Critical chain-link number

Table 7-2. Critical Chain-Link Number, Ncru, of Various Polymers...

Several workers undertook this task. The most notable of these was Perrin. Perrin s special success was due to his technique for preparing particles to suspend that were of uniform and known size. The uniformity was achieved by fractional centrifuging, and the size was established by noting that they could be coagulated into chains whose length could be measured and whose links could be counted. The microscopic observation of these uniform particles enabled Perrin and his students to verify the Einstein results and to make four independent measurements of Avogadro s number. See Fig. 1. These results not only established an understanding of Brownian movement, but also they silenced the last critics of the atomic view of matter. 

At the critical extent of reaction pc for the onset of gelation, the number of cross-links per chain is (see Problem 7.19), whence the critical extent of reaction at the gel point pc is obtained as... 

The exclusion and repulsion effects between links belonging to the same chain manifest themselves through a swelling, which may be characterized by a critical exponent v defining the variation of the chain size with the number of links... 

For polystyrene, Strazielle and Benoit4 deduced from thermodynamical data that the chains used in current scattering experiments have a number of links which is much smaller than the critical number (for demixtion). However, the case of polystyrene is special. We note that demixtion can be observed only above the glass transition temperature and, for polystyrene, this temperature is rather high (7 = 380 K). 

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