Isotherms Kiselev

Fig. 2.17 The adsorption of pentane on different adsorbents, (a) Effect of the nature of the adsorbent on the shape of the isotherm (each isotherm is labelled with the name of the adsorbent), (b) Dependence of ajpentane) on the value of parameter C. (Courtesy Kiselev and Eltekov. )...

Fig. 2.19 Adsorption isotherm of benzene on (I) hydrated, and (II) dehydrated siliea gel. (After Kiselev .)...

Examples are provided by the work of Carman and Raal with CF2CI2 on silica powder, of Zwietering" with nitrogen on silica spherules and of Kiselev" with hexane on carbon black and more recently of Gregg and Langford with nitrogen on alumina spherules compacted at a series of pressures. In all cases, a well defined Type II isotherm obtained with the loose powder became an equally well defined Type IV isotherm with the compact moreover both branches of the hysteresis loop were situated (drove the isotherm for the uncompacted powder, but the pre-hysteresis region was scarcely affected (cf. Fig. 3.4). The results of all these and similar... 

Equation (3.73) is the basis of the method proposed by Kiselev for the evaluation of surface area from the Type IV isotherm. If perfect gas behaviour is assumed it becomes... 

Fig. 3.28 The Kiselev method for calculation of specific surface from the Type IV isotherm of a compact of alumina powder prepared at 64 ton in". (a) Plot of log, (p7p) against n (showing the upper (n,) and lower (n,) limits of the hysteresis loop) for (i) the desorption branch, and (ii) the adsorption branch of the loop. Values of. 4(des) and /4(ads) are obtained from the area under curves (i) or (ii) respectively, between the limits II, and n,. (6) The relevant part of the isotherm.

The results of a comparison between values of n estimated by the DRK and BET methods present a con. used picture. In a number of investigations linear DRK plots have been obtained over restricted ranges of the isotherm, and in some cases reasonable agreement has been reported between the DRK and BET values. Kiselev and his co-workers have pointed out, however, that since the DR and the DRK equations do not reduce to Henry s Law n = const x p) as n - 0, they are not readily susceptible of statistical-thermodynamic treatment. Moreover, it is not easy to see how exactly the same form of equation can apply to two quite diverse processes involving entirely diiferent mechanisms. We are obliged to conclude that the significance of the DRK plot is obscure, and its validity for surface area estimation very doubtful. 

Fig. 5.13 Adsorption isotherms on graphitized and on ungraphitized charcoal, (a) Adsorption of water vapour (fc) adsorption of nitrogen at — 195°C. The adsorption values are expressed in cm of liquid adsorbate per gram of adsorbent. (Courtesy Kiselev. )...

Contrary to the last two isotherms, which take into the account interactions between the neighboring molecities ortiy, the Kiselev model assumes the singlecomponent localized adsorption, with the specific lateral interactions among all the adsorbed molecules in the monolayer [4—6]. The equation of the Kiselev isotherm is given below ... 

Deuterium exchange with DjO was used by Shuravlev and Kiselev (199) in the determination of surface hydroxyl groups of silica gel. Adsorption isotherms of HgO and DjO were determined gravi-metrically they agreed with each other within the limits of experimental error. 

Kiselev, using the above equation by graphical integration of the isotherm between the limits of saturation and hysteresis loop closure, was able to calculate surface areas for wide-pore samples in good agreement with BET measured areas. For micropores, the absence of hysteresis at the low-pressure end of the isotherm indicates that only adsorption and not condensation occurs, thereby rendering Kiselev s method inapplicable. 

A number of different empirical equations have been proposed to allow for the deviations of physisorption isotherms from Henry s law. An approach which is analogous to that used in the treatment of imperfect gases and non-ideal solutions is to adopt a virial treatment. Kiselev and his co-workers (Avgul et al. 1973) favoured the form... 

An early normalizing procedure, proposed by Kiselev (1957) to compare adsorption isotherms of hydrocarbons, water vapour, etc. on a series of different adsorbents, was simply to plot the surface excess concentration F (=n/A), obtained from a knowledge of the BET-nitrogen surface area, A (BET), versus p/p°. It is also possible to plot, instead of f, the reduced adsorption , n/nm, which still relies on the BET method to determine the monolayer capacity nm but does not require knowledge of the molecular cross-sectional area a. 

In the work of Isirikyan and Kiselev (1961), adsorption isotherms of nitrogen were determined at 77 K in considerable detail on four different graphitized thermal blacks (with BET areas in the range 6.5-29.1 m2g 1). The isotherms are plotted in Figure 9.3 in a normalized form, as the amount adsorbed per unit area (in pmol m-2) against the relative pressure, p/p°. Kiselev and his co-workers referred to such isotherm plots as absolute adsorption isotherms , but of course they are not stricdy absolute since they are dependent on the validity of the BET-nitrogen areas - with the usual assumption that o(N2) = 0.162 nm2. 

Figure 9.3, Adsorption isotherm of N2 at 77 K on size different graphitized thermal blacks, at various scales of pjpa (after Isirikyan and Kiselev, 1961).

The early work of Kiselev (1957) revealed that the adsorption isotherms of n-pentane and n-hexane on non-porous quartz were intermediate in character between Types II and m. Values of C(BET) <10 were obtained and the differential enthalpies of adsorption decreased steeply at low surface coverage. More recently, the isotherms of isobutane (at 261 K) and neopentane (at 273 K) on TK800 have been found to be of a similar shape (Carrott et al., 1988 Carrott and Sing, 1989). Unlike those of benzene, these alkane isotherms do not undergo a pronounced change of shape as a result of surface dehydroxylation. This is consistent with the non-specific nature of their molecular interactions (see Chapter 1). 

The first systematic investigations of the adsorption of gases on dehydroxylated silicas were made by Kiselev and his co-workers (Kiselev, 1957,1958). In a study of the adsorption of argon and nitrogen, Aristov and Kiselev (1965) found that, in contrast to nitrogen, the reduced argon isotherm did not appear to depend on the degree of surface hydroxylation. 

As noted in Chapter 1, the specific interactions between polar molecules and silica are virtually eliminated by the removal of all the surface hydroxyls and therefore the effect of partial dehydroxylation is to drastically reduce the adsorption energies of certain molecules. The polar adsorptives studied by Kiselev and his co-workers included alcohols, ketones, ethers and amines (Kiselev, 1965, 1971) with each adsorptive, the reduction in the adsorbent-adsorbate interaction energy was accompanied by a substantial change in the isotherm character. 

The exponential form of the virial isotherm favoured by Kiselev and his coworkers (e.g. Avgul etal., 1973) was Equation (4.4), that is... 

Figure 1 shows the representation of the experimental isotherm (B. G. Aristov, V. Bosacek, A. V. Kiselev, Trans. Faraday Soc. 1967 63, 2057) of xenon adsorption on partly decationized zeolite LiX-1 (the composition of this zeolite is given on p. 185) with the aid of the virial equation in the exponential form with a different number of coefficients in the series i = 1 (Henry constant), i = 2 (second virial coefficient of adsorbate in the adsorbent molecular field), i = 3, and i = 4 (coefficients determined at fixed values of the first and the second coefficients which are found by the method indicated for the adsorption of ethane, see Figure 4 on p. 41). In this case, the isotherm has an inflection point. The figure shows the role of each of these four constants in the description of this isotherm (as was also shown on Figure 3a, p. 41, for the adsorption of ethane on the same zeolite sample). The first two of these constants—Henry constant (the first virial constant) and second virial coefficient of adsorbate-adsorbate interaction in the field of the adsorbent —have definite physical meanings. 

Methods for determining sorption isotherms by gas chromatography have been published by various authorsQ,-, ). The methods used have been elution and frontal chromatography. The first combines sorption and desorption so that any hysteresis in the equilibrium transport from gas to stationary phase and back to the gas phase can produce corresponding errors. The Kiselev-Yashin equation, as shown in Figure 1,... 

The fundamental references in gas-solid adsorption are the works by Fowler and Guggenheim [12], Everett [13], and Hill [14,15], and the books by Young and Crowell [16], de Boer [17], Kiselev [4], and more recently by Ruthven [18] and T6th [19], who gives a clear, logical, and simple presentation of this topic. We present first a few theoretical results obtained in the study of gas-sohd adsorption, results that have been extended semiempirically to liquid-solid adsorption [18]. Then, we describe the various isotherm models that have been used in the study of retention mechanisms in liquid chromatography. 

The behavior of the precipitated silicas with respect to the adsorption of water vapor was even more anomalous (17, 18). Kiselev (11) and others (19) had demonstrated that in the fully hydroxylated form, a wide range of nonporous pyrogenic silicas gave rise to a common reduced water isotherm (i.e., adsorption per unit area versus relative pressure). However, in the... 

Karnaukhov, A. Kiselev, and co-workers (12,14,135-142) investigated the hypothetical geometrical structure describes by a corpuscular model in the form of a system of particles (globules) of uniform size in contact with one another. The diameter of the particles and the number of contacts between particles were taken as the main parameters of the model. An approximate theory of polymolecular adsorption and capillary condensation was developed. The simultaneous process of polymolecular adsorption and capillary condensation was analyzed for porous systems with a globular structure. It was shown that the contribution of both processes determines the form of the adsorption isotherm. The theoretical results obtained were compared with experimental data for different silica adsorbents by using different methods. 

In the 1950s, A. Kiselev, Zhdanov, and co-workers (12, 84, 155-159) showed that when the adsorption isotherms of water are expressed as absolute isotherms (referred to as the unit surface of the SiC>2 sample), widely different forms of amorphous silica having a completely hydroxyl-ated state adsorb the same amount of water at the same relative pressure (p/po <0.3). Thus the plots of absolute adsorption isotherms for different samples showed that the surfaces of these samples are of a similar nature. The adsorption properties of nonporous silica and silica having large pores (i.e., an absence of micropores) depend above all on the presence of OH groups and on the degree of hydroxylation of the surface. 

In recording adsorption isotherms of methanol vapors on aluminum oxide and silica-alumina catalysts of various composition, there was detected the phenomenom of irreversible adsorption, similar to that observed by A. V. Kiselev and his co-workers for the case of methanol adsorption on silica gels of various porosities. 

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