C-curve isotherm

The C-curve isotherm is similar to the H-curve, being characterized by a linear increase, but also passing through the origin. This behavior may be due to a proportional increase of the adsorbing surface as well as to surface accessibility. 

Figure 4.8. Sorption isotherms and concentration profiles, (a) Linear isotherm Gaussian profile, (b) Curved isotherm Mailing , (c),-Curved isotherm fronting ...

The C-curve isotherm is characterized by an initial slope that remains independent of the concentration of a substance in the soil solution until the maximum possible adsorption. This kind of isotherm can be produced either by a constant partitioning of a substance between the interfacial region and an external solution or by a proportional increase in the amount of adsorbing surface as the surface excess of an absorbate increases. The example of parathion (diethyl p-nitrophenyl monothiophosphate) adsorption in Fig. 4.1 shows constant partitioning of this compound between hexane and the layers of water on a soil at 50 per cent relative humidity. The adsorption of amino acids by Ca-montmorillonite also exhibits a... 

C-curve isotherm, this time because the adsorbate can penetrate the interlayer regions of quasicrystals, thereby creating new adsorbing surface for itself. ... 

Fig. XIII-15. Adsorption isotherm for sodium dodecylbenzenesulfonate on cotton. Curve I, 30°C curve II, 0°C. (From Ref. 64.)...

Fig. 5.5 Adsorption isotherms of butane at 0°C on Iceland Spar ground for 1000 h. Curve (i), the solid was outgassed at 25°C. Curve (ii), the solid was outgassed at 1S0°C. O, adsorption p Q, desorption.

This equation is a straight line whose slope is 1/n and whose intercept is k at C = 1. Therefore, if straight line will normally be obtained. However, there are occasions, as explained later, when this is not true. The straight and the curved isotherm lines provide valuable information for predicting adsorption operations. 

Figure 5.30. Schematic drawing showing the construction of an isothermal transformation diagram from measurements of the progress of the transformation at various constant temperatures. This may be done, for instance, by metallographic examination of several specimens, quenched from the 7-field quickly enough to miss the nose of the C-curve and then isothermally annealed for various length of time. Notice that curves for the transformation of different samples may be shown on the same diagram and that more complex trends may be observed in real diagrams of specific alloys. In the example reported, Ms is the temperature at which the alloy will begin to show the martensitic transformation, Mf indicates the temperature below which no additional martensite forms.

Fig.Z Adsorption isotherms of the lattice gas model with (a) nearest neighbor attractive interaction, and (b) nearest neighbor repulsion and next nearest neighbor attraction of the same strength. Only 0 < 1/2 is shown because the isotherms are antisymmetric around the point 0 = 0, + e = 0 in this case, (c) Adsorption isotherms of a lattice gas with non-additive interactions with P = 1.5 (cf. text) for fixed reduced temperature, T/T,. Dotted curve describes the two branches 0 of the coexistence curve separating the two-phase region from the one-phase region. Cases (a), (b) are taken from Binder and Landau, case (c) from Milchev and Binder. )...

Fig. 8. Plots of fractional conversion against log time from isothermal experiments for BADGE/ DDM. Points are experimental solid curves are the 185 °C curve shifted horizontally to superimpose on experimental points (From Ref.77), Fig. 4)...

Figure 2.19. Isotherms of polycaproamide (a) and polyethylene terephthalate) (b) crystallization at different temperatures, a 180°C (curve 1) 184°C (curve 2) 188°C (curve 3) b 180°C (curve 1) 200°C (curve 2) 210°C (curve 3) 220°C (curve 4). Solid lines are calculated in accordance with Eq. (2.48) points are experimental data.

The isotherm EFGH at 21.5 C shows a similar behaviour except that now the liquefication commences at a higher pressure and the horizontal portion FG, representing decrease in volume, becomes smaller. At still higher temperatures, the horizontal portion of the curve becomes shorter and shorter until at 31.1 C it reduces just to a point (represented by X). At this temperature, therefore, the gas passes into liquid state imperceptibly. Above 31.1 C, the isotherm is continuous. There is no evidence of liquefaction at all. Andrews concluded that if the temperature of carbon dioxide is above 31.1 C, it cannot be- liquefied, no matter how high the pressure may be. He called 31.1 C as the critical temperature of carbon dioxide. Since then, other gases have been... 

The comparison of W(C) dependence with Ao(C) isotherm gives a relation between formation of black spots and films, and the adsorption layer state. It has been shown [332] that the W(Q dependences for black spot and black films of a very small radius (25 pm) coincide. The comparison of the W(C) curve of CBF from NaDoS (see Fig. 3.78) with the surface tension isotherm of the same surfactant (see Fig. 3.77) indicates that black spots begin to form when the state of adsorption layers deviates from the ideal one (Henry s region in Aa(Q isotherm). The probability for observation of a black film steeply increases with the increase in surfactant concentration to about 10 5 mol dm 3 where the adsorption layer saturation is... 

The adsorption isotherms of NaDoS vacancies calculated in [424], from Eq. (3.13) with the aid of the values of Q and Co given previously are shown in Fig. 3.90 for 10°C (curve 1), 22°C (curve 2) and 30°C (curve 3). The equilibrium NaDoS concentrations Ce above which NaDoS foam bilayers of infinitely long lifetime are to be obtained are marked by arrows. In practice, this cannot be achieved because CMC < Ce. The hatched area shows the investigated concentration interval in which the gas of NaDoS vacancies in the foam bilayer undergoes a 2D first-order phase transition from a dilute phase (existing metastable bilayer) into a condensed phase (ruptured bilayer). 

Gaussian profile, (b) Curved isotherm tailing. (c) Curvcd isotherm fronting ... 

Of these shapes, long linear isotherms are uncommon for adsorption on solids (Just like type c in fig. 2.8) and occur only if penetration into the solid takes place, leading to a Nemst-type distribution law as in liquid-liquid partitioning, see (1.2.20.1]. Linearity is also found for the (relatively short) initial parts of all isotherms on homogeneous surfaces. We shall call them, as before, Henry isotherms or the Henry parts of curved Isotherms. 

Adsorption of glutathione, which is an acidic peptide, on the crosslinked chitosan fiber (ChF) appeal technically feasible. The experimental equilibrium isotherm (q-C curve) for adsorption of glutathione on ChF was independent of the initial concentration of glutathione. But tite adsorbed amount of glutathione on ChF was effected by the pH value of the solution on tire q-pH curve, significantly. It appeared that the adsorption of glutathione was correlated by the Langmuir equation well. 

The experimental equilibrium isotherm q-C curve) for adsorption of glutathione on ChF was independent of the initial concentration of glutathione. 

Comparison between experimental data (symbols) and curve calculated with the equilibrium-dispersive model, (b) Effect of temperature on the frontal analysis of the (-) enantiomer from right to left, 30, 40, and 50° C. (c) Adsorption isotherms of (-) enantiomer at 30, 40, and 50°C N = 30,... 

From the slope of the linear portion of the y-log C curve (just below the cmc), the surface excess (number of moles of surfactant per unit area at the Uquid/air interface) can be obtained. Then, using the Gibbs adsorption isotherm, dy... 

Rh2(bza)4(2-epyz)](2-epyz= 2-ethyl-pyrazine). tion (b, c), C02 isotherm curves with large leap Contact of C02 at ethyl lever on the channel during phase transition (d), and channel surface (a), topological change of inner space direction change in a single-crystal. 

Fig. 1. Adsorption isotherms on iron catalyst (No. 973) for various gases near their boiling points (4a). Curve lA is for the total CO adsorption at — 183°C. Curve 16 represents the adsorption obtained at —183 C. after evacuating at — 78 C. the sample for which the isotherm lA had been obtained. Solid symbols are for desorption.

It is seen from the von Szyszkowski-Langmuir surface tension isotherm, Eq. (2.41), that at a given temperature the shape of the surface tension isotherm is determined by only one parameter cOg =cO =cd. The other parameter b enters this equation as a dimensionless variable be, in combination with the concentration. Therefore, the value of b does not affect the shape of surface tension isotherm, and only scales this curve with respect to the concentration axis. It should be noted that this dependence on b is characteristic to all the equations presented above. The dependence of the surface pressure isotherm on the molar area co is illustrated by Fig. 2.1. It is seen, that the lower ro is, hence the higher the limiting adsorption T = 1/co, the steeper is the slope of the n(c)-curve. 

Collet et al. (2005) stated that the study of pectinesterase inactivation behavior is important because pectinesterase is responsible for juice cloud stability loss, is composed of several isoenzymes, and occurs naturally in orange. Freshly squeezed juice of Pera orange (Citrus sinensis) was pasteurized at temperatures of 82.5, 85.0, and 87.5°C. At least five runs with different holding times were performed for each temperature. As the isothermal curves obtained showed deviations from the expected first-order kinetics, the data was statistically treated by applying a nonlinear regression, and the estimated best fit was a three-parameter-multicomponent-flrst-order model. At 82.5°C, the isothermal curves showed a nonzero asymptote of inactivation, indicating that at this temperature the most heat-resistant... 

Figure 4.1. General classes of adsorption isotherms. 5 turve, data courtesy of C. S. LeVesque L curve, data from I.C.R. Holford et al. H curve, data from J. Garda-Mirayagaya and A. L. Page, Sorption of trace quantities of cadmium by soils with different chemical and mineralogical composition Water, Air, and Soil Pollution 9 289 (1978) C curve, data from B. Yaron and S. Saltzntan, Influence of water and temperature on adsorption of parathion by soils Soil Sci. Soc. Am, J, 36 583 (1972).

Fig. 4-90 Quotient of Loss Q of the Isothermal Thermogravimetry at 165 °C Curve 3 Bitumen B80/2 Curve 4 PMB/2...

Now, if dissolution was effected at an intermediate temperature, 37°C, an isotherm having an intermediate shape and position was obtained (Figure 6.19, curve c). The crystals, while essentially free from degenerate forms, were rather more heterogeneous in size than for 7 = 35°C. Repetition of the dissolution-crystallization cycle gave a curve (filled circles) which was consistent with an increase in the concentration of nuclei N at least the first part of the isotherm was superimposable on curve b by shifting the log t axis. 

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