We have investigated dibenzylidene sorbitol (DBS) physical gels with different gelator concentrations in a poly(propylene oxide) (PPO) matrix by frequency dependent rheological measurements. Defining the gel point according to the Winter and Chambon criterion, we have obtained the critical gel concentration cg=0.153 wt %. Analyzing the experimental data in the δ−|G*| plot for samples very close to the gel point, we found that a critical gelation concentration range would be more appropriate for describing the gelation process in DBS/PPO system rather than a single concentration value. By extrapolation from the δ−|G*| plot we obtained a characteristic modulus Gex for the samples above the gel point. The analysis of elasticity evolution with increasing gelator concentration revealed the existence of two distinct regimes. A critical domain is identified between cg and a turn-over DBS concentration of about 0.5 wt % in which Gex exhibits power-law dependence on the relative distance from the gel point. Above 0.5 wt % DBS the characteristic modulus is found to scale with the DBS concentration. The results are discussed within the framework of different models describing physically gelling systems.

1.
Arbabi
,
S.
, and
M.
Sahimi
, “
Mechanics of disordered solids. II. Percolation on elastic networks with bond-bending forces
,”
Phys. Rev. B
47
,
703
712
(
1993
).
2.
Axelos
,
M. A. V.
, and
M.
Kolb
, “
Crosslinked biopolymers: Experimental evidence for scalar percolation theory
,”
Phys. Rev. Lett.
64
,
1457
1460
(
1990
).
3.
Benguigui
,
L.
, “
Lattice and continuum percolation transport exponents: Experiments in two-dimensions
,”
Phys. Rev. B
34
,
8176
8178
(
1986
).
4.
Chambon
,
F.
, and
H. H.
Winter
, “
Linear viscoelasticity at the gel point of a crosslinking PDMS with imbalanced stoichiometry
,”
J. Rheol.
31
,
683
697
(
1987
).
5.
Colby
,
R. H.
,
M.
Rubinstein
,
J. R.
Gilmor
, and
T. H.
Mourey
, “
Scaling properties of branched polyesters. 2. Static scaling above the gel point
,”
Macromolecules
25
,
7180
7187
(
1992
).
6.
de Gennes, P. G., Scaling Concepts in Polymer Physics (Cornell University Press, Ithaca, NY, 1979).
7.
Duxbury
,
P. M.
,
D. J.
Jacobs
,
M. F.
Thorpe
, and
C.
Moukarzel
, “
Floppy modes and the free energy: Rigidity and connectivity percolation on Bethe lattices
,”
Phys. Rev. E
59
,
2084
2092
(
1999
).
8.
Fahrländer
,
M.
,
K.
Fuchs
, and
Chr.
Friedrich
, “
Rheological properties of dibenzylidene sorbitol networks in poly(propylene oxide) matrices
,”
J. Rheol.
44
,
1103
1119
(
2000
).
9.
Fahrländer
,
M.
,
K.
Fuchs
,
R.
Mülhaupt
, and
Chr.
Friedrich
, “
Linear and nonlinear rheological properties of self-assembling tectons in polypropylene matrices
,”
Macromolecules
36
,
3749
3757
(
2003
).
10.
Feng
,
S.
,
B. I.
Halperin
, and
P. N.
Sen
, “
Transport properties of continuum systems near the percolation threshold
,”
Phys. Rev. B
35
,
197
214
(
1987
).
11.
Goldbart
,
P.
, and
N.
Goldenfeld
, “
Rigidity and ergodicity of randomly cross-linked macromolecules
,”
Phys. Rev. Lett.
58
,
2676
2679
(
1987
).
12.
Goldbart
,
P.
, and
N.
Goldenfeld
, “
The solid state of crosslinked macromolecules: Basic concepts
,”
Macromolecules
22
,
948
954
(
1989a
).
13.
Goldbart
,
P.
, and
N.
Goldenfeld
, “
Microscopic theory for cross-linked macromolecules. I. Broken symmetry, rigidity, and topology
,”
Phys. Rev. A
39
,
1402
1411
(
1989b
).
14.
Goldbart
,
P.
, and
N.
Goldenfeld
, “
Microscopic theory for cross-linked macromolecules. II. Replica theory of the transition to the solid state
,”
Phys. Rev. A
39
,
1412
1419
(
1989c
).
15.
Goldenfeld
,
N.
, and
P.
Goldbart
, “
Dynamic scaling and spontaneous symmetry breaking at the gel point
,”
Phys. Rev. A
45
,
R5343
R5346
(
1992
).
16.
Guenet
,
J. M.
,
B.
Lotz
, and
J. C.
Wittman
, “
Thermodynamic aspects and morphology of physical gels from isotactic polystyrene
,”
Macromolecules
18
,
420
427
(
1985
).
17.
Guenet, J. M., Thermoreversible gelation of Polymers and Biopolymers (Academic, London, 1992).
18.
Guenet
,
J. M.
, “
Structure versus rheological properties in fibrillar thermoreversible gels from polymers and biopolymers
,”
J. Rheol.
44
,
947
960
(
2000
).
19.
Head
,
D. A.
,
A. J.
Levine
, and
F. C.
MacKintosh
, “
Deformation of cross-linked semiflexible polymer networks
,”
Phys. Rev. Lett.
91
,
108102
(
2003
).
20.
Ilzhoefer
,
J. R.
, and
R. J.
Spontak
, “
Effect of polymer composition on the morphology of self-assembled dibenzylidene sorbitol
,”
Langmuir
11
,
3288
3291
(
1995
).
21.
Ilzhoefer
,
J. R.
,
B. C.
Broom
,
S. M.
Nepa
,
E. A.
Vogler
,
S. A.
Khan
, and
R. J.
Spontak
, “
Evidence of hierarchical order in an amphiphilic graft terpolymer gel
,”
J. Phys. Chem.
99
,
12069
12071
(
1995
).
22.
Jacobs
,
D. J.
, and
M. F.
Thorpe
, “
Generic rigidity percolation: The pebble game
,”
Phys. Rev. Lett.
75
,
4051
4054
(
1995
).
23.
Joly-Duhamel
,
C.
,
D.
Hellio
,
A.
Ajdari
, and
M.
Djabourov
, “
All gelatin networks: 2. The master curve for elasticity
,”
Langmuir
18
,
7158
7166
(
2002
).
24.
Jones
,
J. L.
, and
C. M.
Marques
, “
Rigid polymer networks models
,”
J. Phys. (France)
51
,
1113
1127
(
1990
).
25.
Kantor
,
Y.
, and
I.
Webman
, “
Elastic properties of random percolating systems
,”
Phys. Rev. Lett.
52
,
1891
1894
(
1984
).
26.
Larson, R. G., The Structure and Rheology of Complex Fluids (Oxford University Press, New York 1999).
27.
Latva-Kokko
,
M.
,
J.
Mäkinen
, and
J.
Timonen
, “
Rigidity transition in two-dimensional random fiber networks
,”
Phys. Rev. E
63
,
046113
(
2001
).
28.
Latva-Kokko
,
M.
, and
J.
Timonen
, “
Rigidity of random networks of stiff fibers in the low-density limit
,”
Phys. Rev. E
64
,
066117
(
2001
).
29.
Li
,
L.
, and
Y.
Aoki
, “
Rheological images of poly(vinyl chloride) gels. 1. The dependence of sol-gel transition on concentration
,”
Macromolecules
30
,
7835
7841
(
1997
).
30.
Li
,
L.
, and
Y.
Aoki
, “
Rheological images of poly(vinyl chloride) gels. 3. Elasticity evolution and the scaling law beyond the sol-gel transition
,”
Macromolecules
31
,
740
745
(
1998
).
31.
Mercurio
,
D. J.
, and
R. J.
Spontak
, “
Morphological characteristics of 1,3:2,4-dibenzylidene sorbitol/poly(propylene glycol) organogels
,”
J. Phys. Chem. B
105
,
2091
2098
(
2001
).
32.
Mercurio
,
D. J.
,
S. A.
Khan
, and
R. J.
Spontak
, “
Dynamic rheological behavior of DBS-induced poly(propylene glycol) physical gels
,”
Rheol. Acta
40
,
30
38
(
2001
).
33.
Ramzi
,
M.
,
C.
Rochas
, and
J. M.
Guenet
, “
Structure-properties relation for agarose thermoreversible gels in binary solvents
,”
Macromolecules
31
,
6106
6111
(
1998
).
34.
Schosseler
,
F.
,
M.
Daoud
, and
L.
Leibler
, “
Experimental structure factor of solutions of randomly branched polymers
,”
J. Phys. (France)
51
,
2373
2385
(
1990
).
35.
Stauffer, D., and A. Aharony, Introduction to Percolation Theory, 2nd ed. (Taylor and Francis, London, 1994).
36.
Van der Linden
,
E.
, and
L. M.
Sagis
, “
Isotropic force percolation in protein gels
,”
Langmuir
17
,
5821
5824
(
2001
).
37.
Watase
,
M.
,
Y.
Nakatani
, and
H.
Itagaki
, “
On the origin of the formation and stability of physical gels of di-o-benzylidene-d-sorbitol
,”
J. Phys. Chem. B
103
,
2366
2373
(
1999
).
38.
Watase
,
M.
, and
H.
Itagaki
, “
Thermal and rheological properties of physical gels formed from benzylidene-d-sorbitol derivatives
,”
Bull. Chem. Soc. Jpn.
71
,
1457
1466
(
1998
).
39.
Wilder
,
E. A.
,
C. K.
Hall
,
S. A.
Khan
, and
R. J.
Spontak
, “
Molecular self-organization and gelation efficacy of dibenzilydene sorbitol: An overview
,”
Recent Res. Devel. Mat. Sci.
3
,
93
115
(
2002
).
40.
Wilder
,
E. A.
,
C. K.
Hall
,
S. A.
Khan
, and
R. J.
Spontak
, “
Effects of composition and matrix polarity on network development in organogels of poly(ethylene glycol) and dibenzylidene sorbitol
,”
Langmuir
19
,
6004
6013
(
2003
).
41.
Wilhelm
,
J.
, and
E.
Frey
, “
Elasticity of stiff polymer networks
,”
Phys. Rev. Lett.
91
,
108103
(
2003
).
42.
Winter
,
H. H.
, and
F.
Chambon
, “
Analysis of linear viscoelasticity of a crosslinking polymer at the gel point
,”
J. Rheol.
30
,
367
382
(
1986
).
43.
Wu
,
H.
, and
M.
Morbidelli
, “
A model relating structure of colloidal gels to their elastic prperties
,”
Langmuir
17
,
1030
1036
(
2001
).
44.
Yamasaki
,
S.
, and
H.
Tsutsumi
, “
The dependence of the polarity of solvents on 1,3:2,4-Di-o-benzylidene-d-sorbitol gel
,”
Bull. Chem. Soc. Jpn.
68
,
123
127
(
1995
).
45.
Yamasaki
,
S.
,
Y.
Ohashi
,
H.
Tsutsumi
, and
K.
Tsujii
, “
The aggregated higher-structure of 1,3:2,4-Di-o-benzylidene-d-sorbitol in organic gels
,”
Bull. Chem. Soc. Jpn.
68
,
146
151
(
1995
).
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