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Powder X-ray diffraction
Two models were considered for the description of the arrangement of the
polyisocyanodipeptides discussed here, viz.:
hexagonal
and
orthorhombic
a

a

b
b
In an orthorhombic arrangement the macromolecules are packed in an identical fashion
as in the hexagonal arrangement. Only the molecules in different layers are
inequivalent. This inequivalancy results in a doubling of the unit cell in one direction,
which in the case of the polyisocyanopeptides can probably be attributed to alternating
directions of the stacking of the hydrogen bonds between the side chain amide groups, i.
e. helices pointing in and outward of the plane of the paper. The following mathematical
descriptions can be derived.
In the hexagonal case:
In the orthorhombic case:
|a| = |b| and  = 120°
|b| = 3|a| and  = 90°
from these:
dhk = 3a / 2(h2 + hk + k2)
dhk = a / (h2 + (k/3)2)
and the macromolecular diameter (d):
d = |a|
d = |a|
The experimental data can point to a distortion of the ideal unit cells as described above.
For example when in the orthorhombic lattice the angle   90° a triclinic unit cell is
Chapter 3
formed, described by a different set of vectors. This triclinic arrangement is found in an
oriented film of poly(-phenyl ethyl isocyanide) using electron diffraction.1 Also in the
orthorhombic lattice it is possible that the relation between |a| and |b| deviates from the
model situation, in such cases:
dhk = 1 / (h2/a2 + k2/b2) and the macromolecular diameter (d):
d = |a|
As a representative example the indexation of the peaks observed in PXR diffractogram
of L,L-PIAA measured as a powder (Figure 3B) is given.
dobs
dcalc
(Å)
(Å)
13.72
14.02
hkl (orth)
a = 15.9 Å
b = 29.5 Å
110
9.92
9.84
030
6.95
7.01
220
6.20
6.19
230
5.31
5.31
300
5.18
5.23
310
4.89
4.92
060
4.66
4.67
330
3.93
3.95
410 / 350
3.85
3.85
420
3.59
3.59
180
3.52
3.51
440
Reference:
1
50
Kiamco, E. A. Ph.D.Thesis, University of Missouri-Kansas City, U.S.A. 1975.