Elasticity near the vulcanization transition

Details Elasticity near the vulcanization transition Elasticity near the vulcanization transition

1997-12-03

arxiv.org/abs/cond-mat/9712050v2

Phys. Rev. E 58, R24-R27 (1998)

Physics

Condensed Matter

Disordered Systems and Neural Networks

REVTEX, 5 pages. Minor changes

Scientific paper

10.1103/PhysRevE.58.R24

Signatures of the vulcanization transition--amorphous solidification induced by the random crosslinking of macromolecules--include the random localization of a fraction of the particles and the emergence of a nonzero static shear modulus. A semi-microscopic statistical-mechanical theory is presented of the latter signature that accounts for both thermal fluctuations and quenched disorder. It is found (i) that the shear modulus grows continuously from zero at the transition, and does so with the classical exponent, i.e., with the third power of the excess cross-link density and, quite surprisingly, (ii) that near the transition the external stresses do not spoil the spherical symmetry of the localization clouds of the particles.

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