Concentrated regime, definition

There are four to six concentration regimes (Dautzenberg et al., 1994). Edwards (1966) classified them into three broad types on the basis of the number of polymer chains present, the number and length of the monomer constituting them, and the volume of the monomer relative to the volume Vt. At use levels as low as parts per thousand in food, no one definition of dilute, semidilute, or concentrated encompasses the range of weight-volume or volume-volume concentrations necessary to elicit a par-... 

The authors [42 4] continued to study autoacceleration effect at DMDAACh radical polymerization within the frameworks of fractal and scaling approaches. In paper [39], two hmiting asymptotic regimes for the description of dynamical scaling of the aggregates growth in bath with particles initial concentration c. were considered. For these regimes definition the authors [39] introduced the... 

As mentioned above, we expect two concentration regimes, with C/C smaller or larger than unity. Therefore, we do not expect N and C to act as independent variables for all the properties, but to appear only through the ratio C/C. This scaling behavior occurs in many properties, but we will consider here only the scaling behavior of the radius of gyration R and of the osmotic pressure tt. In both cases, one may write a scaling relation deduced from the definition of the fractal dimension, Eq. (6.10) ... 

In the semi-dilute regime, the rate of shear degradation was found to decrease with the polymer concentration [132, 170]. By extrapolation to the dilute regime, it is frequently argued that chain scission should be nonexistent in the absence of entanglements under laminar conditions. No definite proof for this statement has been reported yet and the problem of isolated polymer chain degradation in simple shear flow remains open to further investigation. 

Most important, however, was the discovery by Simha et al. [152, 153], de Gennes [4] and des Cloizeaux [154] that the overlap concentration is a suitable parameter for the formulation of universal laws by which semi-dilute solutions can be described. Semi-dilute solutions have already many similarities to polymers in the melt. Their understanding has to be considered as the first essential step for an interpretation of materials properties in terms of molecular parameters. Here now the necessity of the dilute solution properties becomes evident. These molecular solution parameters are not universal, but they allow a definition of the overlap concentration, and with this a universal picture of behavior can be designed. This approach was very successful in the field of linear macromolecules. The following outline will demonstrate the utility of this approach also for branched polymers in the semi-dilute regime. 

By the definition of T (f), is the volume of the cavity in which the particular solvent is replaced by the solute. Therefore Vp depends on the particular solvent chosen for the SANS-experiment and also on concentration. For the dilute regime under consideration here the latter dependence can safely be dismissed. 

By definition of the steady-state regime, the steady-state rate of change of the intermediate concentrations equals zero. 

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