A strand between two cross-links has links of length .

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

Condensed Matter Physics, Ch Soft matter: when entropy, not bonding, sets the structure

Problem

A strand between two cross-links has

N_{\rm mon}=800

links of length

b_{\rm mon}=0.50\,\mathrm{nm}

. ((a)) Starting from

F(r_{\rm ee})=\tfrac32\dfrac{k_BT}{N_{\rm mon}b_{\rm mon}^2}r_{\rm ee}^2

, derive the stiffness

K_{\rm ch}

of this strand at

300\,\mathrm{K}

. ((b)) Find the force needed to hold its ends at three times its natural size

R_{\rm ee}=b_{\rm mon}\sqrt{N_{\rm mon}}