Engineering of Small-Molecule Gels Based on the Thermodynamics and Kinetics of Fiber Formation - Soft Fibrillar Materials: Fabrication and Applications - page 87

On the basis of criteria 1 and 3, we would expect that at low supersaturations
the crystallographic mismatch nucleation takes place much more easily in slow
growth crystallographic orientations (Figure 2.5d), whereas at high supersatu-
rations, the crystallographic mismatch nucleation may occur in faster growth
crystallographic orientations (Figure 2.5a). Another reason for the occurrence of
crystallographic mismatch nucleation in faster growth crystallographic orientations
at high supersaturations is that the faster growth crystallographic orientations can
penetrate into the bulk easily, and ''feel'' much higher supersaturations in the bulk.
This will trigger the crystallographic mismatch nucleation at the tips.
In the following sections, we will present the fiber network formation through
branching at different orientations of fibers, that is, at the growing fiber tips and
side surface of fibers.

2.3.3.1 Fiber Tip Branching
As discussed in the previous section, at high supersaturations, the crystallographic
mismatch nucleation and growth will take place at the tips, leading to ''wide-angle''
crystallographic mismatch branching (WA-CMB) (Figure 2.5a,b). The formation
of WA-CMB during GP-1 fiber network (or spherulite) formation has been given
in Figure 2.1B. This pattern of fiber network consists of radius arms initiating
from a core and is initiated by 3D nucleation [6c, 8, 17a]. The radius arms
are often found to be branched with the Cayley tree structure [14]. This 3D
nucleation is a process to create the radial aims from the cores. If we take into
account this fact and the structural characteristics of a Cayley tree of fibrous
networks, the process for the network formation can be regarded as: initial

nucleation-growth-branching-growth-branching (Figure 2.5c). Obviously, one

of the key steps in building up the Cayley tree is the branching at the tips of
growing nanofibers. Unlike dendritic branching, the daughter branches of the
fibers cannot be correlated strictly to the crystallographic orientation of their
parent fibers. Therefore, the branching is referred to as crystallographic mismatch
(or noncrystallographic ) branching.

...

2.3.3.2 Fiber Side Branching
At relatively low supersaturations, owing to the large

G * mis , the crystallographic
mismatch nucleation and growth will only occur at the side faces of needle crystals
as these faces are the slowest growing directions and thus have the largest effective
surface supersaturation. This leads to ''small-angle'' crystallographic mismatch
branching (SA-CMB) (Figure 2.5d) (type I side branching in Figure 2.3). At low
supersaturations, single fibers form first without any branching, as the free-energy
barrier G * mis is reduced),

the branching of fibers initiates from the side faces. With further increasing
supersaturation,

G * mis is very high. As supersaturation increases (

G * mis at the growing tip of fibers becomes very low and tip
branching is favored. Figure 2.5d describes the side branching of fibers based
on the microscopic observation of the occurrence of SA-CMB during GP-1 fiber
network formation (Figure 2.5e). Type II side branching as shown in Figure 2.3 is
normally observed in polymer gels [13].