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Figure 3.4
The deviation of the solubility of small grains of quartz relative to its bulk solubil-
ity (S/S
0
) as a function of the size of the quartz grains being dissolved according to the
modifi ed form of the Kelvin equation. The following values were used to produce this curve:
T = 298 K, ¯ = 22.68
= 350 vmJ/m
2
. At a particle radius of 100 nm, the solu-
bility is indistinguishable from the bulk value. By the time the particle radius is reduced to
1 nm, the predicted solubility is nearly three orders of magnitude higher. (Reprinted from
M.F. Hochella Jr., Nanoscience and technology: the next revolution in the Earth Sciences,
Earth and Planetary Science Letters
,
203
, 593-605, Copyright 2002, with permission from
Elsevier.)
×
10
−
6
m
3
/mol,
γ
this relation is shown in Figure 3.4, which is a plot of
S
S
0
versus particle radius
and
V
¯
values for quartz (Hochella, 2002 ).
Dissolution is generally assumed to be a spontaneous process. As long as particles
are in a solution of constant undersaturation, the rate of dissolution should be
constant. The relation of the normalized dissolution rate (in mol
assuming
γ
m
− 2
min
− 1
),
R
, can
⋅
⋅
be related to the undersaturation,
σ
, via the relationship:
Rk
n
= σ
where
k
is the rate constant and
n
is the effective reaction order (Christoffersen
et al.
, 1994; Budz and Nancollas, 1988).
From these classical models of dissolution, smaller nanoparticles would be
expected to dissolve more quickly than larger particles, and to dissolve to comple-
tion. For a number of systems, including nanoparticles of titanium dioxide (Schmidt
and Vogelsberger, 2006), silica (Roelofs and Vogelsberger, 2004) and zinc oxide
(Yang and Xie, 2006), smaller nanoparticles dissolve more quickly than larger
nanoparticles. Despite this, it is not always clear whether classical models apply to
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