Chemical Processes - Isoconversional Kinetics of Thermally Stimulated Processes - page 218

temporary local equilibria that occur in the vicinity of the solid surface. The effect
can be especially strong when the solid reactants or products have a large surface
area. This is quite common in porous solids or fine powders. In these systems,
gaseous products can participate multiple times in reverse and forward reactions
before they permanently leave the solid phase. Local equilibria may also depend on
the type of a purge gas, its flow rate, and the way it is delivered to the sample. In
addition, they may be affected by size and shape of the sample pans. The removal of
gaseous products is much more efficient from the pans of smaller height and larger
diameter. The bottom line is that the general trends discussed earlier provide but
general guidelines for understanding the kinetics of reversible decomposition. Nev-
ertheless, the effects actually observed can be diminished or enhanced by a variety
of specific factors that should also be taken into consideration.
Reactivity of solids is strongly affected by imperfections or defects of the crys-
talline lattice that are naturally formed during synthesis and processing. The most
drastic imperfection of any crystalline lattice is its surface. The structure of the
surface is unavoidably different from that of the bulk. The surface layer species
(atoms, ions, molecules) are surrounded by and, thus, bound to fewer neighbors
than their bulk counterparts. To satisfy uncompensated chemical bonds, the surface
species undergo drastic spatial rearrangements [ 125 ]. A vivid example is the bond-
length contraction, i.e., shortening the interlayer spacing between the topmost and
the second layer. The resulting surface tension imposes significant stress on chemi-
cal bonds of the surface layer species. Significant stress is concentrated also in other
lattice defects (kinks, ledges, dislocations, etc.) primarily located on the surface.
The mechanically stressed species included in the structural defects possess higher
energy and are more reactive.
The respective increase in the reactivity can be formalized by using the kinetic
theory of the strength of solids developed by Zhurkov [ 126 , 127 ]:

Ea
RT

− σ

ττ =

0 exp

,

(4.90)

where ˄ is the lifetime of a solid, ˄ 0 is the preexponential factor, E is the activation
energy required to break a chemical bond, ˃ is the mechanical stress, and a is the
coefficient that characterizes conversion of the stress to energy. While developed to
describe the mechanical fracture of solids, the theory sets forth an important idea of
coupling two different reaction stimuli, thermal and mechanical. They are respec-
tively represented by two different components of the overall effective activation
energy, E and a˃, in Eq. 4.90. Clearly, the larger the stress, the smaller the overall
energy barrier and the faster a solid breaks or decomposes. The stress term lowers
the energy barrier by increasing the energy of the solid reactant.
Because the surface is the most defective part of a solid, an increase in the sur-
face area generally increases the reactivity of solid reactants. The surface to volume
ratio is increased effectively by decreasing the size of solid reactant particles. Typi-
cally, it takes a significant change in the particle size to reveal its effect on the rate
and activation energy of decomposition. For example, a decrease in the average par-