Volume totally permeated

Next let us consider the differences in molecular architecture between polymers which exclusively display viscous flow and those which display a purely elastic response. To attribute the entire effect to molecular structure we assume the polymers are compared at the same temperature. Crosslinking between different chains is the structural feature responsible for elastic response in polymer samples. If the crosslinking is totally effective, we can regard the entire sample as one giant molecule, since the entire volume is permeated by a continuous network of chains. This result was anticipated in the discussion of the Bueche theory for chain entanglements in the last chapter, when we observed that viscosity would be infinite with entanglements if there were no slippage between chains. 

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... 

Some GPC analysts use totally excluded, rather than totally permeated, flow markers to make flow rate corrections. Most of the previously mentioned requirements for totally permeated flow marker selection still are requirements for a totally excluded flow marker. Coelution effects can often be avoided in this approach. It must be pointed out that species eluting at the excluded volume of a column set are not immune to adsorption problems and may even have variability issues arising from viscosity effects of these necessarily higher molecular weight species from the column. 

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. 

Molecules with relative molecular mass > M, are totally excluded from the stationary phase and have retention volume V0. Molecules with relative molecular mass < M2 totally permeate the stationary phase and elute at ( Vq + Vi). Molecular sizes in between these two partly permeate the stationary phase and elute between VG and ( V0 + Vi). 

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

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. 

Assuming an exclusion volume of 5 ml per column allows construction of Table I from Equation 1. Table I lists the bandwidth in microliters as a function of column plate number and the number of columns in series. The data assume that the plate number may be generated at total exclusion, as well as at total permeation actual measurements made using the smaller pore size column si ibstantiate this. 

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. 

Figure 1. The relationship between SEC and other chromatographic techniques. V(, is the elution volume of an excluded peak (interstitial volume), Vj is the total permeated peak volume (Vo + Vj), and Vj. is the retention volume of an adsorbed component. Reproduced with permission from reference 8. Copyright 1984, Astor Publishing Corp.

Dilution Volume Feed Total Permeate Total Impurity Flux... 

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