Size exclusion mass transfer

The diffusivity in gases is about 4 orders of magnitude higher than that in liquids, and in gas-liquid reactions the mass transfer resistance is almost exclusively on the liquid side. High solubility of the gas-phase component in the liquid or very fast chemical reaction at the interface can change that somewhat. The Sh-number does not change very much with reactor design, and the gas-liquid contact area determines the mass transfer rate, that is, bubble size and gas holdup will determine reactor efficiency. 

The effects of various pore-size distributions, including Gaussian, rectangular distributions, and continuous power-law, coupled with an assumption of cylindrical pores and mass transfer resistance on chromatographic behavior, have been developed by Goto and McCoy [139]. This study utilized the method of moments to determine the effects of the various distributions on mean retention and band spreading in size exclusion chromatography. 

The effect of pore size on CEC separation was also studied in detail [70-75]. Figure 9 shows the van Deemter plots for a series of 7-pm ODS particles with pore size ranging from 10 to 400 nm. The best efficiency achieved with the large pore packing led to a conclusion that intraparticle flow contributes to the mass transfer in a way similar to that of perfusion chromatography and considerably improves column efficiency. The effect of pore size is also involved in the CEC separations of synthetic polymers in size-exclusion mode [76]. 

L. Size exclusion chromatography of proteins Na = M = i 03 D e [E] Slow mass transfer with large molecules. Aqueous solutions. Modest increase in NSk with increasing velocity. [79]... 

As previously indicated, this discussion is organized for chromatograms from very narrow polymer standards for which we can consider that the effect of molecular weight distribution is negligible and for which the unique separation process is size exclusion. With these limitations, the contribution to band broadening is conveniently separated into extra column effects, eddy dispersion, static dispersion, and mass transfer. In the most classical chromatographic interpretation, extra-column effects are not discussed and the three other contributions are considered as Gaussian, so there is simply the addition of their variances. The number of theoretical plates is defined as N = VJaY and the influence of v, the linear velocity of the eluent, is summarized by the so-called Van Deemter equation ... 

An important initial criterion is thus to enhance the stability of these interactions.13 At the same time, the number of nonspecific binding sites will be minimized since there will be a reduction in the amount of free nonassociated functional monomer. However, varying these synthesis-related factors will also affect the morphology of the materials at a meso and macroscopic level,14 which in turn determine their kinetic properties, e.g., diffusional mass transfer limitations, size exclusion effects, bleeding. 

These conclusions differ somewhat from those of Pirkle and Siegell in their analysis of adsorption chromatography in a crossflow magnetically fluidized bed (14). They found the dominant effects to be the width of the feed band and the external mass transfer resistance. It is not surprising that the effect of internal diffusion would be more important in size exclusion chromatography with macromolecular solutes. 

From Eq. (2), the measured diffusivities may be used to determine the mean lifetime of the reactant and product molecules within the individual crystallites under the assumption that the molecular exchange is exclusively controlled by intracrystalline diffusion. These values, being of the order of 30 ms, are found to agree with the real intracrystalline mean lifetime directly determined by NMR tracer desorption studies (208], so that any influence of crystallite surface barriers may be excluded. From an analysis of the time dependence of the intracrystalline concentration of the reactant and product molecules, the intrinsic reaction time constant is found to be on the order of 10 s. This value is much larger than the intracrystalline mean lifetimes determined by PFG NMR, and thus any limiting influence of mass transfer for the considered reaction may be excluded. In agreement with this conclusion, the size of the applied crystallites was found to have no influence on the conversion rates in measurements with a flow reactor (208]. 

Most separations in liquid chromatography are performed at room temperature for convenience and because ambient temperatures provide reasonable column efficiency for low molecular mass solutes. Elevated temperatures are commonly used in ion-exchange chromatography to improve mass transfer kinetics and in size-exclusion chromatography to provide adequate solubility for polymers in useful mobile phases. Wider interest in temperature control and high-temperature separations in general results from improved precision of retention measurements (section 1.1.1), greater column efficiency (section 1.5.2), the use of temperature as a variable for method development (section 4.4.4), and shorter separation times due to the more favorable use of the column inlet pressure [70,71]. 

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