m/z dependent but independent of the energy and spatial spread of the ions. For detection ions are made... 

In the squeezed position, the B radiation is trapped in the gap between the two surfaces and the electrons are backscattered from both of them (J 9). The larger contribution comes from the scattering from the high density material of the metal electrode (due to the Z-dependence of the backscattering power). The f correction which accounts for the backscattering is included in Equation 1. 

An implementation of the resulting operation spec is guaranteed to meet the expectation of anyone who expected either T1 or T2. An invocation of m is valid whenever A is hue (because that would make (A or B or C) true) and is guaranteed to result in X (and perhaps also Y, Z depending on whether B or C was also true). 

Scattering from Thin Amorphous Specimens. The Z contrast technique exploits tRe strong Z dependence of Rutherford scattering into the annular detector. Rutherford scattering is... 

The sensitivity of Z contrast for the detection of small clusters depends not only on the signal Z dependence, but also depends on the microscope resolution, which is governed by the probe size 6. A small cluster containing N atoms of atomic number Zi, supported on a film of effective atomic number Z2 of thickness t, will have a contrast in the annular detector signal given by... 

Figure 5 Diagram showing how the effective Z-dependence of the annular detector changes with inner collection angle 01, as a function of Z.

The collected fluorescence 3F [from Eq. (7.39)] clearly depends on the orientation distribution of the dipoles and the incident polarization through the dependences on 0 and E. We will assume a special but common case here randomly oriented dipoles with a z-dependent concentration near the surface, excited by a p-polarized evanescent wave. 

The presence of the h(z, P) factor makes Eq. (7.44) different from a Laplace transform of C(z). If the z dependence of h(z, P) is ignored,(34 36) then calculated concentrations of fluorophore near an interface derived from collected fluorescence are approximations. Also, the P dependence in the tf1,11 causes the integral in Eq. (7.44) to differ from the form of a Laplace transform even after the excitation term is factored out. 

If the excitation electric field is an s-polanzed evanescent field instead of the above p-polarized example, then wH 11 [ = wHJI(z)] does not depend upon p. Therefore, an approximate C(z) can be calculated from the observed fluorescence (P) (obtained experimentally by varying 0) by ignoring the z dependence in the bracketed term in Eq. (7.45) and by inverse Laplace transforming Eq. (7.44) after the ,(0, /J) 2 term has been factored out.,37 39)... 

Even a molecularly smooth single-crystal face represents a potential energy surface that depends on the lateral position x, y) of the water molecule in addition to the dependence on the normal distance z. One simple way to introduce this surface corrugation is by adding the lattice periodicity. An example of this approach is given by Berkowitz and co-workers for the interaction between water and the 100 and 111 faces of the Pt crystal. In this case, the full (x, y, z) dependent potential was determined by a fit to the full atomistic model of Heinzinger and co-workers (see later discussion). 

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