Polymer solutions dynamic scaling

W. Paul, K. Binder, D. Heermann, K. Kremer. Dynamics of polymer solutions and melts. Reptation prediction and scaling of relaxation times. J Chem Phys 95 7726-7740, 1991. 

Another approach, neglecting the details of the chemical structure and concentrating on the universal elements of chain relaxation, is based on dynamic scaling considerations [4, 11], In particular in polymer solutions, this approach offers an elegant tool to specify the general trends of polymer dynamics, although it suffers from the lack of a molecular interpretation. 

The dynamics of highly diluted star polymers on the scale of segmental diffusion was first calculated by Zimm and Kilb [143] who presented the spectrum of eigenmodes as it is known for linear homopolymers in dilute solutions [see Eq. (77)]. This spectrum was used to calculate macroscopic transport properties, e.g. the intrinsic viscosity [145], However, explicit theoretical calculations of the dynamic structure factor [S(Q, t)] are still missing at present. Instead of this the method of first cumulant was applied to analyze the dynamic properties of such diluted star systems on microscopic scales. 

Dynamic light scattering has traditionally been applied to polymer solutions, and DLS results for block copolymer solutions are discussed in Chapters 3 and 4. A number of recent papers have described the application of the technique to disordered block copolymer melts (Anastasiadis et al. 1993a,6 Boudenne et al. 1996 Floudas et al. 1995 Fytas et al. 1993 Jian et al. 1994a Stepanek and Lodge 1996 Vogt et al. 1994). Due to the limited range of dynamic time-scales that can... 

Rabin Y, Ottinger HCh (1990) Dilute polymer solutions internal viscosity, dynamic scaling, shear thinning, and frequency-dependent viscosity. Europhys Lett 13(5) 423—428 Rallison JM, Hinch EJ (1988) Do we understand the physics in the constitutive equation J Non-Newton Fluid Mech 29(l) 37-55... 

There are three different regimes of polymer dynamics on three different length and time scales for an entangled polymer solution in an athermal solvent. The stress relaxation modulus of such a solution is shown in Fig. 9.9. Two of the regimes are identical to those discussed in Section 9.2.2 and the other regime was discussed in Section 8.5. 

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