Elementary hydration spectra

Several steps are required to perform the analysis of 50 hydration spectra. The first one consists of reducing the number of spectra to be analyzed by decomposing them on the minimum number of elementary hydration spectra Hfv), H2 (v), (v), etc. All experimental... 

Elementary hydration spectra Hfv) i = 1, 2, 3, etc.) are defined from experimental hydration spectra H v,plpo) and are linear combinations of them. In practice, this definition requires successive steps. Thus the first experimental hydration spectra at low hygrome-tries are often proportional to one another. This allows us to define a first elementary spectrum Hfv). Note that Hfv) could be replaced by any spectrum XHfv) proportional to it, with A a coefficient that may take any algebraic value). When hygrometry increases and is... 

These four elementary spectra H (P) are not yet the elementary hydration spectra we are looking for, which correspond to four independent hydration mechanisms. The reason is that the definition of these four elementary spectra only rests on mathematical criteria, and mathematics tells us that instead of taking these four spectra, we may as well have taken any four independent linear combinations of them. We would then have obtained an equally good decomposition of all experimental hydration spectra, with the same statistical errors. 

Figure 114 The four elementary hydration spectra Hj(P) (i = 1 ) of HA, together with the residual spectrum with greatest features, labelled greatest error spectrum . Spectra are offset for clarity.

In Figure 11.6, the two elementary hydration spectra / and W of a sulfonated polyimide membrane, together with the spectrum of the dried membrane, are displayed. The same analysis as described above for HA provides sufficient information to establish the hydration mechanism of this membrane, detailed in Ch. 10 and shown in Figure 10.5. It may be noted that these hydration spectra do not correspond to successive hydration mechanisms, as for HA, but correspond to the ionization of SO3H groups into SO3 HjO by addition of a single H2O molecule (Z ), and to hydration of these 803 H3O+ complexes by HjO molecules (// ). 

Figure 11.6 IR spectrum of a dried sulfonated polyimide membrane (homopolymer) 10 pm thick and the two corresponding elementary hydration spectra / and Dashed vertical lines show corresponding bands.

Both the dimer and the photohydrate from photolysis of uracil have been isolated not only as spots on a chromatogram7 but also as crystalline or amorphous solids—the dimer by Smietanowska and Shugar45 and Swenson and Setlow48 and the hydrate by Gattner and Fahr.45 Many physical properties have not been recorded for these materials. The melting points of the principal dimer is 380°.34 The infrared spectrum is not reported. The elementary composition of the hydrate has been reported.45 ... 

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