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MICROMECHANICAL PROPERTIES

Introduction

Mechanical properties of polymeric materials are important for nearly all applica-
tions in industry, technology, and the household. Particularly, stiffness, strength,
and toughness are decisive properties in many uses. Mechanical properties de-
pend strongly on chemical as well as on supermolecular structure of the polymeric
material. While the chemical, molecular structure defines some basic properties
such as rigidity, thermal softening, and melting behavior, the ultimate mechanical
properties are fixed by the supermolecular structures or morphology. The same
molecular structure can yield to many varied morphologies dependent on factors
such as orientation due to fabrication, different cooling rates, changes in thermal
history, and secondary crystallization.

However, not all of the manifold structural or morphological details influence

the ultimate mechanical properties to the same degree. There are details which
determine properties more than other ones, ie, there are so called “property deter-
mining structures.” Besides, it is not sufficient to study the average structure and
morphology of a material, but the variation of morphological details or extreme
sizes of the details have to be known. Smaller structural details have become in-
creasingly important for a defined improvement of mechanical properties with a
shift from details on the micrometer scale to details on the nanometer scale, eg,
in block copolymer or nanocomposites, Polymer-Clay.

The influence of all of the different structural details on the mechanical

properties is determined by micromechanical processes, which appear under the
applied loading conditions. Depending on the very different structural details and
loading conditions, there is a very large variety of micromechanical processes of
deformation and fracture. These processes define the micromechanical properties
of a polymeric material or the micromechanics. Therefore, micromechanical prop-
erties form the bridge between structure or morphology and ultimate mechani-
cal properties. Improved knowledge of the micromechanical properties allows a
deeper insight into the influence of morphology on the mechanical properties, ie,
it allows a better understanding of structure–property correlations (see Fig. 1).

A detailed knowledge of structure–property correlations is not only of aca-

demic interest but also important for the polymer industry. It enables a defined
modification of the morphology for realizing special desired properties for practi-
cal applications. This way was called “microstructural construction of polymers”
(1). In addition, study of micromechanics in polymeric model materials may reveal
new micromechanical processes, yielding improved, new and up-to-now impossi-
ble combinations of different mechanical properties, eg, combinations of contra-
dictory properties, such as stiffness, strength, and toughness. Transforming such
new micromechanical mechanisms from model samples to technically usable ma-
terials by defined scaling-up may yield new classes of polymers, eg, in the field of
nanostructured materials.

The term “micromechanics” covers all processes on mesoscopic, microscopic,

and nanometer scales that occur inside a material in response to an external load-
ing (2). These processes include reactions of macromolecules, such as stretching or

Encyclopedia of Polymer Science and Technology. Copyright John Wiley & Sons, Inc. All rights reserved.

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MICROMECHANICAL PROPERTIES

279

Polymeri-

zation

Molecular

(chemical)

structure

Supermolecular

structure

(morphology)

Micromechanical

processes of deformation

and fracture

Loading

Mechanical

properties

Processing

Fig. 1.

Correlations between structure, morphology, micromechanical processes, and me-

chanical properties of polymers.

scission of molecular segments, reptation (snake-like) movement, microyielding,
microcavitation, forming of crazes, shear bands or deformation zones up to crack
initiation, propagation, and fracture.

Recently, several different techniques to study micromechanical properties

have been applied. Besides spectroscopic and scattering techniques, the micro-
scopic techniques of electron microscopy and atomic force microscopy are partic-
ularly useful for direct determination of micromechanical properties in polymers
(2–7). A brief overview about successfully applicable techniques is given in this
article. Using these techniques, micromechanical properties of different polymers
that have been studied are also reviewed.

Every study of micromechanical processes must be coupled with a detailed

investigation of the morphology and, in particular, of those structural parameters
of most importance for the property of interest (see “representative volume” -
below). Often, structural defects exist that are responsible for premature failure
of materials. In the following, direct imaging techniques of electron microscopy
and atomic force microscopy are discussed in more detail, since they allow a very
direct determination of the micromechanical processes in dependence on the local
morphology, and yield often a very clear picture of the micromechanical behavior
of the material. Additional information about special micromechanical properties
can be revealed by using several other techniques. However, unlike the direct
microscopic methods, these techniques yield mainly integral results from a larger
sample volume, but complete the picture.

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TEM
(replica)

SEM

SEM
ESEM

SEM
ESEM

SFM

SFM

TEM
-ultra thin section

-replica

TEM

HVEM

(a)

(b)

(c)

Fig. 2.

Survey of (electron and scanning force) microscopic methods for investigating mi-

cromechanical processes in polymers.

σ indicates the applied tension stress and the arrows

indicate area and direction of investigation in the microscope (see text for full details).
(a) fracture surfaces—tension test, impact test, broken pieces; (b) surfaces of deformed
(loaded) bulk samples; (c) in situ deformation of thin samples.

Microscopic Techniques

A survey of successful methods is given in Figure 2, demonstrating three main
techniques (2–4):

(1) Fracture surfaces can be directly investigated in the scanning electron

microscope (sem, microfractography, Fig. 2a), demonstrating most signif-
icantly the final processes of deformation, crack initiation, and crack prop-
agation up to fracture. In particular, structural heterogeneities (defects),
which initiate fracture and influence crack path, can be detected (see
F

RACTOGRAPHY

). Using sem, the surface topography of bulk specimen can

be very easily inspected with the only precondition of coating with a thin
conducting layer. Using thin replicas from the fracture surface, transmis-
sion electron microscopy (tem) can also be applied (however, preparation of
thin replicas from a polymer surface is a relatively difficult procedure) (see
M

ICROSCOPY

).

(2) Deformation of bulk material is followed by investigation of the changes at

the surfaces by sem, environmental scanning electron microscopy (esem,
with the advantage of avoiding any conducting layer), and atomic or scan-
ning force microscopy (sfm) or, after replication, by tem. Changes inside
the bulk material are studied by preparation of ultrathin sections from
deformed regions using a cryo-ultramicrotome (occasionally after selec-
tive chemical staining to improve the contrast) and by tem investigations
(Fig. 2b). In semicrystalline polymers, changes of the crystalline orientation
can be studied by electron diffraction.

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281

(3) Samples of different thicknesses (usually semithin or ultrathin sections

prepared by ultramicrotomy) can be deformed in tensile devices and the
deformed samples investigated directly by sem, esem, sfm, tem, or high
voltage electron microscopy (hvem) (Fig. 2c).

The advantage of techniques 1 and 2 is the possibility of studying bulk mate-

rial, deformed under defined stress conditions and loading temperatures. Disad-
vantages of technique 1 lie in the difficulty of detecting the initial stages of defor-
mation and in the impossibility of carrying out experiments in situ. In technique
2, problems may arise from a possible modification of the deformation structures
at the sample surfaces in sem or sfm studies and from the danger of damaging the
deformation structures by the preparation of ultrathin films (usually by ultrami-
crotomy) in tem studies.

Tests in situ can be performed by technique 2 only using an esem (because

of avoiding a conducting surface layer) and by technique 3 using different micro-
scopes in combination with tensile devices. Additional advantages of technique 3
lie in the investigation of processes by using special tensile devices to perform de-
formation tests at lower or higher temperatures (usually from

−150

◦

C to 200

◦

C).

Using these tensile stages, samples of different thicknesses can be studied: thicker
samples (thick sections) can be investigated in an sem, esem, and sfm, revealing
deformation processes near the surface. A method particularly advantageous is
the investigation of semithin sections, up to several micrometers thick, in a 1000-
kV hvem. Such samples, on one hand, show a relatively high mechanical stability
and often they represent the micromechanical behavior typical for these polymers
and, on the other hand, the investigation in an hvem enables high magnifications
and resolutions. Ultrathin sections or films are necessary for using conventional
100- to 200- kV tem. These ultrathin samples are often mounted for supporting
on a Cu grid (8) or on a film with a hole.

Using sfm, a direct study of surface structures is possible in air without the

need for coating with a conducting layer and without any radiation damage, but
with a resolution in the nanometer range. Therefore, this method is of particular
interest for micromechanical investigations and real in situ tests.

Choice of the appropriate size and thickness of the sample depends on sev-

eral factors, including the morphology of the polymeric material, sample shape or
geometry, and stress state (eg, plane strain or plane stress state). Therefore, the
various techniques mentioned above allow the study of very different polymers.

An often-discussed problem is the “transformation” of results from micro-

scopic investigations on thin samples to the bulk material. The typical dimen-
sions or features of the morphology (the “property determining structures”) must
be smaller than the sample thickness, that is, the samples have to contain a repre-
sentative part of the morphology (a “representative volume”). If the thin sections
contain a representative part of the morphology, the character of the deformation
(the deformation mode) is often unchanged; however, the absolute values of de-
formation (degree of elongation) are usually higher in thin samples than in the
bulk (2–4). Therefore, across the scale of structures, certain scales can correspond
to specific properties. For example, modulus as measured by standard ISO ten-
sile test with specimen cross-section 4 mm by 10 mm scales to volume fraction
crystallinity in semicrystalline polymers, but yield stress, deformation, and crack

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initiation and propagation may well relate to processes in amorphous, interlamel-
lar regions or near molecular scale events five to six orders of magnitude in scale
lower than that of the specimen geometry.

A general problem of all electron microscopic tests of polymers in situ is

radiation damage. Polymers, as organic materials, are particularly sensitive to
electron-beam irradiation with several primary effects (eg, ionization, rupture of
chemical bonds) and secondary effects (eg, mass loss, cross-linking, reduction in
crystallinity, charging up). The sensitivity to irradiation decreases with increas-
ing carbon content in the polymeric material, for example in the sequence polyte-
trafluoroethylene (PTFE), poly (vinyl chloride) (PVC), poly(methyl methacrylate)
(PMMA), polycarbonate (PC), polyethylene (PE), and polystyrene (PS) (9). Irradi-
ation damage occurs very quickly during irradiation in the electron microscope.
Such damaged specimens are frequently well suited for investigating morphology
(10) (except by means of electron diffraction), but are not appropriate for tests in
situ. The damage of the specimen can be somewhat reduced by taking precautions
in the instrumentation and manner of operation (eg, use of “low dose” technique,
highly sensitive photographic material, or of electronic image intensifiers with
coupled image recording, application of higher acceleration voltage in an hvem)
(2,11).

An additional problem associated with the direct investigation of polymeric

materials by electron microscopy is in the usually low contrast between structural
details. In connection with deformation, the effect of “straining-induced contrast
enhancement” is of particular importance. Structural elements, such as particles,
which possess a smaller Young’s modulus than the surrounding material, show
a preferred extensibility or deformation during stretching of the sample. In the
direction of the electron beam, the thickness of the sample decreases at these
places, thus causing a difference in the intensity of the transmitted electron beam
and an enhanced contrast (2,10).

Scattering (Diffraction) Techniques

Different methods of measuring the scatter function of corpuscular as well as wave
radiations are used for indirect measurements of microscopic heterogeneities or
changes in morphology, which develop under the action of load, especially de-
velopment, distribution and size of crazes and craze fibrils in amorphous and
rubber-toughened polymers, and change of lamellae in semicrystalline polymers
(see S

CATTERING

).

As it is well known from the principles of light and x-ray optical instruments,

irradiation of a material having periodic structures results in interference phe-
nomena when wavelength of the incident radiation and structural periodicity are
in the same order of magnitude. X-ray diffraction was the first direct evidence
for the presence of periodicity in inorganic crystalline solids. Correlation between
wavelength of the incident ray, structural periodicity in the material under ex-
amination, and diffraction angle is expressed by Bragg’s Law (1913). Although
Bragg’s Law was primarily used to explore the atomic structure of these solids,
different diffraction techniques have been developed to study the structure of
all states of matter with different beams, such as ions, electrons, neutrons, and

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MICROMECHANICAL PROPERTIES

283

protons, whose wavelength is an integral multiple of the distance between two- or
three-dimensional periodic structures.

Different types of radiation interact elastically with different structural units

of the material to be investigated. So x-rays are scattered on electronic cloud,
while electrons are deflected in the electric field of atomic nuclei. An exception
includes neutron scattering where wavelength of incident radiation is larger than
the diameter of atomic nuclei, so that scattering is independent on diffraction
angle but depends on differences of scattering cross sections of atomic nuclei.

Wide-angle x-ray scattering (waxs) enables us to study changes in crys-

tallinity and orientation (texture analysis) and, for instance, processes of lamellae
twisting in semicrystalline polymers (12).

Small-angle x-ray scattering (saxs) is used to study fibrillar and lamellar

structures and detects appearance of microcavities (13), eg, microvoids between
craze fibrils and interfibrillar spacing (14). Using intense x-ray radiation from a
synchrotron source, real-time measurements can be performed in a low speed and
frequency range (15–19). Thus, some insight into stretching and buckling of craze
fibrils during fatigue (17) and in development of crazes in PC during loading is
gained (18).

Small-angle light scattering (sals) can be used if polymers are able to scatter

light because of density or birefringence fluctuations in the order of wavelength
of the light, eg, in the case of spherulites.

Small-angle scattering of electrons (saes) (15) can be performed in a tem

using ultrathin specimens, yielding long periods of regular deformation structures
(eg, craze fibrils). However, electron diffraction is seldom used for research of
polymeric materials, since it needs a very long camera length and, therefore, a
high apparative expenditure. A recent, and very convenient alternative method
is the Fourier transform analysis of electron micrographs (2).

Small-angle neutron scattering (sans) enlightens the fluctuation of density,

concentration, and magnetic properties in the material and, therefore, it enables
investigation of changes of conformation of macromolecules and makes it possible,
in combination with the other scattering techniques, to compare structures of
crazes grown in samples of different thicknesses (19).

Interference Optics

In transparent materials, the classical methods of light-optical interference are
widely used in the determination of small dimensions that are of the order of the
wavelength of light. Successful applications are investigations of the microme-
chanics of crazes at crack tips in transparent glassy thermoplastics (20). Usually,
fracture-mechanics specimen are used with an artificial crack and a craze ahead
of the crack tip. The specimen, with a polished surface adjacent to the optical ar-
rangement, is illuminated in reflection with monochromatic light under normal
incidence and normal to the crack plane. Typical fringe systems appear because
of the interference between reflections from the two crack faces and at the two
boundaries between crazed and uncrazed material. From the accurately deter-
mined positions of the individual fringes and with the knowledge of the refractive
index of the craze, the crack openings and craze thicknesses can be calculated.

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The interference-optical method can easily be applied to static or very slow-

moving cracks. Special experimental arrangements are necessary to investigate
short-time problems of fast-moving cracks or high frequency fatigue.

Other optical methods include the shadow-optical method of caustics based

on the deflection of light by the elastic-stress field around the crack tip. It gives
direct information on the stress-intensity factor or the strain–energy release rate
(21).

Spectroscopic Techniques (Rheooptical Methods)

A rheooptical method includes a mechanical test under static conditions (ten-
sile test, stress relaxation, cyclic test) carried out simultaneously with an optical
measurement. Among other optical methods such as x-ray scattering, nmr spec-
troscopy, polarized fluorescence or birefringence, the Fourier transform infrared
(ftir) spectroscopy has become one of the most frequently applied tools in rheoop-
tics (22). Advantage of infrared spectroscopy is its sensitivity, rapidity, and the
ability to investigate changes of molecular orientations not only in separate struc-
tural units but also in various phases of multiphase systems. From the ratio of
intensities of beams polarized parallel and perpendicular to the deformation di-
rection, orientation functions can be calculated.

The ftir measurements can be performed both in transmission and in reflec-

tion mode. The transmission mode requires thin samples with thicknesses up to
500

µm depending on the nature of the material and the intensity of the inter-

esting bands. No limit is in the reflection mode, but an extremely flat sample is
required. The difficulty of rheooptical ftir spectroscopy is to find suitable bands
for quantitative orientation measurements.

Microindentation Hardness

The indentation test is one of the simplest ways to measure mechanical proper-
ties of a material. The micromechanical behavior of polymers and the correlation
with microstructure and morphology have been widely investigated over the past
two decades (23). Conventional microindentation instruments are based on the
optical measurement of the residual impression produced by a sharp indenter
penetrating the specimen surface under a given load at a known rate. Microhard-
ness is obtained by dividing the peak load by the contact area of impression. From
a macroscopic point of view, hardness is directly correlated to the yield stress of
the material, ie, the minimum stress at which permanent strain is produced when
the stress is subsequently removed.

Although hardness derived from residual impression measurements is an

indicator of the reversible plastic deformation processes, information about elas-
tic release of the indentation depth is mostly lost. Continuous load-displacement
monitoring (as the indenter is driven into and withdrawn from the film) sub-
stitutes the imaging method used in conventional microindenters. The need to
characterize the surface of very thin films and near surfaces has led to the devel-
opment of ultra- and nanoindentation testers with indentation depths within the
submicrometer scale

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Other Techniques

Additional details of micromechanical properties can be studied using several
other techniques. These additional techniques include the following:

(1)

Dynamic mechanical relaxation tests:

measurement of molecular mobility in different polymer phases as a func-
tion of temperature (24).

(2)

Nuclear magnetic resonance (nmr):

determination of molecular mobility (25).

(3)

Electron spin resonance (esr):

measurement of chain scission and radical formation (13).

(4)

Acoustic emission (AE):

study of fracture processes, eg, rupture of fibers in fiber-reinforced thermo-
plastics (26).

(5)

Acoustic microscopy (ultrasound acoustic microscopy):

determination of cracks near a surface (27).

Classification of Micromechanical Properties

The mechanical behavior of materials under stress can be graphically illustrated
by macroscopically determined stress–elongation curves and characterized by typ-
ical values of moduli, strength, yield stress, strain, toughness, and others. Differ-
ent types of stress–strain curves are schematically shown in Figure 3, which are
connected with different groups of micromechanical processes.

Type a: Linear increase of load with very high modulus and strength with a

low elongation at break; behavior is typical of high strength fibers (eg, highly ori-
ented fibers of PE with ultrahigh molecular weight) and is mainly determined by
the structure of microfibrils, appearance of molecular defects, and entanglements.

Types b and c: Nearly linear increase of load with high modulus up to a

relatively high strength with quasibrittle fracture (type b) or semiductile behavior
(type c) with a relatively small elongation at break. Examples are the amorphous

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a

b

c

d

e

Stress

Elongation

ε

Fig. 3.

Characteristic types of stress–elongation curves of polymers. See text for a de-

scription of types a–e indicated in the figure.

glassy polymers PS, SAN (styrene–acrylonitrile), and PMMA and the amorphous
ductile polymers PVC and PC. Micromechanical properties are connected with
local yield processes (see “Plastic Deformation Processes” below).

Type d: After a more or less pronounced yield point at a medium stress,

a large elongation appears at nearly the same load (cold drawing). The ductile
fracture can be preceded by an additional increase of load (strain hardening).
Typical examples are the rubber-toughened or high impact polymers (HIPS, ABS,
ACS) and the semicrystalline polymers PE or PP. Micromechanical mechanisms
are discussed below in “Toughening Mechanisms,” “Yielding in Semicrystalline
Polymers,” and “Yielding in Block Copolymers.”

Type e: Slow and continuous increase of load, homogeneous deformation, and

fracture at large elongations. This behavior is typical to rubber and rubber-like
materials.

The curves in Figure 3 illustrate the deformation behavior of different poly-

mers at room temperature. However, nearly all polymers can be made to show
tensile engineering stress-engineering strain curves a–e dependent on tempera-
ture, strain rate, geometry, and stress state.

Plastic Deformation Processes in Amorphous Homopolymers

Local plastic deformation processes in amorphous glassy or semiductile polymers
(corresponding to curves b and c in Fig. 3) may appear at different scales, and
are sketched in Figure 4. Also in macroscopic brittle materials, macromolecular
segments are deformed (eg, by stretching or disentanglement) until chain scission
and microvoid formation occur at highly localized places of stress concentration
on a microscopic scale (nanometer scale). A relatively sharp crack propagates
without large energy absorption and produces a brittle fracture (on the top in

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287

microscopic processes

macroscopic

stretching of
molecular
segments

microyielding

single crazes

plastic zone

crazes

shear bands

1 nm

10 m

µ

1 m

µ

Fig. 4.

Schematic representation of basic mechanisms of local, plastic deformation on

different scales in amorphous polymers (group I mechanisms). The left shows what is
visible on the macroscopic scale, while the center illustrates the microscopic processes, as
described on the right (hatched areas are plastically deformed).

Fig. 4). Semibrittle materials show a small volume of plastically stretched poly-
meric material ahead of a crack tip on a micrometer scale, eg, in the form of
crazes or shear bands. Macroscopic fracture is quasibrittle or semiductile, occa-
sionally with necking. Larger plastic deformation involves large volumes on a
mesoscopic scale (10-

µm scale), including formation of larger or multiple crazes

or shear bands. In this sequence (from top to bottom in Fig. 4), the plastic de-
formation involves larger volumes, yielding an increase in the amount of energy
absorption (an increase of toughness).

Crazing in Amorphous, Glassy Polymers.

Deformation structures typ-

ical of amorphous, glassy polymers are the so-called crazes. Crazes are long,
narrow plastic deformation zones, sharply delimited from the surroundings (28).
Polymeric material is to a high degree plastically deformed in crazes (in PS usu-
ally up to about 150–250%). Figure 5a shows a craze in PS having well-ordered
thin fibrils of 5–20 nm in diameter, running in the direction of tension, whereas
the longitudinal directions of the crazes are perpendicular to the tension. An

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Fig. 5.

Structure of a craze in PS (deformed semithin section in HVEM). (a) Fully devel-

oped craze with a clearly pronounced fibrillation; (b) domain-like structure of a pre-craze
ahead of the true craze.

advantageous method of determining the center-to-center distance of fibrils is
optical diffraction of electron micrographs, proving center-to center distances of
10–50 nm (2). The structure first visible ahead of the craze tip, ie, in the transfor-
mation or processing zone of the craze, is shown in the micrograph of Figure 5b,
revealing bright “domain”-like spots of 20–50 nm in diameter. There is a critical
minimum diameter d

min

of less than 20 nm of the domains. These domains appear

brighter than the surrounding material as they are slightly plastically deformed.
All domains are arranged in a narrow band with a thickness of a few tens of
nanometers and a length of usually some micrometers. These zones ahead of the
fully developed crazes are called “pre-crazes” (2,29). They considerably contributed
to better understanding of the formation mechanism of crazes.

The initiation and formation of crazes can be discussed in connection with

the entanglement model (30,31). In amorphous polymers, the macromolecules are
assumed to form topological links, ie, the so-called entanglements, responsible for
strength and deformability of the polymeric material. Entanglements are formed
only if the length or molecular mass of macromolecules are high enough (exis-
tence of a critical entanglement molecular mass, about 17,500 for PS). Adjacent
entanglements can be considered to form a network. The average diameter of the

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289

meshes of this network in PS is about 15 nm (with an entanglement distance
of

∼10 nm). The material between the entanglements (ie, in the meshes of the

network) is assumed to be mechanically weaker. During stretching, the meshes
are preferentially deformed, yielding the domain-like structure of the pre-crazes
(Fig. 5b). After stronger deformation the domains rupture, forming microvoids.
The entangled material between these microvoids is plastically stretched and
transformed into the fibrils of a developed craze (Fig. 5a). During this process the
microvoids coalesce partially and are transformed from a closed cell structure into
an open cell structure. This crazing mechanism based on such an “entanglement
network model” or “domain model” (31) probably describes details of formation of
fibrillated crazes better than other models.

The fibrillar structure of the crazes is typical of PS. Another glassy poly-

mer is styrene–acrylonitrile (SAN) copolymer with a PS content of usually about
74%. In this material the dominant deformation structures are homogeneously
deformed zones, but in many cases they coexist with the fibrillated crazes (2,29).
Depending on the loading conditions (stress state, loading velocity, temperature),
the deformation character can be shifted from one to another. Another typical
glassy polymer is PMMA with a typical appearance of homogeneously deformed
crazes at room temperature (29).

Measurement of microindentation experiments on crazes in the micron range

revealed additional information about micromechanical properties of the craze
fibrils (32). The craze zones’ microhardness was determined and the elastic mod-
uli of the crazed material were calculated from the elastic recovery curves of
indentations. The crazes were created in miniaturized tensile samples of some
amorphous polymers (PS, SAN, PMMA, PVC) during slow crack propagation un-
der fatigue loading at room temperature. The calculated elastic moduli of the
stretched material inside the crazes are higher than those of the bulk material.
This is consistent with the concept of the oriented entanglement network and the
highly oriented polymer chains within the craze.

The transition from the undeformed glassy polymer to the highly plasti-

cally deformed crazes at temperatures below the glass-transition temperature can
also be discussed in connection with the universal appearance of multiple glass-
transition of macromolecules (33). The basic idea is that a localized stress con-
centration increases the local free volume and reduces locally the glass-transition
temperature to the level of test temperature. Therefore, the increase in exter-
nal stress results in a step-by-step transition from the glassy behavior of the
undeformed polymer material to more flexible modes and a mobile state of macro-
molecules. The rapid changes of macromolecular mobility in dependence on stress
state were demonstrated by electron microscopy of the pre-craze structures and
the corresponding real crazes (34).

Although crazes are typical of amorphous glassy polymers, crazes or craze-

like features have also been observed in many other amorphous polymers (see
below), semicrystalline polymers (eg, in PE, PP, PA), and in rubber-modified high
impact polymers (eg, HIPS, ABS). In the literature they were often designated as
microcracks, deformation zones, or yield zones (28).

Yielding in Amorphous Ductile Polymers.

Typical amorphous duc-

tile polymers are PVC and PC. Deformation at room temperature results in the

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formation of shear bands or homogeneous deformation bands (2,29). It is generally
accepted that crazes with a fibrillated internal structure appear if the entangle-
ment density is low, ie, if the distance between entanglements is large (as in PS)
(28,30). With decreasing entanglement distance (or molecular weight), there is a
transition to a finely fibrillated form of crazes and to homogeneous deformation
bands.

The influence of entanglement density on internal structure of crazes and

deformation bands can be demonstrated by a special effect in PC (as an example of
a high-temperature-resistant polymer). Usual bisphenol A polycarbonate (BPA-
PC) shows a glass-transition temperature T

g

of 148

◦

C and chemically modified

versions on the base of trimethylcyclohexane (TMC-PC from Bayer AG) reach a
T

g

of 238

◦

C because of a reduced chain mobility. Because of the good compatibility

with usual PC, blends with T

g

s between 148

◦

C and 238

◦

C are available (35). Here,

blends with T

g

of 180

◦

C and 200

◦

C are used (called PC-2 and PC-3, respectively).

The usual PC as well as the types with higher glass-transition temperatures show
a characteristic transition in the deformation behavior. At room temperature and
somewhat higher temperatures, typical shear bands and homogeneous deforma-
tion zones appear. At temperatures between 60 and 80

◦

C below the particular

glass-transition temperature, there is a transition into the formation of fibrillated
crazes. With increasing deformation temperature, the fibrillation of the crazes be-
comes coarser (increase of the long period of fibrillation). This effect is summarized
in Figures 6 and 7.

These transitions in the deformation character can be understood by pro-

cesses on the macromolecular level. With increasing temperature, the stress
necessary for thermally induced disentanglement drops more rapidly than the
stress necessary for molecular mobility (yield stress). There are three regions de-
pending on temperature of deformation:

(1) T

≈ RT (well below T

g

): High entanglement density and high macromolec-

ular mobility (yield stress lower than disentanglement stress) result in ho-
mogeneous yielding (shear bands and deformation zones).

(2) T

≈ T

g

− T (T = 60–80

◦

C): Thermally induced disentanglement (re-

duced disentanglement stress up to the range of yield stress or reduction of
entanglement density) results in the transition from homogeneous yielding
to crazing.

(3) T

< T

g

(T

≈ T

g

): Intense thermally induced disentanglement (lower disen-

tanglement stress than yield stress) results in coarsening of craze structure
with increasing fibril thickness and fibril spacing.

The effect of coarsening of the fibrillar structure of crazes with increasing

temperature below the glass-transition temperature has been also found in SAN
and PC by electron microscopy and saxs (34).

Fibrillated crazes are usually thinner than the homogeneous deformation

bands. Therefore, the whole content of polymeric material, which is plastically
deformed, is smaller in the crazes and larger in the shear bands or deformation
zones. The result is shown macroscopically in the unusual effect of a decrease of
toughness and an embrittlement with increasing temperature.

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MICROMECHANICAL PROPERTIES

291

Fig. 6.

Influence of the deformation temperature T on type and internal structure of

deformation zones in PC (RT

= room temperature, T

g

= glass-transition temperature;

deformed thin specimens, 200-kV tem).

120 110 100 90

80

70

60

50

40

30

20

10

Crazes

 = 90°

Homogeneous
Deformation Bands and
Crazes

 = 90°

Shear Bands and
Homogeneous
Deformation

 = (45–90°)

Shear Bands

 = 45°

∆T

X

X

X

X

X

X

*

*

*

*

*

*

Fig. 7.

Schematic drawing of the transition in the deformation behavior in dependence

on the difference between test temperature T and glass-transition temperature T

g

of usual

and high temperature PC (

T = T

g

− T; α = angle between length orientation of the

deformation bands or crazes and direction of loading; T

g

of materials used: usual BPA-PC,

148

◦

C; PC-2, 180

◦

C; PC-3, 200

◦

C). x ........ PC-3;

∗—– PC-2; ·—PBA-PC.

292

MICROMECHANICAL PROPERTIES

Vol. 3

Mechanisms of Enhancing the Toughness in Heterogeneous Polymers

The toughness of a material can be enhanced by increasing the ability of the mate-
rial to deform plastically. This is achieved in toughening mechanisms (see I

MPACT

R

ESISTANCE

). The idea common to all of these mechanisms is the initiation of a

very large number of very small local yield events. Mechanisms that have been
discussed and that have been carried out in practice are sketched in Figure 8.
Type A involves the initiation of a large number of microcracks by (usually) inor-
ganic particles, short fibers, or something similar; because the increased energy
absorption occurs only through the creation of new internal surfaces, a noticeable
effect is to be expected only in very brittle material or at low temperatures. In type
B, ductile particles, distributed in a brittle matrix, are plastically stretched in the
area of the crack tip, bridging the two crack surfaces. This “bridging mechanism”

A

B

C

D

Fig. 8.

General mechanisms of enhancing the toughness of structurally modified

polymers-group II mechanisms (in the boxes the crosshatched areas are inorganic particles,
fibers or weak (rubber-like) particles distributed in a bulk matrix polymer;

σ indicates the

applied tension stress).

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MICROMECHANICAL PROPERTIES

293

is also effective only in brittle materials, such as in epoxies (of course, it appears
also in rubber-toughened polymers, but not as a main energy-absorbing factor).
Types C and D behavior involves the initiation of a large number of small plastic
zones (crazes or shear bands), induced by stress concentration at soft structural
heterogeneities, eg, rubber particles. While in type C stress concentration at the
soft rubber particles is sufficient for craze initiation [this mechanism is the typical
mechanism of high impact polystyrene (HIPS)], in type D cavitation inside or at
the particles is necessary for intense plastic yielding between the particles (typical
of toughened semicrystalline polymers such as toughened PP or PA).

A precondition of toughness enhancement is prevention of premature crack

propagation; there are some “crack stop mechanisms” including effects of crack tip
blunting, reduction of critical stress concentrations, or reduction of crack length
and crack propagation velocity (2).

Toughening of a brittle matrix polymer by rubber particles with a volume

content of about 5–25% is of major importance to the plastic industry. It has
proved so effective that the technology has been extended to almost all of the com-
mercial glassy thermoplastics (including PS, SAN, PMMA, PVC), many semicrys-
talline polymers (such as PP and PA), and several thermosetting resins. Rubber
toughening of polymers involves three important steps of deformation, which can
be summarized in a so-called “three-stage mechanism of toughening” (2,36) (see
Fig. 9).

(1) The first step at individual rubber particles is stress concentration

σ

K

and

often cavitation inside the rubber particles.

(2) If the particle volume content is in average above 10%, a remarkable su-

perposition of the individual particle stress fields appears. The result is
a higher stress concentration

σ

K



and the more intense initiation of local

matrix yielding in the form of fibrillated crazes, homogeneous crazes, or
shear yielding.

(3) The third step is stabilizing the deformation structure by preventing a pre-

mature crack propagation (by crack stop mechanisms such as limitation of
crack length or crack tip blunting at or in the rubber particles) and by stabi-
lizing the rubber particle cavities due to the plastically deformed adjacent
rubber and matrix strands.

The dominant matrix deformation mechanism depends mainly on the type of

matrix material, but strongly also on test temperature, strain rate of testing, and
on type, shape, and size of rubber particles (2,36–38). Fibrillated crazes are typical
of toughened PS (HIPS), a coexistence or a transition from fibrillated crazes to
homogeneous ones is typical of toughened SAN (ABS), homogeneous deformation
appears in many grades of ABS, toughened PVC, and toughened PMMA. Shear
yielding is the dominant mechanism of the toughened semicrystalline polymers
PA and PP.

Rubber toughening is often assumed to be identical to the modification by

rubber particles. However, there is an alternative and also very effective possibility
of rubber toughening of amorphous polymers—the rubber network toughening (2).
Here, small thermoplastic particles, eg, PVC particles (about 1

µm in diameter),

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MICROMECHANICAL PROPERTIES

Vol. 3

K

0

0

0

K

 >

K

Fig. 9.

Schematic presentation of the three-stage mechanism of toughening with multiple

initiation of local yield events (eg, crazes as in case C in Fig. 8).

are embedded by a network or honeycomb structure of rubber (for instance EVAc).
Since there are very tiny network layers in the range of a few tens of nanometers,
the rubber content is usually below 10%, ie, the PVC content reaches more than
90%. During loading, the rubber network is stretched, which initiate the PVC par-
ticles to yield and to absorb deformation energy. A deformation mechanism similar
to the network toughening is the so called inclusion yielding, where stiffer ther-
moplastic particles are distributed in a somewhat softer matrix (eg, SAN particles
distributed in a PC matrix) (39). Under load, the particles are forced to deform
plastically. Both mechanisms demonstrate the possibility to transform stresses
via a softer matrix, which are high enough to reach the yield stress of the stiffer
particles.

Most of these micromechanical processes are highly localized and depend

strongly on the local morphology. Therefore, direct imaging by electron microscopy
techniques with a high local resolution are of particular importance, and most of
our knowledge of rubber toughening arises from the application of such techniques
(2,36–38).

Toughened Polymers with Amorphous Matrix.

The fundamental de-

formation step is the formation of crazes in the stress field around the rubber

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MICROMECHANICAL PROPERTIES

295

particles (ie, in the zones of highest stress concentration, the equatorial zones
around the particles). It can clearly be shown that crazes start in the matrix
directly at the interface to the rubber particles. If the distance between rubber
particles is small enough, crazes are intensively formed between the particles (cf
Fig. 9).

HIPS deforms generally by formation of fibrillated crazes, whereas many

ABS grades show the formation of fibrillated crazes and homogeneous crazes (ho-
mogeneous deformation bands, shear deformation). A transition between these
deformation modes appear in dependence on loading velocity and particularly
on test temperature. Such transitions can be advantageously studied by electron
microscopy and using a special tensile holder with cooling and heating facilities
(40).

Very fine and well-dispersed morphologies can be obtained by blending the

glassy polymer with core-shell particles. Successful materials possess three-stage
core-shell particles (40). In the example used here, the particles consist of a single
core of PMMA, surrounded by a 20-nm thick inner shell of grafted and lightly
cross-linked poly(butyl acrylate-co-styrene) (PBA) and an outer grafted shell of
PMMA. This PMMA layer is about 10 nm thick, and is sufficiently miscible with
SAN or PMMA as matrix materials to provide good adhesion between the modifier
particles and the matrix.

The typical micromechanical behavior of this material at room temperature

is shown in Figure 10. The lower magnification in Figure 10a shows a dense pat-
tern of cavitated and elongated rubber particles and plastically deformed matrix
material between the particles. The matrix deformation occurs mainly in the form
of homogeneous shear deformation zones and a small number of short and rela-
tively thin fibrillated crazes (40).

The cavitation mechanism within the modifier particles begins with mi-

crovoid formation and fibrillation in the butyl acrylate shell, as shown in higher
magnification in Figure 10b. The fibrillated shells with the internal PMMA cores
resemble spiders. The fibrils are connected by the PMMA cores, and the cavities in

Fig. 10.

Deformation structures of an SAN/PBA blend. (a) lower magnification; (b) higher

magnification (tem micrographs, deformation direction, see arrow).

296

MICROMECHANICAL PROPERTIES

Vol. 3

material

homo-
geneous
particles

core-shell
particles

single mechanism

superposition

internal cavitation

void coalescence, crack formation,

fracture

stabilization of cavities, intense

yielding of matrix strands

cavitation in the shell, fibri-

llation of the interface

1

2

2

1

Fig. 11.

Comparison of the action of homogeneous and core-shell particles in toughened

polymers concerning the single mechanism at particles and the superposition effect be-
tween particles.

the PBA shells are limited in their size by the fibrils between the core and the outer
shell. This stabilization of cavities by the core-shell structure is an advantage of
this type of particles over homogeneous rubber particles. This remarkable differ-
ence between homogeneous rubber particles and core-shell particles is sketched
in Figure 11. In both cases, the starting mechanisms of cavitation inside the par-
ticles, stress concentration at the surface of the particles, and initiation of plastic
yielding of adjacent matrix parts are very similar. However, if we consider later
stages of deformation, superposition of stresses between the particles occur and
differences become visible. In the often possible case of closely connected homoge-
neous rubber particles, the voids inside the particles can coalesce, leading to larger
voids, crack initiation and, consequently, a premature fracture. Using core-shell
particles, the individual microvoids are stabilized in their size, and void coales-
cence is prevented, with the result of an intense plastic yielding of the matrix.

Usually, the hard polymer cores of the modifier particles are not deformed, as

is visible in the micrographs of Figure 10. This is usually accepted since it hardly
seems possible to deform a glassy polymer core inside a rubbery shell. However,
there are results that show that a plastic yielding of the hard cores should be
possible: fibrils are drawn out from the PMMA cores, leading to a flattening of
the cores. The stretching of the cores into fibrils is very similar to the mechanism
of fibril drawing in craze formation. This mechanism of yielding of glassy cores
inside modifier particles is a new toughening mechanism, contributing to energy
absorption during deformation (1,40). A precondition to this effect is that the
rubbery shell of the modifier particles forms fibrils showing a remarkable strain

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MICROMECHANICAL PROPERTIES

297

hardening effect, leading to stresses in the fibrillated shell, which are high enough
to draw fibrils from the hard core.

The advantage of core-shell particles to toughen PMMA has been demon-

strated by investigation of deformed samples by HVEM (41). Besides core-shell
and homogeneous rubber particles, many other types of rubber particles have
been studied (eg, cells, drops, coils). A qualitative and quantitative estimation of
the size and structure of differently shaped rubber particles on the toughness of
modified PS on the basis of detailed electron microscopic studies can be found in
Reference 42.

Usually, ABS polymers show a good toughness by an intense formation of

stress-induced crazes or homogeneous deformation zones at and between rubber
particles. Recently, a surprising effect has been found in some ABS grades: When
creep tests were performed with loads well below the yield stress and if the speci-
mens were tested afterwards in the tensile mode, samples broke atypically brittle
at a low strain level (43). Such a drastic embrittlement was observed after preload-
ing with stresses between 25 and 55% of the short-term yield stress. Lower and
higher preloading stresses yield only a smaller reduction of toughness.

The microscopic investigation revealed the reason of this effect. The mate-

rials showing the embrittlement possess a pronounced bimodal distribution of
the rubber particles with smaller particles of 50–250 nm and a smaller frac-
tion of bigger ones between 350 nm and 1

µm. During preloading of this ma-

terial, a few extremely long crazes with lengths up to a few millimeters are
formed (Fig. 12). They start at the biggest rubber particles often near the sam-
ple surfaces and propagate in a straight line across the material without being
influenced by the other smaller particles. It seems that, for the long crazes, the
material behaves like a homogeneous material. During subsequent tensile test,
cracks can propagate very quickly in these long crazes and initiate the brittle
fracture.

This special type of craze, for which ABS had not been known up to now, is

called “macrocraze.” The formation of macrocrazes correspond to the large dis-
tance between the very big rubber particles and can be understood in connection
with changes of Young’s modulus both of the matrix and the rubber particles
during loading. It is known that the moduli of thermoplastics and rubber decrease
with decreasing load velocity

.

ε (in tensile test or with decreasing frequency in

torsion pendulum test). This is schematically drawn in Figure 12c for SAN matrix
and small and big rubber particles, as used in the ABS of Figures 12a and b. The
big rubber particles show another constitution than the smaller ones and possess
a higher deformability or lower modulus. This is detectable from in situ deforma-
tion tests of the material in the HVEM (using a technique described in more detail
in Ref. 2. Starting with deformation tests with a very high speed (impact test or
test at low temperatures below glass-transition temperatures of rubber particles),
the modulus of rubber particles is very high, comparable with the modulus of
the glassy SAN matrix (the modulus ratio G

R

/G

M

is nearly 1). Therefore, there is

nearly no stress concentration at the rubber particles (

σ

c

≈ σ

0

), and no crazes are

initiated. With decreasing test speed (with a load rate in the usual application
range or with increasing temperature to room temperature) the modulus of the
glassy matrix is unchanged, but the modulus of rubber particles decreases dras-
tically. In this range, the ratios of moduli G

R

/G

M

are much lower than 1, and the

G

R

ratio

G

M

G

R

G

M

G

R

S

G

M

~

~

~

~

1

G

R

G

M

~

~ 1

G

R

b

G

M

< 1

< 1

0

c

0

c

>

~

~

c

s

0

0

c

b

>

stress

concen-

tration

craze

initiation

SAN matrix

small (s) rubber

big (b) particles

G

ε

˙

(c)

Fig. 12.

(a, b) Formation of very long, tiny crazes (so-called macrocrazes) after preloading

in an ABS with only a few large rubber particles (sample preloaded for 166 h with 40% of
yield stress, stained with OsO

4

, 1-

µm thick ultramicrotome section, HVEM). (a) general

view of two macrocrazes; (b) higher magnification of part of a macrocraze; (c) schematic
of the decrease of the shear modulus G of thermoplastic SAN matrix material and cross-
linked rubber with decreasing load rate

.

ε (corresponding to an increased temperature).

Below: ratio of moduli G

R

and G

M

of rubber and matrix, corresponding stress concentration

and initiation and propagation of crazes. From Reference 16.

298

Vol. 3

MICROMECHANICAL PROPERTIES

299

stress concentration at rubber particles reaches a maximum (

σ

c

/

σ

0

> 1). This re-

sults in an intense initiation of crazes at larger as well as smaller rubber particles
(range of intense plastic energy absorption, range of toughness).

A further decrease of test speed

.

ε down to very low values corresponds to

the situation during creep and static preloading. Here, the modulus of the glassy
SAN matrix decreases to the level of the rubber. Under the action of a tensile
stress this situation can be considered similar to the glass-transition range of
matrix material, discussed in detail in References 33 and 34. While the smaller
(harder) rubber particles show a modulus similar to the matrix modulus (moduli
ratio G

s

R

/G

M

≈ 1) the bigger (weaker) rubber particles are somewhat weaker than

the matrix (moduli ratio G

b

R

/G

M

< 1).

Therefore, only the largest rubber particles are able to stress concentrate

and to initiate crazes. ABS regions with the smaller rubber particles do not show
any differentiation in modulus (they behave like a homogeneous material). Here,
the crazes that are initiated at the largest rubber particles propagate without
modification and can grow to macrocrazes.

Toughened Polymers with Semicrystalline Matrix.

It is well known

that toughness of semicrystalline polymers such as PA (polyamide) and PP can
be increased similar to the amorphous polymers by the addition of relatively
small amounts of rubber particles such as EPR or EPDM. As in HIPS and
ABS, the modifier particles act as stress concentrators, initiating a plastic de-
formation of matrix strands between the particles as the main energy absorp-
tion step. In impact-modified PA and PP at room temperature, plastic defor-
mation takes place through shear deformation (mechanism of multiple shear
deformation).

In contrast to crazing, shear deformation does not involve dilatation of ma-

terial, but relief of local plastic constraint by formation of voids and subsequent
strain field interactions between voids often enhance localized shear yielding and
is an important precondition of effective toughening. Figure 13 shows scanning
force micrographs of highly deformed parts of PP toughened by an addition of
20% EPDM rubber particles. The particles are cavitated and fibrillated and, to-
gether with the adjacent matrix strands, they are strongly plastically deformed,
elongating up to 900%. Details of the influence of particle type, internal struc-
ture, and size of particles, as well as of interparticle distance, are discussed in
References 36, 44, and 45.

Toughened PP shows a decrease of toughness with decreasing temperature.

In stress–strain tests, Young’s modulus and strength increase but elongation at
break and the area below stress–strain curve (corresponding to toughness) de-
crease. This change is connected with changes in micromechanical processes.
Transmission electron micrographs of PP/EPDM deformed at RT and

−40

◦

C are

shown in Figure 14. Figure 14b reveals a coexistence of shear yielding and crazing,
and Figure 14c shows only formation of fibrillated crazes at and between elongated
particles.

The use of core-shell particles has an advantage over homogeneous rubber

particles that is very similar to that discussed above (cf Fig. 11). An additional
advantage is that they enable a low temperature toughness. Deformation tests of
PP with core-shell EPR (ethylene–propylene–rubber) particles at very low tem-
peratures of up to

−100

◦

C revealed that the EP shell is cavitated and elongated

300

MICROMECHANICAL PROPERTIES

Vol. 3

0

14.0 m 0

µ

14.0 m

µ

Fig. 13.

Scanning force micrographs of a deformed PP/EPDM blend revealing the elon-

gated particles with the highly plastically stretched matrix strands in between (deforma-
tion direction from top left to bottom right; sfm tapping mode: left, amplitude signal; right,
phase signal).

σ

(a)

(b)

(c)

3 m

µ

5 m

µ

2 m

µ

Fig. 14.

Deformation structures of PP impact-modified with EPDM at different test tem-

peratures: (a) RT

− cavitated particles as well as adjacent matrix strands are strongly

plastically deformed by shear yielding; (b)

−40

◦

C—coexistence of shear yielding and craz-

ing; (c)

−40

◦

C

− fibrillated crazes between elongated particles (thin sections, deformed and

investigated by hvem (a) and tem (b and c)). From Reference 1.

with fibrillation inside, and the adjacent matrix parts show fibrillated crazes (1).
It is an effect far below the glass-transition temperature of the rubber phase, and
it demonstrates that toughening processes are not limited by the glass-transition
temperature of modifier particles. The important step is local stress concentration
at the voided particles, which initiate the formation of crazes. These micromechan-
ical results reveal that it should be possible to increase low temperature toughness

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MICROMECHANICAL PROPERTIES

301

of PP and other semicrystalline polymers. Essential structural preconditions are
the use of modifier particles that are able to cavitate and to stabilize cavities so
as to avoid growth of voids into cracks.

Polymer Blends.

The aim of producing polymer blends is to improve dif-

ferent properties and to reduce costs. There are many publications and books,
which review preparation and structure of multiphase polymer blends (38). A cen-
tral problem is to realize an optimum morphology, eg, an optimum size of particles
of the polymer, which is in the minority in a matrix of a polymer in majority. One
attractive route to multiphase polymeric materials, which promotes high interfa-
cial adhesion and excellent morphology control, together with related mechanical
properties, is in situ formation of compatibilizing during reactive blending. Using
compatibilizers, the size of dispersed particles in a matrix can be decreased. As
shown in Reference 46, the size of PA 6 particles in a PP matrix can be drastically
reduced using increasing amounts of an SEBS-g-MA compatibilizer, however, not
the smallest, but an optimum size and constitution of particles yielding the best
properties.

Often, blending a polymer with particles of a second polymer is connected

with an increase of toughness. As an example, blends of a metallocene-based high
density ethene/1-hexene copolymer (HDPE, density 0.93 g/cm

3

) with 20 vol% of an

elastomeric ethene/1-hexene copolymer (VLDPE, hexene content 17.2 mol%, den-
sity 0.867 g/cm

3

) were used as model blends to study the morphology development

and the micromechanical behavior (47,48). Use of the sfm tapping mode and a
special force modulation technique enabled local deformations of the sample and
changes in the morphological structures in a defined specimen area to be recorded
directly while the external elongation was successively increased. In order to carry
out in situ deformation experiments, the sfm was equipped with a deformation
unit and a periodic pattern was evaporated on the back side of the sample. Fig-
ure 15 illustrates the positioning of the sample. The optical micrographs show an
overview (Fig. 15a) of the sample with the evaporated pattern and two artificial
notches (diffuse black areas) on the left and on the right, and in Figure 15b the
marked area in the sample center. The sfm phase signal image in Figure 15c shows
the blend morphology with elastomeric particles (appearing bright) in the HDPE
matrix with crystalline lamellae (occurring dark owing to their higher stiffness in
comparison to the adjacent interlamellar amorphous areas).

The micrographs of Figure 16 illustrate typical results of the sfm in situ

tensile test. The images show a sample area of 2

µm × 2 µm marked in

Figure 15c before deformation (at the top) and after a deformation of about 35%
(at the bottom). On the left, the height signal images show the surface topog-
raphy, and on the right-hand side, the sample is visible in phase signal im-
ages. A comparison of the micrographs shows that the area between the dot-
ted lines is nearly homogeneously strained. However, deformations on the sub-
micron range are strongly inhomogeneous. Especially, the strong deformation of
the elastomeric particles is accompanied by a very heterogeneous deformation
of the surrounding semicrystalline matrix. Adjacent segments between particles
(perpendicular to the load direction) reveal a considerably increased elongation,
whereas segments between particles in the direction of loading are nearly not
deformed. This correlates with the distribution of stress concentration around
soft particles. Additionally, the behavior of crystalline lamellae under stress can

302

MICROMECHANICAL PROPERTIES

Vol. 3

Fig. 15.

Specimen from an HDPE/VLDPE blend for in situ sfm deformation test with an

evaporated pattern to observe an area of interest; (a, b) optical micrographs; (c) sfm phase
signal image in tapping mode. From Reference 48.

be directly observed. The appearance of the crystalline lamellae is improved in
Figure 17 after an imaging processing by a high pass filter (48). These micrographs
very clearly reveal that the lamellae are composed of single crystal blocks (in an
appearance as beaded strings). Some types of deformation behavior of lamellae are
visible:

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MICROMECHANICAL PROPERTIES

303

Fig. 16.

Marked specimen area from Figure 15 before deformation (a, b) and after de-

formation (c, d) in sfm tapping mode height images (a, c) and phase signal images (b, d).
From Reference 48.

(1) Lamellar segments perpendicular to the loading direction (segment be-

tween the points A and B in Fig. 17) rotate in stress direction without
changing the segment length.

(2) Lamellae aligned in loading direction (segment between points C and

D) are stretched with an increasing separation of the crystalline
blocks.

(3) Lamellae in other orientations show a combination of both effects; for ex-

ample, segment between the points E and F reveals a rotation and an elon-
gation.

Yielding in Semicrystalline Polymers.

In the literature, it is often as-

sumed that the large plastic deformation of the semicrystalline polymers such as
PE or PP is a continuous orientation of the chain segments in the deformation
direction (ie, a continuous change in the c-texture). This assumption is mainly
based on x-ray scattering measurements. The result of steadily increasing c-axis
orientation is based on averages from a relatively large volume of a sample. Direct
electron microscopic investigations revealed that the improvement of the c-axis
orientation results from a superposition of several local deformation processes. In
detail, the orientation of PE has been divided into three stages (2,4,49). In the first
stage, mainly the amorphous, interlamellar parts contribute to the deformation.

304

MICROMECHANICAL PROPERTIES

Vol. 3

Fig. 17.

Micrographs of Figure 16 after additional image processing; the capitals mark

lamellar segments under different degree of deformation (eg, twisting, stretching, block
separation). From Reference 48.

Larger lamellae can break into shorter pieces, and the lamellae tend to twist with
their length direction toward the deformation direction. The processes of twist-
ing and orientation of the lamellae do not appear homogeneously in the whole
sample. There are smaller regions with a pronounced or stronger orientation and
others with a weaker one. This makes clear that the deformation at the beginning
strongly depends on the yield properties of the amorphous material between the
lamellae. In the second stage a transition from the lamellar appearance into a
microfibrillar arrangement occurs, with the improvement of the c-axis orientation
in the third stage.

Some aspects of the first stage of deformation are visible in the in situ defor-

mation test of a PE blend by sfm in Figures 16 and 17 and are also revealed by
tem studies of crack-tip crazes in PE (48).

Yielding

in

Block

Copolymers.

While

polymer

blends

show

macrophase-separated morphologies, which often lead to a deterioration of
mechanical properties because of the immiscibility of the components, in block
copolymers microphase-separated structures at the typical size scale 10–100 nm

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MICROMECHANICAL PROPERTIES

305

are observed. A wide spectra of mechanical properties and micromechanical de-
formation mechanisms are observed in such block copolymers attributable to the
existence of a large variety of highly ordered microphase separated morphologies
with a periodicity in the range of radius of gyration of the copolymer molecules
(50,51). While a great deal of work has been carried out on morphology and phase
behavior of these fascinating materials, only a little has been done regarding
the correlation between morphology, mechanical properties, and underlying
micromechanical processes of deformation and fracture.

Pioneering works on the micromechanical deformation mechanisms in block

copolymers date back to the mid-eighties when cavitation mechanism in styrene–
butadiene (SB) diblock copolymers containing PB cylinders in a PS matrix was
proposed (52,53). Based mainly on tem investigations, a two-step craze growth
mechanism was proposed:

(1) In the first stage the PB cylinders are strongly deformed till the cavitation

stress of PB is reached. As a consequence, the PB cylinders cavitate resulting
in the formation of voids.

(2) In the second step PS is plastically deformed by local stress concentration

resulting in a cellular deformation structure.

Mechanical behavior of block copolymers are governed by the molecular ar-

chitecture (AB diblock, ABA or ABC triblock, (AB)

n

star block, etc), symmetry of

the blocks, and microphase-separated morphology (50). Most extensively studied
and more interesting from the technical point of view are SBS triblock copolymers
based on polystyrene and polydienes (PB or PI), where the outer glassy styrene
blocks physically cross-link the elastomeric B phase at both the ends. In SBS tri-
block copolymers of sufficient molecular weight, the mechanical properties can
be tailored simply by adjusting its composition. Thermoplastic elastomers having
dispersed glassy phase (spheres or hexagonally arranged cylinders) in a rubbery
matrix like Kraton (Shell Chemical Co.) or Styroflex (BASF AG) have elongations
at break that are severalfold and tensile strengths above 30 MPa. These high
values are contributed with stretching the elastomeric network and rotation and
orientation of the dispersed phase. The tem, ftir spectroscopy, and saxs studies of
SBS triblock copolymers with styrene cylinders revealed that the initial stage of
tensile deformation is governed by preferential orientation of elastomeric chains
and later stages by a breakdown of the glassy domains (54).

Another class of copolymers having interesting mechanical properties are

weakly segregated block copolymers. One of the most striking effect observed in
these block copolymers is a synergism in tensile properties (51,55,56). In a certain
composition range, the tensile strength was found to exceed that of pure PS, as
illustrated in Figure 18. Irrespective of the block copolymer architecture (diblock,
triblock, or star block), this effect was observed and shows that it is attributed
to the widened interface resulting from enhanced phase mixing. Therefore, in tri-
block copolymers this synergistic effect occurs over a broader composition range
than in diblock copolymers because of enhanced miscibility of triblock copolymers.
The deformation structures observed in these block copolymers depend in detail
on type and orientation of the microphase-separated morphology. Particularly in-
teresting are the mechanisms of “craze termination,” “craze tip blunting,” and

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MICROMECHANICAL PROPERTIES

Vol. 3

50

40

30

20

10

0

20

40

60

80

100

error

T

ensile strength, MP

a



PS

, %

Fig. 18.

Dependence of tensile strength on volume fraction of PS for PBMA-b-PS-b-

PBMA triblock copolymers and pure PS and PBMA (strain rate 1.6

× 10

− 4

s

− 1

). From

Reference 51.

“craze deviation” during propagation of crazes through an arrangement of stacks
of lamellae (51,55).

A craze in a block copolymer with lamellar morphology is shown in

Figure 19a with an internal structure of highly extended craze fibrils of PS and
PBMA. The PBMA lamellae are cavitated and, therefore, appear brighter than
the dark, thicker PS lamellae. Because of the microvoids in the PBMA lamellae,
a stress concentration is built up in the adjacent PS lamellae that initiate a large
plastic deformation of these PS lamellae. This is similar to the mechanism as
described by Argon for PS-b-PB diblock copolymers (53). The diameter of the PS
fibrils is 15–25 nm with long periods of about 100–130 nm. In the undeformed
material the PS lamellae are about 80–90 nm thick. This is much larger than

Fig. 19.

hvem micrographs of crazes in PS-b-PBMA diblock copolymers with different

morphology. (a) Lamellar morphology, PS volume content 67%; (b) Hexagonally packed
PBMA cylinders, PS volume content 76%.

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MICROMECHANICAL PROPERTIES

307

Fig. 20.

Tapping mode sfm images of a lamellar SBS triblock copolymer before (left) and

after deformation (right); deformation direction vertical, PS phase appears light.

the thicknesses of the deformed PS lamellae, clearly indicating their large plastic
deformation.

A craze in a block copolymer with PBMA cylinders is shown in Figure 19b

with an internal cellular structure of the craze. The PBMA cylinders are cavitated
in the craze and, therefore, appear bright. This is followed by a large plastic de-
formation of the PS parts (appearing dark) up to fibrils.

In block copolymers with lamellar morphology, mechanical properties and de-

formation structures vary with the orientation of the lamellae with respect to the
direction of applied load. When the material is loaded in a perpendicular direction
to the lamellar orientation, lamellae are folded in a fish-bone-like arrangement
(57). Such a lamellar folding in a solution cast film of an SBS triblock copolymer
is shown in Figure 20 (58).

Nowadays, star-block copolymers are earning growing interest because of

their improved mechanical and rheological properties. Introducing a “tapered
chain” and giving the stars a highly asymmetric block structure lead to the evo-
lution of a nonclassical lamellae-like morphology in spite of a very high styrene
content (about 75%) and correspondingly high ductility (59). Investigating such
asymmetric SB star-block copolymers with alternating PS and PB lamellae con-
firmed the result of a high plastic deformation of the PS lamellae (60) which is
also shown in the crazes of Figure 19. tem micrographs of stained samples of
a star-block copolymer with a PS content of 74% show alternating PS and PB
lamellae (see Fig. 21a). Thicknesses and long periods of the PS lamellae range be-
tween 10–25 nm and 30–50 nm, respectively. Tension of the sample in a parallel
direction to the length direction of the lamellae shows a stretching of the whole
morphology (Fig. 21b). The PS as well as the PB lamellae are highly plastically
deformed in parallel direction to the applied stress. This is clearly indicated by a
reduced thickness and long period of PS lamellae up to 7–15 nm and 20–35 nm,
respectively (see Figs. 21c and 21d). Here, the lamellae are deformed without any
cavitation or microvoid formation and without the formation of local craze-like
deformation bands. The deformation of the lamellae reaches elongations up to
300%; this corresponds to the typical elongations of the fibrils inside the crazes
in PS.

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MICROMECHANICAL PROPERTIES

Vol. 3

(a)

(c)

(d)

100 nm

100 nm

thickness of PS-lamellae, nm

deformed

0

10

20

30

40

0.000

0.100

0.200

0.300

thickness of PS-lamellae/nm

undeformed

0

10

20

30

40

0.000

0.100

0.200

frequency

(b)

Fig. 21.

Morphology of an injection-molded specimen of a star-block copolymer with a

PS content of 74% with lamellar arrangement of PS and PB lamellae before and after
deformation. (a) PS and PB lamellae before deformation; (b) Plastically stretched PS and
PB lamellae deformed in parallel direction to lamellar orientation (a, b tem micrographs
of chemically stained thin sections, PB lamellae appear dark; arrow shows direction of
tension) Frequency distributions of thicknesses of PS lamellae (c) before and (d) after
deformation. From Ref. 60.

This homogeneous yielding of PS lamellae together with adjacent PB ones

can be considered as a new deformation and toughening mechanism, called thin
layer yielding mechanism. This effect appears only in thin PS layers with a thick-
ness smaller than a critical thickness (see Fig. 22). This critical thickness D

crit

is comparable with the maximum thicknesses of the craze fibrils in PS, ie, in
the range of 20 nm. The difference between fibril stretching in PS crazes and
thin layer yielding of PS lamellae is to be seen in the fact that craze fibrils are
stretched between microvoids, whereas the PS lamellae are deformed together
with the adjacent PB lamellae.

These results show that the tensile properties of block copolymers, such as

stiffness, tensile strength, elongation at break, and toughness, can be improved as
compared to those of pure homopolymers, polymer blends, and rubber-toughened
polymers. Moreover, this demonstrates the possibility of creating a new class of
polymers with improved properties based on materials with structures at the
nanometer scale.

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MICROMECHANICAL PROPERTIES

309

Effect

Precondition

D

1

D

2

100

10

D

crit

D

ε

, %

Fig. 22.

Schematic drawing of the principle of the thin layer mechanism (D, D

crit

,

ε,

and

σ stand for PS layer thickness, critical layer thickness, elongation at break, and load

direction).

ACKNOWLEDGMENTS

The author thanks Prof. Dr. U. G¨osele, Max Planck Institute of Microstructure Physics
in Halle/S., for providing the opportunity to carry out deformation tests in the 1000-kV
hvem and Dr. R. Godehardt, Dr. J.U. Starke, W. Lebek, S. Henning, M. Ensslen, and R.
Adhikari for performing deformation tests on several polymers in hvem, tem, and sfm.
He gratefully thanks the Deutsche Forschungsgemeinschaft (DFG) for financial support in
several projects.

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G

OERG

H. M

ICHLER

Martin-Luther-Universit ¨at Halle-Wittenberg