Comparison between Simulation and Theory of the Rouse Model

4 Comparison between Simulation and Theory of the Rouse Model 

The shear relaxation modulus Gs t) and the first normal-stress difference function G i(t), both normalized on a per-segment basis and with kT set to 1, are obtained from the constitutive equation of the Rouse model (Eq. (7.55) with Sp replaced by Tp) as 

Several key predictions of the Rouse theory may be summarized as in the following  

These results are exactly confirmed by the simulations cases (l)-(3) are illustrated in the following The relaxation time in units of the time step as expressed by Eq. (16.8b) allows one to compare the simulated Gs t) curve with that calculated from Eq. (16.14). In Fig. 16.2, such a comparison is made for two-bead, five-bead and ten-bead Rouse chains. The perfect agreements between the simulated and theoretical line shapes without any shift along both the modulus and time-step axes confirm the predicted N and p dependences of the relaxation times of the Rouse normal modes. As predicted by the theory, no nonlinear effect can be observed between the 

Gs t) curves simulated at A = 0.5 and 1 for the Rouse chain model in other words, the shown step strain-simulated Gs t) curves are linear results. In Fig. 16.3, the strain independence of Gs(t) and for a five-bead 

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