Rouse-Zimm model

There is an alternative and very direct way to generalize the Rouse-Zimm model for non-Gaussian chains. This approach takes advantage of the expression given by the original theory for the chain elastic potential energy in terms of normal coordinates ... 

Fig. 5.2 Mode number dependence of the relaxation times and T2 solid lines) found for PIB in dilute solution at 327 K. The dashed-dotted line shows the relaxation time of the Rouse-Zimm model. The horizontal dashed line displays the value of (Reprinted with permission from [186]. Copyright 2001 American Chemical Society)...

Fig. 5.10 Chain dynamic structure factor of PDMS (a) and PIB (b) in toluene solution at 327 K at the Q-values 0.04 A" (empty circle), 0.06 A (filled circle), 0.08 A" (empty square), 0.10 A (filled square), 0,15 A (empty diamond), 0,20 A (filled diamond), 0,25 A (empty triangle), 0.30 A" (filled triangle), 0.40 A" (plus). Solid lines correspond to fitting curves Rouse-Zimm model for PDMS and Rouse-Zimm with intrachain viscosity for PIB (see the text). (Reprinted with permission from [186]. Copyright 2001 American Chemical Society)...

Let us add here some remarks on the normal stress difference. According to the Rouse-Zimm model [132,133] the first normal stress difference may be related to the storage modulus G. Taking into account only the longest relaxation time x, one gets... 

The depolarized scattering for the Rouse-Zimm dynamical model of flexible polymer chains (cf. Section 8.8) may also be calculated. Ono and Okano (1971) have performed this calculation for q = 0 (zero scattering angle) and find that the scattered light spectral density is a series of Lorentzians each with a relaxation time characteristic of one of the Rouse-Zimm model modes. However the contribution of each mode to the spectrum is equal. This behavior should be contrasted with that of the isotropic spectrum where the scattering spectrum is dominated by contributions from the longest wavelength modes. 

Just as the Gaussian chain is the basic paradigm of the statistics of polymer solutions, so is its extension to the bead-spring model still basic to current work in the held of polymer dynamics. The two limiting cases of free draining (no hydrodynamic interaction between beads, characterized by the draining parameter A = 0) and non-free draining (dominant hydrodynamic interaction, A= CO, due to Rouse and Zimm, respectively, are sufficiently familiar that the approach is often known as the Rouse-Zimm model. ... 

The Rouse-Zimm Model Describes the Dynamics of Viscoelastic Fluids... 

Figure 33.9 The Rouse-Zimm model for viscoelasticity. Applying a shear flow to a polymer solution stretches out the chains, indicated here in terms of a beads-and-spring model, leading to an elastic entropic retractive force.

The self-diffusion coefficient is used to describe the center-of-mass motion for a simple liquid. It can also be used in connection with the Rouse-Zimm model to describe the behavior of a long chain. The determination of diffusion coefficient D... 

An alternate explanation of these results comes from the perspective of the Rouse-Zimm model that predicts that the relaxation time for simple polymers above Tg is directly proportional to the product of the molecular weight and viscosity, where the latter increases with increasing molecular weight (ref. 16, p 147). 

Figure 2. A depiction of the bead-and-spring (Rouse Zimm) model for a polymer chain. The chain is represented by n beads and (n-1) springs of length b.

Measurements of using Pecora s analysis " " have been performed on different systems using either polarized or depolarized light-scattering. The experimental values of are in the region of the values predicted by the Rouse-Zimm model, but no molecular weight dependences are reported. 

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