A method for incorporating reptation ideas in a temporary network model is used to predict the fluctuations of entanglement number and monomer density between entanglements in entangled polymeric liquids. The dynamic variables are chosen to be the number of Kuhn steps and the position of the entanglements. A chain of fixed number of Kuhn steps in a bath that fixes the chemical potential conjugate to the number of entanglements is considered. The static equilibrium statistics of such a model can be calculated analytically. Since the dynamics of the model may also be simulated, these analytic expressions may be used to check the algorithm. Also, the damping function is calculated analytically from these distributions, as well as normal stresses following a step shear.
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Jay D. Schieber (2003) studied this question.
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