Equivalent adsorption

Surface type Topmost substrate Adsorption Adsorption Adsorption Equivalent Method References Comments... 

The adsorption isotherm —Equation (8) —associated with this surface equation of state is called the Henry law limit, in analogy with the equation that describes the vapor pressure of dilute solutions. The constant m, then, is the adsorption equivalent of the Henry law constant. When adsorption is described by the Henry law limit, the adsorbed state behaves like a two-dimensional ideal gas. 

A simple tandem reverse-flow reactor scheme has been proposed for this purpose [11] (Fig. 7.5). By condensing the sulfur formed in the reactor outlet and reheating the residual anhydrous inert gas stream, one obtains a thermally efficient integration of the elutive adsorbent regeneration into the reactor operation. The arrangement depicted represents an adsorptive equivalent to the reverse-flow reactor with removal of a hot side-stream [6]. 

From a comparison with the gas adsorption equivalent 11.5.4) we see that hI hI takes the place of /j° and that the standard term now consists of two parts, reflecting the difference in adsorption energy between 1 and 2 from 11.5.6) uld 11.5.5) for this case... 

Figures 2.21 and 2.22 refer to the adsorption of low molecular weight aliphatic alcohols from alcohol + benzene mixtures on montmorillonite. This adsorbent Is a so-called swelling clay mineral, meaning that it consists of packages of thin (aluminosilicate) layers that, under certain conditions, swell to give ultimately a dispersion of the individual sheets. Upon this swelling the specific surface area increases dramatically, it can readily reach several hundreds of m g" On adsorption from solution the swelling is determined by the extent to which one or both of the component(s) penetrate(s) between these sheets. In other words, we are dealing here with a non-inert adsorbent. The gas adsorption equivalent has been illustrated in fig. 1.30.

Spectrum c was obtained from spectrum b by subtracting the adsorption equivalent to the amount of gaseous CO2 indicated by the 4.23-m band in b. Thus, the small band at 4.22 in c is an artifact caused by a slight displacement of the bands and has no significance regarding the question of whether the physically adsorbed CO2 is rotating freely. The intensity of the band due to physically adsorbed CO2 indicates that the surface coverage is 1%. 

Ni = kpispi mol/cm sec Pa Common for a gas adsorption equivalent forms occur in medical problems... 

An equation algebraically equivalent to Eq. XI-4 results if instead of site adsorption the surface region is regarded as an interfacial solution phase, much as in the treatment in Section III-7C. The condition is now that the (constant) volume of the interfacial solution is i = V + JV2V2, where V and Vi are the molar volumes of the solvent and solute, respectively. If the activities of the two components in the interfacial phase are replaced by the volume fractions, the result is... 

Thus the entropy of localized adsorption can range widely, depending on whether the site is viewed as equivalent to a strong adsorption bond of negligible entropy or as a potential box plus a weak bond (see Ref. 12). In addition, estimates of AS ds should include possible surface vibrational contributions in the case of mobile adsorption, and all calculations are faced with possible contributions from a loss in rotational entropy on adsorption as well as from change in the adsorbent structure following adsorption (see Section XVI-4B). These uncertainties make it virtually impossible to affirm what the state of an adsorbed film is from entropy measurements alone for this, additional independent information about surface mobility and vibrational surface states is needed. (However, see Ref. 15 for a somewhat more optimistic conclusion.)... 

Equation XVII-70 bears a strong resemblance to the Langmuir equation (see Ref. 4)—to the point that it is doubtful whether the two could always be distinguished experimentally. An equivalent form obtained by Volmer [53] worked well for data on the adsorption of various organic vapors on mercury [54] (see Problem XVII-40). 

There are B equivalent sites available for adsorption in the first layer. 

Fig. 2.28. The high-pressure branch is still linear (provided mesopores are absent), but when extrapolated to the adsorption axis it gives a positive intercept which is equivalent to the micropore volume. The slope of the linear branch is now proportional to the external surface area of the solid. Microporosity is dealt with in detail in Chapter 4.

The limits of pore size corresponding to each process will, of course, depend both on the pore geometry and the size of the adsorbate molecule. For slit-shaped pores the primary process will be expected to be limited to widths below la, and the secondary to widths between 2a and 5ff. For more complicated shapes such as interstices between small spheres, the equivalent diameter will be somewhat higher, because of the more effective overlap of adsorption fields from neighbouring parts of the pore walls. The tertiary process—the reversible capillary condensation—will not be able to occur at all in slits if the walls are exactly parallel in other pores, this condensation will take place in the region between 5hysteresis loop and in a pore system containing a variety of pore shapes, reversible capillary condensation occurs in such pores as have a suitable shape alongside the irreversible condensation in the main body of pores. 

Forces of Adsorption. Adsorption may be classified as chemisorption or physical adsorption, depending on the nature of the surface forces. In physical adsorption the forces are relatively weak, involving mainly van der Waals (induced dipole—induced dipole) interactions, supplemented in many cases by electrostatic contributions from field gradient—dipole or —quadmpole interactions. By contrast, in chemisorption there is significant electron transfer, equivalent to the formation of a chemical bond between the sorbate and the soHd surface. Such interactions are both stronger and more specific than the forces of physical adsorption and are obviously limited to monolayer coverage. The differences in the general features of physical and chemisorption systems (Table 1) can be understood on the basis of this difference in the nature of the surface forces. 

In the simplest case, for which all adsorption sites are equivalent and do not interact with each other, the fraction of surface covered by adsorbate. 

In a detersive system containing a dilute surfactant solution and a substrate bearing a soHd polar sod, the first effect is adsorption of surfactant at the sod—bath interface. This adsorption is equivalent to the formation of a thin layer of relatively concentrated surfactant solution at the interface, which is continuously renewable and can penetrate the sod phase. Osmotic flow of water and the extmsion of myelin forms foHows the penetration, with ultimate formation of an equdibrium phase. This equdibrium phase may be microemulsion rather than Hquid crystalline, but in any event it is fluid and flushable... 

The quantity of a solute adsorbed can be given conveniently in terms of moles or volume (for adsorption) or ion-equivalents (for ion exchange) per unit mass or volume (dry or wet) of sorbent. Common units for adsorption are moV(m of fluid) for the fluid-phase concentration Cj and moV(kg of clean adsorbent) for adsorbed-phase concentration /ij. For gases, partial pressure may replace concentration. 

In this section, we consider the transient adsorption of a solute from a dilute solution in a constant-volume, well-mixed batch system or, equivalently, adsorption of a pure gas. The solutions provided can approximate the response of a stirred vessel containing suspended adsorbent particles, or that of a very short adsorption bed. Uniform, spherical particles of radius are assumed. These particles, initially of uniform adsorbate concentration, are assumed to be exposed to a step change in concentration of the external fluid. 

Two general cases are considered (1) adsorption under conditions of constant or nearly constant external solution concentration (equivalent to infinite fluid volume) and (2) adsorption in a batch with finite volume. In the latter case, the fluid concentration varies from cf to when equihbrium is eventually attained. = (cf — =... 

For a linear isotherm tij = KjCj), this equation is identical to the con-seiwation equation for sohd diffusion, except that the solid diffusivity D,i is replaced by the equivalent diffusivity = pDj,i/ p + Ppi< ). Thus, Eqs. (16-96) and (16-99) can be used for pore diffusion control with infinite and finite fluid volumes simply by replacing D,j with D. When the adsorption isotherm is nonhnear, a numerical solution is... 

This equation has the same form of that obtained for solid diffusion control with D,j replaced by the equivalent concentration-dependent diffusivity = pDpj/[ pn]Ki l - /i,//i)) ]. Numerical results for the case of adsorption on an initially clean particle are given in Fig. 16-18 for different values of A = = 1 - R. The upt e curves become... 

The technique of IGC may be employed to obtain acid-base information, as suggested by Schultz and Lavielle [99], by using acid and base probe gases on a solid for which the alkane line has already been obtained. If acid-base interaction is involved in the adsorption, the retention volume should be greater than that corresponding to the dispersion force interaction alone, which should be the same as that of the equivalent alkane , i.e. the hypothetical alkane for which the value... 

AC works by attracting and holding certain chemicals as water passes through it. AC is a highly porous material therefore, it has an extremely high surface area for contaminant adsorption. The equivalent surface area of 1 pound of AC ranges from 60 to 150 acres. AC is made of tiny clusters... 

In cases when the two surfaces are non-equivalent (e.g., an attractive substrate on one side, an air on the other side), similar to the problem of a semi-infinite system in contact with a wall, wetting can also occur (the term dewetting appHes if the homogeneous film breaks up upon cooHng into droplets). We consider adsorption of chains only in the case where all monomers experience the same interaction energy with the surface. An important alternative case occurs for chains that are end-grafted at the walls polymer brushes which may also undergo collapse transition when the solvent quality deteriorates. Simulation of polymer brushes has been reviewed recently [9,29] and will not be considered here. 

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