NSE Results from Semi-Dilute Solutions of Linear Homopolymers

2 NSE Results from Semi-Dilute Solutions of Linear Homopolymers Transition from Single Chain to Collective Dynamics 

Under good solvent conditions the dynamics of semi-dilute solutions was investigated by NSE using a PDMS/d-benzene system at T = 343 K and various concentrations 0.02 c 0.25. The critical concentration c as defined by (112) is 0.055. 

The transition from single- to many-chain behavior already becomes obvious qualitatively from a line shape analysis of the NSE spectra (see Fig. 60) [116]. For dilute solutions (c = 0.05) the line shape parameter (3 is equal to about 0.7 for all Q-values, which is characteristic of the Zimm relaxation. In contrast, in semi-dilute solutions (e.g. c = 0.18), ft-values of 0.7 are only found at larger Q-values, whereas P-values of about 1.0, as predicted for collective diffusion [see Eq. (128)] are obtained at small Q-values. A similar observation was reported by [163]. 

Q2 behavior takes place at decreasing Q. The position of the crossover point Q (c) is a direct measure of the dynamic correlation length (c) = 1/Q (c). The plateau value at low Q determines the collective diffusion coefficient Dc. A simultaneous fit of all low Q spectra where a simple exponential decay was found led to the concentration dependence and the numerical values of Dc 

The result is shown in Fig. 62 where the different Dc values, obtained from separate fits at each concentration, are also presented. The dynamic correlation length (c)/A = (3.4 + 0.7) c 067 005 is of the same order of magnitude as the value obtained from a static experiment on the PS/d-cyclohexane system [104]. The exponents for the concentration dependence of Dc and (c) are in agreement 

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