Chemistry Reference
In-Depth Information
where E is the activation energy associated with a jump. With such a modifica-
tion,
Eq. (6-71)
can be rewritten as
!
(6-75)
exp
2γðω
1
V
1
1ω
2
ξ
V
2
Þ
V
FH
D
0
exp
2
E
RT
D
1
5
Equation (6-75)
has been used to calculate the self-diffusions of small molecules
at low concentrations diffusing through polymers with significant success. The dif-
ficulty is to have reliable estimation of the parameters used in the equation.
Example 6-6 illustrates the application of
Eq. (6-75)
and the corresponding parameters
obtained from the literature for the diffusion of n-pentane in polyisobutylene (PIB).
EXAMPLE 6-6
Given the free volume parameters for the n-pentane/PIB mixture as given in
Table 6.1 [20]
,
calculate the self-diffusion coefficients of n-pentane at 50
C in the solution at
low
n-pentane concentrations.
Solution
Dividing
Eq. (6-73)
by γ, one obtains
V
FH
=γ 5ω
1
K
11
=γ(K
21
2T
g1
1T ) 1ω
2
K
12
=γ(K
22
2T
g2
1T )
Therefore,
V
FH
γ
5ω
1
32:41310
23
(238:391323:15) 1 (12ω
1
) 33:16310
24
(2117:931323:15)
5
0
:
686
ω
1
2
0
:
0648
ω
1
1
0
:
0648
5
0
:
621
ω
1
1
0
:
0648
By substituting the above equation in
Eq. (6-75)
,
7
6
5
4
3
2
1
0
0
0.05
0.1
0.15
0.2
0.25
ω
1
FIGURE 6.12
Concentration dependence of the self-diffusion coefficient of n-pentane in polyisobutylene.
