Engineering of Small-Molecule Gels Based on the Thermodynamics and Kinetics of Fiber Formation - Soft Fibrillar Materials: Fabrication and Applications - page 89

(a) (b) Network tuning

Fiber network

(2)
(1)

Normal
processing

(c) (e) (g)

(d) (f) (h)

Figure 2.6 Thermodynamically and additive-
enhanced fiber tip branching. (a) Design of
network architecture. (b) Modification of
micro/nanostructure of 3D interconnecting
fiber network by controlling fiber branching.
(c-f) illustrates the effects of thermodynamic
driving force on the fiber network structure.
(c,e) are fiber networks formed at higher
temperatures (lower thermodynamic driving
force), (d,f) are the corresponding fiber net-
works formed at lower temperatures (higher

thermodynamic driving force). (g,h) illustrate
the fiber network tuning with a polymer addi-
tives EVACP. With EVACP, unbranched fibers
(g) can be converted to three-dimensionally
interconnecting fiber networks (h). (a,b,g,h)
are reprinted with permission from Ref. [24],
Copyright © 2002, American Chemical
Society; (e,f) are reprinted with permission
from Ref. [25], Copyright

© 2009, American

Chemical Society.

As has been mentioned, crystallographic mismatch nucleation is a special case
of heterogeneous nucleation where the substrate is the crystal fiber. Designating
the induction time for the nucleation of new fibers on the host fibers as 1/ J ,

where J is the rate of the crystallographic mismatch nucleation), the average
branching distance can be expressed as

τ ( τ ∼

ξ ∼ R g τ ∼ R g /J (2.21)

According to 3D nucleation model, the nucleation rate J can be expressed as
[20c, 27]

f [ f ] 1 / 2 B exp

G ∗
kT

− J = (2.22)