A semiflexible polymer has contour length much greater than its persistence length

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

A semiflexible polymer has contour length

L

much greater than its persistence length

l_p

, so that it obeys Gaussian-chain statistics with effective Kuhn length

b=2l_p

and

N=L/b

Kuhn segments. ((a)) Using

R_g^2=Nb^2/6

for an ideal chain, show that in this limit

R_g^2 = l_pL/3

. ((b)) A sample of this polymer with contour length

L=2.4\,\mu\mathrm{m}

is studied by small-angle X-ray scattering; the Guinier region of the scattering curve gives

R_g=63\,\mathrm{nm}

. Find the persistence length

l_p

. ((c)) Check that the condition

L\gg l_p

, assumed in part (a), is satisfied by the value of

l_p

found in part (b).