Isotherm plots interpretation

The validity of Johnston s interpretation of the experimental facts in terms of the simple unimolecular dissociation (1) has been questioned by Lindars and Hinshelwood120 and by Reuben and Linnett121. These workers maintain that isothermal plots of k versus p are not smooth curves, but consist of a number of straight lines linked by markedly curved portions. To explain such behaviour they incorporate into their mechanism a collision-induced crossover of vibrationally excited N20 (XS) to repulsive 3II and 3E states. While we incline towards the simpler view held by Johnston105 and others106-116, we feel that this feature of the decomposition kinetics merits further investigation. 

An important case addressed in numerous studies is the adsorption of anionic and cationic surfactants from aqueous solutions on polar surfaces such as metal oxides [5,6]. The shapes of experimental adsorption isotherms, which represent a relationship between the adsorption, T, and the equilibrium surfactant concentration, c, have been thoroughly investigated and some common features noted. A typical adsorption isotherm plotted on a log-log scale can be subdivided into four regions ( Fig. III-8, a), the interpretation of which and... 

For a second active carbon, AG, the DR plot was convex to the logio(p7p) This carbon was believed from X-ray results to have a wider distribution of pores. It was found that the isotherms of both benzene and cyclohexane could be interpreted by postulating that the micropore system consisted of two sub-systems each with its own Wq and and with m = 2 ... 

Using Equations 3-3 and 3-4, we can plot f(0 vs. T 1/2 or T based on the experimental data on the jt-T characteristics (see Figure 12) [39]. Figure 13 indicates that Equation 3-3 is more realistic than Equation 3-4. The correlation coefficient, R, for Equation 3-3 is nearly unity, suggesting that the assumption of the "Coulombic" interaction between the hydrophilic head-groups is essential in the interpretation of the isotherm, especially for the low T(or the large A) region. 

Adsorption isotherms are often plotted for mixtures of adsorbates (humic acid, fatty acids etc.) using collective parameters such as organic carbon. Enumerate the various reasons that make the rational interpretation of such adsorption isotherms difficult. 

Frequently, there is overlapping of these phenomena, and the interpretation of adsorption studies can be complicated. Brunauer has classified adsorption isotherms into the five characteristic types shown in Figure 5.5. To facilitate comparison of isotherms, it is preferable to plot them in terms of relative pressures (p/po), where p0 is the saturation vapour pressure, rather than pressure itself. This also has the advantage of giving a 0 to 1 scale for. all gases. 

The interpretation of surface-pressure and surface-potential measurements.8 Surface pressure F is best plotted against area A, as this shows up the resemblance between the films and three-dimensional PV isothermals. For gaseous films, however, curves with FA as ordinates and F as abscissae are very useful. 

The values of a(BET) in Table 9.1 are the BET-nitrogen areas, which were derived from the linear regions of the BET plots, with the molecular area assumed to be 0.162 nm2. The values of a(ext) in Table 9.1 are obviously much smaller than the corresponding values of a(BET). The question naturally arises does the BET method provide a reliable assessment of the total area (i.e. internal plus the external area) The non-linear character of the low-pressure region of each as-pk>t is a clear indication that the isotherm is distorted in the monolayer region and we may therefore conclude that a(BET) does not represent a real surface area. Additional support for this interpretation comes from the microcalorimetric data, which are discussed later in this section. More detailed discussion of some of the results in Table 9.1 is given in Chapter 12. 

Each comparison plot in Figure 10.27 has two linear sections. Back-extrapolation of the first linear section gives a zero intercept whereas back-extrapolation of the second (multilayer) section gives a positive intercept. The interpretation of the features is based on the principles introduced in Chapter 8. An analysis of the isotherm data is given in Table 10.15. 

The nitrogen isotherm was replotted by Cases et al. (1992) in the usual BET coordinates and as a t plot. The derived BET area of 43.3 m2 g"1 appeared to be not far removed from the value of 45.9 m2 g 1 obtained from the amount adsorbed at Point B. The r-plot was constructed in the manner originally proposed by de Boer et al. (1966), which involved adopting a standard isotherm with the same value of C, which in this case was 485. It was not easy to interpret the /-plot, although three short linear sections were identified. From the initial slope, the total surface area appeared to be c. 50 m2 g-1. Back-extrapolation of a linear region at higher p/p° gave an apparent micropore volume of c. 0.01 cm3 g 1. 

The /-method of isotherm analysis adopted by Cases et al. (1992) is not entirely satisfactory and therefore the interpretation of the results is not altogether straightforward. However, the high BET C value is consistent with the conclusion that there was a small micropore filling contribution. To arrive at a more realistic quantitative assessment of the microporosity it would be desirable to obtain nitrogen isotherm data on a truly non-porous form of Na-montmorillonite. In practice, however, this may be difficult to accomplish and a more pragmatic approach would be to construct a series of comparison plots for the adsorption of N2 (and preferably also Ar) on pairs of samples of differing particle sizes and defect structures. In this way it should be possible to establish quantitative differences in the micropore capacities. 

However, the flow through the brush layer may be ignored in a first approximation [240], whereby the thickness h, appearing in Eq. (3.85), should be identified with the aqueous core thickness, /i2 (rather than hw) [241], The aqueous core thickness is plotted in Fig. 3.36, ( ). The dramatic influence on the interpretation is better seen in Fig. 3.37, ( ). The dependence is linear down to about /itot 90 nm. Thinner films drain faster initially and later on slower than predicted by the linear dependence, i.e. by Reynolds equation. The disjoining pressure isotherm (Fig. 3.38) is no more monotonous. 

Thus, the experimental TT(/j) isotherms of NaDoS films plotted with the Thin Liquid Film-Pressure Balance Technique represent an excellent example of interpretation of long-and short-range interactions and the transition between them. 

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