Engineering of Small-Molecule Gels Based on the Thermodynamics and Kinetics of Fiber Formation - Soft Fibrillar Materials: Fabrication and Applications - page 82

measurement can reveal the influence of both the small aggregates formed at
the early stage and the larger aggregates at the late stage on the elasticity of
the materials. Using the rheological data, Lam et al . characterized the fractal
dimension of 12-hydroxystearic acid (HSA) fibers formed in mineral oil as a
function of cooling rate [19]. At slow cooling rates (i.e., less than 5-7 ◦ Cmin − 1 ),
long fibers were produced with a fractal dimension between 0.95 and 1.05 and for
rapid cooling rates (i.e., greater than 5-7 ◦ Cmin − 1 ) short branched fibers were
produced with a fractal dimension between 1.15 and 1.32. This means that at
higher cooling rates, the fibers are less linear and coincide with a higher degree of
branching.
As has been discussed, the structure of a fiber network in a material is important
since it affects themacroscopic properties of thematerial. Therefore, understanding
the principles of fiber network formation in SMGs is necessary to the development
of strategies to control the micro/nanometer structure in order to acquire materials
with superior macroscopic properties.

2.3
Crystallization of Nanofibers

2.3.1
Thermodynamic Driving Force

The crystalline nature of the fibers in SMGs means that the formation of fibers
in such a material can be controlled thermodynamically as in a conventional
crystallization system. The driving force for the formation of new phases (e.g.,
fibers/crystals) is determined by the difference between the chemical potentials
μ mother and

μ crystal of the growth unit in the mother and the crystalline phases. The
chemical potential μ is defined as [20]

μ = μ mother − μ crystal (2.5)

When

1) μ > 0, the system is supersaturated. This is the thermodynamic precondition

for nucleation and growth of the crystalline phase.

2) μ < 0, the system is undersaturated. Under such a condition, crystals will

dissolve.

3) μ = 0, the mother phase is in equilibrium with the crystalline phase. This

implies that at the given temperature T , pressure P , concentration C ,andso
on, one always has

eq

μ = μ crystal (2.6)

mother

eq

where

mother is the chemical potential of solute molecules in the phase
equilibrium (or coexistence) between the mother and the crystalline phases.

μ