The Kratky-Plot

As a signature of the star architecture the elastic scattering data of the completely labelled stars exhibit a pronounced peak at z = 1.5 in the scaled Kratky representation. In contrast to the PI systems, presented before, the Kratky plot of the measured scattering curve disagrees strongly with the prediction of Eq. (123). The experimental halfwidth of the peak is nearly only 50% of the theoretically predicted one. 

At this position, the reduced relaxation rate Q(Q)/Q3 shows a minimum for stars, where the arms are labelled completely or to 50% at the core site. For these systems the Kratky plot of the static structure exhibits a maximum at the same Q-value... 

Finally we mention the Kratky plot which also may help to detect branching. Here ((S2) q2) Pz (q2) is plotted against q. Figures 26 and 27 show the Kratky plots for regular star-molecules and for the soft sphere model. Linear randomly coiled chains result in... 

The Kratky plot (q xS(q) versus q) leads to a plateau allowing the determination of aVm. These two representations will be used as references for characterizing the anisotropy of the deformed samples. 

One may also estimate n from the scattering data by finding the best fit in the Kratky plots between the experimental and calculated form factor. This is illustrated in Fig. 18 for samples a2 and d2, in Fig. 19 for samples e2 and e3 and in Fig. 20 for sample S2 relaxed for 200s and 3000s. For the last sample, the sensitivity of the form factor to n is illustrated in Fig. 21. 

A can react with group B or C only. In such a system the (Kratky) plot of .Fj( ) vs. shows a maximum. Since many synthetic and biological systems can be modelled by such a scheme, there seem to be many applications of this work. 

Quite instructive is a plot of measured data in the form Sq versus g, known as the Kratky-plot . This is depicted schematically in Fig. 2.10. The plateau region, representing the part of the curve where 5d 1/, contains information about the internal structure of the chain. As the plateau value is given by... 

The effect of branching is even better displayed in the Kratky plot namely (qR P(qR versus qR, as shown in Fig. 5.4. Theoretically, Burchard [18] deduced the scattering factor for AB2-type hyperbranched chains as... 

Figure 4 shows die measurement results on a poly(vinyl acetate) microgel and the Kratky plot of die calculated branching number dependence assuming the soft-sphere model [27]. A characteristic of this plot is the appearance of a maximum as die amount of branching increases. 

As the molecular weight becomes infinite due to gelation, the characteristic divergence of the Kratky plot occurs at - 0 for detailed divergence conditions, refer to the text... 

Both time-resolved SAXS profiles firom the ET-PTMO/TEOS mixtures show the upturn at 0 in the Kratky plots (g I(q) plotted against q with I(q) and q... 

Figure 17 Reduced relaxation rates T/ for a star polymer ( ) and for a one-arm labeled star ( ) as a function of Q. The curves are guides to the eye. The position of the minimum in the relaxation rate of the whole star corresponds to the position of the maximum in the Kratky plot of the form factor. (From Ref. 67.)...

Figure 4 Scattering functions in the form of the Kratky plot for KP cylinders with A/.=1 and indicated Arf values.

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