A flexible synthetic polymer coil in a dilute solvent at has a radius of gyration and…

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Condensed Matter, Materials & Soft Matter · Non-equilibrium statistical mechanics and stochastic thermodynamics

Soft Matter at the Thermal Scale, Ch Polymer dynamics and viscoelasticity

Problem

A flexible synthetic polymer coil in a dilute solvent at T=298 KT=298\,\mathrm{K} has a radius of gyration Rg=40 nmR_g = 40\,\mathrm{nm} and sits in a solvent of viscosity ηs=1.0 mPa s\eta_s = 1.0\,\mathrm{mPa\,s} (water). Treat the coil, together with the solvent it drags along, as a sphere of radius RgR_g. ((a)) Estimate the coil's diffusion coefficient DD. ((b)) Estimate the Zimm relaxation time τZ\tau_{\rm Z} of the coil.

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