Critical dynamics, strongly-interacting

While this helps us to describe the conformation of the unperturbed molecule in a melt, the rheological behavior of a melt is dramatically different from that of a dilute solution if the molecular weight exceeds a certain critical value. This is the result of an extremely important phenomenon that occurs in a melt and has no counterpart in the dilute solution. Over a certain rather narrow range of molecular weights the dynamic interaction between polymer molecules starts to have a very marked effect on the dynamic behavior of the melt. This strong interaction is traditionally said to be due to entanglements, although it is now understood that... 

In most cases polymer solutions are not ideally dilute. In fact they exhibit pronounced intermolecular interactions. First approaches dealing with this phenomenon date back to Bueche [35]. Proceeding from the fundamental work of Debye [36] he was able to show that below a critical molar mass Mw the zero-shear viscosity is directly proportional to Mw whereas above this critical value r 0 is found to be proportional to (Mw3,4) [37,38]. This enhanced drag has been attributed to intermolecular couplings. Ferry and co-workers [39] reported that the dynamic behaviour of polymeric liquids is strongly influenced by coupling points. 

If a 50 pm droplet is inserted in the centre of the filament at d = 1 m after the filament onset, the filament appears unperturbed, although the dynamical balance between Kerr self-focusing and defocusing on the plasma plays a critical role due to the strong non-linearity of the filamentation process. Moreover, the filament length is not affected by the interaction with the droplet. Comparing the filament energy with and without droplet shows very limited losses. Shortly after the interaction with the droplet, the loss is only... 

In recent years the study of mobile soil and groundwater colloids has received considerable attention because of concerns that such a vector may enhance the mobility of strongly sorbing contaminants, a process that is often referred to as facilitated transport. 15-16 However, our ability to predict colloid movement and deposition is often confounded by the complexities of surface interactions in such dynamic, unstable systems. The lack of universally accepted analytical techniques and failure to realize instrumental limitations have made it difficult to compare and critically evaluate the results of different studies. Artifacts associated with ground-water sampling, filtration, and storage, and the dilute nature of most soil and ground-water suspensions further hamper characterization efforts.17-21... 

Thus, the kinematical theory is valid only for very thin crystals that are not diffracting strongly. To interpret the details of the images observed from the much thicker crystals commonly used in TEM (particularly when s = 0), we require a theory that includes the dynamical interaction of the many beams excited in such crystals. The dynamical theory, which is developed in the next chapter, overcomes the critical limiations of the kinematical theory and provides the basis for the interpretation of the images due to crystal defects, which are discussed in detail in Chapter 5. 

There are certain threads that run throughout this series of essays the importance of the transformation of xenobiotics, the association between xenobiotics and components of environmental matrices, and the dynamics of ecosystems. By implication, therefore, environmental hazard assessments should take into account not only the original xenobiotic but also its possible transformation products together with the actual state — free or associated — in which the compound exists in the environment. It should be clearly appreciated that both the persistence and the toxicity of xenobiotics are critically determined by the extent and reversibility of the interactions between low-molecular-weight xenobiotics and polymeric material in the environment. Indeed, the importance of dynamic interactions at both the physicochemical and the molecular levels cannot be too strongly emphasized. 

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