Editing Polymer physics (section)

===Ideal chains=== 
{{anchor|Ideal Chains}}

* The '''freely-jointed''' chain is the simplest model of a polymer. In this model, fixed length polymer segments are linearly connected, and all bond and torsion angles are equiprobable.<ref>H. Yamakawa, "Helical Wormlike Chains in Polymer Solution", (Springer Verlag, Berlin, 1997)</ref> The polymer can therefore be described by a simple random walk and [[ideal chain]]. The model can be extended to include extensible segments in order to represent bond stretching.<ref name=BSG>{{cite journal|last1=Buche|first1=M.R.|last2=Silberstein|first2=M.N.|last3=Grutzik|first3=S.J.|title=Freely jointed chains with extensible links|journal=Phys. Rev. E|volume=106|pages=024502|year=2022|issue=2–1 |doi=10.1103/PhysRevE.106.024502|pmid=36109919 |arxiv=2203.05421 |s2cid=247362917 }}</ref>
* The '''freely-rotating''' chain improves the freely-jointed chain model by taking into account that polymer segments make a fixed bond angle to neighbouring units because of specific chemical bonding. Under this fixed angle, the segments are still free to rotate and all torsion angles are equally likely.
* The '''hindered rotation''' model assumes that the torsion angle is hindered by a potential energy. This makes the probability of each torsion angle proportional to a [[Boltzmann factor]]:

:<math>P(\theta)\propto{}\exp\left(-U(\theta)/kT\right)</math>, where <math>U(\theta)</math> is the potential determining the probability of each value of <math>\theta</math>.

* In the '''rotational isomeric''' state model, the allowed torsion angles are determined by the positions of the minima in the rotational potential energy. Bond lengths and bond angles are constant.
* The '''[[Worm-like chain]]''' is a more complex model.  It takes the [[persistence length]] into account.  Polymers are not completely flexible; bending them requires energy.  At the length scale below persistence length, the polymer behaves more or less like a rigid rod.
* The '''[[FENE model|finite extensible nonlinear elastic model]]''' takes into account non-linearity for finite chains. It is used for computational simulations.