Molecular cross sections

The interactions of photons with molecules are described by molecular cross-sections. For IR spectroscopy the cross-section is some two orders of magnitude smaller with respect to UV or fluorescence spectroscopy but about 10 orders of magnitude bigger than for Raman scattering. The peaks in IR spectra represent the excitation of vibrational modes of the molecules in the sample and thus are associated with the various chemical bonds and functional groups present in the molecules. The frequencies of the characteristic absorption bands lie within a relatively narrow range, almost independent of the composition of the rest of the molecule. The relative constancy of these group frequencies allows determination of the characteristic... 

The equilibrium constants can be approximated by ratios of ion currents in some instances otherwise, the currents are converted to partial pressures by comparison with the evaporation of known amounts of a standard material. Various geometric corrections (K) such as the solid angle subtended by the sample at the orifice, the Clausing factor for orifice geometry, molecular cross-section (o-), which control ionization efficiency, and detector efficiency are included in the general relationship... 

All the systems studied appear to have similar A values, which are however lower than A=0.169 ( 1 = 0.35) according to Equation 5. This difference can be attributed to the real molecular cross-sections different from the circular one assumed in the Argon theory (3). In general, all the systems have molecular parameters (a, z ) similar to the DGEBA/TETA systems studied by Yamani and Young (5) as shown in Table II. 

The molecular cross-sectional area j/ then can be obtained by dividing the planar area, p, by N Ny, the number of molecules in a plane. Thus, by dividing both numerator and denominator of the fraction, V/N,by the number of moles, yields... 

For the condensed LC and S states a molecular interpretation is again possible. In both the values of o° are close to actual molecular cross sections when the molecules are oriented perpendicular to the surface. The difference between these two regions seems to involve the polar part of the molecule more than the hydrocarbon chain, which was more important for the more expanded states. The difference between and o c may involve a more efficient packing of the heads or the formation of fairly specific lateral interactions through hydrogen bonds, for example. The values of o° that are observed for monolayers of saturated w-alkyl compounds are only slightly larger than the close-packed cross sections obtained for these compounds in the bulk solid state by x-ray diffraction. 

SBet was calculated using the molecular cross-sectional area of N2, 0.162 nm2/molecule. 

The area determinations by dye adsorption from solution discussed here are applicable to aqueous dispersions. Although saturation coverage of silver halides by Pseudocyanine remained unchanged in 40% methanol by volume, it is known that in organic solvents where ion-pairs may be adsorbed, the molecular cross section of the cyanine can vary with the dye s anion—cf. Reference 23 for discussion and literature citations. Recent determinations of Agl areas by adsorption of Pseudocyanine were reported to have been unrealistic and salt-dependent (van den Hul, H. J., Lyklema, J., J. Phys. Chem. 90, 3010 (1968)). A likely reason for this result is the circumstance that these investigators carried out their measurements in alcohol dispersions of the substrate where the cited solvent-dependent limitations would apply. 

Solid (S). The headgroups are largely dehydrated. Pressure-area isotherms are linear. Extrapolation to zero film pressure results in an area per molecule that corresponds to the molecular cross-section. For example, lipids with two long-chain fatty acids occupy an extrapolated area of 41 A2, which corresponds to the cross-sectional area of the molecule [585],... 

Here, Nmono is the number of adsorbed molecules to form a monolayer for each probe molecule and surface fractal dimension determined by using the MP method. The probe molecules need not to be spherical, provided they belong to a homologous series for which the ratio [linear extent rm]2 to molecular cross-sectional area Ac is the same for all members, i.e., an isotropic series. In this case, Eq. (13) turns into... 

The ratio of the activation energy EP and ED of two gases are relatively independent of the nature of the polymer. Furthermore, the ratio of Ed values corresponds almost exactly to the ratio of the squares of the molecular cross sectional diameters (a2) of the two gases (Table 9-3). This knowledge allows the estimation of D, S and P values with help of easily obtainable molecular properties (see Section 9.1.3). 

The second stage in the application of the BET method is the calculation of the surface area (often termed the BET area) from the monolayer capacity. This requires a knowledge of the average area, am (molecular cross-sectional area), occupied by the adsorbate molecule in the complete monolayer. Thus... 

Figure 7-30 Plot of Molecular Cross-Sectional Area Versus Free Energy of Adsorption for Davies Theory of Olfaction...

An early normalizing procedure, proposed by Kiselev (1957) to compare adsorption isotherms of hydrocarbons, water vapour, etc. on a series of different adsorbents, was simply to plot the surface excess concentration F (=n/A), obtained from a knowledge of the BET-nitrogen surface area, A (BET), versus p/p°. It is also possible to plot, instead of f, the reduced adsorption , n/nm, which still relies on the BET method to determine the monolayer capacity nm but does not require knowledge of the molecular cross-sectional area a. 

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