We consider statistical mechanical properties of the primitive chain network (PCN) model for entangled polymers from its dynamic equations. We show that the dynamic equation for the segment number of the PCN model does not reduce to the standard Langevin equation which satisfies the detailed balance condition. We propose heuristic modifications for the PCN dynamic equation for the segment number, to make it reduce to the standard Langevin equation. We analyse some equilibrium statistical properties of the modified PCN model, by using the effective free energy obtained from the modified PCN dynamic equations. The PCN effective free energy can be interpreted as the sum of the ideal Gaussian chain free energy and the repulsive interaction energy between slip-links. By using the single chain approximation, we calculate several distribution functions of the PCN model. The obtained distribution functions are qualitatively different from ones for the simple slip-link model without any direct interactions between slip-links.
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14 November 2011
Research Article|
November 10 2011
Detailed balance condition and effective free energy in the primitive chain network model
Takashi Uneyama;
Takashi Uneyama
a)
JST-CREST, Institute for Chemical Research,
Kyoto University
, Gokasho, Uji, Kyoto 611-0011, Japan
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Yuichi Masubuchi
Yuichi Masubuchi
JST-CREST, Institute for Chemical Research,
Kyoto University
, Gokasho, Uji, Kyoto 611-0011, Japan
Search for other works by this author on:
a)
Author to whom correspondence should be addressed. Electronic mail: uneyama@scl.kyoto-u.ac.jp.
J. Chem. Phys. 135, 184904 (2011)
Article history
Received:
July 10 2011
Accepted:
October 17 2011
Citation
Takashi Uneyama, Yuichi Masubuchi; Detailed balance condition and effective free energy in the primitive chain network model. J. Chem. Phys. 14 November 2011; 135 (18): 184904. https://doi.org/10.1063/1.3658775
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