|  | At low densities the polymers only weakly interact. The excluded volume
    interaction between the monomers within a chain is effective and the statistic is that of
    a self-avoiding random walk. The extend of the polymer is the end-to-end distance Re.
      As the concentration of the chains increases, the equivalent spheres of radius Re
    begin to fill space. For large enough concentration the polymers can no longer be
    considered independent. The polymers start to be entangled. The entangled length will be
    an inportant quantity. |