Light scattering on a dilute solution of a synthetic polymer in a theta solvent gives…

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Soft condensed matter · Soft condensed matter

Soft Matter at the Thermal Scale, Ch The size and shape of a polymer chain

Problem

Light scattering on a dilute solution of a synthetic polymer in a theta solvent gives a radius of gyration

R_g = 8.0\,\mathrm{nm}

for chains of

n = 2000

backbone carbon-carbon bonds, each of length

l = 0.154\,\mathrm{nm}

. Treat the chain as ideal, so that

\langle R^2\rangle = 6R_g^2

, and take its fully extended length as the planar all-trans zig-zag at the tetrahedral angle,

R_{\max} = nl\sqrt{2/3}

. ((a)) Find the Kuhn length

b

of this polymer using

b = \langle R^2\rangle/R_{\max}

. ((b)) Find the number of Kuhn segments

N

using

N = R_{\max}^2/\langle R^2\rangle