Theoretical dependencies

Fig. 4 illustrates the time-dependence of the length of top s water column in conical capillary of the dimensions R = 15 pm and lo =310 pm at temperature T = 22°C. Experimental data for the top s column are approximated by the formula (11). The value of A is selected under the requirement to ensure optimum correlation between experimental and theoretical data. It gives Ae =3,810 J. One can see that there is satisfactory correlation between experimental and theoretical dependencies. Moreover, the value Ae has the same order of magnitude as Hamaker constant Ah. But just Ah describes one of the main components of disjoining pressure IT [13]. It confirms the rightness of our physical arguments, described above, to explain the mechanism of two-side liquid penetration into dead-end capillaries. 

We start with the reaction of abstraction of a hydrogen atom by a CH3 radical from molecules of different matrices (see, e.g., Le Roy et al. [1980], Pacey [1979]). These systems were the first to display the need to go beyond the one-dimensional consideration. The experimental data are presented in table 2 together with the barrier heights and widths calculated so as to fit the theoretical dependence (2.1) with a symmetric gaussian barrier. 

Fig. 5.15. Theoretical dependences of HWHM on the rate of rotational energy relaxation perturbation theory asymptotics (1), classical weak-collision. /-diffusion model (2), quantum theory without (3) and with (4) adiabatic correction.

Figure 2.30. Initial sticking coefficient. S0, of the p2-CO state on Ni(100) as a function of the additive coverage. The dashed line represents the theoretical dependence according to the relationship = Sq (1 -0x)-fl 86 Reprinted with permission from Elsevier Science.

The results show a tendency for b to decrease with an increase in pressure, and the higher the critical pressure of a given liquid metal, the less this tendency will be. Thus, in the case of mercury, some correlations show no decrease or a very slight decrease in b over the pressure range compared. However, this theoretical dependence is about three times greater than that observed experimentally with liquid metals, which suggests strongly that these theoretical correlations for CHF require revisions to achieve applicability to liquid metals. 

The results of stress-strain measurements can be summarized as follows (1) the reduced stress S (A- A ) (Ais the extension ratio) is practically independent of strain so that the Mooney-Rivlin constant C2 is practically zero for dry as well as swollen samples (C2/C1=0 0.05) (2) the values of G are practically the same whether obtained on dry or swollen samples (3) assuming that Gee=0, the data are compatible with the chemical contribution and A 1 (4) the difference between the phantom network dependence with the value of A given by Eq.(4) and the experimental moduli fits well the theoretical dependence of G e in Eq.(2) or (3). The proportionality constant in G for series of networks with s equal to 0, 0.2, 0.33, and 0. Ewas practically the same -(8.2, 6.3, 8.8, and 8.5)x10-4 mol/cm with the average value 7.95x10 mol/cm. Results (1) and (2) suggest that phantom network behavior has been reached, but the result(3) is contrary to that. Either the constraints do survive also in the swollen and stressed states, or we have to consider an extra contribution due to the incrossability of "phantom" chains. The latter explanation is somewhat supported by the constancy of in Eq.(2) for a series of samples of different composition. 

Figure 1. Theoretical dependence of sol fraction w vs. molar ratio rA is 2[NH,]/ [epox] for epoxyamine networks containing varying fraction of epoxy groups in monoepoxide s. Final conversion of epoxy groups in mol percent indicated.

The question of the identity of the reactive excited state was left open, although n-n excited state was considered to be more probable.140 The interaction diagram, Fig. 7, shows that a n-n state would have an additional stabilizing interaction Ri(tt) ->-R2(7r) with orbital coefficients in phase for an all-suprafacial concerted reaction. The dominant reaction would theoretically depend upon the relative placements of the several levels, and since no experimental information for maleic and fumarate esters is presently available, a clear choice cannot be made. It is interesting that the reactive excited state could be inferred if both stereochemistry and a good molecular diagram were available. 

Figure 1. Theoretical dependence of / 0 as calculated from equations (4) and (8) solid lines ideal monolayers dashed lines non-ideal. Parameter is q.

Figure 7. Comparison between the experimental phase separation conditions (points) for silicas S6 and SB1 (6) with our theoretical model (full curves). The dashed curve gives the theoretical dependency if in Equation 14 A is replaced by rg.

This equation was calculated numerically for the different values of coefficients D, a, y/v, and d. The theoretical dependence was found to coincide with Equation (13.17) for the coefficient k 8D/3/2 at v/viDO > 0.5. The numerical calculation gave the following equation for the mixed (kinetic and diffusion) regime of oxidation [87] ... 

Theoretical dependence of filter efficiency of a single collector (proportional to the rate at which particle contacts occur between particles and the filter grain by mass transport) on particle diameter. For particles of small diameters transport by diffusion increases with decreasing size. Contact opportunities of the larger particles with the filter grain are due to interception and sedimentation they increase with increasing size. 

Fig. 2.4 Theoretical dependence of the net peak current of reversible reaction (1.1) on the square-root of SW frequency under the influence of uncompensated resistance in the cell. The dotted line is the expected linear relationship in the absence of resistance. A = 0.0147 cm, n=l,D = 5 X 10- cmVs, cj, = 1 X10-3 = U4 k 2, = 20 mV and AS = -5 mV...

Because of the series capacitor and/or the dielectric coating of the electrodes, the negative potentials established on the two electrodes in a plasma system may not be the same. For instance, the ratio of the voltages on the electrodes has been shown to be dependent upon the relative electrode areas (77). The (theoretical) dependence is given by Equation 1, where V is the voltage and A is the area (7d). 

Fig. 14. Theoretical dependence of relaxivity on calculated on the basis of the classical inner-/outer-sphere model (20 MHz, o = 1, = 5 x 10 s, Ty = 20 ps,...

Figure 10. Dependence of the reduced equilibrium modulus of POP triol - MDI networks prepared in the presence of diluent. POP triol Mu= 708 stress-strain measurements in the presence of diluent (o) and after evaporation of the diluent ( ). Flory theory for the values of the front factor A indicated, theoretical dependence including trapped interchain constraints Numbers at curves Indicate the value of ry.

To get better insight into the importance of temperature selection, we have recorded a series of NOESY spectra of cyclo(Pro-Gly) at different temperatures. The dashed lines in fig. 6 show theoretical dependence of the laboratory frame cross-relaxation rate on the correlation time (according to... 

FIGURE 1.12 Theoretical dependence of the bubbling frequency fwith the temperature Q, as expected from the model displayed in Eq. (20), in the range of usual champagnetasting temperatures (from 5 to 15 °C), and for the textbook case fiber displayed in Fig. 1.7. 

Figure 6. Theoretical dependence of Yheg on k2/ki in comparison with values observed for the reaction of DEA over unpromoted and chromia-promoted copper catalysts...

As discussed in detail by Pandis et al. (1995), nucleation theory shows there is a critical sulfuric acid concentration above which binary nucleation of sulfuric acid and water should occur. Based on the work of Jaecker-Voirol and Mirabel (1989), they parameterize the theoretical dependence of this critical concentration needed to generate nuclei at a rate of 1 cm 3 s 1 on the relative humidity (RH, expressed in this case as a fraction, i.e., between 0 and 1) and temperature, T (in K) ... 

The Sagnac effect caused by the rotating platform is therefore due to a rotation in the internal gauge space ((1),(2),(3)), which results in the frequency shift in Eq. (171). The frequency shift is experimentally the same to an observer on and off the platform and is independent of the shape of the area Ar. The holonomy difference (172) derived theoretically depends only on the magnitudes and ff, and these scalars are frame-invariant, as observed experimentally. There is no shape specified for the area Ar in the theory, and only its scalar magnitude enters into Eq. (172), again in agreement with experiment. 

Fig. 2.3.3. Theoretical dependence of the effective linear charge density <7eff on the structural linear charge density a.

Figure 4. Theoretical dependence of rate of IVR as a function of vibrational energy of model molecule CFCl2Br with given anharmonicity constant (from Ref. 1).

Figure 34 Theoretical dependence of /ieff (BM) per Ni atom upon reduced temperature kT/ J for a dinuctear complex (a) without zero field splitting (b) including zero field splitting with z J = 0 (after ref. 2917)...

Fig. 63. Dependence of (S2)1 on M for fibrin initiated by thrombin at 37 °C (- -) curve 1 gives the theoretical dependence for a single strand, curve 3 shows the behavior of fibres with many strands parallel, and curve 2 is the best fit224 ...

In their experiments Holroyd et al.183 have studied the dependence of the photocurrent on the strength of the electric field between the cathode and the anode. The corresponding theoretical dependence was calculated using the function F(x) = 2lx0 Tit) exp k2Ix ) obtained by variation of... 

A key element in the analysis is the correspondence between the observed and the theoretical dependence of the current on the potential. In other words, one compares the theoretical Tafel slope for the postulated mechanisms, or the transfer coefficients which are derived from these, to the experimentally obtained values. 

The method this chapter presents is limited to organic compounds. While it is empirical, it makes use of the theoretical dependence of the enthalpy and entropy of melting upon... 

Figure 8,7 Theoretical dependence of stability ratio on electrolyte concentration calculated from equation (8.2) for a = 1CT8 m, A = 2 x 10 19 J and fa = 76.8 mV = 3kT/e> At high electrolyte concentrations W < 1 owing to coagulation being accelerated by van der Waals attractive forces (reduced flow rate in the narrow inter-particle gap has not been allowed for) (By courtesy of Elsevier Publishing Company)...

Figure 10.11 shows the theoretical dependence of the domain radius on the applied voltage, which was compared to an experimental data obtained in lithium niobate. This calculation was performed in the range of voltages between 0 and 1.4 kV, using Ps = 75/xC/cm2, ec = 30, ea = 84. The surface energy density aw was obtained by a fitting procedure where it was a free parameter as expected, the obtained value aw = 4 mJ/m2 was relatively small. 

Figure 10.11 Theoretical dependence of the domain radius on the applied voltage obtained by taking of the surface energy density as a free parameter and adjustment to the experimental results.

In an attempt to further simplify the caffeine phenotyping test, a trait measure based on the plasma or salivary paraxanthine caffeine concentration ratio between three hours and seven hours after administration of the probe has been suggested (56). High linear correlations (>0.89) have been observed between this trait value and caffeine s oral clearance, and if necessary, a predicted caffeine clearance value may be calculated from the ratio (56). Currently, this phenotyping approach appears to be the simplest and most noninvasive means of readily assessing CYP1A2 activity using caffeine as a probe in addition, the method is reproducible and appears to be robust (56), despite the theoretical dependency of the trait value on the urine flow rate (51). 

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