Segmental dynamics

Substantial studies have compared x of dilute chains with solvent viscosity, q being manipulated by changing the chemical identity of the solvent, the temperature, or the pressure. Experiment supports a generalized Kramers equation 

The original Kramers equation had a = 1 at all /, not the a 0.4-0.8 seen here at larger q. However, as seen in Chapter 5, solvent diffusion actually has the viscosity-dependence of Eq. 15.3 with an 7-dependent a, namely a = 1 at smaller qtoa = 2/3 at q larger than 5 cP. The small-molecule self-diffusion coefficient and the segmental diffusion time thus show consistent dependences on q. The spirit of the Kramers approach, namely that the rate of diffusion-driven molecular motions should track the solution fluidity q in the same way that the rates of solvent and small-molecule diffusion track the solution fluidity, appears to be preserved by experiment. 

Studies that vary solvent quality lead toward the conclusion that r is also sensitive to the local density of segments near each segment, an increase in the local segment density increasing the characteristic relaxation time. The few studies of matrix concentration effects do not appear to agree as to how t is affected by matrix concentration. Some results indicate that r increases dramatically, but only for c above a large transition concentration, while other work finds a smooth increase in r with increasing c. 

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Ewen, B, Richter, Da Neutron Spin Echo Investigations on the Segmental Dynamics of Polymers in Melts, Networks and Solutions. VoL 134, pp, 1-130. 

Neutron Spin Echo Investigations on the Segmental Dynamics... 

The pair-correlation function for the segmental dynamics of a chain is observed if some protonated chains are dissolved in a deuterated matrix. The scattering experiment then observes the result of the interfering partial waves originating from the different monomers of the same chain. The lower part of Fig. 4 displays results of the pair-correlation function on a PDMS melt (Mw = 1.5 x 105, Mw/Mw = 1.1) containing 12% protonated polymers of the same molecular weight. Again, the data are plotted versus the Rouse variable. 

Finally for Cfe(c) 1 the unperturbed (not self-entangled) single-chain re-laxationjust known from good solvent conditions, takes place. S(Q, t)/S(Q, 0) is a universal function of (Q(Q,t)2/3 with Q(Q) = QZ(Q) In Fig 58b a schematic plot of the crossover behavior of the segmental dynamics under 0-conditions is shown. 

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