Planar applications

Figure 6.23 illustrates a variety of situations . We will meet further cases, in Chapter 7, in which the fluxes and hence the gradients are kept constant at the boundary. Naturally the one-dimensional solutions are not restricted to one-dimensional systems (cf. Fig. 6.22). In a suitable pseudo one-dimensional experiment is the application of a diffusion source in the form of a thin strip (e.g. gold) onto a thin film (e.g. a thin sheet of silver) (chemical diffusion). It can also be a thin strip of the same but now radioactive material (different isotope), or the exposure of a slit-shaped opening of the otherwise sealed thin oxide film to a (radioactive or chemically modified) gas atmosphere (tracer diffusion). The analogue in D is the sandwich technique or the planar application of the diffusion source onto the surface (as already considered in Fig. 6.24). If the diffusion source is a gas phase, again sealing is necessary unless the aspect ratio is very favourable, i.e. if the extension is sufficiently small in the direction of diffusion compared with the other directions in space . Otherwise the three-dimensional solution has to be considered.

This type of coil was prepared from copper cladded printed circuit board material by applying photolithographic techniques. The p.c. board material is available with difierent copper thicknesses and with either a stiff or a flexible carrier. The flexible material offers the opportunity to adapt the planar coil to a curved three dimensional test object. In our turbine blade application this is a major advantage. The thickness of the copper layer was chosen to be 17 pm The period of the coil was 100 pm The coils were patterned by wet etching, A major advantage of this approach is the parallel processing with narrow tolerances, resulting in many identical Eddy current probes. An example of such a probe is shown in fig. 10. 

Within this contimiiim approach Calm and Flilliard [48] have studied the universal properties of interfaces. While their elegant scheme is applicable to arbitrary free-energy fiinctionals with a square gradient fomi we illustrate it here for the important special case of the Ginzburg-Landau fomi. For an ideally planar mterface the profile depends only on the distance z from the interfacial plane. In mean field approximation, the profile m(z) minimizes the free-energy fiinctional (B3.6.11). This yields the Euler-Lagrange equation... 

V S, C M Kelly and C R Landis 1991. SHAPES Empirical Force-Field - New Treatment of igular Potentials and Its Application to Square-Planar Transition-Metal Complexes. Journal of American Chemical Society 113 1-12. 

One of the first applications of this technique was to the enrichment of and "B isotopes, present as 18.7 and 81.3 per cent, respectively, in natural abundance. Boron trichloride, BCI3, dissociates when irradiated with a pulsed CO2 laser in the 3g vibrational band at 958 cm (vj is an e vibration of the planar, D j, molecule). One of the products of dissociation was detected by reaction with O2 to form BO which then produced chemiluminescence (emission of radiation as a result of energy gained by chemical reaction) in the visible region due to A U — fluorescence. Irradiation in the 3g band of BCls or "BCI3 resulted in °BO or BO chemiluminescence. The fluorescence of °BO is easily resolved from that of "BO. 

The force exerted on a submerged planar surface of area A is given by F = p A where p is the pressure at the geometrical centroid of the surface. The center of pressure, the point of application of the net force, is always lower than the centroid. For details see, for example. Shames, where may also be found discussion of forces on curved surfaces, buoyancy, and stability of floating bodies. 

While HiickeTs 4n + 2 rule applies only to monocyclic systems, HMO flieory is applicable to many other systems. HMO calculations of fused-ring systems are carried out in much the same way as for monocyclic species and provide energy levels and atomic coefficients for the systems. The incorporation of heteroatoms is also possible. Because of the underlying assumption of orthogonality of the a and n systems of electrons, HMO dieory is restricted to planar molecules. 

The pattern of experimental results on charged species with cyclic conjugated systems is summarized in Table 9.1. It is consistent with the applicability of HiickeTs rule to charged, as well as neutral, conjugated planar cyclic structures. 

Unquestionably, most practical planar chromatographic (PC) analytical problems can be solved by the use of a single thin-layer chromatographic (TLC) plate and for most analytical applications it would be impractical to apply two-dimensional (2-D) TLC. One-dimensional chromatographic systems, however, often have an inadequate capability for the clean resolution of the compounds present in complex biological samples, and because this failure becomes increasingly pronounced as the number of compounds increases (1), multidimensional (MD) separation procedures become especially important for such samples. 

Nowadays, almost all commercially available HPLC stationary phases are also applicable to planar chromatography. In addition to the polar hydroxyl groups present on the surface of native silica, other polar functional groups attached to the silica skeleton can also enter into adsorptive interactions with suitable sample molecules (34). Silica with hydrophilic polar ligands, such as amino, cyano, and diol functions, attached to the silica skeleton by alkyl chains, all of which have been well proven in HPLC, have also been developed for TLC (34). 

On the basis of theory and experimental observations it can be predicted that a zone capacity of ca. 1500 could be achieved by 2-D multiple development. Because the same result can be achieved by application of 2-D forced-flow development on HPTLC plates, it can be stated that the combination of stationary phases, FFPC and "D offers a fruitful future in modem, instmmental planar chromatography. 

L. Botz, Sz. Nyiredy, E. Wehrli and O. Shelter, Applicability of Empore TLC sheets for forced-flow planar cltromatography. I. Characterization of the silica sheets , 7. Liq. Chromatogr. 13 2809-2828 (1990). 

L. Botz, Sz. Nyiredy and O. Sticher, Applicability of long distance oveipressured layer cltromatography , 7. Planar Chromatogr. 4 115-122(1991). 

Sz. Nyiredy, Applicability of planar cliromatography in the analysis and isolation of plant substances , in Proceedings of Biokemia XV, pp. 146-151 (1991). 

According to the Hiickel criteria for aromaticity, a molecule must be cyclic, conjugated (that is, be nearly planar and have ap orbital on each carbon) and have 4n + 2 tt electrons. Nothing in this definition says that the number of p orbitals and the number of nr elections in those orbitals must be the same. In fact, they can he different. The 4n + 2 rule is broadly applicable to many kinds of molecules and ions, not just to neutral hydrocarbons. For example, both the cydopentadienyl anion and the cycloheptatrienyl cation are aromatic. 

---