Molecular cross-sectional area

Finally, the molecular absorption cross-section capture area of a molecule. Operationally, it can be calculated as the (Napierian) absorption coefficient divided by the number N of molecular entities contained in a unit volume of the absorbing medium along the light path ... 

Derivation of the Beer-Lambert Law from considerations at a molecular scale is more interesting than the classical derivation (stating that the fraction of light absorbed by a thin layer of the solution is proportional to the number of absorbing molecules). Each molecule has an associated photon-capture area, called the molecular absorption cross-section a, that depends on the wavelength. A thin layer of thickness dl contains dN molecules. dN is given by... 

DP Speed Factor. Pumping-speed efficiency depends on trap, valve, and system design. For gases having velocities close to the molecular velocity of the DP top jet, system-area utilization factors of 0.24 are the maximum that can be anticipated eg, less than one quarter of the molecules entering the system can be pumped away where the entrance area is the same as the cross-sectional area above the top jet (see Fig. 4). The system speed factor can be quoted together with the rate of contamination from the pump set. Utilization factors of <0.1 for N2 are common. 

G = superficial mass vapor velocity based on the cross-sectional area of the column, Ib/hr-sq ft M = molecular weight, Ib/lb mole N = dimensionless number P = pressure, consistent units [P] = Sugden parachor sg = specific gravity T = temperature, °F U = superficial velocity, ft/hr... 

The active state of luminescence spectrometry today may be judged ly an examination of the 1988 issue of Fundamental Reviews of Analytical Chemistry (78), which divides its report titled Molecular Fluorescence, Phosphorescence, and Chemiluminescence Spectrometry into about 27 specialized topical areas, depending on how you choose to count all the subdivisions. This profusion of luminescence topics in Fundamental Reviews is just the tip of the iceberg, because it omits all publications not primarily concerned with analytical applications. Fundamental Reviews does, however, represent a good cross-section of the available techniques because nearly every method for using luminescence in scientific studies eventually finds a use in some form of chemical analysis. Since it would be impossible to mention here all of the current important applications and developments in the entire universe of luminescence, this report continues with a look at progress in a few current areas that seem significant to the author for their potential impact on future work. 

Molecular size can be a further limiting factor in oral absorption [54]. The Lipinski Rule-of-5 proposes an upper limit of molecular weight (MW) of500 as acceptable for orally absorbed compounds [25]. High-MW compounds tend to undergo biliary excretion. Size and shape parameters are generally not measured, but rather calculated. A measured property is the so-called cross-sectional area, which is obtained from surface activity measurements [55]. 

FIG. 13 A schematic illustration of the effects of the free surface area of lipid bilayer membranes on the permeation of two permeants with the same molecular volume, but different cross-sectional areas, (a) A lower free surface area, (b) A higher free surface area. 

Molecular sieves (zeolites) are artificially prepared aluminosilicates of alXali metals. The most common types for gas chromatography are molecular sieve 5A, a calcium aluminosilicate with an effective pore diameter of 0.5 nm, and molecular sieve 13X, a sodium aluminosilicate with an effective pore diameter of 1 nm. The molecular sieves have a tunnel-liXe pore structure with the pore size being dependent on the geometrical structure of the zeolite and the size of the cation. The pores are essentially microporous as the cross-sectional diameter of the channels is of similar dimensions to those of small molecules. This also contrilsutes to the enormous surface area of these materials. Two features primarily govern retention on molecular sieves. The size of the analyte idiich determines whether it can enter the porous... 

Cation and anion flux across cultured cell monolayers by molecular restricted diffusion within an electrostatic field of force across aqueous pores has been described with a model derived by Adson et al. (1994). The ion fluxes per cross-sectional area of the cell monolayer are defined as... 

Since n72 is the cross-sectional area for flow, and the term under the radical is the average molecular velocity (7), equation 12.2.1 can be written in the form of Fick s first law as... 

Number-average molecular weight of relatively long chains is Mn = 18,500 g/mol. Key for the networks where short chains had M, (g/mol) A, 1,100 O, 660 0, 220. Curves are labelled with the mol percent of short chains in the network. Area below curves represents the rupture energy per unit initial cross sectional area and per unit initial... 

Molecular weight is often taken as the size descriptor of choice, mainly because it is easy to calculate and is generally in the chemist s mind. However, other size and shape properties are equally very simple to calculate and may offer a better guide to estimate potential for permeability. As yet, no systematic studies have been reported which investigate this in detail. Cross-sectional area (Ad, obtained from surface activity measurements) has been reported as being a useful size descriptor to discriminate compounds which can access the brain (Ad < 80 A2) from those that are too large to cross the BBB [62]. Similar studies have been performed to define a cut-off for oral absorption [63]. 

Molecular size has previously been suggested to play a role for substrate recognition by P-gp [28]. Surface activity measurements provide the cross-sectional area, Ad, of substrates and thus allow one to investigate the role of Ad in interaction with P-gp. Combining Eqs. (2) and (6) yields... 

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