Isotherm from mixtures

It has been shown by Harvey et al. (1989) that incorporation of palmitic acid into a monolayer spread from stearoylserine methyl ester (SSME) breaks up intermolecular SSME interactions. The palmitic acid acts as a two-dimensional diluent. Figures 52(A-C) give the Yl/A isotherms for mixtures of FE and SE C-15 6,6 -A with palmitic acid. Dilution of the monolayer cast from the second eluting isomer with 15 mol% palmitic acid separates the diacid molecules from one another on the water surface and perhaps allows for the expression of their stereochemically dependent conformations. The mixed film (15% palmitic acid/85% C-15 6,6 -A) expands at low II and behaves in much the same manner as the single-component monolayer (C-15 6,6 -A) behaves at 30°C. Addition of 15 mole% palmitic acid into a monolayer cast from the FE C-15 diacid has little effect on its energetics of compression, indicating a stronger intermolecular interaction afforded by its stereochemically dependent conformation at the air-water interface. 

Investigation of thermodynamic behavior of monolayers formed from mixtures of bis[2-(n-hexadecanoyl)ethyl]methyl(4-vinylbenzyl) ammonium chloride (1) and dioctadecyl-dimethylammonium bromide (5) serves as the second example [116]. The determined surface-pressure/surface-area isotherms of mono-layers prepared from (1) and (5) and from their mixtures are given in Fig. 8. The isotherms showed the expected behavior following the liquid state there was a transition to the solid state in the region of 20-36 mNm 1. This transition was characterized by a pressure, and by a corresponding area, Aj. All isotherms intersected in the vicinity of 30 mNm-1 and, at surface-pressure/surface-area... 

Surface pressure/area isotherms of mixtures of the cationic lipid (20, n = 12) with distearoylphosphatidylcholine (DSPC) are shown in Fig. 30. For all mixtures only one collapse point is observed. The collapse pressure increases continuously with increasing amount of DSPC, indicating miscibility of the two components. Plotting A versus molar ratio (Fie. 3D results in considerable deviation from linearity, which also suggests miscibility of the two compounds in monolayers. This is also confirmed by the fact that the polymerization rate, as measured by the increase of optical density at 540 nm, is reduced by a factor of 100 when the DSPC molar ratio is increased from 0 to 0.52,... 

Thus, the passage from an adsorption isotherm of a pure substance to the corresponding adsorption isotherm of a mixture is very easy, supposing that the model of a nonuniform surface is applicable and adsorption coefficients are proportional. If, for instance, adsorption of pure gas A is described by the Freundlich isotherm (135), then for adsorption of A from mixture... 

Example 6.7 Binary and ternary isothermal gas mixtures For a binary mixture of gases under isothermal and isobaric conditions and without shear forces, from Eq. (6.213) we have... 

Single-component isotherm parameters cannot always predict elution profiles with satisfied accuracy [122, 123], Therefore, to be able to predict accurate overloaded multi-component elution profiles where competition occurs competitive adsorption isotherm parameters are often necessary. Measurement of isotherms from a mixture is also often necessary because the pure enantiomers are not always accessible in large quantities. However, there exist only a small number of reports on the determination of multi-component adsorption isotherm parameters. FA can be used to determine binary isotherm data but it is time-consuming. The PP method is an alternative method to determine isotherm parameters from binary mixtures. It has been reported that the PP method works well up to weakly non-linear conditions [118, 119],... 

There are, so far, only two reports on the determination of isotherm data from mixtures containing more than two components. In both cases, the FA method was used for ternary mixtures [135, 136], There are no reports on the experimental determination of adsorption isotherms for quaternary mixtures using any chromatographic method. The competitive quaternary adsorption isotherm parameters could be very valuable for the separations of the four isomers of a compound with two chiral centers, or for the preparative separation of two compounds in the presence of one or two impurities. 

Fig. 2.17 Procedure to determine the multi-component isotherms from pure component data with the IAS theory for binary mixtures.

For non-reactive, isothermal, particle mixtures it is customary to assume that all the relevant internal variables can be calculated in some way from the particle volume or diameter. It is natural to use the particle diameter as inner coordinate for the population balance analysis because this choice of inner coordinate coincides with the classical kinetic theory of gases. This inner coordinate is especially useful describing solid particle and incompressible fluid particle dispersions. A statistical description of dispersed multiphase flow can then be obtained by means of a distribution function fd dp,r,t), deflned so that the number of particles with diameters in the range dp and dp + d dp), located in a volume dr around a spatial location r at time t is f dp, r, t)d dp)dr. 

Fig. 22 7i - A isotherms of mixtures of DMPC/DSPE-PEG2000 from 10 to 100mol% DSPE-PEG2000, where the film balance transitions are plotted for each isotherm and the viscoelastic transitions are plotted for 40-100 mol%. The transitions only coincide at 100% DSPE-PEG2000. The different trends underlie the fact that the high pressure transition and viscoelastic transition signify different physical phenomena [42] (modified, with permission from the American Chemical Society)...

Composite adsorption isotherms from binary liquid mixtures... 

Adsorption isotherms of pure N2 and 99% O2 are presented on Figure 2. The selectivity towards N2 is noticeable. On the same figure, the amounts of N2 and O2 adsorbed from a mixture (equilibrium concentration - Cn = 41%) are drawn as functions of the total pressure, to. u2. . illustrate the difference of adsorption from mixtures compared with... 

Fig. 3.76 illustrates surface tension isotherms for mixtures of CiqEOj with Ci2S04Na in 0.01 M NaCl. The agreement between values calculated from the simple Eq. (3.41) and the experimental data is very satisfactory. Comparison of the results calculated from the approximate equations (3.41) and (3.55) with the exact results from Eqs. (3.28) - (3.31) (see Figure 3.65) shows that both models give quite similar results. 

A concerted effort is presently needed to study the mechanisms influencing adsorption behavior in protein mixtures. Does adsorption from mixtures behave as the sum of independent adsorption events determined by specific affinity constants charactertistic of each species Can such a simple explanation suffice to explain the peak in adsorption isotherms seen for fibrinogen from plasma ("the Vroman effect") and also from binary mixtures (56,57) If the differences in adsorption behavior of mixtures compared to single adsorbates are better understood than at present, a greater degree of control of the adsorption process to achieve a desired end (e.g., selection of a desired protein) may be possible. For example, if the Vroman effect is a general feature of all protein mixtures, then clearly there is an optimum concentration for adsorption to achieve the greatest selectivity. 

ABSTRACT. An isosteric sorption system has been used to study the sorption of methane, ethane, ethene, propane, N2 and CO2 and some of their binary mixtures in silicalite-1. Isotherms of some of these sorbates have been determined at equilibrium pressures up to 20 atmospheres. Isosteric heats of sorption have been obtained from the slopes of the isosteres. Separation factors calculated from the Henry s Law constants determined from the initial slopes of the single conq>onent isotherms are found to be in good agreement with experim tal separation factors. The Langmuir-Freundlich equation has be used to lit the single component data and the Ideal Adsorbed Solution theory has be used to predict a binary sorption isotherm from the respective single component data. Comparison of the sorption behaviour of the hydrocarbons in silicalite-1 and NaY zeolites has been made. 

To obtain the entropy of the mixture, we imagine a component going from the pure state at P, T, into the mixture at same pressure and temperature (see Figure.222). This process increases the volume available to this component, from Vi (the molar volume of the pure component) to V (the molar volume of the mixture). This amounts to expanding this component isothermally from volume V = x. V to volume V. The entropy change for this process is... 

Figure 11.4 Nitrogen adsorption-desorption isotherm for a silica film (designated as ZSU-38) prepared from mixtures of cationic and silicone surfactants. The materials were calcined at 500°C in air for 5 h. The corresponding BJH pore-size distribution...

Mesoporous silica with hexagonal order (designated as ZSU-4) was also prepared from mixtures of the silicone surfactants (Figure 11.1) and a PEO-PPO-PEO copolymer [33], as evidenced by electron microscopy and X-ray diffraction (see Figure 11.5). The calcined ZSU-4 gave a BET surface area of 841 m g". The BJH analysis of the isotherm (type IV with a large type-H 2 hysteresis loop) resulted in an average pore size of 8.1 run. 

Figure 11.13 Mesoporous materials with a bimodal pore-size distribution prepared from mixtures of fluorinated and hydrocarbon surfactants, (a) TEM image (b) Nitrogen sorption isotherms, and (c) pore-size distributions. (Reproduced from Ref [60], with permission).

A distinctive feature of adsorption from solution is that the surface is always completely covered and the sorption mechanism involves competition between the components of the liquid phase. Detailed theoretical interpretation of isotherms from liquid mixtures is most often based on binary liquid systems. The isotherms are measured by immersing the solid sample into the liquid phase. The concentration is monitored by UV, refractive index (RI), or other analytical methods. 

Braeuer, P. Salem, M., and Hatting, P Calculation of single adsorption isotherms from gravimetrically measured binary gas mixture adsorption isotherms on activated carbon at high pressures, Sep. Purif Technol., 12(3), 255-263(1997). 

Comparisons with Adsorption from Binary Gas Mixtures.—Compared to pure gas adsorption, the amount of research concerning adsorption of binary gas mixtures on heterogeneous surfaces is sparse. This is not surprising as the latter requires an understanding of the simpler pure gas systems in fact a popular approach in verifying mixed gas adsorption theories is to predict mixed gas isotherms from pure gas isotherms measured at the same temperature. 

---