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We consider statistical mechanical properties of the primitive chain network(PCN) model for entangled polymers from its dynamic equations. We show that thedynamic equation for the segment number of the PCN model does not reduce to thestandard Langevin equation which satisfies the detailed balance condition. Wepropose heuristic modifications for the PCN dynamic equation for the segmentnumber, to make it reduce to the standard Langevin equation. We analyse someequilibrium statistical properties of the modified PCN model, by using theeffective free energy obtained from the modified PCN dynamic equations. The PCNeffective free energy can be interpreted as the sum of the ideal Gaussian chainfree energy and the repulsive interaction energy between slip-links. By usingthe single chain approximation, we calculate several distribution functions ofthe PCN model. The obtained distribution functions are qualitatively differentfrom ones for the simple slip-link model without any direct interactionsbetween slip-links.

Detailed Balance Condition and Effective Free Energy in the Primitive Chain Network Model