Molecular Dynamics and Relaxation of Entangled Polymers

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0072101LarsonFollowing the introduction in 1971 of de Gennes' reptation theory of polymer diffusion and relaxation in entangled polymers, gradual progress has been made in quantitatively predicting the relaxation of simple polymers by recognizing the importance of the additional mechanisms of primative path fluctuations and constraint release. Theoretical concepts introduced by McLeish and co-workers suggest that these same basic mechanisms can allow prediction of the viscoelastic properties of more complex molecular systems, such as melts of molecules with multiple branch points. Heretofore, however, theories have been specialized to particular systems, such as purely linear molecules, or monodisperse or bidisperse stars. Furthermore, the concept of constraint release has taken on two different simplified descriptions, one called tube reorganization and the other tube dilation. In the special case of polydisperse linear polymers, a version of tube reorganization called double reptation appears to successfully describe relaxation data, while for star polymers, constraint release must be manifested in terms of a tube dilation model known as dynamic dilution.In the present grant, a theoretical framework will be developed that is general in scope, which can account for all known mechanisms of slow relaxation in entangled polymers, and unify the concepts of tube reorganization and tube dilution. To develop such a model, the so-far successful notion will be exploited that in many cases entanglements in concentrated polymeric systems can be viewed as a set of pair-wise interactions between two chains. Each entanglement disappears when either chain in the pair moves its chain end through the entanglement position. Thus, the hypothesis is that qualitative and perhaps quantitative predictions of polymer relaxation can be made even for complex mixtures of different topology, by keeping track only of chain ends, chain branch points, and discrete entanglements or slip links that couple pair-wise the relaxation of different chains. A computational algorithm, called the dual slip link algorithm, will be developed that can in principle describe relaxation of any molecular mixture of linear or arbitrarily branched polymers. In preliminary work, for linear polymers, the model reduces to the double reptation theory, which is known to be accurate for many polydisperse linear polymers, while for star polymers, it predicts behavior similar to that of the Ball-McLeish dynamic dilution theory. This preliminary work will be extended by allowing motion of branch points which will then permit simulation of polymer mixtures of arbitrary topolgy and composition. Predictions of this model will be compared with analytic theories and with experimental data for linear molecules, stars and pom-poms, and mixtures thereof, and with simulation results to gain deeper insights into relaxation processes in both simple and complex polymer systems.%%% This grant supports theoretical research on fundamental relaxational properties of mixtures of polymers. Using a newly developed computational algorithm, various other theories of these systems will unified. Besides being of fundamental interest, understanding relaxation in polymer mixtures has wide ranging industrial applications.***