Relaxation entropic

It is to be expected that these relaxations would involve only very small dimensional changes in the sample and would be much smaller than the dimensional and entropic... 

The earliest and simplest approach in this direction starts from Langevin equations with solutions comprising a spectrum of relaxation modes [1-4], Special features are the incorporation of entropic forces (Rouse model, [6]) which relax fluctuations of reduced entropy, and of hydrodynamic interactions (Zimm model, [7]) which couple segmental motions via long-range backflow fields in polymer solutions, and the inclusion of topological constraints or entanglements (reptation or tube model, [8-10]) which are mutually imposed within a dense ensemble of chains. 

This section presents results of the space-time analysis of the above-mentioned motional processes as obtained by the neutron spin echo technique. First, the entropically determined relaxation processes, as described by the Rouse model, will be discussed. We will then examine how topological restrictions are noticed if the chain length is increased. Subsequently, we address the dynamics of highly entangled systems and, finally, we consider the origin of the entanglements. 

In summary, the chain dynamics for short times, where entanglement effects do not yet play a role, are excellently described by the picture of Langevin dynamics with entropic restoring forces. The Rouse model quantitatively describes (1) the Q-dependence of the characteristic relaxation rate, (2) the spectral form of both the self- and the pair correlation, and (3) it establishes the correct relation to the macroscopic viscosity. 

Homopolymers such as poly[(V)-3,7-dimethyloctyl-2-methylpropylsilylene], 117, were initially studied, and the helix-helix transition was discussed in terms of an entropically driven phenomenon in which at temperatures below Tc the side chains of the helical polymer are in a very ordered state and enforce a particular screw sense, whereas above Tc, the side chains become disordered such that the main chain can relax into the opposite screw sense.314 This concept is expressed in Figure 47. 

The two main sources for slow relaxation in polymers are entanglement effects and the glass transition. The first is entropic in origin, whereas the second—at least in chemically realistic polymer models—is primarily enthalpic. We write the largest relaxation time in the melt as... 

To extract a value of the step-mobility h from the grating relaxation experiments [12], we must evaluate the strength of the step-step interaction y. Computational work suggests that ydue to elastic interactions between Si(OOl) steps is 0.2 eV run [29], while, we estimate that the entropic interaction is 10 times larger. (We use a step stiffness P calculated from the geometric mean of P for Sa and Sb steps given in Ref [30] P, 0.03 eV mn-. ) Therefore, entropic repulsion should dominate, and... 

A series or bunch of m initially straight and parallel steps, between heights 0 and m, may be expected to relax with the same asymptotics as a pair of steps. Modifications may occur, already for a pair of steps, when step-step interactions are present in addition to the entropic step repulsion. Here, we merely refer to recent reviews on experiments and theoretical analyses " on the much studied phenomenon of step bunching for vicinal surfaces, which is accompanied by interesting phase transistions. 

This model is based on classic rubber theory, suggesting that elastin is made up of a network of random chains that are kinetically free and exist in a high entropic state. Stretching orders the chains and limits their conformational freedom, thus decreasing the overall entropy of the system (Hoeve and Flory, 1974). This provides the restoring force to the relaxed state. 

Most of the physical properties of networks in the rubbery state can be linked to two groups of quantities that characterize respectively, the equilibrium entropic elasticity and the relaxation kinetics (linked to the segmental mobility). 

Summary In this chapter, a discussion of the viscoelastic properties of selected polymeric materials is performed. The basic concepts of viscoelasticity, dealing with the fact that polymers above glass-transition temperature exhibit high entropic elasticity, are described at beginner level. The analysis of stress-strain for some polymeric materials is shortly described. Dielectric and dynamic mechanical behavior of aliphatic, cyclic saturated and aromatic substituted poly(methacrylate)s is well explained. An interesting approach of the relaxational processes is presented under the experience of the authors in these polymeric systems. The viscoelastic behavior of poly(itaconate)s with mono- and disubstitutions and the effect of the substituents and the functional groups is extensively discussed. The behavior of viscoelastic behavior of different poly(thiocarbonate)s is also analyzed. 

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