Segmental diffusion solution viscosity

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. 

Diffusion theories have been proposed that relate the rate constant of termination to the initial viscosity of the polymerization medium. The rate-determining step of termination, the segmental diffusion of the chain ends, is inversely proportional to the microviscosity of the solution [123]. Yokota and Itoh [124] modified the rate equation to include the viscosity of the medium. According to that equation, the overall polymerization rate constant should be proportional to the square root of the initial viscosity of the system. 

The transition from dilute solution behaviour (isolated polymer coils) to semi-dilute (interpenetration of coils, uniform polymer segment density) usually occurs over a narrow range of concentration, and a critical concentration c identified. This c will, however, depend to some extent upon the particular experiment performed, e.g., solution viscosity, diffusion (cf., e.g., ref. 99) ... 

S. Adams and D. B. Adolph. Viscosity dependence of the local segmental diffusion of anthracene-labeled 1,2-polybutadiene in dilute solution. Macromolecules, 31 (1998), 5794-5799. 

S. Glowinkowski, D. J. Gisser, and M. D. Ediger. Carbon-13 nuclear magnetic resonance measurements of local segmental diffusion of polyisoprene in dilute solution nonlinear viscosity dependence. Macromolecules, 23 (1990), 3520-3530. 

The original Kramers equation had a = 1 at all /, not the a 0.4-0.8 seen here at larger q. However, as seen in Chapter 5, solvent diffusion actually has the viscosity-dependence of Eq. 15.3 with an 7-dependent a, namely a = 1 at smaller qtoa = 2/3 at q larger than 5 cP. The small-molecule self-diffusion coefficient and the segmental diffusion time thus show consistent dependences on q. The spirit of the Kramers approach, namely that the rate of diffusion-driven molecular motions should track the solution fluidity q in the same way that the rates of solvent and small-molecule diffusion track the solution fluidity, appears to be preserved by experiment. 

Thus, carried out analysis shows, that the studies of the viscosity of polymeric solutions permits sufficiently accurately to estimate the characteristic times of the segmental and translational movements, on the basis of which the coefficients of diffusion of polymeric chains into solutions can be calculated. 

In low-molar-mass liquids, the diffusion coefficients of dissolved substances initially decrease strongly with increasing solvent viscosity (Figure 7-1). They then remain practically constant for solvents consisting of polymers of not too high molar mass. This allows the conclusion that the diffusion of the solute is only dependent on the segment mobility of the solvent molecules and not on the mobility of the molecular centers of gravity. 

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