Transmission Electron Microscopy Analysis
of Crystalline Polymers
Super-Helically Twisted MPDI Fibers
An application example for multi-scale structural
characterization of crystalline polymers
This study has been performed at the University
of Michigan, Ann Arbor. For more information
contact:
Dr. Christian Kübel
Fraunhofer Institute for Production Technology and Applied
Materials Science
Wiener Straße 12
28359 Bremen
Germany
Phone: +49 (421) 2246-452
E-mail: [email protected]
Prof. David Martin
Department of Materials Science and Engineering
University of Michigan
H.H.Dow Bldg
2300 Hayward St.
48109 Ann Arbor, Michigan
United States of America
Phone: +1 (734) 936-3161
E-mail: [email protected]
The structure and properties of biological and
synthetic materials are determined by complex
molecular and mesoscopic interactions. One of
the common structural motifs are helices, which
are observed on different length scales ranging
from molecular to macroscopic.
Figure 1: TEM overview image of twisted polymer fibers.
Each fiber consists of up to 8 individual strands, which are
twisting around each other in a way similar to a rope.
Despite the macroscopic twisting, the fibers exhibit a well-
defined diffraction pattern.
C. Kübel, D.P. Lawrence, D.C. Martin, Macromolecules,
2001, 34(26), 9053-9058. Copyright (2001) American
Chemical Society.
On the molecular level, helical structures are
highly regular, governed by strong intra- and
intermolecular interactions. On the supramole-
cular level, the twisting of a meso- or macro-
scopic assembly is geometrically incompatible
with three-dimensional, long-range order of
500 nm
crystalline materials, and thus necessarily involves
the formation of defects. Here we show a
detailed studies of the achiral polymer poly(m-
phenylene diisophthalamide) (MPDI) that
spontaneously assembles into regularly twisted
fibers, which exhibit helical structures at three
different levels superimposed onto each other.
Low-dose high-resolution electron microscopy
(LD-HREM) made it possible to image the helical
molecular structures and the supramolecular
twisting as well as the defects necessary to
mediate the mesoscopic twisting.
LD-HRTEM Characterization
To analyze the molecular structure and the supra-
molecular packing of the MPDI fibers, low-dose
high-resolution electron microscopy with a dose
of 3500 e/nm2 was used to exclude any beam
damage artifacts for the polymer fibers (end-
point dose of MPDI ~40000 e/nm2) .
The LD-HRTEM images locally exhibit lattice
fringes with characteristic d-spacings of about
1.4 nm, 0.82 nm, and 0.54 nm (Fig. 2a). Only at
a lower magnification overview, it becomes
obvious that the different lattice fringes form a
highly regular pattern throughout the whole fiber
(Fig. 2b). This can be explained by a uniform
rotation of the crystallographic orientation of the
fiber along it’s axis (Fig. 2c). This crystallographic
twisting is observed for the fiber as a whole and
not just for the individual strands, suggesting that
the individual strands in one fiber are strongly
correlated.
Figure 2: a) LD-HRTEM image of MPDI exhibiting three
different sets of lattice fringes corresponding to different
molecular projections.
b) LD-HRTEM overview image revealing a uniform crystallo-
graphic twisting of the whole fiber. The different molecular
projections (1.4 nm, 0.82 nm, and 0.54 nm lattice fringes)
appear periodically along the fiber axis; the pitch increases
with fiber thickness. Despite the twisting, the separate
strands maintain a uniform crystallographic orientation
across the whole fiber.
c) Schematic representation of the twisting of the MPDI
fiber together with indexing of the observed crystallo-
graphic zones.
C. Kübel, D.P. Lawrence, D.C. Martin, Macromolecules,
2001, 34(26), 9053-9058. Copyright (2001) American
Chemical Society.
11 1. . 44 4
nn nmm m
00 0. . 88 8
22 2 nn n
mm m
00 0. . 55 5
44 4 nn n
mm m
00 0. . 55 5
44 4 nn n
mm m
11 1. . 44 4
nn nmm m
Electron Tomography
Even though the BF-TEM images (Fig. 1)
suggested that each fiber consists of several
individual strands, LD-HRTEM already indicated
that the strands within each fiber are highly
correlated. This is only possible if the strands
within a fiber are well-connected. We used
electron tomography to evaluate the shape of the
overall fiber and did not find any gaps or holes
between the different fibers indicating that the
fiber is uniform and continuous (Fig. 3).
Figure 3: 3D visualization of the electron tomographic
reconstruction of a MPDI fiber. The digital cross-sections do
not show any holes or gaps.
Adapted from D.C. Martin, J. Chen, J.Yang, L.F. Drummy,
C. Kübel, Journal of Polymer Science Part B: Polymer
Physics, 2005, 43, 1749-1778.
Molecular Structure
The LD-HRTEM images reveal the angle between
the different crystallographic zones as well as the
corresponding lattice spacings. This information
enabled the determination of the unit-cell
parameters with a relative error of 0.2% only
using HRTEM data. The hexagonal symmetry and
the unit-cell dimensions obtain this way restrict
the possible molecular conformations and made
a molecular modeling approach feasible, which
revealed a helical molecular structure.
d-Spacing
(obs.)
Angle
(obs.)
d-Spacing
(calc.)
Angle
(calc.) Indexing
1.43 nm 0/60º 1.429 nm 0/60º 100
0.825 nm 30/90º 0.826 nm 30/90º 110
0.715 nm 0/60º 0.715 nm 0/60º 200
0.54 nm 20/40/80º 0.540 nm 19/41/79º 210
0.473 nm 0/60º 0.477 nm 0/60º 300
0.413 nm FFT 0.413 nm 30/90º 220
0.400 nm FFT 0.397 nm 14/46/74º 310
0.358 nm FFT 0.357 nm 0/60º 400
0.286 nm FFT 0.286 nm 0/60º 500
0.378 nm 0-360º 0.378 nm 0-360º 001
Table 1: Directly observed and calculated lattice spacings.
Various molecular conformations related to the
well-known bulk structure of MPDI were
evaluated for the structural analysis, but we could
not find any extended linear chain configuration
(including dimmers and trimers) that would fit to
the observed unit cell parameters. However, a 31
helical structure results in a good, low-energy
match to the experimental data (Fig. 4).
Figure 4: Helical molecular structure for MPDI determined
using a combined molecular dynamics and energy
minimization approach in Cerius2 based on the
experimental unit cell (001 and 100 projection shown). The
simulated fiber diffraction pattern is in good agreement
with the experimental data.
C. Kübel, D.P. Lawrence, D.C. Martin, Macromolecules,
2001, 34(26), 9053-9058. Copyright (2001) American
Chemical Society.
Mesoscopic and Crystallographic Twisting
The pitch for the rotation of the crystallographic
orientation and the pitch for the twisting of the
strands around each other both correlate with
the fiber diameter. However, surprisingly both
pitches are significantly different indicating two
independent modes for the twisting (Fig. 3).
Figure 3: Comparison of the pitch for mesoscopic twisting
(solid symbols, two different batches of MPDI) with the
pitch for crystallographic twisting (hollow squares).
C. Kübel, D.P. Lawrence, D.C. Martin, Macromolecules,
2001, 34(26), 9053-9058. Copyright (2001) American
Chemical Society.
Defects
The crystallographic twisting of the MPDI fibers
would correspond to a strain of a about 7% for
polymer chains on the inside compared to the
outside of a single strand. The strain is reduced
by shift-disorder along the fiber axis as can be
directly seen by LD-HRTEM. The shift-disorder
results in an ordered hexagonal columnar liquid
crystalline like phase (Colho), which also explains
the streaking of the 001 reflection (Fig. 1).
Figure 6: a) Schematic representation of the path-length
difference on the inside and outside of a strand.
b) LD-HRTEM image of the MPDI helices. The 1.43 nm
lattice fringes outline the molecular helix and the 0.38 nm
fringes represent a single helix turn. The image reveals
shift-disorder in the 0.38 nm lattice fringes, which appear
to be “wobbeling” and are displaced between neighboring
polymer helices.
C. Kübel, D.P. Lawrence, D.C. Martin, Macromolecules,
2001, 34(26), 9053-9058. Copyright (2001) American
Chemical Society.