Curve crossing pseudo

Drawing pseudo-binaryjy—x phase diagrams for the mixture to be separated is the easiest way to identify the distillate product component. A pseudo-binary phase diagram is one in which the VLE data for the azeotropic constituents (components 1 and 2) are plotted on a solvent-free basis. When no solvent is present, the pseudo-binaryjy—x diagram is the tme binaryjy—x diagram (Eig. 8a). At the azeotrope, where the VLE curve crosses the 45° line,... 

When Ei,Vi E2,Vj, it is necessary before applying Eq. (5.1.12) to vertically shift one of the potentials to ensure strict energy degeneracy. The new curve crossing point obtained in this way is called a pseudo-crossing point (Miller, 1968). 

If these data are replotted as mol fraction of ether in the vapor vs. mol fraction of ether in the liquid, assuming that the vapors obey the perfect-gas law, one obtains the results given in Fig. 4-11. The value of the mol fraction of ether in the vapor increases very rapidly with the mol fraction in the liquid and becomes constant at 0.916 in the two-phase-liquid region. The vapor-liquid curve crosses the 45° line at a composition of 0.915 mol per cent ether. The mixture of this composition is a pseudo-azeotrope. For mol fractions of ether greater than... 

Fig. 33. Comparisons of the pseudo-solubility data of Figs. 31 and 29 with model calculations assuming various values of parameter A DH, the binding energy of a positive donor D + and H into DH, AE2, the binding energy of 2H° into H2, and eA, the position of the hydrogen acceptor level relative to midgap. Plots (a) and (b) correspond respectively to the values 1.8 and 1.4 eV for A E2- In each of these, curves are shown for four combinations of the other parameters full curves, AEDH = 0.435 eV, eA = 0 dashed curves, AEDH = 0.835 eV, ea = 0 dotted curves AEDH = 0.435 eV, eA = 0.4eV dot-dash curves, A DH = 0.835 eV, eA = 0.4 eV. The chemical potential fi is constant on each curve and has been chosen to make the model curve pass through one of the experimental points of donor doping near 1017 cm-3, as shown. The solid circles are experimental points for arsenic obtained from Fig. 29 as described in the text. The other points are extrapolations of the phosphorus curves of Fig. 31 to zero depth, as described for Fig. 32, with open circles for the newer data and crosses for the older.

Fig. 3. Correlation diagram of the doublet states relating weak (left) and strong (right) tetragonal perturbations. In the strong field limit the splitting pattern is determined by pseudo-/l quantum numbers. Note the crossing point on the lowest energy curve...

Mitroy et al. (1984) carried out an extensive configuration-interaction calculation of the structure amplitude (q/ 0) for correlated target and ion states. The long-dashed curve in fig. 11.7(a) shows their momentum distribution multiplied by 2. They found that the dominant contribution came from the pseudo-orbital 3d, calculated by the natural-orbital transformation. Pseudo-orbitals are localised to the same part of space as the occupied 3s and 3p Hartree—Fock orbitals and therefore contribute to the cross section at much higher momenta than the diffuse Hartree—Fock 3d and 4d orbitals. The measurements show that the 4d orbital has a larger weight than is calculated by Mitroy et al, who overestimate the 3d component. 

Figure. 12. PES slices (radial potentials) Vj(R, y 0) energies are given inkcal/mol left panel 18 doublet PES s calculated with the contribution of S-O interaction are ascribed to 4 uncoupled groups of 1, 3, 6, 8 states with Mj =7/2, 5/2, 3/2, 1/2 shown with dash-dotted, dotted, dashed, and solid curves respectively free-fragment correlations are assigned for the example of triple pseudo-crossing in the group of 8 states with Mj =l/2 right panel 8 PES s calculated without contribution of the S-O interaction are ascribed to irreducible representations ( X + Z + rt-+- A) of the symmetry group C v-...

Figure 22.2 Schematic view of the potential energy curve (unidimensional picture) of the M + X2 system (M alkali atom X2 halogen molecule). Both neutral M +X2 and ionic M+ +X configurations are displayed. Notice the (pseudo)-crossing at distance R. Adapted from Gonzalez Urefia Cinetica Quimica (1991)...

Fig. 31. Pseudo-crossing of potential energy curves for singlet (/ — I) and triplet (II — II) states of olefin-radical system...

In the vulcanized rubber, the elastic force / is proportional to the number of chemical cross-link-1 and that of the pseudo-cross-link-2. For rapid deformation, the force is elastic and proportional to the sum of link-1 and link-2 and the stress-strain curve in extension coincides with that of retraction, but slow deformation induces slip of link-2 and is accompanied by hysteresis H. For filled rubber, H is very large. Elastic force in extension,... 

In other cases the y,x curve may not cross the diagonal in the two-phase region, and such mixtures do not form pseudo-azeotropes, but they may form, and usually do, true azeotropes in one of their singlephase regions. 

This reaction is a non-adiabatic process. The potential curves for the Nal molecule are shown in Fig. 4.7. It is seen that there is a pseudo-crossing between the curves of the excited covalent state and ionic ground electronic state. The femtosecond light pulse forms the coherent nuclear wave package in the excited electronic state. We mentioned above that the intramolecular dynamics could be interpreted... 

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