Molecular Gels and their Fibrillar Networks - Soft Fibrillar Materials: Fabrication and Applications - page 52

Another kinetic study has been conducted on the aromatic-linker-steroid gelators,
79 [15, 43a,b], which are known to make spherulites

or rod-like fibers (depending on the liquid and the protocol for cooling the sol phase)
in the

( CNC ; see Section 1.2.3) and 80

s of their organogels. The kinetics of formation of these gels has been
interpreted according to the Avrami equation (Equation 1.4) [74] and the Dickinson
fractal model (Equation 1.5) [147]. In these equations, as modified for gels, X is the
volume fraction of the gelator participating in the SAFIN , K is a type of rate constant,
n is the ''Avrami exponent'' which is indicative of the type of growth leading to phase
separation [148], D f is the fractal dimension of the

SAFIN

, C is a constant, and t is
time. The original articles should be consulted for the conditions under which these
equations can and cannot be applied to

SAFIN

gel systems. Several interesting
modifications of the Avrami equation and re-interpretations of its exponents may
make this equation expand its utility to the study of gel formation [149].

LMOG

H

O

H H

N
H

O

H

79

H

O

H H

N
H

O

80

in n -alkanes from four different techniques - CD, FL,
rheology, and SANS - are consistent with a process involving 1D growth and
''instantaneous nucleation'' (i.e., an Avrami exponent, n , close to 1 was always
found) [15, 149]. At all temperatures investigated, the D f values calculated from
Equation 1.5 for these gels were between 1 and 2, consistent with the conclusions
based on Equation 1.4 of one-dimensional aggregation and growth during gelation.
That conclusion is also borne out by the optical micrographs in Figure 1.23 (Section
1.2.3), which show 1D objects being formed at all temperatures of incubation
examined.
ln[ln (1

Data on gelation of 79

X ) −1 ] − = ln K + n ln t (1.4)

D f ]ln t (1.5)
However, there are clear changes in the sizes of the spherulites and, very
near the gelation temperature, a change to rods rather than spherulites, whose
origin can be traced to differing modes of

ln X = C + [(3 − D f ) /

formation. The inverse of K ,
from data using three of the experimental techniques versus different incubation

SAFIN