lnb 0 value, the initial crystal size is larger, but not any more at a longer time
scale. However, some reservations have to be made: (a) the crystals are not
spheres but platelets, ratio of length to width to thickness, e.g., 50 : 10 : 1,
though this ratio will depend on fat composition and supersaturation, which
change during the process. (b) The crystals have soon formed a network,
and the development of crystal size after that is poorly defined (see below).
(c) Figure 17.21 concerns crystals of a ‘‘narrow’’ composition, only a few
closely similar triglycerides. This fat did not show significant secondary
nucleation. However, many natural fats have a far wider compositional
range, and these may give copious secondary nucleation at high super-
saturation. This means that smaller crystals will result at such conditions.
A Fractal Network? It may appear logical to assume that the fat
crystal network eventually formed will also be fractal. However, the results
shown in Figure 17.22 counteract this assumption. Plots of logBor of logG^0
versus logjshould be linear, which they are over the short range ofjvalues
available, but the slopes are too high: 5.2 and 6.0 in frame (a) and 4.5 and
7.1 in frame (b). These values would correspond to fractal dimensionalities
of 2.5–2.7, i.e., far higher than the value of 1.7 observed for the fractal
aggregates. Moreover, extrapolation toj¼0.01, at which concentration a
space-filling network is already formed, leads to quite unrealistic values. For
aBvalue of 10^6 m^2 , the largest pores will be at least 2 mm in diameter
(B¼R^2 g=K, whereKis always>1) and hence be visible to the naked eye,
which they are certainly not. A permeability of 10^8 m^2 is about the highest
one could expect, and the value may be significantly smaller. The thin lines
in the figure give the range of what would be reasonable values; here, it is
taken into account that ongoing deposition of solid fat onto the existing fat
crystal network would somewhat decrease theBvalue, roughly as for heat-
set protein gels (see Figure 17.19). The experimental results are very
different. Something similar applies to the values of the modulus. Near the
vertical axis, estimated values atjvalues near 0.01 are shown, and these
differ widely from the extrapolated values.
We must thus conclude thatthe network is not fractal. It appears more
likely that the network forms as is schematically depicted in Figure 17.23.
Frame 1 shows that nuclei form and grow into small crystals. In frame 2 the
crystals have become larger and started to form small (fractal) aggregates.
In the mean time, nucleation and growth go on. In frame 3, the aggregation
has led to a space-filling fractal network, but not nearly all of the
crystallizable material is incorporated into the network. Nucleation and
subsequent aggregation of newly formed crystals go on, and in frame 4, we
see again small fractal aggregates. In frame 5 these ‘‘secondary aggregates’’
have grown out to a size comparable to that of the larger pores in the