Yield isothermal

To scan the hysteresis loop from the adsorption to the desorption isotherm, the sample, immersed in the coolant, is equilibrated with a gas mixture with a relative pressure corresponding to the start of the scan on the adsorption isotherm. The adsorbate concentration is then reduced to a value corresponding to a relative pressure between the adsorption and desorption isotherms. When equilibrium is reached, as indicated by a constant detector signal, the coolant is removed and the resulting desorption signal is calibrated. Repetition of this procedure, each time using a slightly different relative pressure between the adsorption and desorption isotherms, yields a hysteresis scan from the adsorption to the desorption isotherm. 

Typical adsorption isotherms that obey Eqs. (5) and (7) are shown in Figs. 2.1 and 2.2, respectively. It should be noted that a linear Langmuir plot can be obtained by plotting l/[nA]s against 1/P where the slope is 1/k and the intercept is l/[ng] as seen after rearrangement of Eq. (7). The adsorption isotherms are utilized primarily to determine the surface area of porous solids and the heats of adsorption. The isotherms yield the amount of gas adsorbed. By multiplying with the area occupied per molecule... 

In the /3-hydrides with low susceptibihty, explicit temperature effects are probably unimportant. Indeed, all four pressure/NMR shift isotherms taken on the Pd black between 273 and 350 K give the same composition/NMR shift relationship (64) Equation (21) with 5(0) = -34 ppm and 5i = 85 ppm (0.60 < X < 0.75). The NMR isotherms have also been studied in a 0.2-ixm powder at temperatures between 273 and 383 K (66). Only the two lowest temperature isotherms yield a common shift/composition relationship, with 5(0) 76 ppm and 5, 152 ppm. The results for the Pd black... 

In spite of the composite nature of the stratum corneum, its water sorption isotherm is qualitatively identical to those of the more simple protein systems shown, suggesting that water interacts predominately with the protein components of the corneum. This conclusion is supported further by the results of chloroform-methanol (3/1 by volume) extraction which removed as much as 25% of the original dry weight (lipids and low molecular weight water-soluble components) but did not quantitatively alter the isotherm in the low relative humidities (18). The application of the Zimm-Lundberg cluster theory (56, 57) to the isotherm yields additional information as to the state of the sorbed water in the corneum. The tendency of water to cluster is expressed in this theory by the cluster function CiGn ... 

The rate equation specifies the mathematical fimction (g(ur) = ktox AodAt = k f(ur)) that represents (with greatest statistical accuracy. Chapter 3) the isothermal yield a) - time data for the reaction. For reactions of solids these equations are derived from geometric kinetic models (Chapter 3) involving processes such as nucleation and growth, advance of an interface and/or diflEusion. f( ir) and g(ar) are known as conversion functions and some of these may resemble the concentration functions in homogeneous kinetics which give rise to the definition of order of reaction. 

Finally, the Cahn construction analysis (see Sect. 3.1.1) performed for all segregation isotherms, yielded the bare surface energy derivative (—dfs/dc]))s evaluated at different surface concentrations < >s for all four studied temperatures (data sets corresponding to different temperatures are marked by different sym-... 

The present discussion is limited for the most part to low temperature nitrogen adsorption studies and sintering experiments. An adsorption-desorption isotherm yields at once surface area, pore volume, average pore radius and an approximate pore size distribution. Such an isotherm is thus an excellent fingerprint of the physical structure of the catalyst. Sintering curves, or temperature-area plots, obviously demonstrate relative thermal stabilities of these structures under the conditions... 

Since nitrogen adsorption-desorption isotherms provide considerable information on the physical structure of cracking catalysts, the methods used in interpreting isotherm data will be briefly considered. In this connection it will be convenient to refer to the isotherms of some representative cracking catalysts and certain related materials presented in Fig. 2. More detailed plots of the isotherms may be found in subsequent sections. In all cases of hysteresis presented in Fig. 2 the upper portion of the hysteresis loop represents desorption and the lower curve represents adsorption. Catalyst characteristics of principal significance obtained from these plots are listed in Table I. As pointed out above the adsorption-desorption isotherms yield at once surface area, pore volume, and pore radius information. 

A drop of a dilute solution (1%) of an amphiphile in a solvent is typically placed on the water surface. The solvent evaporates, leaving behind a monolayer of molecules, which can be described as a two-dimensional gas, due to the large separation between the molecules (figure C2.4.3). The movable barrier pushes the molecules at the surface closer together, while pressure and area per molecule are recorded. The pressure-area isotherm yields information about the stability of monolayers at the water surface, a possible reorientation of the molecules in the two-dimensional system, phase transitions and changes in the conformation. While being pushed together, the layer at... 

Simons s pioneering efforts anticipated the need for a detailed examination of pore connectivity in carbons. This issue continues to be in need of careful experimental assessment [171-174]. For example. Figure 1.9 reproduces the approach proposed by Ldpez-Ramdn et al. [174] The smaller adsorptive species probes all the pores, and its adsorption isotherm yields the complete PSD. The larger species is excluded from the smaller pores and also from the larger pore that is shielded by the smaller pores. So the PSD obtained using the larger species is (i) zero for pores that are smaller than the molecules of that species and... 

The adsorption isotherm yields the amount of gas adsorbed on the surface. Unless the molecular area occupied by the adsorbed gas is known, the adsorption isotherm yields only relative surface areas rather than the absolute values. This is the reason for using only one gas (nitrogen or krypton) to determine the surface areas of different solids. However, Harkins and Jura [45] developed an absolute method of... 

Denbigh gave some figures for example values of activation energies and showed that for a highest yield of 25 percent under isothermal conditions the optimum temperature trajectory gave over 60 percent thus, more than double the best isothermal yield was possible. 

Isothermal Yield and Selectivity For a network of parallel and/or consecutive reactions mass transfer may affect drastically the target product yield. For consecutive first order reactions and in the absence of mass transfer influence we obtain for the transformation rate of the reactant and the production rate of the intermediate (the target product) ... 

Isothermal Yield and Selectivity The influence of transport phenomena on selectivity and yield is often more important than on the effective catalyst activity. The following analysis is restricted to two important schemes for complex reactions [28] ... 

Behaviors of the 17 vs. log i relation expected under various experimental conditions are reproduced in Figure 9 for the case of the positive Temkin isotherm. The shape is naturally dependent upon the adsorption isotherm, but several conclusions below can be drawn without having precise information concerning the isotherm. Generally speaking, the use of the Temkin isotherm yields smoother curves, and possibly better fit with experiment, than the use of the Langmuir isotherm. ... 

The isothermal yield process the nature of the load drop... 

The Isothermal Yield Process The Nature of the Load Drop... 

Adsorption isotherms of dodecylsulfate (Ds ) and salicylate (Sal ) ions, are presented in Fig. 3. They were fitted with Langmuir isotherm yielding ... 

The interaction between polymers (P) and amphiphiles (A) can be concretely represented by a binding isotherm, and analysis of the isotherm yields an estimate of the change of the thermodynamic variables upon binding. Many mathematical descriptions of binding have appeared but only a few of the more common models are introduced in this section. 

The experimental procedure consists of the determination of the enhancement factor e through two distinct titrations. In the first titration, a rectangular hyperbola describing the change of e as the [E]( to [M]j ratio increases is reported (Figure 5). The treatment of the obtained binding isotherm yields the value of and the product In the second titration, the behaviour of is monitored at fixed macromolecule concentration by changing the metal complex concentration. Results are conveniently expressed under the form of a Scatchard s plot ... 

Applieation of the T equation to the monolayer domain of the ethane isotherm yields a value of equal to that caleulated by the equation BET(N2 ). The term BET(N2 ) indicates the original BET equation applied to the nitrogen isotherm measured at 77.3 K. Evidently, all other equations relate to the ethane isotherm in question. 

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