Entanglement translational

Polymerizations Above Tg. Let the polymerization begin in pure monomer. As the concentration of polymer chains increases initially one observes a relatively small increase in the termination rate constant. This is related to the effect of polymer concentration on coil size. A reduction in coil size increases the probability of finding a chain end near the surface and hence causes an increase in k-. Soon thereafter at conversions 15-20 polymer chains begin to entangle causing a dramatic reduction in radical chain translational mobility giving a rapid drop in k-j. ... 

Combining the above descriptions leads to a picture that describes the experimentally observed concentration dependence of the polymer diffusion coefficient. At low concentrations the decrease of the translational diffusion coefficient is due to hydrodynamic interactions that increase the friction coefficient and thereby slow down the motion of the polymer chain. At high concentrations the system becomes an entangled network. The cooperative diffusion of the chains becomes a cooperative process, and the diffusion of the chains increases with increasing polymer concentration. This description requires two different expressions in the two concentration regimes. A microscopic, hydrodynamic theory should be capable of explaining the observed behavior at all concentrations. 

When the solution is dilute, the three diffusion coefficients in Eq. (40a, b) may be calculated only by taking the intramolecular hydrodynamic interaction into account. In what follows, the diffusion coefficients at infinite dilution are signified by the subscript 0 (i.e, D, 0, D10> and Dr0). As the polymer concentration increases, the intermolecular interaction starts to become important to polymer dynamics. The chain incrossability or topological interaction hinders the translational and rotational motions of chains, and slows down the three diffusion processes. These are usually called the entanglement effect on the rotational and transverse diffusions and the jamming effect on the longitudinal diffusion. In solving Eq. (39), these effects are taken into account by use of effective diffusion coefficients as will be discussed in Sect. 6.3. 

Generally, T2 relaxation times are very sensitive to slower relative translational motions of the polymer chains and can provide information on intramolecular couplings, such as chemical crosslinks and chain entanglements. Numerous studies on both permanent and temporary networks are presented in a series of papers by Charlesby and co-workers 74,86 94). In the case of extracted polymer networks, T2s relaxation is observed in the crosslinked (gel) fraction, while T2 relaxation occurs in the soluble fraction of the irradiated polymer86 . It is shown that the fraction of more mobile protons, (1-f). has the same general trend with increasing... 

The superscript 0 on the diffusivities listed above refers to the fact that these are for dilute solutions. In a concentrated system the rate of rotation will be slowed down considerably because of steric hinderance from nearest neighbors. The nature of the entanglements from other rods onto a test rod is such that the translational motion perpendicular to the rod axis becomes highly constrained. The translation along the chain axis, on the other hand, is for the most part unaffected. The steric interactions imposed by the neighboring rods on a single test rod can be modeled by placing such a rod within a tube of radius ac... 

Similarly, Are momentum transfer associated with a collision of photons with atoms is used regularly to cool atoms [242], that is, to alter the translational energy of an atom. Indeed, the momentum of large numbers of photons (over 140-photon momenta) have been successfully transferred coherently to atoms [243], This suggests the possibility of preparing an initial superposition of internal states of a molecule, followed by tire state-specific absorption of photon momenta of one of the internal states in order to form the required entangled supeiposition of the translational and internal states. 

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