Elution volume calibration curves for

This equation describes the elution volume calibration curve for Mx- The elution volume (Vg) that corresponds to a GPC peak in the unknown polymer is used to obtain a value of log Mg from the polystyrene standard curve (Fig. 4.27) that has been obtained in the same column and solvent, and Mx is then calculated from Eq. (4.149). An alternative procedure is simply to choose a number of values of Vg and construct a new calibration curve for the polymer under study from the standard curve such as Fig. 4.27 and Eq. (4.143). 

Construct an elution volume calibration curve for poly(vinyl bromide) in tetrahydrofuran at 25°C, given that the MHS constants for this system are K = 1.59 x 10 cm /g and a = 0.64 [A. Ciferri, M. Kryezewski, and G. Weil, J. Polym. ScL, 27,167 (1958)], and calculate the weight average molecular weight of the polymer. 

Similarly, Ogawa et al. [40] obtained a molecular mass-elution volume calibration curve for polypropylene from a plot of log(My) against elution volume curve for fractionated polystyrene. The relations [rj i M against elution volume and were compared. When both curves were converted into... 

FIGURE 4.43 Calibration curves for globular proteins on toyopearl resins. Column 22 mm X 30 cm. Sample Protein standards. Elution 0.06 A1 phosphate buffer, pH 7, in 0.06 A1 KCI. Legend elution volume V column volume. 

Calibration curves for PS and PMMA are shown in Figs. 15.3-15.5. The slight differences in courses of calibration curves for PS in THF, chloroform, and toluene, as well as the curve for PMMA in THF (Fig. 15.3), can be explained by the flow rate variations for different pumping systems and by the hydrodynamic volume effects, respectively. The calibration curves for PMMA in mixed eluents THF/toluene are shown in Fig. 15.4. Three percent of THF in toluene assured a reasonable SEC elution of PMMA. However, more chloroform was needed to obtain a good SEC elution of PMMA in mixed eluent chloroform/toluene... 

In SEC, universal calibration is often utilized to characterize a molecular weight distribution. For a universal calibration curve, one must determine the product of log(intrinsic viscosity molecular weight), or log([7j] M). The universal calibration method originally described by Benoit et al. (9) employs the hydro-dynamic radius or volume, the product of [tj] M as the separation parameter. The calibration curves for a variety of polymers will converge toward a single curve when plotted as log([7j] M) versus elution volume (VJ, rather than plotted the conventional way as log(M) versus V, (5). Universal calibration behavior is highly dependent on the absence of any secondary separation effects. Most failures of universal calibration are normally due to the absence of a pure size exclusion mechanism. 

For investigation of GPC behavior, a series of M.W. calibration curves (log MW vs. elution volume) was obtained for a number... 

Figure 1. Calibration curve for a series of narrow MWD PS standards. Linear least squares fit for log (MW) versus elution volume.

Figure 5 Calibration curve for polydisperse dextran standard using a linear method. Plot of log (MW) vs. elution volume. Horizontally, each - represents 0.U8 units.

We have recently reported (1 )) the use of this technique for characterization of various compounds. Experimental data obtained for a number of compounds are shown in Figure 2. We calculated the "size factors" for a number of small molecules and oligomers. This factor is a measure of the deviation of the elution volume of a given species from the calibration curve for n-alkanes which is assigned a size factor of 1. This size factor, F, is defined to be equal to A/M, where M is the molecular weight of the compound and A is the molecular weight of a real or hypothetical n-alkane which will elute at the same retention volume as the compound. Size factors for a number of... 

Our primary calibration curve obtained with narrow MWD linear polystyrene samples could now be used to determine the molecular weight distribution of branched PVAc (B ) by means of eqs. (39), (40) and (17). The calibration curve for branched PVAc was not linear but showed a slight upturn at the low elution volume range as shown in Fig. 9. The calibration curve in Fig. 9 could be represented by... 

Fig. 7. PDC-calibration curves for polystyrene in cyclohexane measured 3> at eight temperatures, as indiciated, and an overall rate of the column liquid of 15 cm3/h (ordinate is normalized as indicated). The 15 °C-calibration curve dyn is measured, whereas the dashed curve 15 °C therm is extrapolated from the measured part of the dyn curve (cf. Fig. 8), and corresponds to reversible-thermodynamic equilibrium of the PDC-column. The difference between both curves shows a pronounced PDC-effect at 15 °C for P = 1082. Elution volume V = Ve and zero volume V0 = are expressed in counts (1 count = 0.51423 cm3). For the definition of r0 see Eq. (5 b)...

For determining the molar mass of branched polymers gel permeation chromatography can be used. An important quantity in this connection is the hydrodynamic volume of the polymer coil, which, as shown before in Eq. (9.27), is proportional to the product [rj M. According to Benoit and co-workers (1966) the hydrodynamic volume is the key size parameter in the establishment of a universal calibration curve for gel permeation chromatography columns (see Chap. 2) if log (h/]M) is plotted versus the elution volume for a variety of polymers, the data fit a single curve. 

Gel permeation chromatography separates the sample components in a highly predictable manner. The larger molecules always elute from the column first. Also, the maximum amount of mobile phase required to elute all sample components is equivalent to one column volume. Furthermore, the elution volume of a molecule can be predicted from a calibration curve for a given set of columns. 

For polymer systems without UV activity the combination of a RI detector with a density (D) detector can be used. The working principle of the density detector is based on the mechanical oscillator method. Since this detector yields a signal for every polymer, provided that its density is different from the density of the mobile phase, this detector can be regarded as universal [29,30,36]. The separation of mixtures of polystyrene and polybutadiene by SEC with dual den-sity-RI detection is presented in Figs. 7 and 8. In a first set of experiments, the response factors of both polymers in both detectors have to be determined. Then from the intensity of each slice of the elution curves in both detectors, the mass distribution of both polymers across the elution volume axis can be calculated. As can be seen in Fig. 7, a separation into the component peaks is obtained due to the fact that the molar masses of PS and PB are sufficiently different. For both components the individual elution profiles can be determined and using corresponding calibration curves for PS and PB the individual MMDs can be calculated. The same information can be extracted from an experiment where the molar masses of the components are similar and SEC separation does not work (see Fig. 8). Again the individual mass distributions are obtained and the MMDs for PS and PB can be determined. 

Assuming that universal calibration is valid, construct a calibration curve for the molecular weight-elution volume of poly(dimethylsiloxane) in chloroform at 35°C. The MHS constants in chloroform at 35°C may be taken as for... 

The molecular weight poly(dimethylsiloxane) corresponding to each elution volume is determined from the elution calibration curve for this polymer in Fig. 4.30. The corresponding weight fraction Wi is computed from the refractive index difference by the relation... 

The SEC columns were calibrated using narrow molecular weight distribution water soluble polymer standards sodium polystyrene sulfonate, NaPSS (Pressure Chemical Company, Pittsburgh, PA) and dextrans (Pharmacia Fine Chemicals, Piscataway, NJ). The universal calibration curve proposed by Grubisic et al. (13) was found not to be applicable for these polymer standards. The alternative calibration procedure of Coll and Prusinowski (J ) which incorporates excluded volume effects in the numerical value of the Flory parameter was found to be applicable for this system ( ). The calibration curve for the two-column network system described above is shown in Figure 3. The Kyyy parameter used on the abscissa of Figure 3 is a normalized elution volume parameter defined by Equation 1,... 

Figure 2.6 shows the calibration curves for poly(n-butyl methacrylate) (PnBMA), poly(decyl methacrylate) (PDMA), poly(methyl methacrylate) (PMMA), poly(ferfbutyl methacrylate) (PtBMA). It can be seen that the lines are almost parallel to each other, which implies that the slope hi is approximately constant, whereas bo varies. The changes in bo correspond to a change in the molar mass, and they may be quite large. For instance, when tetrahy-drofuran (TUF) is used as a solvent, polystyrene (at a given elution volume) has a mass tirat is about two times the mass of polycarbonate. It can be concluded that every polymer has its own calibration line, corresponding to a specific set of values for bo and b in Eq. 2.25. 

SEC-MALDI also proves useful in cases where the production of high polymers is accompanied by the formation of sizeable amotmts of cyclic oligomers. The presence of a mixture of linear and cyclic chains in low molar mass polymers causes difficulties in establishing an appropriate SEC calibration curve for such samples. The theoiy predicts that cycles are eluted at later times with respect to linear chains.In fact, for a given polymer there is a small but defined difference between the hydrodynamic volumes of linear and cyclic oligomers of the same molar mass, and this difference is reflected in the elution volumes (Ve) of the linear and cyclic species of the... 

Empirical approach. In SEC, a calibration curve of log molecular mass (log M) V. retention volume (Fr) must first be constructed in order to calculate molecular mass averages of the polymers in question. It is usual to report the results as polystyrene equivalent molecular masses, using a calibration curve constructed with polystyrenes of known molecular masses having narrow MMD. For accurate estimation of copolymer molecular weight, one must use a calibration curve for the copolymer in question. Therefore, it is necessary and important to estimate molecular mass of the copolymer species eluted at retention volume i. 

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