Comparison with the Experiment

Intermolecular interactions in the gas phase have been measured in a series of cases using mass spectrometry 134-147). From the temperature dependence of the equilibrium constants, besides the free energies, the enthalpies and the entropies of the involved reactions were evaluated. The corresponding data are useful for comparison with the results of theoretical calculations (see Table 3). In order to compare the calculated interaction energies with the measured reaction enthalpies, a series of contributions has to be taken into account. Concerning these correction terms some inconsistencies arise in the literature. Therefore the list of them is given here in detail according to Ref. 148)  

A(AEe)298 is the change in the calculated electronic interaction energy between 298 K and 0 K. This term is negligible unless electronically excited states are important. AE is the difference between the zero-point vibrational energies of reactants and product. 

AEf8 is the translational energy change due to the change in the number of degrees of translational freedom. 

The calculation of the vibrational terms is straightforward but rather time consuming (see e.g.149)). 

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Sauer, J., Ugliengo, P., Garrone, E., Saunders, V. R., 1994, Theoretical Study of Van der Waals Complexes at Surface Sites in Comparison With the Experiment , Chem. Rev., 94, 2095. 

Multiple calculations and comparisons with the experiment allowed arranging the unified averaged figure-nomogram of degree of structural interaction and solubility (p) dependence upon coefficient a [2],... 

In order to indicate the theoretical ideas involved in LEED crystallography, we now outline the main dynamical (i.e., multiple-scattering) methods used to compute 1-V curves for comparison with the experiment (cf., also References 2a and 2f). 

Table 14.1 shows both H2 and 02 evolutions from several kinds of aqueous suspension of Pt/Ti02. An aqueous suspension includes a prescribed amount of inorganic salt as an additive. In the case of no additives, a small amount of H2 evolved however, 02 evolution was not observed. Upon the addition of a sodium salt, i.e., NaOH, NaCl, Na2S04, Na3P04, NaHP04, respectively, the H2 evolution rate slightly increased in comparison with the experiment conducted without an additive, however, it decreased to zero with reaction time. There was no 02 evolution in the gas phase over long periods. On the other hand, upon addition of... 

Note that there is a parametrically small nonanomalous correction to Eq. 1 due to returns after multiple scatterings, Sp xx/p — 0.2/ o/ 2 [15]. To compare the results of simulations [15] with the theoretical results in a wider region of parameters [3, / o, we substract Spxx/p from the numerical curves. Theoretical and numerical [15] results are plotted in Fig. 5. in the universal units, Spxx/p/3o versus z = /3// o- It is seen, that the theoretical and numerical results are in a very good agreement. The comparison with the experiment [16] is more difficult, because of the 50% uncertainty in the sizes of the antidots. However, a good agreement with the experiment can be achieved by appropriate choice of a in the uncertainty interval [15]. 

Figure 25 Calculated (full circles) lowest allowed excitonic gaps for the different Si-NWs and their comparison with the experiments. Down triangles correspond to the data of Zhang and Bayliss [162], whereas up triangles correspond to the data of Wolkin et al. [18].

Fig. 13.33 Fractional coverage predicted by simulations (solid circles) in comparison with the experiments of Taylor (62) (open diamond) and Hyzyak and Koelling (67). [Reprinted by permission from V. Gauri and K. W. Koelling, Gas-assisted Displacement of Viscoelastic Fluids Flow Dynamics at the Bubble Front, J. Non-Newt. Fluid Meek, 83, 183-203 (1999).]...

Figure 4.6. Linear susceptibility, real part. Comparison with the experiment [64] for the frequencies 30 Hz (a), 80 Hz (b), 220 Hz (c), 840 Hz (d). Volume averaging is performed with the magnetic and statistical parameters according to Table I. Entry 1 indicated by thick solid lines, entry 2 indicated by thick dashed lines, entry 3 indicated by thin solid lines, entry 4 indicated by thin dashed lines. Almost everywhere the two latter visually coincide. The vertical scale coincides with the one adopted in Refs. 64 and 65 for the experimental data.

J. Sauer, Theoretical study of van derWaals complexes at surface sites in comparison with the experiment. Chem. Rev. 94, 2095-2160 (1994)... 

Our target is to develop a theory for the Lamb shift and the fine structure in these two atomic systems. Eventually we need to determine the 2s — 2pi/2 splitting in the helium ion (for comparison with the experiment [6]), difference of the Lamb shifts ER(2s) — ER(3s) in 4He+ (for the project [7]) and the 2p3/2 — 2s interval in hydrogen-like nitrogen. The difference mentioned is necessary [12,1] if one needs to compare the results of the Lamb shift (n = 2) measurement [6] and the 2s — 3s experiment. 

As there is no circulation pump present in the experimental set-up, part of the described phenomenas could be due to poor mixing. Therefore we performed a test in a microbalance. A BEA sample was pre-treated in a helium flow at 573 K. The sample was cooled down to 383 K in a helium flow. After cooling down the helium flow was switched to an n-butane/helium mixture. Comparison with the experiment described before revealed that the rate of adsorption was faster, but still much slower than without any noble gas present and that the amount adsorbed was even less than in the described experiments with a noble gas present. 

Adsorption equilibrium and adsorption dynamics on MSC were evaluated for each organics in supercritical CO2 fluid mixed with adsorbate by chromatographic measurement. The dependencies of adsorption equilibrium constants, K, and micropore diffiisivity, D, of toluene, benzene and m-xylene, on molarity of toluene with each parameters of temperature or pressure were obtained. It was found that the values of K and D for an organic substance depended on the amount adsorbed of other organics strongly. The state of the molecule could be observed by the molecular simulation. As for the amount adsorbed, the simulation is small, in comparison with the experiment. 

The organization of the paper is the following. The material characteristics and the dynamic experimental setup are described in the next section. Finite element implementations are presented afterwards and the simulation results and the comparisons with the experiments are discussed at the end. 

In order to make comparison with the experiment [Park 2000], we chose the frequency = 5 meV, which corresponds to a (, m quantum dot interacting with gold electrodes via the Lennard-Jones potentials. For the electron temperatures ksT = 0.4 meV, the vibrational amplitude is xo 0.03A, and hence only the zero-point mode is active, provided O > kj j. The equilibrium distance D/2 6.2Aseparates the center-of-mass of the quantum dot from both leads. When eV < Q, the frequency shifts un are negligible, since the system "leads + dot" is cold ksT < Q, and therefore vn = F xn = xn/D < nVL. 

Thiele et al.8°) modeled the initial polymerization of styrene. A comparison with the experiment showed that there is a satisfactory correlation of W and P up to q < 0.4. On the basis of the literature and experimental data, it has been concluded that kt in isothermal suspension polymerization becomes diffusion-controlled at q > 0.25 initiation efficiency if) becomes diffusion-controlled at q > 0.4 and kp and km become diffusion-controlled at q > 0.75. 

The quantitative comparison with the experiment is hampered by the difficulty of the experimental determination of free paths in the expressions obtained. Scattering on the quasi-classical impurities does not at all affect conductivity, while the scattering with- the reverse of momentum leads to... 

The case of the GFP chromophore is important since its gas-phase spectra are available and one can make a direct comparison with the experiment at various level (gas phase, solution, protein matrix) [27,49]. Such comparison is schematically reported in Scheme 12.4. Inspection of these data reveals that the gas-phase absorption maximum is substantially closer to the protein absorption maximum than to the solution absorption maximum. This suggests the rather naive idea that the GFP protein cavity offers an environment more similar to the gas phase than to the solution. 

Another comparison with the experiments bears on the phase shift of the oscillations that is elicited by the addition of reaction product at different moments over the period. As indicated by fig. 2.8b, the product ADP, which oscillates in phase with NADH, induces an immediate phase shift that is reflected by a delay of more than 1 min when 0.7 mM ADP is added near the minimum of the product oscillations. However, the same perturbation administered near the maximum of ADP leaves the phase unaltered. The model provides an explanation at the molecu-... 

Vaporization in Vacnnm In 1882, Heinrich Hertz, at the age of 25, published a paper [19] dealing with a study of the vaporization rate of mercury in vacuum and a comparison of the experimental data obtained with theory. Hertz apparently recognized the difficulties encountered in a direct theoretical calculation of the vaporization rate (the experience accumulated over more than a century of research in this area is in agreement with this appraisal). Therefore he decided, instead, to calculate the maximum rate of the reverse process, i.e., the condensation of vapour. A theoretical analysis and comparison with the experiments conducted by Hertz led to two fundamental conclusions. First, every substance has a maximum rate of evaporation which is dependent only upon the surface temperature and the properties of the substance and, second, the maximum rate of evaporation cannot exceed the number of molecules from the vapour phase that are incident upon the surface of the condensate when equilibrium conditions are established. 

For comparison with the experiments, the special case of spheroids has been found suitable. They are characterized by coincidence of two of the three elementary axes. One distinguishes elongated or prolate spheroids with B = C and distinguishes flattened or oblate spheroids with A = B. In the following, A is always the major axis and B the minor axis of the spheroid. Accordingly, only two factors Gi(e) and G2(e) are relevant, depending on the eccentricity e, defined for a spheroid as... 

Unsteady development of such a flow w also investigated numerically and analytically in Ref. [92] both for a constant flow rate and constant pressure drop. In the analytical approach, it was considered that the fiow stops after a ten-fold viscosity growth. A step model of viscosity variation was also used, but of more complex form than is assumed by Eq. (3). A comparison with the experiment has shown that the analytical model describes better longer periods of time, while the numerical approach works better in the initial stages. This indicates only an unsuccessful choice of the computational algorithm and demonstrates a typical process of error accumulation during calculations caused first of aU by a too roi fixed two-dimtai-sional network (17 x 13 in the most exact case). 

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