Narrow Distribution Samples

It is useful to note that even so-called monodisperse samples have polydispersities that are rarely smaller than 1.01. But even at this low value, the sample contains some high and low-molecular weight material. This is illustrated in Fig. 2.2, which shows the distributions calculated using the log-normal distribution (Eq. 2.70) for M = 100,000 and polydispersity index values of 1.01, 1.03 and 1.1. We see that even the material with the smallest PI has a small amount of polymer with M 20% higher or lower than the mean. 

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Another TSK combination (precolumn -I- PWM -I 6000 -I 5000 -I- 4000 -I-3000) was tested on differences in separation performance between individual narrow distributed samples and mixtures of several narrow distributed samples. The result is summarized in Eig. 16.31 within experimental error the summed chromatograms (theory) of four narrow distributed glucans (dextran) match perfectly with the experimentally determined chromatogram of the mixture. The (theory/experimental) ratio, plotted for quantification of the match, in-... 

X 0.75 cm) Ve i = 28 ml = 50 ml eluent 0.05 M NaCI flow rate 0.80 ml/min detection Optilab 903 interferometric differential refractometer applied sample mass/volume 200 /tl of 2-mg/ml aqueous solutions sum of individual chromatograms (theory —) and (theory/experimental) ratio (—) plotted for quantification of deviations in separation performance between narrow distributed samples and broad distributed samples. 

In terms of accuracy of measurement, for a narrow distribution sample, there appears to be no preferred wavelength for signal detection in the UV range. 

Comment on the resolution of the chromatograph in relation to (a) the plate count and (b) to separation between the members of a pair of narrow distribution samples. 

Confirming an earlier conjecture (195), the data on several linear polymers follow a similar pattern. Figures 5.16 and 5.17 contain results for narrow distribution samples of 1,4 polyisoprene (166, 167, 196, 197) and poly (a-methyl styrene) (161,176, 198-201). The onset of (cAf)-1 behavior seems clearly related to the same processes that produce the plateau region and the transition in t 0 vs M behavior. In almost all cases (cM)-1 dependence in JeR begins at a... 

Fig. 8.6. Shear rate dependence of viscosity as a function of concentration. Data were obtained on a single narrow distribution sample of polystyrene (Mw = 411000) in n-butyl benzene (155) at 30° C. (Reproduced from Transactions of the Society of Rheologie, Volume 11, Fig. 2, p. 273, New York Wiley Sons.)...

Fig. 8.8. Shear rate dependence of viscosity in reduced formas a function of concentration. Data were obtained on one narrow distribution sample (Mw= 1820000) of poly(

Fig. 12.13 Extrudate swelling data for polystyrene melts , broad molecular weight sample O, , A, narrow distribution sample data at various temperatures. [Reprinted by permission from W. W. Graessley, S. D. Glasscock, and R. L. Crawley, Die Swell in Molten Polymers, Trans. Soc. Rheol., 14, 519 (1970).]...

We now consider how the elution volume axis of a raw chromatogram, such as shown in Fig. 4.25, can be translated into a molecular weight scale. This necessitates a calibration of the particular GPC column for the particular polymer-solvent system used. Such a calibration requires the establishment of a relationship between the volume of solution eluted (or, equivalently, the elution time for a given flow rate of solution) and molecular weight of monodisperse fractions of the same polymer. The main problem encountered in this task is that monodisperse or very narrow distribution samples of most polymers are not generally available. However, such samples are available for a few specific polymers. A notable example is polystyrene for which anionically polymerized samples of narrow mole-... 

Samples A and C have wide distributions, as indicated by the number- and weight-average diameters determined by electron microscopy. This is reflected in the large disparity between electron microscopy results and the other techniques used. Closer agreement among the methods is seen for the narrow distribution sample 6. However, even in this case, the results are lower for electron microscopy for reasons of particle shrinkage in the beam. 

Figure 2.13 shows the mass spectrum of a polystyrene sample recorded using an instrument equipped with a Direct Chemical Ionization (DCI) Ion Source. The peaks are due to protonated ions. The authors obtained Mn and Mw using Eqs. (2.1) and (2.2). The result was Mn = 3906 and Mw = 4090, which compares well with the values Mn = 3744 and Mw = 4142 obtained by SEC. DCI can be used for the analysis of narrow-distributed samples in the range below 5 kDa. A series of PEG samples obtained by anionic polymerization was analyzed using an instrument equipped with an Electrospray Ion Source and an FT-ICR cell (ESI-FT), and Mn and Mw... 

Firstly, eq 1.20 predicts that the spinodals for homologous polymers different in polydispeisity but identical in form a single curve. Scholte [14] in 1971 and Derham et al. [4] in 1974 demonstrated that this prediction did not hold for polystyrene in cyclohexane. Figure 9-14 displays the data of Derham et al. Here, the spinodal labeled PS 166 is for a narrow-distribution sample with My, = 166 X 10 and one labeled PSM5 is for a binary mixture with My, = 165 X10 and M /My, = 3.68. The two curves do not superimpose but intersect at = 0.075. 

SEC is routinely used to produce narrow distribution samples by fractionation. However, even with preparative SEC columns the procedure is not particularly effective, and many repeated fractionations are required to produce more than milligram samples. Nevertheless, such samples are invaluable in crystallization-rate [70] and other studies where molecular mass exclusion is very important. Coupling molecular mass with temperature-rising elution fractionation, in which molecular species separate by composition, in copolymers, or by degree of branching and tacticity, in homopolymers, makes this a most important method for separating molecular mass and chemical effects in crystallization studies [17]. 

Storage-modulus master curves for narrow-distribution samples of linear polystyrenes with widely different molecular weights [18] are shown in Fig. 3.14. Note the increase in plateau width with increasing molecular weight and the... 

Figure 3.45 demonstrates the extreme importance of the distribution breadth in melt elasticity. Die swell D /D begins to increase at much lower capillary shear stress for the broad-distribution sample, and the change is more gradual than that for the narrow-distribution samples. The sensitivity of die swell to the distribution breadth follows naturally from the Tanner expression (Eq. (3.34)), according to which De/D is a function of the ratio N /g alone. With the approximation N 2 from Eq. (3.28), N /a 27g or. Thus, since increases rapidly with the distribution breadth, die swell at constant shear stress should increase with the distribution breadth of the polymer. 

Figure 10.6 Damping functions for polystyrene melts with polydispersity indexes of 1.1 (PS50124) and 2.5 (PS606). Also shown are the DE model predictions with and without the lA assumption which are quite similar to each other. The data for the broad MWD sample are higher, and those for the narrow distribution sample conform more closely to the predicted curves. From Urakawa etal. [241.

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