Polystyrenes elution curve

Fig. 9. GPC elution curve for a reaction product of tetra-chain star-shaped polystyrene, coded S-A. For details, see text...

Even this rather primitive apparatus, working with a mean reproducibility of only some per cent, shows a strong dependence of the resolution on the column temperature 2), as can be seen from Fig. 2 While the measured elution curve of a 1 1-mixture of two anionically prepared polystyrenes (I Mw = 135,000 and II Mw = 415,000) shows a light shoulder at 27 °C, a practically complete resolution is achieved at 25 °C — a result which could not be obtained in GPC at that time. 

Fig. 2. Elution curves of a 1 1-mixture by weight of two samples of anionically prepared polystyrenes for three temperatures as indicated Mw = 135,000 (I) and 415,000 (II) (300 mg in 20 ml of cyclohexane 1,2))...

This can well be seen from Fig. 24 showing three measured PDC-elution curves of the same standard anionic polystyrene PCC K-l 10000 (Pw = 1080) at 23 °C (very narrow), 17 °C (medium broad) and 15 °C (very broad). Only the very broad elution curve at 15 °C allows a simple caclulation of the MWD by means of the strip method S , because only 8% of the curve-width is caused by spreading and 92% by resolution (crD/cr = 0.08), whereas the inversion method G or K described above must be applied when the MWD is calculated from the elution curve 17 °C or even 23 °C, where 73 % of the curve-width is caused by spreading and only 27 %... 

Fig. 24. PDC-elution curves D(V) of standard anionic polystyrene PCC K-l 10,000 (Pw = 1080) measured at three column temperatures, as indicated...

Fig. 25. Distribution of the degree of polymerization of polystyrene sample PCC K-l 10,000 calculated from the elution curves Fig. 24 at 15 °C (O), at 23 °C ( ), and at 25 °C ( ) (not shown in Fig. 24, cf. text). For comparison incorrect distribution of the degree of polymerization of the same sample calculated from GPC without correction for spreading (strip method, A)...

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. 

Fig. 3-9. Gel permeation chromatography elution curve.s for anionic polystyrene standards used for calibi ation. The polystyrene standard samples were measured separately use of a mixture of polymers may cause elution volumes of very high molecular weight standards to be erroneously low [I8J.

Figure 6. Differences in peak elution times as a function of molecular weight calculated from the polystyrene calibration curves for each detector.

MWD polystyrene samples used with the particular GPC column and the GPC solvent, yields a set of GPC chromatograms as shown in Fig. 4.26. The peak elution volumes and the corresponding molecular weights provide a calibration curve (Fig. 4.27) for polystyrene in the particular GPC column and solvent used. The next step is to translate this polystyrene calibration curve to one that will be effective for another given polymer in the same apparatus and solvent. This technique is called a universal calibration. 

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). 

To construct an elution cab bration curve CJWi vs. V ) for poly(dimethylsiloxane), various values of are assumed and corresponding to each value the corresponding Ms is first obtained from the polystyrene calibration curve (Fig. 4.27) and then M from the above expression. A semilog plot of versus gives the required calibration curve (Fig. 4.30). 

Figure 4.23 Elution calibration curve (Mx vs. Ve) for polymer X (Problem 4.20) derived from polystyrene calibration curve and MHS constants.

The distribution of oligomers as calculated in mole % from the peak areas is shown in Table 1 (only peaks for dimers and trimers elute separately, tetramers and probably higher oligomers appear as a shoulder). Peak molecular weights, polydispersity indices and corresponding number of THN units, as calculated from a polystyrene calibration curve, are also given. 

The Styragel 1000 column (1.0 x 42 cm) was prepared from resin swollen with benzene-methanol (90 10 v/v). Polystyrene standards were used for molecular weight calibration, and an exclusion limit of 28,000 was determined. The Sephadex-excluded asphaltene fraction was chromatographed on the Styragel 1000 column and a continuous elution curve was obtained from molecular weight 22,000 to 1000. 

Polymerization Polystyrene-block-polyethyleneoxide samples were prepared by sequential anionic polymerization in THF with cumyl potassium as the initiator. The PEO block lengths were varied from 1 to 25 mole%. Samples were characterized by SEC and H-NMR. Results are summarized in Table I. The monomer to initiator ratio was chosen so that molecular weights of about 50.000 g/mole could be expected for all polymers. The actual molecular weights which were found by SEC were higher. This can be explained by partial precipitation of the initiator in the stock solution. It must be noted also, that SEC elution volumes had been transformed to molecular weights by means of a polystyrene calibration curve. For this reason, some deviation of the actual molecular weight of the styrene/ethyleneoxide block copolymers is expected. 

Figures 3.20, 3.21 and 3.22 show how the monomer conversion, number average molar mass (Mn), polydispersity index (Mw/Wn) and SEC curves of polystyrene evolved during the ATRP process. As shown in Fig. 3.20, the plot of semi-logarithmic of ln(l/(l-conversion)) versus t presents a linear relation, indicating the polymerization meets the required criteria of a living system. Figure 3.21 shows that the experimental Mn increases linearly with the conversion, and the M /Mn rapidly decreases with the conversion and reaches a minimum of 1.14 at the end of polymerization, indicating the whole ATRP process is well-controlled, which is also reflected in the symmetric and narrowly distributed elution curves (Fig. 3.22).

FIGURE 4.38 Calibration curves for TSK-GEL Hxl columns with polyst/rene standards. Column TSK-GEL Hxl series, two 7.8 mm x 30 cm columns in series. Sample Polystyrene standards. Elution Tetrahydrofuran. Flow rate 1.0 ml/min. Detection Rl. 

Figure 6.3 shows a comparison of elution patterns of standard polystyrene between a linear-type column and a standard-type column. Because of the high linearity of its calibration curve, the linear series has improved the efficiency of oligomer domain separation. 

The ISO method prescribes polystyrene standards with tetrahydrofuran as the eluent, but this equation can also be used with other narrow distribution standards, provided the same elution solvent and the same standards are used for a comparison. Further, the ISO method requires the result to be greater than 6 for one decade of the molar mass. Because calibration curves are usually not linear, this decade should lie nearly symmetrically around the peak maxima of the samples in question. The required value of 6 is easy to fulfill, as results of 10 or more are usual with modern columns. If so-named linear or mixed... 

FIGURE 22.7 Elution behavior of polystyrene standards in THE in PCHdC with different packing diameters , 1.40 /tm A, 1.91 m and , 0.87 /tm. Theoretical curves according to Eq. (I), where C = 3.7. (Reprinted from j. Chromatogr., 506,554, Copyright 1990, with permission from Elsevier Science.)... 

The most widely used molecular weight characterization method has been GPC, which separates compounds based on hydrodynamic volume. State-of-the-art GPC instruments are equipped with a concentration detector (e.g., differential refractometer, UV, and/or IR) in combination with viscosity or light scattering. A viscosity detector provides in-line solution viscosity data at each elution volume, which in combination with a concentration measurement can be converted to specific viscosity. Since the polymer concentration at each elution volume is quite dilute, the specific viscosity is considered a reasonable approximation for the dilute solution s intrinsic viscosity. The plot of log[r]]M versus elution volume (where [) ] is the intrinsic viscosity) provides a universal calibration curve from which absolute molecular weights of a variety of polymers can be obtained. Unfortunately, many reported analyses for phenolic oligomers and resins are simply based on polystyrene standards and only provide relative molecular weights instead of absolute numbers. 

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