Molecular weight calibration curves

Linear type columns are especially designed to have wider linear molecular weight ranges. These linear-type columns are highly recommended for correcting nonlinear sections of molecular weight calibration curves (Table 6.2). 

Herein are reported improved methods of molecular weight calibration where simultaneously, peak broadening parameters (a) are obtained through the use of multiple polydisperse molecular weight standards. There are two basic methods covered. The first and most reliable method employs the universal molecular weight calibration curve obtained using narrow MWD polystyrene standards. 

The second method assumes that the molecular weight calibration curve is linear on a semilog plot and should be employed where universal calibration is not practical as with aqueous SEC. Several variants of these methods involving different molecular weight data for the standards are discussed. The proposed methods have been evaluated using aqueous SEC and polydextran standards and nonaqueous SEC with polyvinylchloride standards. 

Those which employ one or more broad MWD standards with known M or [n] and assume a linear molecular weight calibration curve and finally those which employ one broad MWD... 

Mjj and My or [q] for the broad MWD standard are taken as known quantities. Fy(v) is the normalized chromatogram for the broad MWD standard obtained with a mass detector. D2 is the slope of the molecular weight calibration curve at the peak position of the chromatogram (the equation of the tangent is given by M(v) = Dj exp(-D2v). is the variance of the single-species chromatogram... 

Methods Based on Universal Molecular Weight Calibration Curve... 

The nonlinear universal molecular weight calibration curve may be expressed as shown in equation ( ). 

There are three imknowns, K, a and. One might question the availability of Mark-Houwink constants for the polymer in the open literature. Mark-Houwink constants in the literature differ widely for the same polymer and it is difficult to decide on the correct pair to employ. Another problem which can arise is that the universal molecular weight calibration curve may not apply exactly for the polymer in question. The use of the true Mark-Houwink constants would therefore introduce an error in the molecular weight calibration. Calibration with a broad MWD standard should eliminate this error. The Mark Houwink constants obtained in the calibration would in this instance be effective rather than true values. 

Methods which assume a linear molecular weight calibration curve will now be briefly considered. 

The assumed form of the linear molecular weight calibration curve is given in equation (lO)... 

Figure L Molecular weight calibration curve for polystyrene an universal molecular weight calibration curve based on polystyrene ((%) [rj]Mw (U) w)...

The molecular weight calibration curves obtained for PVC are shown plotted in Figure 3. Table III shows an investigation of the effect of the peak broadening parameter (a) assumed when a single broad MWD PVC standard is used. The corrections for imperfect resolution for PV2 and PVC with a a = 0.5 are now reduced to about k% for both standards. It is of interest to note that with a reduced correction for imperfect resolution the Mark-Houwink exponent obtained is closer to published literature values for PVC in THF (13). The use of the associated molecular weight calibration curve for PVC would reproduce the M j and M of the PVC standards with errors of about 15. ... 

Figure 3. Molecular weight calibration curves for polyvinyl chloride obtained using universal calibration and one and two broad MWD standards (two broad standard method (0) [rj = 7.06 X 10 single broad standard method ...

We now move on to aqueous SEC and the use of the method of calibration based on a linear molecular weight calibration curve and two broad MWD polydext ran s with known and M. ... 

Figure 4. Molecular weight calibration curves for polydextran obtaimd u g linear calibration and two broad M WD standards and by plotting Mrm ( / Mif Mw) vs, peak retention volume ((%) Mrms, (---------) M(v) = 0,37 X exp(—OJ v))...

This behavior shows that the dimensions of these polymers are independent of pH, ionic strength (in the ranges studied) and presence or absence of Tergitol or polyethyleneoxide. This result is of considerable help in interpretation of GPC behavior since in the absence of polymer-glass substrate interactions, the molecular weight calibration curves (log MW vs. elution volume) should be independent of pH, ionic strength or the two nonionic surfactants investigated. 

Figure 2. Molecular weight calibration curves for nonionic polyacrylamide for a single column (4 ft X Vs in. i.d.) containing 2000 A CPG-10 (200/400 mesh) packing with aqueous salt solutions as mobile phase.

Figure 7. Molecular weight calibration curve for nonionic polyacrylamides for a 6-column combination (each 4 ft X in, Ld.) with 3000 A, 3000 A, 2000 A, 1000 A, 729 A, and 500 A CPG-10 (200/400 mesh) packing.

Number and weight average molecular weights for Polysciences Standards and McMaster Standard B, calculated from raw chromatograms using the molecular weight calibration curve M(V) = 0.20 X 10 exp(-0.341 V - 0.006 V ) with V in counts (1 count = 5 ml). 2... 

P = exp(-(D2a) /2) with D2 the slope of the molecular weight calibration curve at the peak position of the chromatogram of the Standard. 

Peedc-to-peak resolution in SEC can be calculated by the ratio of peak separation at the peak maxiaut to the sum of the baseline peak widths. This general definition of resolution is less useful in SEC, where a measure of the ability of the column to separate solutes of different molecular weight is required. For this purposes, we define a new term, the specific resolution factor, R, which relates peak resolution to sample molecular weight, assuming all measurements are made within the linear region of the molecular weight calibration curve, equation (4.41)... 

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