Chemistry Reference
In-Depth Information
The tracer diffusion coefficient can be thought of as a measure of the mobility
of a trace amount of species A in a medium containing species B (i.e., self-
diffusion of A in B). When the concentration of species A is very low, it can be
assumed that each molecule of species A is surrounded only by the molecules of
species B. In this case, each molecule of species A undergoes a random walk
because of its thermal energy but under the influence of species B. In other
words, tracer diffusion concerns the mobility of a highly dilute component in a
binary mixture. Although the term self-diffusion is first defined for pure systems,
workers in the field tend to use the terms self-diffusion and tracer diffusion inter-
changeably to signify the mobility of the molecules. Since both self-diffusion and
tracer diffusion coefficients are equilibrium properties, determination of them
using either experimental techniques such as nuclear magnetic resonance or com-
putationally using molecular dynamics simulation is much easier than that of the
mutual diffusion coefficient. As alluded to in the previous discussion, the self-
diffusion coefficient is attributed to the thermal motion (entropic in origin). For
binary mixtures, averaging the self-diffusion coefficients of the components using
simple mixing rules such as D
5
x
A
D
sA
1
x
B
D
sB
to yield the mutual diffusion
coefficient is only appropriate for systems in which there exists little difference in
the intermolecular interactions between species A and B. If a significant differ-
ence in the intermolecular interactions (enthalpic in nature) exists between the
components, the above mixing rule cannot be used. This is because such interac-
tions (attraction or repulsion) can diminish or enhance the motions of the mole-
cules. One has to account for this enthalpic effect
in order to yield a good
estimation of the mutual diffusion coefficient.
6.4
Mutual Diffusion
It has been shown that in the absence of external fields, the driving force for
mass transfer at constant temperature is the gradient of the chemical potential. As
shown in Section 3.1.1, the chemical potential of species A in an ideal binary
solution (i.e., the intermolecular interaction between species A and B is similar to
those of species A and A as well as of species B and B) is given by:
n
A
n
A
1
G
A
1
μ
A
5
RT ln
(6-9)
n
B
where n
A
and n
B
are the number of moles of species A and B, respectively. Here,
Eq. (6-9)
shows that the gradient of the chemical potential is related to the gradi-
ent of the logarithm of concentration. In the case of nonideal binary mixtures, the
mole fraction of species A in
Eq. (6-9)
is replaced by its activity, a quantity that
depends on the intermolecular interactions experienced by species A in the mix-
ture. Since activity is concentration dependent, this simply means that the mutual
diffusion coefficient is also concentration dependent. In other words, mutual dif-
fusion depends on the thermodynamic behavior of the components involved.
