Engineering of Small-Molecule Gels Based on the Thermodynamics and Kinetics of Fiber Formation - Soft Fibrillar Materials: Fabrication and Applications - page 77

Nucleation
center

Nucleation Growth of

arms

Branching

(A)

(a) (b)

(c)

Fiber nucleation center

25 μ m

(d) (e) (f)

(B)

Figure 2.1 (A) Schematic illustration of
fiber network formation through nucleation
and growth of fiber. (B) Optical microscopic
observation of the process of N -lauroyl- L -
glutamic acid di- n -butylamide (GP-1) fiber
network formation. Primary fibers initiate
from a nucleation center (a). The growth

and branching process is shown by (b-f ) in
which the time interval between two neigh-
boring photos is 0.2 s. Solvent: 1,2-Propylene
glycol (PG); σ = 6.92; T = 330 K. Reprinted
with permission from Ref. [22], Copyright ©

2005, Springer.

For a soft material with a fiber network, the storagemodulus, G , is directly associ-
ated with the network structure. As an important parameter, the correlation length
ξ (cf. Figure 2.2b), determined by the average mesh size of fiber networks, deter-

mines the rheological property of soft materials. The correlation length is defined
for networks with a large (maximum) number of loops (i.e. Figure 2.3b). For trees,
which are by definition acyclic, the basic fiber length plays the role of the correlation
length in cyclic graphs (i.e. Figure 2.3c). Generally, G decreases initially sharply as
the correlation length for cyclic networks or the fiber length for trees increases (or

increases initially sharply with the junction density). It follows from our simulation
and experiments that the power law G max ∼ ξ − p

ξ

( p

= ∼

1.7 (i.e. Figure 2.2c),
depending on the type of networks) holds for gels consisting of single fibers.
The Cayley tree-like networks, as illustrated by the left image of Figure 2.3c,
are a type of fiber network which can easily give rise to the spherulitic pattern

0.5