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: ck@ifam.fraunhofer.de

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: milty@engin.umich.edu

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.