Discrete and continuum chain models

If we take the limit of the rod length Iq — 0 and the number of rods N — oc such that the polymer length is kept constant L = Nlo, we have an integral instead of a summation  

These two parts constitutes the energy for a worm-like nematic polymer. The first part (Equation 2.96) demands a slow reversal as a chain evolves and favors parallel alignment, but the second term (Equation 2.97) prefers both anti-parallel and parallel alignments, and a rapid reversal of 

it becomes the case of the discrete picture and jointed-rods are applicable. If lo, however, the elastically discrete polymer evolves into a worm chain, i.e., an elastically homogeneous chain. The orientation change can then take place over a length comparable to Iq. With this continuum of allowed orientational states, the worm chain accurately represents the angular entropy of the real polymer. 

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