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For an ideal chain, Flory Huggins theory gives us a distribution which is like a Gaussian.

$$P(l, r) \sim \left(\frac{3}{2 \pi l^2}\right)^{3/2} e^{\frac{-3 r^2}{2 l^2}}$$

where, $l$ is the monomer to monomer distance(also known as Kuhn length) and $R$ is the size of the monomer

This is great but what are the approximation away from an ideal chain polymer? I want to understand how one can go beyond Flory Huggins Theory.

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The assumptions made in the Flory-Huggins theory are

  • Quasi-solid lattice in the liquid
  • Inter-changeability of segments (not necessarily the same as the polymer structure units) of polymer and solvent molecules in the lattice
  • Independence of lattice constants on composition (artificial)
  • Polymer molecules are of same size
  • Average concentration of polymer segments in cells adjacent to cells unoccupied by the polymeric solute is taken to be equal to the overall average concentration
  • The expected number of available positions for each successive segment is overestimated in the formulation as the formula includes double counting of segments, separated by 2 or more segments in the same chain, that will fall on the same position twice

In particular the assumption that polymer molecules are of the same size is a very unrealistic one, which was later removed in the Flory-Krigbaum theory

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