Spectroscopy linear variation functions

The alpha values of synthetically prepared mordenltes are within the range of 10 -10°. There Ls only a small variation In a values of siliceous mordenlte as the aluminum content of the material varies. This Ls In contrast to dealumlnated mordenltes, which exhibit a much larger variation Ln alpha values as the aluminum content varies. These catalytic results on synthetic and acid dealumlnated mordenltes Indicate that factors other than the total aluminum content must contribute to the variation In activity of the catalysts. The linear correlation of alpha versus aluminum content reported for some zeolites (26) does not apply to the acid dealumlnated samples. Evidence has been presented for the presence of both Bronsted sites and Lewis sites enhancing the strong acidity of zeolite catalysts (27). The presence of extra-lattice aluminum Ln acid dealumlnated mordenlte samples was confirmed by 2 A1 NMR spectroscopy. The presence of both framework aluminum and extra-lattice aluminum Ln the acid treated materials may account for the wide variation Ln alpha values as a function of aluminum content. 

We will discuss in this section the variations of the viscoelastic parameters derived from linear viscoelastic measurements all these parameters may be derived from any t3rpe of measurement (relaxation or creep experiment, mechanical spectroscopy) performed in the relevant time or frequency domain. The discussion will be focused however on the complex shear modulus which is the basic function derived from isothermal frequency sweep measurements performed with modem rotary rheometers. 

Figure 3.73. Variation in iimit of linear approximation [Eq. (1.82)] depending on maximum value Amsx of LO energy loss function lm(1/ 2) and angle of incidence of radiation, = (1) 60°, (2)y> = 75°, (3)y) = 80° 03 = 15, fc3 = 60, v = 1000cm . Reprinted, by permission, from V. P. Tolstoy, Methods ofUV-Vis and IR Spectroscopy of Nanolayers, St. Petersburg University Press, St. Petersburg, 1998, p. 189, Fig. 5.21. Copyright St. Petersburg University Press.

---