T - plot

Construct a v versus t plot for the data of Problem 11 (assume that Table XVII-4 can be used) and calculate the specific surface area of the rutile. 

Figure C3.6.14 Space-time (y,t) plot of the minima (black) in the cubic autocatalysis front ( )(y,t) in equation C3.6.16 showing the nature of the spatio-temporal chaos.

Deviation from the standard isotherm in the high-pressure region offers a means of detecting the occurrence of capillary condensation in the crevices l>etween the particles of a solid and in any mesopores present within the particles themselves. A convenient device for detecting deviations from the standard is the t-plot . In the next section the nature and uses of t-plots will be discussed, together with a,-plots, a later development from them. As will l>e shown, both of these plots may l>e used not only for the detection of capillary condensation in mesopores, but also for showing up the presence of micropores and evaluating their volume. 

The isotherm under test is then re-drawn as a t-plot, i.e. a curve of the amount adsorbed plotted against t rather than against p/p° the change of independent variable from p/p° to t is effected by reference to the standard t-curve. If the isotherm under test is identical in shape with the standard, the t-plot must be a straight line passing through the origin its slope = b say) must be equal to nja, since the number of molecular layers is equal to both t/ff and n/n ... 

If micropores are introduced into a solid which originally gave a standard Type II isotherm, the uptake is enhanced in the low-pressure region and the isotherm is correspondingly distorted. The effect on the t-plot is indicated in... 

The f-curve and its associated t-plot were originally devised as a means of allowing for the thickness of the adsorbed layer on the walls of the pores when calculating pore size distribution from the (Type IV) isotherm (Chapter 3). For the purpose of testing for conformity to the standard isotherm, however, a knowledge of the numerical thickness is irrelevant since the object is merely to compare the shape of the isotherm under test with that of the standard isotherm, it is not necessary to involve the number of molecular layers n/fi or even the monolayer capacity itself. 

It is sufficient, as Sing has pointed out, merely to replace as normalizing factor by the amount adsorbed at some fixed relative pressure (p/p ), in practice taken as (p/p°), = 0-4. The normalized adsorption n/ o (= j). obtained from the isotherm on a reference sample of the solid, is then plotted against p/p°, to obtain a standard a,-curve rather than a t-curve. The a,-curve can then be used to construct an a,-plot from the isotherm of a test sample of the solid, just as the t-curve can be used to produce a t-plot. If a straight line through the origin results, one may infer that the isotherm under test is identical in shape with the standard the slope b, of the linear branch of the j-plot will be equal totio 4 Just as the slope b, of the t-plot was equal to nja (cf. Equation (2.34)). 

Fig. 4.11 (o) Adsorption isotherm for (i) a powder made up of nonporous particles (ii) a solid which is wholly microporous (iii) a powder with the same external surface as in (i) but made up of microporous particles having a total micropore volume given by the plateau of isotherm (ii). The adsorption is expressed in arbitrary units, (b) t-Plots corresponding to isotherms (i) and (iii). The o,-plots are similar, except for the scale of... 

The t and a.-methods, the nature of which was explained in Chapter 2, may be used to arrive at a value of the micropore volume. If the surface of the solid has standard properties, the t-plot (or a,-plot) corresponding to the isotherm of the nonporous powder in Fig. 4.11(a) will be a straight line passing through the origin (cf. curve (i) of Fig. 4.11(6)) and having a slope proportional to the specific surface of the powder. For the microporous powder which yields the isotherm (iii).of Fig. 4.11(a), the t-plot (or Oj-plot) will have the form of curve (iii) of Fig. 4.11(6) the linear branch of this curve will be parallel to curve (i), since it corresponds to the area of the outside of the particles which is identical with that of the nonporous parent particles. 

The intercept on the adsorption axis of the extrapolated linear branch gives the micropore contribution, and when converted to a liquid volume may be taken as equal to the micropore volume itself. It is sometimes convenient indeed to convert all the uptakes into liquid volumes (by use of the liquid density) before drawing the t-plots or the a,-plots. If mesopores are present (in addition to micropores) the plots will show an upward deviation at high relative pressures corresponding to the occurrence of capillary condensation (Fig. 4.12(6)). The slope of the linear branch will then be proportional to the area of the mesopore walls together with the... 

The slope of the tjV versus t plot indieates the filter eake resistanee. Note, however, that in praetiee the tjV versus t plots do not pass through the origin, due to the resistanee of the filter eloth and any assoeiated partieles entrapped within it (Figure 4.8). 

Figure 2-t. Plot of Eq. (2-10), where ca/c% is the fraction of initial reactant concentration remaining after the lapse of n half-lives. 

Plantagenkautschuk, m. tk n. plantation rubber. Planung,/. planning plan, design planing, planzelchnen, v.t. plot. 

An example of the determination of activation enthalpies is shown in Figs. 11 and 12. A valuable indication for associating the correct minimum with the ionic conductivity is the migration effect of the minimum with the temperature (Fig. 11) and the linear dependence in the cr(T versus 1/T plot (Fig. 12). However, the linearity may be disturbed by phase transitions, crystallization processes, chemical reactions with the electrodes, or the influence of the electronic leads. 

When n < 0.7, the ln[—ln(l — a)] against In t plots show curvature and linearity is improved if the latter parameter is replaced by t. This reduces the Weibull distribution to a log-normal distribution. Since both exponential and normal distributions are special cases of the more general gamma distribution, Kolar-Anic and Veljkovic [441] compared the applicability of the Weibull and the gamma distributions. The shape parameter of the latter (e) was shown to depend exclusively on the shape parameter of the former (n). 

The l/x vs-T plot is shown in Fig. 1. It should be noted that the same set of parameters fits all six expected transitions of the optical spectrum. For Pu(VII) this is the only known magnetic measurement in the temperature range between 4 and 300 K. 

The change is positive (an increase), as expected. Note that, as remarked earlier, the change in entropy is equal to the area beneath the graph of C/T plotted against T. 

The benefits of the method are appreciated when the textural parameters are compared. Data derived from N2-physisorption isotherms show that Fenton detemplation leads to improved textural parameters, with BET areas around 945 m g for a pore volume of 1.33 cm g , while calcination leads to reduced textural parameters (667m g 0.96cm g ). T-plot analysis, strictly speaking, is not apphcable for these bi-modal materials but it gives a good estimate. It shows that the micropore volume is doubled, which corresponds to an increase in the calculated micropore area from about... 

The electrical resistivity of the Si-doped quaternary thiospinel, Cus.sSiDi.s Fe4Sni2S32 has been measured, in the temperature range 100 K to 300 K. It was found that it behaves like a semiconductor from room temperature down to 100 K. From the log p ys 1/T plot (see inset of Fig. 15.4) the band gap is found to be 0.107 eV in the temperature range (170 -300 K). The room-temperature resistivity is around 3.1x10 Q-cm (Fig. 15.4). 

Magnetic studies show that the above compound is paramagnetic in nature in the temperature range 5-300 K. The magnetic susceptibility (xm) along with (Xm) vs T plots (1 Tesla) obtained from a DC-magnetization study of the powdered... 

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