Fractional rejection

As a result, most systems are limited, to achieving a mole fraction reject of 0.1 or less (see Membrane technology). 

Fractions rejected by 1.0 KDa (C>i) and permeated through 0.5 KDa (C0 5) membranes were also subjected to TLC analysis. In Figure 3 are reported the values relevant to the various spots detected in the two samples as a function of an arbitrary polymerisation degree (DP). The good linear correlation between these parameters allows to hypothesise a difference of one monomer units between the subsequent spots [32]. Consequently, C0.5 would correspond to the monomer, Cj to an homologous series fi om the monomer to the hexamer. 

Three new methods to characterize the pore structure and pore size distribution in the top layer of asymmetric membranes have been developed or refined in our laboratory during the past few years a) the gas ad-sorption/desorption method, b) thermoporometry and o) selective permeation (fractional rejection). 

Pore size distributions are determined from the hysteresis loop in gas adsorption/desorption isotherms and from calorimetric measurements by the shift in the melting (or freezing) peak for a phase transition of water inside the pores. The determination of the fractional rejection properties is done by permeation experiments of a macromolecular solute with a broad molecular weight distribution (MWD). The MWD of permeate and feed are compared and translated into a fractional rejection curve. The comparison of results obtained from these three independent methods for some characteristic membranes gives an indication of the strength and weakness of each of the methods studied. 

Selective permeation. In order to come to a more precise characterization of the rejection properties of an UF membrane we developed ameth-od (11) in which the molecular weight distribution (MWD) of macromolecules present in the permeate is compared tp the one present in the feed. For these experiments a macromolecular solute is used with a broad MWD For example Polyethylene Glycol (PEG) 100 000 or mixtures of various PEGs. Comparing the MWD of the feed with the MWD of the permeate, the fractional rejection (Rjj.) is defined as follows ... 

A comparison of the fractional rejection (R. ) with the classical cut-off curve, which can be seen in the upper part of Figure 5... 

Figure 5. (Intrinsic) fractional rejection (Rjj.) and (intrinsic) classical rejection (R) curves for a PSf membrane, using PEG 100 000 as solute.

Together, fractional rejection curve (Rjj.) and traditional cut off curve will give more information on the rejection characteristics of ultrafiltration membranes. 

Uitrafiltration membranes have a range of pore sizes in the selective layer, and they are often characterized by a molecular weight cutoff based on measurements of fraction rejected versus molecular weight.Molecules larger than the... 

Partial rejection of solutes. In many applications of UF, the membrane selected has some pores that are larger than the solute molecules, and the solute is only partially rejected. The fraction rejected, R, is sometimes defined using the feed and permeate concentrations ... 

Where the term vL/D is less than 2.0, solute diffusion has a significant effect on the rejection. Because diffusion lowers the rejection at low permeate flux and concentration polarization is important at high flux, the fraction rejected is predicted to go through a maximum with permeate flux. The diffusion effect should be quite pronounced if the active layer is very thin, say, 0.1 to 0.2 pm, but there are not enough data to confirm this. 

Example 30.5. Ultrafiltration tests with a 1.5-cm tubular membrane at — 25,000 gave a permeate flux of 40 L/m -h and 75 percent rejection for a 5 percent polymer solution. The polymer has an average molecular weight of 30,000, and the estimated diffusivity is 5 x 10 cm s. (fl) Neglecting the effect of molecular diffusion in the pores, predict the fraction rejected for a flux of 20 L/m -h, and predict the maximum rejection, (b) Estimate the fraction rejected for the low-molecular-weight fraction of the pol3mier with M 10,000. (c) If the selective layer thickness is 0.2 fan, does molecular diffusion have a significant effect on the rejection for case (a) ... 

The terms Ald)i have been calculated from the measured permeability coefficients, as shown earlier in Equation (4). For these calculations the diffusion coefficient of KCl was taken as 1.89 x 10" cm s" the measured permeability of KCl was 5.7 X 12" cm s when the feed side concentration was 0.1 M. With these data the fractional rejection was found to be 0.995, indicating the very high efficiency with which the ion exchange fiber operates in dilute electrolyte solutions. When the ionic strength of the medium is higher, the semi-permeability would of course be somewhat lower, as shown by the CrOJ data presented earlier. 

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