Adsorbed molecule projection area

In the Langmuir derivation the adsorbed molecules are allowed to interact with the adsorbent but not with each other The adsorbed layer is assumed to be ideal. This necessarily limits adsorption to a monolayer. Once the surface is covered with adsorbed molecules, it has no further influence on the system. The assumption that adsorption is limited to monolayer formation was explicitly made in writing Equations (72) and (73) for the saturation value of the ordinate. Ii is an experimental fact, however, that adsorption frequently proceeds to an extent that exceeds the monolayer capacity of the surface for any plausible molecular orientation at the surface. That is, if monolayer coverage is postulated, the apparent area per molecule is only a small fraction of any likely projected area of the actual molecules. In this case the assumption that adsorption is limited to the monolayer fails to apply. A model based on multilayer adsorption is indicated in this situation. This is easier to handle in the case of gas adsorption, so we defer until Chapter 9 a discussion of multilayer adsorption. 

If a molecule adsorbs at the interface as a separate coil, it should occupy an area of the order of the projected area of the molecule in the bulk solution, i.e. R j [221,222], The figures obtained (ca. 2 nm2) are much lower and therefore, the PEO chains are crowding the solution/air interface and stretched, i.e. they form a brush [221-223], Its thickness can be calculated form the simple brush model [221,222]... 

The value of a has been the subject of considerable investigation. Emmett and Brunauer proposed that a is the projected area of a molecule on the surface when the molecules are arranged in close two-dimensional packing. This value is slightly larger than that obtained by assuming that the adsorbed molecules are spherical and their projected area on the surface is circular. The proposed equation is... 

Using the previous example, the values are shown in the fourth column of Table 3.11-1. The surface area and the slope of the reference sample is 81 mVg and 29.42 cc STP/g. Figure 3.11-3 shows a plot of the amount adsorbed versus a. The slope of the first line of the test sample is 474 cc STP/g. Thus the total surface area is calculated using eq. (3.11-6) and its value is 1305 mVg. This is exactly the same as that obtained by the t-plot. The slope of the second line is 15 cc STP/g (or 4.03 x 10 ° molecules/g). Knowing the projection area of nitrogen molecule as 0.162 nm /molecule, we obtain the external surface area as 65 mVg, compared to... 

The area assigned to an adsorbed molecule is the area of projection on to a flat surface as illustrated in Figure 4.9. When adsorbate molecules occupy such sites as are modeled in Figure 4.3, the unreality of the concept of surface area becomes that much more apparent. The concept is essentially one of quantitatively describing comparative adsorption capacities (without providing further details of where the adsorption takes place), to satisfy the requirements of human awareness. 

Areas covered by adsorbate molecules, as commonly used, are listed in Table 4.1. It has to be emphasized that such values of area do not reflect the actual area of projection within porosities. The problems of part filling of porosity and of volume Ailing have already been explained in terms as shown in Figure 4.3. Further, the packing density of adsorbate molecules is not constant under all conditions but is a function of the dimensions of the porosity into which it is adsorbed. The areas in Table 4.1 are then of an empirical nature, and are indicative. 

Figure 4.9. Projection of area of an adsorbed molecule to the surface of an adsorbent (modeled). This area is used to calculate specific surface of a solid (usually porous).

Figure 1.6 Right Density of states (DOS) of a bare Ti02 anatase nanostructure (a) and functionalized with phenyl-acac (b) and 3-acac-pyran-2-one (c). The solid-black areas in (b) and (c) are the projected DOS of the adsorbate molecules. Red and blue arrows point to electronic states with a predominant contributions to the absorption. Left Solar spectrum model based on a black body at 5523...

Naviroj et al. [28] reported that VS and MPS were adsorbed on silica (surface area of 130 m2/g) at 0.35 and 0.24 monolayer equivalents, respectively. Space projections of MPS molecules in the perpendicular and parallel orientations of the extended form were reported to be about 24 and 55 A2, respectively [48], Therefore, it is expected that a single molecular layer coverage of MPS would differ by a factor of about 2 for the two different orientations. The difference by a factor of about 2 from our experiments may also be due to similar effects. 

In order to substantiate the mechanism postulated, the IR spectra of GLY adsorbed on the strong-add cation-exchange resin originally in the H -ion form were measured [22,23]. The samples with various amounts of GLY adsorbed were prepared, and the dependence of the ratio of the integrated peak area of the bands at 1599-1600 cm" and 1754-1749 cm" on the D values was investigated. It was found that when D was < 1, the ratios were independent of the D values, while when D was > 1, the ratios increased with each increase of the D values. The mechanism projected thus seems to be supported by this result. As shown in Eq. (23), when D > 1 and the formation of a second layer of molecules occurs, the carboxyls of the first layer of amino acid molecules are certain to be dissociated so that they may serve as the new exchange sites. 

On the basis of the film thickness of 24 A compared to 20 A for AHS, an increase in the density of molecules of 20% can be estimated. Hence the density of DHS after adsorption from the solution is approximately 6 x 10 / cm , with a corresponding space requirement of 167 A / molecule. The surface-projected space requirement per OH group then amounts to an area of approximately 11 A /OH for a layer that has been fully deprotected at the surface and of 9 A /OH for a DHS layer that has been adsorbed from solution. However, it has to be borne in mind that the functional groups are homogeneously distributed through the adsorbed layer. For comparison, a densely packed f ane chain layer corresponds to approximately 22 A /molecule. ... 

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