Diffusivity Molecular weight relationship

CR, cryoscopic method DV, diffusion constant and intrinsic viscosity EB, ebullioscopic method EG, end-group titration IV, intrinsic viscosity-molecular weight relationship in other solvents LS, light scattering MV, melt viscosity-molecular weight relationship OS, osmotic pressure PR, analysis of polymerization rate SD, sedimentation and diffusion constants SE, sedimentation equilibrium (Archibald s method) SV, sedimentation constant and intrinsic viscosity [see Eq. (72)]. 

Empirical or semiempirical methods GPC, gel permeation chromatography LV, limiting viscosity-number-molecular-weight relationship SD, sedimentation diffusion. 

E. Polymolecularity Correction Factors for Diffusion Coefficient versus Molecular Weight Relationship... 

E. DIFFUSION COEFFICIENT VERSUS MOLECULAR WEIGHT RELATIONSHIP... 

Porin channels are impHcated in the transport of cephalosporins because ceds deficient in porins are much more impermeable than are ceds that are rich in porins. The porins appear to function as a molecular sieve, adowing molecules of relatively low molecular weight to gain access to the periplasmic space by passive diffusion. In enterobacteria, a clear correlation exists between porin quantity and cephalosporin resistance, suggesting that the outer membrane is the sole barrier to permeabdity. However, such a relationship is not clearly defined for Pseudomonas aeruginosa where additional barriers may be involved (139,144,146). 

The major problem in this procedure is not in obtaining an accurate value for the solute diffusivity from peak width measurements (which is relatively straightforward) but in identifying the best relationship between diffusivity and molecular weight to employ in the subsequent data processing. 

Unfortunately, there are many expressions in the literature that give molecular weight as a function of diffusivity, and the most appropriate expression must be identified in order to permit a reasonably accurate value for the molecular weight to be calculated. Thus, the diffusivities of a large number of solutes of known molecular weight need to be measured in a solvent that is commonly used in the liquid chromatography, so that a practical relationship between diffusivity and molecular weight can be identified. 

To day peak widths are rarely used in chromatographic analysis except for the purpose of calculating peak areas. Peak widths, however, can provide a means of measuring the diffusivity of a solute which is a function of the molecular weight. Consequently, if a reliable relationship between diffusivity and molecular weight can be identified, then the molecular weight of the solute can be assessed. Peak widths of solutes eluted from an open tube can give very precise values of diffusivity. There are a number of equations that purport to relate diffusivity to... 

The interdiffusion of polymer chains occurs by two basic processes. When the joint is first made chain loops between entanglements cross the interface but this motion is restricted by the entanglements and independent of molecular weight. Whole chains also start to cross the interface by reptation, but this is a rather slower process and requires that the diffusion of the chain across the interface is led by a chain end. The initial rate of this process is thus strongly influenced by the distribution of the chain ends close to the interface. Although these diffusion processes are fairly well understood, it is clear from the discussion above on immiscible polymers that the relationships between the failure stress of the interface and the interface structure are less understood. The most common assumptions used have been that the interface can bear a stress that is either proportional to the length of chain that has reptated across the interface or proportional to some measure of the density of cross interface entanglements or loops. Each of these criteria can be used with the micro-mechanical models but it is unclear which, if either, assumption is correct. 

With this relationship for all samples was calculated from ninh This M is used for evaluating the reaction data. The ultracen rifuge (u.c measurements were carried out in a Spinco model E analytical ultracentrifuge, with 0.4% solutions in 90% formic acid containing 2.3 M KCl. By means of the sedimenta- ion diffusion equilibrium method of Scholte (13) we determine M, M and M. The buoyancy factor (1- vd = -0.086) necessary for tSe calculation of these molecular weights from ultracentrifugation data was measured by means of a PEER DMA/50 digital density meter. 

The method preferred in our laboratory for determining the UWL permeability is based on the pH dependence of effective permeabilities of ionizable molecules [Eq. (7.52)]. Nonionizable molecules cannot be directly analyzed this way. However, an approximate method may be devised, based on the assumption that the UWL depends on the aqueous diffusivity of the molecule, and furthermore, that the diffusivity depends on the molecular weight of the molecule. The thickness of the unstirred water layer can be determined from ionizable molecules, and applied to nonionizable substances, using the (symmetric) relationship Pu = Daq/ 2/iaq. Fortunately, empirical methods for estimating values of Daq exist. From the Stokes-Einstein equation, applied to spherical molecules, diffusivity is expected to depend on the inverse square root of the molecular weight. A plot of log Daq versus log MW should be linear, with a slope of —0.5. Figure 7.37 shows such a log-log plot for 55 molecules, with measured diffusivities taken from several... 

Molecules with a large molecular weight or size are confined to the transcellular route and its requirements related to the hydrophobicity of the molecule. The transcellular pathway has been evaluated for many years and is thought to be the main route of absorption of many drugs, both with respect to carrier-mediated transport and passive diffusion. The most well-known requirement for the passive part of this route is hydrophobicity, and a relationship between permeability coefficients across cell monolayers such as the Caco-2 versus log P and log D 7.4 or 6.5 have been established [102, 117]. However, this relationship appears to be nonlinear and reaches a plateau at around log P of 2, while higher lipophilicities result in reduced permeability [102, 117, 118]. Because of this, much more attention has recently been paid towards molecular descriptors other than lipophilicity [86, 119-125] (see section 5.5.6.). The relative contribution between the para-cellular and transcellular components has also been evaluated using Caco-2 cells, and for a variety of compounds with different charges [110, 112] and sizes [112] (see Section 5.4.5). 

Musculus and Meyer (12) measured the diffusion rates of some starches and dextrins in 1881. The work was designed to determine the relationship of these "isomeric or polymeric" forms to the simple sugars from which they were formed. They concluded that dextrin molecules must be much larger than those of the sugars. This work, however, preceeded Raoult s (13) development of the cryoscopic technique for the determination of the molecular weights of dissolved substances, and van t Hoff s (14) formulation of the solution laws. Further, since the vapor density method was obviously inapplicable, it was not possible for them to actually determine the degree of polymerization. 

For the solubility of TPA in prepolymer, no data are available and the polymer-solvent interaction parameter X of the Flory-Huggins relationship is not accurately known. No experimental data are available for the vapour pressures of dimer or trimer. The published values for the diffusion coefficient of EG in solid and molten PET vary by orders of magnitude. For the diffusion of water, acetaldehyde and DEG in polymer, no reliable data are available. It is not even agreed upon if the mutual diffusion coefficients depend on the polymer molecular weight or on the melt viscosity, and if they are linear or exponential functions of temperature. Molecular modelling, accompanied by the rapid growth of computer performance, will hopefully help to solve this problem in the near future. The mass-transfer mechanisms for by-products in solid PET are not established, and the dependency of the solid-state polycondensation rate on crystallinity is still a matter of assumptions. 

Pugh WJ, Degim IT, Hadgraft J (1996) Epidermal permeability-penetrant structure relationships 4. QSAR of permeant diffusion across human stratum corneum in terms of molecular weight, H-bonding and electronic charge. Int J Pharm 197 203-211. 

Among the many industrial applications, one can recall the analyses on carbon black, where FIFFF and SdFFF were used in synergy, and on carbon nanotube, for which a frit inlet AsFlFFF channel was used. Water-soluble polydisperse polymers were fractionated, with a very high selectivity, according to differences in the diffusion coefficient, yielding a diffusion coefficient spectrum which was then converted into a molecular weight (M) distribution curve based on the relationship between D and molecular weight [36]. 

Notice the similarity in form of Eq. (4.65) with Eq. (4.7), which used the packing fraction to estimate the viscosity. In this case, however, the dependences are the inverse of packing fraction and molecular weight to those in Eq. (4.7). In other words, whatever factors that change viscosity will have the opposite effect on diffusion. As viscosity goes up, diffusivity goes down the inverse is true as well. This relationship is stated... 

In these relationships, Ya, is the mass fraction that enters the channel, Da is the diffusion coefficient of species A relative to the bulk fluid, and IV is the mean molecular weight. Based on the scaling and the nondimensional groups, discuss the circumstances under which the axial diffusion may be neglected. Show also how the nondimensional axial coordinate z may be written in terms of the Reynolds and Schmidt numbers. 

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