NSE Results from the Transition Regime

We are now going to compare the results of mode analysis with measurements of viscosity on polyethylene melts. With the aid of Eq. (30), which links the viscosity to the relaxation times, we can predict the viscosity using the results of spin-echo measurements and compare it with the viscosity measurement 

Neutron Spin Echo Investigations on the Segmental Dynamics 

In addition to the Rouse model, the Hess theory contains two further parameters the critical monomer number Nc and the relative strength of the entanglement friction A (0)/ . Furthermore, the change in the monomeric friction coefficient with molecular mass has to be taken into account. Using results for (M) from viscosity data [47], Fig. 16 displays the results of the data fitting, varying only the two model parameters Nc and A (0)/ for the samples with the molecular masses Mw = 3600 and Mw = 6500 g/mol. 

In this fitting procedure the time-dependent diffusion coefficient as discussed above has been taken explicitly into account. As can be seen, with only two parameters both sets of spectra are well described. This holds also for the other two samples. For the model parameters, the fit reveals Nc = 150 and A (0)/ = 0.18 ns. Nc is very close to Nc = 138 as obtained from the NSE experiments on long-chain PE (see next section). 

According to Hess, the relative strength of the entanglement friction can be related to the more microscopic parameter q , describing the range of the true interchain interaction potential. A value of q 1 = 7 A, close to the average interchain distance of about 4.7 A, is obtained. 

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