Molecules: adsorbed, areas covered

A fractal surface of dimension D = 2.5 would show an apparent area A app that varies with the cross-sectional area a of the adsorbate molecules used to cover it. Derive the equation relating 31 app and a. Calculate the value of the constant in this equation for 3l app in and a in A /molecule if 1 /tmol of molecules of 18 A cross section will cover the surface. What would A app be if molecules of A were used ... 

The model implies that at any pressure below the saturation vapour pressure, the fractions of the surface covered with 1, 2,. .., i molecules will be 6 02,.., 0i respectively, so that the thickness of the adsorbed layer will not be constant throughout. On the specific surface area A, therefore, the total number Z of molecules adsorbed will be... 

Langmuir (1916), whp put forward the fir quantitative theory of the adsorption of a gaS, assumed that a gas molecule condensing from the gas phase-would adhere to the surface fora short time before evaporating and that the condensed layer was only one atom or molecule thick. If 0 is the fraction of the surface area covered by adsorbed molecules at any time, the rate of desorption is proportional to 0 and equal to k 0 where is a constant at constant temperature. Similarly the rate of adsorption will be proportional to the area of bare surface and to the rate at which the molecules strike the surface (proportional to the gas pressurep). At equilibrium the rate of desorption equals the rate of adsorption... 

If Type I adsorption behavior is obeyed, a plot of PA/v versus PA should be linear with slope l/vm. Once the volume corresponding to a mono-layer has been determined, it can be converted to the number of molecules adsorbed by dividing by the molal volume at the reference conditions and multiplying by Avogadro s number (N0). When this number of molecules is multiplied in turn by the area covered per adsorbed molecule (a), the total surface area of the catalyst (S) is obtained. Thus,... 

U linear velocity a area covered per adsorbed molecule... 

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 ... 

The success of kinetic theories directed toward the measurements of surface areas depends upon their ability to predict the number of adsorbate molecules required to exactly cover the solid with a single molecular layer. Equally important is the cross-sectional area of each molecule or the effective area covered by each adsorbed molecule on the surface. The surface area then, is the product of the number of molecules in a completed monolayer and the effective cross-sectional area of an adsorbate molecule. The number of molecules required for the completion of a monolayer will be considered in this chapter and the adsorbate cross-sectional area will be discussed in Chapter 6. 

According to Maxted (36), at low temperatures the molecule would be adsorbed through sulfur atom anchoring. Around this point the hydrocarbon chain could, thanks to its free rotation, inhibit adsorption over the whole adjacent surface. A comparison of the toxicities of hexanethiol and propanethiol shows that the ratio of these toxicities is exactly equal to the ratio of the surface area covered by the two molecules. 

Throughout this analysis, it is assumed that all molecular species are adsorbed on the same sites, so that an area covered by molecules of one species will not admit molecules of another species. Seldom is sufficient information available concerning the properties of the surface to justify any other assumption. 

Nandi and Walker [499J compared the uptakes of two acidic and one basic dye by coals, chars, and activated carbons and noted that the area covered by a dye molecule would depend on the nature of the solid surface. They concluded that the removal of acidic groups by heat treatment had an effect on dye uptake for one activated carbon but had no effect for another. The authors did not report the pH of the adsorption measurements, nor did they characterize the surface chemistry of the adsorbents. McKay [500] did report the pH and even studied the effect of pH (in the range 5.2-8.5) on the rate of adsorption of Telon blue (an acidic dye), but the effect was neither clarified nor found to be significant. In contrast, Perineau et al. [501] noted major effects of pH on the adsorption of both an acidic and a basic dye and concluded that pH values of about 2 are the best for the adsorption of acid dyes whereas less acidic values (pH > 5) are to be preferred for the removal of basic dyes. ... 

A, the area covered by each adsorbate molecule, m2/molecule... 

Obviously, the amoimt, qi, of the component i that is adsorbed at equilibrium is proportional to the surface area covered by its molecule so the competitive isotherm is written... 

Among the molecule or ion adsorption methods, gas adsorption is the most important one. It uses a reversible van der Waals adsorption or physisorption. A gas molecule adsorbed on the sample surface occupies a specific space. For example, the nitrogen molecule N2 requires a surface area of 16.2x 10 m. If one assumes that the entire surface of a powder sample, including those pores that are accessible to the molecules, is covered with a monomolecular layer of the adsorbate, the surface can be calculated from the number of adsorbed molecules and their space requirement. Measurements of the adsorbed amount of gas can be accomplished either volumetrically or gravimetrically and by means of carrier gas or radioactive methods. 

Other important organic electrolytes are the dye molecules. The adsorption of dyes is of interest largely because they are pollutants frequently found in textile wastewaters and because some of them were proposed as molecular probes to characterize the pore texture of carbon adsorbents. However, this last apphcation should be viewed with caution [1] because dye adsorption is profoundly affected by the carbon surface chemistry and solution pH. Thus, Graham [40] found a good linear relationship between a decreased uptake of the anionic metanil yellow and an increased carbon surface acidity. This author concluded that acidic groups on the carbon surface tend to reduce the capacity for anionic adsorbates in general. The adsorption of dyes was subsequendy investigated by other authors [1]. For instance, Nandi and Walker [41] studied the adsorption of acid and basic dyes on different carbon materials and found that the area covered by a dye molecule depended on the nature of the solid surface. 

The volume can be readily converted to the number of molecules adsorbed. However, to determine the absolute surface area it is necessary to select a value for the area covered by one adsorbed molecule. If this is a, the total surface area is given by... 

The accuracy with which this can be expressed as square meters of surface depends on the exactness with which the number of adsorbed layers can be determined, and on the closeness with which one can approximate the average area covered by each adsorbed molecule. Beyond this, the definition of the area so measured presents some difficulty. Langmuir has pointed out that there must be spaces of all sizes and shapes on a charcoal surface. On a plane surface, a single adsorbed molecule, may be attached to a single carbon atom whereas, in crevices and pores the same size molecule may cover several carbon atoms. Much depends on the size and orientation of an adsorbed molecule. Thus, an aliphatic acid molecule that lies flat on the surface will cover more carbon atoms than when attached at one end. Therefore, it is to be anticipated that the measured surface will depend on the structure of the adsorbate.1,2... 

In order to discuss the adsorbed state and adsorptivity for the substances investigated, the values of p and AG ad were obtained based on the same isotherm given by equation (7). The results are listed in Table 1, in which the p values serve to estimate the areas covered by one adsorbed molecule by comparison with that of an adsorbed water molecule. 

Here refers to the area which a molecule of 1 covers on the adsorbent surface. Fowkes (19) has pointed out that the y values of most organic compounds are approximately equal to their surface tensions y. Consequently, to a first approximation y[ of Eq. (3-Id) may be replaced by the surface tension of I (yj). 

The calculation of the area covered by an adsorbed sample molecule is generally straightforward, as discussed in Section 3-4A. The configuration of the adsorbed molecule must be known, but for aromatic compounds we can usually assume flat adsorption. The configuration of an adsorbed aliphatic compound is often less clear, as discussed below. If we express A as the sum of contributions a, from each group i in the sample molecule, the calculation of A is greatly simplified ... 

The formation of monolayers of cerotic, be-henic, and stearic acids adsorbed from cis-decahydronaphthalene and w-hexadecane solutions onto glass was studied by electron microscopy. Platinum preshadowed carbon replicas of the monolayered glass surfaces were examined in a JEM 6-A electron microscope. The acids adsorb initially in discrete patches the average patch diameter depends on the length of the acid molecule, becoming smaller for shorter acids. The area covered by the unimolecular film increases as the adsorption time or concentration of adsorbate solution increases. Contact angle measurements on partially monolayered surfaces show the contact angle to be dependent upon the fraction of substrate covered. Direct evidence of metastable incorporation of hexadecane in acid mono-layers was obtained. 

Surface Area Determination. Specific surface areas were required to determine the fraction of adsorbent surface covered by the virus at equilibrium. This in turn is required for adsorption free-energy evaluations. BET-N2 (21) methods were used where applicable and Kozeny (22) permeametry methods were used for confirmation. Values are listed in Table I. Although the values measured by the two methods are not directly comparable, trends shown by the two sets of values are similar. The BET method measures all surface accessible to adsorbing N2 molecules and generally is considered to be the most reliable... 

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