Adsorption isotherm Everett

It is not necessary to limit the model to idealized sites Everett [5] has extended the treatment by incorporating surface activity coefficients as corrections to N and N2. The adsorption enthalpy can be calculated from the temperature dependence of the adsorption isotherm [6]. If the solution is taken to be ideal, then... 

Fig. 4.2 Adsorption isotherms of benzene at 25°C on (1) a charcoal from anthracite coal, activated to 56% yield (2) an activated coconut charcoal. (After Cadenhead and Everett.)...

A summary of developments in physical adsorption during the period from 1943 to 1955 has been given recently by Everett 94). The chief difference between the approach used by Brunauer in his book published in 1943 and that in vogue in 1955 is in the great development of the thermodynamic aspects of the subject. Prior to 1943, the main effort was in developing theories to predict the shape of adsorption isotherms. Since then, emphasis has shifted towards the thermodynamic properties of the adsorbed phase, particularly its entropy. 

Stoeckli (1993) has pointed out that the Dubinin-Astakhov equation (Equation (4.45)) can be derived from Equation (4.52), but McEnaney (1988) and others (e.g. Jaroniec et al. 1997) have drawn attention to the difficulty in arriving at an unambiguous interpretation of the energy distribution function. Indeed, Stoeckli et al. (1998) have now pointed out that Equation (4.45) can be usefully applied to a number of adsorption isotherms on non-porous solids. A comprehensive review of the significance and application of Equation (4.52) is given by Rudzinski and Everett (1992). 

A first distinction must be made between the methods which use one sample for each point on the adsorption isotherm (i.e. immersion methods) and those using a single sample through which the solution of increasing concentration is allowed to flow (i.e. flow-through methods). A critical outline of most of these methods is given by Everett (1986). 

Stoeckli (1981), McEnaney and Mays (1991), Hutson and Yang (1997) and others (see Rudzinski and Everett, 1992) have attempted to provide a theoretical basis for the DR and DA equations in terms of an integral transform or a generalized adsorption isotherm, which may be expressed in the form of Equation (4.52). However, in practice the DR and DA equations are usually applied empirically and consequently the derived quantities (micropore volume, characteristic energy and structural constant) are not always easy to interpret. 

In another words, the negative slope of the excess adsorption isotherm in the linear region is equal to the volume of adsorbed layer, which was derived from the consideration of the adsorption process and not from a prior introduction of the model. A similar expression was derived by Everett [27]. 

Figure 1.39. Adsorption isotherms of Xenon on Vycor glass. Temperatures relative to the bulk critical temperatures of xenon (289.7 K). Above T = 0.94 hysteresis is no longer observed. (Redrawn from S. Nuttall, Ph.D. Thesis. Univ. of Bristol (1974). See also C.G.V. Burgess, D.H. Everett and S. Nuttall, Pure AppL Chem. 61 (1989) 1845 (Courtesy of D.H. Everett).)...

The calorimetric studies of the surface heterogeneity of oxides were initiated half a century ago, and experimental findings as well as their theoretical interpretation have been recently reviewed by Rudzinski and Everett [2]. The last two decades have brought a true Renaissance of adsorption calorimetry. A new generation of fully automatized and computerized microcalorimeters has been developed, far more accurate and easy to manipulate. This was stimulated by the still better recognized fact that calorimetric data are much more sensitive to the nature of an adsorption system than adsorption isotherm for instance. It is related to the fact that calorimetric effects are related to temperature derivatives of appropriate thermodynamic functions, and tempearture appears generally... 

S, and H, are the total or integral entropy and heat content of the one-component system of adsorbed molecules. An isosteric calculation [Eqs. (52) and (53)] from neighboring adsorption isotherms gives the differential entropy and heat content, (dS,/dnf)a.r and (dHJdnfja,t-The integral entropy is the quantity of direct statistical mechanical significance, being related to the number of possible quantum states of We adopt the H, and 3C notation of Everett (86), for clarity. 

Figure Bl.26.3. The lUPAC classification of adsorption isotherms for gas-solid equilibria (Sing K S W, Everett D H, Haul R A W, Mosoul L, Pierotti R A, Rouguerol J and Siemieniewska T 1985 Pure. Appl. Chem. 57 603-19).

Physical adsorption isotherms are generally obtained experimentally using a volumetric or gravimetric method. Before we tiy to obtain meaningftil results from the theoretical expressions we have arrived at using Hill s or Hill and Everett s... 

Experimental studies concerning the development in the measurements of gas adsorption isotherms on solid adsorbents and the various experimental techniques have been reviewed and summarized in detail (see reviews [56-60] and references therein). With regard to the solid/liquid interface the comprehensive literature on the subject was presented by Kipling [7], Everett [61], Dabrowski and Jaroniec [21]. 

An interesting point of comparison between the theoretical predictions and the experimental data may be made. For the case of trajectories starting from an initial wet state (Tl, T2, and T3), the theory underestimates the actual moisture content. However, when the trajectories start from an initial dry state, the agreement between the theoretical prediction and experimental data is very good. Similar behavior has been found when more such trajectories were investigated [33]. The reason seems to be the fact that the moisture density function is estimated from approximate data for the desorption and adsorption isotherms between 90% and 100% RH. More accurate data in this region should provide better theoretical estimates. It appears that the theory of independent domain complexions advanced by Everett and coworkers is indeed applicable for paper materials showing moisture sorption hysteresis. 

The original purpose of the lUPAC (compiled by Everett et al. [40]) round-robin investigation was to create some confidence in the methodology of adsorption isotherm measurements. Standard samples from the same production batches were used and various laboratories performed the same experiments. The results were not intended as standard curves but the agreement between the various laboratories was generally very good, within 2%. Therefore, these would be as good standards as one would be able to... 

The HILDA method developed by House and Jaycock [100] may be considered a modified, numerical version of the iterative procedure proposed by Adamson and Ling [126]. An excellent short presentations of the method can be found in the review by House [127] or in the monograph by Rudzinski and Everett [6]. This procedure can be outlined as follows The form of local isotherm is assumed and the distribution function is evaluated by using the iterative routine for each iterative step appropriate adjustments in distribution are made to bring the calculated and experimental isotherms into the best possible coincidence the condensation-approximation is used to determine the first approximation of the distribution. The Adamson-Ling method was widely applied to evaluate the energy distribution function from the measmed adsorption isotherm [97,122,128-135]. 

The majority of articles devoted to physical adsorption at the hquid-soUd interface concerns adsorption from binary solutions. The Langmuir-type model for this process has been discussed by Everett in terms of statistical thermodynamics [197]. He has proposed the well-known equation of the adsorption isotherm ... 

Everett concludes that in systems where pore blocking can occur, pore size distribution curves derived from the desorption branch of the isotherm are likely to give a misleading picture of the pore structure in particular the size distribution will appear to be much narrower than it actually is. Thus the adsorption branch is to be preferred unless network effects are known to be absent. 

The hysteresis effect appears to be affected by the length of the equilibration period. Nye and Tinker (1977) point out that a true hysteresis effect would persist no matter what length of time was given for a true equilibrium to establish. In contrast, if the difference between an adsorption and a desorption isotherm is eliminated by extending the equilibration time, this would be considered a relaxation effect (Everett and Whitton, 1952). 

Various attempts have been made to modify the Langmuir model. One of the best known is that of Fowler and Guggenheim (1939), which allowed for adsorbate-adsorbate interactions in a localized monolayer on a uniform surface. However, on an empirical basis the Fowler-Guggenheim equation turns out to be no more successful than the original Langmuir isotherm. The highly complex problem of localized adsorption on heterogeneous surfaces has been discussed by Rudzinski and Everett (1992). 

The close proximity of the pore walls in the narrowest micropores produces an increased adsorbent-adsorbate interaction energy and this in turn results in the distortion of the initial part of the isotherm. If the pore width w is no more than a few molecular diameters d, the enhanced interactions lead to complete pore filling at very low pip0. In slit-shaped pores, the increased adsorption energy is unlikely to be significant beyond a pore width of about 2d, whereas in cylindrical pores the enhancement may extend up to a pore diameter of 3-4d (see Figure 4.5 Everett and Powl, 1976). 

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. 

In the studies on monolayer adsorption of gases Rudzihski and Everett [2] showed that a correction for physically reasonable limited domain Ac, i.e existence of minimum and maximum values and e[ should be made to arrive at an isotherm equation reducing correctly to Henry s region. 

Adsorption capacity can be calculated from excess isotherms by various methods. The best known of these is the so-called Everett-Schay function[31] ... 

For modeling and simulation of preparative chromatography experimentally determined adsorption equilibrium data have to be represented by suitable mathematical equations. From the literature a multitude of different isotherm equations is known. Many of these equations are derived from equations developed for gas phase adsorption. Detailed literature can be found, for example, in the textbooks of Guiochon et al. (2006), Everett (1984), and Ruthven (1984) or articles of Seidel-Morgenstern and Nicoud (1996) or Bellot and Condoret (1993). 

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