Susceptibility isotherms method

Preliminary data on a few other systems have been obtained in the writer s laboratory and as they show the general scope of the susceptibility isotherm method they will be described briefly. 

From the susceptibility isotherms it may be expected that three kinds of information may be obtained first, the oxidation state of the paramagnetic ion second, evidence of intercation covalence and third, the effectiveness of dispersion of the paramagnetic ions. There will now be presented specific applications of the method. 

Magnetic susceptibility measurements were made on the several samples by the Gouy method. Susceptibility isotherms for two temperatures are shown in Fig. 9. These curves gives the susceptibility per gram of chromium in the several catalysts, as a function of chromium concentration. The expected rise of susceptibility with decreasing chromium concentration, and the position of point I are clearly shown, especially at low temperatures. In calculating the susceptibility of chromium in each sample it has been assumed that the susceptibilities of aluminum ions and oxide ions remain constant. This procedure is... 

Chromia-alumina catalysts are often prepared by procedures other than the method of impregnation. A precipitated chromia was prepared as follows y-alumina was suspended in 25 per cent ammonium hydroxide solution. The mixture was stirred rapidly while chromic nitrate solution was added from a buret. The resulting mixture was then dried, ignited, and reduced in the same manner as for impregnated samples. A total of four samples was prepared. The susceptibility isotherm for this series is of the same general form as for the impregnation series except that point I is virtually absent. But the most striking... 

The results of a comparison between values of n estimated by the DRK and BET methods present a con. used picture. In a number of investigations linear DRK plots have been obtained over restricted ranges of the isotherm, and in some cases reasonable agreement has been reported between the DRK and BET values. Kiselev and his co-workers have pointed out, however, that since the DR and the DRK equations do not reduce to Henry s Law n = const x p) as n - 0, they are not readily susceptible of statistical-thermodynamic treatment. Moreover, it is not easy to see how exactly the same form of equation can apply to two quite diverse processes involving entirely diiferent mechanisms. We are obliged to conclude that the significance of the DRK plot is obscure, and its validity for surface area estimation very doubtful. 

The dosing requirement of gravimetric and volumetric apparatus can lead to pressure overshoot which may produce data off the isotherm in the hysteresis region. The continuous flow method is not susceptible to this phenomenon. 

As already mentioned, induction methods, such as AC susceptibility measurements, yield the value of the differential adiabatic susceptibility. This can be scanned either in the single mode (giving rise to xl) or, alternatively, in the dual mode (when the dispersion x and the absorption x are distinguished). The adiabatic susceptibility approaches the isothermal susceptibility only when the frequency of the alternating field is small. 

Parameters of a-relaxation times spectrum were determined using the least-squares method by isothermal creep s and photocieep curves that were obtained for several temperamres in glass transition regioa Experimentally was proved, that relaxation spectrum for shear pliability and strain electromagnetic susceptibility is identical. More one evidence of shear pliability s and strain electromagnetic susceptibility s spectrums coincidence may be slight discrepancy not more than 10% of photocreep s values, converted to mechanical scale (with use of relaxation spectmm s parameters defined by creep s curves) by dependence from the real experimental values. 

In summary, it may be cmcluded that the gas adsorptum-desorptUm method is simple if a suitable apparatus is available. The main problem is to relate the pore geometry to a model which allows the pore size and pore size distribution to be determined from the isotherms. Dead-end pores which do not contribute towards transport are measured by this technique. Ceramic membranes often give better results because their structure is generally more uniform and the membranes less susceptible to capillary forces. 

The temperature-modulated mode of operation has been well known for many decades in calorimetry [33], but became well established only during the 1990s, when commercial DSC was modified this way [34], The idea is to examine the behavior of the sample for periodic rather than for isothermal or constant-heating-rate temperature changes. In this way it is possible to obtain information on time-dependent processes within the sample that result in a time-dependent generalized (excess) heat capacity function or, equivalently, in a complex frequency-dependent quantity. Similar complex quantities (electric susceptibility, Young s modulus) are known from other dynamic (dielectric or mechanical) measurement methods. They are widely u.sed to investigate, say, relaxation processes of the material. 

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