2001_gahleitner_melt rheology of polyolefins

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Melt rheology of polyole®ns

Markus Gahleitner

Department RAPP, Borealis GmbH, Research Location Linz, St. Peterstr. 25, A-4021 Linz, Austria

Received 8 January 2001; revised 11 March 2001; accepted 12 March 2001

Abstract

Rheology has a key position in polymer research, being an important link in the so-called `chain of knowledge'

reaching from the production of polymers to their end-use properties. A review of the melt rheology of polyole®ns,

which are the most widely used group of thermoplastic polymers today, is given in this paper both in terms of

application and characterisation aspects. The materials are discussed according to their phase structures (single-

and multi-phase polymers) and their chain structures (linear and branched). Aspects of the molar mass distribution,

the chain structure and topology are discussed both from an experimental and theoretical point for the single-phase

systems. For the technically more important types of multi-phase polymers like compounds and blends, the

importance of rheological properties in the development of the phase structure is outlined as well as the possibility

to use rheometry for structure investigations. In any case, the importance of considering the stress or strain history

of a material sample in a rheological investigation is discussed. Finally, an outlook on the present and future

developments in the ®eld of polyole®ns is given. q 2001 Elsevier Science Ltd. All rights reserved.

Keywords: Polyethylene; Polymer blends; Polypropylene; Polymer; Polymer processing; Polymer melts; Review

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 896

1.1. Material classes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 896

1.2. Rheological properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 898

1.3. Application areas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 899

2. Single phase systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 900

2.1. Molar mass effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 900

2.2. Chain structure effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 909

2.2.1. Linear chains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 909

2.2.2. Branched chains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 910

2.2.3. Partially crosslinked chains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 919

3. Multiphase systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 920

3.1. Inhomogeneous products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 921

Prog. Polym. Sci. 26 (2001) 895±944

0079-6700/01/$ - see front matter q 2001 Elsevier Science Ltd. All rights reserved.

PII: S0079-6700(01)00011-9

www.elsevier.com/locate/ppolysci

E-mail address: [email protected] (M. Gahleitner).



3.2. Filled and reinforced polyole®ns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 922

3.3. Crystallizing polyole®ns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 926

3.4. Elastomer blends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 927

3.4.1. Extruder blends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 928

3.4.2. Reactor blends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9323.5. Blends with other polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 935

4. Actual and future trends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 938

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 940

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 940

1. Introduction

For thermoplastic polymers, the knowledge and moreover the design of ¯ow behaviour is essential for

all forms of production and processing, as big parts of these occur in the molten state [1]. Additionally,rheology has attained a key position in polymer research, being an important link in the correlation chain(see Fig. 1) from the catalyst over polymerisation and chain structure to processing behaviour and ®nal

properties [2]. Thereby it forms an important knot in the so-called `chain of knowledge' reaching fromthe production of polymers to their end-use properties, which has become increasingly important in viewof the increasing speed of material development as a result of quickly changing customer requirements.

1.1. Material classes

Polyole®ns, which are normally de®ned as polymers based on alkene-1 monomers ora-ole®ns, are the

most widely used group of thermoplastic polymers today. Based on their monomeric units and theirchain structures, they can be divided into the following subgroups:

² Ethylene-based materials Ð polyethylenes (PEs) Ð produced under low pressure conditions withtransition metal catalysts of various types and showing a predominantly linear chain structure. Thissubgroup includes high density PE (HDPE), medium density PE (MDPE), linear-low density PE(LLDPE) and other varieties, which are distinguished through the regulation of density and subse-

quently mechanical properties through the incorporation of higher a-ole®ns (mostly butene, hexeneand octene) as comonomers. The linear nature of their polymeric chains can be disturbed twofold: by

longer comonomers like butene, hexene or octene acting as short side chains [3] and by catalystsforming polymerisationally active oligomers being incorporated further as long chain branches

(LCBs). Examples for the latter case including implications for the rheology of such systems aregiven by Yan et al. [4].

² Ethylene-based polymers (PEs) produced in a radical polymerisation under high pressures with

oxygen or peroxides as chain initiators and showing a predominantly branched chain structure.According to their reduced crystallinities and densities, these materials are termed low densitypolyethylenes (LDPEs). A variation of the degree of branching is possible by various measures

like temperature control, peroxide feed, residence time etc., which strongly affects the material'srheological and terminal properties [5].

² Propylene-based polymers produced with transition-metal catalysts Ð polypropylene (PP) and its

M. Gahleitner / Prog. Polym. Sci. 26 (2001) 895± 944896



copolymers Ð showing a linear chain structure with stereospeci®c arrangement of the propylene

units. Mostly, the isotactic species Ð iPP Ð is used today, but also syndiotactic Ð sPP Ð or specialstereoblock structures have become technically relevant, as they are available from single-site cata-

lysts. A wide variation of material properties can be achieved with the incorporation of ethylene and/ or higher a-ole®ns in various fashions; single-phase and multiphase materials are possible [6].

²

Polymers based predominantly or exclusively on higher a-ole®ns (e.g. poly-butene-1), produced withtransition-metal catalysts and having a linear and stereospeci®c chain structure.² Ole®nic elastomers based on transition metal or single-site catalysts, with or without the incorpora-

tion of dienes, which make these materials partially crosslinkable. These polymers are normally basedon ethylene and propylene, mostly amorphous with high molar masses and rarely homogeneous in

their phase structures. Nowadays, such elastomers are sometimes substituted with metallocene-basedultra-low density PEs (ULDPEs) termed plastomers [7], which have a more homogeneous structure

and can be varied in their properties more easily.

Also of importance are an inhomogeneous group of materials that are based inhomogeneous group onblends of different polyole®ns. The terminology is not completely `sharp' here; extruder-based mixtures

with solid substances (®llers and reinforcements) and elastomers of any kind as well as other polyole®ns arenormally called `compounds', while similarly produced mixtures with non-PO polymers (and also elasto-mers) as well as reactively produced mixtures incorporating grafting steps are called `blends'. All of these

materials have attained importance in areas where the physical limits of polyole®ns need to be exceeded orbasic characteristics of their chemical nature (e.g. hydrophobicity and apolarity) need to be changed.

Some limiting cases will not be treated within this review. These include wax-like atactic PP (used

e.g. in glue systems and as asphalt modi®ers) as well as ole®n-oligomers produced as constituents forlubri®cation systems. Common to these materials is their low molar masses, which goes along withNewtonian behaviour in the molten state or even a liquid nature at room temperature.

M. Gahleitner / Prog. Polym. Sci. 26 (2001) 895± 944 897

Fig. 1. Rheological parameters acting as a `link' between molecular structure and ®nal properties of a polymer.



1.2. Rheological properties

Before going into details, the scope of this paper should be clari®ed. It will cover the melt rheology of

polyole®ns, including the limiting case of solidi®cation Ð which is, in case of practically all technicallyrelevant polyole®ns, crystallisation. From a theoretical point of view, these properties can be split into:

² Linear viscoelastic properties, the range of material behaviour where a linear relationship betweenstress and strain exists. These are theoretically the simplest properties, having a direct relation to the

molecular structure or superstructure in case of multiphase systems and being mainly used forinvestigation of the same. Normally, the determination of storage and loss moduli (G

0, G00(v ))

combining low material and time demand with high precision [8] is used for this purpose. However,

creep and relaxation measurements Ð J (t ) and G(t ) Ð have an important position here [9], givingimproved access to the long-time (low frequency/rate) behaviour of viscoelastic materials.

² Non-linear viscoelasticity, indicating the stress (or strain) sensitivity of material behaviour. Techni-

cally most relevant is the classical determination of the ¯ow curve, forming the base for all simpletypes of ¯ow modelling. The most simple case of steady-state viscosity measurements is the deter-mination of the melt ¯ow rate (MFR) as outlined e.g. by Bremner et al. [10], but for meaningfulvalues a good de®nition of the state of deformation during and even before the measurement is

necessary. Problems in reproducibility and comparability frequently have their origin in a neglectof these in¯uence factors. Also, a differentiation between stress- and strain-controlled measurementsmust be made [11,12]. This has lead to two different philosophies in instrument design with differentstrengths and weaknesses, depending on the nature of the investigated systems.

Other non-linear properties include normal stresses (or normal stress coef®cients) and measures forelasticity. These are mostly relevant in free-surface moulding processes like extrusion, blow moulding orfoaming, and their determination is normally less straightforward. This also puts a practical limitation to

viscoelastic modelling of such processes through the limited availability of the necessary data.Although capillary measurements have lost some importance in recent years, these instruments are

still very valuable for steady-shear investigations at very high shear rates for the determination of melt

fracture phenomena [13] and related effects (sharkskin structure, oscillations and pumping, spurt effect,etc.). Mostly, purely optical detection is used for quantifying these effects, which are effectively limitingthe output rates in all extrusion-type conversion processes. No uniform classi®cation of melt fracture

phenomena can be found for different types of polymers, also because of the signi®cant in¯uence of thepolymer chain structure.

Extensional properties still have a special position in the whole ®eld of melt rheology. Partially, theproblem can be de®ned with `what should we measure Ð what is relevant'; and not even for the normalcase of uniaxial extension a standard measuring procedure is available [14,15]. Depending on whether

somebody wants to determine `pure' rheological properties or rather processing behaviour in technol-ogies with a strong elongational ¯ow component (e.g. ®lm blowing, foaming, coating, etc.) the choice of an `appropriate' measuring technique will have to be different. Details will be discussed in Section 2.2.2.

Generally, the appropriate range of deformation (strain) or load (stress) will have to be used inobtaining the relevant parameters for a given process (see Fig. 2). Also, time dependence and historyeffects have to be considered.




1.3. Application areas

Polyole®ns are nowadays used in practically all application areas of thermoplastics and are processedwith all standard conversion techniques. Despite the fact that they are considered to be `well established'and `well known' materials, a multitude of new grades continuously appearing on the market and having

partially new structural features are demanding special attention [16±18].Moreover, the development of polymeric materials can be seen as a `push±pull-approach'. Both the

input of new knowledge and results from the scienti®c side of the development Ð new catalysts, newpolymers or basic facts on ¯ow or solidi®cation processes Ð and the steady change of the marketsituation Ð through customer demands, general trends or the overall socio-economic situation Ð are

contributing to the speed of evolution.The main types of processing, for which rheological requirements need to be considered, are:

² Extrusion Ð ¯at (cast) ®lm, blown ®lm including biaxially oriented ®lm (BOPP), pipe and pro®le

[19,20]² Extrusion coating and foaming [21]

² Injection moulding [22,23]² Extrusion blow moulding, injection-stretch blow moulding (ISBM) and thermorming [24]

² Fibre spinning [25]

² Special processes like rotomoulding or powder-slush moulding [26,27]

Processing simulations today are still mostly limited to the viscous part of the behaviour of polymer

melts and frequently make use of generalised newtonian models for description (as shortly discussed inSection 2.1). This is certainly not suf®cient in case of free-surface or elongational-¯ow dominatedconversion processes. But even if the full viscoelastic nature of a material is taken into account, the


Fig. 2. Typical viscosity curve of a polyole®n Ð PP-homopolymer, MFR (2308C/2.16 kg) of 8 g/10 min Ð at 2308C with

indication of the shear rate regions of different conversion techniques.



solidi®cation as an integral part of the forming process still remains open. In case of polyole®ns,solidi®cation means crystallisation, which will strongly interact with the ¯ow processes as such. This

will be discussed to some extent in Section 3.3.

2. Single phase systems

The case of single-phase (homogeneous) polymers is the most simple one to be considered. Here, thepolydisperse nature of technical systems characterised by the molar mass distribution (MMD) can be

directly correlated to the viscoelastic behaviour. The only additional factor for these systems is thenature of the polymer chain, its stereostructure and eventual branching, which will strongly affect theperformance.

2.1. Molar mass effects

For a technical polymer, the MMD is a direct result of the statistics of the polymerisation process. Inthe process itself, it results from:

² The nature of the catalyst: Conventional Ziegler/Natta type catalysts [6] have a variety of active siteswith different chemical natures and characteristics regarding hydrogen response, comonomer inser-tion and stereostructure. In contrast, `single-site' like metallocene-based systems [28] have identical

characteristics for each active site, allowing for a much more homogeneous polymer structure. Otheropportunities added by single-site catalysts include the incorporation of a much wider variety of

comonomers (e.g. styrene, conjugated dienes or even polar components) and the unsaturated termi-nation of polymer chains, the consequences of which will be further outlined below.

² Design and operational mode of the polymerisation reactor: Depending on the reactor geometry Ðstirred tank, tubular/loop, ¯uzidised bed etc. Ð and the chosen operating conditions Ð temperature,pressure and ¯ow Ð even identical catalysts will produce different polymers, because of the different

residence time distributions of the system. A totally new range of properties has been opened here justin recent years by the application of supercritical conditions for ole®n polymerisation in the liquidphase.

² Monomer composition and feed mode: Even in single-phase systems, differences in catalyst reactiv-

ities not only affect the chain composition, but also the MMD. Moreover, the variation of the catalystsystem (donor type) and the monomer feed composition in serial reactors allows for the control of

tacticity and comonomer distribution over the MMD. The term `bimodal' is frequently used, althoughtruly bimodal products (i.e. showing two clearly separated peaks in the MMD) are the exceptionrather than the rule. Of equal interest and probably less problematic in its consequence to product

homogeneity (see Section 3.1) is the bimodal distribution of tacticity or comonomer content.

Further changes are possible in post-polymerisation processes. In case of PP, degradation withperoxides in the molten state is normally called `visbreaking' or a `controlled rheology'-(CR)-process[29,30], resulting in polymers with a signi®cantly more narrow molar mass distributions. An example for

a series of PP-homopolymers produced from one base polymer with different peroxide amounts is givenin Table 1 and Fig. 3. Adjusting the ¯owability (MFR) of a certain grade in the CR-process allows one toproduce a reduced number of reactor grades, thus facilitating production and storage logistics as well as




reducing the `transition' quantities produced when changing the grade in the reactor. CR±PP also showsa number of speci®c advantages regarding processability and the ®nal material pro®le in mechanics and

optics. Both the type of peroxide used and the design of extruder used (speci®c energy input andrelaxation time distribution) will tend to de®ne the product properties in detail [29].

In contrast, the peroxide treatment of PE-based systems normally results in branching and cross-linking reactions with an increase of the average molar mass and broadening of the MMD [31]. These

different consequences of radical reactions in the polymer have to be considered when planning oranalysing reactive modi®cation processes [32], which are often involving multiphase systems comprising

both PP-based and PE-based phases. The consequences of this will be further discussed in Section 3.4.2.


Table 1

Degradation series of PP-homopolymers Ð evolution of MMD, rheological and mechanical properties (basic polymer M0 from

standard liquid bulk process, Bis(tert.butylperoxy-isopropyl)benzene Ð DIPP Ð used as peroxide, degradation in COLLIN

50 mm twin-screw extruder at 210±2208C; MMD-data from GPC, MFR ISO 1133 at 2308C/2.16 kg, ¯exural modulus DIN

53452/57, Charpy Impact ISO 179 1 eA Ð V-notch at 1238C; materials as in Ref. [29])

Material cP (wt%) M W (kg mol21) M W / M n MFR

2308C/2.16 kg

(g/10 min)

Flexural mod.

(MPa)

Charpy impact

(kJ m22)

M0 0 766 5.5 0.4 1419 7.5

M1 0.026 453 3.5 3.4 1247 4.7

M2 0.051 318 3.1 8.6 1213 3.9

M3 0.108 231 2.8 28 1208 3.0

M4 0.146 181 2.7 51 1175 2.6

M5 0.175 157 2.7 81 1157 2.4

M6 0.24 135 2.5 149 1150 1.9

Fig. 3. Evolution of the viscosity curve at 2308C (calculated from dynamic test in plate/plate geometry using Cox/Merz-

relation) in the degradation series of Table 1.



Only recently it has been shown that such `buildup'-reactions are also possible and technicallyrelevant for PP. These radical reactions can either be initiated by gamma radiation under vacuum

[34] or by very high peroxide concentrations [34]. As an example, the development of MFR over

time for different peroxide concentrations are given in Fig. 4. While for low concentrations onlydegradation effects are found, the material reacts with chain buildup and viscosity increase at higher

concentrations. Apart from the quantity, also the type and especially the decomposition temperature andvelocity of the applied peroxide have an important effect here. Peroxides with a lower decomposition

temperature becoming active in an earlier stage of the extrusion process are advantageous for buildupreactions.

Moreover, the absence of oxygen as well as the chain structure and crystalline morphology have been

shown to be essential in the radiation initiation of these reactions [34]. In all cases, long chain branchedstructures are created which will be further discussed in Section 2.2.2.

Also for PE, degradation processes are possible [35]. The reaction to free radicals is strongly


Fig. 4. Dependence of the MFR of PP-homopolymer on the decomposition time of a peroxide (Di-tert.butyl-peroxide, DTBP) at

a reaction temperature of 1298C and various concentrations: (1) 4.62; (2) 9.25: (3) 18.5; (4) 37.0; (5) 74.4; (6) 100.0, (7) 139.0

and (8) 200.0 mmol kg21 PP (from Ref. [34]; reprinted with permission of Wiley, 2000).



dependent on the catalyst type. For chromium-based catalysts, branching is normally predominant, whilefor titanium-based catalysts, degradation is more important.

As a result of all these possibilities, the shape and moments of the MMD can be varied over a wide

range. In principle, correlations to all rheological properties are possible from the MMD if all chains arefully linear. Based on a spectral assumption, for a polydisperse polymer, correlations can be setup

between the molar mass of each fraction and the respective relaxation time, but interactions betweenthe different molar mass fractions have to be considered as well. The mathematical formulations

developed for this are called `mixing rules' [1].As an example, one can start with the formulation for Lodge's `rubberlike liquid' Ð model relating

the stress and strain of a viscoelastic substance

s t 2 p11Zt

21

mt 2 t 0C 21

t 0 dt

01

where s stands for the stress in the system, m for the memory function, C 21 for the Finger tensordescribing the state of deformation and the term - p 1 for the isotropic pressure contribution. If thememory function is developed in the usual way of a generalised Maxwell model (with N elements, where

N should allow a density of 1±2 relaxation times per decade), one obtains

mt 2 t 0

X N

i1

gi exp 2t 2 t 0 = t i 2

where gi, t i are the N pairs of relaxation times and strengths of a discrete relaxation time spectrum(RTS). These are connected to the relaxation modulus in the following way:

Gt X N

i1gi exp2t = t i 3

The most simple correlation between rheology and the molar mass distribution (MMD) can be

formulated between M W and the zero shear viscosity h 0 (also valid for the viscosity in dilute solution).Two regions are clearly separated: below the critical molar mass M C a relation of h 0 / M W holds, whileabove M C the proportionality changes to h 0 / M

3;4W : The critical molar mass M C< 2 M E, where M E is the

average molar mass between two entanglements in the system. Based on this it is also possible toestablish a more profound relation between rheology and MMD. Using the above discrete relaxationtime spectrum, the relaxation times can be converted by

t i aM 3;4

i

4

to the average molar masses of a respective number of fractions of the MMD. A closer look however

shows the necessity to take the in¯uence of the environment on every molecule into account; the relationthen changes to

t i; m aM 3;42bi M

bW;m with b < 1; 4 5

Formulations like Eq. (4) are the basis of the so-called mixing rules for the realistic description of polydisperse systems.

In recent years, a multitude of research works has been published dealing with the problem of




interconversion between linear viscoelastic data and the MMD of a polymer. Roughly, these papers canbe split into three categories:

² Development of empirical or semi-theoretical correlations between singular parameters of the linearviscoelasticity Ð like zero shear viscosity h 0, equilibrium compliance J e,0, crossover frequency and

modulus of G 0,G 00 (v ), etc. Ð and parameters of the MMD like weight average M W or polydispersity

M W / M N [36±42]. In some cases, also more general rheological data like the melt ¯ow rate (MFR) areincluded within these considerations [10]. These correlations have a general problem of limited

validity and are restricted to narrow groups of materials only.

² Full-scale interconversions between the MMD and linear viscoelastic curves like G(t ) or G0,G 00(v ),

which make up the majority of work in this area [43±51]. These correlations can also be expanded to

predictions or interpretations of the processing behaviour [25]. A common problem of this secondtype is the fact that the calculation is straightforward only in one direction, i.e. from the MMD to

viscoelasticity. The reverse is an ill-posed problem which allows for the calculation of different forms

of MMDs based on one set of linear viscoelasticity data.² Another independent way of interrelating MMD and rheology data is the application of statistical

methods like multivariate analysis (MVA). With MVA, big data sets like complete MMD- andrheology-curves can be easily interrelated, creating a set of `latent variables'. Although the resulting

equations and related parameters are not necessarily physically meaningful, this method is very wellsuited both in quality control and for the determination of development trends [52,53]. Moreover,other parameters Ð of a mechanical or an analytical nature Ð can be included in the correlation.

The most `popular' parameter correlations are the ones involving the zero shear viscosity, which istheoretically a nice parameter, but dif®cult to determine in case of wide molar mass distributions. An

example from earlier work within our group [42] is given in Fig. 5 for two different series of PP-homopolymers from a commercial process and from a pilot-scale polymerisation, based on 4th


Fig. 5. Correlation between weight average of the MMD and zero shear viscosity for three series of PP-homopolymers of

different origin (K Ð Ziegler/Natta-(ZN)-type catalyst, CR-grade; £ Ð ZN-type catalyst, reactor grade; V Ð Single-site

catalyst); data from Ref. [42].



generation Ziegler/Natta type (ZN) or metallocene catalysts (MC). The zero shear viscosity h 0 wasdetermined from creep measurements, which are advantageous for such measurements in the long time/

low frequency range as has also been demonstrated [54,55]. Other frequently used empirical relations

involve the `crossover'-parameters of the dynamic moduliGC G 0

v C G 00v C and v C 6

which have no clear theoretical basis but are easier to determine. According to Zeichner and Patel [36],v C can be correlated to M W and 1/ GC to the polydispersity M W / M N. The validity of this correlation for

materials with a similar shape of the MMD has been demonstrated several times. In both cases it is easierto predict the average molar mass than the polydispersity.

As a consequence, a number of other parameters have been de®ned over time Ð mostly by industrial

rheologists Ð which are related to the polydispersity. A nice review of several of these parameters hasbeen given by Steeman [40], who used numerically calculated rheological data based on `model-MMDs'to evaluate the applicability and limits of such quantities. While the correlations between M W and h 0 of

the general form

h 0 h K M aW with a 3:2 to 3:6 7

were found to be hardly affected by the polydispersity ( M W / M N) as well as by higher moments of theMMD, no such simple relation could be established for J e,0. Different formulations like

J e;0 2

5

M Z11 M Z

M Wr RT 8

or

J e;0 /

M Z

M W a

9

were tested. Examples of the results are presented in Figs. 6 and 7, where the asymmetry parameter

H M Z = M W = M W = M N 10

was varied and a double-reptation model combined with BSW-parameters [45] was used for calculatingthe linear-viscoelastic material functions from the simulated MMD. As can be seen, none of the appliedformulations allows for a reasonable prediction of the J e,0 value. The same applied for empirical

parameters like the MODSEP-parameter [38], which is calculated from the distance between G 0 and

G00 on the frequency axis like

MODSEP v G0

10:000 Pa = v G00

10:000 Pa 11

Generally no uniform correlation to the MMD polydispersity could be established. This is also true forthe `shear thinning index' (SHI), which was developed in Borealis R and D and is used within ourorganisation as a quality control parameter. The SHI-value can be calculated according to

SHI0 = A h 0 = h Gp

A kPa 12

where the value of A can be 10, 50 or 130 depending on the molar mass area of the polymer in question.Another possible way to determine MMD-related parameters is the application of generalised

Newtonian ¯ow models for the viscosity curve h (g 0). One example is the generalised Carreau or




Carreau±Yasuda model [37] of the form

h g 0 h 011 lg Bn2 1 = B 13

where h 0 is the zero shear viscosity,l the characteristic relaxation time, n the power law Ð index, and B

is the transition parameter for which both h 0 and l can be correlated to M W, while B can be correlated to

the polydispersity [37].


Fig. 7. Steady-state compliance of model polymers plotted as a function of M z / M W; the solid curve indicates the dependence

proposed by Kurata (from Ref. [40]; reprinted with permission of Steinkopff Verlag, 2000).

Fig. 6. Steady-state compliance of model polymers plotted as a function of M z11 M z / M W M n; the straight line indicates the

dependence proposed by Ferry (from Ref. [40]; reprinted with permission of Steinkopff Verlag, 2000).



The present status of full-scale interconversions is somewhat hard to judge, as the number of papers

and even theories proposed is in contrast to the efforts taken to experimentally verify the theories. Anexample for the possibility to calculate linear-viscoelastic data from the MMD Ð taken from a work by

Carrot et al. [49]Ð is given in Fig. 8. In this paper, a series of 10 different polypropylenes covering acertain range of M W and polydispersity was investigated both rheologically and with GPC, combining

the obtained data with the double reptation model, for which the ®rst part of the relaxation modulus of apolydisperse sample composed of N types of different species with relaxation times t i and corresponding

weight fractions W i can be expressed as

G N t G0N

Xi

X j

W iW jF 1 = 2

t ; t iF 1 = 2

t ; t j 14

in case that both M i and M j are higher than M C. In this case, the running index i denotes the relaxing chain

and j the environment; it represents the effective contribution of chain entanglements. F is a functionallowing to reach G N t G

0 N (plateau modulus) for small values of t . The part of the polymer with

molar mass below M C can additionally be represented by a Rouse spectrum such as

G Rt p 2

6M eG

0N Xi

W i

M i

F t ; t i" # 15

In this case, the relaxation time of the fraction remains unchanged by the environment. The third partof the system are the chains between entanglements and the can also be formulated in a Rouse spectrum

as

GEt p 2

6M eG

0N

Xi

W iF t ; t ee

" #16

where t ee is the theoretical relaxation time of a chain of length M e. The three contributions can then be


Fig. 8. Dynamic moduli of a PP-homopolymer (reactor grade; M W 165 kg mol21; M N 25:1 kg mol21

; M W = M N 6:6) at

1858C from experiments Ð A storage and W loss modulus Ð and calculated from full spectrum (full line) and reducedspectrum (dashed line) using the double reptation concept (from Ref. [49]; reprinted with permission of Wiley, 2000).



summed up to give

Gt G N t 1GEt 1G Rt 17

Based on these equations and some basic data for the polymer Ð namely M e and G0

N Ð the MMD asdetermined by GPC can be converted to a relaxation spectrum with a high number of modes and, ®nally,into linear viscoelastic material functions like G(t ) or G

0,G 00 (v ). As Carrot et al. [49] shows, this can begreatly facilitated by reducing the number of modes used for the actual conversion without losing too

much information. The actual comparison between calculation and measurement in Fig. 8 shows,however, the problem of a conversion in this direction as a deviation in the low frequency region.

This is caused by the limited sensitivity of GPC at high molar masses. Consequently, the precision of these calculations tends to increase with reduced M W and polydispersities.

In any case, most correlations are presently limited to shear ¯ow. It has however also been demon-strated that extremely wide or bimodal MMDs are also re¯ected in the behaviour under extensional ¯ow

[19,56]. Strain hardening effects Ð which will be discussed in Section 2.2.2 Ð can appear for such

materials, signi®cantly improving their processability for example in ®lm blowing [57] and blowmolding [58]. Non-linear formulations like varietes of the K-BKZ form

s t 2 p11Zt

21

mt 2 t 0hl1; l2C 21t 0 dt 0 18

with p 1 again denoting the isotropic pressure contribution, m the purely time-dependent memory

function, h the damping function depending on deformation and deformation rate and C 21 the Finger

tensor used as a deformation measure, have to be used here. In addition to determining the time

dependent component of the material behaviour (m(t 2 t 0) or g(t ), relaxation time spectrum), thedeformation dependent component (h, damping function) also has to be determined.

In addition the continuum approach needs to be replaced by a type of element modelling like theFEM-calculation, taking into account the various strain histories of different segments of the movingmelt.

Apart from the purely rheological and processing behaviour [59], changes in the MMD always havesome `side effects', which are of relevance for the mechanical and optical properties of the polymers.Examples for the case of PE are given by Shroff et al. [60] and by Jordens et al. [41], for PP byTzoganakis et al. [61] and by Bailey and Varrall [62].

The concept of `tie molecules' is essential to the work of Huang and Brown [63], who demonstrated asigni®cant improvement in the slow crack growth dependence on the MMD shape and especially on the

presence of high molar mass fractions. For linear PE grades with very high toughness requirements,however, the amount and distribution of comonomer plays an even bigger role for the ®nal properties

[64]. Single-site catalysts allow for an improved design of polymer properties by controlling thecomonomer incorporation over the MMD for PE or the tacticity distribution for PP.

Another good example is the effect of the MMD on the mechanics for PP-homopolymers, which can

be explained by differences in the crystallisation behaviour in¯uenced in turn by the MMD. An increasein the polydispersity does not only lead to an increased nucleation density in quiescent crystallisation[65], but also to enhancement of strain-induced structure development [66,67]. Details of this effect will

be discussed in Section 3.3. It must however be clearly stated that such correlations are practically neveruniversal. MC-based PP-grades for example, which have been shown to require signi®cantly differentmachine settings in conversion processes [68] do not ®t into this picture because of their reduced




tacticities and the fact that MMD-measurements do not necessarily account for very small fractions of

high molar masses [69]. The general dependence of the nucleation density on the polydispersity ispresented in Fig. 9, from which the effect of long-chain molecules acting as nuclei on crystallisation

is re¯ected in an increase of N C with M W / M N.From both examples it becomes clear that polyole®ns with a wide or even bimodal MMD can be

advantageous with respect to both processing behaviour and end-use properties, leading to importantdevelopments in this direction [70]. A possible problem in the technical production of such materials is,

however, inhomogeneity induced by the presence of high- and low-viscosity fractions. This will bediscussed in Section 3.1.

2.2. Chain structure effects

A closer look at the structures of polymers shows us that there are actually two levels or dimensions of `structure'. For a given polymer, the local chain structure can be affected by the stereochemistry Ðwherever it is relevant, e.g. for PP and PB-1 Ð and by comonomers forming zones of higher ¯exibility

in the chain Ð like ethylene in PP Ð or very short side chains Ð like butene in PE. The global structureor topology, which affects rheological behaviour to a greater extent, is determined mainly by chainbranching. Normally, chains with local structural disturbances are still considered to be linear, although

their viscoelastic behaviours may be signi®cantly altered.

2.2.1. Linear chains

Copolymerisation is used to control the mechanical and optical properties of polyole®ns for matchingcustomers' requirements. In the case of a purely random incorporation and distribution of the comono-mer, (which is mainly achieved at low concentrations) the system remains single-phase. Apart from the

amount of comonomer, the catalyst and process type will also determine the transition from this simplecase to the more complex case of heterophasic copolymers which will be discussed later in Section 3.4.2.

For polyethlyene, where stereochemistry does not play any role, the local structure is only affected by


Fig. 9. In¯uence of the polydispersity M W / M N of PP-homopolymers based on Ziegler/Natta type catalysts on the nucleationdensity N c at 1108C showing the nucleating effect of high molar mass fractions; data from Ref. [69].



copolymers acting as very short chain branches. The effect of comonomers on rheology in case of

LLDPE-type polymers has been investigated several times [19,62,71]. It appears that while the como-nomer has a certain effect on rheology Ð especially on the relation between MMD and viscoelasticity

Ð signi®cant changes like the appearance of strain hardening are only found in case of long side chains(. M C), which appear frequently with the use of single-site catalysts [4,72] and are even favored onpurpose to improve the processability of such materials [73]. Such materials are directed at applicationareas presently covered by LLDPE/LDPE-blends [74,75] because of melt strength requirements, e.g. inthe blow molding of large containers or ®lm blowing.

For polymers with stereospeci®ty, tacticity effects have to be considered alongside with comonomerinsertions. In case of isotactic, atactic and syndiotactic PP produced with metallocene catalysts, separate

relations between M W and h 0 as well as other pairs of MMD- and rheology-parameters were found fordifferent degrees of tacticity by Friedrich [18,76,77]. The measurements, which were carried out in a

combination of creep and dynamic tests to cover a wide time/frequency-range, showed changes in theactivation energies (E 1a-values were found to be 31 kJ mol21 for iPP and 57 kJ mol21 for MC-based

sPP), the h 0 / M W-relation (see Fig. 10) the plateau modulus and even the entanglement molar mass ( M E).An explanation can be given based on the Rouse model. If sPP has a different and more `bulky' chainconformation (predominant all-trans) in the melt, this will change both the effective tube diameter andfriction factor of the system, leading to a higher relaxation time for molecules with identical length.

2.2.2. Branched chains

Polymers with long-chain branching (LCB polymers) exhibit a completely different rheologicalbehaviour, which has only recently been formulated for the ®rst time in a consistent viscoelasticmodel. The `pom±pom'-model developed by Mc Leish and Larson [78] is based on a phased reptation


Fig. 10. Zero shear viscosity h 0 versus weight average molar mass M W in a log/log-plot for syndiotactic PP (A) and isotactic PP

(X); note the identical slope but different position of the line ®ts (from Ref. [77]; reprinted with permission of VCH Wiley,

2000).



process of the side- and backbone-chains of the system and has meanwhile also been applied for the

description of technical LDPE [79,80].The assumption of this model is a mixture of pom±pom molecules consisting of a backbone and a

number of q. 1 dangling arms at each end (for q 2; an H-structure is reached). A system consisting of such molecules will have two timescales of relaxation, the shorter one resulting from the relaxation of

the dangling arms alone having an effective relaxation time of

t a x t 0exp15

4sa

12 x2

22 12 f b

12 x3

3

" #with Sa M a = M e 19

where t 0 is the relaxation time for a fully retracted arm, x is the relaxing arm fraction, M a the molar massof each arm and f b the backbone fraction of the system. The second, longer contribution results from therelaxation of the backbone part, for which the relaxation time can be calculated as

t b 4

p 2s

2bf bt a0q with Sb M b = M e 20

where M b is the molar mass of the backbone. Based on this, a constitutive equation for a polymer

consisting of such molecules can be constructed [78].In a recent paper by Inkson et al. [80], the model performance has been checked against the behaviour

of different LDPE types, where data for shear and extensional viscosity were taken into account. An

example including three different deformation types is given in Fig. 11. The good accordance betweenmodel calculations and measured results was achieved for a very limited number of `modes', i.e.different molecular species.

Apart from a change in the viscosity curve and the linear-viscoelastic behaviour in shear, which isschematically presented in Fig. 12, the material's behaviour in extensional ¯ow is altered completely.In a transient experiment, strain hardening effects are observed resulting from an increased resistance of


Fig. 11. Transient uniaxial extensional, planar extensional and shear viscosity of an 11-mode pom-pom melt in start-up plotted

against measurement results for `IUPAC X' LDPE, shear/elongation rate 0.01 s21 and temperature 1408C (from Ref. [79],

reprinted with permission of The Society of Rheology Inc., 2000).



the material to disentanglement. For some types of conversion such as ®lm blowing, the blow mouldingof large containers, foaming etc. this is of great importance for processing behaviour. The extent and

strain dependence of this effect is determined by both composition and branching distribution effects[5,75,81,82].

Moreover, LCB polymers normally show a distinct dependence on their ¯ow histories. Technically

this is used for the shear modi®cation of LDPE, but it can also occur as a processing problem, forexample in the foaming of PP with long chain branching (LCB-PP). Various model assumptions have

been made for this process which is especially characterised by its reversibility and its drastic conse-quences on the processing behaviour [83±85].

An example of the effect is given in Fig. 13 for a modi®ed polypropylene with long-chain branches.

These investigations were initiated in the course of developing PP with high melt strength (HMS-PP) fordetermining the effect of different processing conditions on the material performance. For this purpose,the Rheotens-setup, which will be described in some detail below, was combined with a feed extruder

and a melt pump including a bypass valve, allowing the maintenance of a constant die velocity whilevarying the shear energy input in the extruder. This combination had originally been proposed by

Wagner for allowing a rheologically meaningful evaluation of Rheotens results.

The materials were extruded at extrusion pressures between 20 and 300 bar; the strands coming out of the die of the extruder were collected for the further investigations. Rheological investigations donebefore and after the extrusion were: Rheotens experiments at an acceleration of 120 mm s22, creep andoscillatory experiments. Additionally, the molar mass distribution was examined before and after the

extrusion by GPC in order to see whether mechanical scission of chains occurred in the extruder. As Fig.13 shows for the case of an LCB-PP, the melt strength decreases dramatically with the extrusionpressure, while drawability remains rather constant. While no signi®cant effect of this treatmentcould be seen in the dynamic moduli, the creep measurement resulted in a change of the equilibrium

compliance J e,0 which proved to be fully reversible upon dissolution in hot xylene and solvent evaporation.


Fig. 12. Schematic presentation of the change of the viscosity curve and the storage modulus with long chain branching; linear

polymer Ð solid lines, LCB polymer Ð dashed lines.



The changes in rheological behaviour caused by extrusion occur without any change in the molar massdistribution; that means that no chains are cut by this process. Similar effects were found for LDPE,

while no changes appeared for a linear PP and only marginal changes for a bimodal HDPE.The changes induced by this `shear modi®cation' can also be seen in the die swell, as shown in Fig. 14.

For this investigation by Rokudai [83], a technical LDPE sample (over-stabilised with antioxidant) wassheared intensely in a Brabender twin-blade kneader for different times and then tested in a capillary

rheometre recording especially the die swell. Performing this operation at a lower melt temperature reduced

the effect; by dissolution in hotxylene and evaporation of the solvent theeffect could be reverted completely.Technically, this process can be used for improving processing behaviour [86] and product quality, espe-

cially surface smoothness and transparency. The reduction of the melt elasticity leads to a higher criticalshear stress and less melt fracture, allowing for an output increase in conversion processes.

In general, various processing effects are induced by LCB. For example, the reduction of melt fracture


Fig. 14. Effect of shearing in a twin-blade kneader on the melt elasticity (die swell) of an LDPE melt (MFR 1908C/5 kg 8.1 g/

10 min; density 0.914 g cm23); 0 Ð Brabender shearing at 1308C, D Ð Brabender shearing at 1908C, ®lled symbols represent

materials after solvent treatment (from Ref. [83]; reprinted with permission of Wiley, 2000).

Fig. 13. Effect of pre-shearing in the feed extruder on the melt strength (Rheotens curve) of a chemically modi®ed PP with

long-chain branching (n 0:15 per 1000 C).



[2] by addition of LCB fractions to otherwise linear polymers has been shown for PE [87] and PP [13];the effects are however not identical for both polymers. Apart from the fact that the MMD plays an

identically important role in de®ning the sensitivity of a certain material to melt fracture as the degree of branching, the relation is not a linear one. While a certain amount of melt elasticity (secured by M W / polydispersity and/or branching) appears to be required for stable extrusion, too much melt elasticitybecomes detrimental again. This has initiated attempts like the use of hyperbranched processing aids

[88] to boost the upper limit of processing speed in ®lm extrusion. Such rather expensive solutions willhowever have to compete with other technical approaches like die coating or the addition of ¯uorinated

polymers as processing aids (at least the latter one is a well-established method in the case of HDPE).Also the behaviour in ®bre spinning [89] and the stability in ®lm blowing [5] can be improved, both

due to a strong elongational ¯ow component in the process. In case of PP, LCB also leads to a signi®cantincrease of the nucleation density and, consequently, to a higher crystallisation temperature of the

materials.LDPE can be considered as the `classical' LCB material because of its long and widespread applica-tion for a variety of purposes. A good deal of the popularity of this material results from its uncompli-cated behaviour in ®lm blowing which is a result of its molecular structure. Due to the purely statisticalcreation of side chains in the high-pressure radical polymerisation process, it has a very complex

structure and the problem of a well-de®ned production as well as the characterisation of the resultingproduct has been addressed frequently in recent years [90±92]. Branching effects are in principle also

recognised in shear ¯ow [93], where LCBs lead to an increased slope of the viscosity curve at compar-able MMDs (see Fig. 12). Such measurements and also conventional dynamic rheometry can be used for

the determination of the activation energy from the zero shear viscosity or shift factor values, demon-strating a signi®cantly higher temperature dependence of the viscoelastic material functions for

branched systems. As Table 2, in which shift factors (aT ) and activation energies calculated from anArrhenius-type temperature dependence

aT ek T 2T 0 with k E a = R 21

clearly shows, this is equally true for PE and PP.

As mentioned before, LLDPE-grades based on metallocene (MC)- or single-site-catalysts can alsoshow a certain extent of LCB. This is a side-effect of MC catalysts, which are able to incorporate vinylterminated chains as comonomers. In industry, this has been recognised as a possible way to improve the


Table 2

Shift factors for time/temperature superposition determined from dynamic moduli measurements in plate/plate-geometry and

activation energies calculated from an Arrhenius plot (LCB-PP Ð Daploy HMS 130D, LDPE Ð Daplen 1840 D, HDPE Ð

Daplen BF 5272 bimod, PP Ð Daplen BE 50)

LCB-PP LDPE HDPE PP

T (8C) aT T (8C) aT T (8C) aT T (8C) aT

260 0.484 210 0.676 210 0.890 240 0.657

230 1.000 200 1.000 200 1.000 220 1.000

200 2.155 190 1.480 190 1.191 200 1.504

E a 52.2 kJ mol21 E a 72.9 kJ mol21 E a 27.1 kJ mol21 Ea 41.8 kJ mol21



processing behaviour of these narrow MMD materials [5,73,94,95]. The catalyst system used as well as

the polymerisation conditions play an important role in the amount of LCB reached in the ®nal product.An example comparing two different MC-LLDPEs with and witout LCBs as a result of the used

catalyst to LDPE is given in Fig. 15. In a comparative study [72,95] several different single-site(metallocene) catalysts were used for producing LLDPEs with hexene-1 as a comonomer. While theactual comonomer content dominating the density of the resulting materials was found to have very little

effect on the rheology, the catalyst type determined whether predominantly linear or branched structureswere produced. In Fig. 15, the measuring results of a MuÈndstedt-setup (see below for explanation) aregiven for one product each of [n-but-Cp]2ZrCl2 (Cat. 2, NP5) and a siloxy-substituted derivative of

Et(Ind)2ZrCl2 (Cat. 4, NP1), both in combination with MAO. In addition to the strain hardening effectfound for some of the products, the branched structure of these materials was also proven by determina-

tion of the activation energy and in combined GPC/viscometry measurements.

In contrast to PE, there is presently no published way to produce PP with a branched structure directlyin the reactor. LCB- or high melt strength Ð PP (HMS-PP) is therefore produced by post-reactormodi®cation with various techniques [96,97]. Technical processes today combine the creation of radi-cals by irradiation or the addition of peroxides with a local crosslinking step, with our without the

application of a bifunctional crosslinking agent. The absence of oxygen is very important in this process,as has been shown in other circumstances [33,34] in Section 2.1.

As the formation of gels must be avoided, the achieved degrees of branching are signi®cantly smallercompared to LDPE, which is already obvious from the differences in E a between the respective linear

and branched materials in Table 2. The altered rheological properties of this material [98,99] lead to


Fig. 15. Time dependence of the elongational viscosity in uniaxial extension at 150 8C for two single-site based LLDPEs (see

text for explanation) in comparison to a conventional LDPE (materials as in Ref. [95]).



important changes in the processing behaviour. While foam production was originally the main target of this development [100], the possibilities of melt strength improvement, also in mixtures of linear and

LCB-PP are meanwhile being recognised in other areas as well [101,102]. An example comparing

differently produced HMS-PP grades is given in Fig. 16; the three differently modi®ed materials arebased on the same linear PP-homopolymer [97]. According to this study by Sugimoto et al., the

application of ionising radiation and peroxide treatment leads to different branching structures, whichhowever exhibit very similar strain hardening behaviours. Generally, branching occurs mostly in the

high molar mass fractions of the polymer, with the potential danger of the formation of crosslinkedparticles (permanent gels).

In contrast to linear polymers, where linear-viscoelastic techniques are a well established experimen-

tal base for rheological characterisation, this cannot be said yet for branched systems. Some of the mostimportant rheological characterisation techniques for LCB will therefore be outlined here below:

X Rheotens-test . This setup copies industrial spinning and extrusion processes. In principle (see Fig.17) a melt is pressed or extruded through a round die and the resulting thread is hauled off. The stress on

the extrudate is recorded as a function of melt properties and measuring parameters (especially the ratiobetween output and haul-off speed, practically a measure for the extension rate). The method can be used

for a wide variety of materials, but it has some principal problems, which may be separated into twocategories: (a) ¯ow geometry of the spinning process, and (b) problems of thermal equilibrium.Concerning (a) it has to be said that the spinning experiment is a non-stationary test. Even if for each


Fig. 16. Time dependence of the elongational viscosity in uniaxial extension at 1808C for an unmodi®ed (linear) PP (D) and

three differently modi®ed LCB-PPs produced by ionising radiation (B, C) and peroxide addition (E) with different branching

degrees (from Ref. [97]; reprinted with permission of Wiley, 2000).



extension rate a steady state with constant shape of the extrudate can be reached, the ¯uid elements are

not necessarily in equilibrium as a consequence of their deformation prehistories. As the effect of molecular orientations plays a major role on rheology, the measurement is not only in¯uenced by the

intentional parameters Ð die diameter, output rate haul-off speed Ð but also by the prehistory of themelt. With this, the results of the measurement

e 0 2pv Rw = H ln 8pv Rw = DR 22

and

s E lF = p R2 v 8 RwF = R

3 D 23

where R is the die diameter, H the distance between die exit and takeup point (extrudate length), RW the

diameter of takeup-wheels, v the rpm of takeup-wheels D the apparent (wall) shear rate in the die, and F

is the takeup-force (extrudate stress) can be used for calculating h E s E = e 0 only within limits [103]. A

time dependence of the quantities can hardly be investigated. Moreover one obtains average valuesacross the whole length of extrudate, in which the extension rate and therefore also the extensional

viscosity vary over a wide range. Regarding (b) it is clear that this is no isothermal experiment, and thatonly for the case of high haul-off speed is extrudate at nearly the same temperature as the material in thereservoir (where the measuring temperature is normally determined. This problem of thermal equili-

brium is slightly reduced by weak heat transfer between the surrounding air and the polymer melt. Insemicrystalline polymers it must furthermore be considered that high overall extensions accelerate thecrystallisation process, thereby in¯uencing the mechanical properties of the `melt'.

Details about a rheologically meaningful evaluation of this test, which have been developed inwagners group can be found in the literature [104]. The combination of single run results obtained atdifferent die geometries into so-called `grand master curves' allows for the calculation of apparent


Fig. 17. Schematic presentation of the Rheotens setup (left) and the Meissner setup in the original form (right) for determination

of elongational properties of polymer melts.



elongational viscosities. A curve example is given in Fig. 18. Note the dependence of the die exitvelocity, which is in accordance with the pre-shear effects discussed before.

X Meissner-setup [105,106]. In this setup, one tries to approach the ideal assumption of an in®nitesample extended at constant rate while overcoming the problem of sample ®xation with ®xed clamps,

which can cause local damage and premature break of the sample in the clamping region. This problem

was ®nally solved in the mobile clamping device developed by Meissner (see also Fig. 17). The sample¯oats on an oil bath (silicone oil), which also facilitates temperature adjustment, but may create

problems through oil absorbed by the sample, thus changing its properties. In the latest developmentof Meissner's apparatus the bath was therefore substituted by a cushion of nitrogen gas emerging from aporous surface.

Even here, one problem remains: the relation between extensional rate and speed of extension. As thesample thickness decreases, reaching e 0 const: requires a logarithmically increasing speed of exten-sion. This makes a wide RPM-range of the drive elements necessary, even more complicated in connec-

tion with suspension elements which must allow a precise stress measurement. All in all, high values of total extension and especially stationary terminal values appear to be hard to reach. Great care must

furthermore be taken in sample preparation as only a homogeneous and isotropic samples can guarantee

representative results.X Laun/MuÈ ndstedt-setup [9,107]. While using the same sample geometry as the Meissner setup, the

®xation problem is overcome here by pasting the sample ends to ¯at carrier plates avoiding any damagein this way. The geometry is operated with verital samples, reducing suspension problems but also

limiting the applicable temperature range. As a possible way around the speed dilemma mentionedbefore, creep-type measurements (constant stress applied) can be used. In thus way, stationarity of theextension test is achieved much faster.

XConverging ¯ow analysis [14,15]. In this technique, which is also called the `Cogswell-method', the

pressure drop in the in¯ow zone of a capillary rheometre is used for calculating extensional properties of


Fig. 18. Apparent elongational viscosity h (g 0) of LDPE A 18 as calculated from Rheotens mastercurves for different die exit

velocities v0 at T 1908C; comparison to shear velocity h (g 0) (from Ref. [104], reprinted with permission of The Society of

Rheology Inc., 2000).



polymer melts. Assumptions of the shear/extension rate dependence of shear and extensional viscosity

as well as ®rst normal stress coef®cient C 1 are required for being able to do this calculation and thegeometry of the entry zone is important. The comparability to other methods is not good [14]; the results

are only suitable for comparing similar materials.

X Opposed jet setup [92]. This measuring geometry was originally developed for low viscosity ¯uids

like spinning solutions and only later adapted for polymer melts. In this geometry, two deformationmodes are possible: With a peripheral in¯ow and out¯ow through a pair of opposed dies, a uniaxial

extensional ¯ow in the stagnation point in the centre is reached, while with an in¯ow through the dies abiaxial extensional ¯ow in the midplane vertical to the die axis develops. Apart from the constructivesolution, the development of a mathematical procedure for evaluation was decisive. The main disad-vantage of the system is the fact that in principle only steady-state measurements are possible. Startupeffects can be detected only approximately. As an example, a comparison of steady state shear- and

extensional viscosity for a PP melt (MFR (2308C/2.16 kg) 0.4 g/10 min) is presented in Fig. 19.

X Apart from these measurements of extensional viscosity, LCB-structures can also be investigated

indirectly via linear region measurements in oscillation, relaxation or creep [108,109].In any case, the results can be correlated to processability, mainly for processes with a high elonga-

tional component in ¯ow like ®lm blowing [106], foaming [100], ®bre spinning or paper coating, butalso for the secondary stage of blow molding and ISBM and special cases of injection molding.

2.2.3. Partially crosslinked chains

As mentioned before (see Section 2.1), radical reactions are frequently used in the post-polymerisa-

tion modi®cation of polyole®ns. Partial crosslinking of a thermoplastic material can be technicallyinteresting for various reasons, from creating melt strength for processing behaviour over reachingrubberlike elasticity to an improvement of the heat de¯ection temperature.

In principle, the changes of rheological behaviour with the degree of crosslinking can be seencompletely only in a parallel measurement of viscous and elastic parameters of the system. A decisivepoint in the network evolution is the gel point [110], from which onward the material shows predominantly


Fig. 19. Stationary viscosity in shear and extension for PP homopolymer (Daplen BE 50, MFR 230 8C/2.16 kg 0.4 g/10 min)

at 2308C (h calculated from dynamical data, h E from stagnation point Ð apparatus as described in detail in Ref. [92]).



solid-like behaviour (see Fig. 20). For materials where thermoplastic processing is required, higher

degrees of crosslinking are not relevant.An example in the area of polyole®ns where high crosslinking densities are of interest are EPR- and

EPDM-elastomers. Elastomers normally have their own kinds of rheologies, especially if the materials

have a further tendency to react and crosslink in the molten phase. A frequently used quantity to de®nethe viscosity of elastomeric materials is the Mooney-viscosity which is determined in a plate/plate setup

at a given time after heating up from room temperature and therefore combines melting and possiblecrosslinking effects in one result.

These materials are hardly ever used in pure form; much more relevant is the behaviour in hetero-

phasic systems [111±113], which will be treated in more detail in Section 3.4. An example for the effectof a partially crosslinked EPDM dispersed in a PP matrix is given in Fig. 21, where the reduction of thein¯uence of the disperse phase on the system rheology with increasing shear stress (and rate) is quite

obvious.

3. Multiphase systems

Multiphase systems combining the properties of two structurally different materials are highly rele-vant for a number of different technical applications of polymers. Especially for PP, these systems allow

a widening of the property range by combining the advantages of the various phases [114,115]. Forexample, most high-impact materials are heterophasic, normally creating problems for optical propertieslike transparency and even surface gloss [116]. Multiphase structures can be created in various ways,

both in the polymerisation step and during post-polymerisation modi®cation as will be shown below.What makes these systems even more interesting from the rheologist's point of view is the interaction

between morphology and rheology: The component rheology determines the developed morphology,

which in turn affects the system rheology and also Ð technically most relevant Ð the mechanical andoptical end-use properties. The subsequent investigation must also account for the sensitivity of suchstructures to various probing techniques, especially to deformation.


Fig. 20. Schematic plot of steady shear viscosity h and equilibrium modulus G1 of a crosslinking polymer, t c indicates the time

of the gel point (based on information from Ref. [110]).



3.1. Inhomogeneous products

The special advantages of polyole®ns with broad or bimodal MMD values have been mentioned

before. Such materials are desirable both for their better processabilities [57] and for their end-useproperties [117] in different areas. As was outlined in Section 2.1, bimodal MMDs can lead to strain-

hardening behaviour and offer mechanical advantages due to the presence of very high molar massfractions.

One problem with these products is, however, the potential danger of inhomogeneities within the

material even in case of an identical chemical composition of both high and low molar mass fractions(e.g. homopolymer). Despite the fact that in the polymerisation step, both fractions are created on thesame catalyst particles, only in serial reactors with different hydrogen contents has, it been found that not

even the polymer powder shows a homogeneous distribution of molar masses over the particles. Thismay be due to the multi-site nature of the still mostly used ZN-type catalysts and can possibly be

overcome in case of single-site polymerisations. In any case, the subsequent pelletisation in a twin-

screw extruder is not always suf®cient to render the material homogeneous after production due to themassive viscosity differences of the fractions (remember: a scaling law with a power of 3±4 appliesbetween molar mass and viscosity!).

Such inhomogeneity effects can be clearly seen in the rheological behaviour [8], as Fig. 22 shows for

the case of bimodal PP-homopolymer. While a molten powder is still pretty inhomogeneous and has arather low overall viscosity due to a dispersion of the high molar mass domains in a low molar mass melt, thesame material has a higher viscosityafter homogenisation in a twin-screw extruder with two sets of kneading

blocks. In this particular case, the dispersion has an additional effect of increasing Tc in the DSC experimentby nearly 4 K, pointing to the nucleating ability of high molar mass tail mentioned in Section 2.1 [69].


Fig. 21. Composition dependence of the melt viscosity h of PP/EPDM (PPB) blends as determined in a capillary rheometre at

2008C and a ratio of length/diameter of 20; the wall shear stress t W is: (A) 14 £ 104, (B) 18 £ 104, (C) 20 £ 104 and (D)

22 £ 104 Nm22 (from Ref. [111], reprinted with permission of Elsevier Scienti®c, 2000).



Other negative effects of inhomogeneity include processing problems like surface distortion and even

melt fracture [17,118] as well as a signi®cant deterioration of the mechanical and optical performance of these products [119,120]. An important practical aspect is the fact that inhomogeneity can be seen as one

of the main reasons for the appearance of so-called `gels' in both PE- and PP-®lms [121,122]. From theoriginal de®nition, these are formed by high molar mass or even crosslinked parts (from Latin `gelare').

Generally, however, a differentiation of practically appearing gels by their underlying origins is neces-sary. Inhomogeneities called `gels' in practice can result from the polymer itself, from decompositionproducts and from non-polymeric impurities. These can for example be additive agglomerates or dirtparticles from the production environment (like cellulose ®bres from bags etc.).

Another example for the efforts necessary to achieve homogeneity in a polymer with wide MMD is

given in Fig. 23. Here the dissolution of high molar mass domains (polymer-based gels) in case of abimodal HDPE is shown during homogenisation in a Brabender-type two-paddle kneader, where

samples were taken out at different time intervals to check for homogeneities with light microscopy.It can be clearly seen that only after going through a maximum in energy uptake is homogeneity

achieved. Taking these results for reactor-based systems (where high and low molar masses are alreadydistributed in the primary particles), it can be easily understood how complicated it is to achieve

extruder-based mixtures with signi®cant viscosity differences between the respective components!

3.2. Filled and reinforced polyole®ns

The main targets of ®lling and reinforcing polyole®ns are twofold: improving the mechanical proper-ties, mainly stiffness (modulus) and heat de¯ection temperature, and Ð in case of mineral ®llers and

inexpensive organic ®llers mostly Ð also reducing the overall cost of the material [123]. In recent years,the second target has so lost importance due to the pressure towards weight reduction, especially in thecase of technical applications.


Fig. 22. Homogenisation effect on storage modulus G 0 (o ) and complex viscosity h p ( 0), both from plate/plate geometry at

2308C, of bimodal PP-homopolymer grade; open symbols refer to compressed powder sample, ®lled symbols to compounded

sample.



There is a wide variety of ®llers and reinforcing ®bres presently used for the modi®cation of PP and

(less frequently) PE, which can be categorised as follows [124,125]:

² Mineral ®llers Ð talc, calcium carbonate, kaolin, wollastonite, mica, barium sulphate, etc.² Natural organic ®llers Ð ®bres of wood, hemp, jute, ¯ax, etc.

²

Synthetic organic ®llers Ð ®bres of cellulose and fully synthetic polymers like polyester or aramide,carbon ®bres² Glass and other mineral-based ®bres

² Fillers with special purposes Ð iron oxide (magnetism), collodial silver (antibacterial), etc.

In a broad sense, also carbon black and other particulate pigments can be included into this group of substances, although they are hardly ever present in the material in quantities suf®cient to change the

rheological behaviour of the material.Relevant parameters of ®llers/®bres are particle size and size distribution, the shape factor (length/

diameter Ð ratio), matrix adhesion, stability against or tendency towards agglomeration, hydrophilic orhydrophobic natures, the surface polarity and ®nally the purity (mainly with respect to the absence of

metal ions catalysing polymer degradation like iron or copper) of the ®ller. Furthermore, the effects of additives and processing aids [126,127] have to be considered which can contribute strongly to thedispersion quality (examples of substances used frequently for this purpose are glycerin-monostearate

and calcium stearate, both amphiphilic in nature).Another set of relevant parameters comes from mixing and compounding operations. The importance

of a proper selection of mixing equipment and components is given for example in a review by Todd

[128], who stresses the importance of adapting the applied compounding system to the respective task.The fact that the degree of dispersion additionally affects the rheological properties of a system [129]allows us to use this property change for an assessment of product quality without the necessity for


Fig. 23. Homogenisation of a bimodal HDPE in a twin-blade kneader (Brabender Plasticorder); torque curve over time and

optical micrographs (magni®cation 100 £ ) of samples taken at different mixing times.



mechanical testing (as will be outlined further below). However, it also makes the system behaviour lesspredictable. Compounds are similar to blends discussed in the following sections.

The rheological consequences of ®ller addition are most simple for the Newtonian case, where the

viscosity increase can easily be formulated according to Einstein:h h s11 2; 5f 24

for the dilute case, where h s is the viscosity of the suspending liquid and f is the volume content of solids. It is obvious that in this equation neither shape nor size of the dispersed particles are re¯ected.Any expansion for higher ®ller concentrations will need to consider this. An example is the Krieger±

Dougherty equation for the case of spherical particles which reads

h h s11f = f m2h f m

25

with f m being the maximum packing fraction and [h ] is the intrinsic viscosity.

In case of viscoelastic systems, the situation is much more complex. The addition of ®llers here leadsto a change in the relaxation time spectrum with an addition of long relaxation times resulting fromparticle-matrix- and particle±particle interactions. In a dynamic-mechanical test this is re¯ected in a

plateau development of the storage modulus at low frequencies, similar to network development incrosslinking. The extent of this change is affected by all of the above mentioned factors [130±133]. It has

also been described as the development of a yield stress, for which case the stress in shear ¯ow can bewritten as

s 12 h _g Y

11 4 = 3t 2eff _g 2

q 1 f f G0t eff _g 26

with

t eff t 0

11 at 0 _g 27

where Y is the yield stress level, G0 the modulus and t 0 is the characteristic relaxation time of the un®lled

system and f (f ) a function describing the modulus change by ®lling the polymer with non-interactingspheres. What makes this formulation somewhat dif®cult is the necessity to determine the value of Y in

an extrapolation of s 12 towards a zero shear rate.A similar effect will be discussed in Sections 3.4 and 3.5 for the case of polymer blends. This change

of the relaxation behaviour is also re¯ected in elasticity-dominated effects like die swell and meltfracture [130]. A modi®cation of the ®ller surface will additionally affect the variation [133].

As already mentioned, a correlation of the rheology of ®lled systems to structure and mechanics ispossible to some extent, because of identical in¯uence factors on both properties. This quality controlchance has been tested [134]; the determination of discrete relaxation spectra from the dynamic moduli

of base polymer and compounds (see Fig. 24) allows for the identi®cation of a secondary relaxationmaximum resulting from the ®ller interaction. In Table 3, the results for one compound (which is rathercritical regarding producibility because of the very ®ne talc ®ller used) are given. The values for

t igi(max) were obtained using the BSW-model [45] and discrete spectra with four relaxation timesper decade. Similar correlations can be obtained for a variation of the particle size of the ®ller, whereimpact strength and added viscoelasticity also correlate positively.




What remains is a problem of measurement, as the materials exhibit solid-like behaviour at low strain

rates (yield stress effect) due to the long relaxation times of the ®ller contribution. This is combined witha pronounced non-linearity starting at very low stress/strain levels already and a strong response to

sample preparation and pre-deformation effects [135±137]. These effects make it very complicated tocompare results from different laboratories and measuring geometries, as was shown in a round-robintest [137], in which the reproducibility for G 0,G 00(v )-measurements of un®lled PP was found to bearound ^10%, while for a PP/talc-compound similar to the material discussed in Table 3 a level of

^40% was reached, with special problems at low frequencies, where pre-deformation effectively

destroys the `network effect'. A use of the Cox/Merz-relation as well as the combination of dynamicaland steady-shear results (e.g. capillary data) is virtually excluded.

In practice of production and conversion of such products, also the `side effects' of ®lling in conver-sion and application need to be considered. These include adsorption of additives like antioxidants [138],

promotion of degradation through a catalytically active ®ller surface, degradation-related die lip bulidup[20] and promoted melt fracture. Also, defects in molded articles or ®lms are frequently related to


Fig. 24. Effect of dispersion quality on the rheology of a 30 wt% PP/CaCO3 Ð compound produced on three different

compounding machines (G 0(v ) from plate/plate measurement at 2308C) compared to base polymer; better dispersion leads

to elasticity at long relaxation times and also improves mechanical properties.

Table 3

Mechanical and rheological parameters of a PP-based talc compound (Daplen KSR 45251 30 wt% talc Naintsch A3) re¯ecting

the degree of dispersion (data from Ref. [134])

Extruder Flex. modulus (MPa) Charpy notched 1238C (kJ m22) git i (max) (Pa s)

ZE 25 `short' 2973 8.8 3.5

ZE 25 `long' 2564 9.8 15



agglomeration phenomena. The effects of water adsorption promoting the agglomeration tendency of ®llers need to be considered here.

Finally, some special cases should be discussed. Additives and processing aids [121] are a special type

of `®ller' with very small volume fractions in case that they remain solid in the molten polymer. If this isnot the case Ð as for slip agents like erucamide or oleamide, but also for calcium stearate Ð they can

act quite differently on the system behaviour. One of the possible problems appearing in the rheologicaltesting of polymers containing such `internal lubricants' is a wall slip effect in the measuring instrument.

Pigments and carbon black can have a rheological effect already at very low concentrations due to theirvery small particle sizes and Ð especially in case of carbon black Ð good interactions with thepolymer.

Other special cases include network-forming nucleating agents of the sorbitol-derivative type andnanosised particles, which allow for special perfomances of compounds with respect to mechanics

[139,140] but also barrier properties. Only limited information is available so far on the behaviour of the resulting `nanocomposites' in rheological tests, but a certain similarity to very ®ne ®llers can be

assumed.

3.3. Crystallizing polyole®ns

As polyole®ns are semicrystalline materials, not only the degree of crystallinity but also the form anddistribution of crystalline structures in the ®nal material have a decisive effect on end-use properties.

This relates to both mechanical and optical performances, on also to long-term stabilities and agingbehaviours.

During the conversion step, rheological properties and the crystallisation process strongly interact

with each other. The complexity of this interaction and the extent to which morphologies are determined

by the rheology of the converted material are de®ned by the type of conversion process.In their rheological behaviour, crystallizing polymers can be seen as special case of ®lled systems, i.e.with crystals behaving like a ®ne dispersion of solid particles [141] or as crosslinking systems with the

forming crystals acting as crosslinks between the molecules [142]. Using the ®rst of these assumptions,one arrives at a formulation like

G00 Rt G 00

t = G 00t 0 12

f

f m

22

28

with G00(t ) giving the time evolution of the modulus in a crystallisation experiment, f the crystallised

volume and f m Ð as above for ®lled systems Ð the maximum crystalline volume at impingement of the spherulites. For the remaining crystallisable fraction v(f ), Carrot [141] arrives at

G 0 R21 = a

G 00 R21 = 2

vf 12x t

x 129

where x de®nes the degree of crystallinity. As the long relaxation times are affected most by crystal-lisation, the measurement is most sensitive at low frequencies.

This opens an interesting possibility to monitor crystallisation processes with rheological methods. An

inherent problem in such tests is the in¯uence of the strain-induced creation of nuclei, effectively the ®rststep of shear-induced crystallisation. If the quiescent crystallisation should be studied in an undisturbedform [142, 143], only very low stresses and reversible deformations like in a dynamic test can be applied.




However, a combination of unidirectional and dynamic shear tests also allows for determination of thesensitivity of a material to deformation- or stress-induced crystallisation. Such investigations have been

published for iPP [67,144±146] and poly-1-butene [147]. An example for iPP is given in Fig. 25, itclearly shows the acceleration of the crystallisation process through a pre-shearing step.

Especially for the case of iPP, it can be seen from the quoted literature that the MMD affects both

rheology and crystallisation behaviour. This is also re¯ected in processing behaviour and morphologyformation [66]. The fact that polymers with a higher molar masses and polydispersities show signi®-cantly more oriented structures (like shear-induced skin layers in injection moulding) is a direct conse-quence of this interaction [65]. It is further enhanced by the `gelation effect' of forming crystallites (see

above), which makes the process self-accelerating.

3.4. Elastomer blends

This section covers a wide area of technically applied systems. Generally, elastomer blends are notlimited to polyole®n-based systems, and the principle of impact modi®ed materials is applied also in

chemically different material classes like polystyrene on polyamide. The combination of stiff matrixmaterials with ¯exible, particular inclusions being able to absorb stresses in case of deformation and

preventing crack propagation and failure is a general design principle for many synthetic materials.This area will be used here to outline the principles of polymer blend theory, which is based mainly on

the work of Utracki [148,149]. The phase structure is mainly a function of the relationship between the

viscosities of the disperse and matrix phases

l h Disp: = h Matrix 30


Fig. 25. Development of storage modulus G 0 and tangent of loss angle tan(d ) for iPP-homopolymer with M W 500 kg mol21;

M W = M N 5:0 during a quench to 1388C after melting at 2608C and subsequent shearing during the indicated times at

g 0 5 s21 (from Ref. [67]; reprinted with permission of Steinkopff Verlag, 2000).



and the capillary- or Weber-number of the mixing process

We g 0h Matrix R = a 31

where R is the (original) radius of the disperse phase particles anda is the interfacial tension between thephases. In the mixing process, additional particle breakup only takes place in case of We.Wecrit, with

Wecrit being determined by l and normally reaching a realistic value only for 0.1 , l , 1. This concepthas several weaknesses. Firstly, it only considers dispersion (breakup) processes and no agglomerations,

which play an important role in structure development as well. The ®nal particle size distribution asoutlined in Fig. 26 is always rather wide, as the stabilty limit for the particle diameter is different for both

processes. This equilibrium has been investigated in the group of Moldenaers [150±152] using rheolo-gical techniques for the characterisation of polymer blends, both model systems and technically relevant

ones. An important fact for this development is the stability of very small particles which resist agglom-eration due to their high surface tensions.

For the rheological investigation of such blend systems the same caution as mentioned before for ®lledpolymers is necessary. As for ®llers, the shape and size of the dispersed particles both in¯uence thesystem behaviour. Unlike ®ller particles these can be massively changed in a ¯ow ®eld. Again, only anapplication of low and dynamic stresses and strains makes the results representative for the equilibrium

structure of the investigated material.

3.4.1. Extruder blends

Different types of elastomers with or without crosslinking are in practical use for the modi®cation of polyole®ns. Roughly, these can be separated into

² Ole®n-based types like amorphous ethylene-propylene copolymers (EPR), ethylenene-propylene-

diene rubbers (EPDM) and single-site catalyst based plastomers (MC-LLDPE).² Non-ole®n based types like styrene-ethylene-butadiene rubbers (SEBS), natural rubber (NR), buta-

diene rubber (BR) and ethylene-vinylacetate-copolymers (EVA).

The second category also adds polarity to the blends is normally used only if special properties, e.g.polarity, are required, as the higher cost of these components prevents a more general application.

Again, the design parameters include not only the components and mass ratios selected for the blend,but also the mixing equipment used. Mostly used are twin screw extruders with special mixing sections(e.g. kneading blocks, distribution disks), but also other types are in use. For EPR- or EPDM-types


Fig. 26. Effect of dispersion (B) and agglomeration (C) processes on the particle size distribution of a 2-phase polymer system.



supplied in bales instead of granules (very low crystallinity grades), batch mixers similar to a Brabendertwin-blade kneader are in use (possible in combination with a granulation extruder like in a Farell-type).

Also, the co-kneader geometry of Buss is frequently used, which has shown advantages for feeding

liquid components like peroxides for partially crosslinked systems.An important difference between crosslinked and non-crosslinked systems is the different behaviour

of the particles in ¯ow. While non-crosslinked elastomers will deform and eventually break up in a ¯ow®eld [153], the deformation will be followed by a recoil. Thus, systems with crosslinked elastomers likethermoplastic vulcanisates (TPVs) are much less sensitive to processing effects [111±113,154]. These

phase effects are re¯ected in the rheological behaviour only to a limited extent, especially if steady-stateshear properties like in a capillary experiment (for example see Fig. 27) are investigated.

Mostly, the morphology development is determined by the phase viscosities. An example for PP/

EPDM-mixtures is given in Table 4 and Fig. 28, where the viscosity of the matrix PP was variedsystematically, resulting in different particle sizes and impact strengths for the resulting systems. The

formation of an equlibrium particle size distribution in such systems by breakup and coalescence

processes, as outlined before, is described in the literature [150,151].An additional effect of phase compatibility, expressed in the interfacial tension a between the matrix

and elastomer phase, has been shown for PP/EPR-systems [155,156] and other elastomers like MC-based plastomers [157,158]. An example for this effect is the improvement of both phase structure and

mechanical properties by changing the matrix of a PP/EPR-blend from a homopolymer to an EP-randomcopolymer. Some results of a recent development study [156] are shown in Table 5 and Figs. 29 and 30.This principle of improved phase compatibility, the importance of which will become even more evidentin case of blends with chemically different polymers, has been applied in the development of copolymers

with an improved transparency/toughness ratio [116]. The closer chemical and mechanical similarity


Fig. 27. Capillary rheology of PP/EPDM-blends (2008C) based on a PP-homopolymer (B) and EPDM CO038 (X); blends with

20 wt% (A), 40 wt% (L), 60 wt% (K) and 80 wt%(W) of EPDM (from Ref. [153]; reprinted with permission of Elsevier

Scienti®c, 2000).



between the phases leads to an additional improvement of the stress whitening behaviour due to a changeof the micro-deformation processes in the material. The combination of smaller elastomer particles and a

reduction of the modulus difference between matrix and dispersed phase results in a transition fromcrazing to shear yielding, eliminating the formation of microvoids at already low deformations.

For a detailed analysis of the rheological effects, the interfacial contributions in blend rheologyhave to be discussed. A blend system without signi®cant interactions between the phases should be

characterised by a logarithmic behaviour like

Gp

mixv 10

Xi

f ilogGp

j v

32

for the complex modulus Gp of the blend, where the G

p

i are the moduli and f i are the volume fractions of the components. This formulation approximates the rheology of PP/EPR-systems quite closely, as can be

seen in Fig. 31. If interface tension or particle/particle-interactions contribute to the system behaviour,both positive and negative deviations from Eq. (32) can be found. The addition of long relaxation times

and elasticity to the system [159,160] will be discussed in latter. For pure PO-systems, also viscositydepression in mixtures has been reported [161]. In any case, knowing the phase morphology is very


Table 4

Effect of viscosity ratio between matrix and elastomer phase on morphology and mechanics of PP/EPDM-blends (base

polymers: Daplen PP; elastomer: Dutral CO 038 Ð viscosity approx. identical to DS 10)

Material Matrix Matrix MFR (g/10 min) Flex. test (MPa) IZOD notched (kJ m22

) Particles (mm)

2308C/2,16 kg Modulus 1238C 08C 2208C Diam.

4512/01 BE 50 0.3 1110 58.2 5.71 3.88 0.2±0.6

4512/02 DS 10 2.4 1145 6.43 3.34 3.21 ±

4512/03 KS 10 8 1070 4.18 2.42 2.87 1.0±3.0

4512/04 MT 58 13 1140 3.66 2.55 2.60 ±

4512/05 RT 58 25 1155 2.90 2.00 2.06 10±50

Fig. 28. Effect of viscosity ratio between matrix and elastomer phase on the impact strength above and below the glass transition

of the matrix; for details of the material composition see Table 3.



important if the rheological data should be used for the calculation of system parameters. Here, it isimportant to distinguish between particle and pro®le size distribution [162].

Rheological studies of PO-blends also allow correlations to the processing behaviour. The hetero-

phasic structure can result in a signi®cant elasticity increase, surface defects and melt fracture [163].Also, the correlation to ®nal properties is possible within limits. Both particle size distribution and EPRfraction are re¯ected in the rheology of the systems [164,165]. As shown in Figs. 32 and 33, which come

from a dilution series of a reactor-blend as described before [116] made for a systematic variation of theinterparticle distance at constant particle size [165], a higher elastomer content is re¯ected both in

mechanical and rheological behaviour.In industrial practice, frequently a combination of EPR and HDPE is used for the modi®cation of PP,

resulting in three-phase systems [166±168]. In contrast the present trend towards application of pureMC-plastomers Ð mainly because of their availability in a wide range of MFR (MMD) and density(comonomer content) Ð results in two-phase systems [169,170].


Table 5

Morphological and mechanical characteristics of model compounds and a reactor product comparable to mat. 8825/01; effect of

increased compatibility in case of copolymer matrix (data from Ref. [157])

Material Matrix Avg. particle size (mm) Flex. modulus1238C (MPa)

Charpy U-notch1238C (kJ m22)

8825/04 KS 101 2.5 1085 8.3

8825/01 KFC 2004 1.3 885 11.8

8825/02 KFC 2006 1.0 737 14.3

8825/03 KFC 2008 0.8 618 15.1

6473/02 Reactor product 0.25 604 20.1

Fig. 29. Dynamic viscosity (calculated from plate/plate-test at 2308C) and viscosity ratio for the system of Table 5 and Fig. 30;

PP matrix (A) Ð Daplen KFC 2006 Ð and EPR (W) Ð Exxelor VM42E.



3.4.2. Reactor blends

Similar application properties can be achieved by the production of heterophasic EP-copolymers,

which have a signi®cant economical advantage over extruder-based systems. The polymerisationsequence of various fractions in a reactor cascade and the volume ratio between the same allows for

a wide range of possible product characteristics. The accessible product range can be further expandednowadays with new MC-catalysts through incorporation of new monomers and improved distribution of the comonomers [6,171].

As for the extruder-based blends, the phase structure dominates the behaviour of heterophasic copo-lymers. These are basically three-phase systems, the structure development from the reactor powder is

shown in Fig. 34. The system rheology is also very similar to extruder blends [155,172]. Details of this


Fig. 31. Rheology of PP/EPR-blend from Table 5 and Fig. 29 (KFC 2006/VM42E) compared to sum of components (loga-

rithmic mixing rule) Ð plate/plate 2308C.

Fig. 30. Morphology of blends from Table 5; KS 101/VM42 (left) and KFC 2008/VM42 (right).



development are important because of the structure effects on the toughness, as a consequence of microdeformation processes ocurring at the interface matrix-elastomer and inside the elastomer particles

[173].Also, these materials open additional modi®cation possibilities through a combination with other

components in extrusion mixing. Different elastomers, but also HDPE and ®llers can be added, resultingin very complex compounds. This kind of property design [115] is of great importance for technically

challenging applications. An interesting trend here is the partial substitution of mineral-®lled compoundswith high crystallinity PP matrices, resulting in various advantages like weight reduction, better

organoleptic properties and improved scratch resistances.Important for PP/EPR-systems, both from extruder and reactor, are degradation effects in the


Fig. 32. Dynamic viscosity of pure RAHECO SVA-279 (dashed line), mixture with 30 wt% matrix polymer (A) and pure matrix

polymer KFC 2008 (solid line); from dilution series in Fig. 33.

Fig. 33. Elastomer concentration effect on stiffness and impact strength at identical particle size distrbution; dilution series

based on experimental RAHECO-grade SVA-279 with KFC 2208 as matrix component.



CR-process or even in normal compounding or conversion steps. The different effect of radicals orperoxide on matrix and elastomer (discussed before in Section 2.1) leads to a change in phase structure

and properties [174]. The composition and structure of the original system allows a partial compensationof these negative effects, as can be seen for three different degradation series from Table 6. This isclosely connected to the rheology and morphology of the materials as shown in Figs. 35 and 36; an

extreme consequence can be the formation of crosslinked gels.The application areas are strongly related to the mechanical pro®le of these materials, with low-

temperature impact strength as the most important property. Also other relevant application propertieslike surface replication etc. are related to phase structure and component properties, also of the exter-nally added components.


Fig. 34. Phase structure development in a heterophasic EP-copolymer; starting from the reactor particle in a melting step (A) a

primary morphology develops, which can change in a high strain environment (B) by further breakup and dispersion, in a low

strain environment (C) by agglomeration (see also Fig. 23).

Table 6

MMD development in the degradation of the three polymer types for total polymer and xylene solubles (XS) content (HOMO

Ð homopolymer, HECO Ð heterophasic copolymer with 12 mol% ethylene, RAHECO Ð random-heterophasic copolymer

with 25 mol% ethylene; data from Ref. [174])

Material MFR (g/10 min) XS (wt%) GPC total (kg mol21) GPC(XS) (kg mol21)

2308C/2,16 kg M W M W / M N M W

B-HOMO 0.5 ± 1061 6.4 ±

BHD2 5 ± 322 3.4 ±

BHD3 50 ± 196 3.5 ±

B-HECO 0.5 12.0 1069 5.6 532

BCD2 5 13.2 322 3.2 267

BCD3 50 13.0 152 3.0 158

B-RAHECO 0.5 25.0 667 4.9 534

BRD2 5 27.7 266 3.0 263

BRD3 50 26.1 124 2.4 157



3.5. Blends with other polymers

Different principles apply for blends between chemically very different polymers. Here, an effectivecompatibilisation between the main phases by a third component is necessary to optimize the morphol-

ogy, and to ensure processing stability and appropriate mechanics [148]. Essentially, a blend compati-bilizer has two functions: reducing the interfacial tension in the melt phase for achieving an optimumphase structure, and improving the phase interaction in the solid phase.

Before going to practical examples, the principles of morphology development and rheologicalproperties of PO-blends with non-ole®nic polymers will be outlined brie¯y. In principle, the behaviouris similar to Sections 3.1 and 3.2, although a much stronger interface effect and non-linearity is found,

resulting in a high relevance of predeformation and non-linearity effects as in Section 3.2 [176]. Fordescribing the rheology, an interfacial term G

p

IF as in

Gp

mixv 10

Xi

f ilogGp

j v

1 Gp

IF 33


Fig. 35. Evolution of the rheological behaviour in the HOMO- (left) and the RAHECO- (right) degradation series of Table 5

(solid lines Ð storage modulus G 0, dashed lines Ð complex viscosity h p).

Fig. 36. Effect of degradation on morphology in the RAHECO-series of Table 5 and Fig. 31 (left Ð MFR 0.5, right Ð MFR

50); TEM-pictures after RuO4-staining (magni®cation approx. 2.500 £ ).



has to be added. Different formulations have been proposed for analysing this component to gainadditional system information [159,160]. In practice, the method of Gramespacher and Meissner

[160] has proven quite successful, in which the characteristic relaxation time t IF for Gp

IF is determined

as described before using a discrete relaxation time spectrum. If the average particle radius R of thesystem is known (e.g. from SEM- or TEM-investigations as described in Ref. [162]), the interfacial

tension a can be calculated from

t h M R

a

19k 1 16 = 2k 1 3

40k 1 1with k h D = h M 34

where h D and h M are the viscosities of the disperse and the matrix phase, respectively. Both this methodand the dispersion model developed by Palierne [159,177] are however limited to systems with a ratherlow contents of disperse phase, as otherwise co-continuous structures are developed, for which no clear

particle dimension can be determined.

Practical examples, which demonstrate the importance of component selection, application of compa-tibilizers and blend production will be discussed for two pairs of polymers:

² Polypropylene/Polyamide-6 (PP/PA-6). This system was very well investigated in the late 80s and

early 90s by various companies, although little of the developments made were ultimately commer-cialised. Literature data are available [175,176,178], discussing composition effects on morphology,

rheology and mechanics of these blends. Different types of compatibilizers were used in these studies,mostly polyole®ns Ð PP or EPR Ð grafted with maleic anhydride (MAH) to ensure compatibilitywith the PA-6 phase. Another class of promising polymers for this purpose were styrene-elastomers

like styrene-ethylene-butadiene-copolymers (SEBS) grafted with MAH, which showed excellent

behaviour regarding blend mechanics due to their elastomeric nature.² An example of the rheology and morphology of such a system based on PP-homopolymer, PA-6 and

SEBS-g-MAH is given in Figs. 37 and 38. The comparison between the calculation result accordingto Eq. (32) and the measured data for the storage modulus in Fig. 37 clearly demonstrates thementioned interfacial contribution. A rather ®ne morphology is achieved with the applied amount

of 5 wt% of compatibilizer; a close look at Fig. 38 shows that this is reached with a more or lesscomplete coverage of the dispersed PA-6 particles with the SEBS-g-MAH. The consequences of selecting type and quantity of compatibilizer on the mechanics of PP/PA blends becomes clear from a

look at Table 7, where different blends with identical main components and PA-contents arecompared.

² Polyethylene/Polystyrene (PE/PS). For this system, some more recent examples have been published

[179,180]. Despite its limited thermomechanical stability T G 90 ± 1008C; PS is an interestingblend partner for PO's from mechanical reasons as well as paintability and printability. Styrene-elastomers like SEBS can be used as compatibilizers, but also reactive blending using styrene/ peroxide Ð combinations have proven to be viable. High impact strengths for these systems can

only be reached with the incorporation of an additional elastomeric phase, prefrentially at theinterface.

In any case, the development of such blends must be targeted at properties not achievable in purePO-based systems to justify the certain additional effort and cost. For this, also a combination with




elastomers is of interest, possibly already as compatibilisers, and ®llers for creation of network-likestructures are possible.

Despite the original expectations, the application of PO-blends with non-ole®nic polymers hasremained limited to applications in which properties like polarity, high HDT, HF-weldability and barrier

properties are important. Also reactive blends dominating the market in which the second phase and thecompatibilizer are produced in one step, leading to improved process and product economics.


Fig. 38. Morphology of PP/PA-blend as in Fig. 37.

Fig. 37. Rheology of a PP/PA-blend (75 wt% PP Daplen BE 50, 20 wt% PA Durethan B30S, 5 wt% SEBS-g-MAH); storage

modulus of components, calculated curve with moxing rule and measured curve (2308C, plate/plate after drying).



4. Actual and future trends

A basic requirement for following future trends in the polymer industry is to understand the principlesof market growth as shown for the case of PP in Fig. 39. More than 75% of the volume growth of polyole®ns results from intermaterial substitution, still more than 50% from inter-polymer substitution.

One of the main developments during the 90s was the replacement of `technopolymers' (or `engineeringthermoplastics', ETPs) like polyamides or ABS with polyole®ns, especially by PP. This cost-drivenprocess was partly facilitated by constructional improvements within the concerned parts, but mostly by

signi®cant expansions of the property range of these polyole®n materials.There is more to come; several upcoming developments will ensure a continuation of this trend over

the next decade:

² Metallocene catalysts, which have already had a major impact for PE [181] and elastomers will gainin importance for PP [18]. The key advantages of this catalyst family like narrow MMD, possibility toincorporate new comonomers and to achieve a better randomness, generally better control of thepolymer structure Ð will allow for an even wider property range. Although the speed of market

introduction has so far been lower than expected (partially the process was retarded by legalproblems), this development will remain among the dominating ones.

² New polymerisation technologies giving access to a wider range of products [70] are constantlygaining ground. The possibilities of polymerisation under supercritical conditions have so far not

been fully exploited for the market. A problem for widening the application range may, however,arise from the increasing plant size, which makes it virtually impossible to produce small-volumegrades for market niches. On-line production control by rheological techniques will gain in

importance.² Ultrahigh MFR materials, which have good mechanical properties, are a development dictated by the

market. New and faster processing technologies as well as wall thickness reduction (downgauging)

for economical and ecological reasons are the underlying reasons. Here, present rheological tech-niques are challenged by the low viscosity of these materials.

² Controlled LCB systems, produced via polymerisation and/or reactive compounding, should allow


Table 7

Mechanical properties of PP/PA-blends as in¯uenced by compatibiliser type and quantity (all properties determined on

injection-moulded plates 150 £ 80 £ 2 mm2 parallel to injection direction; FWI Ð falling weight impact, Charpy DV Ð

double V-notch)

M 5969 M 5976 M 5972 M 5984

PP type Daplen BE 50 Daplen BE 50 Daplen BE 50 Daplen BE 50

PA type ± Durethan B30S Durethan B30S Durethan B30S Durethan B30S

PA quantity wt% 20 20 20 20

Comp. type ± None Kraton G 1901X Kraton G 1901X Admer GR2

Comp. quantity wt% 0 1 5 5

MFR g/10 min 2.03 0.96 0.24 0.33

Flex. modulus MPa 1420 1540 1560 1480

FWI (Wtot) J 1.5 2.3 43.9 4.9

Charpy DV kJ m22 7.6 11.0 45.2 42.8



the access of PP to areas presently occupied by glassy polymers. Beyond extrusion foaming, there isalso ISBM as a potential growth area. As outlined in Section 2.2.2, rheological means of material

characterisation are most important here.² New ®ller types, especially organic ®bres, which presently show an above average market growth,

may help property development in various ways. For one, the ecological factor of sustainability mustbe considered, and weight reduction will remain an important argument. Also, energetic recycling isfacilitated.

² Nanocomposites, which are already now a very interesting material family, have not yet demonstratedtheir full range of possibilities. For a more widespread market penetration, however, signi®cantly

cheaper ways of production will have to be found. The rheological properties of these materials arechallenging as has been shown already [139,140].

² Selective crosslinking in multiphase systems, which already helps in optimizing property pro®les,will gain in importance as one of the possible modi®cation technologies allowing for the production

of a multitude of tailor-made grades for market niches that are based on one reactor grade of polymer.

A much used, but less often considered tool in speeding up market-oriented product development isthe so-called chain of knowledge, which should ideally stretch from the catalyst to the long-termbehaviour of the ®nal part, and possibly even include the recycling possibilities. One important pre-

requisite for a growing understanding of interactions between different steps of the production chain andalso onward into conversion and application is the necessity to `talk one language' throughout polymerdevelopment. Some of the requirements seem trivial Ð like the consistent use of SI units in reporting

and publishing Ð some other are less so. Interdisciplinary efforts for creating new, value-added materi-als will have the biggest chances for success in years to come and should be promoted especially inacademia and education.


Fig. 39. Market growth of PP in Western Europe 1993±1998 segmented by growth motivators (economical development, new

applications and material substitution).



Acknowledgements

I would like to thank several people, who have contributed to the creation of this Review: In the

startup phase, Prof. Otto Vogl, New York, for encouraging me to write it as well as Prof. ManfredWagner, Berlin, and Prof. Alois Schausberger, Linz, for helping me to the right selection of literature.Then my fellow rheologists in this company for supplying data: Svein Eggen from Rùnningen, Anneli

Malmberg from Porvoo, Tonja Schedenig from Schwechat and Bernhard Knogler from Linz. And at last,all of my colleagues who helped me ®nishing the work with discussions, corrections and hints Ðespecially Norbert Reichelt and Klaus Bernreitner in Linz and Pirjo JaÈaÈskelaÈinen in Porvoo.

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