Monolayer volumes

Figure 5.18 shows a plot of the data in Tab. 5.1, according to Eq. (13). The slope and intercept result in a monolayer volume of Vb = 1616 pL. Because each N2 molecule occupies 0.16 nm we can convert the monolayer volume into the total area of the catalyst 6.4 m. Since this was for a sample of 0.2 g, the area per gram of catalyst corresponds to 32 m g . ... 

The surface areas of the iridium and palladium catalysts were determined by chemisorption of hydrogen and carbon monoxide, respectively, the monolayer volume being determined from an adsorption isotherm taken at 20°C. 

A typical N2 adsorption measurement versus relative pressure over a solid that has both micropores and mesopores first involves essentially a mono-layer coverage of the surface up to point B shown in isotherm IV (lUPAC classification) in Figure 13.1. Up to and near point B the isotherm is similar to a Langmuir isotherm for which equilibrium is established between molecules adsorbing from the gas phase onto the bare surface and molecules desorbing from the adsorbed layer. The volume of adsorbed N2 that covers a monolayer volume, hence the surface area of N2 can then be determined from the slope of the linearized Langmuir plot when P/V is plotted against P ... 

Here P is the equilibrium pressure during the adsorption measurements, V the adsorbed volume of N2, the monolayer volume and is a constant. 

Specific surface area per gram of solid Contact angle Moles adsorbed per gram Surface concentration Boltzman s constant Relative equilibrium pressure of adsorbate Monolayer volume of adsorbed gas or vapor per gram of solid... 

Fig. 26a and b. The effect of water content in the adsorbent on the retention volumes of standards in hexane (a) and determination of adsorbent activity a and monolayer volume (b) after reaching the critical conditions in binary solvents given in Fig. 25. Xo = 1.71 styrene, 2.02 naphthalene, 2.14 acenaphthylene, 3.02 benzopyrene-3,4 641...

An equivalent surface area of 460 m g was determined from the monolayer volume, Vj. The value obtained for the dimensionless energetic constant, C=260, was characteristic of a microporous material. Although the BET surface area may not be a physically precise quantity due to the fact that the nitrogen molecule does not exhibit the same cross-sectional area in a microporous environment as on a flat surface, the BET value is useful for comparisons of relative porosities among a related class of adsorbents. For instance, smectite clays pillared by metal oxide aggregates typically exhibit BET surface areas in the range 150 - 400 m /g. Thus, the TSLS complex is among the more porous intercalated nanocomposites derived from smectite clays. 

Electric double layers at phase boundaries pervade the entire realm of Interface and colloid science. Especially in aqueous systems, double layers tend to form spontaneously. Hence, special precautions have to be taken to ensure the absence of charges on the surfaces of particles. Insight into the properties of double layers is mandatory, in describing for Instance electrosorption, ion exchange, electrokinetics (chapter 4), charged monolayers (Volume III), colloid stability, polyelectrolytes and proteins, and micelle formation of ionic surfactants, topics that are intended to be treated in later Volumes. The present chapter is meant to Introduce the basic features. 

Although interpretation In terms of surface pressures is relatively straightforward and informative. Investigators are unaccustomed to apply it to charged solid surfaces. In the mercury double layer field and with monolayers (Volume III) it is more common... 

However, Dubinin and co-workers do not accept the concept of monolayer formation in micropores and propose determining the microporous volume, Fq, on the basis of the thermodynamic theory of Polanyi adsorption. However, one can observe that the monolayer volume, Vm, when expressed in liquid nitrogen volume per unit mass, is very close to the Dubinin volume, Vo. The proportionality of the BET monolayer volume, Vm, and the so-called micropore volume, Va, (Vo 11 Vm) has been observed for many materials, as shown in different studies [2, 3]. This means that both variables are correlated, so determining one is equivalent to the determining the other. The discussion on the physicochemical meaning of these parameters may be interesting from a theoretical point of view but as far as practical characterization of porous materials is concerned, both methods can often be considered as equivalent. 

Figure 1. a) Adsorption isotherms for k-mets adsorbed on l-D with diilerent values of the parameter c. Lines correspond to exact theoretical results and symbols represent data from Monte Carlo simlation. b) Fitting of experimental adsorption isotherms of Ar, N2 / nonporous silica, through the linearized dimer isotherm equation (9). The resulting values of the parameter c and the monolayer volume v. are shown in the figure. 

Excepting these really few ideal cases and regardless of the fact that the BET method is routinely used for the determination of the monolayer volume even for systems which are poorly described by the BET equation, the above equations are not found to describe accurately adsorption equilibrium on most adsorbents of chemical interest. 

In the present studies, a-alumina, a non porous alumina, has been used as a standard. The surface area of this sample is 9 m /g and monolayer volume is 2 cc/g.It can be concluded from the Figure 2 that v-a plot for AD-101 is almost a straight line passing origin. Treatment of AD-101 with alkali shows an upward deviation from straight line which shows an increase in mesopore. However, the upward deviation is minimised in the acid treated sample which is in agreement with the pore size distribution for these samples. ... 

Based on their respective monolayer volumes as determined by the BET analysis of water sorption (see column 6 in Table I), the... 

Test these data for adherence to the Langmuir isotherm. What is the monolayer volume in each case Are these results consistent ... 

Vg molar volume of gas, volume/mol at 1 atm and adsorption temperature Vm volume adsorbed at saturation, monolayer volume Vi residual functions, equations (iii), Illustration 3.4 Wc weight of catalyst, typically g... 

There are various ways in which the monolayer volume can be measured. In the static method, successive small doses of the adsorbate are admitted, and the number of adsorbed molecules after equilibrium has been reached are deduced either gravimetrically (possible with carbon monoxide, difficult with hydrogen) or volumetrically from the residual pressure or by some other technique such as NMR or XANES. " The procedure is repeated until no further uptake occurs, when the monolayer capacity will be known. If chemisorption on the metal is strong and... 

Specific to the metal, the adsorption isotherm will show an initial rapid increase of uptake with pressure, followed by a linear region of low slope. The monolayer capacity is often reported (when anything at all is said) as the intercept at zero pressure obtained by extrapolation of the linear part. Alternatively, and perhaps better, the results are plotted according to the one of the linearised forms of the Langmuir equation from which the monolayer volume can be obtained. 

Over what range of pressure should the isotherm be measured Careful work over an extended pressure range shows that there may be no sharp knee corresponding to the completion of a monolayer on the metal, but rather continuing uptake which appears to approach some saturation limit without ever quite getting there. This implies that the zero-pressure monolayer volume obtained by extrapolation depends upon the pressure range over which the isotherm has been measured (see Figure 3.14). 

The volumetric method has very often been used with platinum catalysts for which quite satisfactory results are generally obtained it is usual to assume that the monolayer volume or amount, obtained as just described or by extrapolation corresponds to an H Ms (hydrogen atom to metal surface atom) ratio of 1 1. Some justification for this assumption is to be found, at least for particles of moderate size, in the adsorption stoichiometry shown by films and single crystals, but for very small particles and at high pressures the H/Mj ratio can exceed unity quite substantially this is especially so with rhodium" and iridium (see below). Care is however needed with palladium " " because of the risk of forming the hydride however, monolayer coverage is obtained at pressures below which dissolution starts. The base metals iron, cobalt and nickel have been... 

For illustration of the BET-SILP theory, Figure 6.13a depicts the influence of the limiting number of adsorption layers (Wg) on the adsorbed volume (relative to monolayer volume) for Cggj = 59, which is the value of [EMlM][NTf2] supported on silica. For this system rij equals 11, and then-layer BETequation (Eq. (6.41/6.49)) of adsorption in a limited space approaches the B ET equation of an unlimited number... 

When plotting the isotherm taken for the sample under investigation vs. t rather than plpo, a linear relationship is observed that may be combined with an offset (see Figure 21.27). For a nonmicroporous sample a line through the origin is expected, with the slope being proportional to the monolayer volume Fmi ... 

Figure 21.27. -plot (left) and otj-plot (right) of the same isotherm of a carbon aerogel. The f-plot results in an intercept dashed line) at zero layer thickness of an adsorbed volume of 150 cm (STP)/g and a slope corresponding to a monolayer volume of 35.9 cm (STP)/g (equal to a specific surface area of about 155 mVg). The dashed-dotted lines indicate the series of tangent used for the MP method. 

Sg (m /g) = total surface area per unit weight of catalyst sample Vm = monolayer volume (cm )... 

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