form a paste. Assuming a typical value for the diffusion coefficient
of a molecule in solution (D = 0.5 ¥ 10-9 m2 s-1), and a mean
diffusion path length of the order of the particle size (say d =
0.1 mm), the diffusion time (t = d2/2D) is 10 s. This is clearly
compatible with the short reaction times that we have observed in
our present and previous studies.5
The factors that determine the rate of mass transport by
diffusion, and hence the reaction rate, are as follows:
(1) Diffusion medium. Addition of a small amount of solvent in
which the reactant is soluble provides a clearly identifiable medium
in which diffusion can take place. The transport rate will increase
with increasing solubility of the reactant in the solvent.
solvent, i.e. they are actually solvent-assisted reactions. A case
in point is the reaction between nickel(II) nitrate hexahydrate and
phenanthroline;1,2,11 this reaction produces water as a by-product,
and this can act in the same way as added solvent. It is interesting
to note that the reported very short reaction time (2 min) is similar
to the times that we have observed in our solvent-assisted reactions.
The above arguments clearly indicate the need for a clearer focus
on the role of molecular diffusion in mechanochemical reactions.
This allows an understanding of observations that are otherwise
difficult to comprehend, and suggests ways in which the scope of
mechanochemistry can be considerably extended.
(2) Surface area. Since diffusion takes place from the surface
of the solid, an increase in surface area results in an increase
in transport rate. Reduction of the particle size d (by grinding)
increases the solid surface area, and it can easily be shown that
the surface area of a given amount of a powdered substance is
proportional to 1/d.
Acknowledgements
We thank AINSE for financial support (Grants No. 02190, 03011).
Notes and references
(3) Diffusion path length. The rate of diffusion is inversely
proportional to the square of the diffusion path length, so that
a reduction in the diffusion path length results in a large increase
in diffusion rate. The diffusion path length is reduced by using the
minimum amount of solvent and by reducing the particle size (by
grinding). The kinetics of diffusion are such that the diffusion rate
is proportional to the inverse square of the diffusion path length8
and hence, according to the above, to 1/d2.
‡ Crystal data: C74H60Cu2N2P4S2, M = 1292.3. Monoclinic, P21/◦c,
˚
a = 23.6170(4), b = 13.5021(2), c = 20.1922(3) A, b = 105.453(2) ,
3
˚
V = 6206 A , T ca. 100 K. 26401 unique CCD reflections (Rint = 0.058;
14188 > 2s(I)), R1 = 0.041, wR2 = 0.103. A disordered component was
resolved for SCN(1), major, minor site occupancies refining to 0.828(2)
and complement; no disorder was discernible elsewhere in the structure.
The phase is isomorphous with its azide counterpart.12
§ About 0.1 mmol of compound was ground using an agate mortar and
pestle of the type normally used to prepare samples for IR spectroscopy.
For the solvent-assisted reactions 1 drop of solvent was added using a small
pipette. The solvent was removed after grinding for about two minutes
by allowing the mixture to stand for a few minutes in air at ambient
temperature. No reaction was observed if large crystals of the reactant
were treated with solvent without grinding. IR spectra were recorded on
dry powders using a Perkin Elmer Spectrum 100 FT-IR spectrometer
equipped with a Universal ATR sampling accessory. The 31P CPMAS
NMR data were acquired at 9.4 T on a Bruker MSL-400 spectrometer
operating at a 31P frequency of 161.92 MHz.
Combining factors (2) and (3) leads to a very strong (1/d3)
dependence of transport rate on paticle size, which provides an
explanation for the dramatic increase in conversion with successive
periods of grinding that is suggested by the IR data in Fig. 2(b)–
(d). The dramatic increase in reaction rate that we observe upon
addition of a very small amount of a suitable solvent and reducing
the reactant particle size by grinding is clearly consistent with the
key role played by diffusion in the reaction mechanism.
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Further consideration of factor number (1) above raises the
question of the relevance of the diffusion mechanism in “dry”
(solvent-free) mechanochemical reactions. Diffusion can take
place in solids as well as in fluids, but the diffusion rate under
normal conditions is negligible. The diffusion coefficient can
however be increased by increasing the temperature, and an
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the solid during high energy mechanical milling in a ball mill. This
has been suggested before,9 and provides a possible explanation for
the role of frictional heating in dry mechanochemical synthesis,
where a number of mechanisms involving mass transport have
been suggested in cases where the heating is insufficient to cause
melting.1,2,10
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It is also possible that enhancement of diffusion by frictional
heating is not necessary in some of the previously reported solvent-
free mechanochemical reactions, because the enhancement may
be caused by the presence of small amounts of adventitious
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5292 | Dalton Trans., 2008, 5290–5292
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