Proteins are biological nanomaterials. For “cylindrical” proteins of radius R, a

Question

Proteins are biological nanomaterials. For “cylindrical” proteins of radius R, and
length L, AH ~ 2kTroom.
a) Show that the nonretarded van der Waals interaction free energy is greater
than kT for R = 1 nm, L= 5nm, and separation distance D = 0.2 nm.
b) As a general rule of thumb, how far do cylinders have to be apart for the
attraction to be less than kT?
(Units note: Hamaker constants are often expressed in zeptojoules (zJ) where 1 zJ
= 10-21 J = 10-14 erg. Make sure you always check the units when looking up
constants and giving your final answer and use railroad tracks to make sure your
units work out).

Explanation / Answer

a) Free energy = [-(Aham/ 24l 3/2 )]R1/2 L

= [-(2/24)5/0.089] kT

= 5kT

which is greater than AH = 2kT

b) As a general rule of thumb, separation has to be less than the size L >> D

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