Obtaining data isothermal

Alternatively, q x may be obtained from the application of Eq. XVII-107 to adsorption data at two or more temperatures (see Ref. 89). Similarly, q is obtainable from isotherm data by means of Eq. XVII-115, but now only provided that isotherms down to low pressures are available so that Gibbs integrations to obtain v values are possible. 

The partial molar entropy of adsorption AI2 may be determined from q j or qsi through Eq. XVII-118, and hence is obtainable either from calorimetric heats plus an adsorption isotherm or from adsorption isotherms at more than one temperature. The integral entropy of adsorption can be obtained from isotherm data at more than one temperature, through Eqs. XVII-110 and XVII-119, in which case complete isotherms are needed. Alternatively, AS2 can be obtained from the calorimetric plus a single complete adsorption isotherm, using Eq. XVII-115. This last approach has been recommended by Jura and Hill [121] as giving more accurate integral entropy values (see also Ref. 124). 

The research programme into n-butyl lithium initiated, anionic polymerization started at Leeds in 1972 and involved the construction of a pilot scale, continuous stirred tank reactor. This was operated isothermally, to obtain data under a typical range of industrial operating conditions. 

The pressure profiles obtained from isothermal runs at five different temperatures using this method are shown in Figure 2. It can be observed that in general, the pressure rise is fairly linear for most of the duration of the experiments so that a zero-order approximation may be used to fit the data. This linearity was found to hold even after 5 days for the 175 °C isotherm, reaching a pressure level of approximately 300 psia (this was the longest duration of all the experiments). In the case of the 225 °C isotherm, the pressure accumulation finally levels off at approximately 1100 psia after one day. 

Montaudo and co-workers have used direct pyrolysis mass spectrometry (DPMS) to analyse the high-temperature (>500°C) pyrolysis compounds evolved from several condensation polymers, including poly(bisphenol-A-carbonate) [69], poly(ether sulfone) (PES) and poly(phenylene oxide) (PPO) [72] and poly(phenylene sulfide) (PPS) [73]. Additionally, in order to obtain data on the involatile charred residue formed during the isothermal pyrolysis process, the pyrolysis residue was subjected to aminolysis, and then the aminolyzed residue analysed using fast atom bombardment (FAB) MS. During the DPMS measurements, EI-MS scans were made every 3 s continuously over the mass range 10-1,000 Da with an interscan time of 3 s. 

Because the catalytic reaction A R is highly exothermic with rate highly temperature-dependent, a long tubular flow reactor immersed in a trough of water, as shown in Fig. P18.39, is used to obtain essentially isothermal kinetic data. Pure A at 0°C and 1 atm flows through this tube at 10 cm / sec, and the stream composition is analyzed at various locations. 

These empirical correlations were originally based mainly on data obtained for isothermal horizontal flow at pressures close to atmospheric (to 50 psi), normal temperatures, and pipe diameters to one inch using air and eight different liquids. In order to apply these equations to singlecomponent two-phase flow with mass transfer between phases, Martinelli... 

Figure 2-20 Plot of log k (obtained from isothermal reaction data in the previous figure) versus liT. The slope of this line is -E/R, and the intercept where 1/T = 0 is the pre-exponential factor kg.

The adsorption of reactant in the Cd(II)-I system [44], and the influence of electrolyte concentration (1-6 M NaCl04) on the parameters of the Frumkin isotherm system were investigated [45]. The obtained data indicated that the maximum surface concentration of Cdl2 (/kaax = 1 x... 

From the experimental kinetic data obtained by isothermal and adiabatic calorimetry, a technique for determining the kinetic and thermodynamic parameters for a somewhat simplified Scheme (8) has been developed. Table 2 presents thermodynamic parameters for two models and a real systems. 

The idea that the fractional free-volume at glass temperature as found experimentally depends on the mode of molecular motions was put forward in 196746 47 as a result of calculating/g from data obtained from isothermal volume relaxation for some polymer systems. By estimating average relaxation time at different temperatures it was possible to find the fractional free-volume/g at Te according to WLF theory. If we accept the validity of the theory as regards the universal dependence of the reduction factor aT on (T - Tg), then on the basis of data on Aa and theoretical values aT calculated from universal values of the coefficients C and C, it is possible to make an estimate of/g. In this case the value found corresponds to the universal one. If, however, we use the experimental values aT, the fractional free-... 

The first directly-measured evidence that C—H bond rupture in the methyl group is the rate-determining step in the thermal de compn of TNT has been obtained with isothermal differential scanning calorimetric (DSC) analysis using deuterium isotope effects (Ref 96), DSC analysis has also been used to determine the kinetic parameters of thermal decompn (Ref 92). Others (Ref 101) have also studied the mechanism of the reaction using the deuterium isotope effect. Data are available on heat generation in... 

In addition, comparison of data obtained by isothermal titration and melting profile methods must assume... 

Practically all experimentally obtained data on chemisorption isotherms may, in fact, be expressed in either Eq. (74) or Eq. (76). 

The two data sets fall on a single curve (within experimental error), indicating that the fluid density is the prime factor in determining the value of n. The data for the other fluids was obtained under isothermal conditions. 

W have previously reported (3, 5) studies of the adsorption of argon at 77° and 90° K on muscovite mica which had been treated to replace the exchangeable surface potassium ions with other cations. The adsorption isotherms and thermodynamic functions evaluated from them showed significant differences among the various ion exchanged forms of mica. We have now obtained data for the adsorption of krypton on these substrates, and wish to discuss the differences in the behavior of the argon-mica and krypton-mica systems. 

Equation (4.47) and obtain an isotherm equation in which the distribution function, (B) was expressed in an analytical form (Huber et al., 1978 Bansal et al., 1988). In principle, f(fl) provides an elegant basis for relating the micropore size distribution to the adsorption data. However, it must be kept in mind that the validity of the approach rests on the assumption that the DR equation is applicable to each pore group and that there are no other complicating factors such as differences in surface heterogeneity. 

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. 

Figure 1.23. Plot according to [1.5.341 for the isotherms of fig. 1.22 including three more temperatures. Open circles are obtained from isotherm data with V(mon) = 40 pmol/g for the two low temperatures and 39 pmol/g for the higher temperatures. Open triangles are obtained from isotherm data at 0 and -19.7°C with V(mon) chosen as 50 pmol/g.

Although GC techniques are very fast compared to the conventional methods, any error in the experimental data is magnified and propagated in the calculations due to integration. There are also problems associated with polynomial fitting for the retention volume in terms of composition in order to obtain binary isotherms [5,7]. 

Figure 8 Structural relaxation times for quench-cooled glassy disaccharides as determined from enthalpy relaxation data. Structural relaxation times were obtained by a fit of the data to the stretched exponential function (see [37,50]). ( ) Data for sucrose obtained by differential scanning calorimetry on annealed samples [37], (O) Data for sucrose obtained by isothermal microcalorimetry [50]. (A) Data for trehalose obtained by isothermal microcalorimetry [50].

Less favorable is the situation with analyses of obtained data, viz. the most common cases of solids containing both micro- and meso-pores. Here the Brunauer-Emmet-Teller (BET) isotherm is nearly always incorrectly applied. The t-plot method [1] is only of limited applicability because it requires knowledge of adsorption isotherms on non-porous solids of the same chemical nature as the measured sample (master isotherm). Only recently it was shown in this Laboratory [2] that an extension of BET isotherm together with non-linear parameter fitting could solve this problem. 

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