Chemistry Reference
In-Depth Information
O
NH
H
O
O
O
Ga
O
O
OO
Ga
O
H
OO
NH
O
[Ga
2
L
2
]
2-
(a)
(b)
open
a
Ga
〈
x
,
y
,
z
〉
d
÷
n
Ga
〈
0,0,0
〉
Ga
〈
0,0,0
〉
Ga
r
d
opt
x
,
y
,
z
〈
〉
EM
÷
a
-3
EM
÷
d
-3/2
Figure 3.4 Modelling effective molarity of macrocyclization in supramolecular self-assembly
illustrated with a Ga(III) complex. (a) Connecting a freely jointed chain. (b) Connecting a lig-
and of an optimal length to preorganized binding sites separated with
a
[13].
Reproduced by
permission of The Royal Society of Chemistry.
First, for binding sites connected with a flexible chain, the effective concentration can
be accessed by statistical theory [23] and modelled as the probability density
W
(
x
,
y
,
z
)of
finding one site <
x
,
y
,
z
> at a distance
r
from the other site placed in the origin <0,0,0>;
for a visual illustration see Figure 3.4a.
b
depends on the chain length expressed as the
r
2
i
(Equation 3.3).
mean square end to end distance
h
3
3
b
p
3
2
r
2
W
ð
x
;
y
;
z
Þ¼
exp
ðb
Þ;
b ¼
ð
3
:
3
Þ
0:5
2
h
r
2
i
If the binding sites connect to the same receptor,
r
tends to 0. It was shown that in this
case the effective molarity (mol/dm
3
) is proportional to the total length of the chain
d
and
we can write
c
eff
:
d
3=2
.
The second situation accounts for a receptor where the binding sites are held at a fixed
distance
r
¼
a
by a rigid chain (Figure 3.4b). These sites are connected with a ditopic
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