Engineering of Small-Molecule Gels Based on the Thermodynamics and Kinetics of Fiber Formation - Soft Fibrillar Materials: Fabrication and Applications - page 79

(a)

Cross-over

Transient junction

Tip branching of fiber

Permanent junctions

Side branching of fiber

Type II

Type I

(b) (c)

Fibers

Fibers

Nodes

Nodes

Cayley tree like network

Figure 2.3 (a) Different types of junctions
occurring in fibrous networks and illustration
of fiber networks commonly observed in soft
materials. (b) Interconnecting fiber network
consisting of fibers and joints (or nodes)
with closed loops. (c) Cayley tree like net-
work (left) with open loops, and spherulite
as a typical Cayley tree like network (right).
Pictures in (c) are reprinted with permission

from Ref. [10], Copyright © 2010, American
Chemical Society. The pictures of tip branch-
ing of fibers and Type I side branching of
fibers are reproduced with permission from
Ref. [5], Copyright © 2002, Wiley-VCH Ver-
lag GmbH & Co. KGaA. The picture of Type
II side branching of fiber is reproduced with
permission from Ref. [4], Copyright © 2007,

American Chemical Society.

occur frequently in gels. Obviously, the nodes of a multi-domain network are
the individual spherulites. The ''links'' between the individual spherulites are the
physical contacts or interactions between neighboring spherulites. As the contacts
between fibers belonging to adjacent spherulites are transient and weak in most
cases, the strength of a multi-domain network is normally low. Let G fiber be
the storage modulus of a single spherulite and G domain the storage modulus of
the multi-domain network. We can expect that G domain vs the correlation length of
the multi-domain fiber network ζ will follow the power law G domain ∼ ζ − r , similar