Rule extraction from data condition

The MO measurements provide information about the angular distribution of molecules in the x, y, and z film coordinates. To extract MO data from IR spectra, the general selection rule equation (1.27) is invoked, which states that the absorption of linearly polarized radiation depends upon the orientation of the TDM of the given mode relative to the local electric field vector. If the TDM vector is distributed anisotropically in the sample, the macroscopic result is selective absorption of linearly polarized radiation propagating in different directions, as described by an anisotropic permittivity tensor e. Thus, it is the anisotropic optical constants of the ultrathin film (or their ratios) that are measured and then correlated with the MO parameters. Unlike for thick samples, this problem is complicated by optical effects in the IR spectra of ultrathin films, so that optical theory (Sections 1.5-1.7) must be considered, in addition to the statistical formulas that establish the connection between the principal values of the permittivity tensor s and the MO parameters. In fact, a thorough study of the MO in ultrathin films requires judicious selection not only of the theoretical model for extracting MO data from the IR spectra (this section) but also of the optimum experimental technique and conditions [angle(s) of incidence] for these measurements (Section 3.11.5). 

The precision of the technique for seawater analysis as presented in the literature (i, 5) tends to be considerably better than we have observed here. The values obtained in other papers were for duplicate analysis of the same sample and were most likely extracted sequentially from the same bulk sample and analyzed one directly after the other. This was not the case here because the data analyzed in this paper were not generated specifically to analyze the ultimate precision of the technique. Line water samples run normally were as a rule interspersed throughout the test samples. A number of water samples would be drawn at the start of an experiment and stored unacidified in 4-1. polypropylene bottles. Over the course of up to 6 or 8 hr, extractions would be performed so that difiFerences in trace metal concentration might be expected between replicates run early and late in the experiments. This factor, which allows for significant adsorption and/or desorption of trace components, could readily explain our high standard deviations. We feel that this approach is valid to determine the precision of the technique in the field where non-optimum conditions often occur and where the factor of time between sampling and analysis is often an uncontrollable variable. It is likely that the actual precision of this technique in the field lies between those values calculated here and elsewhere (1,5). 

An increase in the amount of solvent used results in a movement of the nuxing point M toward G, while a reduction in solvent causes it to approach the point D. When M coincides with D, the amount of solvenf is at a minimum and the amoimt of extract is infinitesimally small. This follows from the lever rule. Equation 6.8f. Under these conditions, any solvent present in the system resides entirely in the raffinate phase. Conversely, the point G represents the maximum amount of solvent we can use and is attended by an infinitesimally small amount of raffinate. Evidently, the actual amount of solvent will lie somewhere between the two extremes. Note that these two limiting values are established from the intersection of the operating lines with the solubility curve and do not require any tie-line data. 

---