Diffusion obstructive factor

An obstruction factor t i is included in the numerator of this term to account for the obstruction to free diffusion caused by packed beds. Some typical values of i r are given in Table 3. The faster the mobile phase moves, the less time the zone is in the column, the less time there is for diffusion, and the lower is the broadening due to diffusion. Consequently, this term... 

During the diffusion of small molecules (with molecular weights less than about 1000 g/mol or molar volumes less than about 0.500 m3/kg) in protein solution, the diffusion may be blocked by the large molecules. In order to account for this effect, we need the diffusivity l)Mi of solute A in water alone, the water of hydration on the protein, and an obstruction factor. A semitheoretical relation to approximate the diffusivity of solute in a globular-type protein solution is... 

The B constant is a function of longitudinal diffusion that serves to spread analyte molecules apart and is linearly dependent on D, the diffusion coefficient of an analyte in the mobile phase according to an obstruction factor designated... 

The velocity-independent term A characterises the contribution of eddy (radial) diffusion to band broadening and is a function of the size and the distribution of interparticle channels and of possible non-uniformiiies in the packed bed (coefficient A.) it is directly proportional to the mean diameter of the column packing particles, dp. The term B describes the effect of the molecular (longitudinal) diffusion in the axial direction and is directly proportional to the solute diffusion coefficient in the mobile phase, D, . The obstruction factor y takes into account the hindrance to the rate of diffusion by the particle skeleton. 

The diffusion coefficient must be reduced in packed columns because there are obstructions that prevent simple linear diffusion. This is given a dimensionless measure as an obstructive factor, y, with a value of approximately 0.6. Simple substitution... 

B — longitudinal diffusion term = 2jDm y obstruction factor Dm = diffusion coefficient... 

When using a support with sufficiently large pores and/or a completely nonporous support, or in the case that the pores of a microporous support are completely filled with the appUed Uquid sorbent, the term al C ) can be omitted. When the liquid sorbent forms a completely continuous film on the support (a situation which may occur in an ideal case when using a macroporous support or when using a capillary column), then q in the term al(Cg)) has a value of 2/3, whereas in the case of a microporous support with the pores filled completely with the liquid sorbent, q in the term o (Cs,) equals l/SOyg and df = dp, where is the obstructive factor for diffusion of the solute in the liquid sorbent inside the pores. 

Care must be taken with the definition of the velocity. S ne part of the obstruction factor can be explained by an inappropriate definition of the velocity. We must keep in mind that it refers to the residence time in the mobile phase of the sample compound whose diffusion is measured. This residence time is not necessarily identical to the residence time of an unretained sample compound, which is used to measure the linear velocity. Also, we implicitly assimied that the diffusion coefficient in the pores is the same as the diffusion coefficient in the interstitial mobile phase. This is also not necessarily the case. If me pore size is less than about 10 times larger than the size of the molecule, the diffusion coefficient depends on the ratio of the size of the sample molecule to w pore size of the packing. 

Figure 5 The variation of the obstruction factor A defined as the reduced self-diffusion coefficient D/Do of small solvent molecules in solutions as a function of the volume fraction of obstructing particles of different geometries. Curve a denotes spheres b, long prolates c, d, and e. oblates of axial ratios 1 5. 1 10, and 1 100, respectively and f, large (i.e., infinite) oblates. (Redrawn from...

Anderson and Wennerstrom [33] calculated the geometrical obstruction factors of the self-diffusion of surfactant and solvent molecules in ordered bicontinuous microstructures, which serve as good approximations also for the disordered bicontinuous microemulsions and L3 (sponge) phases. The geometrical obstruction factor is defined as the relative diffusion coefficient DIDq, where D is the diffusion coefficient in the structured surfactant system and Z)q is the diffusion coefficient in the pure solvent. In a bicontinuous microemulsion the geometrical obstruction factor depends on the water/oil ratio. An expansion around the balanced (equal volumes of water and oil) state gives, to leading order. 

The first was the physical restriction of the jjeptide motion, more specifically its diffusion within the water cylinders, owing to the geometric constrain of hexagonal architecture. The second factor is the chemical interactions of the peptide with the polar heads of monoolein. These two effects were separated and quantified by SD-NMR analysis (SD-NMR). Rankin s model [43] was used to calculate the theoretical diffusion coefficients of desmopressin within the channels of the Hu mesophase, assuming no interactions of the peptide with GMO and TAG. Using the theoretical diffusion coefficient of the drug and the measured diffusion values, the observed decrease in diffusion coefficients of the peptide in the Hn mesophase was clarified (Fig. 12.23), defining two obstruction factors. The obstruction factors enabled quantification of the effects of both physical restriction (p) and the chemical interactions (y). 

Band spreading is also related to an obstructive factor that is not a constant in a column bed. Both Kubin [6] and Pfannkoch et al. [11] have shown that plate height varies as a function of K. It appears that as its molecular size approaches the pore dimensions, a solute experiences diffusion limitations, decreasing its effective diffusion coefficient. This influence of restricted molecular movement on plate height (//) can be readily observed in SEC profiles. The first peak to elute after the void volume marker is frequently the broadest peak in the chromatogram. If one were able to obtain columns with different pore diameters but similar plate counts, pore volumes, and calibration curve slopes, it would be best to select a column on which would be 0.2 or greater for the solutes to minimize the effect of the obstructive factor. 

The contributions to plate height of particle diameter, obstructive factor, and linear velocity are either inherent in a column or arise from the way it is operated. There is another set of variables, however, that arise from the sample itself The contribution of these variables to band broadening is through the diffusion coefficient (Dm)- The Einstein equation ... 

Obstruction factor, which takes into account the obstruction of the free longitudinal diffusion due to collisions with particles of the column packing... 

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