Isothermal behavior, quasi

Strongly exothermic or endothermic reactions may cause a temperature profile within the catalyst layer, and reaction rates and thus selectivity may be altered. The importance of the temperature profile depends on the reaction rate, the layer thickness, the reaction enthalpy, AHR, the activation energy, E, and the thermal conductivity of the porous catalyst, le. To achieve what is considered quasi-isothermal behavior, the observed rate, reff, must not differ from the rate at uniform temperature by more than about 5%. The following criterion, designed for a catalyst layer in a microchannel, can be formulated ... 

In the case of strongly exothermic and endothermic reactions, the reactions may give rise to a temperature profile within the catalytic layer, which is dependent on reaction enthalpy AH ), activation energy ( ), and the thermal conductivity of the porous catalytic material X ). For quasi-isothermal behavior, the observed rate, j, should not differ from the rate that would be observed at constant temperature by more than 5%, and thus the resulting criterion for quasi-isothermal catalytic wall behavior is given by... 

The methyl esters of stearoylalanine [1] and stearoylserine [2] were considered as quasi-racemate candidates because of their slight structural differences. No quasi-racemate behavior was observed, however, in their force-area isotherms although clear diastereomeric discrimination was seen for this combination (Verbiar, 1983). We have seen no indication of quasi-racemate behavior for any other mixed chiral monolayers. 

The cyclic voltammograms of these systems display quasi-reversible behavior, with AEv/v being increased because of slow electrochemical kinetics. Standard electrochemical rate constants, ( s,h)obs> were obtained from the cyclic voltammograms by matching them with digital simulations. This approach enabled the effects of IR drop (the spatial dependence of potential due to current flow through a resistive solution) to be included in the digital simulation by use of measured solution resistances. These experiments were performed with a non-isothermal cell, in which the reference electrode is maintained at a constant temperature... 

In an open system such as a CSTR chemical reactions can undergo self-sustained oscillations even though all external conditions such as feed rate and concentrations are held constant. The Belousov-Zhabotinskii reaction can undergo such oscillations under isothermal conditions. As has been demonstrated both by experiments [1] and by calculations 12,3] this reaction can produce a variety of oscillation types from simple relaxation oscillations to complicated multipeaked periodic oscillations. Evidence has also been given that chaotic behavior, as opposed to periodic or quasi-periodic behavior, can take place with this reaction [4-12]. In addition, it has been shown in recent theoretical studies that chaos can occur in open chemical reactors [11,13-17]. 

Several common local sorption processes have been examined here by way of illustrating such effects sorption by geologically immature soft-carbon organic matter, which results in quasi-linear sorption isotherms, sorption by common mineral phases within concentration regions where linear behavior is exhibited, and sorption by diagenetically altered hard-carbon organic matter... 

In most cases, chromatography is performed with a simple initial condition, C(f = 0,z) = q t = 0,z) = 0. TTie column is empty of solute and the stationary and mobile phases are under equilibrium. There are some cases, however, in which pulses of solute are injected on top of a concentration plateau (see Chapter 3, Section 3.5.4). The behavior of positive concentration pulses injected xmder such conditions is similar to that of the same pulses injected in a column empty of solute and they exhibit similar profiles. Even imder nonlinear conditions (high plateau concentration), a pulse that is sufficiently small can exhibit a quasi-linear behavior and give a Gaussian elution profile. Its retention time is linearly related to the slope of the isotherm at the plateau concentration. Measuring this slope is the purpose of the pulse method of measurement of isotherm data. Large pulses may also be injected and they will give overloaded elution profiles similar to those obtained with a column empty of solute. 

Fig. 4.123. The reversing melting is observed in the low-temperature range, where one expects the lower-molar-mass crystals to melt. The quasi-isothermal TMDSC experiments with decreasing temperature allow more perfect crystals to grow, and only a gradually changing reversing heat capacity is observed on cooling and second heating, similar to the behavior of extended-chain crystals of paraffins and polyethylene (see Sect. 6.2.1). Only at perhaps 200 K is the vibrational Cp reached.

Numerous efforts have been made to explain the abnormal behavior of supercritical adsorption isotherms and several theories were proposed. Overheated liquid [9] or quasi-hquid [10] conceptions were used to model the supercritical adsorption isotherms on the basis of the theory available for vapors. However, isotherms with maximum cannot be described in this way. The model based on the Ono-Kondo equation [11] was able to predict an isotherm with maximum, but its parameters were found to be unrealistic from the physical viewpoint [12]. Models based on the equation of state [13] and density functional theory [14] can satisfactorily describe the experimental adsorption isotherms. However, the number of parameters in such models is much larger than 3, the usual number of parameters in conventional isotherm equations. In fact, the multiple model parameters cannot provide the required information about adsorbents regarding their specific surface area, pore-volume and pore size distribution as it was usually done with conventional isotherm models. 

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