Specific amount adsorbed

A careful observation of Equations 10.35 and 10.36 prompts some caution. In principle, the isotherm is expressed in terms of specific amounts adsorbed and These are however meaningless unless one is able to assess which part of the liquid is in the adsorption sphere (viz. the position of the Gibbs dividing plane). 

Two-dimensional phase diagrams are often displayed in the form of In [p] against 1/7 (at a constant specific amount adsorbed), which provides a convenient way of indicating the conditions for the coexistence of two phases (see Figure 4.3). Indeed, the application of the Phase Rule indicates that when two adsorbed phases coexist in equilibrium, the system has one degree of freedom therefore, at constant... 

The isosteric method can be considered, for adsorption from solution, in a similar manner as for gas adsorption (see Section 2.6.1). For example, by equating the chemical potentials of component 2 (the solute) in its adsorbed state and the liquid phase, by keeping the specific amounts adsorbed constant and by considering a dilute solution, so that the activity can be replaced by a molality (b2 = 1000 n2/mi), we obtain ... 

This equation is written on the basis of a unit mass, usually a gram or a kdogram, of solid adsorbent. Thus n is the specific amount adsorbed, i.e., the number of moles of adsorbate per unit mass of adsorbent. Moreover, area A is defined as the specific surface area, i.e., the area per unit mass of adsorbent, a qrrantity characteristic of a particular adsorbent. The molar area, a = A/ , is the surface area per mole of adsorbate. 

The prediction of mixed-gas adsorption equilibria by ideal-adsorbed-solution theorf is based onEqs. (14.124) and (14.128). The following is a brief outline of the procedure. Since there are N "r 1 degrees of freedom, both T and P, as well as the gas-phase composition, must be specified. Solution is for the adsorbate compositionand the specific amount adsorbed. Adsorption isotherms for eachpure species must be known over the pressure range from zero to the value that produces the spreading pressure of the mixed-gas adsorbate. For purposes of illustration we assume Eq. (14.107), the Langmuir isotherm, to apply for each pure species, writing it ... 

Predictions of adsorption equilibria by ideal-adsorbed-solution theory are usually satisfactory when the specific amount adsorbed is less than a third of the saturation value for mono-layer coverage. At higher adsorbed amounts, appreciable negative deviations from ideality are promoted by differences in size of the adsorbate molecules and by adsorbent heterogeneity. One must then have recourse to Eq. (14.123). The difficulty is in obtaining valnes of the activity coefficients, which are strong functions of both spreading pressnre and temperatnre. This is in contrast to activity coefficients for liquid phases, which for most applications are insensitive to pressure. This topic is treated by Talu et ai. ... 

As the concentration of the solute is increased, the specific amount adsorbed levels off to a constant value (Fig. 4-1). At the higher concentrations, the surface of the adsorbent is coated with a mono-molecular layer of the solute, and no further material may be adsorbed. One might say that the adsorbent was saturated. 

Whether the adsorption isotherm has been determined experimentally or theoretically from molecular simulation, the data points must be fitted with analytical equations for interpolation, extrapolation, and for the calculation of thermodynamic properties by numerical integration or differentiation. The adsorption isotherm for a pure gas is the relation between the specific amount adsorbed n (moles of gas per kilogram of solid) and P, the external pressure in the gas phase. For now, the discussion is restricted to adsorption of a pure gas mixtures will be discussed later. A typical set of adsorption isotherms is shown in Figure 1. Most supercritical isotherms, including these, may be fit accurately by a modified virial equation. ... 

The specific amount adsorbed of the solute, n, or the amount adsorbed per square meter of solid surface, T, were calculated from the experimental data using the equations... 

The specific amount adsorbed ( j, mol/g-solid) is the surface concentration (r, mol/m ) multiplied by the specific surface area of the solid (A p, mVg-solid). 

FIGURE 7.28 Adsorption of N2 on soils with high organic matter content at 77 K (a) plot of the specific amount adsorbed as a function of Nj pressure, showing a Brunauer-Emmet-Teller (BET) isotherm shape, (b) Plot of the data as Equation 7.23. (Reprinted with permission from Chiou, C.T. et al., 1990, Environmental Science Technology, 24, no. 8, 1164-1166. Copyright 2003 American Chemical Society.)... 

Although a calculation of the uncertainty in the absolute amormt adsorbed is best suited for molecular simulation [4], such a calculation requires a detailed knowledge of the pore volume for porous materials or specific surface area for non-porous materials [5]. Despite the volume calculation omission, we believe that it is equally important to make an analysis of the uncertainty in the selected EoS as their selection impacts initially on the uncertainty in the specific surface excess amount and then on the uncertainty in the absolute specific amount adsorbed, due to their linear combination, Eq. (2). 

Smith, Van Ness and Abbott (2001) have reported that lAST predictions are usually satisfactory when the specific amount adsorbed is less than a third of the saturation value for monolayer coverage. 

Adsorption experiments are conducted at constant temperature, and an empirical or theoretical representation of the amount adsorbed as a function of the equilibrium gas pressure is called an adsorption isotherm. Adsorption isotherms are studied for a variety of reasons, some of which focus on the adsorbate while others are more concerned with the solid adsorbent. In Chapter 7 we saw that adsorbed molecules can be described as existing in an assortment of two-dimensional states. Although the discussion in that chapter was concerned with adsorption at liquid surfaces, there is no reason to doubt that similar two-dimensional states describe adsorption at solid surfaces also. Adsorption also provides some information about solid surfaces. The total area accessible to adsorption for a unit mass of solid —the specific area Asp — is the most widely encountered result determined from adsorption studies. The energy of adsorbate-adsorbent interaction is also of considerable interest, as we see below. 

The BET specific surface area [28] was calculated in the relative pressure range between 0.04 and 0.2. The total pore volume was determined from the amount adsorbed at a relative pressure of 0.99 [28], The primary mesopore volume and external surface area were evaluated using the as-plot method [24, 28, 29] with the reference adsorption isotherm for macroporous silica [29], The pore size distributions were determined using the Kruk-Jaroniec-Sayari (KJS) equation [30] and the calculation procedure proposed by Barrett, Joyner and Halenda (BJH) [31]. 

MCM-41 samples usually exhibit certain external surface area, so the amount adsorbed on the external surface also needs to be accounted for. This amount can be described as the amount adsorbed on the macroporous reference adsorbent, vref(p/po), multiplied by the MCM-41 external surface area, Sex, divided by the specific surface area, Srer, of the reference adsorbent used to evaluate Sex. Therefore, the model nitrogen adsorption isotherm for the MCM-41 sample with the capillary condensation pressure of pc/po, primary mesopore adsorption capacity of vp>max and external surface area of Sex is described by the following equation ... 

The amount of adsorbate that can be held depends on the concentration or partial pressure and temperature, on the chemical nature of the fluid, and on the nature, specific surface, method of preparation, and regeneration history of the solid. For single adsorbable components of gases, the relations between amount adsorbed and the partial pressure have been classified into the six types shown in Figure 15.2. Many common systems conform to Type I, for example, some of the curves of Figure 15.3. Adsorption data are not highly reproducible because small contents of impurities and the history of the adsorbent have strong influences on their behavior. 

There are differences in isotherm shape, and for DTAB the behavior is not amenable to a simple explanation. Of particular interest are plots of the amount adsorbed against the mean ionic activity of the surface active agent (including the counterion of the added electrolyte). In the case of DTAB all the data, including others at various salt concentrations up to 0.5M, lie on one line which, after an initial steep rise, is linear to the c.m.c. This indicates that for other than the initial strong adsorption at low concentrations (possibly because of specific interactions with the surface) the adsorption follows the law of mass action. For SDS a similar result is obtained except that positive deviations from the straight line occur below a — 4 X 10 3M for the cases (salt concentration < O.lAf) when there is a point of inflection in the isotherm. These deviations may reflect specific interactions of the DS" with the surface when the ions are adsorbed in parallel orientation. 

An important question is how much of a material is adsorbed to an interface. This is described by the adsorption function T = /(/, T), which is determined experimentally. It indicates the number of adsorbed moles per unit area. In general, it depends on the temperature. A graph of T versus P at constant temperature is called an adsorption isotherm. For a better understanding of adsorption and to predict the amount adsorbed, adsorption isotherm equations are derived. They depend on the specific theoretical model used. For some complicated models the equation might not even be an analytical expression. 

Sensors using quartz crystal are very sensitive and can detect samples of the order of pg. Usually, an organic thin film is pasted on quartz surface since the crystal surface hardly absorbs any chemical species. The organic thin film provides the potential to detect various kinds of volatilities with high selectivity and sensitivity. The principle of the gas sensor is based on Eq. (1) [32]. The quartz oscillator has a specific resonance frequency with an oscillating circuit. Its frequency is decreased by the absorption of volatilities on the quartz surface due to the increase in mass. The frequency shift caused by exposure to a volatile depends on the amount adsorbed. With a 9 MHz quartz oscillator, the frequency is decreased by 400 Hz upon adsorption of 1 pg of a compound. A resonance oscillator with a higher resonance frequency can detect smaller amounts. 

The volumetric method is mainly used for the purpose of determining specific surface areas of solids from gas (particularly nitrogen) adsorption measurements (see page 134). The gas is contained in a gas burette, and its pressure is measured with a manometer (see Figure 5.4). All of the volumes in the apparatus are calibrated so that when the gas is admitted to the adsorbent sample the amount adsorbed can be calculated from the equilibrium pressure reading. The adsorption isotherm is obtained from a series of measurements at different pressures. 

The specific surface area of the adsorbent can be obtained from the adsorption data if the number of molecules in the monolayer and the area effectively occupied by an adsorbed molecule in the monolayer, Am (i.e., its cross-sectional area), are known. The amount adsorbed per gram of solid to complete a monolayer, nm, can be obtained by applying Equations 4.4 and 4.5 to the adsorption isotherm. The surface area of the adsorbent (S) expressed in m2/g, is... 

The specific surface excess amount is what is typically measured in practical adsorption studies (see Section 6.4). This parameter is almost equal to the amount adsorbed, a, and is dependent on the equilibrium adsorption pressure, P, at constant adsorbent temperature, T. Accordingly, gas adsorption data is, in practice, expressed by the adsorption isotherm ... 

Adsorption is normally exothermic thus a decrease in temperature will increase the extent of adsorption whereas an increase in temperature will increase the adsorption capacity for chemisorption (normally endothermic). The heat of adsorption, AHads, is defined as the total amount of heat evolved per a specific amount of adsorbate adsorbed on an adsorbent. Because adsorption from an aqueous solution occurs, AHads is small, and thus small changes in temperature do not alter the adsorption process much. The effect of temperature on adsorption can be expressed by ... 

Nitrogen adsorption isotherms for the OMMs studied were recorded at 77K using a Micromeritics ASAP 2010 adsorption analyzer. All samples prior to adsorption analysis were degassed at 120°C for 2h under vacuum. The BET specific surface area was calculated from the adsorption data in the range of the relative pressure from 0.04 to 0.2 according to the BET method.46 The total pore volume was estimated from the amount adsorbed taken at the relative pressure about 0.99.47 The pore width was estimated at the pore size distribution maximum obtained by the KJS method.48... 

For the sake of simplicity in some later sections of this book, we adopt the symbol n to denote the specific surface excess amount n°lm. Also, for convenience, this quantity will be often referred to as amount adsorbed. 

The way in which Lippens and de Boer (1965) made use of the universal /-curve is simple. The experimental isotherm is transformed into a /-plot in the following manner the amount adsorbed, n, is replotted against /, the standard multilayer thickness on the reference non-porous material at the corresponding p/p°. Any difference in shape between the experimental isotherm and the standard /-curve is thus revealed as a non-linear region of the /-plot and/or a finite (positive or negative) intercept of the extrapolated /-plot (i.e. at / = 0). By this method a specific surface area, denoted a(t), can be calculated from the slope, s, = nft, of a linear section. From Equations (6.10), (6.11) and (6.15) we then get ... 

It is customary to take the total specific pore volume, vp, of an adsorbent as the liquid volume adsorbed at a predetermined p/p° (e.g. at p/p° = 0.95). This procedure is not always satisfactory, however, because the adsorption capacity (i.e. the amount adsorbed as p/p° — 1) is dependent on the magnitude of the external area and also on the upper limit of the pore size distribution. 

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