03/20/2013 Lecture 27&28&29
Martin M. PHGY Tutor
1. To see how random walks of diffusion apply to polymers
a. Can be described well as random walks.
2. To learn how to define the entropy of a random walk coil
a. With an entropy description defined by the usual Gaussian function
3. To learn the difference between a random walk and a self avoiding walk, and the size of
real polymer chains
a. SAWs are longer than random walks and can't cross over paths
Polymer behaviour is mostly entropic. Polymers behave differently than molecules, and all our
impressive features like skin, bone, muscle, DNA are ALL polymers. Same with out plastics and
stuff. The larger the polymer, the more shapes.
A simple model for polymers is N segments of size "a". The total length = .
N is extremely variable but "a" is usually 3-10 Angstroms. The end-to-end coil length is √
Coil Entropy ΔS =-3/2 [ r /R2 02 + R /0 ] 2
r= the raduis we want to know the entropy of
R0= most likely random walk of radius a √
First term: energy penalty for stretching
Second term: energy penalty for compression
Using the √ rule doesn't give us the perfect length, real coils are actually longer. Diffusion
theory works well for gas molecules, but polymer coils can't be in the same space at different
times. No crossing over is allowed; it is a self avoiding walk. SAWs are much longer than
random walks. Experimentally, the highest entropy is actually:
A balance between entropy and enthalpy is the base of ALL self-organizing material. Folded
polymers are held by enthalpic bonds (hydrogen, ionic bonds, and hydrophobic bonds).
DNA is simple and well known, folding only due to H bonds and coil entropy.
AT enthalpy: 21kJ/mol (MP~82)
CG enthalpy: 29kL/mol (MP~96)
At a critical T, enthalpy wins out. DNA doesn't melt at one temperature but depends on the
DNA origami: A computer program can make ANY shape you want by feeding different