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A new scaling for rotational diffusion of molecular probes in polymer solutions

Abstract

In the present work, we propose a new scaling form for the rotational diffusion coefficient of molecular probes in semi-dilute polymer solutions, based on a theoretical study. Mean-field theory for depletion effect and semi-empirical scaling equation for macroscopic viscosity of polymer solutions are properly incorporated to specify the space-dependent concentration and viscosity profiles in the vicinity of the probe surface. Following the scheme of classical fluid mechanics, we numerically evaluate the shear torque exerted on the probes, which then allows us to further calculate the rotational diffusion coefficient $D_r$. Particular attentions are put on the scaling behavior of the retardation factor $R^{\rot}\equiv D_0^r/D_r$ with $D_0^r$ being the diffusion coefficient in pure solvent. We find out that ${R}^{\rot}$ has little relevance to the macroscopic viscosity of the polymer solution, while can be well featured by the characteristic length scale $r_h/\delta$, i.e., the ratio between the hydrodynamic radius of the probe $r_h$ and the depletion thickness $\delta$. Correspondingly, we obtain a novel scaling form for the rotational retardation factor, following ${R}^{\rot}= \exp\left[a(r_h/\delta)^{b}\right]$ with rather robust parameters $a\simeq 0.51$ and $b\simeq 0.56$. We apply the theory to an extensive calculation for various probes in specific polymer solutions of poly(ethylene glycol) (PEG) and dextran. Our theoretical results show good agreements with the experimental data, and demonstrate clearly the validity of the new scaling form. In addition, the difference of the scaling behavior between translational and rotational diffusions is clarified, from which we conclude that depletion effect plays more significant role on the local rotational diffusion rather than the long-range translation diffusion.

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Publication details

The article was accepted on 07 Nov 2017 and first published on 07 Nov 2017


Article type: Paper
DOI: 10.1039/C7CP07047K
Citation: Phys. Chem. Chem. Phys., 2017, Accepted Manuscript
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    A new scaling for rotational diffusion of molecular probes in polymer solutions

    J. Qing, A. Chen and N. Zhao, Phys. Chem. Chem. Phys., 2017, Accepted Manuscript , DOI: 10.1039/C7CP07047K

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