Issue |
Europhys. Lett.
Volume 57, Number 3, February 2002
|
|
---|---|---|
Page(s) | 458 - 463 | |
Section | Condensed matter: electronic structure, electrical, magnetic, and optical properties | |
DOI | https://doi.org/10.1209/epl/i2002-00482-6 | |
Published online | 01 September 2002 |
Entropic elasticity at the sol-gel transition
School of Physics and Astronomy, Raymond and Beverly
Sackler Faculty of Exact Sciences, Tel Aviv University - Tel
Aviv 69 978, Israel
Corresponding author: farago@mrl.ucsb.edu
Received:
3
September
2001
Accepted:
6
November
2001
The sol-gel transition is studied in two purely entropic models
consisting of hard spheres in continuous three-dimensional space, with
a fraction p of nearest-neighbor spheres tethered by inextensible
bonds. When all the tethers are present (p=1) the two systems have
connectivities of simple cubic and face-centered cubic lattices. For
all p above the percolation threshold pc, the elasticity has a
cubic symmetry characterized by two distinct shear moduli. When p
approaches pc, both shear moduli decay as , where
for each type of connectivity. This result is similar
to the behavior of the conductivity in random resistor networks, and
is consistent with many experimental studies of gel elasticity. The
difference between the shear moduli that measures the deviation from
isotropy decays as
, with
.
PACS: 82.70.Gg – Gels and sols / 62.20.Dc – Elasticity, elastic constants / 61.43.-j – Disordered solids
© EDP Sciences, 2002
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