Analytical Ultracentrifugation of Polymers and Nanoparticles

Analytical ultracentrifugation (AUC) is a powerful method for the characterization of polymers, biopolymers, polyelectrolytes, nanoparticles, dispersions, and other colloidal systems. The method is able to determine the molar mass, the particle size, the

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;XZQVOMZ4IJWZI\WZa5IV]IT[QV8WTaUMZ;KQMVKM 8I[KPMZTIO*MZTQV0MQLMTJMZO 8ZQV\MLQV/MZUIVa 0.5 is valid for the first time. The coupled I(t) curve is now constructed in the following way: from the standard I(t) curve, only those points (I /Is )i /ti holding 0 < i < k are taken without any change. To these, those points from the I(t) curve of increased concentration cII holding k < i ≤ z are added in a modified form. This is purely a mathematical modification, which transforms the measured light intensities (I /Is )h,I to the standard concentration cI according to (I /Is )I,i



= I /Is

ccIII

(3.27)

II,i

(Equation (3.27) results from a combination of Lambert-Beer’s law, (3.19), and (3.21).) The assigned travel times ti , however, are taken without modification. The

78

3 Sedimentation Velocity

Fig. 3.18. Scheme of two simultaneously measured I(t) curves of an extremely broadly distributed dispersion to illustrate the particle size distribution coupling technique, measured at two different concentrations: cI = cstandard and cII = chigh (reprinted with permission from [22])

coupled I(t) curve constructed in this manner is then transformed into a PSD curve in the same way as a standard I(t) curve, as described in Fig. 3.14. We call this transformed PSD curve the coupling PSD. The coupling procedure ensures that both coarse and fine particles are detected appropriately by the turbidity detector. By this procedure, it is possible to measure even 20-nm particles (which show, as mentioned above, extremely low specific turbidity) besides 2000-nm particles by applying turbidity optics. Nevertheless, very small particles should be detected with other detectors, if possible (cf. above). Figure 3.19 shows a well-known measuring example of a very broad particle size distribution obtained by the coupling PSD technique. This is the measurement of a defined mixture of ten different aqueous polystyrene latices exhibiting particle sizes between 67 and 1220nm. The ten, narrowly distributed standard latices were mixed at 10 wt% each [27]. The upper part of Fig. 3.19 shows the two primary measured I(t) curves at cI = 0.35 and cII = 3.5g/l, the N(t) function, and the coupling point 0.5/tc . As expected, at the beginning of the run, 0 < t < 2500s, the high concentration signal I(t) is zero. By contrast, at the end of the run in the higher concentration I(t) curve, the I(t) step of the smallest particles, 67nm, which are not visible in the standard concentration I(t) curve, is now clearly seen. The lower part of Fig. 3.19, the final coupling PSD, shows that both the particle diameters dp and the mass portions mi (the original concentration of all ten components was 10 wt%) are reproduced within an error of 5%. The peaks in the differential PSD are obtained with baseline resolution for all ten components, also

3.5 Sedimentation Velocity Runs on Particles to Measure Average dp and PSD

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Fig. 3.19. Coupling PSD analysis of a mixture of ten narrowly distributed polystyrene dispersions with 67 < dp < 1220 nm. Upper part two s

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