Cooperativity length

Figure 7. Experimental data (symbols) for TNB s viscosity [78] superimposed on the results of the fitting procedure (line) from Lubchenko and Wolynes [47] are shown. Ta is diown by a tickmark. (TNB = trinaphthyl benzene). The temperature Ter signifies a crossover from activated to collisional viscosity, dominant at the lower and higher temperatures, respectively (see text). The temperature is varied between the boiling point and the glass transition. The right-hand side panel depicts the temperature dependence of the length scales of cooperative motions in the liquid. The thick solid and dashed lines are the critical radius and the cooperativity length respectively. Taken from Ref. [47] with permission.

All-or-none transition is highly cooperative with N being the cooperative length of a transition. 

Ellison CJ, Mundra MK, Torkelson JM (2005) Impacts of polystyrene molecular weight and modification to the repeat unit structure on the glass transition-nanoconfinement effect and the cooperativity length scale. Macromolecules 38 1767-1778... 

For studies of polymers cmifined inside nanoporous host systems, the most comprehensive study was reported for polyfdimethyl siloxane) and polyfmethylphenyl siloxane) down to 5 nm by neutron scattering and dielectric and calorimetric measurements [165], An increase of molecular mobility, implying a decrease of Tg, was observed on decreasing the pore size. The increment of the specific heat capacity at the glass transition normalized by the mass of cmifined polymers also decreases with pore size, indicating a concomitant decrease of the cooperative length scale with a decrease of Tg. An explanation has been offered [163]. 

Contradictoiy results have been reported for the helical content 0 where the ultrasonic relaxation time or amplitude go through a maximum, when the polymer chain length becomes comparable to the cooperative length. The theory (I7b) predicts that the maximum should then occur at 0 < 0.5 This prediction has been confirmed in references (23) and (28). On the contrary a maximum at 0 > 0.5 was found for short-chain PGA and attributed to fluctuations of the number of helix sequences (30,31 ) More experiments should be performed to check this point which is of considerable importance since it concerns the attribution of the excess absorption of PGA. 

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