Chain configurational relaxation

Fig. 1.5 Schematic illustration of the bond fluctuation model in three dimensions. An effective monomer blocks a cube containing eight lattice sites for occupation by other monomers. The length f of the bonds connecting two neighboring cubes along the chain must be taken from the set = 2, VE, 3, /i0. Chain configurations relax by random diffusive hops of the effective monomers by one lattice spacing in a randomly chosen lattice direction. (From Deutsch and Binder. )...

If a steady systematic motion is imposed, those topological arrangements which present barriers to configuration relaxation will come into play. As in dilute solutions the chains are continually drawn into a disturbed distribution of configurations by the external motions and respond by diffusing collectively toward an equilibrium distribution. In concentrated systems each chain must... 

Williams has derived the molecular weight and concentration dependence of a viscoelastic time constant t0 (actually the characteristic time governing the onset of shear rate dependence in the viscosity) from his theory (217-219). Employing a dimensional argument, he equates the parameters which control the shear rate dependence of chain configuration and the intermolecular correlation function. The result agrees with the observed form of characteristic relaxation time in concentrated systems [Eq.(6.62)] ... 

The Eyring analysis does not explicity take chain structures into account, so its molecular picture is not obviously applicable to polymer systems. It also does not appear to predict normal stress differences in shear flow. Consequently, the mechanism of shear-rate dependence and the physical interpretation of the characteristic time t0 are unclear, as are their relationships to molecular structure and to cooperative configurational relaxation as reflected by the linear viscoelastic behavior. At the present time it is uncertain whether the agreement with experiment is simply fortuitous, or whether it signifies some kind of underlying unity in the shear rate dependence of concentrated systems of identical particles, regardless of their structure and the mechanism of interaction. 

It is certain that the relaxation behavior of filled rubbers at large strains involves numerous complications beyond the phenomena of linear viscoelasticity in unfilled amorphous polymers. Breakdown of filler structure, strain amplification, failure of the polymer-filler bond, scission of highly extended network chains and changes in network chain configuration probably all play important roles in certain ranges of time, strain rate, and temperature. A clear understanding of the interplay of these effects is not yet at hand. 

When a polymer chain stretches, entropy tends to return the coil to its equilibrium configuration, leading to an elastic restoring force. Thus, elastic stresses are generated as the polymer chain stretches and relaxes in response to flow. A liquid exhibiting both elastic and viscous stresses is viscoelastic. We note that the ratio of a viscosity r/ to an elastic modulus G yields a characteristic relaxation time X rj/G characterizing the memory of a fluid of its past deformation history or the timescale for a stretched polymer chain to relax toward equilibrium. 

These studies demonstrate considerable progress in sorting out the relative importance of bridging versus charge neutralization, as affected by die configurational relaxation of the sorbed chains. One suspects, however, that rational design of processes must still rely cm empirical studies of the systems of interest. 

This quantity is easily calculated from the computer simulation and Fig. 4 shows a comparison [8] of the results from the simulation (lines) to the experimental data (symbols) for a momentum transfer range of q = 0.05 to q = 0.3 It turned out that there is an overall difference in center of mass diffusivity of about 20% between simulation and experiment similar to earlier experience [19], so for the figure the experimental time points are rescaled by a factor 0.8. This makes the whole set of scattering curves, measuring the configurational relaxation of the polymer chain on different length scales superimpose. 

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