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136   SILICA GEL, MCM, AND ACTIVATED ALUMINA

                     by various titration methods, for example, by titration with hexamethyldisilazane
                     (Vansant et al., 1995):


                      2Si − OH + (CH 3 ) 3 − Si − NH − Si − (CH 3 ) 3 ⇒ 2Si − O − Si(CH 3 ) 3 + NH 3
                     For deuterium exchange, D in D 2 O exchanges with only the H atoms of the
                     hydroxyl groups on the surface but not with those in the interior of silica.
                       Many early calculations were made on the “theoretical” silanol number (Iler,
                     1979). The silica gels are mostly heat-stabilized amorphous silica. Cristobalite and
                     tridymite, which are crystalline, have been used as models for amorphous silicas
                     because their densities and refractive indices are similar. Using the (111) face of the
                     octahedral cristobalite and assuming 1 OH per surface Si, De Boer and Vleeskens
                                                                                    2
                     (1958) and De Boer (1958) calculated the silanol number as 4.55 OH/nm .A
                                                               2
                     similar calculation using tridymite gave 4.6 OH/nm (Iler, 1979).
                       Zhuravlev (1987; 1993) has shown that for 100 different samples of amorphous
                                                                          2
                     silicas with a wide range of surface areas (from 9.5 to 945 m /g), the silanol
                                                                   2
                     numbers fell within a narrow range of 4.3–5.8 OH/nm . These samples differed
                     in the methods of synthesis and in their structural characteristics.
                       It seems that on the heat-stabilized, amorphous silicas that are fully hydrox-
                                                        2
                     ylated, the silanol number is 4–5 OH/nm . However, this “universal” number
                     could be misleading because it could be very different for many new silica
                     materials. Unger et al. (2001) showed that the silanol numbers are

                                       Silica           Silanol Number,
                                                           OH/nm 2

                                       MCM-41                2–4
                                       MCM-48                 3
                                       MCMoidal              5–6
                                       Silica Xerogel        8–9


                       Dehydroxylation commences upon heat-treatment at temperatures above
                        ◦
                     200 C. The silanol number decreases with temperature. Typical data on the
                     temperature dependence of the silanol number are shown in Figure 6.4. There
                                                                  ◦
                     are two regions in this figure. At temperatures <400 C, both free OH groups
                                                                                     ◦
                     and H-bonded OH groups are being dehydroxylated. At temperatures >400 C,
                     only free hydroxyls are dehydroxylated. By drawing a straight line through the
                                                                                  ◦
                     second region (i.e., the high-temperature region) and extrapolating to 200 C, the
                     difference between the two lines gives the amount of the H-bonded OH groups
                     that are being dehydroxylated.
                       The direct involvement of the surface hydroxyls in adsorption of a large variety
                     of gas molecules on silica has been studied extensively by using IR spectroscopy
                     (Hair, 1967; Kiselev and Lygin, 1975). Upon adsorption, the stretching vibra-
                                                                −1
                     tion frequency of the free OH groups (at 3750 cm ) is shifted toward lower
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