Contents 2 THEORETICAL METHODS

In connection with the content of this section, dynamic features of ion transports through polyvinyl chloride membranes [27,28], ion-exchange resin membranes [29,30], or BLMs [31-36] have been discussed in the light of VCTTMs. For wide and pertinent applications of the VCTTM, however, further investigations have been required on the experimental and theoretical methods to analyze VCTTM quantitatively. 

The Ti4+ distribution in TS-1 has also been studied by computational methods (34,62,160-163). The actual location of the Ti atoms in the framework of titanosilicates is difficult to determine experimentally because of the low Ti content (Section II), and information obtained from theoretical methods is, therefore, of considerable interest. In the orthorhombic MFI structure, substitution can take place at 12 crystallographically different tetrahedral (T) sites (T1-T12) (Fig. 1 and Section II.A.l.b). In the monoclinic MFI framework, the mirror symmetry is lost and 24 crystallographically different T sites can be distinguished (Fig. 31) (160). 

The theoretical method can provide initial guidance in setting particle size specifications to avoid poor content uniformity of low-dose dmg products. These new modifications have made the theoretical model easier to use. However, those theoretical models do not take into account the particle size and size distribution of excipients used in a unit formula. Chapter 3 presents more detailed discussions of the theoretical consideration of the relationship between the dmg particle size and product content uniformity. 

The method for the quantitative determination of copovidone given by the Ph.Eur. monograph measures the nitrogen content (theoretical value 7.1%) by the Kjeldahl method. 

Other methods attempt to probe the stmcture of the foam indirectly, without directly imaging it. Eor example, since the Hquid portion of the foam typically contains electrolytes, it conducts electrical current, and much work has been done on relating the electrical conductivity of a foam to its Hquid content, both experimentally (15) and theoretically (16). The value of the conductivity depends in a very complex fashion on not only the Hquid content and its distribution between films and borders, but the geometrical stmcture of the bubble packing arrangement. Thus electrical measurements offer only a rather cmde probe of the gas Hquid ratio, a quantity that can be accurately estimated from the foam s mass density. 

Burning Pyrites. The burning of pyrite is considerably more difficult to control than the burning of sulfur, although many of the difficulties have been overcome ia mechanical pyrite burners. The pyrite is burned on multiple trays which are subject to mechanical raking. The theoretical maximum SO2 content is 16.2 wt %, and levels of 10—14 wt % are generally attained. As much as 13 wt % of the sulfur content of the pyrite can be converted to sulfur trioxide ia these burners. In most appHcations, the separation of dust is necessary when sulfur dioxide is made from pyrite. Several methods can be employed for this, but for many purposes the use of water-spray towers is the most satisfactory. The latter method also removes some of the sulfur... 

The wet analysis assumes that the water vapor is present. The maximum theoretical carbon dioxide content is 9.66 per cent. The zirconia cell method of measuring oxygen is on the wet basis. 

Comparative method. Sometimes, as in the analysis of a mineral, it may be impossible to prepare solid synthetic samples of the desired composition. It is then necessary to resort to standard samples of the material in question (mineral, ore, alloy, etc.) in which the content of the constituent sought has been determined by one or more supposedly accurate methods of analysis. This comparative method, involving secondary standards, is obviously not altogether satisfactory from the theoretical standpoint, but is nevertheless very useful in applied analysis. Standard samples can be obtained from various sources (see Section 4.5). 

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