Chemistry Reference
In-Depth Information
We have in general [cf. Eq.(160)],
t
dt
2
t
1
0
kT
mβ
α
1
1
2
(
t
)
2
γ
2
=
t
2
)
2
−
α
F
(
t
1
)
F
(
t
2
)
dt
1
(
α
−
1)
(
t
1
−
0
For the ramped gradient shape [cf. Eq. (70)],
t
1
dt
G
t
−
δ
F
(
t
1
)
=
−
(171)
δ
0
so that
Gt
1
−
Gt
2
−
Gt
1
2
δ
Gt
2
2
δ
F
(
t
1
)
F
(
t
2
)
θ
(
t
1
)
θ
(
t
2
)
=
(172)
Thus,
2
(
t
)
Gt
2
−
dt
2
t
2
0
2
δ
2
kTγ
2
mβ
α
Gt
2
2
δ
dt
1
(
α
1
=
−
(
t
2
−
t
1
)
2
−
α
1)
0
Gt
1
−
Gt
1
2
δ
(173)
that is
2
2
(
t
)
Dγ
2
G
2
(2
δ
)
2
+
α
α
(
α
+
3)
=
(174)
(5
+
α
)
When
α
→
1, the expression becomes the normal diffusion case, Eq. (70).
Now for the triangular configuration,
dt
2
t
2
0
2
Gt
2
δ
t
1
)
2
−
α
Gt
1
δ
2
2
kTγ
2
mβ
α
dt
1
(
α
1
2
=
(175)
−
1)
(
t
2
−
δ
δ
0
→
0
δ
2
2
→
δ
=
Gt
2
2
dt
2
4
−
+
2
kTγ
2
mβ
α
2
t
2
δ
Gδ
2
δ
2
t
2
t
1
)
2
−
α
Gt
1
4
−
+
dt
1
(
α
1
2
t
1
δ
Gδ
2
×
(176)
−
1)
(
t
2
−
2
δ
2
2
Gt
1
2
dt
2
3
δ
2
2
kTγ
2
mβ
α
6
δ
−
t
1
Gδ
2
2
=
−
4
Gδ
+
3
δ
δ
→
δ
t
2
t
1
)
2
−
α
Gt
1
2
(177)
6
−
δ
−
4
Gδ
dt
1
(
α
1
t
1
Gδ
×
+
−
(
t
2
−
1)
2
δ
