Chemistry Reference
In-Depth Information
similar repeating PDF peaks extend out to much greater distances for the crystal,
re
ecting the greater long-range order in the crystal. From this and many other studies
using estimates of the PDF pro
le of amorphous solids, it has been possible to
conclude that local structures of amorphous solids, closely related to the unit cell of the
corresponding crystal, are maintained in the amorphous state under all conditions,
despite the lack of long-range order.
Although amorphous solids, like liquids, do not exhibit long-range order, it is of
interest to have some understanding of the manner in which molecules are organized
beyond NN and NNN distances to form the bulk solid structure. Structural features of
amorphous solids in the supercooled state at temperatures above
T
g
can best be
understood by what is generally known about the structure of simple liquids, where it
is assumed that molecules are packed randomly as polyhedral clusters that minimize
the overall free energy of the system without crystallizing [14]. Typically, the densest
possible packing of spheres of the same size, as in a face-centered cubic crystal, would
have the spheres occupying a maximum of 0.74 of the total volume occupied by the
material, while the remainder would be taken up by the volume fraction of void space
equal to 0.26. The random close packing (RCP) model is an empirical statistical model
that considers the packing of an object that has almost no period packing structure, as
when pouring spheres into a container. Mathematical modeling of such a system
reveals that at closest packing the spheres must occupy a volume fraction of
0.64 and
that such a model can describe the structure of simple liquids quite well. In general, it
appears that molecules in the supercooled liquid state contain fairly homogeneously
sized polyhedral structures down to temperatures roughly on the order of 1.5
T
g
,at
which point the molecular structures then become distorted by
<
into a
more spatially heterogeneous system with a distribution of cluster sizes [15]. Such a
temperature is generally termed the crossover temperature
T
c
. As will be discussed
more fully subsequently, because of such structural changes, at temperatures between
T
g
and
T
c
, the mobility of molecules in the system will undergo decrease by orders of
magnitude as the system becomes more
“
jamming up
”
and approaches the glassy state.
When the system goes below
T
g
into the glassy state, we would expect there to be
further
“
solid-like
”
and a tendency for the molecules to readjust into a distinctly
different structure, while retaining essentially the same local structure. Indeed,
application of a modi
“
jamming
”
ed form of the RCP to organic glasses reveals that its structure
is best described by small highly dense local clusters of molecules having a size of
roughly 2.0
2.5 nm, surrounded by interfacial regions of less densely packed mol-
ecules in a higher state of energy [12]. Such a structure might be considered analogous
to a polycrystalline mass, containing many small crystallites surrounded by a higher
energy region of grain boundaries. An analysis of amorphous indomethacin in the
glassy state, for example, led to a structure consistent with this picture, as illustrated in
Figure 1.8 [12]. Further analysis suggested that the higher energy region, termed the
microstructure, represents about 10% of the total mass, and that it was very likely the
region of the glass that spontaneously anneals or ages when held at temperature just
below
T
g
, as illustrated earlier in Figure 1.4. It is also believed to be the likely region
that acts to retard the rate at which the local domains nucleate and undergo
crystallization.
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