Crossover molecular weight

Crowding Volume Fractions vc, Crossover Molecular Weights Mbt and Crossover End-to-End Distances lb as Functions of the Salt Concentration c and Pure Aqueous d-Value d0... 

The pattern for recoverable compliance is similar. Below some crossover molecular weight, designated M, the Rouse prediction - Eq. (3.41) as shown by the dashed line in Fig. 3.36 - is quite reasonable, especially considering that there are no adjustable parameters. Beyond M, the behavior changes, J° becoming independent of molecular weight. Thus,... 

Fig. 3. Schematic of Chambon-Winter gel spectrum. The longest relaxation time diverges to infinity. The relaxation time X0 marks the crossover to the short-time behavior, which depends on the material. The depicted case corresponds to a low-molecular-weight precursor (crossover to glass transition region)...

As known from the broad crossover phenomena observed in the macroscopic chain dynamics (such as the molecular weight dependence of the melt viscosity) very important limiting mechanisms must exist that affect the confinement limit of the reptation process. These processes increase in importance as the chain length decreases. The two main mechanisms are [62] ... 

Table 8.2 Changes in molecular weights and molecular weight distributions in radical crossover reactions of 43...

We recall that comparatively sharp and even nonmonotonous crossover from Ising to mean-field behavior has been deduced from experiments for a diversity of ionic systems. We note that this unusually sharp crossover is a striking feature of some other complex systems as well we quote, for example, solutions of polymers in low-molecular-weight solvents [307], polymer blends [308-311], and microemulsion systems [312], Apart from the fact that application of the Ginzburg criterion to ionic fluids yields no particularly... 

The polyethenes prepared with catalyst 2 (Fig. 3a) have greatly elevated elastic modulus G values due to LCB compared to the linear polymers shown in Fig. 3b. LCB also shifts the crossover point to lower frequencies and modulus values. The measured complex viscosities of branched polymers (see also Table 2) are more than an order of magnitude higher than calculated zero shear viscosities of polymers having the same molecular weight but a linear structure. The linear polymers have, in turn, t] (0.02 radvs)... 

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