Microscopic Model and General Statistical Mechanical Formulas
Extensible Freely Jointed Chain (FJC) Model
Qualitative Description of Single Chain Stretching
The simplest useful model for such a flexible chain is the freely jointed chain model. Here we assume bond vectors that are independent of the conformation of the chain. The chain is stretched from its equilibrium length.
Now the free energy of an ensemble of chains is
F = E - TS
which is simply
F = -TS.
Say I model a polymer as a freely jointed chain in 3D with N bonds of length L each. If I stretch the chain initially, I consider that the deformation energy is zero when the chain has its equilibrium dimensions. I now take into account a small amount of longitudinal along-chain deformation.
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