Molecular cross-section area

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... 

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

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 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. 

The best value for the effective molecular cross-sectional area, o(Kr), of krypton in the BET monolayer at 77 K has been under discussion for many years. In their original work on krypton adsorption, Beebe et al. (1945) recommended the value 0.195 nm2 for o(Kr) and this empirical value is still used by many investigators. For the adsorption of krypton on graphitized carbon, Ismail (1990, 1992) gives preference to the value molecular area calculated from the liquid density and determined by X-ray scattering. This, of course, implies that Kr and N2 molecules undergo localized adsorption on the same sites. For ungraphitized carbons, Ismail (1992) recommends cr(Kr) = 0.214 nm2. 

Nitrogen adsorption/condensation measurements were performed using an Autosorb-1 analyzer to calculate sample surface area and pore size distribution. BET analysis at 77 K was applied for extracting the monolayer capacity from the adsorption isotherm and a N molecular cross-sectional area of 0.162 nm2 was used to relate tne monolayer capacity to surface area. PSD s were calculated from the desorption branches of the isotherms using a modified form of the BJH method [18]. Mercury intrusion measurements were performed using an Autoscan-33 continuous scanning mercury porosimeter (12-33000 psia) and a contact angle of 140°. 

Here, the mole fraction of/ in the mobile phase is given asN, and/ b is the molecular cross-sectional area (A> value) of solvent molecules. When the... 

The calculation of the adsorbent surface area using BET theory involves the estimation of the molecular cross-sectional area of nitrogen molecule [15]. In general it is assumed to be equal to 16.2 per nitrogen molecule on the surface, but this value is the subject of intense criticism during the past 30 years [72]. 

It therefore follows that the apparent BET surface area, derived with a molecular cross-sectional area suited for adsorption on a flat surface, is, by principle, smaller than the reality in the case of ultra-micropores, larger than the reality in the case of broader super-micropores and satisfactory in the case of mesopores and, of course, macropores. 

The prediction of the molecular cross-sectional area is based on the correlations derived by McClellan and Harnsberger, which were developed based on the assumption that the same surface area was obtained by adsorption of different adsorbates. However, this is not true if the particle surface is rough. Adsorbate molecules having larger cross-sectional area cannot access the finer structure of the surface. Therefore the determination of Ds from the second method might not be accurate. 

Gerebtzoff, G. and Seelig, A. (2006) In silico prediction of blood-brain barrier permeation using the calculated molecular cross-sectional area as main parameter. Journal of Chemical Information and Modeling, 46, 2638-2650. 

Figure 5. Molecular cross-sectional areas of sterols (1)...

A (a) Molecular cross-sectional area of a polymer chain. 

Membrane permnability decreases exponentially with increasing molecular size, where the latter is expressed in terms of molecular cross-sectional area. 

It is likely that experimentally found values of molecular cross-sectional areas do not correspond to the equilibrium states of the protein layers but reflect only the transition state configuration, as assumed by MacRitchie [16] and depicted in Fig. 1. The problem of adsorption reversibility is basic for understanding the protein behavior at interfaces. The belief in the protein adsorption irreversibility is mainly based on drastic conformational changes in interfacial film and the great difficulty of desorbing a protein from this film [15], However, these criteria are not always a proof of irreversibility. It was shown in many cases [3,24,39-41] that proteins can be desorbed... 

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