Triple lines

Organic chemists have found a way to draw complex molecular structures in a very simple way, by not showing the C and H atoms explicitly. A line structure represents a chain of carbon atoms by a zigzag line, where each short line indicates a bond and the end of each line represents a carbon atom. Atoms other than C and H are shown by their symbols. Double bonds are represented by a double line and triple bonds by a triple line. Because carbon almost always forms four bonds in organic compounds, there is no need to show the C—FI bonds explicitly. We just fill in the correct number of hydrogen atoms mentally compare the line structure of 2-chlorobutane, QT3C1TC1CF12C]T3 (3a), with its structural form (3b). Line... 

A range of symbolic conventions is used in representing atomic and molecular stractures at the electronic level. So for example double and triple lines are used for multiple bonds. This seems a clear convention, which helps keep check of valency rales. However the symbol = for a double bond is not intended to imply two equal bonds (which the symmetry of the symbol could seem to suggest) as u and TT components have different geometries, contributions to bond strength , and consequences for chemical properties. The novice learner may well find interpreting such representations a considerable challenge. 

The eqnilibrium at the solid (S), liquid (L), and vapor (V) triple line is described by Young s eqnation [1] in the form... 

More complete analyses have been effected [6,23], but we shall present here a simple scaling procedure in order to isolate the essential nature of the wetting ridge. Consider a zone of typical linear dimension to in the vicinity of the triple line, which corresponds to the solid disturbed by the capillary force 7 sin 0. Within this region, a stress of order of... 

Schematic representation of disturbed triple-line region on a soft solid.

FIG. 2 Results of white-light interferometric microscopy observation near the triple line of a drop of tricresyl phosphate (TCP) on a soft silicone rubber (RTV 615, General Electric Co.). 

Consider the work, Ei, effected when the vertical component of liquid surface tension, 7 sin 0, lifts the local solid to a height h—that of the wetting ridge. This work, per unit length of triple line, is simply hy sin 0. Using Eq. (5), we obtain ... 

In fact, the horizontal component of liquid surface tension, 7 cos 0, is not without effect, since the triple-line region now protrudes from the bulk solid. This component leads to a stretching of the surface layer of solid on the vapor-phase side of the triple line for 0 < tt/2 or on the liquid side for 0 > 77/2. By analogy with Eq. (8), we have a second contribution to the work effected, E2. 

Equilibrium at the triple line satisfies Young s equation [Eq. (1)], but if the contact angle as a function of time, 0(0, is greater than 6o, then there is a net spreading force acting per nnit length of triple line and given by [5] ... 

It has been shown that the kinetics of the spreading of a liquid on a rubber is largely dependent on viscoelastic dissipation in the wetting ridge of the substrate near the triple line. This behavior may, in practice, be slightly altered by moderate swelling that modifies the solid/liquid interactions for long contact times. 

From simple considerations of the local force balance near the triple line, or of free energy changes, the global driving force for dewetting per unit length of triple line, F , is... 

In the case where the material used to make the capillary tube is a soft rubber, Eq. (46) does not apply any more, due to the viscoelastic braking induced by the displacement of the wetting ridge. The viscoelastic braking force, / per unit of length of the triple line depends on the flow speed U according to ... 

The predominant form of released petroleum products is a liquid that is immiscible with water this is called the free product (in this section it will be referred to as oil). The behavior of water and oil in soil depends on the interaction of the three phases water, oil, and soil. The affinity of water or oil with the soil can be estimated by establishing the contact angle of oil/water/soil triple line. 

FIGURE 5.2 A schematic model of multiple X Y interactions. Black dots are unpaired electrons the central, big black dot is the point of EPR observation. Straight lines are interactions a single straight line symbolizes the electronic Zeeman interaction S B double lines represent central and ligand hyperfine interactions S I triple lines are zero-field interactions S S between electrons (i) around a single metal (ii) at different centers within a molecule and (iii) at centers in different molecules. 

Another type of DOUBLE ENDOR, called special TRIPLE , has been introduced by Dinse et al.90 to study proton hf interactions of free radicals in solution. In a special TRIPLE experiment two rf fields with frequencies vp + Av and vp — Av are swept simultaneously. For systems with Tln < T,i this leads to a considerable signal-to-noise improvement and to TRIPLE line intensities which are directly proportional to the number of nuclei with the same hf coupling constant. It should be remembered, however, that in transition metal complexes in the solid state the resonance frequencies are not, in general, symmetrically placed about the free proton frequency vp and that the condition Tln < Tj,i is not always fulfilled. 

Fig. 28. Numbering for peaks of G1 (cf. Fig. 7 b) and isomer distribution in peaks 1-5. Dashed horizontal lines symbolize mirror planes (enantiomers) vertical triple lines indicate equivalent identities...

Again, applying the principle of a summarized chirality as governing the sequence of elution of the 5 peaks of G1 leads to the distribution of components shown in Fig. 28 extending the information from Fig. 27 by addition of mirror planes (dashed lines), indicating equivalent identities (vertical triple lines) and by enclosing meso forms and racemates in boxes to symbolize the relative molar ratios of the various forms. The compounds within one box relate to those in the other boxes as diastereoisomers. 

Thus, triple-/ MP2 energies at double-/ MP2 geometries are augmented with a correction for doubles contributions beyond second order (line 2 on the r.h.s. of Eq. (7.57)) and a correction for basis set size increase beyond triple-/ (line 3 on the r.h.s. of Eq. (7.57) where the T superscript in the first basis set implies that polarization functions from cc-pVTZ were used in conjunction with valence functions from cc-pVQZ). 

Fig. 22. Phase image of a thin film of a hydrogenated polybutadiene-polyethyleneoxide blockcopolymer (3700-2900 g/mol) on mica. The film was crystallised at 38 C close to a triple line caused by dewetting. Courtesy of G. Reiter [275]...

---