Adsorption isotherms static method

Static Involving Use of Adsorption Isotherms BRUNAUER, EMMETT, AND TELLER (B.E.T.). In this method tire surface area is not measured directly, but the number of molecules of the adsorbed substance required to give a monolayer (N) is determined. If the mean area per molecule (a) of the adsorbed substance is known by other means, the area of the solid may... 

This is easy to explain because values derived from the elution partial isotherm only pay regard to the amount adsorbed in the mesopores and the outer surface area. By contrast, the static method is not able to distinguish between these contributions and the micropore part of adsorption. Therefore the obtained values are higher but have no physical meaning whereas the elution values give a more realistic picture. The results for the standard carbon are very similar to the static values. This means that there are almost no micropores and the sorption processes take place in the mesopores and the outer surface area. This is confirmed by the huge difference in the thermodesorption peak of both materials. 

The time required to conduct an interfacial tension experiment depends largely on the properties of the surfactants and less on the chosen measurement method. A notable exception is the drop volume technique, which, due to the measurement principle, requires substantial ly more time than the drop shape analysis method. Regardless of the method used, 1 day or more may be required to accurately determine, e.g., the adsorption isotherm (unit D3.s) of a protein. This is because, at low protein concentrations, it can take several hours to reach full equilibrium between proteins in the bulk phase and those at the surface due to structural rearrangement processes. This is especially important for static interfacial tension measurements (see Basic Protocol 1 and Alternate Protocols 1 and 2). If the interfacial tension is measured before the exchange of molecules... 

Ikeda et al. (1984b) plotted Eq. (4.42) by determining the equilibrium concentrations from adsorption isotherms for S(H), S(NH4), and NH4, and using the pH value to determine [H+]. This plot shows good linearity (Fig. 4.11), which confirms that the mechanism hypothesized in Eq. (4.40) is operational. The kv and k- values for Eq. (4.42) can then be calculated from the slope and intercept of Fig. 4.11, and the kinetic Keq can be determined from the ratio kjk x (Table 4.2). It is important to notice that the values calculated kinetically and statically (equilibrium method) are similar, which indicates that the rate constants one calculates from p-jump experiments are chemical kinetics rate constants. These data also verify... 

In principle, a continuous procedure can be used to construct the isotherm under quasi-equilibrium conditions the pure adsorptive is admitted (or removed) at a slow and constant rate and a volumetric or gravimetric technique used to follow the variation of the amount adsorbed with increase (or decrease) in pressure. A carrier gas technique, making use of conventional gas chromatrographic equipment, may be employed to measure the amount adsorbed provided that the adsorption of the carrier gas is negligible. In all types of measurement involving gas flow it is essential to confirm that the results are not affected by change in flow rate and to check the agreement with representative isotherms determined by a static method. 

The heat of adsorption of Ar was also measured for acidity evaluation. In the case of Ar-TPD, an effect of the probe molecule diffusion in micropores is observed with some samples, such as zeoUtes, at high temperature-programmed rates. The adsorption method is not influenced by diffusion of the adsorbed molecule because the Ar isotherm is measured at static equilibrium. It is also advantageous that the usual BET apparatus can be used to obtain the adsorption isotherm. In addition, the adsorption behavior of Ar is of the Henry type at temperatures around room temperature. 

The primary use of isotherm data measurements carried out on single-component elution profiles or breakthrough curves is the determination of the single-component adsorption isotherms. This could also be done directly, by conventional static methods. However, these methods are slow and less accurate than chromatographic methods, which, for these reasons, have become very popular. Five direct chromatographic methods are available for this purpose frontal analysis (FA) [132,133], frontal analysis by characteristic point (FACP) [134], elution by characteristic point (ECP) [134,135], pulse methods e.g., elution on a plateau or step and pulse method) [136], and the retention time method (RTM) [137]. 

There is a dearth of competitive adsorption data, in a large part because they are difficult to measme, but also because little interest has been devoted to them, as, until recently, there were few problems of importance whose solution depended on their understanding. Besides the static methods, which are extremely long and tedious and require a large amoimt of material, the main methods of measurement of competitive isotherms use column chromatography. Frontal analysis can be extended to competitive binary isotherms [14,73,93-99], as well as pulse techniques [100-104]. The hodograph transform is a powerful method that permits an approach similar to FACP for competitive binary isotherms [105,106]. 

Using this method, we constructed a number of dynamic adsorption isotherms for several proteins on different surfaces. Here we present information for two proteins. The adsorption isotherm for bovine serum albumin (BSA) (87% monomer, 13% dimer described by the supplier as 100% monomer) is shown in Figure 6. A plateau concentration for BSA on an amine/ silane surface was 3.5 mg/m2, which is comparable with monolayer adsorption reported previously in a static system (3). [The effect of flow rate, ionic strength, and temperature is reported elsewhere (18).] Perhaps more interesting are the data for plasma fibronectin (produced and purified extensively in our laboratory), because adsorption characteristics of this protein have not been reported elsewhere. Since it is a protein intimately involved in cellular adhesion, its surface behavior is particularly relevant to implant biocompatibility. We found a plateau uptake of approximately 7.0 mg/m2 on both amine and dimethyldimethoxymethylsilane, and based on the assumption of monolayer coverage and a published axial ratio (20), we calculated that the molecule has dimensions of approximately 130 X 80 X 100 A. 

In the thesis of polyethylenimine-coated supports there is variability introduced by the polyamine as well as the cbrace of ooss-linker employed. For instance, cross-linking is prevalent during the polymerization of ethy-lenimine and there is normally a distribution of 25% primary amines, 50% secondary amines, and 25% tertiary amines (.101). Berause of the chemical variability in these stationary phases several methods, such as the use of test solutes of varying hydrophobidty and static adsorption isotherms, have been employed in the duuacterization of these phases (37-40,102). 

The theoretical basis for the chromatographic analysis of adsorption phenomena in gas and/or liquid phase was given by Don DeVault (ref. 1) and Glueckauf (ref. 2, 3). The mathematical procedure developed by these authors enables one to determine the adsorption isotherm of a solute from its elution profiles in column chromatography. The experimental procedure required for this method is far less laborious than those for the conventional static methods of adsorption measurement, and many experimental works have appeared since (ref. 4, 5). Many of these works, however, dealt with adsorption from gaseous phases, and applications to liquid phases are scarce (ref. 6, 7). 

The extent of adsorption of eommereial surfaetants developed for use in reservoir recovery proeesses ean vary from near zero to as high as 2.5 mg/g. Surfactant adsorption on rock surfaces is usually measured by either static (batch) or dynamic (coreflood) experiments. The static adsorption method, employing crushed rock samples, is essentially the classical method for determining adsorption isotherms at the aqueous solution/solid interface and involves batch equilibrations of particles in solutions of different initial surfactant concentration. The dynamic coreflood method is more involved but employs a greater solid to liquid ratio and is therefore more sensitive, see references [J69-J7J]. Temperature, brine salinity and hardness, solution pH, rock type, wettability, and the presence of a residual oil phase have all been found to influence the extent of adsorption of different surfactants [116,152,172],... 

A relatively recent development in the determination of acid site strength and quantity is the application of Ar adsorption (39). This technique, which is related to Ar TPD but stated not to suffer limitations of diffusion in micropores since it involves the determination of Ar adsorption isotherms under static equilibrium, involves the determination of heats of adsorption extracted from Henry or Langmuir regimes. Listed advantages of this method are that it can be applied... 

The enthalpies of adsorption for carbon dioxide on active carbon were determined from adsorption isotherms at 25 and 30°C the values vary between 40 and 25 kJ mol with increase of coverage [89]. The differences from the static method results are 2 kJ mol". The results obtained for adsorption of argon, oxygen, nitrogen, carbon dioxide and methane on carbon and silica at infinite dilution do not agree with calorimetric and isosteric data, the difference reaching as much as 2 kJ mol" [90] (Table 4.8). Some contributions [88, 91, 92] mention greater precision... 

The method of determining adsorption isotherms described above is less accurate than frontal analysis, which is often preferred [133—144] because it ignores all kinetic factors and volume changes of the gas phase caused by adsorption of vapours. However it is considerably faster and simpler, and the adsorption isotherms it yields correspond to those of static methods provided that experimental conditions are so chosen that the errors are minimized [1,126]. Sinailarly, due to the short contact time of adsorbent and adsorbate, GSC allows the determination of adsorption isotherms whenever the injected substance undergoes both adsorption and dissolution in polymer provided that the latter process is slow. 

The BET Brunauer, Emmett, Teller) (26-28) method of-calculating speciiic surface area from an adsorption isotherm has been mainly applied to nitrogen as the adsorbate at -196 C, Innes (29) developed a rapid automatic technique for measuring the isotherm. Lippens and Hermans described suitable apparatus in detail (30, 31). Also, commercial equipment has been developed using the static equilibrium method, which does not require calibration and gives surface area by automatic digital readout (e.g., Micromeritics, Inc.). 

Markowski et al. (44) have applied sandwich TLC for the evaluation of adsorption isotherms, comparing this method to the breakthrough and static methods. All three methods have given similar results. 

The CONTINUOUS FLOW method doses adsorptive onto the sample at a constant and pre-determined flow rate which is low enough to enable quasi-equilibration to occur. The flexibility of this technique is enhanced through the use of a mass flow controller,as is used in the OMNISORP instruments. Rouquerol et al (3) have shown that no appreciable difference is found in the isotherms when compared to static method if the correct mass flow controller setting is used. They also describe how this setting can be confirmed. Theoretically resolution with this method is infinite in practice it is normally unnecessary to exceed 1000 data points but the great advantage of this method is that it is fast. Analysis times are usually significantly less than with the static method. 

In principle, dynamic aspects of polymer adsorption can be determined with the same methods as one uses to characterize static properties of the adsorbed polymer layer. Fleer et al. [1] have presented an overview of experimental methods for the determination of adsorption isotherms, the adsorbed layer thickness, the bound fraction, and the volume fraction profile. However, in order to determine the dynamics of some property of the adsorbed polymer layer, the characteristic time of the experimental method should be shorter than that of the process investigated. Moreover, flie geometry of the experimental system is often of crucial importance. These factors severely limit the applicability of some experimental methods. In this section we will particularly review those methods which have been successfully applied for characterizing the kinetics of polymer adsorption. 

Recently, some techniques have been presented in the literature making use of volumetric titrations of surface sites in liquids, of different polar and protic characteristics, to determine the amount of acid sites and relevant acid strength effective acidity). Two different methods will be here discussed the first one is based on a pulse liquid chromatographic method (a dynamic method) [8] and the second one on a liquid recirculation chromatographic method (a Masi-static method) [9]. When surface acidity studies are concerned, the measurements may be performed in apolar, aprotic liquid (like cyclohexane), for the determination of the intrinsic acidity, or in several other liquids with polar/protic characteristics, for the determination of the effective acidity. Basic probes of different basicity (following the pK scale) may be used (e.g., 2-phenylethylamine, PEA, aniline, AN, pyridine, PY, etc.). Titration temperatures may be varied from room temperature (r.t.) up to the normal boiling point of the liquid used in order to calculate, from the collected isotherms of adsorption, the isosteric heats of adsorption which can be related to the acid strength of the surface sites [10, 11]. 

The adsorption equilibria measurements of N2 and CO2 on activated carbon were performed using a standard static gravimetric method. Further details of these measurements are reported elsewhere." " The Sips isotherm extended to multi-component adsorption was adopted to fit the experimental equilibrium data (Table 9.2). This model has the Langmuirian form applied to non-uniform surfaces and it has been extensively used to model gas adsorption on micro-porous adsorbents and PSA systems. Optimal parameters were found for the adsorption isotherm model, by fitting simultaneously all the data at multiple temperatures. A global isotherm was obtained for each species as illustrated in Figure 9.15." ... 

In this thesis, we will use force field based computational methods. This means that we know exactly all interactions between the atoms of our system. Once we know these interactions, we are able to calculate a variety of static and dynamic properties like heats of adsorption, adsorption isotherms, and diffusion coefficients. In general, there are two methods to obtain a molecular force field ... 

Both kinetic and equilibrium experimental methods are used to characterize and compare adsorption of aqueous pollutants in active carbons. In the simplest kinetic method, the uptake of a pollutant from a static, isothermal solution is measured as a function of time. This approach may also yield equilibrium adsorption data, i.e., amounts adsorbed for different solution concentrations in the limit t —> qo. A more practical kinetic method is a continuous flow reactor, as illustrated in Fig. 5. 

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