A tracer sphere with radius is suspended in a dilute solution of polymer coils with radii of gyration . In a model with hard-sphere interactions, the centers of mass of the polymer coils cannot pass the dashed surface with radius .
We model the polymer coils as hard spheres of radius concerning the interactions with the tracer sphere and as solid sphere of radius and a no-slip boundary condition on the surface concerning the interactions with the solvent.
and (solid blue and dashed red lines, respectively) defined via as functions of for different values of the ratio . The value of for neighboring curves for the lowest six curves differs by 0.1. Squares and circles indicate the results for the long and short time diffusion constants of hard spheres , respectively, according to Ref. 5.
and (solid blue and dashed red lines, respectively) for large polymers in good solvent conditions as function of . Also shown is the result for the generalized Stokes–Einstein relation equation (28), which is independent of . In this approximation short and long time diffusion constants are equal.
Diffusion coefficient of a polystyrene sphere of radius in a solution of PEO polymers with molecular masses of 18 500 amu (squares), (circles), and (triangles) from Ref. 8. The solid, dashed, and dashed-dotted lines, respectively, indicate the theoretical predictions for according to Eq. (25). There is no adjustable parameter.
Normalized diffusion coefficients of spheres with radius and 51.7 nm (circle and square, respectively) in a solution of PEO with a molecular mass of from Ref. 8. Dashed and dashed-dotted lines are theoretical predictions for and for in first order in polymer concentration from Eqs. (25) and (21), respectively. For , and are almost identical (corresponding to , see Fig. 4) and we only plot (solid line).
The exponents from Eq. (31) as measured in experiments compared to our theoretical prediction given by Eq. (33).
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