Permeation volume

Select mobile phases for HPSEC based on their ability to dissolve the sample and their compatibility with the column. Zorbax PSM columns are compatible with a wide variety of organic and aqueous mobile phases (Table 3.4), but analysts should avoid aqueous mobile phases with a pH greater than 8.5. As mentioned earlier, select mobile phases that minimize adsorption between samples and silica-based packings. Sample elution from the column after the permeation volume indicates that adsorption has occurred. If adsorption is observed or suspected, select a mobile phase that will be more strongly adsorbed onto the silica surface than the sample. For example, N,N-dimethyl-formamide (DMF) is often used for polyurethanes and polyacrylonitrile because it eliminates adsorption and dissolves the polymers. When aqueous mobile phases are required, highly polar macromolecules such as Carbowax can be used to coat the silica surface and eliminate adsorption. Table 3.5 provides a list of recommended mobile-phase conditions for some common polymers. 

Most GPC columns are provided with vendor estimates of the plate count of the column and a chromatogram of a series of test peaks. These plate count estimates are usually obtained using small molecule analytes that elute at the total permeation volume (Vp) of the column. The Gaussian peak shape model... 

Flow markers are often chosen to be chemically pure small molecules that can fully permeate the GPC packing and elute as a sharp peak at the total permeation volume (Vp) of the column. Examples of a few common flow markers reported in the literature for nonaqueous GPC include xylene, dioctyl phthalate, ethylbenzene, and sulfur. The flow marker must in no way perturb the chromatography of the analyte, either by coeluting with the analyte peak of interest or by influencing the retention of the analyte. In all cases it is essential that the flow marker experience no adsorption on the stationary phase of the column. The variability that occurs in a flow marker when it experiences differences in how it adsorbs to a column is more than sufficient to obscure the flow rate deviations that one is trying to monitor and correct for. 

The use of totally permeated flow markers in aqueous GPC offers similar advantages along with many of the same shortcomings that one finds in nonaqueous GPC. One problem commonly found in aqueous GPC is that salt peaks due to the on-column ion exchange of counter ions of a polyelectrolyte with dissimilar ions in the GPC mobile phase will occur at or near the total permeation volume of the column. These salt peaks will often obscure the flow marker used in the analysis. Short of preconditioning the sample to exchange... 

Reverse osmosis plant are always subject to an insidious and gradual loss of permeate volume output or quality deterioration due to membrane fouling. The rate of decline is strongly influenced by the input RW quality. Therefore, any and all features, such as those above, that can be employed to delay the onset and degree of fouling and extend membrane life are to be recommended. 

FIGURE 23.10 Permeated volume versus time for gas permeation test. 

As can be seen from Figure 2, pore permeation increases with ionic strength, but the curves are not linear and in particular show poor resolution at MW less thcui a million. Complete loss of resolution in this MW reuige is seen at 0.5 M NaCl reflecting, presumably total permeation. However the total permeated volume (as measured with NaCl) is significantly greater than the polymer elution voliame at 0.5 M NaCl. Such a volume difference could be explained if a fraction of the pores is inaccessible to even the lowest M.W. polymer investigated. 

Flow Flux, Permeability, Conversion The productivity of a membrane module is described by its flux J = volumetric permeate flow rate/membrane area with units of volume per area per time. Relatively high flux rates imply that relatively small membrane areas are required. The permeate volume is usually greater than the feed volume for a given process. Flux is also the magnitude of the normal flow velocity with units of distance per time. 

System sizing involves integration of Eq. (20-69) using a flux model to give Eq. (20-71), where Vp is the permeate volume and J is the average flux. Note the direct tradeoff between area and process time. Table 20-19 shows the concentration and diafiltration steps separated and processing time. 

N, and solute passage Si needed to produce desired retentate product with impurity concentrations Cj and retentate product yield Mj/Mjo. Permeate product characteristics for batch operation can be determined by mass balances using a permeate volume of Vp = Vo(l 1/X + N/X), a mass of solute i in the permeate as Mj perme e = Mjo(l — and the permeate concentration as the ratio of the... 

Basic Principles of Operation Gas-separation literature often uses nomenclature derived from distillation, a practice that will generally be followed here. L is the molar feed rate, V is the molar permeate rate, R is the molar residue (L — V). Mole fractions of components i, j, in the feed-residue phase will be Xj, Xj. .. and in the permeate phase yi,yj.... Stage cut, 0, is permeate volume/feed volume, or V/L. 

VT = Retention volume for a component that has full access to all the pores of the support (or total permeation volume). 

SEC can be used to accomplish a class separation in which one component of the sample elutes in either excluded volume or permeation volume we term this application as group fractionation. Alternatively, SEC can be used to resolve two or more species within the included volume (e.g., between V0 and VP). We term this application simply as fractionation. 

The critical operational assumption that makes it possible to draw conclusions in a given comparison situation about the effect of plate and pore amount is that a constant volume and a constant absolute amount of solute was injected per column to normalize comparisons. If pore amount per column is constant, then increase in resolution with several columns of the same kind in series is due only to the increased amount of plates. Conversely, if plates of a column bank are the same, then differences in resolution are due to differences in the amount of pores of appropriate size. Also, all the other appropriate operating parameters are constant for each comparison. The following group of comparisons will illustrate different issues involving the interplay of pores, plates, and resolving power. The times on the figures are maximum values for total permeation volumes at a flow rate of 1 ml/min. 

Effect of Injection Volume. Table II shows the effect of injection volume on peak broadening and measured column efficiency. The bandwidths listed in Table II are due to injection volume alone, and were measured using an injector connected directly into the flowcell of a low-bandwidth detector. The plate reductions were then calculated for a 24,000 plate column, such as that represented by the bottom line of Table I, assuming 5 and 10 ml, respectively, for exclusion and total permeation volumes. Efficiencies of 23,000 plates at exclusion and 25,000 plates at permeation were actually measured for the column indicated in Table II. The effect of large injection volumes is thus to lose 25 to 50% of the potential column efficiency. 

Use of Kq Instead of Vg in the calibration of columns produces a calibration curve that is independent of column dimensions and pore volume. To obtain Kq for any species requires the determination of Vg and Vj in addition to Vg. Vg is usually taken as the elution volume of an excluded polymer while Vj is equal to V-j - Vg. The volume V-j is the total permeation volume of the column and is measured with a low molecular weight compound that totally permeates particle matrices. 

From these studies with SynChropak SEC packings and controlled porosity glass, it is concluded that the silica packing contains a population of micropores which are differentially accessible to low molecular weight probes of total permeation volume. It is not known, however, if the microporosity in the 100 and 300A SynChropak SEC packings is the result of the rather wide pore-size distribution and whether all silicas contain micropores. 

In view of Freeman s studies on the use of normal alkanes and polystyrenes to probe the macroporosity of porous materials (24), the results presented here would suggest that low molecular weight species ranging from twenty (deuterium oxide) to several thousand daltons may be used to define microporosity of a SBC support. The ease with which this is achieved may allow routine examination of microporosity in new support materials and a more exact definition of total permeation volume in SBC. 

Polymer-assisted ultrafiltration. The functionalized dendrimer described above was used to remove boron from an aqueous feed stream. With the polymer in the holding cell (see Figure 3), the feed was added at the same rate that the permeate left the system. The differential equation describing the change in total boron concentration in the holding cell as a function of permeate volume is simply d(Bt)... 

Figure 6. Concentration of boron in the permeate (solid squares) as a function of permeate volume as the 1.63 mM boric acid feed (pH 9) was diafiltered through the holding cell containing 100 ml water and 4.755 g GP3 dendrimer. The permeate pH rose from 5.02 at the beginning of the run to 7.75 at the end. Model parameters Rg, 88.5 A K, 6300 K2,105 Mw, 55471 fp, 0.024.

The salt flux through the membrane is given by the product of the permeate volume flux. /,. and the permeate salt concentration c,p. For dilute liquids the permeate volume flux is within 1 or 2% of the volume flux on the feed side of the membrane because the densities of the two solutions are almost equal. This means that, at steady state, the net salt flux at any point within the boundary layer must also be equal to the permeate salt flux Jvcip. In the boundary layer this net salt flux is also equal to the convective salt flux towards the membrane Jvc, minus the diffusive salt flux away from the membrane expressed by Fick s law (Didcildx). So, from simple mass balance, transport of salt at any point within the boundary layer can be described by the equation... 

---