Determination from isotherms

Experiments Sorption equihbria are measured using apparatuses and methods classified as volumetric, gravimetric, flow-through (frontal analysis), and chromatographic. Apparatuses are discussed by Yang (gen. refs.). Heats of adsorption can be determined from isotherms measured at different temperatures or measured independently by calorimetric methods. 

Equation constants determined from isotherm curve fitting... 

Figure 6. Dimensionless interaction parameters as determined from isothermal fits at various temperatures ((- -) KBr-water ( ) NaCl—water)...

Figures 7 and 8 illustrate the behavior of the intercepts and slopes from Figure 6 corresponding to the functional forms of Equation 29. The error bars on Figures 7 and 8 represent one standard deviation as determined from isothermal fits. The intercepts have deviations on the order of 0.5% which is consistent with an apparatus analysis. The slopes, however, have much larger uncertainties ranging up to 15%. Increasing the pressure range would greatly reduce this large and important error.

N2 02, neopentane) in the zeolites A, X, L, mordenite, omega, and a synthetic offretite type have been determined from isotherms. These have been compared with the void volumes calculated from the known crystal structures. For most adsorbates the measured and calculated void volumes are in good agreement. However, helium and nitrogen exhibit anomalous behavior. A void volume-framework density relation for zeolites is given. 

In this work the temperature dependencies of Pitzer parameters and equilibrium constants were largely determined from isothermal data sets that were then fit to the following equation ... 

The subscript G specifies elasticity determined from isothermal equilibrium measurements, such as for the spreading pressure-area method, which is a thermodynamic property and is termed the Gibbs surface elasticity, EG. EG occurs in very thin films where the number of molecules is so low that the surfactant cannot restore the equilibrium surface concentration after deformation. 

Until around 1995, it was unusual to find kinetic data determined from isothermal microcalorimetric studies - and this was especially true for long, slow reaction systems. However, the modem microcalorimeter has excellent long-term stability (1 /xW or better over 24 h) and hence slow reactions can readily be investigated even those for which a complete reaction is not observed. Willson et al. showed that quantitative kinetic and thermodynamic data could be determined for reactions that had half lives of up to 2500 years. Commencing with a conventional (here simple for clarity) rate expression such as... 

Pan et al. [34] used the nonlocal density functional theory (DFT) [35] and the three-process Langmuir model (TPLM) [36] to predict the adsorption heats of propane and butane on carbon and compared these results with experimental data determined from isotherms measured on BAX-activated carbon (Westvaco) in the 297—333 K temperature interval. Both models agreed in showing that the adsorption heat for butane was c. 10 kj/mol higher than that of propane at the same loading. The satisfactory agreement found prompted the authors to propose the use of the DFT method as it requires only one experimental isotherm in contrast with the numerous isotherms required by the classic technique. 

The composition of the residue is C6HI)6O0)i. A mechanism including chain breaking at the ether linkage has been proposed. Subsequent reactions of the phenoxyradical give crosslinking and formation of C02, CO, CH4, H2 and H20. The proportion volatile sublimate residue is about 13% 66% 21%, as determined from isothermal experiments at 450, 550 and 620°C. 

The heats of formation of potassium, rubidium, and caesium hexachlorotellu-rates(iv) have been found from their heats of solution, and those of crystalline TeCU and the metal chlorides determined from isothermal calorimetry. Thermal and elastic properties of the alkali-metal hexachlorotellurates have also been investigated. Spectroscopic studies on a series of dialkyltellurium tetraiodides have been carried out. ... 

Generally, the Fanning friction factor/is determined from isothermal pressure drop data (no heat transfer across the core). The hot friction factor/versus Re curve should be close to the isothermal/versus Re curve, particularly when the variations in the fluid properties are... 

The TMR can also be determined from isothermal DSC data - A test is initially carried out using scanning DSC to obtain the overall heat released, A//, and the specific heat, C. Several isothermal DSC experiments (Figure 4.30) are then carried out at different temperatures near to the exotherm onset temperature detected in the scanning DSC run. 

Fig. 10.45 Transition temperature as a function of oscillatory frequency during temperature ramp with a rate 1 °C/min. The triangle point at zero frequency is the transition temperature determined from isothermal frequency sweep (Wei et al. 2011)...

BET surface areas and pore structures of Al-CT and Si-CT were determined from isotherms of nitrogen sorption. The samples after calcination at high temperature were used, instead of the samples degassed at high temperature, since the basal spacing of the degassed... 

Figure 6. Critical temperature of HMX and HMX—dg determined from isothermal time—to-explosion tests. ...

The term G in Eq 4.16 can be determined from isotherms of sorption of free polymer, filler, and filled polymer. Based on the data on the sorption by free polymer, it is possible to find the magnitude of NiAGi,g + N2AG2,s, and from the data on the sorption by filled polymer, NsAGi g + N4AGr4,g + N2AGg can be found,... 

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