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Topological rubber elasticity theory. II. SCL networks

机译:Topological rubber elasticity theory. II. SCL networks

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The theory presented in part I lsqb;Iwata, J. Chem. Phys. 76, 6363 (1982)rsqb; is applied to networks having a simplehyphen;cubichyphen;lattice (SCL) regular connection pattern, for which the projection matrixGgr;*is computed easily. Derivatives of elastic free energies in regard to parameter lgr; for macroscopic deformationpart;Ftilde;e/part;lgr;are computed numerically for isotropic deformations (swelling or deswelling) and for simple deformations (extension or contraction under swelling by agr; times). The initial arrangement of junction pointsr0is assumed to be exactly SCL, anddgr; = d0/ngr;bis chosen as one of parameters in the calculation, whered0is an endhyphen;tohyphen;end distance of the strands at the time of network formation, ngr; is a degree of polymerization in regard to the strands, andbis a statistical length per monomer. A repeating cell is chosen as a cube composed of3times;3times;3 ( = 27)junction points and3times;27 ( = 81)strands. The following are found in this work. (1) Among four termspart;F0,ph/part;lgr;,part;Ftilde;0,top/part;lgr;,part;Ftilde;1/part;lgr;,andpart;Ftilde;2/part;lgr;of the derivative of the elastic free energy, the principal term ispart;Ftilde;0,top/part;lgr;,which comes from the topological interaction among the strands; the phantom network termpart;F0,ph/part;lgr;is only a small correction to the net stress. (2) In isotropic deformations, the elastic free energy takes a minimum atlgr;0,a little belowlgr; = 1;for compression belowlgr;0,a strong postitive inner pressure, which comes from the topological repulsive forces among the strands, arises. (3) In simple deformations, the Mooneyndash;Rivlin term appears for unswollen systems and it disappears as swelling of the network proceeds. Experimental plans are proposed which will reveal the existence of the topological repulsive interactions in the networks.

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