Single-point method

The assumption of a zero intercept reduces the BET equation to equation (5.3). This assumption is, of course, not realizable since it would require a BET C value of infinity. Nevertheless, many samples possess sufficiently high C values to make the error associated with the single-point method acceptably small (see Chapter 5 and Table 5.1). 

Using the zero intercept assumption, the BET equation can be written as 

Using nitrogen as the adsorbate at a concentration of 0.3 mole fraction and assuming Pq is 15 torrs above ambient pressure, equation (15.14) can be expressed as 

Assuming that ambient pressure P is 760 torrs and ambient temperature T is 295 K, equation (15.15) reduces to 

the total surface area contained in the sample cell is given by the simple linear relationship above when F is in cubic centimeters. 

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The existence of this situation (for nonporous solids) explains why the ratio test discussed above and exemplified by the data in Table XVII-3 works so well. Essentially, any isotherm fitting data in the multilayer region must contain a parameter that will be found to be proportional to surface area. In fact, this observation explains the success of Ae point B method (as in Fig. XVII-7) and other single-point methods, since for any P/P value in the characteristic isotherm region, the measured n is related to the surface area of the solid by a proportionality constant that is independent of the nature of the solid. 

The general vaUdity of single-point methods has been questioned, however (28). An even simpler but equally useful method is to approximate the limiting... 

Frequently occurs that extrapolations do not have a common value at their origin ordinates. These deviations may be caused by inadequate lineal extrapolations. The above mentioned is the routine method used for [q] determination. The procedure is laborious and consumes a considerable amount of time and reactive because of this, several equations were developed which estimate intrinsic viscosity at one single concentration and do not require a graphic. They are known as "single-point" methods. 

Chee (1987) and Rao Yaseen (1986) have examined the applicability of the single-point method and have found that some equations are inadequate or applicable only to some specific macromolecule-solvent systems. 

For single point methods fit with minor errors of 3.54%, but the method of Solomon-Ciuta is only valid for concentrations below 0.25% wt of gelatin. Double point error is low of 2.00%. 

The surface area of graphite is determined by nitrogen adsorption using a BET single point method (equipment is available from Quatachrome Instruments, Boynton Beach, FL, USA). 

The theory for single-point BET measurements is similar however, an assumption is made that the intercept of the PIV(P0-P) versus PIPQ plot equals zero. This assumption is not always valid and can result in surface area values that differ from multipoint values. When the assumption is valid, the single-point method is simpler and faster, and it results in accurate surface area values. 

Since IV measurements are quite laborious and time consuming, a simplified single-point method is often used by measuring the solution s specific viscosity,... 

Tang, H.-S. and Hu, O.Y.-P., Assessment of liver function using a novel galactose single point method. Digestion, 52, 222-231,1992. 

Multivariate analysis of single point NIR spectra has become a mainstay for a wide range of pharmaceutical applications. Single point methods are generally based on a relatively small number of individually collected reference spectra, with the quahty of a method dependent on how well the reference spectra model the unknown sample. With a robust method, highly accurate concentration estimates of sample components can be extracted from unknown mixture spectra. 

The BET theory requires that a plot of [W Pq/P — 1)] versus P/Pq be linear with a finite intercept [cf. equation (4.38) and Fig. 4.1]. By reducing the experimental requirement to only one data point, the single-point method offers the advantages of simplicity and speed often with little loss in accuracy. 

The total surface area as measured by the single point method is then... 

The error introduced by the single-point method can be evaluated by examining the difference between as determined by equations (5.3) and... 

Subtracting equation (5.3) from (5.5) and dividing by equation (5.5) gives the relative error associated with the single-point method, that is. 

The subscripts mp and sp above, refer to the multi- and single-point methods. 

Table 5.1 shows the relative error of the single-point method compared to the multipoint method as a function of P/Pq and C as calculated from equation (5.6). 

The last column of Table 5.1 is established by substituting equation Table 5.1 Relative error using the single-point method at various relative pressures... 

A more explicit insight into the mathematical differences of the multi-and single-point methods is obtained by considering a single-point analysis using a relative pressure of 0.3 with a corresponding multipoint C value of 100. 

The term (lF )5p refers to the monolayer weight as determined by the single-point method and is the experimental weight adsorbed at the relative pressure of 0.3. 

The analysis immediately above discloses that, when the BET C value is 100, the single-point method using a relative pressure more than three... 

LALS) in THF and the intrinsic viscosity of five of the samples was measured by the single point method. Combining the LALS data with the intrinsic viscosity work allows one to obtain the Mark-Houwink constants, and a, by plotting log[77] vs logMw. For PIPTBK, and a in THF at 25° were found to be 5xlO-3 ml/g and 0.75 respectively. 

The use of such single-point methods is inadvisable when n + 1 or the reaction is in other ways complex 22). 

Assays have been developed to determine DM and DX in plasma or saliva (Bolden et al. 2002 Hu et al 1998 Chladek et al. 2000 Hartter et al. 1996). The use of saliva or plasma for CYP2D6 phenotyping has been developed for subject convenience, or for the development of single point methods to be easily incorporated in the cocktail methods . Good correlation between metabolic ratios calculated from plasma, saliva samples and those obtained from urine have been observed. 

Rheology is a complex subject, and in the formulated colorant industry two simplified approaches have served well in the majority of cases. These are the single-point method, melt flow, and the molding simulation test, spiral flow. 

The validity of this simplifying assumption is evidently dependent on the isotherm shape the error is likely to be within a few percent provided that C 100. Experience confirms that the errors in the estimation of rtm by the single point method become appreciable when C < 80. 

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