Monodisperse chromatograms

Figure 6.4 A typical gel permeation chromatogram using monodisperse polystyrene standards...

Since the modified iterative method is completely numerical, data can be used directly from the monodisperse chromatograms to characterize the axial dispersion, eliminating the need for a specific axial dispersion function. The monodisperse standards were used to represent the spreading behavior for particle ranges as given in reference (27). 

Calibration refers to characterizing the residence time in the GPC as a function of molecular weight. Axial dispersion refers to the chromatogram being a spread curve even for a monodisperse sample. A polydisperse sample then is the result of a series of overlapping, unseen, spread curves. 

One possibility is that although averages for polystyrene standards require correction, those for PMMA would not According to symmetrical axial dispersion theory (5) the correction depends upon both the slope of the calibration curve (different for each polymer type) and the variance of the chromatogram of a truly monodisperse sample. Furthermore, the calibration curve to be utilized can be obtained from a broad standard as well as from monodisperse samples. The broad standard method may itself incorporate some axial dispersion correction depending upon how the standard was characterized. 

An important by-product of the development of this approach is that Orthogonal Chromatography provides a direct method of estimating the shape of the chromatogram for extremely narrow molecular weight distributions. This shape function is fundamental information for axial dispersion evaluation and is not otherwise easily obtained. Even commercially available monodisperse standards synthesized by anionic polymerization are too polydisperse. 

Figure 20 shows an example of its use. As expected, the GPC 2 chromatogram of a fraction of a monodisperse standard (obtained by sampling it with GPC 2 at its peak) is narrower than the whole standard which in turn is narrower than chromatograms of slices of broad polystyrene distributions. In Figure 20, two examples of the latter show the difference obtained by improving resolution in GPC 1. 

Axial dispersion characterization is a valuable by-product of coupling GPCs. By sampling chromatograms with the second GPC, extremely monodisperse fractions can be obtained and the concentration of misplaced molecules in any chromatogram slice revealed. 

Resolution factor (= l./(2 x variance of chromatogram of truly monodisperse sample))... 

There are many facets of this study which we feel merit further investigation. In particular it is necessary to consider am extension of the proposed model, which in its present form is confined to the performance of a simple column, to cover the behaviour of any set of columns since it is column sets which are normally used. In addition, it is important to consider the input to the model which should be truly representative of polymers with a molecular weight distribution and not merely a concentration pulse of perfectly monodisperse polymer. In relation to this latter suggestion it would be significant if it were possible to link this model to the very real problem of deconvolution, i.e. the removal of instrumental and column broadening from the observed chromatogram to produce the true molecular weight distri-... 

The spreading factor C is the variance of the chromatograms of the monodisperse polymer species, i.e. of the instrumental spreading fimction G(V,Vr), If O g varies linearly vd.th the retention volume of the monodisperse polymer, then<0 > is numerically equal to the interpolated value 0 (v) of the function (T (Vr) for the polydisperse sample at its mean elution volume. 

Some studies have successfully demonstrated separations of linear copolymers using HPLC. However, it is important to realize that unlike in the HPLC of small molecules where a peak shows the concentration of only one type of molecule, the SEC chromatogram of a complex polymer is really an envelope covering possibly thousands of different components. Even with modem detectors it is often very difficult to ascertain that the desired fractionation has really been accomplished. Universal calibration in SEC is of practical utility because the same fractionation (i.e., a fractionation according to molecular size) occurs whether monodisperse, polydisperse or complex polymer molecules are involved. The fractionation is reliable. This is a very difficult requirement for HPLC methods because of the variety of complex molecules that can be present. 

Figures 2 and 3 as additional proof to Equation 5. The two solid lines in the upper left corner of Figure 2 are the M - [77] M curves for styrene and butadiene homopolymers. The data points for block copolymers shown as cross and open circle fall in between these two curves. When plotted as M — [77] M curve, all points fall on or near the curve for polystyrene shown as a solid line in the lower right part of Figure 2. The behavior of these copolymers in toluene and dioxane is shown in Figure 3. Since these block copolymers cover a wide range of composition (% S = 3.6-45.9) as well as molecular weight (M = 34,000-620,000), these results prove unequivocally the adequacy of Equation 5. Tliis equation will make it possible to interpretate the chromatogram of block copolymer without preparing monodispersed copolymers which is something difficult, if not impossible.

Estimation of the Spreading Function. When the injected sample is monodispersed, peak broadening occurs solely due to axial dispersion if y is the mean retention volume of the chromatogram, then the detector response is given by ... 

Calibration Curve. The chromatograms of standard monodisperse samples may be used to construct a calibration curve relating the particle diameter D with its mean retention volume, y, by ... 

The chromatograms of the several injected PVAc samples were corrected for axial dispersion (8-11) and number and weight average diameters were estimated. The resulting distributions and diameter averages showed that the latex samples from the batch runs were "almost monodispersed (8). This was further supported by the fact that estimated average diameters were very close to the "peak" average diameters (Table III). 

The particle-sizes and particle-size distribution of the two monodisperse carboxylated S/B latexes are shown in the hydrodynamic chromatograms of Figure 1. The average diameters of the large, Df, and the small, Dg, relatively monodisperse latexes were 2100A and 720Arespectively. 

Gel Permeation Chromatography (GPC). GPC was used to determine molecular-size distributions of asphalts and their fractions. Chromatograms were obtained by means of a Waters Associates ALC/GPC 301 chromatograph equipped with 8.5 x 103-, 103-, 500-, and 70-A Styragel columns. The instrument was operated at ambient temperature. Tetrahydrofuran (THF) was used as the solvent. Concentration of the sample in tetrahydrofuran was less than 0.5 wt %. The flow rate was 1 mL/min. Monodispersed polystyrene standards provided by Waters Associates were used to calibrate the system. Thus, weight-average molecular weights (Mw) determined represent relative molecular size only. 

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