Phase discontinuity

It has been pointed out that a different array of atomic orbitals might be conceived of in large conjugated rings. The array, called a Mobius twist, results in there being one point in the ring at which the atomic orbitals would show a phase discontinuity. ... 

Thus, the chemical reactivity of the elements in seawater is reflected by the residence time. It is important to note, however, that while residence times tell us something about the relative reactivities, they also tell us nothing about the nature of the reactions. The best source of clues for imderstanding these reactions is to study the shape of dissolved profiles of the different elements. When we do this we find that there are six main characteristic types of profiles as described in Table 10-8. Notice that most of these reactions occur at the phase discontinuities between the atmosphere, biosphere, hydrosphere, and lithosphere. 

For the EAG-snbstimted alkenes, the transition states are non-cycUc E-Il-EAG systems. Polarization of Ft, induced by the delocalization from Ft to EAG and E, determines the regioselectivities. The polarization is analogous to that in the TMM dication (Sect. 2.1.4). The cyclic interaction occurs among the electron-accepting orbital eag ) of the substituent, e, n, and n. The a addition is favored by the orbital phase continuity while the P addition is disfavored by the phase discontinuity (Scheme 16). 

Orbital phase discontinuity for the participation of an electron-accepting geminal bond... 

Scheme 44 Long N-N bonds and orbital phase discontinuity in pyrazolone N,N-dioxides...

Fig. 6a-c Through-bond interactions in the singlet state of 1,3-diradical, a Mechanism of electron delocalization and polarization of a-spin electrons, b Cyclic orbital interaction, c Orbital phase discontinuity (denoted by the dotted lines)... 

Orbital phase discontinuity in singlet state. In contrast to the triplet state, orbital phase continuity conditions cannot be satisfied simultaneously (denoted by the dashed line in Fig. 6c) in the singlet. Thus, the singlet 1,3-diradical suffers from the orbital phase discontinuity. According to the orbital phase properties, the triplet states of TMM (1) and TM (2) were predicted to be more stable than their singlet states by the orbital phase theory [29, 31]. 

T gap (cf. references collected in Table 1). This correlates well with a disfavored cyclic six-orbital interaction by the phase discontinuity in the triplet state of 7 [29] (shown in Fig. 11). In addition, TME is an important topological unit which appears frequently in many non-Kekule diradicals (as exemplified by 15-17 in Fig. 13). 

There are six % electrons in 13. The delocalization of six n electrons in the four p-orbitals of the linear conjngation is disfavored by the orbital phase discontinuity... 

Short column or column operated at high pressure or with the liquid phase discontinuous... 

Figure 4.82 Actual schematic of the two-phase discontinuous flyback converter.

Figure 4.83 SPICE model of a single phase discontinuous flyback converter.

Instead of having one phase discontinuous and in the form of separate particles, it is possible to have the phase as a continuous matrix with pores of very fine dimensions running through it. This is a porous mass, or membrane, also known as a... 

While this book treats several topics similar to those found in an analytical chemistry text, it endeavors to consider the spatial and temporal scales of the reactions in nature as distinctly different from those of the laboratoiy. For example, in chemical analysis, precipitates (frequently of metastable and active compounds) are formed from strongly oversaturated solutions, whereas in natural water systems, the solid phase is often formed under conditions of slight supersaturation often crystal growth and aging may continue over geological time spans. Interfacial phenomena are particularly important because chemical processes of significance often occur only at phase discontinuities. 

Most chemical reactions that occur in natural waters take place at phase discontinuities, that is, at atmosphere-hydrosphere and lithosphere-hydrosphere interfaces. In this chapter the discussion deals primarily with the solid-solution interface. This is still a very broad topic. 

High capacity in foaming system. Trayed columns use the continuous liquid phase to create a froth that is difficult to separate. Packed towers make the vapor phase continuous, and the liquid phase discontinuous. 

T vo minor complications may occur when using expressions such as (4.14) in structural chemistry research. Firstly, if the fragment geometries are described by torsion angles, it is necessary to allow for the phase discontinuity at 180°. This is... 

Lenses created by leave-behind are generally oriented parallel to the local direction of flow (i.e., the pore-level flow that created them), and do not make the gas phase discontinuous. If leave-behind is the only form of lens or lamella generation, a continuous-gas foam results. Ransohoff and Radke (60) found that foam generated solely by leave-behind gave approximately a five-fold reduction in steady-state gas permeability, whereas discontinuous-gas foams created by snap-off resulted in a several hundred-fold reduction in gas mobility (20, 61). 

Zhou FX, Wang ZT (1999) Phase discontinuity of the SST interannual oscillation between the South China Sea and its adjoining west Pacific region. Oceanol Limnol Sin 30(6) 679-686 (in Chinese with English abstract)... 

FIGURE 34.8 Three models for the distribution of two phases in a material, (a) Parallel slabs, (b) continuous matrix phase, discontinuous particulate dispersion, and (c) large isolated grains separated by a continuous minor phase. 

Bitumen emulsions are emulsions in which the dispersed phase (discontinuous phase) is bitumen and the water or aqueous solution is the continuous phase. 

---