Isothermal methods

Fig. XVI-2. Comparison of the pore volume distribution curves obtained from porosimeter data assuming contact angles of 140° and 130° with the distribution curve obtained by the isotherm method for a charcoal. (From Ref. 38.)...

For prehminary screening and easibility studies or for rough cost estimates, one may wish to employ a version of the isothermal method which assumes that the liquid temperatures in the tower are everywhere equal to the inlet-liquid temperature. In their analysis of packed-tower designs, von Stockar and Wilke [Ind. Eng. Chem. Fun-dam. 16, 89 (1977)] showed that the isothermal method tended to underestimate the reqmred depth of packing by a factor of as much as 1.5 to 2. Thus, for rough estimates one may wish to employ the assumption that the temperature is equal to the inlet-liquid temperature and then apply a design fac tor to the result. 

In this method, data are obtained for reaction proceeding at a series of different heating rates [539,560,561]. This reduces the advantage of the non-isothermal method and one might just as well perform a series of isothermal measurements for which the subsequent analysis will be both more accurate and much simpler. Use of the technique can be illustrated by reference to the work of Ozawa [561] which is quoted as typical. The Doyle equation [eqn. (25)] above can be written... 

Solid-state reactions have usually been studied either by isothermal or by non-isothermal methods, with few attempts to combine the advantages of these alternative and sometimes complementary approaches. For reasons stated in Chap. 3, the kinetic information obtained from isothermal studies appears to be more accurate and reliable, and these studies are emphasised in this review. Wherever appropriate, however, account is taken of non-isothermal studies as a valuable source of complementary information. 

The lanthanide formates decompose above 670 K [1040] and the chemical changes proceed through the oxyformate [1041] and the oxy-carbonate to Ln203. Values of E determined by non-isothermal methods [1040] decreased with increase in atomic number for reaction in air but were approximately equal for reactions in vacuum. 

It is believed [1135,1136] that the decomposition of metal complexes of salicyaldoxime and related ligands is not initiated by scission of the coordination bond M—L, but by cleavage of another bond (L—L) in the chelate ring which has been weakened on M—L bond formation. Decomposition temperatures and values of E, measured by several non-isothermal methods were obtained for the compounds M(L—L)2 where M = Cu(II), Ni(II) or Co(II) and (L—L) = salicylaldoxime. There was parallel behaviour between the thermal stability of the solid and of the complex in solution, i.e. Co < Ni < Cu. A similar parallel did not occur when (L—L) = 2-indolecarboxylic acid, and reasons for the difference are discussed... 

There are two well-established experimental techniques for determining the distribution of pore radii. They are the mercury penetration technique and the desorption isotherm method. 

Figure 8.7 First stage of the stepped isothermal method (SIM) for oriented polyester fibres. Creep strain is measured under a single load while the temperature is increased...

Figure 12.9 Scheme of a DSC curve for the study of an endothermic process by the isothermal method (a) and of the corresponding zero line (b). The numbers represent differences to the temperature 7"e. 

In principle, any system studied by the dynamic method can also be studied by the isothermal method, provided that the kinetics of the process is not too slow at the onset temperature. Very slow events result in shallow and broad peaks, which may be difficult to integrate accurately. 

Considering now a few common methods and techniques for the experimental definition of a phase diagram, it may be useful to refer to their usual classification into two groups polythermal and isothermal methods. 

Isothermal methods. In principle these methods imply the preparation of a certain number of alloy specimens of different compositions and their examination at the same given temperature. Important methods are those based on observations carried out under a microscope. An example of such an analysis is given in Fig. 2.41 where the photomicrographs of two alloys of the Cu-Mg phase diagram are shown. These pictures, taken with a reflection microscope, allow identification... 

The second section will concentrate on methods of determining phase diagrams. The first part will examine non-isothermal methods, such as differential thermal analysis and cooling curve determinations, while the second will concentrate on isothermal methods, such as metallography, X-ray measurements, etc. The various limitations of both methods will be discussed and some novel techniques introduced. 

The accuracy of some isothermal techniques, particularly those that rely on observation of phases, is limited by the number of different compositions that are prepared. For example, if two samples are separated by a composition of 2at%, and one is single-phase while the other two-phase, dien formally the phase boundary can only be defined to within an accuracy of 2at%. This makes isothermal techniques more labour intensive than some of the non-isothermal methods. However, because it is now possible to directly determine compositions of phases by techniques such as electron microprobe analysis (EPMA), a substantially more quantitative exposition of the phase equilibria is possible. 

The isothermal method for such expls as PETN, RDX, NG and Tetryl is complicated by autocatalysis to such an extent that one cannot determine the intrinsic (pure explosive) decompn rate from the logw vs t curves and their change with temperature. Hence, the results obtd by the adiabatic(sensitivity) methods may be more reliable from this viewpoint (Ref 8, p 177)... 

Gonzalez, J. L., and Salvador, F. (1984), Comparative studies of non-isothermal methods in Unear and non-linear temperature variation, React. Kinet. Catal. Lett., 25(1-2), 125-130. 

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