Flow induced crystallization of polymers : precursors and nuclei Citation for published version (APA): Ma, Z. (2012). Flow induced crystallization of polymers : precursors and nuclei. Technische Universiteit Eindhoven. https://doi.org/10.6100/IR740176 DOI: 10.6100/IR740176 Document status and date: Published: 01/01/2012 Document Version: Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers) Please check the document version of this publication: • A submitted manuscript is the version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, please follow below link for the End User Agreement: www.tue.nl/taverne Take down policy If you believe that this document breaches copyright please contact us at: [email protected]providing details and we will investigate your claim. Download date: 26. Dec. 2020
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Flow induced crystallization of polymers : precursors andnucleiCitation for published version (APA):Ma, Z. (2012). Flow induced crystallization of polymers : precursors and nuclei. Technische UniversiteitEindhoven. https://doi.org/10.6100/IR740176
DOI:10.6100/IR740176
Document status and date:Published: 01/01/2012
Document Version:Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers)
Please check the document version of this publication:
• A submitted manuscript is the version of the article upon submission and before peer-review. There can beimportant differences between the submitted version and the official published version of record. Peopleinterested in the research are advised to contact the author for the final version of the publication, or visit theDOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and pagenumbers.Link to publication
General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.
• Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal.
If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, pleasefollow below link for the End User Agreement:www.tue.nl/taverne
Take down policyIf you believe that this document breaches copyright please contact us at:[email protected] details and we will investigate your claim.
Flow induced crystallization of polymers:Precursors and Nuclei
Flow induced crystallization of polymers: Precursors and Nuclei / by Zhe Ma.Technische Universiteit Eindhoven, 2012.
A catalogue record is available from the Eindhoven University of Technology Library.ISBN: 978-90-386-3299-5
This thesis was prepared with the LATEX2ε documentation system.Reproduction: University Press Facilities, Eindhoven, The Netherlands.Cover design: Zhe Ma and Paul Verspaget
This research forms part of the research programme of the Dutch Polymer Institute(DPI), DPI project #714.
Flow induced crystallization of polymers:Precursors and Nuclei
PROEFSCHRIFT
ter verkrijging van de graad van doctor aan deTechnische Universiteit Eindhoven, op gezag van derector magnificus, prof.dr.ir. C.J. van Duijn, voor een
commissie aangewezen door het College voorPromoties in het openbaar te verdedigen
op maandag 3 december 2012 om 16.00 uur
door
Zhe Ma
geboren te Hejian, Hebei, China
Dit proefschrift is goedgekeurd door de promotoren:
Semi-crystalline polymers cover over two thirds of commercial applications ofpolymeric materials. With most industrial processing technologies, semi-crystallinepolymers are brought in the molten state and then deformed for different reasons:i.e. to create specific properties like a high modulus with fiber spinning or to shapegeometrically complex parts as with injection molding. The deformation not onlyaccelerates the crystallization kinetics but also can cause crystalline structures to changefrom isotropic spherulites to the highly oriented cylindrical structures (e.g. shish-kebab) which determine the ultimate properties. Therefore, understanding the interplaybetween flow fields and the resulting crystalline structures is of great importance. Itenables the design of processing procedures and tailoring final product properties. Theobjective of this thesis is to reveal how a flow field affects the crystal structures bystudying the early stages of the crystallization process which are dominated by thecreation of shear-induced precursors and nuclei.
Polymer crystallization involves two steps: nucleation and growth. Nucleationprovides quantitative (more or less) and qualitative (isotropic or oriented) nuclei andthese are the templates for further crystal growth that, ultimately, will fill the full space.The nucleation step is very sensitive and is often controlled by additives (nucleatingagents) or/and imposing a flow field. The formation and features of nuclei are, therefore,the key factors that determine the crystalline structures. Probing and quantifying nucleiis the main work of this thesis.
According to the resulting morphology, nuclei can be divided into two groups: point-like nuclei and fibrillar nuclei. The former give rise to spherulites, the latter mainlyinduce oriented structures like the well-known shish-kebab; i.e. fibrils with transverselamellae. Oriented nuclei can be further classified into row nuclei and shish nuclei bywhether they can be directly observed with X-ray characterizations. In the first part ofthis thesis, the creation of point-like nuclei is studied for an isotactic polypropylene witha nucleating agent, with and without applied shear deformation. For such a system,nucleation is dramatically enhanced by both the nucleating agent (U-Phthalocyanine)and the flow. The nucleation density is that large and, therefore the crystallite sizeso small that optical microscope is not suitable to count nuclei numbers. Therefore, asuspension-based rheological model is used to quantify the nuclei density.
ix
x Summary
In the second part, precursors of row nuclei in a bimodal Polyethylene (PE) arestudied. Since row nuclei cannot be observed directly by X-ray characterizations, thecrystallization step is triggered by increasing the pressure which raises the equilibriummelting temperature and thus the under-cooling: a so-called pressure quench. It isshown that shear-induced precursors can be generated at a temperature close to thenominal melting temperature and the unstable ones can relax.
Next, the formation of shish nuclei during flow is studied by using fast (30 frame/s),time resolved X-ray scattering in combination with rheological measurements. It isfound that a critical shear rate exists for the formation of shish nuclei within very shortflow times (0.25 s). Shish precursors are formed during flow and these were found todevelop into shish afterwards, during or after flow depending on the flow strength.
Besides the external effects, the nuclei formation is also influenced by the molecularstructure. Therefore, in the last part, the effect of the molecular architecture onshear-induced crystallization is studied for isotactic polypropylene (iPP) and twopropylene/ethylene random copolymers with varying ethylene monomer contents. Thesethree grades had very similar rheological behavior; there is only a small but importantdifference in the longest relaxation time. Flow enhanced nucleation density was foundto be the lowest for the iPP homopolymer which is due to the shorter longest relaxationtime. However the reduced growth rate due to the added ethylene monomer leadsto slower overall crystallization kinetics of the random copolymers compared to thehomopolymer at similar thermal conditions.
Chapter one
Introduction
1.1 Background
Human history is closely accompanied by the progress in material development.
Advances in material are crucial for affecting people’s way of life because it can
significantly change the way of working and improve output efficiency. The consequence
of the material evolution is particularly obvious at the primary stages of civilization.
For example, the innovation of iron farming tools such as plows and sickles, made the
farming processes much faster and easier and, as a consequence, people produced enough
food to survive and also gained extra time to exploit other activities. Considering such
great importance, anthropologists even define historical epochs by the materials used
at that moment, such as the Stone, Bronze and Iron ages. To meet the continuously
increasing need of new functions, synthetic materials appeared and have been widely
applied. Among current synthetic creations, plastic is quite prominent in our society
due to its wide range of applicability. Just looking around, plastic products can be
easily found at any time and any place. They may be a coffee stirrer, mobile shell,
computer screen, bumper, greenhouse, construction and building parts, and so on.
Actually, the development of truly synthetic plastics started only around one hundred
years ago. The first completely synthetic one is poly(phenol-co-formaldehyde), a densely
cross-linked thermoset polymeric material, well known as Bakelite, commercialized in
1909 and applied for electrical appliances and phonograph records [1]. After its birth,
plastic has developed dramatically during the past century. On one hand, more and
more new plastics were synthesized and manufactured. Some major examples are:
poly(vinyl chloride) (PVC) in 1920s, polyamide (Nylon) 66 in 1930s, linear high-density
polyethylene (HDPE) and isotactic polypropylene (iPP) in 1950s, poly(p-phenylene
terephthalamide) (known as Kevlar) in 1960s. [1, 2]
1
2 Chapter 1
1950 1960 1970 1980 1990 2000 20100
50
100
150
200
250
3002010: 265
2009: 250
2002: 204
1989: 99
1976: 47
Mtonne
year1950: 1.5
Figure 1.1: World plastics production between 1950 and 2010. Data are obtained fromreference [3]. Only continuous growth is shown and temporary fluctuation is notincluded.
On the other hand, the total amount of the plastic being used also increased
tremendously, as shown in Figure 1.1. The world plastic production has risen from
1.5 million tonnes in 1950 to 265 million tonnes in 2010, [3] equal to an averaged annual
growth rate of 9% during sixty years.
Polymers can be amorphous or semi-crystalline, depending on the degree of ordering
of the molecular arrangement. Due to crystallization, semi-crystalline polymers can
still be used as a solid material above the glass transition temperature. For example,
although the glass transition temperature of HDPE is -80◦C, [1] its high crystallinity
enables HDPE to be used as a solid-material at normal environmental temperatures.
Therefore, semi-crystalline polymers, especially polyolefins such as HDPE and iPP, have
become the most widely used polymeric materials, see Figure 1.2.
1.2 Structure-properties relation
Ultimate properties, e.g. mechanical and optical, of end-use plastic products strongly
depend on the structure of the material [4, 5]. The manufacturing history includes two
major processes: a) synthesis, starting with small molecules and b) processing, where
the final product is given its shape. Therefore, the general issue “structure” includes
two classes of defining features: the intrinsic chemical structures of the macromolecules
and the physical arrangement structure of these macromolecules.
The intrinsic chemical structure includes chemical composition (various monomers,
dom/block, etc.) and configuration, molecular weight, and so on. These molecular
Chapter 1 3
Figure 1.2: European plastics demand by polymer type in 2010. [3]
properties are controlled and dominated by the polymerization process.
For amorphous polymers, considerable knowledge has been developed to understand
the relationship between the basic molecular structure and mechanical behavior. Semi-
crystalline polymers contain both amorphous and crystalline phases where an identical
polymer chain often is involved in these different phases. The crystal phase has the
hierarchic structures of conformation, crystal lattice, lamellar crystal, spherulitical or
cylindrical assembling form of lamellae, etc. These crystal micro-structures cover a
broad range of length scales from sub-nanometer up to microns. Polymer crystallization
is determined by the molecular structures and, often in a very strong way, on the
processing conditions. Therefore, when discussing structure-properties relation of semi-
crystalline polymers, specific features of the crystal microstructure like crystallinity,
lamellar thickness and orientation, should be taken into account. A typical and
illustrative example [6] is shown in Figure 1.3, where an injection molded plate of HDPE
is shown. From the optical micrographs it is observed that different structures appear
in the thickness direction. These skin and core layers are due to the varying cooling
and flow conditions as experienced by the material at different positions. Moreover,
the thickness of these layers strongly depends on the position along flow path. Finally,
for the same polymer material of HDPE, these distinct structures lead to completely
different mechanical properties between specimens cut from the same plate but at
different locations and in different directions. The failure mode varies from brittle
to tough, the latter showing necking in one case and homogeneous deformation in the
other.
Next to molecular properties, full understanding on how crystal structures are formed
during processing and how these subsequently affect the properties is a prerequisite of
tailoring the ultimate properties of plastic products. This thesis focuses on the second
step in the above knowledge chain, i.e. how polymer crystallizes under processing-
relevant conditions.
4 Chapter 1
70 x 70 x 1 mm
injection ofpolymer
A B
C
A
B
C
Figure 1.3: Variation in microstructure over the thickness in an injection molded HDPEplate. Right column shows the resulting mechanical properties of threespecimens cut from the same plate but different positions. [6]
1.3 Processing-structures relation
Semi-crystalline polymers are often processed from the molten states and subjected
to flow to transport the material and shape the product. Flow gradients affect
crystallization by altering the amount, size and orientation of nuclei. In this way,
processing-relevant flows are able to accelerate the crystallization kinetics by several
orders of magnitude and induce anisotropic structures. According to the resulting
morphology, flow-induced nuclei can roughly be divided into two groups: point-like
nuclei and oriented fibrillar nuclei. During quiescent crystallization, only point-like
nuclei are formed. The average crystal structure is isotropic and may grow into large
spherulites because of the relatively low nuclei density, see Figure 1.4a. Depending on
the competition between flow strength and molecular mobility, there are mild and strong
flows. Mild flow forms extra point-like nuclei, i.e. increase nuclei density which results
in more but smaller spherulites, see Figure 1.4b. In contrast, strong flow completely
changes the isotropic morphology into oriented crystals. As an example highly oriented
shish-kebab structures are shown in Figure 1.4c. [7]
If the flow should effectively alter the crystallization behavior, the nuclei that are
generated should be stable. However, in many cases flow-induced ordered structures
are so-called “precursors”, instead of stable nuclei. These flow-induced precursors have
Chapter 1 5
(a) (b) (c)
Figure 1.4: Typical morphologies of: a) less and large spherulites; b) more but smallspherulites; c) oriented shish-kebab [7].
a degree of ordering (position or/and orientation; intra- or/and inter- molecule) and
favor further development to nuclei for sufficient under-cooling, or may relax back to
amorphous melt in case of relatively high temperatures. When the unstable precursors
are inclined to disappear, the slow kinetics of precursor relaxation may cause significant
memory effect on subsequent crystallization, since cooling stabilizes and reactivates the
residual precursors. [8]
By stretching polymer chains and aligning segments parallel to each other, flow
promotes nucleation in polymer. On the other hand, foreign substances, known as
nucleating agent (NA), are added to the polymer melt and the additional surfaces
lower the surface energy change in an efficient way and decrease the critical size for
nucleation [9]. Moreover, specific nucleating agents can control the phase modification of
growing crystals. For example, β-NA is utilized to induce formation of iPP hexagonal β-
crystals [10–12]. Understanding how the amount and orientation of nuclei are controlled
by flow or/and NA is a key step in revealing processing-structure relations.
1.4 Scope of the thesis
The aim of this thesis is to gain understanding on how polymer crystallization under
processing-relevant conditions (flow and NA) takes place by exploring the creation and
evolution of precursors/nuclei. During processing, a continuous flow imposed during
solidification, may influence both nucleation and crystal growth. To separate the
influence of flow on these two aspects from rheological changes due to crystallization,
Janeschitz-Kriegl and co-workers introduced the “short-term shearing” method [13].
Flow duration is so short that structure formation and a related change in the viscosity
can be minimized. The flow-induced precursors/nuclei can be revealed by direct
observations, using state of the art experimental techniques, or by examining subsequent
crystallization. In this thesis, we use both approaches to study (probe or/and quantify)
precursors/nuclei induced by various flow strength. Moreover, the validity of “short-
6 Chapter 1
term flow” is verified for strong shear conditions. The polymers investigated are grades
of a high density polyethylene (HDPE) and an isotactic polypropylene (iPP). They are
not only the most used polymers but also the simplest macromolecules and provide
suitable model systems for the academic research.
First of all, generation of extra point-like nuclei is studied in Chapter 2. Addition of
nucleating agents (U-Phthalocyanine) and imposition of mild flow are both utilized to
enhance formation of point-like nuclei in an iPP system. A suspension-based rheological
model [14,15] is applied to quantify nucleation density. In this way, the nucleation effects
of this nucleating agent and mild flows applied are assessed.
Oriented nuclei are investigated in Chapter 3-6. Oriented nuclei can be classified
as row nuclei and shish, according to whether such nuclei can be detected by X-ray
characterization.
Chapter 3 focuses on the precursors of the X-ray invisible row nuclei. Shear-induced
precursors cannot be observed directly by X-ray. Therefore, after increasing the under-
cooling, subsequent crystallization kinetics and orientation evolution is examined to
reflect the underlying precursors. A pressure quench method is presented, which
provides an efficient way of achieving sufficient under-cooling in a fast way for triggering
crystallization and effectively “lightens up” precursors.
In the case of very strong shear, X-ray observable shish appear during flow. In
Chapter 4, the combination of a slit flow with time resolved X-ray measurements
provides the possibility to study in-situ structure formation of iPP during flow. In this
way, shish formations during and after flow can be distinguished. Also the evolution
of the average rheological behavior is tracked. The appearance of shish structure and
the rise of the apparent viscosity identify the validity of the conditions for “short-term
flow”, i.e. how short is short depends on shear strength.
For the weakest flow conditions studied in Chapter 4, X-ray and rheology fail to detect
shear-induced structures during flow. Therefore, in Chapter 5, birefringence is employed
to probe the potential precursors in these flows. Subsequent crystallization features
such as kinetics, orientation and β-crystals are tracked in time, in order to establish a
correlation between the precursors/nuclei and their influences on crystallization.
The effect of flow strength in relation with molecular structure (defects present in the
molecular chain and high molecular tail) on crystallization is explored in Chapter 6, by
comparing the amount of oriented nuclei in an iPP and two ethylene/propylene random
copolymers with various ethylene content. A pressure-driven slit flow device [16, 17]
is employed to impose strong flows with a wall stress of up to 0.11 MPa. With this
novel device, the “depth sectioning” method [18] can be applied to extract the polymer
crystallization in certain layers and correlate that with the specific stress. In this way,
the effect of molecular structures on flow induced nucleation can be revealed.
[10] J. Garbarczyk and D. Paukszta. Polymer 22(4):562–564, 1981.
[11] W. Stocker, M. Schumacher, S. Graff, A. Thierry, J. C. Wittmann, and B. Lotz. Macromolecules
31(3):807–814, 1998.
[12] F. Luo, C. Geng, K. Wang, H. Deng, F. Chen, Q. Fu, and B. Na. Macromolecules 42(23):9325–
9331, 2009.
[13] S Liedauer, G Eder, H Janeschitz-Kriegl, P Jerschow, W Geymayer, and E. Ingolic. International
Polymer Processing 8:236–244, 1993.
[14] R. J. A. Steenbakkers and G. W. M. Peters. Rheologica Acta 47(5-6):643–665, 2008.
[15] J. W. Housmans, R. J. A. Steenbakkers, P. C. Roozemond, G. W. M. Peters, and H. E. H. Meijer.
Macromolecules 42(15):5728–5740, 2009.
[16] G. Kumaraswamy, R. K. Verma, and J. A. Kornfield. Review of Scientific Instruments 70(4):2097–
2104, 1999.
[17] G. Kumaraswamy, A. M. Issaian, and J. A. Kornfield. Macromolecules 32(22):7537–7547, 1999.
[18] L. Fernandez-Ballester, D. W. Thurman, and J. A. Kornfield. Journal of Rheology 53(5):1229–
1254, 2009.
Chapter two
Using rheometry to determine
nucleation density in a colored
system containing a nucleating
agent
Abstract
A new suspension-based rheological method was applied to experimentally study the
crystallization of a nucleating agent (NA) filled isotactic polypropylene. This method
allows for determination of point nucleation densities where other methods fail. For
example, optical microscopy can fail because nucleation densities become too high to
be counted (materials with effective NA) or crystallites are not easily visible (colored
materials), while differential scanning calorimetry does not allow the effect of flow to be
studied. Both quiescent and mild-shear induced crystallization were investigated. The
results show that the addition of a nucleating agent increases the nucleation density by
six decades for quiescent crystallization. The effect of shear on crystallization in the
presence of a nucleating agent was assessed and it is demonstrated that, at least for
this system, the effect of applied shear is much smaller than the effect of the nucleating
agent.
This chapter is based on : Zhe Ma, Rudi J.A. Steenbakkers, Julien Giboz, Gerrit W.M. Peters.Rheologica Acta 50:909–915, 2011
9
10 Chapter 2
2.1 Introduction
Semi-crystalline polymers cover over two thirds of the products used in our daily life.
Adding a nucleating agent to a semi-crystalline polymer is a common way to control
crystallization and tailor mechanical and optical properties [1–4]. The interface between
the nucleating agent and the polymer melt has a high surface energy, which reduces
the energy barrier associated with the formation of a nucleus. Introducing a large
amount of nucleating agent particles therefore greatly increases the nucleation density
and consequently accelerates crystallization [5]. In general, a higher nucleation density
leads to more desirable properties. Several methods are available to determine the
nucleation density in polymer crystallization. These include (a) microscopy to directly
count the number of nuclei in the melt, (b) differential scanning calorimetry (DSC) [6],
or (c) dilatometry [7]. The latter two indirectly measure the crystallization evolution in
order to calculate the nucleation density using a kinetics equation. However, for colored
nucleating agent systems, the nucleation density can become too large to be counted
and also can change the optical properties dramatically [4], making quantification of
the nucleation density difficult with optical microscopy (Figure 2.1).
Figure 2.1: Morphology during quiescent crystallization at T = 151 ◦C.
Flow is another crucial factor affecting polymer crystallization, especially the
nucleation step. The number of nuclei can increase dramatically [8, 9] and for a strong
enough flow the formation of shish-kebab structures will occur [10]. The combined
effect of nucleating agent and flow has hardly been studied. In this work we will restrict
ourselves to point-like nucleation which will occur for moderate flow only. How much
a flow will change the kinetics of nucleating agent crystallization depends on the type
of nucleating agent [11]. Knowledge of the individual effect of nucleating agent and
shear on nucleation density is a prerequisite for understanding the combined nucleation
mechanism and to provide input for models to predict resulting structures.
Chapter 2 11
To achieve this goal, conventional DSC and classical dilatometry are not suited since
they do not allow one to impose a flow on the material. A new type of dilatometer,
the Pirouette [12], developed in our group [13, 14], does allow for applying shear to
the sample and thus for using the measured time dependent specific volume for our
purpose; determining the nucleation density. However, in this chapter we will use a
rheometer that first serves as flow device (with the possibility to vary the shear rate
and the shear time) and, subsequently, as a mechanical spectrometer that measures
the changing complex modulus due to the progressing crystallization process. Using an
analytical relation between space filling and the modulus, it is possible to determine
the nucleation density. This solves both problems: dealing with large numbers of nuclei
and poor visibility of crystalline structures. The aim of this study is to explain this
approach and to demonstrate its effectiveness for colored nucleating agent systems, for
both quiescent and flow-induced crystallization.
2.2 Experimental
2.2.1 Materials
The polymer used in this study is an isotactic polypropylene (iPP; HD601CF,
Borealis, previously known as HD120MO). It has a weight average molecular weight
Mw = 365 kg/mol and a polydispersity Mw/Mn = 5.4 [9]. The nominal melting
temperature is 163 ◦C. The polymer was compounded with an organic nucleating
agent, U-Phthalocyanine of molecular weight 310 kg/mol [15] at a concentration of
0.2wt%. This nucleating agent was also used by Lee Wo and Tanner [16] who found
non-spherical crystallites that we did not observe, see section 2.4. From the neat iPP
and the artificially nucleated material (NA-iPP), 1.1-mm-thick plates were injection
molded and from those plates circular disks were cut with a diameter of 8mm. The
NA-iPP samples were blue due to the coloring effect of the nucleating agent.
2.2.2 Rheological characterization
For the rheological measurements, a Rheometrics ARES rheometer with a plate-plate
geometry was used. Samples were first heated to 230 ◦C and kept on that temperature
for 10 min to erase the thermal and mechanical history. Next, the melt was cooled to
the desired temperature at a rate of 15 ◦C/min and kept at this temperature for the
isothermal crystallization. During cooling, gap adjustment was performed continuously
to compensate for the thermal shrinkage of tools and sample. Two minutes of delay
time was used to equilibrate the sample temperature before starting the dynamic
measurements. Temperatures for crystallization were chosen between 133 and 140 ◦C
12 Chapter 2
for the neat iPP and between 143 and 151 ◦C for the NA-iPP. Experiments with shear
were carried out at temperatures of 148 and 151 ◦C. Steady shear at a rate of γ = 60 s−1
was imposed for shear times ts = 2, 4 and 6 s. Small-amplitude oscillatory shear
measurements were employed to track the time evolution of the storage modulus (G′)
and loss modulus (G′′) using an angular frequency of 5 rad/s and a strain of 0.5%. All
experiments were performed in a N2 atmosphere to prevent the material from degrading.
2.2.3 X-ray characterization
Polypropylene can crystallize in different phases. To check if both the neat iPP and
the NA-iPP had crystallized in the α-phase, the samples were analyzed afterwards using
X-ray scattering. Wide angle X-ray diffraction (WAXD) measurements were carried
out at the Dutch-Belgian (DUBBLE) beamline BM26B of the European Synchrotron
Radiation Facility in Grenoble, France. [17] A Photonica CCD detector with 2004×1335
pixels of 44µm× 44µm was placed at 178mm. The wavelength used was 1.033 A and
the exposure time was 10 s. WAXD data were integrated with the software FIT2D.
2.3 Data analysis
A linear viscoelastic version of the three dimensional generalized self-consistent
method of Christensen et al. [18] is used to couple the amount of space filling, caused
by point-like nucleation and spherulitic growth, to the measured dynamic (or complex)
modulus. See also the work of Christensen et al. [19,20]. This model has been validated
experimentally in our previous work [21]. If spherulites are formed, the relative dynamic
modulus f ∗
G = G∗/G∗
0 can be obtained from
A∗f ∗
G2 +B∗f ∗
G + C∗ = 0 , (2.1)
where G∗ and G∗
0 are the complex dynamic modulus of the suspension and the
amorphous phase, respectively. The complex coefficients A∗, B∗, and C∗ depend on
space filling φ, the ratio of the complex moduli of the amorphous (G∗
0) and crystalline
phase (G∗
1), and the Poisson ratios of both phases, ν0 and ν1. Notice that all moduli
are frequency and temperature dependent. Expressions for the coefficients are given in
Appendix A of Steenbakkers et al. [21]. In this case, space filling is the unknown and
is obtained by sloving Eq. (2.1) using the measured f ∗
G.
Next the space filling has to be related to the nucleation density. For a fixed number
density of nuclei N(T ), the Kolmogorov –Avrami –Evans equation [22–25] describes the
Chapter 2 13
progress of space filling in time during isothermal crystallization at temperature T ,
φ(t, T ) = 1− exp
(
−4π
3N(T )G3(T )t3
)
(2.2)
from which the nucleation density can be obtained:
N(T ) = −3 ln (1− φ)
4πG3(T )t3(2.3)
with growth rate G(T ) depending on the temperature only. The main requirement here
is that the growth rate is independent of the nucleation density, even when this density
is influenced by a nucleating agent or by flow. Flow experiments are so-called short
term shear experiments; the flow can generate extra nuclei but the growth takes place
after the flow has stopped. The growth rate for iPP is well known [26]. Note that there
are different empirical and theoretical relations describing the temperature dependence
of the growth rate, see Eq. (2.4) [8] and Eq. (2.5) [27]:
G(T ) = Gref exp[
−cG(T − TG,ref)2]
(2.4)
G(T ) = G0 exp
[
− U∗
R (T − Tg + T∞)
]
× exp
[
−κGT2m (Tm + T )
2T 2 (Tm − T )
]
(2.5)
One could think of using other approaches than Eq. (2.1) by applying more simple
models [28–32] or empirically based scaling laws between the space filling and the storage
modulus [33–35]. However, it was demonstrated by Steenbakkers and Peters [21] that
such approaches do perform less than the suspension model as used here, and therefore,
we will not apply them to our results. Summarizing, by measuring the complex modulus
G∗(t, T, γ, ts) for different temperatures, shear rates γ, and shear times ts, we can
determine the space filling φ(t, T ) using Eq. (2.1) and the nucleation density N(T, γ, ts)
using Eq. (2.3), provided that only spherulitic growth from predetermined point-like
nuclei occurs.
14 Chapter 2
2.4 Results and Discussion
2.4.1 Determination of the nucleation density for NA-iPP
First of all, Figure 2.1 shows that the structures formed during crystallization with
nucleating agent do not show any unusual structure as was found by Lee Wo et al. [16] for
a similar system (a commercial iPP with different concentrations of U-Phthalocyanine),
so the above method can be applied to convert the time evolution of the rheological
properties into kinetics of space filling. Figure 2.2 shows the time evolution of the
storage modulus G′ of the nucleating agent system during crystallization at different
temperatures. It should be noticed that for T = 145 ◦C the initial value of G′ is not
the same as those for the other temperatures. The method is based on the assumption
of isothermal crystallization. If the degree of undercooling is large with respect to
the cooling rate, crystallization already sets in during cooling. The problem is made
even worse due to the 2-min delay time we used in order to equilibrate the sample
temperature. This is the case for T = 145 ◦C; crystallization has already started before
we begin to track the rheological evolution (indicated by an increased initial value of
G′). Faster cooling rates are required when studying higher levels of undercooling.
Nevertheless, we still want to show this result to demonstrate the limitations of the
method.
10 100 1000 10000
104
105
151 oC148 oC147 oC145 oC
106
107
108
G' (
Pa)
time (s)
Figure 2.2: Time evolution of the storage modulus for NA-iPP samples crystallized atdifferent temperatures.
The related space filling, determined by Eq. (2.1), is shown in Figure 2.3. For the high
experimental temperature range used here, the growth rate is better captured by Eq.
(2.4) [8, 26], so this expression was applied. Figure 2.4 shows the diffraction patterns
of NA-iPP samples after quiescent crystallization and demonstrates that nucleating
Chapter 2 15
10 100 1000 10000
0.0
0.2
0.4
0.6
0.8
1.0
151 oC 148 oC 147 oC 145 oC
spac
e fil
ling
time (s)
Figure 2.3: Time evolution of space filling derived from the dynamic modulus for NA-iPPsamples crystallized at different temperatures.
9 10 11 12 13 14 15
145 oC
147 oC
148 oC
(-131)(111)(130)(040)
Inte
nsity
(a.u
.)
2 (o)
(110)
151 oC
Figure 2.4: One-dimensional WAXD curves of NA-iPP samples crystallized at differenttemperatures.
agent crystallization results in the same α-modification as crystallization of the neat
iPP. Consequently, the same growth kinetics, Eq. (2.4), applies. The number density
of nuclei determined by Eq. (2.3) is plotted versus space filling in Figure 2.5. It is
nearly constant between φ ≈ 0.1 and φ ≈ 0.9, except for the experiment at T = 145 ◦C,
where crystallization has already set in before the dynamic measurements have started.
Much higher values are found in the early stage, but N(T ) becomes nearly constant
when φ ≈ 0.4 for all temperatures. The influence of the unknown initial space filling is
relatively smaller for higher degrees of space filling, i.e., in later stages of the process.
We have taken the average value for a space filling between φ = 0.5 and φ = 0.9 as a
reasonable approximation. Nucleation densities from all experiments are plotted as a
function of the experimental temperature in Figure 2.6. It can be concluded that this
type of nucleating agent is very effective as it increases the nucleation density by up to
16 Chapter 2
0.0 0.2 0.4 0.6 0.8 1.0
151 oC148 oC147 oC
145 oC
1014
1016
1018
1020
N (m
-3)
space filling
1022
Figure 2.5: Nucleation density versus space filling for NA-iPP samples crystallized atdifferent temperatures.
130 135 140 145 150 155
1013
1015
1017
1011
NA+iPPiPP
N (m
-3)
temperature (oC)
1019
Figure 2.6: Nucleation density of iPP and NA-iPP versus temperature.
six decades. Notice that the temperature dependency of the nucleation density is very
similar for the neat iPP and the NA-iPP, and that the results for T = 145 ◦C, although
less reliable for φ < 0.4, are well in line with the results for higher temperatures.
Results for relatively low temperatures should be treated with some caution.
2.4.2 Reproducibility
First we compare the results of Housmans et al. [9], obtained with the same method
and for the same iPP, to the results presented here. For a temperature T = 138 ◦C,
they found, for quiescent conditions, a nucleation density N = 8 × 1011m−3, while we
obtain the (interpolated) value N = 6 × 1012m−3. We ascribe this difference to the
Chapter 2 17
sample preparation procedure. Our neat iPP and nucleated samples were processed by
injection molding, which means that the sample preparation step already induced extra
nuclei due to the applied (uncontrolled) flow. The samples used by Housmans et al. [9]
were prepared by means of compression molding.
130 135 140 145 150 155
temperature (oC)
1st Series NA+iPP1st Series iPP2nd Series NA+iPP2nd Series iPP
1011
1013
1015
1017
1019
N (m
-3)
Figure 2.7: Nucleation density of iPP and NA-iPP versus temperature for two series ofexperiments.
We repeated our experiments to check for reproducibility. The time lapse between the
two series of experiments was about 8 weeks. The results of these repeated experiments
(2nd series) are shown in Figure 2.7, together with the previous results (1st series). We
want to stress the importance of a good temperature control. An error of 1 ◦C typically
gives a factor two difference in the number of nuclei. Notice that in the second series
of experiments we managed to get good results for temperatures as low as T = 143 ◦C
while in the first series we already encountered problems at T = 145 ◦C.
2.4.3 Effect of mild flow
Figure 2.8 shows the evolution of G′ during crystallization at 148 ◦C under quiescent
conditions and after different flows (fixed shear rate and variable shear time). For a
shear rate of 60 s−1, a shear time of 2 s shows clearly accelerated kinetics. Further
increase of the shear time to 4 s does not change the kinetics much. The acceleration
of crystallization seems to become (nearly) independent of the shear time beyond 4 s,
indicating that the shear-enhanced point-like nucleation saturates. This effect was also
observed by Housmans et al. [9] for this and two other iPPs. The time evolution of
the storage modulus of the sheared nucleating agent system has the same shape as in
the quiescent nucleating agent system, meaning that the growth mechanism is the same
and only spherulites are formed. This implies that our method can still be applied
18 Chapter 2
to determine space filling for crystallization after shear. Moreover, the results can be
compared to those of Housmans et al. [9].
10 100 1000 10000
024
time (s)
104
105
106
107
108
G' (
Pa)
shear time (s)6
Figure 2.8: Time evolution of the storage modulus for NA-iPP under quiescent conditionsand after short term shear (γ = 60 s−1, ts = 2, 4, 6 s) at T = 148 ◦C.
For flow-induced crystallization experiments, an adequate measure of the flow
strength is the Weissenberg number, based on the stretch relaxation time of the high
molecular weight (HMW) tail of the molecular weight distribution:
Wis(T, γ) = τHMWs (T ) γ (2.6)
Recent modeling work [36] suggests that the creation rate of point-like nucleation
precursors depends not only on the average stretch of the HMW molecules, but also
explicitly on the temperature: the prefactor of the creation rate was found to be
proportional to the time-temperature shift factor aT . Therefore we use aTWis as a
criterion to compare experiments, which scales as a2T , since τHMWs in Eq. 2.6 scales
with aT as well. From the linear viscoelastic data and the stretch relaxation time τHMWs
reported by Housmans et al. [9], we find Wis(148◦C) = 13, Wis(151
◦C) = 12, and
aT (151◦C)Wis(151
◦C)
aT (138 ◦C)Wis(138 ◦C)= 1.1 , (2.7)
where Wis(138◦C) = 8 for the strongest flow applied by Housmans et al. [9] to the same
neat iPP as used here. Hence, these two data sets are reasonably comparable in terms
of flow conditions.
The calculated nucleation densities are plotted in Figure 2.9. The saturated
nucleation density at 148 ◦C after shear is around 40× 1016m−3, six times higher than
7× 1016m−3 for quiescent crystallization, i.e., adding typically ∼ 1017m−3 nuclei. This
Chapter 2 19
0 2 4 6
1017
1016
1015
1018
151 oC 148 oC
N (m
-3)
shear time (s)
Figure 2.9: Nucleation density of NA-iPP under quiescent conditions and after shear atT = 148 ◦C and T = 151 ◦C (γ = 60 s−1).
130 135 140 145 150 155temperature (oC)
1st Series NA+iPP1st Series iPP1st Series shear2nd Series NA+iPP2nd Series iPP
1011
1013
1015
1017
1019
N (m
-3)
Figure 2.10: Nucleation densities of iPP and NA-iPP under quiescent and shear conditions.
elevated number is much more than what was added by imposing shear to the neat iPP
in the experiments of Housmans et al. [9]; mild flow raised the point-like nucleation
density of the neat iPP by one to two decades before the shear effect saturated, i.e.
adding typically ∼ 1013m−3 nuclei. This indicates that, in the presence of nucleating
agent, shear-induced point nucleation can be much more effective. This should be
directly related to the nucleating agent, i.e., the local amplification of flow effects due
to the presence of the nucleation particles, see for example the work of Hwang et al. [37],
and not to a change in the rheological properties, which we expect to be very small due
to the, in this respect, still very low space filling of nuclei.
20 Chapter 2
2.5 Conclusions
A new method to determine nucleation densities, based on rheometry, was used
on quiescent and sheared samples of a neat and an artificially nucleated isotactic
polypropylene. All calculated nucleation densities are summarized in Figure 2.10. It
is quantitatively shown that U-Phthalocyanine is very effective for nucleating isotactic
polypropylene. Moreover, it was found that the effect of shear is enhanced by the
presence of the nucleating agent. This rheological method is easy to apply since it
requires a standard rheometer, available in most academic and industrial labs.
References
[1] J. Kurja and N. A. Mehl. Nucleating agents for semicrystalline polymers. In: H. Zweifel, editor,
[34] The linear low molecular weight polyethylene (LMWPE) matrix, supplied by Basell
Polyolefine GmbH (Frankfurt, Germany), has a Mw = 45 kg/mol and polydispersity
Mw/Mn = 3. The critical overlap concentration of high molecular weight molecules can
be calculated with [35, 36]
c∗ =3Mw
4π〈Rg2〉3/2ρNA
(3.1)
where 〈Rg2〉 is mean-square radius of gyration of chain related to the molecular weight by
〈Rg2〉1/2 = 0.46Mw
1/2, [37] ρ is the density andNA is Avogadro’s number. The estimated
critical concentration of UHMWPE is around 0.35wt%, i.e., much smaller than the
3wt% in our bimodal blend, meaning that a significant number of entanglements exist
between the UHMWPE molecules.
The bimodal system was prepared by solution blending to achieve mixing at a
molecular scale. The UHMWPE was first dissolved in a xylene solution at 130 ◦C, and
subsequently LMWPE was added to dissolve, where the concentration of total PE’s is
2.5% with an antioxidant (IRGANOX1010) added at a concentration of 2000 ppm. This
solution was stirred for 1 h under a nitrogen atmosphere. Next, the hot xylene solution
was poured into a large excess of stirred cold methanol. The precipitated gel was filtered
and washed with methanol several times and then dried in vacuum at 80 ◦C for 2 days.
After further addition of 2000 ppm of antioxidant (IRGANOX1010), in order to avoid
degradation during sample preparation, the bimodal blend was compression molded at
160 ◦C into strips to fit the test cell.
Chapter 3 27
3.2.2 Protocol
The slit flow device developed in Eindhoven [18,38] is an evolution of the Multi-Pass
Rheometer of Eland Engineering Co Ltd. (UK) [39] (see Figure 3.1). The flow cell is
specifically designed for online scattering and therefore equipped with diamond windows
(opening angle of 45◦). The specimen (L = 200mm, W = 6mm, and H = 1.5mm)
is confined between two servo hydraulically driven rectangular pistons. An important
advantage of this slit-flow device is the possibility to impose and release pressure. The
maximum pressure is 800 bar and the maximum temperature 250 ◦C. The procedures
for flow, pressurization, and depressurization are illustrated in Figure 3.1.
(a) (b) (c)
Figure 3.1: Schematic of the flow device and flow, pressurization, and depressurizationprocedures. Moving directions of the pistons are indicated by arrows. Heatingrods and the heating/cooling channels are not shown.
Moving the two pistons in the same direction introduces a shear flow to the sample
(Figure 3.1a), while moving the two pistons toward or away from each other will
pressurize (Figure 3.1b) or depressurize (Figure 3.1c) the sample, respectively, without
causing any flow at the observation point (center of the slit). The pressure difference
during flow is recorded by means of two pressure transducers.
The experimental protocol used in this chapter is shown in Figure 3.2. The polymer
in the test cell is first heated up and annealed at 190 ◦C for 10 min to erase the memory
of previous thermal and mechanical histories and then cooled to 134 ◦C at which shear,
pressurization, and depressurization are performed. To avoid temperature fluctuations,
the cell is stabilized by means of an oil bath, while the top and bottom barrels are
always kept at high temperature (190 ◦C) in order to have the pressure transducers
functioning properly. Next, flow is imposed with a piston speed of 15mm/s for 0.8 s.
28 Chapter 3
time
pre
ssure
shear
tem
pera
ture
ta
Figure 3.2: Experimental protocol. The annealing time ta is between cessation of flow andpressurization.
The shear rate and Weissenberg number (Wi) distributions over the slit thickness were
estimated considering the rheology of the material and are shown in Figure 3.3 (see also
the Appendix). The shear rate varies nonlinearly from 0 at the slit center to a maximum
of 67 s−1 at the wall. The Weissenberg number, Wi = γτRouse, is used to estimate the
molecular stretch induced by flow. When Wi > 1, molecules become stretched, and
this is a requirement for the creation of precursors. [40] The longest Rouse times of
UHMWPE and LMWPE at 134 ◦C are 4.9×10−2 and 4.5×10−5 s (see section 3.3.3 for
the calculation), respectively, so the Weissenberg number for molecular stretch at the
wall is 3.3 for HMW tail but nearly zero for LMW matrix.
In order to obtain good filling of the slit and rule out wall slippage, a reference
pressure of 50 bar was kept on the specimen. The average pressure during flow,
PAverage = Plower +12△Psensor, where Plower and △Psensor are the lower pressure (around
15 bar) and the pressure difference between the two pressure sensors (see Figure 3.4),
is around 70 bar totally, so the influence of flow on the pressure level is negligible.
A pressure of 300 bar was chosen as the elevated pressure level to increase the melt
undercooling. Figure 3.2 also shows that pressurization can be applied right after flow
(ta = 0) or after annealing (ta = 22 min) with the same flow. Both protocols were
employed in this work. The former (ta = 0) is used to see if any precursors were formed
during flow, and the latter (ta = 22 min) is to show how precursors develop with time.
Chapter 3 29
centerwall wall
0.15 0.30 0.45 0.60 0.75
0
1
2
3
4
LMWPE matrix
distance from center (mm)
UHMWPE
We
issen
be
rg n
um
be
r
0.75 0.60 0.45 0.30 0.15 0.00
0
20
40
60
80
distance from center (mm)
she
ar
rate
(1/s
)
Figure 3.3: Distributions of shear rate and Weissenberg numbers for stretching HMW tailand LMW matrix over the slit thickness direction.
3.2.3 X-ray characterization
X-ray measurements were carried out at the Dutch-Belgian (DUBBLE) beamline
BM26B of the European Synchrotron Radiation Facility (ESRF) in Grenoble, France,
with a wavelength of 0.95 A. [41] A Frelon detector with a resolution of 2048 × 2048
pixels of 48.8µm × 48.8µm, and placed at a distance of 0.195m, was used for wide-
angle X-ray diffraction (WAXD). The measuring time of each WAXD frame, including
exposure and readout of data, was 8.5 s.
WAXD images were processed with the software package FIT2D to obtain intensity
versus scattering angle (2θ) profiles. Crystallinity was calculated after deconvolution
of the total intensity scattered by the crystalline (Acrystal) and amorphous (Aamorphous)
domains:
X =Acrystal
Acrystal + Aamorphous× 100% (3.2)
Flow-induced crystallization depends on the strength of the local flow field. In the
slit geometry, the shear rate changes from a minimum in the center to a maximum at
the wall, as shown in Figure 3.3, so shear-induced crystalline layers will form mostly
next to the two walls. X-ray going through the whole sample thickness will scatter from
the two shear layers, and therefore, values calculated in this way do not represent the
real crystallinity in certain specific layer but rather an “apparent” crystallinity averaged
over the optical path of the X-ray beam through whole sample.
30 Chapter 3
3.3 Results and Discussion
3.3.1 Reference experiment: no pressure quench after flow
The formation and development of flow-induced precursors are investigated with a
shear pulse (γ = 67 s−1, ts = 0.8 s) under 50 bar at 134 ◦C. First of all, the structural
development during flow was examined through the rheological response of the polymer
melt. Figure 3.4 shows the evolution of pressure difference during flow, which first
increases rapidly, subsequently shows a small overshoot, and reaches a steady-state
plateau. This behavior can be related to the usual nonlinear rheological response of
the sheared molten polymer. Scelsi et al. [42] reported a buildup of pressure difference
(HDPE, 130 ◦C, Wi for stretch is estimated around 60) during flow in a channel with
a contraction in the middle section and associated it to continuous crystal formation
concentrated in the region of slit exit. Such a pressure difference buildup during flow
was not observed in our experiments (134 ◦C, Wi = 3.3). Therefore, our results imply
that crystals do not form during flow or that the viscosity does not change even if
precursors form (as discussed later).
0.0 0.2 0.4 0.6 0.80
20
40
60
80
100
120
140
160
pres
sure
diff
eren
ce (b
ar)
time (s)
experiment 1 experiment 2
Figure 3.4: Pressure difference during flow. Two experiments are shown to demonstrate thereproducibility of the flow history.
Based on the nano- and mesoscale structures of crystalline planes and density
differences, both SAXS and WAXD were employed to examine, at different length scales,
structural aspects of flow-induced precursors. However, in-situ synchrotron SAXS and
WAXD data acquired after flow did not show any observable signal, which confirms
that no detectable crystallization takes place neither during flow nor within the next 20
min when the sample is kept isothermal (data not shown since no detectable signal was
found). More in detail, despite the Wi number for stretching the HMW tail is larger
Chapter 3 31
than unity in the region close to the wall (see Figure 3.3); neither crystalline nor densely
packed scatterers are observed. This can be a consequence of a low concentration of
precursors, i.e., below the experimental detection limit. Therefore, crystallization has to
be triggered to reflect the features of precursors. For PE, WAXD is sufficient to fulfill
this purpose of characterizing crystallization features (i.e., orientation, crystallinity,
twisted lamellae) which will be shown in the following results. Therefore, we use only
WAXD [43] to track PE crystallization and show that a pressure quench is a suitable
method to visualize precursors even at these very low concentrations.
3.3.2 Pressure quench after flow
In order to investigate the formation of flow-induced precursors, after the application
of the same flow as in section 3.3.1, a pressure quench, with the pressure history shown
in Figure 3.5, is performed. The pressure is raised linearly from the reference pressure
of 50 to 300 bar without overshoot. The synchronous top and bottom pressures indicate
that the pressure field is homogeneously distributed over the specimen and that there
is no flow at the observation point (center of the slit). With pressure, undercooling is
generated and immediately triggers crystallization, illustrated by the WAXD images in
Figure 3.6.
0 10 20 300
100
200
300
pressure - top pressure - bottom
pres
sure
(bar
)
time (s)
Figure 3.5: Pressure profile during a pressure quench.
As soon as the maximum pressure is achieved, arched (110) and (200) reflections
appear in the equator direction (Figure 3.6a), indicating the formation of the
orthorhombic unit cell with c-axis aligned in the flow direction. According to Keller
et al. [6], the diffraction pattern of Figure 3.6a can be produced both by the extended
chain crystals of shish and by the folded chain crystals of untwisted lamellae.
Figure 3.6: 2DWAXD patterns under a pressure quench after flow. Flow is along the verticaldirection. The reference time is the moment when 300 bar is reached.
For the purpose of this work, it is not essential to make such a distinction. The most
important observation is the presence of highly oriented crystals. In fact, as the sample
is pressurized in absence of extra flow, these oriented crystals originate from deformed
molecules involved in precursors induced by the flow during the shear step.
As crystallization proceeds, the (110) reflection broadens in the azimuthal direction
(Figure 3.6b) and, at tc = 17 s, splits into off-axis diffraction together with the clear
appearance of off-axis (200) diffractions (Figure 3.6c). These off-axis (110) diffractions
are the result of the lateral growth of twisted lamellae. During this process, the
lamellar propagation direction holds perpendicular to the flow direction, but crystal
units rotate along the b-axis. [6] Twisting leads to randomization in the orientation
of c-axes. Keller et al. [6, 44] proposed two extremes of lamellar orientation for flow-
induced PE crystallization: “Keller/Machin I” and “Keller/Machin II”. The former
(KM-I) corresponds to the fully twisted lamellae producing off-axis (110) and meridional
(200) diffractions. The latter refers to the flat, nontwisted lamellae (all c-axes parallel
with flow direction) producing equatorial (110) and (200) diffractions. In the transition
from one to another an “intermediate” state is observed showing the off-axis (110) and
(200) patterns. [6, 45] Therefore, the azimuthal features of the (200) diffraction reflect
the lateral growth of lamellae. [6, 9, 45]
In a later stage, the diffraction of isotropic structures is also observed, e.g. isotropic
(110), (200) diffractions at 102 s (see Figure 3.6d). These two crystallization processes,
fast oriented crystallization and slow isotropic crystallization, characterized by different
degrees of orientation and time scales can be rationalized by considering that the
inhomogeneous flow field in the slit gives rise to inhomogeneous molecular stretch as
shown by Figure 3.3. At the wall, where the stress reaches a maximum, molecules
experience the largest stretch and many flow-induced precursors are generated. These
are the domains where highly oriented crystals are formed upon pressurization. Toward
the centerline, molecules experience little or no stretch and the probability of forming
oriented precursors vanishes. In this part of the sample, isotropic crystallization can
be triggered purely by pressure. The WAXD images (Figure 3.6a-d) are indicative of
Chapter 3 33
structures averaged over the optical path of the X-ray beam (thickness of the samples),
and therefore, they contain information on both these two processes.
Next, the effect of precursors on crystallization kinetics is illustrated in Figure 3.7a
where the apparent crystallinity is plotted as a function of time for shear-induced
crystallization under a pressure quench and two reference experiments (shear-induced
crystallization without pressure quench and quiescent crystallization with pressure
quench). It is evident that when shear is applied, crystallization starts as soon as
the 300 bar pressure is reached. On the other hand, without shear, crystallization
starts only after 25 s from reaching 300 bar. Eventually, without applying pressure,
crystallization of the sheared polymer does not occur in the experimental time window
of 20 min. The results show that there is a remarkable interplay between flow and
pressure on crystallization kinetics and morphology.
Figure 3.7: (a) Crystallinity evolution for shear-induced crystallization with pressure quench(◦), quiescent crystallization with pressure quench (△), and shear-inducedcrystallization without pressure quench (�). (b) 2D WAXD pattern of quiescentcrystallization under pressure quench at tc = 34 s.
From the above results, we conclude that oriented precursors are generated by the
flow, but prior to pressurization, they are invisible to X-rays (see section 3.3.1). It is
clear that a pressure quench effectively provides the additional undercooling that triggers
crystallization by raising the equilibrium melting temperature. The equilibrium melting
temperature of PE at 1 bar is T 0m = 414.6 K. [46] Its increase with pressure, described
by the Clausius-Clapeyron relation, can be approximated by T (p) = T 0m+(dT p
m/dp)△p,
where dT pm/dp = 35.2 K/kbar. [46] In this way, the equilibrium melting temperatures
corresponding to 50 and 300 bar are calculated as 416.4 and 425.2 K, respectively.
With pressurization from 50 to 300 bar, the undercooling △T pexp = T p
m − Texp increases
34 Chapter 3
from △T 50bar134 ≈ 9K to △T 300 bar
134 ≈ 18K (experimental temperature 407.15 K). Thus, a
pressure quench from 50 to 300 bar increases the undercooling by 9 K within 25 s. Such a
pressure quench, around 22 K/min, is comparable to a temperature quench in small lab-
scale device. On the other hand, it is much more efficient than lowering the temperature
of such large metal device with a cooling medium, especially since the cooling rate
decreases when approaching the target temperature, and thus it usually takes much
longer time (minutes) to stabilize at the desired undercooling (see the Appendix).
The azimuthally homogeneous (110) diffraction in Figure 3.7b shows that pressurizing
does not cause flow at the observation point which might have influenced crystallization.
Concluding, oriented crystals (Figure 3.6) and faster kinetics (Figure 3.7a) show
that precursors can form in a sheared melt, where only the HMW chain is stretched.
This demonstrates that the HMW tail determine the formation precursors, consistent
with the findings of Mykhaylyk et al. [15] A pressure quench triggers crystallization
and effectively “lightens up” these flow-induced precursors which could not be detected
otherwise for these conditions (134 ◦C, 50 bar).
3.3.3 Pressure quench after annealing
The effect of partial dissolution of flow-induced precursors can be semi-qualitatively
estimated by introducing an annealing step (during which pressure is kept at 50 bar)
between the flow pulse and the pressure quench. During the annealing step, whose length
is arbitrarily fixed at 22 min, no structural changes were observed by SAXS/WAXD
(data not shown). Figure 3.8 shows the 2D WAXD patterns after applying a pressure
quench to the sheared and annealed specimen. The equatorial (110) diffraction in Figure
3.8a indicates the survival of orientation in the precursors with annealing.
that the relaxation of the most unstable “shear-induced bundles”, observable with
SAXS, follows the reptation dynamics of the longest chains whereas stable precursors
survive on time scales much longer than the rheological ones.
Systematical studies on “relaxing” shear-induced “nucleation precursors” that are
invisible to SAXS were done by Alfonso and co-workers. [14] They found that, in iPP,
at temperatures as high as 190 ◦C (above nominal melting temperature but not beyond
equilibrium melting temperature), “nucleation precursors” can survive much longer than
the longest rheological relaxation times, and that the characteristic survival time can
be increased by a stronger or longer flow. The change in relaxation times implies that
other effects are determining the dissolution of precursors. This idea is supported by the
different relaxation behaviors of the flow-induced helices in iPP as observed by An et
36 Chapter 3
al. [49] They suggested that interactions between flow-induced helices of iPP dominate
the dissolution rates and the helices with interactions relax slower than those without.
Considering the long lifetime of X-ray unobservable oriented precursors, in our
results, it is reasonable to infer that interactions between PE chain segments
(comparable to very local crystallization events) contribute to the long lifetime beyond
the rheological times. According to the classical nucleation theory, a precursor below the
critical size tends to relax; the interaction decreases the relaxation kinetics. Once the
total interaction (contributed by the increased volume as well) is sufficient, the volume
free energy overcomes the surface energy, and the precursors can develop to nuclei that
are stable. Long-term stable precursors were also observed by Mykhaylyk et al. [15] for
hydrogenated polybutadiene; the precursors survived within the experimental window
which was as long as 10 h. Interestingly, in our experiments, when these segmental
interactions are initiated during flow, they do not cooperate significantly to change the
viscosity of the whole melt as observed from the pressure difference in the presence of
precursors (see Figure 3.4).
0102030405060708090
10
20
30
40
Azimuthal angle ( o)
Inte
nsity
(a.u
.)
time
0s
110s
51s
(a)
0102030405060708090
10
20
30
40
Azimuthal angle ( o)
Inte
nsity
(a.u
.)
time
0s
85s
(b)
Figure 3.9: Change in the azimuthal distribution of (200) diffraction during pressure quenchcrystallizations for (a) unannealed and (b) annealed samples.
The structures surviving the 22 min annealing step show some specific features
that can be captured by looking at the (200) reflection. Figure 3.9a shows that the
(200) diffraction of the unannealed sample occurs at low azimuthal angle and moves
toward higher value with time. After about 51 s, the majority of the (200) diffractions
tends to develop around the azimuthal angle of 50◦, quite similar to the “intermediate”
Chapter 3 37
orientation mode. In contrast, for annealed samples, the (200) diffraction is found along
the meridional direction (see Figure 3.9b), indicating a pronounced Keller/Machin I
mode. The data of Figure 3.9 show that, during crystallization without annealing, a
higher fraction of flat lamellae formed in comparison with the annealed sample.
The different morphology must be associated with nuclei density which is larger in
the unannealed sample. This result is consistent with the finding of Keum et al. [9]
that twisted lamellae are more prominent when the shish density is smaller due to
lower shear strength (at the lower shear rate 20 s−1 compared with 70 s−1 for the
same flow time). Thus, the lower nuclei density in the annealed sample indicates that
some unstable shear-induced precursors relaxed during annealing. The crystallinity
developments of the annealed and unannealed samples are compared in Figure 3.10 with
quiescent crystallization as reference. The lower crystallinity in the annealed sample
confirms the decrease in the total nuclei number, consistent with 2D patterns comparison
between Figures 3.6 and 3.8.
0 20 40 60 80 100
0
5
10
15 un-annealed annealed quiescent
appa
rent
cry
stal
linity
(%)
time (s)
Figure 3.10: Crystallinity evolution for (◦) unannealed, (⋄) annealed, and (△) quiescentcrystallization under pressure quench.
Concluding, both stable and unstable precursors are generated by the flow in a
slit with varying flow strength over the thickness. The stable precursors orient and
accelerate the following crystallization while unstable ones disappear during annealing
leading to a larger space for overgrowth and higher fraction of twisted lamellae.
These precursor evolutions, i.e., survival and relaxation, can be distinguished only by
crystallization started with high enough undercooling, which, in this work, is obtained
by a pressure quench.
38 Chapter 3
3.3.4 Inverse quench by depressurization
Finally, we present the results for resetting the pressure from 300 bar back to 50
bar before reaching complete crystallization. Depressurization suddenly eliminates
the increased undercooling (the experimental temperature is kept 134 ◦C). Figure
3.11a shows crystallinity evolutions after depressurization (prior to depressurization
the annealed and unannealed sample have been crystallized for about 100 s). For
both samples, crystallinity decreases but does not vanish completely. The residual
crystallinity in the unannealed sample is around 2%, 4 times larger than that of the
annealed sample (final level around 0.5%). Crystallinity decrease after depressurization
is ascribed to melting of the lamellae due to the reduced undercooling by depressurizing,
which acts as “inverse quench”. [50]
0 100 200 300 400 500
0
2
4
6
8
10
12 un-annealed annealed
appa
rent
cry
stal
linity
(%)
time (s)
(a) (b) (c)
Figure 3.11: (a) Crystallinity evolution of (◦) unannealed and (⋄) annealed samples duringmelting. t = 0 when pressure reaches 50 bar. The 2D WAXD images of (b)unannealed sample at 527 s and (c) annealed sample at 408 s during melting.
Cho et al. [51] suggested that PE lamellae may further thicken in an isothermal
process. Thus, when the crystallization time is not long enough for all crystals to finish
thickening, as in our work, the early formed crystals have thicker lamellae compared to
those created in the late stages. The resulting lamellar distribution leads to variation
in thermal stability. Thus, after depressurization the stable (thick) crystals can survive
but unstable (thin) ones melt. As a result, the unannealed sample with more nuclei
has more stable (thicker) crystals than the annealed sample. Figure 3.10 shows that
oriented crystallization sets in before unoriented crystallization; therefore, oriented
crystals experience longer isothermal thickening, and this makes them more likely to
survive in inverse quenching. This is confirmed by the results shown in Figure 3.11c.
Chapter 3 39
3.4 Conclusions
The pressure quench is a relatively simple way to mimic a temperature quench.
It has a number of advantages compared to thermal quenching (reverse cooling by
depressurizing, avoiding temperature gradients, introducing complex thermal histories).
It was applied for (a) crystallizations under quiescent condition and (b) flow and with
and without subsequent annealing. For quiescent crystallization it is demonstrated that
rising pressure to 300 bar is enough to trigger crystallization. Application on sheared
samples shows that a pressure quench effectively visualizes the shear-induced precursors
which are invisible to X-ray scattering. Crystallization kinetics is faster in this case,
and oriented morphology is observed. The orientation in the outmost layer can survive
annealing for 22 min, but the average nuclei density along the whole sample does relax.
In addition, depressurization before complete crystallization leads to partially melting
of the crystals which is explained by the variation in lamellar stability.
References
[1] H. E. H. Meijer and L. E. Govaert. Progress in Polymer Science 30(8-9):915–938, 2005.
[2] B. A. G. Schrauwen, R. P. M. Janssen, L. E. Govaert, and H. E. H. Meijer. Macromolecules
37(16):6069–6078, 2004.
[3] B. A. G. Schrauwen, L. C. A. Von Breemen, A. B. Spoelstra, L. E. Govaert, G. W. M. Peters,
and H. E. H. Meijer. Macromolecules 37(23):8618–8633, 2004.
[4] M. Kristiansen, M. Werner, T. Tervoort, P. Smith, M. Blomenhofer, and H. Schmidt.
Macromolecules 36(14):5150–5156, 2003.
[5] G. Eder and H. Janeschitz-Kriegl. Structure development during processing: crystallization. In:
H. E. H. Meijer, editor, Processing of Polymers, number 18 in Materials Science and Technology:
a Comprehensive Treatment, 269–342. Wiley-VCH, Weinheim, 1997.
[6] A. Keller and H. W. H. Kolnaar. Flow-induced orientation and structure formation,. In: H. E. H.
Meijer, editor, Processing of Polymers, number 18 in Materials Science and Technology: a
The so-called “short-term flow” is widely applied in experimental flow-induced
crystallization studies in order to separate the nucleation and subsequent growth
processes. The basis of “short-term flow” is the assumption that structure development
during flow can be minimized and the polymer rheological behavior, i.e. the viscosity,
does not change. In this chapter we explore the validity of this assumption for short
but strong flow and reveal the structure formation in the early stages of crystallization.
Viscosity and structure evolution of an isotactic polypropylene (iPP) melt at 145 ◦C are
measured during short-term flow (0.20-0.25 s) using the combination of a slit rheometer
and fast X-ray scattering measurements. For high enough shear rates (≥ 240 s−1)
a viscosity rise is observed during flow, i.e. the conditions for “short-term flow” are
not satisfied. Such a viscosity rise indicates structure formation in the slit which is
considered as the formation of shish or their precursors. With a time delay of about
0.1 s with respect to the viscosity rise the development of shish is observed by means
of time resolved SAXS measurements in the middle of the slit. Depending on the shear
rate these shish are detected during flow (shear rates ≥ 400 s−1) or after flow (400
s−1 > shear rates ≥ 240 s−1). For shear rates between 80 and 160 s−1, the viscosity
This chapter is based on : Zhe Ma, Luigi Balzano, Tim van Erp, Giuseppe Portale, Gerrit W. M.Peters. to be submitted, 2012
45
46 Chapter 4
does not change significantly and, instead of shish, oriented row nuclei are generated.
These flows qualify as short-term flow conditions, but the transient and inhomogeneous
behavior, both in flow and in flow gradient direction, has to be taken into account when
characterizing the flow field in future studies.
4.1 Introduction
Semi-crystalline polymers, especially polyethylene (PE) and isotactic polypropylene
(iPP), are widely used materials because of their low cost, easy processing, good
chemical resistance, etc. These materials are often processed from the molten state and
therefore subjected to flow fields when molded into final products. It is well known that
these flow fields can not only accelerate crystallization kinetics by orders of magnitude,
but also radically change the crystalline morphology from isotropic spherulites to
highly oriented shish-kebab. Such a morphological transition is important since the
morphological building blocks determine the final (mechanical and other) properties
of products. [1, 2] Therefore, a full understanding of the relation between flow fields,
crystallization kinetics and the resulting morphology is required to design processing
procedures for optimal properties.
Initial studies on flow-induced crystallization of polymer melts focused on the
structure evolution during continuous flow fields. [3–7] Crystallization of polymers is
governed by nucleation and growth and both these processes are influenced by the
flow. [8, 9] When crystals nucleate/grow, the viscosity of the melt increases and this
enhances the effect of flow on crystallization, giving rise to a self-enhancing mechanism.
To simplify this kind of experiments, Janeschitz-Kriegl and co-workers proposed a
“short-term shearing” method [10], where the shear duration is chosen short enough
so that during flow the effects of crystallization on viscosity and structure changes are
minimized. It is assumed that only nuclei or their precursors are created during flow and
that these structures crystallize and grow after the flow ceases. In this way, the features
of flow-induced nuclei are revealed indirectly by studying the resulting crystallization
kinetics and morphology. This “short-term flow” has been widely used in studies on flow
induced crystallization in order to separate the nucleation and growth processes. [10–19]
Based on the assumption that viscosity is not changed by the flow, the effect of the
flow can be characterized by using flow characteristics and rheological properties. For
instance, the mechanical work [20]
w = η
∫ ts
0
γ 2(t)dt (4.1)
with the averaged viscosity η, shear rate γ(t) and shear time ts, is often considered
as the controlling factor in flow-enhanced nucleation [20] and formation of oriented
Chapter 4 47
structures [16, 18]. For the constant shear rate applied, often the steady state viscosity
is used. The key assumption to ensure this approach to be useful is that no change in
the rheological properties occurs during flow time.
In more recent work [21–23] fast time-resolved experimental methods were used
to investigate structure development, also during a short flow pulse, for conditions
where the Weissenberg number related to the stretch of the high molecular weight
tail (WiR−HMWtail) is large. Kumaraswamy et al. [21] performed slit-flow experiments
with constant wall stress (0.06 MPa) and attributed the observed unusual upturn
in birefringence to the generation of long-lived oriented structures. Balzano et al.
[23] observed the appearance of X-ray diffraction peaks indicating the formation of
crystalline structures during flows shorter than 1 s. These evidences imply that the
short-term flow protocols employed were not sufficiently short to prevent structure
formation, even though the shear time is much less than the characteristic crystallization
time.
These findings raise questions concerning short-term flow: can viscosity change
during flow? If so, under what conditions and how fast and, finally, what is the relation
between a viscosity change and structure formation in these early stages?
In addition, the early stages of shear-induced crystallization, from a structural
point of view, are still under debate. It has been proposed that so called dormant
nuclei already preexist in the amorphous melt and are activated by flow to trigger
crystallization. [24,25] The unusual birefringence upturn observed by Kumaraswamy et
al. [21, 22] points towards the formation of “shear-induced oriented structures” [21].
However, X-ray scattering measurements could not resolve these structures at the
relatively high temperatures applied (168 and 173 ◦C). [26] On the other hand, density
fluctuations were observed during extrusion of iPP [27] and this was interpreted as a
process where crystallization is preceded by spinodal-assisted phase separation enhanced
by flow [28]. Balzano et al. [17] found shear-induced “bundles” generated by flow
and, in line with a more classical view on crystallization, they suggested that the
bundle dimensions determine the subsequent evolution of crystallization or relaxation.
Obviously, a variety of structures can be generated by flow. The current understanding
on shear-induced crystallization, especially concerning the initial stage during flow, is
not yet clear enough to answer the above questions.
The present study focuses on structure formation and viscosity changes (other than
the normal transient response of a start-up flow) during short-term shear flow (max.
0.25 s) and explores the flow strength dependency of these events. For this purpose, a
slit rheometer and fast X-ray scattering measurements are combined to achieve a time
resolution sufficient to resolve the phenomena studied.
48 Chapter 4
4.2 Experimental
4.2.1 Material
The material used in this work is a commercial isotactic polypropylene (iPP)
homopolymer (HD601CF) provided by Borealis GmbH, Austria. This iPP has a weight
average molecular mass, Mw ≈ 365 kg/mol and a molecular weight distribution Mw/Mn
of 5.4. Its nominal melting and crystallization temperatures are 163 and 113 ◦C,
respectively. [18] A full characterization of the crystallization kinetics of this grade,
both for quiescent and flow enhanced, are given in refs [18, 29, 30].
For sample preparation, the material was first compression molded at 220 ◦C to plates
with thickness of 1.5 mm. Next, strips were machined of H ×W ×Ltot = 1.5× 6× 200
mm3 that fit in the slit flow cell.
4.2.2 Methods
The slit flow cell is operated on a multipass rheometer [31]. The specimen is confined
between two servo-hydraulically driven rectangular pistons that fit tightly in the slit, see
Figure 4.1. When pistons move together in one direction, they impose a shear field to
the polymer melt. The top and bottom barrels are equipped with pressure transducers
(distance between the transducers L = 160 mm) to measure the pressure history in the
slit during flow. The pressure difference △P is used to determine the apparent viscosity.
A pair of diamond windows placed in the middle of the flow cell allows for in-situ X-ray
characterization during and after flow.
X-ray
e-
ESRF slit rheometer “Pilatus” detector
synchrotron
radiation
Figure 4.1: Combined in-situ synchrotron X-ray scattering and slit rheometry.
The polymer in the slit is first heated to 220 ◦C and annealed for 10 min in order
Chapter 4 49
to erase the sample preparation history. Next, it is cooled to 145 ◦C and pressurized
to 50 bar by moving the pistons towards each other. During cooling, the reference
pressure of 50 bar is kept on the sample to prevent shrinkage holes. The sample is then
sheared and subsequently isothermally crystallized at 145 ◦C. To avoid fluctuations, the
temperature of the cell is stabilized by means of an oil bath. On the other hand, the top
and bottom barrels are kept at high temperature (220 ◦C) to ensure proper functioning
of the pressure transducers. After isothermal crystallization, the slit is cooled to room
temperature and the sample is removed for ex-situ analysis.
The flow strength was varied by choosing piston speeds, Vpiston, from 20 mm/s to 140
mm/s and the apparent wall shear rate is calculated by [32]
γ =6Q
WH2(4.2)
where Q is the volumetric flow rate, W is the slit width (6 mm) and H is the slit
thickness (1.5 mm). Apparent wall shear rates range from 80 to 560 s−1. The shear
duration is fixed at 0.25 s for shear rates from 80 to 400 s−1 and shortened to 0.23 and
0.20 s for 480 and 560 s−1, respectively, due to limitations in the piston displacement.
The apparent wall shear stress and the corresponding apparent viscosity are given by:
σ =H△P
2(1 +H/W )L(4.3)
η =σ
γ=
H2
12(1 +H/W )L× △P
Vpiston(4.4)
Both small-angle X-ray scattering (SAXS) and wide-angle X-ray diffraction (WAXD)
were employed to characterize the flow-induced structures. Synchrotron X-ray
measurements were carried out at the Dutch-Belgian (DUBBLE) beamline BM26B of
the European Synchrotron Radiation Facility (ESRF) in Grenoble, France. [33] The
wavelength used was 1.033 A. Fast acquisitions of SAXS and WAXD were performed
with a Pilatus 1M detector and a Pilatus 300K detector, respectively. This fast step is
carried out at an acquisition rate of 30 frame/s and lasts for 1 s. Both detectors are
triggered by the start of the piston displacement. The Pilatus 1M detector (981 × 1043
pixels of 172 µm × 172 µm) was placed at a distance of 7.117 m and used for SAXS, the
Pilatus 300K detector (1472 × 195 pixels of 172 µm× 172 µm) was placed at a distance
of 0.240 m and used for collecting the equatorial part of WAXD images.
Figure 4.2 shows a typical SAXS pattern (so-called streak) which is the result of a
highly oriented structure. The appearance of such streaks means that the structure
formed has a electron density which is different from its surroundings. Their equatorial
distribution implies that the maximum density contrast is perpendicular to the flow
direction, i.e. these fibrillar objects are oriented along the (vertical) flow direction.
50 Chapter 4
flow
SAXS streak
( )az
(1/ )q nm
Figure 4.2: A typical SAXS pattern with equatorial streaks. The integrating region fordetermination of the equatorial intensity ISAXS is indicated. Flow direction isvertical.
To describe the evolution of these SAXS streaks, we define a SAXS equatorial
intensity ISAXS integrated over the specific equatorial region:
ISAXS =
∫ 0.2
0.018
∫ 10◦
−10◦I(az, q)dazdq (4.5)
where az is the azimuthal angle and q is the norm of the scattering vector. The scattering
vector q = 4πsin(θ)/λ is defined as with the scattering angle 2θ and the wavelength λ
of X-ray.
4.2.3 Optical microscopy
Optical microscopy was used to visualize the morphology over the sample thickness
direction and to determine the thickness of final shear layers at different positions in the
slit. Cross-sections of 5 µm thick were prepared at a low temperature (approximately
−20 ◦C) using a microtone (Leica RM2165) equipped with a glass knife. Two crossed
polarizers are rotated to ±45◦ with respect to the flow direction and optical micrographs
were taken with an Axioplan imaging 2 microscope combined with an AxioCam camera.
The AxioVision software was used to analyze the micrographs and determine the shear
layer thickness.
4.3 Results
4.3.1 Rheological evolution during flow
Figure 4.3a shows the evolution of pressure difference △P between the transducers
during shear. This pressure difference scales directly with the wall stress and thus with
the apparent viscosity, see Figure 4.3b. The apparent viscosity is an average over the
material in the flow channel between the two pressure transducers. The kink in the
Chapter 4 51
0.0 0.1 0.2 0.3 0.40
150
300
450
600
750
900
P
(bar
)
time(s)
apparent wall shear rate
560s-1
400s-1
240s-1
80s-1160s-1
560 s-1
480 s-1
400 s-1
320 s-1
240 s-1
160 s-1
80 s-1
(a)
0.01 0.1 1
5x102
103
1.5x103
appa
rent
vis
cosi
ty (P
a*s)
time(s)
560s-1
480s-1
400s-1
320s-1
240s-1
160s-1
80s-1
(b)
Figure 4.3: (a) Pressure difference△P evolution during flow for different apparent wall shearrates. (b) The corresponding transient apparent viscosities. For shear rates of560 and 480 s−1, some pressure data points are missing just before flow stops.These points were extrapolated with a linear function, as shown by the dashedlines in Figure 4.3a.
slope (d△P/dtime) at very short times is an artifact due to a small deviation of the
piston movement during startup. First of all, Figure 4.3a clearly shows that, prior
to any structure formation, the stress is not immediately constant after imposition of
flow. Considering this, we found the apparent wall shear rate to be more suitable to
characterize the strength of flow field than the shear stress which significantly evolves
with time. Secondly, the iPP melt exhibits different behavior with increasing flow
strength; two distinct responses can be distinguished for shear rates ≤ 160 s−1 and
shear rates ≥ 240 s−1.
For relatively low shear rates (80 and 160 s−1) the pressure difference △P first shows
an overshoot, then decreases and, eventually, approaches a steady-state level. This
nonlinear rheological behavior is typical for polymer melts subjected to start-up shear
flow with a constant shear rate. [32] For shear rates ≥ 240 s−1, the trend of △P is rather
different; after the overshoot, △P increases with time rather than leveling off. With
increasing shear rate, this upturn takes place at shorter times and the time-evolution
becomes steeper. Such an unusual trend of △P indicates that, during flow, viscosity
changes due to structure formation. Since crystallinity is still rather low (see next
section) we exclude a suspension-like rheological effect (part of the melt changes into
deformable solid particles, i.e. the crystalline structures) and consider the structures
formed to act as physical cross-links at a molecular level. A clear rise of the dynamic
viscosity at low levels of crystallinity was also observed in quiescent crystallization for
a HDPE by Roozemond et al. [34] and it was found that this rise at the early stage
of crystallization could not be captured by a suspension model. From now on, we will
denote this structure as the “cross-linking structure”.
52 Chapter 4
What kind of structure is able to change the rheology-related behavior of a polymer
melt? Two examples of deviation from the “normal” rheological behavior during flow
are reported. Scelsi et al. [35] found a “buildup” of △P in high density polyethylene
during flow (the apparent wall shear rate ≈ 200 s−1 and shear time = 2 s at 130 ◦C)
similar to Figure 4.3a. They associated it to a growing crystalline layer in a slit that is
fed from a reservoir. Kumaraswamy et al. [21] observed a birefringence (proportional
to the stress) upturn during flow at constant pressure, different from the typical melt
rheology, and attributed it to the formation of a “highly oriented structure” that, in a
later stage, contributes to formation of a skin layer. These “highly oriented structures”
were examined with in-situ WAXD by Kumaraswamy et al. [12] as well, and a correlation
between these highly oriented structure and crystal formation was found for relatively
low temperatures (141 and 163 ◦C) only. This could not be directly linked to the results
for high temperatures (168 and 173 ◦C). Therefore, the origin of the deviations (viscosity
and birefringence) from the amorphous melt behavior remains unclear.
The absence of a viscosity rise during the short flow period at shear rates of 80 and
160 s−1 does not mean that flow-induced structures are absent. Therefore, to reveal the
origin of viscosity rise during strong flows (shear rates≥ 240 s−1) and probe the potential
Illustrative SAXS and WAXD patterns, collected during and just after flow, for a
shear rate of 400 s−1 are shown in Figure 4.4. The first three patterns are taken during
flow. Interestingly, after 0.23 s from the beginning of flow, the simultaneous appearance
of SAXS equatorial streaks and WAXD (110) diffraction of monoclinic α-form crystal is
observed. The SAXS equatorial streaks are associated to the formation of fibrils oriented
in the flow direction. In addition, the simultaneous appearance of SAXS streaks and
the WAXD (110) diffraction suggests that these fibrils are already (partially) crystalline
and, therefore, we consider these as crystalline shish. For this case the onset time of
shish is during flow, just before the end of the flow time (0.25 s).
To further illustrate the differences between strong flows, the SAXS results for shear
rates below and above 400 s−1 are shown in detail in Figure 4.5 (we do not show all
WAXD results since the shish formed at 320 and 560−1 are also crystalline. A detailed
crystallization evolution will be presented in chapter 5).
For a wall shear rate γ = 560 s−1 the SAXS streaks appear at 0.17 s, which is still
within the flow period of 0.20 s, while for a wall shear rate γ = 320 s−1 the equatorial
streaks appear at 0.33 s, i.e. after cessation of flow. For γ = 560 s−1 shish start to
develop already during the brief shear pulse while for γ = 320 s−1 shish develop after
cessation of flow.
Chapter 4 53
time
0.20s
0.23s
0.27s
0.40s
0.10s
(110)shish
streak
WAXDSAXS
(110)
(110)
(040)(130)
Figure 4.4: SAXS and WAXD patterns during and just after flow at γ = 400 s−1. Flow timeis 0.25 s. The images acquired after flow are indicated by the time in red. Flowdirection is vertical.
t = 0.13s
t = 0.17s
t = 0.20s
t = 0.26s
t = 0.33s
t = 0.40s
streak
320s-1 for 0.25s560s-1 for 0.2s
Figure 4.5: SAXS patterns for flow rates of 560 s−1 and 320 s−1. The images acquired afterflow are indicated by the time in red. Flow direction is vertical.
The formation of shish may affect the rheological behavior of the material and, thus,
contributes to the deviation of △P from a melt-like behavior. The relation between the
onset of shish and △P is clarified by examining the experiment with wall shear rate
of γ = 400 s−1. In this experiment, the △P upturn time is ∼ 0.1 s, see Figure 4.6a.
As shown in Figure 4.6b, ISAXS initially fluctuates around 0.04 but then at ∼ 0.2 s,
with the onset of the streaks, starts a quick rise that continues after the cessation of flow.
54 Chapter 4
0.0 0.1 0.2 0.3 0.40
150
300
450
600
750
time(s)
P (b
ar)
"upturn"
(a)
0.0 0.1 0.2 0.3 0.40.02
0.04
0.06
0.08
0.10
SAX
S eq
uato
rial i
nten
sity
(a.u
.)
time(s)
onset time
flow cessation
(b)
Figure 4.6: (a) △P evolution during flow and (b) SAXS equatorial intensity during and justafter flow. Lines are drawn to guide the eyes. The shear rate is 400 s−1 and theflow duration is 0.25 s.
Clearly, the time required to form an amount of shish sufficient to produce a
noticeable increase of ISAXS is longer than the time characterizing the △P upturn.
From this distinct difference in onset times it seems that the apparent viscosity rise
(averaged over the channel part between pressure transducers) does not result directly
from shish formation in the middle of the slit (X-ray observation window). Or precursors
for shish are the initial cause for the pressure upswing, or shish is first created at another
(upstream) location in the slit.
Figure 4.7a shows the evolution of the ISAXS for all shear conditions in the first second
(the beginning of flow is the reference time). For wall shear rates higher than the critical
value for viscosity upturn (between 160 and 240 s−1), ISAXS increases significantly due
to formation and “densification” of shish. This is illustrated by the equatorial streaks
in the 2D images (Figure 4.7b). To improve the signal-to-noise ratio, the patterns of
240 and 160 s−1 were averaged over ten frames (between 0.67 and 1 s). The slightly
higher intensity left and right of the beam stop for 160 s−1 are due to the beam itself;
they do not correspond to an equatorial SAXS streak signal.
It is clear that, just after flow, neither a viscosity upturn nor shish appearance is
found at the low shear rates of 80 and 160 s−1. However, the absence of a viscosity
rise and SAXS streaks cannot exclude the generation of precursor structures during
flow. Therefore, for these two weakest flows (wall shear rates of 80 and 160 s−1), we
show for prolonged isothermal crystallization the WAXD diffraction patterns at 1000 s,
see Figure 4.8. For both conditions, the (040) diffraction is mainly distributed at the
equator, implying that oriented crystals are formed and this orientation finds its origin
in oriented structures generated by flow. From this we conclude that precursors are also
generated by the weak flows and develop to some oriented nuclei, instead of shish.
Figure 4.7: (a) SAXS equatorial intensity evolution during and just after flow and (b) 2DSAXS pattern at 1 s for different shear rates. Flow direction is vertical.
(040)
(a)
(040)
(b)
Figure 4.8: 2D WAXD patterns of isothermal crystallization at 1000 s after flow pulses atshear rate (a) 160 s−1 and (b) 80 s−1. Flow direction is vertical.
All results of the △P upturn time and the shish onset time are summarized in the
Figure 4.9. Both decrease with increasing shear rate. The SAXS streaks for a wall shear
rate of 240 s−1 do appear after flow but it is hard to determine the precise onset time
for these streaks. Based on Figure 4.9, it is concluded that structure development can
occur during or after flow, depending on the shear strength.
Summarizing above results, for the short flow conditions applied, a critical apparent
wall shear rate is found for the deviation of the rheology from the expected melt-like
behavior. For the iPP used in this work, this critical value lies between 160 and 240
s−1 at 145 ◦C. When shear rate is beyond this threshold, the viscosity rises during flow,
indicating that these short-term flows (0.20−0.25 s) are not short enough from the
56 Chapter 4
0 100 200 300 400 500 600 700 8000.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
flow cessation
after flow
SAXS streak viscosity rise
time
(s)
shear rate (1/s)
during flow
Figure 4.9: Onset times for △P rise and occurrence of the SAXS streaks for different wallshear rates. The gray region indicates the flow period for these shear rates.Onset time for SAXS streaks at a shear rate of 240 s−1 can not be determinedaccurately.
rheological point of view. This viscosity rise is followed by a subsequent appearance
of shish in the middle of the slit where the SAXS is measured. This suggests that the
viscosity rise is caused by formation of shish or their precursors before actual scattering
objects are formed in the slit middle of observation window. However, the real delay time
between viscosity rise and shish formation is not exactly known since the location where
the structure formation occurs that corresponds to the viscosity rise is not necessarily
the centre of the slit where SAXS is measured. The delay time should be something
between 0 and 0.1 s. This is discussed further in the next section. Another shear rate
threshold is between 320 and 400 s−1 for which shish occur during flow. In that case,
the short durations are even not sufficiently short from a structural point of view.
4.4 Discussion
For short flows of 0.20−0.25 s, when the wall shear rate is strong enough (≥ 240
s−1) both, a viscosity rise and shish formation are observed. Comparison of rheological
and SAXS data shows that the viscosity rise and the shish formation are not observed
at the same time. Unexpectedly, the former is observed first. This implies that prior
to shish appearance in the middle of the slit, where the SAXS measurements are done,
some structures have already formed in the flow channel and they, behaving as physical
cross-links, increase locally the viscosity. The reason that these structures are not
observed with SAXS can be twofold: a) the contrast (or concentration) is too low, b)
structure formation is not homogeneous over the slit length and precursors may form
first upstream where the pressure is highest. Especially the latter implies that the
Chapter 4 57
interpretation of the delay in occurrence of shish should be considered with caution.
No strong statements can be made about case a) unless we can exclude case b). In the
following we will first show that we cannot neglect the possibility of case b). Next we
will discuss the explanation for case a) should b) not the cause of the delay.
4.4.1 SAXS delay time
The choice of a slit geometry has the advantages of allowing for very high shear rates
and pressurizing the sample (preventing shrinkage holes) but, at the same time, brings
some complications. For high shear rates, also high pressure gradients will occur. High
pressures (107−108 Pa) will not only shift the equilibrium melting temperature, but
also will change the viscosity, the (flow induced) crystallization kinetics and, moreover,
compressibility can become important. The coupling between these variables is highly
non-linear. Only with a full numerical model [36–38] the interplay between all these
material functions can be investigated quantitatively. Here, we will discuss these issues
in a qualitative way only. For this purpose, the morphology of the sample subjected to
the flow with an apparent shear rate of 240 s−1 is examined along the flowing direction.
1 2 3 4 5
Figure 4.10: Optical microscopy pictures of cross-sections of samples along the flow directionfor an apparent shear rate of 240 s−1. The sample positions are illustratedby the top drawing and the corresponding images are viewed between twopolarizers at ±45◦. The scale bar is 0.2 mm.
An ex-situ micrograph of the structure distribution over the sample length is shown
in Figure 4.10. The variation in the thickness of the shear layer demonstrates that the
structure formation depends on the position in the flow direction. Position 1 is where
the polymer that is kept at a high temperature (220 ◦C) enters the test section of the
slit, i.e. T = 145 ◦C. The high temperature of the melt allows for molecular relaxation
and leads to a thin shear layer. On the other hand, the polymer at the positions 2−5
58 Chapter 4
is at the set experimental temperature of 145 ◦C. In these positions there is indeed a
slight but clear gradient in the shear layer thickness going from high to low pressure
zone (i.e. going in the flow direction), see Figure 4.11.
-60 -40 -20 0 20 40 600.0
0.1
0.2
0.3
0.4
0.5th
ickn
ess o
f she
ar la
yer (
mm
)
distance from X-ray window (mm)
flow direction
Figure 4.11: The thickness of shear layer at various positions along the flow direction foran apparent shear rate of 240 s−1. The reference position is the observationwindow, before and after which positions are indicated by negative and positivenumbers, respectively.
How large the effect is in terms of the time difference cannot be determined from these
experiments but we can estimate the order of the differences of flow enhanced nucleation
and shish generation at different locations in the slit by using the characterization of
this grade given in van Erp’s work [30], where the flow enhanced nucleation rate and
the shish growth rate were determined for a range of temperatures, pressures and shear
histories. Only pressure differences are of importance until the pressure upswing occurs,
since temperature and flow history are practically the same for all locations 1−5. With
a pressure difference of 100 bar (estimated form the results in Figure 4.3a between the
centre and the upstream position 1 (see Figure 4.10) it can be estimated that the flow
induced nucleation rate might be slightly larger (20%), but the shish growth rate is
considerably enhanced (200%). From this we conclude that indeed structure formation
is not homogeneous over the slit length and shish will occur upstream first where the
pressure is highest.
A much stronger non-linear coupling between the viscosity rise and the flow enhanced
crystallization may happen for more severe flow conditions. The resulting morphology
distribution along the flow direction is shown for the extreme case (shear rate 560 s−1
and flow time 0.20 s) in Figure 4.12. Even for the three positions close to the middle,
2, 3 and 4, the gradient is clearly visible (average coverage of the shear layers: 92%,
87% and 84%). With a pressure difference of 200 bar for this case (see Figure 4.3),
Chapter 4 59
flow induced nucleation rate and shish growth rate are increased by 40% and 900%,
respectively, i.e. the pressure effects are dramatically increased compared to the case
with a shear rate 240 s−1. Concluding, there definitely is an influence of the location
in the slit and structure formation most probably will occur first upstream. Again, this
coupling effect will not be quantitatively discussed here, since it is too complex without
simulation tools, which is out of the scope of this work.
1 2 3 4 5
Figure 4.12: Optical microscopy pictures of cross-sections of samples along the flow directionfor an apparent shear rate of 560 s−1. The sample positions are illustratedby the top drawing and the corresponding images are viewed between twopolarizers at ±45◦. The scale bar is 0.5 mm.
In the following we will discuss our results in terms of shish and precursors for
shish assuming a time difference between rheological changes and nucleation of shish
somewhere between 0 and 0.1 s.
4.4.2 Implications of the viscosity rise
Flow gradients can have remarkable effects on generating structures since they
effectively orient and stretch polymer chains. Due to stretch, iPP molecules
change their conformations to adapt to the increased segmental distance between
entanglements and form ordered units of 3/1 helices along the flow direction. [15, 39]
The molecular orientation and stretch increase the equilibrium melting temperature
providing additional thermodynamic driving force (under-cooling) for crystallization.
These parallel segments are similar to their arrangement state in the nuclei and crystals.
Thus the kinetic barrier of transforming the chain segments from random coils into
ordered structures is lowered. The consequence is the formation of locally ordered
aggregates, or precursors, which can be considered as the cradle for nuclei and/or
shish. It is hypothesized that due to the interactions between helices [39], the molecular
60 Chapter 4
segments are restricted inside precursors and, as a consequence, the involved chains
cannot move freely as they do in entangled melts. Therefore, these precursors can act
as physical cross-links and slow down relaxation dynamics. [36] As precursors are being
generated continuously during flow, the very early stage of shear-induced crystallization
is a “cross-linking” process. Precursors can crystallize; this is the nucleation step. The
time between precursor formation and nucleation is unknown but should be (much) less
than 0.1 s. Once the density of precursors (and nuclei) is high enough, the resulting
increase in viscosity is sufficient for rheological observation; see Figure 4.3. The viscosity
rise in our results indicates a high concentration of precursors/nuclei generated by strong
flows (shear rates ≥ 240 s−1).
This cross-linking process during flow seems very similar to the physical gelation
process found in quiescent crystallization of iPP by Pogodina et al. [40, 41] However,
they found a crystallinity of around 1% at the gel point [40], whereas we did not observe
any crystallinity when viscosity starts to change. It should be noted that, in the work
of Pogodina et al. [40], low degrees of under-cooling (10-26K) were used for quiescent
crystallization for which the nucleation density is determined by temperature only. A
low under-cooling corresponds to relatively few nuclei and, therefore, the cross-linking
effect is too low to form a sufficiently dense network; gelation is not observed in the very
early stage of crystallization. However, with increasing crystallinity, more chains get
involved in the network until this is sufficient for observing a viscosity rise. So for low
under-cooling, large clusters (size of ∼ 1 µm [41]) and a crystallinity of ≈ 1% [40] are
required for achieving a sufficient network. Our case with strong flows is quite different;
a precursor/nuclei density increase of orders of magnitude is possible, and viscosity can
rise as a consequence of network formation without noticeable crystal formation.
The precursors formed under shear rates ≤ 160 s−1 (indicated by the appearance
of oriented crystals during isothermal crystallization) are too dilute (or weak) to rise
the viscosity during flow. Assuming that the specific “cross-linking” capability is the
same for different precursors, it is inferred that the precursor concentration is the major
difference. The case of low shear rates (≤ 160 s−1) is then more similar to quiescent
crystallization [40] in terms of absence of significant viscosity change; i.e. a relatively
low nucleation density and further crystallization is required to form a sufficient network
for a detectable change in the viscosity.
4.4.3 Conditions of the viscosity rise
Macroscopic flow is able to generate precursors for row nuclei or for shish. Molecular
stretch of the high molecular weight tail is the prerequisite for the creation of
precursors. [42] To illustrate the flow strength dependence of the structures formed,
two characteristic Weissenberg numbers are defined [43]: Wi0 = γτrep which is related
Chapter 4 61
to molecular orientation, and Wis = γτRouse which is related to molecular stretch. τrepand τRouse are the reptation and Rouse time related to the high molecular weight tail,
respectively. At 145 ◦C, the relaxation times τrep and τRouse for the iPP used in this
work are 48 and 0.23 s, respectively. [18] The values of Weissenberg numbers for the
different flows are summarized in Table 4.1. Wi0 ≫ 103 while Wis > 10 for all shear
rates.
Table 4.1: Weissenberg numbers Wi0 and Wis for HMW tail at 145 ◦C
This means that all shear rates applied can effectively orient the contour path
along the flow direction and stretch molecular segments to deviate from the rotational
isomerization corresponding to the equilibrium Gaussian configuration. [43] However,
rheological results in Figure 4.3a show that viscosity rise only occurs for γ ≥ 240 s−1.
This indicates that stretch of the HMW tail is the necessary but not a sufficient factor
for viscosity rise. [16,44] The HMW tail stretch should be above a critical value to start
the growth of fibrillar nuclei. [37] Since the Deborah number > 1 (De = relaxation time
/ shear time) for ts < 0.23 s, which is nearly the same as the max flow time, the long
chain deformations can be considered as affine during flow and the molecular stretch
scales with the macroscopic strain (= shear time × shear rate). The stretch values
obtained in this way are 20 and 40 for the shear rates of 80 and 160 s−1, respectively.
This would imply that the critical stretch at the wall is 40 or more. For shear rates
≥ 240 s−1 all stretch values are ≥ 60 but the stretch values obtained from the onset
time of the viscosity rise for these shear rates are 36, 38, 39, 35, 35. This matches quite
well with the critical value of 40 estimated from the shear rate of 160 s−1. Fibrillar
precursors are created for shear rates > 160 while for shear rates ≤ 160 s−1 this is not
the case due to the too short shear duration. Finally, the critical stretch value compares
surprisingly well with the critical value used by Custodio et al. [37] (critical stretch =
40). Although this does not mean that we should attribute too much meaning to the
exact value of the critical stretch, the results are quite consistent. If a critical stretch
is the criterion for the start of forming oriented shish precursors, it is questionable if a
work criterion as defined with Eq. 4.1 is applicable since most of the period for reaching
this value is transient.
62 Chapter 4
4.5 Conclusions
The rheological and structural evolution during and after short-term flow of
0.20−0.25 s at 145 ◦C were studied for iPP. The rheological results show that viscosity
rises beyond the normal pressure overshoot for apparent shear rates ≥ 240 s−1, and
the onset time for this rise decreases with increasing shear rate. This viscosity rise
implies that these flows do not satisfy the basic requirement for a “short-term flow”,
i.e. that the polymer viscosity does change during flow. Therefore, for these cases, a
more advanced analysis is required. For example, these results can be combined with a
detailed model for flow induced crystallization including a fully characterized non-linear
viscoelastic model [36,37] from which the relaxation times are coupled to the structural
development.
X-ray measurements do not show simultaneous structure development with the
viscosity rise; the observation of shish is delayed, typically ∼ 0.1 s. The viscosity
rise may partially be explained by the creation of shish or precursors for shish that
act as physical cross-links. However, we can not be sure about the exact value of the
delay time; the influence of the pressure on the local values of rheological and kinetic
parameters will cause nucleation events to occur first upstream. Only a numerical model
can help to reveal this complex interaction. The development from precursors to shish
can occur during (γ ≥ 400 s−1) or after flow (400 > γ ≥ 240 s−1).
Shear rates (160 and 80 s−1) below the threshold also generate precursors which, due
to their low concentration, do not change the melt viscosity and develop into row nuclei.
These flows can be considered as “short-term shear flows”.
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Chapter five
The influence of flow induced
precursors and nuclei on
crystallization of isotactic
polypropylene
Abstract
By using ultra-fast WAXD and SAXS measurements we were able to explore shish
formation during and just after flow in a slit, within a short period of 1 s. Moreover, by
using two WAXD detectors with different acquisition rates we achieved a full track
of the entire crystallization process, from the start-up of flow up to completion of
crystallization. The flow duration is very short, max 0.25 s. The X-ray results show that
for apparent wall shear rates ≥ 400 s−1, shish appear during flow and that for apparent
wall shear rates at 320 and 240 s−1, shish precursors are generated during flow and
develop to shish after flow cessation. In contrast, no shish or shish precursors are found
for 160 and 80 s−1. Therefore, birefringence is applied for these two relatively weak
flows to probe potential shear-induced structures, where SAXS fails. The birefringence
measurements of 160 s−1 show an unusual rise during flow and a partial relaxation
after flow, implying a sort of long-lived oriented structures generated by flow. Neither
SAXS nor birefringence signals of precursors are observed for 80 s−1, but the subsequent
crystallization, observed with WAXD, does show accelerated kinetics and an oriented
morphology. These WAXD results demonstrate existence of oriented precursors which
This Chapter is based on: Zhe Ma, Luigi Balzano, Giuseppe Portale, Gerrit W. M. Peters. to be
submitted, 2012
65
66 Chapter 5
are below the detection limitations of SAXS and birefringence. By combing results from
different characterization methods (SAXS, WAXD and birefringence) we can distinguish
between different shear-induced structures. They are classified into various types: shish,
shish precursors, threadlike precursors and needlelike precursors, according to whether
they can be detected by SAXS and/or birefringence.
Besides this detailed picture of the initial stages of flow induced nucleation, tracking
the entire structure evolution reveals further interesting issues on crystallization. Firstly,
daughter lamellae appear later than parent lamellae and the ratio between parent and
daughter lamellae can be varied by flow. Secondly, orientation of the initial shish is high
and lamellar orientation decreases with lateral growth. Finally, depending on the shear
strength, β-phase of iPP can be induced at the experimental temperature of 145 ◦C.
5.1 Introduction
For semi-crystalline polymers, the ultimate mechanical properties of end products
strongly depend on the crystalline structures formed, i.e. crystal modification,
degree of crystallinity, lamellar thickness, orientation, etc. According to the classical
crystallization theory, polymer crystallization is a two-step process: nucleation and
crystal growth. [1] To start polymer crystallization, stable nuclei are required.
Formation of stable nuclei follows the thermodynamic rule that the total Gibbs free
energy change from melt to nuclei, △G=Gnuclei–Gmelt, has to be negative. This free
energy change can be expressed as: △G=△Gb+△Gs, where △Gb is the bulk free energy
change (a negative value) and △Gs surface free energy change (a positive value) [1], i.e.
the nucleation process is determined by the competition between bulk and surface free
energy changes, of which the former should overcome the latter to generate stable nuclei.
In a pure polymer melt without foreign objects, the surface free energy is associated to
the sum of contribution of all surfaces, i.e. △Gs=ΣγA (with γ the specific surface energy
and A the corresponding surface area). In general, homogeneous nucleation requires a
large driving force, i.e. a sufficient under-cooling. [2, 3] However, in practice polymers
contain contaminates like catalyst residues. These foreign objects provide extra surface
and consequently lower the nucleation barrier (the change of free surface energy). This
heterogeneous nucleation occurs much easier (in terms of nucleation temperature and
nucleation rate) than the homogeneous case. Knowing the effective approach of utilizing
the foreign surface to lower the surface free energy change, addition of nucleating agents
is, therefore, frequently used to enhance nucleation and control optical properties (e.g.
transparency and color). Flow, on the other hand, affects crystallization in a different
way. From a thermodynamic point of view, the application of flow raises the free
energy, decreasing △Gb further and, therefore, promotes nucleation. Flow also induces
anisotropy to the final morphology, for example, the typical shish-kebab structure [4]
which consists of fibrillar core oriented along the flow direction (shish) with transverse,
Chapter 5 67
periodically stacked lamellae (kebab). Shear-induced structures can be stable nuclei,
capable of initiating crystal growth, or “precursors” with a degree of ordering (positional
or/and orientational; intra- or/and inter- molecule) which can nucleate under sufficient
under-cooling or may relax in case of a relatively high temperature.
Considerable work has been devoted to the effects of various precursors/nuclei on
crystallization. Cavallo et al. [5] found that unstable “precursors for nucleation”
of isotactic polypropylene (iPP) disappear with time above the nominal melting
temperature. As a consequence, this relaxation of “precursors for nucleation”
results in reduced final orientation and slower crystallization kinetics. Similar, for
polyethylene (PE), relaxation of shear-induced precursors leads to a larger fraction of
twisted lamellae. [6] The threadlike precursors of a “shear-induced structure” found
by Kumaraswamy et al. [7], possess oriented molecular segments, detectable with
birefringence, which causes the appearance of a skin layer. Shear-induced “bundles”
that are densely packed and observable by SAXS can start crystallization in the vicinity
of the melting temperature [8, 9]. Moreover, shear is even able to determine crystal
modification, for example, shear-induced iPP α-row nuclei (by means of fiber-pulling)
can initiate the growth of the β-phase as well as the monoclinic α-phase. [10]
To explore flow-induced precursors/nuclei and their influences on crystallization,
the ideal experimental strategy should cover both the initial generation process
of precursors/nuclei (from start of flow) and the subsequent growth process (until
completion of crystallization). However, precursors/nuclei can form quite rapidly, e.g.
shorter than 1 second [11], which puts severe demands on the experimental methods
used. The first step is really a challenge, i.e. to achieve the in-situ tracking of
nuclei/precursors’ formation. Most of the previous studies focus on the crystallization
after cessation of flow and infer the formation and property of nuclei through the kinetics
and morphology of the resulting crystallization. In this chapter, we investigated the
rapid formation of structure in detail using synchrotron radiation X-ray with a high
time resolution. For sufficient high shear rates, the combined results of small angle
X-ray scattering (SAXS) and wide angle X-ray diffraction (WAXD) demonstrate that
crystalline shish form during a short flow time (0.20-0.25 s). Moreover, shish precursors
can be distinguished from shish; the former develop to shish after flow. However, no
structures are detected during and shortly after flow by X-ray for some relatively weak
flows, probably because the density contrast and crystalline order are not sufficient
or concentration is too low. Therefore, the more sensitive experimental method of
birefringence is utilized to probe structure development which is below the detection
limit of X-ray. Once precursors/nuclei are characterized, the next step is to explore how
the subsequent isothermal crystallization is affected by them.
The present work aims to clarify what kind of precursors/nuclei are generated for
various flow conditions and to bridge the gap between various nuclei and the resulting
crystallization process.
68 Chapter 5
5.2 Experimental
5.2.1 Material
A commercial isotactic polypropylene (iPP, Borealis HD601CF) is used in this work.
Material properties are summarized in Table 5.1. The melting (Tm) and crystallization
(Tc) temperatures are measured using DSC at a heating/cooling rate of 10 ◦C/min,
sample weight: 3±0.5 mg.
Table 5.1: Properties of the isotactic polypropylene used.
Material Mw (kg/mol) Mw/Mn Tm(◦C) Tc(
◦C)iPP 365 5.4 163 113
5.2.2 Flow device
The flow device used in this work is a slit flow based on a multipass rheometer which
has been described elsewhere [6]. The sample is confined between two servo hydraulically
driven pistons in a slit with a cross-section, A, of 6mm×1.5mm (width, W × height,
H). To impose a shear field to the molten polymer the two pistons move simultaneously
in one direction. Two diamond windows are mounted in the middle section of the flow
cell allowing the passage of X-ray and laser light for in-situ characterization of structure
evolution during and after flow.
The sample was first heated and kept at 220 ◦C for 10 min in order to erase previous
thermo- and mechanical histories from sample preparation. Next, the sample was cooled
to 145 ◦C. All experiments were performed at this temperature. The applied piston
speeds, Vpiston, were 20, 40, 60, 80, 100, 120 and 140 mm/s. The apparent wall shear
rates are 80, 160, 240, 320, 400, 480 and 560 s−1, determined by γ = 6QWH2 [12] with the
volumetric flow rate Q = Vpiston × A. The flow time is fixed at 0.25 s for piston speeds
ranging from 20 to 100 mm/s, and shortened to 0.23 and 0.20 s for 120 and 140 mm/s,
respectively, due to limitation in the maximum piston displacement.
5.2.3 X-ray characterization
Wide angle X-ray diffraction (WAXD) and small angle X-ray scattering (SAXS)
were used to characterize the entire isothermal crystallization process, including the
period of flow. All measurements were performed at the Dutch-Belgian (DUBBLE)
beamline BM26B of the European Synchrotron Radiation Facility (ESRF) in Grenoble,
France. [13] The wavelength used was 1.033 A.
Two WAXD detectors (Pilatus and Frelon, see Figure 5.1) with different acquisition
Chapter 5 69
rates and different pixel resolutions were used. The Pilatus (300K) detector has a high
acquisition rate mode of 30 frame/s, enabling the tracking of the structural evolution
during (0.20-0.25 s) and just after flow for a period of 2 s. After this period the Pilatus
detector was switched to the regular “slow” acquisition mode (exposure time of 4.9 s,
total acquisition time 5.7 s per frame) to follow the resulting isothermal crystallization.
This Pilatus (300K) detector has a resolution of 1472×195 pixels of 172µm×172µm.
The sample-to-detector distance was fixed at 0.240 m.
time
flow 0.2- 0.25s
2s
10s
fast
fast slow
slow
1000s
Frelon
WAXD
Pilatus
1s
fast slowSAXS
Figure 5.1: Structural evolution is measured by the combination of the Pilatus and FrelonX-ray detectors. The scheme shows how the detetors are used during differentperiods.
SAXS measurements were performed with a Pilatus (1M) detector (981×1043 pixels
of 172µm×172µm) placed at a distance of 7.117 m. For SAXS, the fast step was carried
out at an acquisition rate of 30 frame/s for 1 s and the slow step had an exposure period
of 5.7 s for the following isothermal process.
Figure 5.2a shows a typical WAXD pattern obtained with the Pilatus (300K)
detector. For the chosen distance, the azimuthal range of this detector is less than
90◦ for iPP α-phase. The diffractions in the equatorial region are related to the highly
oriented crystals including shish and parent lamellae. In order to explore other crystals
oriented along different directions, such as daughter lamellae, a WAXD azimuthal region
beyond a quarter is required. For this purpose, the Frelon detector was employed, which
has a resolution of 2048×2048 pixels of 48.8µm×48.8µm. The corresponding 2D Frelon
pattern is shown in Figure 5.2b. A full diffraction pattern can be obtained by using
symmetry considerations. The measurements with the Frelon detector also include a
fast and a slow period, see Figure 5.1. Since the maximum acquisition rate of Frelon
detector is 3 frame/s, one order slower than that of Pilatus, the Frelon fast step covers
70 Chapter 5
(110)(040)
(a)
(110)(040)
(b)
(c)
parent
daughter
isotropic part
155o
192o
isotropicpart
azimuthal
angle
Figure 5.2: WAXD patterns obtained with (a) Pilatus detector and (b) Frelon detector.(c) Azimuthal scan of (110) diffraction of the Pilatus WAXD pattern at tc = 25s. Flow direction is vertical.
(110)(040)
(a)
(110)(040)
overlapped
(b)
(c)
Figure 5.3: WAXD patterns obtained with (a) Pilatus detector and (b) Frelon detector.(c) Integrated intensity versus scattering angle (2θ) of the Frelon WAXD patternat tc = 900 s. Flow direction is vertical.
the first 10 s (from start of flow) with an acquisition period of 0.33 s, including an
exposure time of 0.1 s, per frame. The slow step has an exposure time of 2 s and an
acquisition period of 4.5 s. The distance from sample to the Frelon detector is 0.228 m.
The combination of the ultra-fast Pilatus detector and the Frelon detector provides
the possibility to record crystallization from start-up of flow until completion of growth
for both parent and daughter lamellae.
Chapter 5 71
In our results of shear-induced crystallization of iPP the monoclinic α-phase is the
dominant crystal modification (see Figure 5.2a and 5.2b). It is clear that the azimuthal
locations of the (110) plane diffractions can be in either the equatorial or the meridional
region. This is due to the different c-axes orientation in parent and daughter lamellae
with respect to the flow direction. Therefore, we use the azimuthal scan of the (110)
reflection to separate parent and daughter lamellae. On the other hand, parent and
daughter lamellae possess the same b-axis, so the equatorial (040) reflection without
the isotropic contribution, as shown in Figure 5.3b, demonstrates that only oriented
crystals are grown. Considering this, when we see the non-perfectly separated (110)
diffraction between parent and daughter lamellae, as shown in Figure 5.3b, we know that
overlapping intensities come from the broad azimuthal distribution of (110) parent and
daughter diffractions, instead of from isotropic crystals. Therefore, the (110) azimuthal
scan indeed can be used to quantify oriented parent and daughter lamellae.
To extract the signal of crystalline fraction from the total intensity which includes
contribution of amorphous phases as well, two methods are introduced in the following.
In the 2D WAXD pattern, the scattered intensity I(2θ, az) of a specific point is
associated to its two coordinate variables, scattering angle (2θ), and azimuthal angle
(az). This means that two types of one-dimensional (1D) integration curve can be
obtained. In our data analysis, the 1D intensity vs. azimuthal angle curve, see Figure
5.2c, is averaged over the scattering angle range between 9.29◦ and 9.51◦, and 1D
intensity vs. scattering angle curve, see Figure 5.3c, is averaged over a 90◦ azimuthal
range.
Method I: When the degree of crystal orientation is very high, usually due to a strong
flow or at the very beginning of crystallization, parent and daughter lamellae can be
easily distinguished by their distinct azimuthal (110) distributions, as shown by Figure
5.2b. In this case, the minimum intensity of (110) azimuthal scan (i.e. the intensity vs.
azimuthal angle curve), directly presents the amorphous contribution, see Figure 5.2c.
Method II: When the orientation is not high enough, the (110) diffractions might
be azimuthally so broad that 1) Pilatus detector is not able to acquire all equatorial
diffraction, see Figure 5.3a, or/and that 2) parent and daughter diffractions may overlap,
see Figure 5.3b. For either case, amorphous diffraction can not be determined from the
minimum value of (110) azimuthal scan, as done in Method I. Then, we use the intensity
vs. the scattering angle (I vs. 2θ) curve to estimate the amorphous contribution, since
from the only oriented (040) we know that all crystals are oriented.
Figure 5.3c shows the 1D intensity vs. scattering angle data including the crystalline
and amorphous contributions. After substracting air and detector backgrounds, the
diffraction of the amorphous fraction is scaled to fit the amorphous halo region, see
Figure 5.3c, and subtracted from the total scattering intensity to obtain the diffraction
signal of the (110) plane only. The (110) peak is fitted with a Lorentzian function to
72 Chapter 5
verify the construction of the baseline of the amorphous phase. As stated before, the
azimuthal (110) scan is averaged over the 2θ range from 9.29◦ to 9.51◦. Then, for this
2θ region, the contribution of the amorphous fraction is equal to:
Iamorp
Itot=
∫ 9.51◦
9.29◦Iamorp(2θ) d2θ
∫ 9.51◦
9.29◦Itot(2θ) d2θ
(5.1)
Subtracting the amorphous baseline from the total intensity gives the distribution of
diffraction intensity with azimuth of (110) planes.
When the curves for the intensity of the oriented crystalline fraction vs. azimuth are
obtained, Lorentzian functions are used to fit parent and daughter lamellae together.
The fitting area, Area, and the full width at half maximum, FWHM, are measures
for the amount of crystals and the degree of orientation, respectively. Note that the
equatorial (110) diffraction is associated to highly oriented crystals that include both
crystalline shish and parent lamellae.
Since the two detectors have different resolutions, fitting area values, Areaequatorial110,
of frames at 25 s from these two detectors are used to determine the ratio between the
absolute intensity values.
5.2.4 Birefringence
laser
shear cell
1
2 3linear polarizer
aligned at 45o
polarizing beam splitter
aligned at -45o
D
D
Figure 5.4: Optical train used for birefringence characterization.
Figure 5.4 shows a schematic picture of the optical train used for the birefringence
characterization. We used a 2mW HeNe laser (wavelength = 633 nm) and two
photodiode detectors (Thor Labs Inc.) D‖ and D⊥ that read the intensity of parallel
(Iparallel) and crossed (Icrossed) light intensity, respectively. The sum of parallel and
crossed light intensity is the total intensity transmitted, Itot = Iparallel + Icrossed.
time of observing the first SAXS streaksduring shear after shear
0.17 0.20 0.23 0.33 < 1
SAXS equatorial streaks cannot be detected (within 1 s) for the relatively weak
flows of shear rate ≤ 160 s−1. The absence of SAXS equatorial streaks could be
due to the fact that the shear-induced structures, if any, have no sufficient density
contrast with their surrounding melt or that the concentration is too low to be detected.
The isothermal crystallization after flow is examined in order to indirectly explore
potential shear-induced precursors. Since quiescent crystallization needs over 1000 s to
become noticeable (data not shown), substantial appearance of an oriented crystalline
morphology during the first 1000 s has a two-folded meaning for these conditions (see
also Figure 4.8 in Chapter 4 and the next section). Such accelerated kinetics shows that
indeed precursors are generated by flow, although they are below the detection limit of
SAXS. The oriented feature of precursors induced by these conditions is demonstrated
by the resulting oriented morphology.
74 Chapter 5
Therefore, birefringence was applied to characterize the orientation of shear-induced
precursors generated by the relatively weak flows (shear rate ≤ 160 s−1). In
birefringence, molecular orientation becomes manifested in Icrossed/Itot. Figure 5.5 shows
the birefringence evolution during flow (0.25 s) and after flow. By comparing the results
for shear rates of 80 and 160 s−1 it is observed that the melt behaves differently in both
periods, i.e. during and after flow. Figure 5.5a shows that Icrossed/Itot of shear at 80 s−1
first increases quickly and subsequently reaches a plateau. Immediately after cessation of
this flow (lasting 0.25 s), the birefringence signal Icrossed/Itot completely relaxes to zero.
In contrast, the birefringence signal Icrossed/Itot shows an additional increase instead of
reaching plateau during shear at 160 s−1, see inset Figure 5.5b. After flow cessation,
Icrossed/Itot decays to a nonzero value and rises again.
0 2 4 6 8 10
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.0 0.1 0.2 0.3 0.40.2
0.3
0.4
0.5
0.6
I cros
sed/I
tot
time(s)
flow time 0.25s
I cros
sed/I
tot
time(s)
(a)
0 2 4 6 8 10
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0.0 0.1 0.2 0.3 0.40.5
0.6
0.7
0.8
0.9
I cros
sed/I
tot
time(s)
flow time 0.25s
I cros
sed/I
tot
time(s)
(b)
Figure 5.5: Birefringence during and after short-term (0.25 s) flows. Shear rate: (a) 80 s−1,(b) 160 s−1 at 145 ◦C.
In the case of flow at a shear rate of 80 s−1, the transient response on shearing and
cessation of flow (increase, steady-state plateau and complete relaxation) is the typical
nonlinear rheological behavior for polymer melts. [12] So far, birefringence and SAXS
results suggest that precursors generated by the flow at shear rate of 80 s−1 for 0.25 s,
possess a poor packing and orientation order. These precursors will be called “needlelike
precursors” in this work.
In contrast, for a shear rate of 160 s−1 the birefringence shows an unusual raise
during flow and only partial relaxation after cessation of flow. This demonstrates
the generation of some long-lived structure, invisible for SAXS but clearly reflected
in birefringence. Such oriented structures are denoted as “threadlike precursors” [7,14]
in this work. The combination of birefringence and SAXS distinguishes this “threadlike
precursors” from shish that has a density contrast with the surrounding melt and a
sufficient concentration for SAXS detection. Similar results for precursors were found
Chapter 5 75
by Fernandez-Ballester et al. [15] They employed simultaneous birefringence, SAXS
and WAXD, and found a sort of shear-induced precursor in iPP melt at 160 ◦C with
a birefringence “upturn” signal during flow and a nonzero low birefringence after flow,
without detectable SAXS or WAXD signal. In fact, the shear-induced precursor they
found is consistent with the “threadlike precursors” in our results.
Therefore, different flow-induced structures can be formed: shish, precursors for
shish, threadlike precursors and needlelike precursors, depending on the flow conditions.
By using a combination of SAXS, WAXD and birefringence we can distinguish between
these structures. Next, we explore how these precursors/nuclei affect the successive
crystallization. Moreover, by studying the resulting crystallization features (kinetics and
orientation), a better understanding on the “needlelike precursors” should be gained,
since direct characterizations by SAXS and birefringence fail.
5.3.2 Isothermal crystallization
The detailed study of the whole crystallization evolution is realized by combining
the Pilatus detector, aiming for a high time-resolved characterization during and
just after flow, and the Frelon detector to acquire 2D WAXD patterns covering the
azimuthal range beyond 90◦ during further isothermal crystallization. In this way, the
crystallization process can be fully tracked, from start-up of short-duration flow until the
end of the crystallization process. Specific crystallization aspects, including growth of
parent and daughter lamellae, orientation, and polymorphism are revealed and related
to the various precursors/nuclei generated by flow.
Kinetics affected by various precursors/nuclei
Shish (shear rate ≥ 400 s−1)
Figure 5.6 shows Pilatus WAXD patterns of the early stage, i.e. during and just after
the strongest flow applied (560 s−1 for 0.20 s). The first diffraction appears at 0.17 s, i.e
during flow, and belongs to (110) planes of monoclinic α-phase of iPP. Other diffraction
patterns, (040) and (130) of α-phase, are observed as crystallization further develops,
see Figure 5.6. When α-crystals are highly oriented along flow direction, diffractions of
the (111) and (-131) planes are in the off-axis direction rather than in the equatorial
region, so these diffractions were not observed by the Pilatus detector.
Remarkably, the time of the first WAXD appearance (0.17 s) is exactly the same as
for observing the first SAXS equatorial streaks, see Table 5.2 (and Figure 4.5 and 4.9 in
Chapter 4). This excellent agreement between SAXS and WAXD in terms of formation
time demonstrates that α-crystal shish are formed during flow of 560 s−1. The SAXS
results show that for shear rates ≥ 400 s−1 densely packed objects appear during flow
76 Chapter 5
WAXD
(110)
time
0.17s
flow
cessation
(110)
(110)
(040)(130)
0.20s
0.27s
0.13s
Figure 5.6: Pilatus WAXD patterns during and after shear of 560 s−1 (shear time = 0.20 s).Flow direction is vertical.
and the present WAXD results reveal that these fibrillar structures correspond with
crystalline shish (data of 480 s−1 is not shown and that of 400 s−1 is shown in Figure 4.4
of Chapter 4). Shish crystals provide the ideal lattice-matching template to effectively
and efficiently initiate further crystallization (lamellar growth).
Figure 5.7 represents in a quantitative way the entire evolution of α-crystals of
both parent and daughter lamellae during and after the strongest flow. The equatorial
(110) intensity quickly starts rising during flow. After cessation of flow, the crystalline
structures continue to develop. The evolutions of the equatorial (110) diffractions of the
Pilatus and Frelon detectors overlap with each other. The agreement demonstrates the
success of this approach of combining two detectors to fully characterize the whole
crystallization process. The crystallization rate is so fast that nearly half of the
intensity level reached at a long crystallization time (around 800 s) is achieved within
10 s. The equatorial diffraction may have contributions from both shish crystals and
parent lamellae, and their contributions cannot be separated. Considering the fact that
the shear-induced shish crystals directly provide a perfect crystal lattice to nucleate
subsequent crystal growth and considering the fast evolution rate of equatorial (110)
diffraction, we qualitatively associate the first appearance of WAXD diffraction with
crystalline shish and relate the main of the following significant increase to the growth
of parent lamellae.
Chapter 5 77
10s
6.7s
1.7s
daughter
lamellae
0.01 0.1 1 10 100 1000
0
5000
10000
15000
20000
25000
30000
35000Equatorial (110)-Pilatus-fast
Equatorial (110)-Pilatus-slow
Equatorial (110)-Frelon-fast
Equatorial (110)-Frelon-slow
Daughter (110)-Frelon-fast
Daughter (110)-Frelon-slow
Are
a 1
10 (
a.u.)
time(s)
flow
Figure 5.7: Time evolution of the area of equatorial and daughter (110) diffractions duringand after flow (560 s−1 for 0.20 s). Selected Frelon patterns are shown in theright column. Flow direction is vertical.
Daughter lamellae evolve differently from the parent lamellae; they appear later.
Figure 5.7 shows that parent lamellae have already grown significantly within the first
1.7 s, whereas daughter lamellae can not be observed yet. The first noticeable daughter
diffraction is detected at 3.3 s. Daughter lamellae are nucleated on the (010) lateral
surface of existing α-crystals due to homoepitaxy. [16] This means that the number of
nucleation sites for daughter lamellae depends on the amount of (010) surface from the
parent lamella. Although the parent lamellae develop significantly within the first 1.7 s,
the time is too short for generating sufficient nucleation sites and the daughter lamellae
nucleated, if any, have limited time to grow enough for detection. As crystallization
proceeds, the growing parent lamellae provide more lateral surface for nucleation and
the daughter lamellae initially nucleated grow further. At a later stage of crystallization,
daughter lamellae diffraction becomes comparable to parent diffraction.
Two other, relatively intensive flow conditions in which crystalline shish are generated
during flow are shear rates of 480 and 400 s−1 for 0.23 and 0.25 s, respectively. Figure
5.8 shows the time evolution of parent and daughter lamellae for these two flows. In
both cases the growth of parent lamellae is initiated by crystalline shish and this growth
continues after cessation of flow. Similarly, daughter lamellae appear later than parent
lamellae. Since daughter diffraction is initially very weak, each 5 frames of the Frelon
WAXD results in the fast acquisition period are added to get a better signal-noise ratio.
Considering the time-resolution of 1.7 s/frame, appearance of daughter lamellae is 3.3
s for shear rate of 480 s−1 and 6.7 s for shear rate of 400 s−1.
Figure 5.8: Time evolution of the area of equatorial and daughter (110) diffractions duringand after flow (a) shear rate = 480 s−1 and shear time = 0.23 s and (b) shearrate = 400 s−1 and shear time = 0.25 s.
These strong shear flows work similarly in generating crystalline shish. A difference
is found when comparing parent and daughter diffractions in the late crystallization
stage. As seen in Figure 5.7, for a shear rate of 560 s−1, after 800 s the (110)
diffraction of the daughter lamellae approaches a level comparable with that of
parent lamellae. Differently, Figure 5.8 shows that for 480 and 400 s−1, daughter
diffraction levels exceed that of the parent lamellae. It is found that decreasing the
shear rate from 560 to 400 s−1 changes the relative diffraction intensity between
parent and daughter lamellae. Note that for parent and daughter lamellae of iPP,
the Area110 ratio estimated from diffraction pattern is not equal to the real weight
ratio of crystals. [17] Applying geometrical correction [17] gives parent/daughter ratio
at tc=800 s of around 4.4 and 2.7 for 560 s−1 and 400 s−1, respectively. We will
not apply this correction further for our results, since it does not work well (for yet
unknown reasons) for the lower shear rates. Moreover, we are more interested in the
relative time scales rather than in absolute values. So the qualitative conclusion can
still be drawn that lowering the shear rate from 560 s−1 to 400 s−1 decreases the
parent/daughter ratio. For quiescent crystallization, the ratio between iPP parent and
daughter lamellae is a function of crystallization temperature. For the flow-induced
isothermal case, Fernandez-Ballester et al. [18] found that stronger flow can increase the
relative ratio between parent and daughter lamellae, which is consistent with our results.
Shish precursors (400 s−1 > shear rate ≥ 240 s−1)
When lowering the shear rate to 360 and 240 s−1, shish precursors are generated
instead of crystalline shish. These precursors develop into densely packed structures
upon cessation of flow. The crystallization after shearing at a rate of 320 s−1 for 0.25s
is considered as an example. Since no crystal diffractions appear during flow, these
Chapter 5 79
WAXD
(110)
time
0.33s
flow cessation
at 0.25s
(110)
(110)
(040)(130)
1s
7.7s
0.26s
Figure 5.9: Pilatus WAXD patterns after flow of 320 s−1 (shear time = 0.25 s). Flowdirection is vertical.
10s
daughterlamellae
flow
0.01 0.1 1 10 100 1000
0
5000
10000
15000
20000
Equatorial (110)-Pilatus-fast
Equatorial (110)-Pilatus-slow
Equatorial (110)-Frelon-fast
Equatorial (110)-Frelon-slow
Daughter (110)-Frelon-fast
Daughter (110)-Frelon-slow
Are
a 110 (
a.u
.)
time(s)
flow (0.25s)
(a)
0.01 0.1 1 10 100 1000
0
2000
4000
6000
8000
10000
12000
Are
a1
10 (
a.u
.)
Equatorial (110)-Pilatus-slow
Equatorial (110)-Frelon-slow
Daughter (110)-Frelon-slow
time(s)
flow (0.25s)
7.8s
2s
flow
direction
(b)
Figure 5.10: Time evolution of area of equatorial and daughter (110) diffractions for differentflows (a) shear rate = 320 s−1 and (b) shear rate = 240 s−1, with the same sheartime of 0.25 s. Figure 5.10a inset image is tilted to make the weak diffractionpatterns more clear. The arrow shows flow direction. The initial diffraction forthe shear rate of 240 s−1 is too weak to quantify the start of crystallization.
80 Chapter 5
frames are not shown. Figure 5.9 shows the WAXD results immediately after flow. No
crystal diffraction appears at 0.26 s (shear time is 0.25 s) and weak (110) diffraction is
observed at 0.33 s. The same holds for the onset time of SAXS streaks, see Table 5.2.
This indicates formation of crystalline shish after flow of 320 s−1.
The ability to distinguish between shish formation during and after flow is crucial
for understanding what is exactly generated by the flow. Most in-situ tracking on
crystallization is performed with acquisition periods which are in the order of seconds,
much longer than 0.033 s we achieved. In that case the exposure period covers not only
the flow duration but also some time after flow, and the structure that appears is very
often thought to be generated during flow. In fact, our results show that validity of
such interpretation depends on the flow conditions. Crystalline shish are indeed formed
during flow for shear rate between 400 and 560 s−1, while for 320 s−1 crystalline shish
actually appear after flow, which, in other words, means the structures generated during
flow are just shish precursors.
Moreover, for shear rates from 320 to 560 s−1, once the densely packed structures
are observed, they are crystal, irrespective of whether they appear during or after flow.
For 240 s−1, SAXS streaks are also observed within 1 s but SAXS and WAXD signals
are both too weak to precisely determine whether they appear at the same time.
The nucleation effectiveness of the shear-generated shish precursors are expected
to have similar impact on crystallization as shear-generated crystalline shish. Figure
5.10a shows the crystallization evolution after formation of shish precursors by a flow
at 320 s−1 for 0.25 s. Parent lamellae develop continuously after the occurrence of
shish. Daughter lamellae appear later, as also observed for stronger flow conditions.
Figure 5.10a shows that the amount of daughter lamellae is very little at the beginning.
However, daughter lamellae grow quite fast with time.
Threadlike precursors (shear rate = 160 s−1)
Further lowering the shear rate to 160 s−1 leads to the formation of “threadlike
precursors”. This is confirmed by the characteristic birefringence raise during flow
and the absence of SAXS equatorial streaks. Such threadlike precursors comprise
oriented molecular segments and can survive upon cessation of flow. In addition,
Figure 5.5b shows that the residual birefringence signal increases gradually during
subsequent isothermal crystallization. Thus, at 145 ◦C, the residual precursors will
develop into activated nuclei, called threadlike nuclei accordingly, and as a consequence,
start crystallization.
However, the WAXD results do not show any crystallization in the first 2 s (data not
shown). This is due to the low crystallization rate at the beginning, as also shown by
the little rise of birefringence within the initial 2 s in Figure 5.5b.
Chapter 5 81
Figure 5.11a shows 1D WAXD evolution of isothermal crystallization for “threadlike
precursors”. Results show that the first weak (110) diffraction is observed at 7.8 s and
rises as crystallization proceeds. Although threadlike precursors are not crystals that
provide exactly matched substrates, they are able to effectively trigger crystallization
at 145 ◦C. It is imagined that the stretched and oriented segments arrange into local
ordered aggregations and subsequently promote nucleation. In addition, Figure 5.11b
shows that WAXD (110) and (040) diffractions mainly locate in the equatorial direction,
implying high degree of crystal orientation. The anisotropic growth of crystallization
confirms the orientation of these “threadlike precursors”. Our results indicate that a
shear rate of 160 s−1 generates “threadlike precursors”, which develop into stable nuclei
to accelerate crystallization kinetics and orient the resulting crystalline structures.
8 9 10 11 12
600
800
1000
1200
1400
1600
1800
amorphous phase
1000s
(040)(110)
Inte
nsi
ty (
a.u.)
2 (o)
7.8s
(a)
(110)
(040)
(b)Figure 5.11: (a) 1D WAXD evolution during isothermal crystallization after flow of 160 s−1
(shear time = 0.25 s) and (b) 2D WAXD pattern at a crystallization time of13.5 s. Flow direction is vertical.
It is interesting to find these threadlike precursors, which are birefringence visible
but below the limitation of X-ray characterizations (SAXS and WAXD). When
X-ray technique is used only, revealing threadlike precursors depends on whether
crystallization can be triggered, i.e. the degree of undercooling. When the experimental
temperature is relatively low, undercooling is sufficient to trigger crystallization and,
consequently, make the effect of these flow-induced precursors detectable, as shown
by our results at 145 ◦C. Without crystallization, these threadlike precursors can not
be observed but might survive for long time. For example, Fernandez-Ballester et
al. [15] found that “oriented precursors” (the same structure indicated by “threadlike
precursors” in this work) can survive as long as 20 min at 160 ◦C. In this case, cooling
can activate these surviving precursors and thus influence subsequent crystallization.
82 Chapter 5
Needlelike precursors (shear rate = 80 s−1)
Neither X-ray nor birefringence measurements show structure formation during flow
for a shear rate of 80 s−1 for 0.25 s. When these direct methods fail in probing
shear-induced precursors/nuclei, the subsequent crystallization can be used to indirectly
explore the consequences of this flow.
The isothermal crystallization process at 145 ◦C after the weakest flow applied (80
s−1 for 0.25 s) is shown in Figure 5.12a. Observable (040) and (110) diffractions show
up at a crystallization time of around 200 s. Previous rheological measurements on the
same iPP find that even at a 140 ◦C (lower than the 145 ◦C used in this work), quiescent
crystallization takes more than 1000 s to be detected. The much faster crystallization
kinetics after flow implies the formation of extra nuclei. The nucleation density is lower
than that for other stronger flows, so it takes much more time to form a sufficient
amount of crystals for detection.
8 9 10 11 12
600
800
1000
1200
1400
1600
(040)(110)
Inte
nsi
ty (
a.u
.)
2 (o)
1000s
7.8s
200s
(a) (b)
Figure 5.12: (a) 1D WAXD evolution during isothermal crystallization after flow of 80 s−1
(shear time = 0.25 s) and (b) 2D WAXD pattern at a crystallization time of1000 s. Flow direction is vertical.
In addition, the crystallization orientation is studied by looking at the (040)
diffraction which was shared by the oriented parent and daughter lamellae with the
same b-axis. Figure 5.12b shows that the (040) diffraction of crystallization at 1000
s is located in the equatorial direction, implying the shear-induced nuclei are indeed
oriented, although they are not reflected in birefringence. Another issue we want to point
out is the absence of isotropic (040) diffraction in Figure 5.12b. The low orientation
in the late stage is due to the low orientation of nuclei and lamellar curving and
twisting during lateral growth [17], which excludes the possibility of a mixed morphology
comprising of highly oriented lamellae and isotropic spherulites. These nuclei must be
Chapter 5 83
related to some precursors generated by flow.
In conclusion, one more “kind” of oriented precursors is found, which is neither
visible for X-ray nor for birefringence. In this work, such precursors are denoted
as “needlelike precursors” to differentiate them from shish (observed with X-ray)
and threadlike precursors (observed with birefringence). Actually, these needlelike
precursors which are below X-ray and birefringence but are able to ultimately nucleate
oriented crystallization, were hidden in the results of Kumaraswamy’s systematical
study on flow-induced iPP crystallization. [7, 14] For the material “PP-300/6” used by
Kumaraswamy et al., the “oriented structures” indicated by the birefringence “upturn”
signal, similar to “threadlike precursors” in our results, only appear under intense flows,
i.e. for 0.06 MPa the shear time has to be larger than 4 s (for 0.03 MPa a flow time up
to 16 s is insufficient). [7] On the other hand, their X-ray results [14] show that oriented
crystallization occurs for the flow conditions of 0.06 MPa for 2 s and 0.03 MPa for 2 s,
which are actually weaker than the above mentioned threshold for forming birefringence
detectable “oriented structures” [7].
Crystal orientation
Shear-induced structures provide not only nucleating sites but also orientation
templates for crystal growth. The influences of the different nuclei on orientation are
explored as well. The FWHM values, based on equatorial (110) diffractions, indicating
the orientation degree of crystals affected by various flows and their time evolutions are
shown in Figure 5.13.
For shear rates of 320-560 s−1, crystallization orientation starts with a similar low
FWHM value of around 4◦. At the very beginning, crystal growth strictly follows the
orientation of nuclei/precursors, so the initial small FWHM reflects the high orientation
of shish nuclei/precursors generated under these conditions, i.e. shear rates of 320-560
s−1. For a lower shear rate of 240 s−1, the equatorial (110) diffraction is too weak in the
beginning (period of 2 s) to accurately determine the FWHM evolution. However, the
equatorial (110) diffraction is quite narrow azimuthally, see the 2D pattern of Figure
5.10b inset-2s, and qualitatively demonstrates the strong orientation of generated shish
precursors.
Therefore, it is found that shish and shish precursors all possess a high orientation
with respect to the flow direction. Moreover, crystallization after a flow (160 s−1 and
0.25 s) is first observed at 7.8 s, rather than during the initial 2 s. The FWHM of early
crystallization is also very small, around 6◦ at 7.8 s. This indicates that threadlike
precursors are also highly oriented, which is consistent with the birefringence signal
shown in Figure 5.5b.
84 Chapter 5
0.1 1 10 100 10000
5
10
15
20 240s
-1 (0.25s) -- Pilatus
240s-1
(0.25s)-- Frelon
320s-1
(0.25s)-- Pilatus
320s-1
(0.25s)-- Frelon
400s-1
(0.25s)-- Pilatus
400s-1
(0.25s)-- Frelon
480s-1
(0.23s)-- Pilatus
480s-1
(0.23s)-- Frelon
560s-1
(0.20s)-- Pilatus
560s-1
(0.20s)-- Frelon
FW
HM
equ
ato
ria
l 11
0 (
o)
time (s)
50 100 150 2000
10
20
30
Inte
nsi
ty (
a.u
.)
azimuthal angle (o)
50 100 150 2000
10
20
30
Inte
nsi
ty (
a.u
.)
azimuthal angle (o)
(a) (b)
(c)
Figure 5.13: (a) FWHM evolution of equatorial (110) diffraction during crystallization afterflows at shear rates from 240 s−1 to 560 s−1. The azimuthal distribution of(110) diffraction after crystallizing for 1000 s after flows at shear rates of (b)80 s−1 and (c) 160 s−1.
Figure 5.13a also shows that the orientation decreases (indicated by increase of
FWHM) as crystallization proceeds. This is due to imperfect lamellar growth: curving
and twisting. [17] It is clear that final FWHM values for the two strongest flows are
still very low, i.e. around 6◦. For shear rates of 400, 320 and 240 s−1 (the same flow
time 0.25 s), the FWHM reaches various orientation levels of ≈9.6◦, ≈11◦, ≈14.5◦,
respectively. Figure 5.13b and 5.13c show the overlapping diffraction of parent and
daughter lamellae at t=1000 s for the relatively weak flows (80 and 160 s−1 for 0.25 s).
Their final FWHM values are around 50◦ and 40◦, although the latter starts with a high
orientation level. Therefore, the orientation of the ultimate structure depends on both
the orientation of initial nuclei/precursors and on the evolution during crystallization
where the contribution of curving and twisting depends on the available lateral space for
growth, which is associated to the nucleation density. For a higher nucleation density,
the average distance between neighboring nuclei is smaller leaving less space for lateral
growth and, consequently, less room for change in lamellar orientation, while in case of a
low nucleation density the orientation may decrease dramatically because of significantly
curving and twisting during the imperfect lamellar growth. Cavallo et al. [5] found
that when starting with the same oriented nuclei, the final crystallization orientation
decreases with reduction of nuclei density due to the relaxation. Notice that in our
results, the orientation is averaged over all interior layers experienced with various flow
histories, so the final orientation is determined by the corresponding average nuclei
density.
Chapter 5 85
Crystallization polymorphism: β-phase
As a polymorphous polymer, sheared iPP melt may crystallize into various crystal
modifications, i.e. the α-, β- and γ-phase. In this section, the influence of flow strength
on crystallization polymorphism is discussed for this specific temperature of 145 ◦C.
Figure 5.14 shows the WAXD results for different flows. The longer crystallization
times were chosen to present results after flow at lower shear rates to compensate for the
slower kinetics and thus lower crystallinity levels. The substantial (110) and (040) peaks
of iPP α-phase appear for all flow conditions. Differently, the weak (300) diffraction
related to the β-phase, can be distinguished only for shear rates from 240 to 560 s−1,
while for shear rates of 160 and 80 s−1 it was not observed, even after crystallizing for
1000 s. The formation of β-crystals thus depends on the flow conditions.
8 9 10 11 12
320s-1
560s-1
Inte
nsi
ty (
a.u.)
2 (o)
240s-1
160s-1
80s-1
400s-1
480s-1
8 9 10 11 12
80s-1
160s-1
2 (o)
240s-1
(300)
(040)
(110)
Figure 5.14: 1D WAXD curves at different crystallization times after varying flow strength,in terms of apparent shear rates: 560 s−1(at 48 s), 480 s−1(at 48 s), 400 s−1(at500 s), 320 s−1(at 500 s), 240 s−1(at 500 s), 160 s−1(at 1000 s), 80 s−1(at 1000s). The crystallization temperature is 145 ◦C.
Varga et al. [10, 19] used fiber pulling to shear a polymer melt and found that the
shear-induced α-row nuclei can nucleate β-crystals. When the growth rate of β-crystals
is larger than that of α-crystals, typically in a temperature range between 105 and
140 ◦C, the resulting crystalline structure can be polymorphous and consists of mainly
β-crystals based on the α-phase core. [10] Somani et al. [20] found that, at 140 ◦C,
the amount of β-crystal depends on the shear rate for a fixed strain and can go up
to 65%-70% of the total crystallinity. It was suggested that the growth of β-crystals is
associated with the total surface area of oriented α-crystals. Therefore, in our isothermal
crystallization at 145 ◦C, the substantial growth of parent lamellae of α-crystals is
sufficient to nucleate β-crystals. The much lower intensity of (300) diffraction compared
86 Chapter 5
to those of (110) and (040) diffractions, qualitatively indicates that the total amount of
β-crystals formed is very little.
The orientation of the β-crystals formed is explored as well. To quantify the degree of
orientation, the FWHM values of β-crystal (300) diffraction are determined and shown
in Figure 5.15. It can be seen that all FWHM values are less than 13◦ and slightly
decrease with increasing shear rate. Clearly, for all flow conditions applied in this study
the β-crystals are oriented even after long-term crystallization for 500 s. This is different
from the observations of Somani et al. [20] and Chen et al. [21] that initially occurring
β-crystals are oriented and the further spontaneous growth without any preferential
orientation leads to an oriented-to-isotropic transformation. The appearance of oriented
β-crystals in our work can be explained from the growth point of view.
160 240 320 400 480 560 6400
5
10
15
20
FW
HM
(30
0) (
o)
apparent shear rate (s-1)
30o
(300)
Figure 5.15: FWHM of azimuthal (300) diffraction at the crystallization time of 500 s afterdifferent flows. Inset is the WAXD image for 480 s−1 after crystallization for500 s. Flow direction is vertical.
It is known that α-crystals and β-crystals both can be nucleated by the same α-crystal
assemblies (e.g. α-row nuclei) and these two phases are growing in competition. [10,19]
At 145 ◦C the growth rate of α-crystal is faster than that of β-crystal. [22] In this
case, continuous growth of β-crystals might be suppressed by the growth of α-crystals.
For example, oriented nuclei initiate dense appearance of α-crystals and β-crystals
and both develop outwards. Initially, α- and β-lamellae are growing in parallel and
perpendicular to the flow direction because of spatial confinement along the nuclei
orientation direction. However, with crystallization, the faster growing front of α-
crystals can exceed to that of β-crystals and, may grow into the potential space for their
neighboring β-crystals. The initial grown β-crystals are oriented and soon stopped by
α-crystals. Therefore, the fraction of β-crystals is little and keeps a high orientation, as
shown in our results.
Chapter 5 87
When the crystallization temperature is between 105 and 140 ◦C, where growth rate
of α-crystals is slower than β-crystals, Varga et al. [10] found that β-crystals can be the
dominant crystal. Moreover, van Erp et al. [23] found the prevailing γ-crystals in Ziegler-
Natta iPP homopolymer crystallization with shear and a mild pressure (maximum 1200
bar), instead of α- or β-crystals. This is due to a similar kinetic reason that high
crystallization temperature and pressure result in the faster growth rate of γ-crystals
than for α-crystals. [24]
5.4 Conclusions
We utilized WAXD, SAXS, and birefringence to explore the development of shear-
induced structures in iPP starting from the beginning of their creation. Depending on
the flow strength, oriented precursors or nuclei are generated that differ in terms of their
detection level. For strong enough flow, shish were detected during short term flow (0.20-
0.25 s) by means of WAXD/SAXS. Birefringence is used to measure the early stages
of flow induced structures which were below the detection limitation of WAXD/SAXS.
They are also investigated indirectly by measuring the resulting crystallization (faster
kinetics and oriented morphology). The upturn in the birefringence during flow and
the non-zero relaxation after flow demonstrates that “threadlike precursors” are formed
during flow at 160 s−1 for 0.25 s; they have sufficient orientation to be observable by
birefringence. In contrast, “needlelike precursors” that are generated by the flow at 80
s−1 for 0.25 s possess a too low density and orientation to be detected by birefringence.
By combining two different WAXD detectors (Pilatus and Frelon) the entire
crystallization during and after flow could be tracked. It is found that parent
lamellae are directly nucleated on shish formed during flow or developed from
precursors for shish, while “threadlike precursors” and “needlelike precursors” need
time to start crystallization. Daughter lamellae show up later than parent lamellae
and the parent/daughter ratio depends on the flow strength. In the early stages
the crystallization orientation follows the high orientation of nuclei. With further
crystallization, imperfect growth (curving and twisting) of lamellae will decrease the
orientation. This effect is stronger for lower average nuclei concentration. It is also
found that both shish and precursors for shish can induce appearance of β-phase of
Figure 6.2: 2D depth-sectioned diffraction patterns (top row) corresponding to thecrystallization of specific layers (bottom row) in iPP at t = 88 s after a wallshear pulse of 0.11 MPa and 2 s. The layer depths and corresponding boundarystresses are indicated. Flow is along the horizontal direction.
area and full width at half maximum (FWHM) from the parent and daughter lamellae
can be determined; they are relative measures of the amount of crystals and degree of
orientation for the parent and daughter lamellae, respectively.
0 90 180 270 360
daughter lamellae
parent lamellae
Inte
nsity
(a.u
.)
azimuthal angle (o)
FWHM
Figure 6.3: Azimuthal scan of the oriented (110) diffraction of iPP at t = 88 s for the L1layer after thickness normalization and geometrical correction. The solid linecorresponds to the Lorentzian fittings.
96 Chapter 6
6.4 Results and Discussion
The depth sectioned X-ray patterns are first used to examine the influence of shear
stress on the crystallization kinetics and orientation of each of the three materials; the
homopolymer (iPP) and two random copolymers (RACO3 and RACO7). Next, the
crystallization kinetics of these three different polymers is compared at a specific level
of shear stress to reveal the effect of the macromolecular architecture, i.e. copolymer
content, on crystallization.
6.4.1 iPP homopolymer
Prior to flow, the diffraction pattern of the iPP shows only an isotropic broad ring
(data not shown), irrespective of the layer, i.e. application of depth sectioning. This is
consistent with the undeformed amorphous melt with no crystallinity and no orientation.
Selected 2D WAXD depth sectioned patterns during shear and following isothermal
crystallization of the iPP for various layers are shown in Figure 6.4.
43s 208s13s 28s
(110)
parent
(110)
daughter
L1
13s 28s 43s 208s
L2
13s 28s 43s
L3
208s
(040)
(110)
daughter
(110)
parent
(110)
Figure 6.4: WAXD depth-sectioned patterns of isothermal iPP crystallization at 137 ◦C fora wall shear stress of 0.11 MPa for 2 s. The positions and corresponding stressesof layer L1 (top row), L2 (middle row) and L3 (bottom row) are illustrated byFigure 6.2. The flow direction is horizontal.
Chapter 6 97
The results clearly show that stress has a remarkable influence on triggering
crystallization. The different layers, from L1 to L3, exhibit various crystallization
behaviors because of the decreasing local stress. Figure 6.4-L1 presents the structural
evolution in the outermost layer L1, subjected to the highest stress range 0.11-0.103
MPa. A pair of clear arc-like diffractions emerge quickly after flow at a scattering
vector of q = 10.0 nm−1 in the vertical direction perpendicular to shear (Figure 6.4-
L1-13s). These WAXD diffraction arcs correspond to the (110) diffraction plane [39]
of monoclinic α-phase in iPP, which indicates that the oriented α-phase forms quickly
after shear and that the c-axis aligns along the flow direction in the so-called parent
lamellae. Differently, crystallization under lower shear stresses in the L2 and L3 layer
is more sluggish and requires a longer time, ∼ 28 s, to form detectable parent crystals
(Figure 6.4-L2 and L3). Likewise, in the two outermost layers L1 and L2, daughter
lamellae, also described as lamellar branches at an angle of 80◦ to a specific parent
lamellar surface [40], are already observed at 28 s as two pairs of (110) diffraction arcs
located close to the meridian (Figure 6.4-L1-28s and L2-28s). In contrast, for the L3
layer, daughter lamellae only appear at later times (43 s).
It should be noticed that only the α-phase appears in the 2D diffraction patterns.
Although some studies have observed the emergence of dominant β-phase crystals in
shear-induced iPP crystallization, [41,42] the appearance of only α-phase in our results
is consistent with previous studies [27,29] that found only or predominantly α-phase as
a result of shear-induced crystallization.
The results in Figure 6.4 indicate that the imposition of a shear pulse generates
nuclei which can significantly speed up crystallization kinetics and orient the crystal
morphology [12,18,43]. At 137 ◦C, quiescent crystallization of iPP is too slow to generate
any detectable structure within 400 s (data not shown), and only isotropic crystallites
would ultimately form. In contrast, 208 s after the imposition of flow, the diffractions
patterns for the L1 layer are quite narrow in the azimuthally direction (see Figure 6.4L1-
208s) implying that crystal morphology in the layer that was subjected to the highest
stress range is highly oriented. For the inner layers subjected to lower levels of shear
stress, however, the orientation of structures is qualitatively lower at 208 s. Therefore,
depth-sectioned WAXD images qualitatively show that stress has a significant influence
on the start and evolution of crystallization, which is quantitatively analyzed below.
Next, a quantitative evolution of the amount of crystals and the degree of orientation
is extracted from the area and FWHM of the azimuthal (110) peak corresponding to
the parent lamellae, see Figure 6.5a and b. Irrespective of the layer considered, parent
lamellae grow rapidly in the early stage and then reach a shoulder, after which they
either halt their growth or they continue to grow at a much slower rate. Knowing
that the growth is stopped by the impingement of the growth fronts of the parent
lamellae, a shorter time to reach this shoulder must relate to less space between
neighboring nuclei. Therefore, more nuclei are generated in the outer layer by the
98 Chapter 6
0 200 400 600 800 1000 12000
1x105
2x105
3x105
4x105
5x105
6x105
L3
L2
L1
time(s)
Are
a P.1
10 (a
.u.)
(a)
0 200 400 600 800 1000 12000
10
20
30
time(s)
FWH
M (o )
L3
L2
L1
(b)
Figure 6.5: Evolution of (a) area and (b) FWHM of parent (110) diffraction in iPPisothermal crystallization in different layers. Layer positions and theircorresponding stresses are illustrated by Figure 6.2.
higher stress [29]. Interestingly, the crystallization in the L1 layer not only shows the
fastest kinetics at the early stages, but it also has the highest value when it reaches
the shoulder. The larger value results from the combined effect of flow-enhanced
crystallization and parent/daughter lamellae ratio when crystallization is completed,
as found by Fernandez-Ballester et al. [29] that the relative ratio between parent and
daughter lamellae is higher in the outer layer than in the inner layers of lower stress.
Shear-induced nuclei are known to template the oriented growth of parent lamellae
in the early stage. The orientation of parent lamellae was illustrated by the FWHM
of the parent (110) diffraction, see Figure 6.5b. Lower FWHM values refer to a higher
average lamellar orientation. The initial FWHM in the L1 layer is the lowest, around
6◦, but the larger ones in the L2 and L3 layers are quite similar (≈ 9◦) in the first short
period of tens of seconds. These low FWHM values in the initial stage of crystallization
suggest that nuclei generated at various stress levels have a high orientation. This result
is consistent with the observation of Fernandez-Ballester et al. [29], where crystallites
induced by the three strongest conditions all show very high and similar degrees of
orientation at the beginning (see Figure 9b in ref [29]).
As crystallization proceeds, the change in the orientation becomes more pronounced
for the inner layers with lower shear stress. For the highest stress range of 0.11-0.103
MPa the FWHM stays nearly constant during the observation period, whereas those for
0.103-0.091 and 0.091-0.079 MPa vary from 9◦ to 12◦ and from 9◦ to 19◦, respectively.
The change in the orientation indicates that lamellar growth does not strictly follow
that of the nuclei or initially grown lamellae because of occurrence of lamellar curving
and twisting during lateral growth. [38] This orientation variation depends on the space
between neighboring nuclei. When nuclei density is smaller, there is more space between
nuclei for lateral growth during which the possibility to curve increases leading to the
Chapter 6 99
reduction of orientation [29, 44]. Therefore, orientation evolution shows that the L3
layer has the least nuclei, which is consistent with the results of Area evolution.
6.4.2 Propylene/ethylene random copolymers
Only three out of the four wall shear stresses for the homopolymer were imposed on
the random copolymers (0.11, 0.103, and 0.091 MPa). For the random copolymers, the
crystallization at a wall stress of 0.091 MPa was quite sluggish, so the stress was not
lowered further to 0.079 MPa. Therefore, the innermost layer of random copolymers
(named L3+L4, see Figure 6.6) should be compared to the sum of the two individual
L3 and L4 layers in iPP. Note that at the same experimental temperature Texp, iPP
and random copolymers have different undercooling △T = T 0m − Texp, where T 0
m is the
equilibrium melting temperature, because the addition of ethylene monomer decreases
the equilibrium melting temperature T 0m [34]. Accordingly, the lamellar linear growth
rate under quiescent conditions decreases with the increase of ethylene content (see
section 6.4.3).
13s 28s 73s
13s 103s 208s 703s
L1
L2
208s 13s 28s 73s qqI
(110)
daughter
13s 28s 103s 208s
L3+4
Figure 6.6: WAXD depth-sectioned patterns of isothermal RACO3 crystallization at 137 ◦Cfor a wall shear stress of 0.11 MPa for 2 s. The positions and stresses of layer L1(top row), L2 (middle row) and L3+4 (bottom row) are illustrated by Figure 6.2.The flow direction is horizontal. Images are tilted to make the weak diffractionpatterns more clear.
100 Chapter 6
Figure 6.6 shows a representative series of depth-sectioned WAXD patterns for
RACO3. The influence of stress is also found to be significant for RACO3: in the
outermost L1 layer, some oriented crystallites can already be observed within the first
13 s after imposing the shear pulse, while in the inner L2 and L3+4 layers, crystallites
can only be detected after 28 s and 103 s, respectively. The faster kinetics in the outer
layer indicates that, as for iPP, increasing applied shear stress induces more nuclei also
for RACO3. Compared with iPP, the crystallization of RACO3 in the L1 and L2 layer
starts at the same time (13 s and 28 s, respectively), but in the L3+4 layer it is much
slower than for iPP in the L3 layer (see Figure 6.4L3-28s and Figure 6.6L3+4-103s).
Interestingly, all layers of RACO3 show a time lag between the development of
parent and daughter lamellae. For instance, in the L1 layer, RACO3 parent lamellae
development is pronounced from 13 to 28 s, while no daughter lamellae are observed at
all at 28 s. Similarly, for low stresses (shown by Figure 6.6L2-28s and Figure 6.6L3+4-
103s) the first crystals that develop after flow belong to parent lamellae only. This
growth lag between different lamellae is not specific for RACO3; it is also observed
for iPP in the L3 layer (Figure 6.4L3-28s) and for RACO7 in the L1 layer (data not
shown). In fact, this time lag is consistent with the mechanism of initiation of parent
and daughter lamellae: Parent lamellae are templated from shear-induced nuclei while
daughter lamellae are nucleated by the homoepitaxy on the lateral (010) faces of existing
parent lamellae with monoclinic α-modification [40]. In other words, daughter lamellae
need parent lamellae to initiate the second-generation growth.
0 200 400 600 800 1000 12000
1x105
2x105
3x105
4x105
5x105
6x105
10 100 1000
0.0
5.0x103
1.0x104
1.5x104
L3+4
L3+4
L1
L2
time(s)
Are
a P.1
10 (a
.u.)
(a)
0 200 400 600 800 1000 12000
10
20
30
L2
L1
time(s)
FWH
M (o )
(b)
Figure 6.7: Evolution of (a) area and (b) FWHM of parent (110) diffraction in RACO3during shear and isothermal crystallization. Layer positions and theircorresponding stresses are illustrated by Figure 6.2.
RACO3 orientation evolution is shown in Figure 6.7b. Layers L1 and L2 have a
quite similar orientation at the beginning but develop differently with time. This is
qualitatively consistent with the difference in nuclei density in the different layers; again,
Chapter 6 101
the larger space between neighboring nuclei allows for curving and twisting resulting in
a lower orientation (a larger FWHM value).
For an ethylene content of 7.3 mol% in RACO7, the nominal melting temperature
decreases to 138 ◦C. Quiescent crystallization will not be detected at the experimental
temperature of 137 ◦C, since this is just 1 ◦C lower than its nominal melting temperature
and, as a consequence, the quiescent nucleation density and the linear growth rate are
both very small. However, crystallization of RACO7 in L1 layer proceeds immediately
after flow and for the L2 layer, some crystallites become observable at ∼ 200 s (Figure
6.8a), providing a clear example of the effect of shear stress on crystallization even in
the vicinity of the nominal melting temperature. The linear growth rate is the same
as under quiescent conditions, so the accelerated rate of oriented crystallization results
from the abundant oriented nuclei generated by the high shear stresses applied.
0 200 400 600 800 1000 12000
1x105
2x105
3x105
4x105
5x105
6x105
L2
L1
Are
a P.1
10 (a
.u.)
time(s)
(040)
(040)
L3+4 (1003s)
flow
(a)
0 200 400 600 800 1000 12000
10
20
30
L1
FWH
M (o )
time(s)
(b)
Figure 6.8: Evolution of (a) area and (b) FWHM of parent (110) diffraction in RACO7during shear and isothermal crystallization. Inset is the WAXD image forRACO7 after crystallization for 1003 s. Layer positions and their correspondingstresses are illustrated by Figure 6.2.
Comparing with iPP and RACO3, the time at which crystallization can first
be detected for RACO7 is similar in L1 but much slower in L2 and L3. During
crystallization, FWHM varies from ∼5◦ to ∼8◦, see Figure 6.8b. Interestingly, the
slow RACO7 crystallization in L1 layer is comparable to that of iPP in L3 layer, but
the orientation in RACO7 is much higher.
Based on above results, a qualitative conclusion can be drawn that for each of the
three materials: the number of nuclei formed increases with applied shear stress, i.e.
from the inner to the outer layers. For a given material, the comparison is simple
because the quiescent growth rate of lamellae is fixed. However, polymers with various
ethylene contents have different quiescent growth rates which affect the crystallization
102 Chapter 6
kinetics. Therefore, to quantitatively study the effects of stress and ethylene content
on polymer crystallization, the kinetic model [45–48] is used to estimate the amount of
oriented nuclei formed by shear in the different materials below.
6.4.3 Quantification of nuclei
In the Kolmogorov−Avrami−Evans model [45–48], the progress of space filling in
time,Φ(t), can be described by the expression:
Φ(t) = 1− exp(−kGmtn) (6.3)
where k is the factor involving the nuclei density, G the linear growth rate, m the
exponent indicating the growth dimension (1, 2 or 3-directional) and n the nucleation
mechanism (sporadic, n = m + 1 or predetermined, n = m). For shear-induced
crystallization, the number of nuclei is fixed prior to growth and does not increase with
space filling, so the exponent number n equals the growth dimension m. In the present
work, oriented nuclei are dominant and space is mainly filled by the lamellar growth that
develops perpendicular to these nuclei. Structural “perfection” (e.g. lamellar perfection,
branching and thickening) behind the growth front is not taken into account for space
filling. Therefore, we assume that the space filling Φ(t) is directly proportional to the
development of the parent lamellae diffraction A(t). With this assumption, space filling
can be obtained by:
Φ(t) = (A(t)− A0)/(A∞ −A0) (6.4)
where A0 is the (110) diffraction area at t = 0 that is caused by flow, and A∞ the
shoulder (110) diffraction area when space filling is completed. Since the first data point
for the L1 layer is obtained after flow and nonzero, it contains information concerning
both the 2s of shear and the 13s of isothermal crystallization, A0 cannot be determined
directly for all L1 layer cases. On the other hand, for most of the results in the L1 layer,
after crystallizing for 13 s, A0 is still very low with respective to the shoulder value, so
the contribution of A0 to space filling is negligible and will be assumed to be 0 in the
calculation of space filling. Therefore, space filling can be assessed by Φ(t) = A(t)A∞
.
Assuming that the linear growth rateG is constant in time, the crystallization kinetics
is examined by plotting the rewritten form of Eq. 6.3 (see Figure 6.9):
ln{−ln[1− Φ(t)]} = nln(t) + ln(kGm) (6.5)
The fitted exponent n are all in the range 1.6−2 (n = 2 is for ideal 2D growth with
predetermined nuclei) while all initial slopes are nearly 2. Therefore, the theoretical
integer exponent n = 2 will be used for the assessment of nucleation density. The
Chapter 6 103
2 3 4 5 6 7
-4
-2
0
2
iPP_L1 iPP_L2 iPP_L3 RACO3_L1 RACO3_L2 RACO7_L1
Ln(-Ln
(1-))
Ln(t)
2
Figure 6.9: Avrami plots of space filling evolution for different materials in various layers.
description of 2-dimensional growth reads [49]:
Φ(t) = 1− exp(−πlNG2t2) (6.6)
where l is the long period of stacked lamellae, N is the number of lamellae and total
length of nuclei per volume, L, can be easily derived from the time for filling half space,
t1/2:
l ×N = L =ln2
π(G× t1/2)2(6.7)
Note that for the random copolymers the addition of ethylene leads to defects in the
regular polypropylene chain and, consequently, decreases the crystallization ability and
the linear growth rate G.
120 130 140 150 1600.0
0.5
1.0
1.5
2.0
2.5
3.0 iPP RACO3 RACO7
Log(G/(n
m/s))
temperature (oC)
Figure 6.10: Open points are measured growth rates and solid lines represent linear fittings.
104 Chapter 6
Table 6.2: Fitting parameters and the estimated growth rates at 137 ◦C.
y=a+b×T a b growth rate at 137 ◦C (nm/s)iPP 12.17 0.079 24.5
RACO3 12.24 0.085 4.4RACO7 11.15 0.079 2.1
The quiescent growth rates for the three materials at different temperatures are
plotted in Figure 6.10. Because the measured temperature range is limited, a linear
function [50] (Log(G) vs. T ) is used to estimate growth rates at 137◦C, obtaining 24.5,
4.4 and 2.1 nm/s for iPP, RACO3 and RACO7, respectively. All fitting parameters are
listed in Table 6.2. The growth rate of RACO7 at 137◦C was estimated by extrapolating
experimental results, since 137◦C is too high to measure the quiescent growth rate.
Using these growth rate values, we calculated the estimated lengths of the oriented
nuclei per volume given in Table 6.3.
Table 6.3: Total length per volume (L) of oriented nuclei calculated for iPP, RACO3 andRACO7 for different layers.
Total length per volumeiPP (×1011) RACO3 (×1011) RACO7 (×1011)
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