Biology Reference
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codes were interchangeable, the three independent self-assembly
critical concentrations would collapse into one critical concentration
and the highly twisted tetrachloro perylene diimide would assemble
at much lower concentrations than in the homogeneous case.
Consequently, we have defined a new physical quantity,
c
, to
describe the extent of cross-assembly, and related it to the perylene
code-enabling twist angles. To a concentrated homogeneous solution
of monomer A, a trace amount of B was spiked in, and the chemical
shifts of each monomer in the mixture were observed (
CA
d
) and
compared to their chemical shifts in infinitely dilute homogeneous
solutions (
obs
). This provides a numerical measurement for the extent
of cross-assembly (
d
dil
c
c
) between differently twisted units, where
CA
CA
equals 1 for indistinguishable
(redundant) codes and 0 for completely independent codes. Table 5.1
displays the measured
= (
d
−
d
)/(
d
−
d
). Thus,
c
B,dil
B,obs
A,dil
A,obs
CA
c
c
values
suggest that planar, dibromo, and tetrachloro perylene diimide
establish mostly unique molecular codes, while monobromo perylene
diimide exhibits significant cross-assembly with planar and dibromo
perylene diimide. The
values for each mixture. These
CA
CA
c
value is widely independent of monomer
A concentration. Importantly, cross-assembly is limited except for
similarly twisted compounds. A
CA
value less than 0.2 results in
essentially separate codes, corresponding to a
c
CA
∆
q
of approximately
15
, provides at least
three distinguishable codes. Two distinguishable codes should
direct two independent self-assemblies. In other words, molecules
with two distinguishable codes do not co-mingle to form a single
assembly. Therefore, molecular shapes enable selective molecular
codes for self-organization.
°
. The twist angle alone, ranging from 0
−
37
°
Table 5.1
Cross-assembly extent,
),
reports code uniqueness between two compounds A and B.
c
= (
d
-
d
)/(
d
−
d
CA
B,dil
B,obs
A,dil
A,obs
a
Compound
Planar
Monobromo
Dibromo
Tetrachloro
1.00
b
0.02
b
Planar
0.57
0.18
Monobromo
1.00
0.36
0.04
Dibromo
1.00
0.15
Tetrachloro
1.00
a
Concentrated compound A in left column, dilute compound B along top.
b
c
= 1 for indistinguishable codes (no selectivity) and equal to 0 for completely
independent codes (absolute selectivity).
CA
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