Understanding of the mechanical response of semicrystalline

Understanding of the mechanical response of semicrystalline polymers based on the block-like substructure of crystalline lamellae

A comprehensive study of mechanical relaxation, tensile deformation and yielding properties of two model polymers: polyethylene and syndiotactic polypropylene

Inaugural-Dissertation zur Erlangung des Doktorgrades der Fakult at f ur Physik der Albert-Ludwigs-Universit at Freiburg i. Brsg.

vorgelegt von Yongfeng Men aus Wulanhaote China

Juli 2001

Dekan: Leiter der Arbeit: Referent: Koreferent:

Prof. Prof. Prof. Prof.

Dr. Dr. Dr. Dr.

K. Konigsman G. R. Strobl G. R. Strobl R. Brenn

Tag der Verkundung des Prufungsergebnisses: 04.10.2001

to Yuqing

Contents 1 Introduction

3

2 Basic concepts

2.1 Structure of semicrystalline polymers . . . . . . 2.1.1 Chain and lattice packing . . . . . . . . 2.1.2 Lamellar crystal . . . . . . . . . . . . . . 2.1.3 Summary . . . . . . . . . . . . . . . . . 2.2 Mechanical properties . . . . . . . . . . . . . . . 2.2.1 Tensile deformation . . . . . . . . . . . . 2.2.2 Young's modulus and yielding properties 2.2.3 Mechanical relaxation . . . . . . . . . .

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3 Experimental methods

3.1 Materials and sample preparation . . . . . . . . . . . . 3.2 Characterization by means of DSC and SAXS . . . . . 3.2.1 Two partial melting mechanism of PE . . . . . 3.2.2 Crystallization, melting and structure of s-PP . 3.3 Studies of deformation and recovery . . . . . . . . . . . 3.3.1 Video-controlled uniaxial tensile test . . . . . . 3.3.2 Step-cycle test . . . . . . . . . . . . . . . . . . . 3.3.3 Free shrinkage . . . . . . . . . . . . . . . . . . . 3.4 Dynamic mechanical analysis (DMA) . . . . . . . . . . 3.5 Texture determination by Wide Angle X-ray Scattering

4 The critical strain law

4.1 Experiments on polyethylene . . . . . . . . . . . . . . . 4.1.1 Eect of temperature on deformation behaviour 4.1.2 Eect of strain rate on deformation behaviour . 4.1.3 Discussion . . . . . . . . . . . . . . . . . . . . 4.2 Experiments on syndiotactic polypropylene . . . . . . . 4.2.1 Tensile deformation behavior . . . . . . . . . . 4.2.2 Strain recovery - critical points of deformation 1

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42 42 49 50 55 56 58

2

CONTENTS

4.2.3 Orientational Changes during Deformation . . . . . . . . . . . 4.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

60 67

5 Young's modulus and yield stress

68

6 The relaxation of s-PP

76

5.1 The eect of temperature . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 The relationship between modulus and yield stress . . . . . . . . . . . . 5.3 summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Isotropic s-PP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Oriented s-PP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7 The in uence of the molecular weight 7.1 7.2 7.3 7.4

The plateau elastic strain . . . . . . . . . . . Higher order entanglement-The knots model The transition in the yield properties . . . . Summary . . . . . . . . . . . . . . . . . . .

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68 72 74 77 89 92

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8 Conclusions - Zusammenfassung

105

Bibliography

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Chapter 1 Introduction Polymers are long chain molecules which are constructed by small molecular units (monomers) via covalent bonds. Natural polymers exist as proteins and cellulose and, they play an unsubstituted role in every living organism. For many years, polymers were treated as a colloid which was built up by small units via the adhesion between neighbouring units. The rst widely used polymer was vulcanized rubber. It was discovered by Goodyear in 1830s when he mixed natural rubber with sulphur to produce a special elastic material [1]. However, the revolution on the understanding of the structure of polymers did not happen until 1920 when Staudinger rst pointed out that polymers were long chain molecules. This idea became more and more accepted and nally led to a rapid growing of the number of the synthetic polymers. Nowadays, polymers are found everywhere in ordinary life. Examples are uncountable like plastics, rubbers and bers. They are widely used attributing to their unique properties, easy processing and very low costs. Within those huge number of polymers, plastics is an important family. They can be found as pipes, packages, toys, even furniture and so on. One important property of plastics, namely mechanical property, plays the major role for these large number of applications. How a plastics responds under a stress eld becomes primarily important. Since the discovery of polymers, there have been a large number of studies on their mechanical properties [2, 3]. However, the mechanical properties of polymers are still not fully understood because they are tightly related with their complex inner structure. Most of the plastics are semi-crystalline polymers which just crystallize in part due to the long chain eect [4]. Entanglements existing in the melt state can not be resolved under normal crystallization rate. They are just shifted into the noncrystalline region. We thus can understand the deformation of the semi-crystalline polymers as the stretching of a network under high inner viscosity due to the existence of the entanlgements and the crystallites. This view can be proved by the observation that the drawn samples show an almost complete retraction to their original length when heating up to the melting point [5, 6], and by the modeling of the stress-strain 3

4

CHAPTER 1.

INTRODUCTION

behaviour of sime-crystalline polymers which often equals the extension curve of an ideal rubber with viscous elements superposed [7, 8]. Under a small mechanical stress eld, semi-crystalline polymers may react as an ideal Hookean elastic body which go back to its original shape rapidly after the stress is removed. Increasing the stress normally leads to a yielding process where the change in the sample shape can not be recovered when the stress is released. Further increasing of the stress nally leads to the fracture of the sample. Along this deformation process, the crystallites inside the plastics change their orientation, break into pieces, and even are destroyed. The changes of the crystallites during the deformation provide the plasticity of plastics. The study of the mechanical properties of plastics is thus mainly concerned with the basic underlying mechanism of the deformation process. Two general but distinct dierent mechanisms have been suggested. Firstly, the deformation process of a semi-crystalline polymer can be described by a partial melting and recrystallization [9]; Secondly, it can be illustrated as slips of crystallites. Two slip processes, an interlamellar sliding and a crystallographic intralamellar slip of type (100)[001], have been discovered by X-ray scattering experiments on oriented polyethylene samples when they were deformed by uniaxial compression [10, 11, 12, 13] and also by the transmission electron microscopy (TEM) experiments on isotropic polyethylenes when they were deformed by compression and shearing [14, 15] as well as uniaxial drawing [16]. The intralamellar slip can be accomplished by a homogeneous shearing of layerlike crystallites or by relative displacement of blocks [16, 17]. Dierent deformation mechanisms existing together implies that the structure feature of semicrystalline polymers are not completely understood. Recent years, the development of modern technics especially the atomic force microscopy (AFM) provides a direct view of the crystallites which show a clearly blocklike substructure of lamellae [18, 19]. This special blocky feature of lamellae has found theoretical treatment [20] which suggests that the crystallization of an entangled polymer melt is always a multi-step process passing over intermediate states. Before the formation of lamellar crystallites the system always creates a mesomorphic layer, which then solidi es through a cooperative structure transition to produce a granular crystalline layer before nally transforms into a homogeneous lamellar crystallites which are built up by blocks with thin boundary in between. Such a view together with mechanical studies on a series of polyethylenes has shown a general common description of the deformation mechanism [21]. Four characteristic points are found along the true stress-strain curves of all semi-crystalline polyethylenes where the dierential compliance and the recovery property change. The strains at these four points remain constant for all samples. This can be only understood if the block slip is generally activated during the deformation process. The aim of this work is to understand the mechanical response of semi-crystalline polymer systems based on the blocky lamellar substructure feature. After brief descriptions on the basic concepts of polymer crystalline structure and mechanical properties in chapter 2 and the experimental methods used in this work in chapter 3, we discuss

5 the critical strain law behaviour for polyethylenes under dierent testing temperatures and strain rates as well as for syndiotactic polypropylene with dierent lammellar thicknesses in chapter 4. As it will be shown, the critical strain law holds in all cases. It strongly implies that the tensile deformation behaviour of melt crystallized polymers follows a same general description due to the block slip being the main deformation mechanism. In chapter 5, we study the origin of Young's modulus and the yield stress in simecrystalline polymers. We pay special attention on the eect of temperature which nally brings us to the conclusion that the block coupling is the decisive factor for both Young's modulus and the yield stress. The linear relationship between Young's modulus and the yield stress is understood as the result of the critical strain law. It is always of great interest to learn the response of semi-crystalline polymers under a periodically varying stress eld. The high temperature relaxation is normally assigned as the motions in the crystalline phase. It is thus our interest to study the motions of blocks in a dynamic mechanical analysis experiment which leads to the nding of the process in syndiotactic polypropylene. In chapter 6 we discuss the unusual behaviour of the block motions. Finally, before the conclusions of all in chapter 8, we demonstrate the role of the entanglements inside the semicrystalline polymers during deformation in chapter 7. Analysis of the crystallinity dependent elasticity and studies on the molecular weight dependent critical strains shows us the physical background of the critical strains.

Chapter 2 Basic concepts The mechanical properties of polymers have been studied for many years. Most of the fundamental works were carried out based on normal plastics like polyethylene and polypropylene. They are chosen for their simple chemical structure. However, the understanding of the mechanical response of plastics is strongly related to the knowledge of their structure. The purpose of this chapter is thus to provide some detail information on the structure features of semicrystalline polymers and give some of the general ideas of the background of the mechanical properties of polymers.

2.1 Structure of semicrystalline polymers Crystallization of polymers can occur either from solutions or from melt states. A majority of daily use polymers are processed from their melt states via extrusion, lm blowing and injection molding to form a certain shape. We thus will focus on the structure feature which is formed through a melt crystallization process.

2.1.1 Chain and lattice packing A crystal from polymer means there is periodicity in the three spatial directions via chain packing. It is thus obvious that this packing may depend on the chemical structure of polymer chains. For this reason, let us rst look on our samples.

Polyethylene Polyethylene (PE) is the chemically simplest polymer which is composed by methylene group -CH2 -. Due to the fact that synthesis of PE is based on ethylene, the name polyethylene is adopt. Figure 2.1 gives the chemical structure of ethylene and polyethylene. As shown in gure 2.2, PE can form a crystalline state by chain packing. Because of the regularity in the chemical structure, an orthorhombic crystal lattice is formed in which the chain has a planar zigzag 6

2.1.

STRUCTURE OF SEMICRYSTALLINE POLYMERS

H H

C

C

H H

H

H

H

H

C

C

C

C

H

H

H

H

7

Figure 2.1: Ethylene and polyethylene. , b=7.417 conformation. The lattice parameters are a=4.945A A and c=2.547 A. Normally, the c axis is always along the chain direction [22].

Figure 2.2: Crystal lattice of polyethylene.(from [23])

Syndiotactic polypropylene In case of polypropylene, the situation changes. In propylene monomer (left in the gure 2.3) there is an asymmetric carbon atom, carrying the CH3 group(denoted as R in gure 2.3).Three possible con gurations of polypropylene thus appear (right in gure 2.3), showing as isotactic polypropylene(right top in gure 2.3) in which CH3 groups are arranged at the same side of main chain, sydiotactic polypropylene (right middle in gure 2.3)in which the CH3 groups are arranged alternatively on both sides of the main chain, and atactic ploypropylene (right under in gure 2.3) in which CH3 groups are arranged in a random way. Clearly, not all of them should be expected to form crystals which has a three dimensional spatial periodicity. In fact, crystal can be achieved only for isotactic and sydiotactic polymers but not for atactic polymers. In this work, our study will focus on syndiotactic polypropylene. As indicated in gure 2.4, unlike polyethylene, syndiotactic polypropylene chain shows either all-trans planar

8

CHAPTER 2.

BASIC CONCEPTS

Isotactic configuration

R H

C

C

H H

R=CH3

R

H

R

H

R

H

R

H

R

H

C

C

C

C

C

C

C

C

C

C

H

H

H

H

H

H

H

H

H

H

Syndiotactic configuration

R

H

H

H

R

H

H

H

R H

C

C

C

C

C

C

C

C

C

C

H

H

R

H

H

H

R

H

H

H

Atactic configuration

R

H

R

H

H

H

H

H

R H

C

C

C

C

C

C

C

C

C

C

H

H

H

H

R

H

R

H

H

H

Figure 2.3: Propylene and polypropylene.

zigzag conformation or a twofold helical t2 g2 form in the crystalline state when the condition of crystallization is changed.

Figure 2.4: Molecule conformations of sPP (A) twofold helical conformation; and (B) Planar all-trans conformation. (from [24]) It can be seen in gure 2.5 that three dierent crystal structures may be formed based on the helical conformation [25, 26]. In addition, a crystal structure with the all-trans planar conformation is also possible [27, 28]. Crystallization from isotropic melt at high temperature always leads to a unit cell with antichiral chains packed along a and b axes (cell III). The lattice parameters of cell III are a = 14:5 A, b = 11:2 A and c = 7:4 A. When the crystallization temperature is lower, cell II with antichiral packing along a axis is obtained which has the same a and c lattice parameters as cell III and half value of b compared with cell

2.1.


9

Figure 2.5: Unit cells of sPP: (A) C-centered cell I;(B) cell II with antichiral packing of chains along the a axis; (C) cell III with antichiral packing of chains along a and b axes; (D) unit cell containing molecules with all trans conformation(R: right-handed helices; L: left-handed helices). (from [24])

III. If the system is quenched from the melt to room temperature, a c-centered cell I can be obtained with same lattice parameter as cell II. When the sample is cold drawn below the glass transition temperature, it exhibits a crystal structure containing the zigzag chains( gure 2.5D) with lattice parameters a = 5:22 A, b = 11:17 A and c = 5:05 A [29].

2.1.2 Lamellar crystal It is already clear that dierent crystalline structures can be formed from dierent polymers or even from one polymer when the crystallization condition is changed. These dierences are generated from the dierences in chemical structure, and are always in the scale of several A. If we consider the dierent polymer systems in a larger scale up to several nm, we do nd they have something in general. Dierent from low molar mass compounds polymer systems never turn into perfect crystals but always end up in a metastable partially crystallized state due to the eect of the entanglement network. In the semicrystalline state, the crystallites represent always a lamellar structure which are separated by amorphous lays. Entanglements can not be resolved under normal crystallization condition in a sample with normal molecular weight. They are just shifted into the amorphous part. The formation mechanism of lamellae crystallites has been argued since long time before. Basic studies were rst

10

CHAPTER 2.

BASIC CONCEPTS

Figure 2.6: Sketch of the lamellae formation route into polymer melt. (from Strobl [20])

carried out on the crystallization of the dilute polymer solution systems. Due to the fact that the thickness of the single crystal thus obtained is always far smaller than the chain length, a fold chain model was proposed [30, 31]. In this model, polymer chains are folded back on the lamellar surface. Although several modi cations have been argued, the fold chain lamellae concept has be accepted based on a large number of observations. In the case of crystallization from a polymer melt, a lamellar structure

Figure 2.7: Sketch of the changes in the internal layer structure: liquid-like packing in the mesomorphic state (right), pattern of crystal blocks after the transition in the granular state (center), and lamellar crystals with mosaic block structure(left). (from Strobl [20]) is also obtained. And the fold chain model has been thus considered for many years. However the situation changes greatly from the dilute solution to the melt state. In the melt state the system presents a high viscous condition and, the regular chain folding is obviously impossible at normal crystallization rate [9]. The perfect crystalline structure inside the lamellae should also not be expected. The formation of the lamellae in the system of polymer melt thus must have dierent mechanism comparing to the crystallization process from the polymer dilute solution.

2.1.


11

Figure 2.8: Tapping mode AFM phase image of s-PP isothermal crystallized at 135 Æ C . Image obtained at ambient temperature. (from Hugel et al. [18])

Figures 2.6 and 2.7 show how the lamellae are formed into the polymer melt. It can be seen that the formation of lamellae is a multi-step process passing over intermediate states. A mesomorphic layer is always created rst and it solidi es though a cooperative structure transition when the spontaneous thickening of this mesomorphic layer is up to a critical value. This transition produces a granular crystalline layer which transfers into the nal homogeneous lamellar crystallites in the last step. The whole process is illustrated in gure 2.6 and 2.7 from right to left. As shown in gure 2.7, the nal lamellar crystallites are built up by mosaic blocks with thin grain boundaries. In real polymer system, this blocky substructure of lamellae is often observed. As an example gure 2.8 shows a typical Atomic force microscopy (AFM) image of s-PP direct after the isothermal crystallization. The similar result can be seen in the AFM experiment carried out on PE by Loos et al. [19]. We will see in the following chapters that this special blocky structure feature is the basis to understand their mechanical response.

2.1.3 Summary In summary, we have described the structural features of melt crystallized semicrystalline polymers from the examples of PE and s-PP. It has been shown that both types of polymers form lamellar crystallites which are separated by amorphous lays. Although they are built up by dierent molecular units namely ethylene and propylene, they both present a block-like substructure as their basic building unit.

12

CHAPTER 2.

BASIC CONCEPTS

2.2 Mechanical properties 2.2.1 Tensile deformation When a polymer sample with a length L0 and cross section A0 is stretched uniaxially by a force F , it will be elongated by L in the direction of F . Correspondingly, the cross section will shrink for. A nominal strain is de ned by L ; (2.1) L0 which denotes the relative change in length. Similarly, extension ratio is used in some cases. It is de ned as L L + L = 1 + nom : (2.2) nom := = 0 L0 L0 When the volume of the sample remains constant during deformation,

nom :=

L0 A0 = LA ;

(2.3)

the extension ratio as well as the nominal strain can be derived from the relative change of the cross section. Combining equations 2.2 and 2.3 we get

L A0 = = nom + 1 : L0 A The force per unit area is de ned as stress. A nominal stress nom =

nom := and a true stress

F A0

(2.4)

(2.5)

F F A0 = = nom nom : (2.6) A A0 A are often used. Having these physical quantities we can now describe the deformation behaviour of a sample by means of a stress(force)-strain(extension) curve. However,the above mentioned method works well only for a homogeneous deformation throughout the whole sample. Sometimes samples deform in an inhomogeneous way, which often happens for plastics when they are uniaxially drawn. Figure 2.9 shows a typical force-extension curve of a sample of high density polyethylene (HDPE) under drawing. The force increases at low deformation but then, reaching the yield-point, it passes over a maximum and a neck forms somewhere in the sample. Drawing further, the neck will extend over the sample while the tensile force keeps essentially unchanged. Finally, after the whole cold-drawing, the force increases again until the break point t :=

2.2.

13

MECHANICAL PROPERTIES

Figure 2.9: Typical load-extension curve of HDPE. The changes in the shape of the sample are schematically indicated.

is reached. The changes in the shape of the sample are schematically indicated in the gure. When we analyze the mechanical behaviour of plastics the problem appears that due to the neck we cannot obtain a true stress-strain curve. Fortunately, under the condition of constant volume we still can describe the true strain as a function of position. Recall equation 2.4, we can write now,

(z ) =

A0 = (z ) + 1 : A(z )

(2.7)

Here z is the position along the sample. Equation 2.7 thus yields the local extension ratio (z ) as well as the local strain (z ). For a necking sample gure 2.10 shows the true strain distribution along the sample. The local true stress can be derived from

(z ) = correspondingly.

F F = (z ) A(z ) A0

(2.8)

14

CHAPTER 2.

BASIC CONCEPTS

Figure 2.10: True strain t as a function of the position on the sample z . The neck pro le is shown below.

It seems that we have obtained all required quantities for describing the tensile deformation both in homogeneous and inhomogeneous way. However, if we consider a jumpwise deformation situation, we will nd that the above de ned strain or extension ratio does not satisfy the important requirement of additivity [32]. Let us now calculate the strains in two cases: on the one hand the sample is stretched to L0 + L1 + L2 continuously from original length L0 , and on the other hand the stretching is performed jumpwise by L1 and L2 successively.

in the case of continuous stretching:

1+2 =

L1 + L2 (L1 )L0 + (L2 )L0 + (L1 )2 + (L1 )(L2 ) = L0 L0 (L0 + L1 )

(2.9)

in the case of jumpwise stretching: L L2 (L1 )L0 + (L2 )L0 + (L1 )2 1 + 2 = 1 + = L0 L0 + L1 L0 (L0 + L1 )

(2.10)

2.2.

15


A comparison of equation 2.9 and 2.10 shows that 1+2 6= 1 + 2 ,i.e. the total strain achieved jumpwise is not equal to the sum of two successive strains, which is obviously meaningless. In order to satisfy the additivity requirement, we have to constrain the elongation L1 and L2 being small as compared with L0 . In that case, the term (L1 )(L2 ) in equation 2.9 is a high order of small quantity and, can be omitted, and thus 1+2 = 1 + 2 holds. In our case, polymers are often extended to a very large deformation, which certainly leads us to the above unsatis ed situation. The problem arises from the de nition of strain as L=L0 where the value of L is not mentioned. If L is small, it will be certainly true to refer it to L0 . But if L is not small, it will be more reasonable to refer an in nitesimal change of length dL to the current value of the length L. In this way, an in nitesimal strain dH is given by

dH =

dL : L

(2.11)

Considering the initial condition of the absence of deformation at L = L0 , we obtain

H =

Z L L0

L dL = ln = ln(1 + ) : L L0

(2.12)

The quantity H is called Hencky's measure of extension and widely used in the rheological experiments. By using of the Hencky strain, we now turn back to the consideration of the two successive extensions. In the case of jumpwise test we get L1 L0 +L1 +L2 = ln L0 +L1 +L2 H;1 + H;2 = ln L0 + L0 + ln L0 +L1 L0

which is equal to the strain in the case of continuous stretching H;1+2 . The additivity requirement is thus full lled. In this work, we will use the Hencky strain as the basic quantity of extension.

2.2.2 Young's modulus and yielding properties Young's modulus is an important material property which is de ned as the force needed to elongate the material in a small amount of deformation where the stress and strain are linearly related. We thus can write

= E:

(2.13)

E is the Young's modulus of the material. It denotes the ability of the material to keep equilibrium against the external force. In case of plastics, as we see in gure 2.9, linear stress-strain relationship is always constrained in a small range < 5%. In this small deformation, the plastic responds like an ideal spring. The deformation can be

16

CHAPTER 2.

BASIC CONCEPTS

eliminated quickly while the stress is removed. Since the Young's modulus is measured at a small deformation, we can also de ne it as

d ( ! 0) : (2.14) d This de nition allows us to use any kind of strain discussed in last section. As we can prove that when ! 0, we have E :=

H = ln(1 + nom ) ' nom ( ! 0) :

(2.15)

Based on equation 2.15, we derive Young's modulus from true stress-Hencky strain curves in this work. Looking at the gure 2.9 further, we reach a point which shows a stress maximum. This point is called the yield point. The stress and strain at yield point are named yield stress and yield strain which are represented by y and y correspondingly. One always nds an irreversible strain after releasing the imposed stress. This macroscopic plasticity needs a certain change of the micro-structure in the sample which is stable under the condition of the absence of the stress. Basically, this could be achieved by the shearing of the structure elements to a new stable position. Due to the fact that the yield point is located close to the linear stress-strain response region, the equation 2.13 is thought still to be true around yield point. Thus we have y ' Ey : (2.16) The ' sign in equation 2.16 shows that the relation between the yield stress y and the elastic modulus E represented in above equation is not exact which can also be found in gure 2.9 that the linear stress-strain behaviour starts to be lost before the yield point. Nevertheless, equation 2.16 is used in many cases to estimate the mechanical properties if some of the parameters are known.

2.2.3 Mechanical relaxation It is well known that the low molar mass liquids develop viscous forces and conventional crystalline solids represent perfectly elastic bodies under an imposed stress eld. In the case of polymers, we nd a dierent situations. Not only the polymeric solids but also the polymer melt always show a combination of the elasticity and viscosity. They are therefore addressed as 'viscoelastic'. This viscoelastic behaviour does not only mean a superposition of the viscous and elastic forces but also includes a coupling of the two forces. A result of this coupling is that a part of the elastic deformation, although being reversible, needs a certain time to become established after a stress is applied. This phenomenon is known as 'anelasticity'.The contributions of the above three parts during deformation can be observed clearly in a creep experiment shown in gure 2.11.

2.2.

17


ε(t)

creep

recovery ε1

ε2

ε3

ε1

t1

t2

t

Figure 2.11: Schematic representation of the creep and recovery experiment.

This experiment is achieved by imposing a small stress on the sample at time t1 and measuring the change in the strain as a function of time. After a creep measurement, a recovery curve is usual obtained, as given by the strain recovery after the stress is removed at t2 . Looking at the result, we nd three contributions as indicated in gure 2.11. They are:

a perfect elastic strain (1 ) which responds to the imposed stress instantaneously;

a retarded elastic strain (anelastic part 2 ) which develops as a function of time; a viscous ow (3 ) which cannot be recovered after the stress is removed.

The three parts are separated in the creep experiment. They possess dierent weights to the total mechanical response for dierent polymers and dierent testing temperatures. The later case is specially important for the usage of a polymeric material. As we have see in a creep experiment, the polymeric materials show an anelasticity which depends on the temperature and time. This special property has a strong in uence on the daily use of those materials. Detail knowledge of this behaviour are needed and, can be obtained from a dynamic mechanical experiment. Figure 2.12 shows a sketch of this experiment. Sample is exposed to a periodically varying stress eld

(t) = 0 ei!t :

(2.17)

18

CHAPTER 2.

BASIC CONCEPTS

σ (t) ε(t)

0

5

10

15

ωt

Figure 2.12: Schematic representation of the time dependence of stress (t) and strain (t) in a dynamic-mechanical experiment.

The time dependent strain (t) in response to such a stress eld is also shown in gure 2.12. It varies with the frequency of stress , but shows generally a phase-lag. It can be written then (t) = 0 ei( Æ+!t) : (2.18) In last section, we have discussed the Young's modulus in the case of a uniaxial extension experiment. Similarly, we can also de ne a dynamic tensile modulus E (! ) if the dynamic mechanical experiment is carried out under the condition of tensile extension . E (! ) is a complex quantity, and de ned as

E (! ) :=

(t) = E0 eiÆ = E 0 + iE 00 (t)

(2.19)

where E0 = 00 , E 0 = E0 cosÆ and E 00 = E0 sinÆ . The real part of the dynamic mechanical modulus, E 0 ,denotes the storage modulus and, the imaginary part E 00 represents the loss modulus. The relative weight between the two modulus EE is a dimensionless quantity and called loss factor or loss tangent. It follows from equation 2.19 that 00 0

E 00 : (2.20) E0 The dynamic modulus as well as the loss tangent of a viscoelastic material is a function of time (or frequency) and temperature. Figure 2.13 shows a typical relaxation tanÆ :=

2.2.

19


G la s s y s ta te

V is c o e la s tic s ta te

R u b b e ry s ta te

log[E '( ω ,T )] tan δ

log[E ''( ω ,T )]

log( ω ) decreasing T increasing

Figure 2.13: Schematic representation of the storage and loss modulus and loss tangent as a function of frequency or temperature for a normal viscoelastic material.

spectrum for a viscoelastic material without owing. Two noteworthy features in gure 2.13 should be pointed out:

When the frequency (temperature) is low (high), the material behaves like a rubber with very low modulus. As the frequency (temperature) is increased (decreased), the storage modulus increases rapidly while the loss modulus and loss tangent pass over a maximum. At very high (low) frequency (temperature), the material behaves generally like a glass with very high storage modulus and low loss modulus. Such a behaviour is easy to understand. Any macroscopic relaxation re ects the underlying microscopic dynamics. Motions of molecules (or group of molecules) are the basis of these relaxation phenomena. At certain temperature these motions need certain characteristic time. If the frequency of the stress eld is too slow, the motions can easily keep up with it, and consequently, the retardation is very small. If the frequency is too high comparing with the characteristic time scale, the motions have no chance to follow the external stress at all, therefore the retardation is also very small. Only in the intermediate range, the external stress frequency is comparable with the relaxation time scale. A large retardation can be obtained. Changing of temperature has the eect of changing the characteristic frequency of the relaxation motions. If the activation energy of a relaxation motion is A the relaxation time normally follows the

20

CHAPTER 2.

Arrhenius law

e RTA

BASIC CONCEPTS

(2.21)

where R is the ideal gas constant.

If we consider the eects of temperature and time(frequency) together, we are led to another interesting feature of the relaxation process. As it is shown in gure 2.13, the increase of the temperature has the same eect as the decrease of the frequency. This implies that the same relaxation process can be observed either at low temperature with a long time or at higher temperature with very short time. Mathematically,we describe this process as

E (T; log! ) = E (T0 ; log! + logaT )

(2.22)

where aT is called the shift factor. The above relationship is called the principle of time-temperature superposition [4, 33]. For many amorphous polymers the shift factor aT obeys an empirical equation

C1 (T Ts ) (2.23) C2 + T Ts where C1 and C2 are empirical constants and Ts is the reference temperature. The above equation is the well known `WLF equation'which was postulated by Williams, Landel and Ferry. logaT =

Chapter 3 Experimental methods 3.1 Materials and sample preparation Materials used in this work are polyethylene and syndiotactic polypropylene. A wide range of polyethylene are used to cover a large range of crystallinity and molecular weight. Three polyethylene were selected for a study of the temperature and strain rate dependence of the yielding properties: A linear polyethylene (Hoechst AG, Frankfurt) with 76% crystallinity (PE27), a branched polyethylene (BASF AG, Ludwigshafen) with 33CH3 per 1000 C atoms and 46% crystallinity (LDPE33) and a polyethylenevinylacetate copolymer (Exxon Chemical Europe, Machelen, Belgium) with 17.5% VA content and a crystallinity of 26% (PEVA18). For the study of molecular weight eect, a series of linear polyethylene with dierent molecular weight were used. Their basic properties are listed in Table 3.1. The s-PP used in this study was supplied by Fina Oil & Chemical. It has 81% syndiotactic pentates as indicated by 13 C NMR. The molecular weight of this sample is Mw = 2:64 105 according to the measurement of gel permeation chromatography (GPC). Samples for mechanical testing were prepared by pressing the pellets at 160 Æ C into a sheet form. The melt sheets were kept at this temperature for 20-30 minutes for completing the polymer chain relaxation. For the PE series crystallization occurred during a controlled slow cooling of the pressure plates down to room temperature. For s-PP the melt sheets were either transferred quickly into a temperature preset oven or stored at room temperature after being quenched in liquid nitrogen. Film thicknesses were in the range of 0.2-0.5 mm. Samples with the standard `dog bone'form were obtained with the aid of a stamp. The specimens for DSC and SAXS experiments were also cut from the melt-pressed sheet. 21

22

CHAPTER 3.

EXPERIMENTAL METHODS

Table 3.1: Linear polyethylenes used for the study of molecular weight eect. sample trade M Mw Mw =Mn name 105 105 name PE5 PEII5 0.5 0.67 7.5 PE8 PEII8 1.0 1.34 7.5 PE9 PEII9 5.6 7.5 7.5 PE11 PEII11 1.7 2.3 7.5 PEII12 11 14.7 7.5 PE12 PE18 PEII18 27 36 7.5 PE26 PEII26 4.1 5.5 7.5 PE27 PEII27 2.9 3.9 7.5 bayera VestolenA 6016 0.52 0.58 8.17 bayerb VestolenA 6014 0.75 0.71 6.45 6.61 bayerc VestolenA 6013 0.88 0.8 bayerd VestolenA 6012 1.13 1.08 9.08 bayere Lopolen 6021D 1.61 1.83 7.22 bayerf Lopolen 5661B 1.73 bayerg Lopolen 5261Z 2.48 4.78 12.22

3.2 Characterization by means of DSC and SAXS Due to the fact that the mechanical properties of polymers are tightly related to their inner structure, we characterized our samples carefully by means of dierential scanning calorimetry(DSC) for studying the thermal properties, and small angle x-ray scattering(SAXS) for learning about the basic morphology. Following a brief discussion of the principles of the DSC and SAXS, we will give the main structure features of the polyethylenes and polypropylene studied in this work.

Dierential Scanning Calorimetry (DSC) For the thermal property characterization, a Perkin-Elmer DSC4 is adopted in this work. Figure 3.1 illustrates the basic structure of a DSC system. The base of the sample holder assembly is placed in a reservoir of coolant. The sample and reference holders are individually equipped with resistance sensors to measure the respective temperatures of the base. If a temperature dierence between the sample and the reference is detected, for example, due to a phase change in the sample, a resistance heater starts to supply energy until the temperature dierence is less than a threshold value. A consideration of the thermal properties of this con guration shows that the energy input is proportional to the heat capacity of the sample. A change in the heat capacity as a function of temperature or time is thus obtained if the energy input per time unit is recorded as a function

3.2.

CHARACTERIZATION BY MEANS OF DSC AND SAXS

Figure 3.1: Block diagram of a DSC system. (from [34])

t0

t1/2

t / a.u.

23

Figure 3.2: Schematic illustration of an isothermal crystallization process of a polymer system as registered by DSC where t0 denotes the moment when the system is brought at the desired temperature.

Heat flow / a.u.

24

CHAPTER 3.


of temperature or time. In the present work, we use DSC in two ways:

{ To measure the heat ow during a heating process to the nal melting range

to calculate the crystallinity of our mechanical testing samples. { To measure the isothermal crytallization rate of syndiotactic polypropylene by cooling the sample fastly from the melt state to a desired crystallization temperature. When an isothermal crystallization process is performed, a curve like gure 3.2 is obtained. As shown on the curve, let t0 = 0, we choose the minimum point in the plot of heat ow vs. time as the half time t1=2 of the crystallization process.

Small Angle X-ray Scattering (SAXS) It is well known that Bragg law holds when x-ray is scattered by periodical structure. A diraction peak can be found at angle 2# for a certain wavelength if there is a periodical parallel interplanar spacing d:

(3.1) 2d For normal spacing between crystallographic planes, the distance is in the order of few Angstroms, and when is equal to 1 A, the scattering angle 2# is typically about 20Æ . On the other hand, the scattering angle 2# is very small when a lamellar structure of semi-crystalline system is under investigated which has the length scale of few nm. The task of a scattering experiment is to determine the structure of the studied system. X-rays are scattered mainly by electrons. Let the electron density of the system be (r). The amplitude of the scattered x-ray ,A(q), is the Fourier transformation of (r): sin# =

Z

A(q) = (r)e iqrdr

(3.2)

q is the scattering vector de ned as q := k k0

(3.3)

where k0 and k denote the wave vectors of the incident and the scattered waves. In a scattering experiment the result is normally expressed by giving the intensity distribution in q-space, I(q). The intensity I(q) is the absolute square of the amplitude of the scattered x-ray. We have

I(q) = jA(q)j2 = A(q) A(q) :

(3.4)

25


It follows from equations 3.2 and 3.4 that Z

I(q) = A(q) A(q) = [ (u0 )e If a new variable r = u0 Z Z

(r)

Z

du0 ][ (u)eiqudu] :

u is introduced, we have

I(q) = [ (u)(u + r)du]e where

iqu0

iqr

dr =

Z

(r)e

iqr

dr

(3.5)

(3.6)

is called autocorrelation function of (r) and de ned as (r) :=

Z

(u)(u + r)du :

(3.7)

According to equation 3.6, the intensity distribution I(q) can be obtained from

ρ(r)

Fourier transform

A(q)

Inverse Fourier transform

Γρ(r)

Squaring

Autocorrelation

3.2.

Fourier transform Inverse Fourier transform

Figure 3.3: Relationship among (r), A(q),

I(q)

(r)

and I(q). from [35]

the Fourier transformation of the autocorrelation function of (r). On the other hand, if we take the inverse Fourier transformation of the experimentally obtained intensity distribution I(q), we get (r). The four above mentioned physical quantities (r), A(q), (r) and I(q) are related with each other as shown in gure 3.3. It is clear from gure 3.3 that we can calculate the experimentally obtained intensity distribution I(q) from a known electron density distribution (r), but the inverse is not true. We cannot evaluate the electron density distribution of an unknown system directly from the experimentally registered intensity distribution I(q). Often, a comparison between I(q) and a calculated intensity for a model is used to explain the scattering data. For the system of semi-crystalline polymers it can be assumed that we have isotropically distributed stacks of parallel lamellar crystallites. In this case, the scattering behaviour can be related

26

CHAPTER 3.


to the one dimensional electron density distribution (z) where z is the normal direction of lamellae. (z) shows a periodical distribution with values c (z) denoting the electron density of crystallites and a (z) denoting the electron density of amorphous part. For such a two-phase system, the autocorrelation function has a characteristic shape ([4] Appendix). In our experiment, we use a conventional X-ray Cu K tube and a Kratky compact camera combined with a sample holder with heating facilities and a temperature control. Scattering data were analyzed by calculating the one dimensional autocorrelation function and the second derivative of the autocorrelation function which gives the interface distance distribution function [36, 37]. Both curves provide the information about crystalline and amorphous layers thicknesses and yield the linear crystallinity.

3.2.1 Two partial melting mechanism of PE To study the temperature dependence of a polymer's mechanical properties, it is important to know the eect that heating has on the morphology. DSC is a suitable method to determine the temperature dependent crystallinity, which follows at each temperature from the remaining heat of fusion. SAXS gives an information about changes in lamellar structure during heating. 30 25

dc d / nm

20 15

da

10 5 0 20

40

60

80

100

120

T / °C

Figure 3.4: Temperature dependence of the thicknesses of the crystalline lamella dc and of the amorphous layers da for the PE27 sample

3.2.


27

1.0 PE27 (SAXS) PE27 (DSC) LDPE33 (DSC) PEVA18 (DSC)

0.9 0.8

Crystallinity

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 20

40

60

80

100

120

T/

Figure 3.5: Temperature dependence of the crystallinity derived from SAXS curves for PE27 and from DSC for all samples

Figure 3.4 gives the results of the temperature dependent SAXS experiments for linear high density PE27. Observations are indicative for a reversible surface melting (compare Strobl [4], chapter 4.3) as the thickness da of the amorphous layers increases and the thickness of the crystalline lamellae correspondingly decreases on heating (at 110Æ C the surface melting is superposed by an irreversible crystal thickening) . The DSC melting curves of LDPE33 and PEVA18 indicate that the secondary crystallization during cooling here produced lamellae with a wide range of thicknesses which during heating then melt in reverse order(compare Hobeika [38]). Figure 3.5 shows the temperature dependence of the crystallinity for the three samples in the range of the mechanical tests. SAXS and DSC give equal results for PE27 both indicating that changes in crystallinity caused by the surface melting are much smaller than those following from the melting of the inserted lamellae in LDPE33 and PEVA18. We thus get two dierent temperature dependencies of the morphology of the two samples: A change in the number of crystallites on heating in the case of LDPE33 and PEVA18 on the one hand, and no in uence of temperature on this number for the PE27 sample on the other hand.

28

CHAPTER 3.


3.2.2 Crystallization, melting and structure of s-PP Crystallization kinetics It is well known that the crystallization of polymers is kinetically controlled. The isothermal crystallization process strongly depends on the crystallization condition. An increase of the crystallization temperature leads to an increase of the lamellar thickness. This is always accompanied by an increase of the crystallization time. The knowledge of this kinetic process has primary technical importance in the sample preparation process. In this work, we study the isothermal crystallization time of s-PP with DSC measurements. Figure 3.6 shows the results. The half time of the isothermal crystallization of s-PP varies from several minutes to hour when the isothermal crystallization temperature changes from 90 Æ C to 110 Æ C . The change of the crystallization time with temperature shows an exponential dependence as usual. 90 80 70

t / min.

60 50 40 30 20 10 0 90

95

100

105

110

TC /

Figure 3.6: s-PP: Half time of isothermal crystallization process as indicated by DSC thermograms.

Melting properties DSC thermograms which indicate the melting properties of the isothermally crystallized s-PPs are shown in gures 3.7a and 3.7b. Increasing the crystallization temperature leads to a systematic change in the melting behavior. The higher the crystallization temperature, the higher the temperature at the main melting peak. For the quenched

3.2.


29

a T c / °C

15

H eat flow / a.u.

95

10

100

105 5

110

0

20

H eat flow / a.u.

8

40

60

80

100

120

140

160

60

80

100

120

140

160

b

6

24 4

2

0 20

40

T / °C

Figure 3.7: DSC thermograms measured for s-PP isothermally crystallized at the given temperatures coming from the melt (a) or the glassy state (b) (heating rate: 10Kmin 1).

sample in gure 3.7b, the higher melting peak temperature is due to a recrystallization. Several peaks can be found in the DSC thermograms. Their meanings are well-known from previous studies. For an explanation we choose the sample sPP110 as an example. Four peaks appear, located at 50 Æ C , 100 Æ C , 120 Æ C , and 130 Æ C . They have to be attributed to

30

CHAPTER 3.


1. the melting of initial granular crystal lamellae ( 120 Æ C ), 2. the melting of perfect lamellar crystallites ( 130 Æ C ), 3. the melting of secondary lamellae formed on cooling to room temperature ( 100 Æ C ), and 4. the melting of imperfect block-like structures formed during storage at room temperature ( 50 Æ C ). The additional peak observed for the samples sPP95 and sPP100 on the high temperature side of the main melting peak indicates a recrystallization after melting of the primary lamellae. For all samples weight fraction crystallinities w were determined directly after the isothermal crystallization. As can be seen in gure 3.10, the crystallinity, when determined by a heating from Tc , is constant over all crystallization temperatures, with a value w (Tc ) = 0:230:01. When cooling to room temperature, the crystallinity further increases due to secondary crystallization. Increasing the crystallization temperature therefore leads to an increase in the nal crystallinity w (27 Æ C ). If the quenched sample is crystallized at room temperature, one obtains again w =0.23, i.e. the same value as always at Tc .

Tc -dependence of crystal-amorphous structure 30

spp95 spp100 spp105 spp110 qspp24

25

//

K (z) / nm

-8

20 15 10 5 0 -5 -10 0

2

4

6

8

10

12

14

16

18

20

22

24

z / nm

Figure 3.8: Interface distance distribution functions K 00 (z) for the dierent samples as derived from SAXS data at the respective Tc s.

3.2.

31


The lamellar thicknesses were derived from the second derivative of one dimensional autocorrelation function (K 00 -curves) like those shown in gure 3.8. One can easily read o the crystallite thicknesses of the dierent samples. Let us choose, for example, sample sPP110. The two maxima at 5.6 nm and 12.4 nm correspond to the crystalline and amorphous layer thicknesses dc and da respectively, and the minimum at 18 nm gives the long spacing L. A linear crystallinity can be derived from the SAXS data as d l = c : L l is 0:31 0:01 for all samples, as shown in gure 3.10. Comparing l with the weight fraction crystallinity w derived from DSC, we nd always l > w , as was also the case for ethene-octene-copolymers in previous studies [39]. This is due to the granular substructure of the crystal lamellae. Melting temperatures Tf can also be determined by SAXS experiments, by heating the sample after the isothermal crystallization. The thus obtained values Tf agreed with the ones measured by DSC. 200 C

180 160

T/

140

M1 M2 M3

120 100 80 60 40 20 0.00

0.05

0.10

0.15

0.20 -1

0.25

0.30

0.35

0.40

-1

dc / nm

Figure 3.9: Lines: Relationships between Tc and dc 1 ( crystallization line C ) and Tf versus dc 1 ( Gibbs-Thomson melting lines M1, M2, M3 ) as derived from timeand temperature dependent SAXS experiments for s-PP and poly(propene-co-octene)s (from [40]). Symbols indicate the corresponding relationships for the sample used in this study. In previous studies of the crystallization mechanism of s-PP and a series of propeneoctene-copolymers [40] ,SAXS data were always represented in the form shown in gure

32

CHAPTER 3.


0.6

0.5

from DSC scans from 27 scans from T c

from SAXS measurement at T c

φl/w

0.4

0.3

0.2

0.1

0.0 20

90

100

110

120

Tc /

Figure 3.10: Crystallinities after isothermal crystallizations at dierent Tc s: Weight fraction crystallinity w derived from DSC and linear crystallinity l deduced from SAXS data. Crystallinities after cooling and storage at room temperature, obtained by DSC.

3.9, by plotting dc 1 versus Tc (`crystallization line' C) and dc 1 versus Tf (`melting lines' M1, M2, and M3 found for three samples with dierent co-unit content). The open symbols in gure 3.9 show the relationship between dc 1 and Tc for the samples used in this study; the lled symbols determine the melting line dc 1 versus Tf . On comparing the crystallization and melting of this commercial s-PP with the other s-PPs one nds that it ts into the general scheme.

3.3 Studies of deformation and recovery It has been discussed in the last chapter that the tensile deformation of plastics is always inhomogeneous due to the neck. As shown in gure 2.10, the formation of a neck strongly aects the measured stress-strain curves. It is thus very diÆcult to compare the deformation behaviour of dierent samples merely based on the engineering stressstrain curves. This comparison only can been achieved when true stress-true strain curves are registered under a constant strain rate. At this condition, we have a much easier situation. This kind of measurement is achieved via a video-controlled uniaxial tensile test setup. We will brie y describe the basic principle of this set-up and its applications in this section.

3.3.

STUDIES OF DEFORMATION AND RECOVERY

33

3.3.1 Video-controlled uniaxial tensile test The purpose of the video-controlled uniaxial tensile test setup is to obtain the true stress-true strain curves under a constant strain rate. The schematical illustration of this setup is given in gure 3.11. It was built up several years ago under the continuous eorts rst by Dr. Hiss [41] then by Dr. Hobeika [38]. It comes close to the device developed and used by G'Sell and his co-workers [42, 43]. The basic units of this setup are a Instron 4301 tensile testing machine, a CCD camera and a computer controlling system.

Figure 3.11: Schematic illustration of the video-contralled tensile testing machine. When a neck begins to form, its pro le is registered with the aid of a CCD camera. Assuming a constant sample volume during the deformation, the local strain in the center of the neck can be derived from the minimum diameter. The related local stress can be calculated simultaneously. It follows from the tensile force and the crosssectional area at the neck center, applying in addition a correction factor accounting for the stress enhancement at the curved neck surface. This factor, , as derived by Bridgman [44] depends on the diameter b and the radius of curvature Rc of the neck

34 and reads

CHAPTER 3.


4Rc b )log (1 + )] 1 : (3.8) b 4Rc In a stretching run, the true values of stress and strain are continuously registered with the aid of the video camera connected to a computer via a frame grabber. The results are used to adjust the cross-head speed in such a way that a constant local strain rate is maintained in the center of the neck. Recalling equation 2.12 we have,

= [(1 +

H = ln(1 + ) = ln

(3.9)

where denotes the extension ratio. A constant Hencky strain rate H_ means a constant relative length change per second, resulting in an exponential length growth with time

= expH_ t :

(3.10)

Typical strain rates in our experiments were H_ = 10 2 10 3 s 1 . They could be accomplished with regulation period for the readjustment of the cross-head speed on the order of 300 ms. the task to be carried out during a period by the various sensors, moving parts, and the computer includes the measurement of the tensile force, the video registration of the pro le, its digitization and evaluation to get b and Rc , the calculation of strain and strain rate, and the change of the cross-head speed of the Instron. The controlling software was written in PASCAL which includes several (PID-)regulation parameters [41]. Figure 3.12 shows the typical result of a stretching run. A high density polyethylene sample was stretched at constant Hencky strain rate of 5 10 3 s 1 . The true stress-true strain curve is given in the top plot. the cross head speed of the Instron machine as well as the deviation of the true strain rate are also plotted in a function of Hencky strain. Comparing with gure 2.9, the rst impressive fact from this measurement is that the stress maximum in an engineering stress-strain curve, which is characteristic for a necking sample, was disappeared. The true stress-true strain curve represents a result without the eect of neck! It is thus possible to compare the deformation behaviour between dierent samples based on this technics. Look at the middle plot in gure 3.12 one nds an exponential increase of the cross-head speed. This can be easily proved if we calculate the cross-head speed based on equation 3.10. Consider d that the cross head speed is V = dL dt = dt L0 we have _ 0 = L0 H_ expH_ t = L0 H_ expH : V = L

(3.11)

In equation 3.11, L0 and H_ are constant, and we do obtain a exponential increasing of cross-head speed V with the Hencky strain H . Finally, from the lowest plot in gure 3.12, we obtain the relative deviation of the Hencky strain rate. It can be clearly seen that the relative deviation is well controlled inside 10%.

3.3.

35


300

250

σ / MPa

200

150

100

50

0 0.0

0.5

1.0

1.5

2.0

0.5

1.0

1.5

2.0

0.5

1.0

1.5

2.0

50

V / mm/min

40

30

20

10

0 0.0 50

∆εH / %

25

0

-25

-50 0.0

εH

Figure 3.12: Same sample as used in gure 2.9: an example for a video-controlled tensile test: true stress (top), cross head speed of machine (middle), and deviation of Hencky strain rate (bottom) in dependence on the Hencky strain. Dotted lines in the bottom curve represent the relative deviation of Hencky strain rate with values from -10% to 10%.

As an obvious fact, the imposed strain on a polymeric sample is generally made up of a recoverable and a remaining part. Dierent portions depend on time and temperature due to the relaxation process: pro-longed storing and heating after the deformation generally leads to a reduction of the remaining part. These properties can

36

CHAPTER 3.


be learnt by the above mentioned video-controlled tensile test setup via basically two ways, a step-cycle test and a free shrinkage experiment.

3.3.2 Step-cycle test First let us consider a step-cycle test. In this measurement, the sample is extended step-by-step with a constant Hencky strain rate as shown in gure 3.13. After each step, the sample's speed of extension is inverted and used to contract the sample until a stress of zero is achieved. Thereupon, the sample is extended again, at this given speed, until it re-reaches the point at which it left the regulated curve. This experiment leads to a decomposition of the total strain into a base (plastic) and a cyclic (elastic) part.

16 14

εH,t

σ / MPa

12 10 8 6 4

εH,b

2 0 0.0

0.2

0.4

0.6

0.8

1.0

εH Figure 3.13: Illustration of the step-cycle test. The total strain of each step H is split into two parts: the base part H;b represents the irreversible strain, and the cyclic part H;c = H H;b represents the recovery strain after each loop.

3.3.

37


3.3.3 Free shrinkage The second experimental method for the recovery properties is the free shrinkage test. After extending with a constant strain rate to a predetermined end strain, the lower clamp is released, and the change in the sample width is monitored via the CCD camera in real-time. An example of a free shrinkage experiment is given in gure 3.14. After an abrupt unloading, one nds in the rst moment a rapid shrinkage which can not be resolved by the apparatus, and then, over a longer period, a further slow retraction. After about 5 minutes, the shrinkage is already very slow. We used typically 10 minutes for this process. This experiment again leads to a partition of the total strain H into two parts: H;s , associated with the shrinkage, and H;r , representing the nonrecovered part.

εH

ε H ,s

ε H ,r

t/s

Figure 3.14: Illustration of a free shrinkage experiment: the total strain H is split into two parts: the rest H;r represents the irreversible strain, and the shrinkage H;s = H H;r represents the recovered strain. After a free shrinkage experiment, a sample can be heated up to its melting point. This procedure leads to a further shrinkage. Only that deformation which is still present after heating is truly irreversible. This is indicated in gure 3.15. The truly irreversible strain after heating is denoted as H;i .

38

CHAPTER 3.


εH

ε H ,i

T / °C

εH

ε H ,r

t/s

Figure 3.15: Heating the sample up after a free shrinkage test.

3.4 Dynamic mechanical analysis (DMA) Frequency- and temperature-dependent dynamic mechanical measurements were carried out with the DMTA MKII of Polymer Laboratories, covering the frequency range from 10 1 to 102 Hz and using temperatures from ambient to 110 Æ C . In the dynamic measurements, samples were kept under a constant force of 0.5N which produced a pre-strain of less than 1%. The amplitude of the elongations in the oscillations was set at a constant value of 16 m corresponding to strains in the order of 0.1%. For completion we also carried out in the neighboring Freiburg Material Research Center (FMF) some measurements with the Solid Analyzer II of Rheometrics, thereby extending the frequency range down to 10 2 Hz.

3.5 Texture determination by Wide Angle X-ray Scattering Wide angle X-ray scattering (WAXS) is a powerful means for the structure analysis of crystalline materials. As we have discussed in section 3.2, an atomic scale periodic

3.5.

TEXTURE DETERMINATION BY WIDE ANGLE X-RAY SCATTERING

39

structure can be resolved with WAXS measurement. Besides using Bragg's law shown in equation 3.1, it is helpful to understand the scattering phenomenon by introducing the reciprocal lattice G. The use of the reciprocal lattice is based on the fact that the X-ray scattering pattern of a crystalline material shows also a unique regular structure in reciprocal space like the crystalline lattice in real space. In fact, these two quantities are related with each other by a Fourier transform relationship. If the reciprocal lattice is taken into account, scattering can occur only if the scattering vector q in equation 3.3 is equal to G. In that case, we have the Laue condition as following

G = k k0 :

(3.12)

In case of elastic scattering with jkj = jk0 j the Laue condition can be illustrated by

Figure 3.16: Ewald construction the using the Ewald construction. For isotropic semi-crystalline polymers, the crystalline lattice vector as well as the reciprocal lattice vector is distributed in all possible directions. This is shown in gure 3.16. The reciprocal lattice vector G resides on the surface of a sphere which is called the re ection sphere. The scattering happens when the Ewald sphere ,which is constructed from equation 3.12 with a radius of jk0 j, intersects the re ection sphere. If a 2 dimensional detector is used, we obtain a circle for isotropic samples. This circle is called Debye circle. For an anisotropic sample, it is possible to determine the orientational distribution of certain lattice plane by using the distribution of the registered scattering intensity along the Debye circle. It has

40

CHAPTER 3.


been shown by Polanyi [45] long ago that the orientation angle of a lattice plane ,, is related with the azimuthal angle along the Debye circle,, by the equation

cos = cos#hkl cos

(3.13)

where #hkl denotes the Bragg scattering angle. In our experiments, we use a rotating Cu anode generator (Fa. Schneider, Oenburg) at the point focus and registered with an image plate detector (Fa. Schneider, Oenburg) the wide angle X-ray scattering from semi-crystalline samples. Using a Mini-Instron (Rheometric Scienti c Mini Mat 2000), samples could be kept under stress during the exposure.

Chapter 4 The critical strain law Deformation of semicrystalline polymers is always accompanied by changes in the microscopic structure that result in an alteration of sample properties during deformation. In a recent study (Hiss [21]), the eect of crystallinity on the mechanical, elastic and structural behaviour of polyethylene and related copolymers by means of videocontrolled uniaxial drawing with constant strain rate, step-cycle tensile tests analysing the elastic recovery and wide angle X-ray scattering experiments for texture determinations under load was investigated. It was found that in spite of the large variations in the global mechanical properties from solid-like to rubber-like the deformation behaviour follows a common general scheme. There exist four transition points, denoted A, B, C and D, where the dierential compliance, the reversibility of the imposed strain and the crystallite texture change simultaneously. These points may be associated with: 1. the onset of isolated inter- and intralamellar slip processes (point A), 2. a change into a collective activity of slips (point B), 3. the beginning of bril formation after a fragmentation of the lamellar crystals (point C) and 4. chain disentanglement (point D). While the stresses at these points greatly vary with crystallinity the strains remain essentially constant. Crystal textures are found to be a function of the imposed strain only, the dependencies being common for all samples. Obviously, crystallites are able to easily react to the imposed deformation in a well-de ned manner, only determined by the strain. This suggests that `coarse' block-slip processes are generally activated, for linear polyethylene and the copolymers likewise, thus providing suÆcient degrees of freedom for accomplishing any deformation. In fact, as we have discussed in chapter 2, recent studies of various crystallizing polymers by time-dependent SAXS and AFM [18, 39, 20] have shown that the building-up of the lamellae is always a multi-step 41

42

CHAPTER 4.

THE CRITICAL STRAIN LAW

process, beginning with the formation of blocks which then fuse into layers. As a memory to this building process lamellae retain a granular substructure. Obvious questions arising from the work were: 1. If crystallinity does not change these critical strains, does a variation of temperature and strain rate have any eect? 2. If the deformation behaviour of polyethylenes is simply controlled by the imposed strain due to the blocky substructure of lamellar crystal, does this critical strain law hold for other semi-crystalline polymers? We therefore continued our studies in this work by varying these parameters. As is described in the following, we found that the critical states of deformation are independent of them. In the following sections, we will study the eects of temperature and strain rate on the critical strain law for three polyethylenes with dierent crystallinity and for syndiotactic polypropylene with dierent crystalline thicknesses.

4.1 Experiments on polyethylene 4.1.1 Eect of temperature on deformation behaviour True stress-strain curves for all samples measured at dierent temperatures are shown in Figure 4.1. Increasing the temperature leads to a general reduction of the applied stress. As shown in the previous work, from the stress-strain curves the transition point B, which comes near to the yield point observed in engineering tensile tests, can be determined. It is located in the range with the largest changes in the dierential compliance, i.e. the maximum curvature of the stress-strain curve. It can clearly be seen, that although the stresses at the yield points remarkably decrease with temperature, the yield strains essentially remain constant at H 0:12. At all four transition points characteristic changes take place in the elastic recovery properties of the samples. As described in chapter 3, the recovery of the imposed deformation was investigated by performing step-cycle tests, now with the focus on the eect of temperature. Step-cycle tests give a partitioning of a total imposed strain into two components, a spontaneously reversible "cyclic part" and a "base part" which is irreversible on the time-scale of this experiment. Figure 4.2 shows the changes with temperature of the total strain, base part and the recoverable cyclic component, as obtained for PEVA18 as a function of the applied stress. The clearest change in elastic behaviour is given by the cyclic component reaching a plateau. This marks the transition point C, where, as shown in the previous work, brillation sets in. Note that although the stresses at point C decrease with increasing temperature, the related total strain remains constant at H 0:6.

4.1.

43

EXPERIMENTS ON POLYETHYLENE

180

23 50 70 110

σ / MPa

160 140 120 100 80 60 40 20 0 0.0

0.2

0.6

0.8

1.0

1.2

1.4

1.6

1.8

0.6

0.8

1.0

1.2

1.4

1.6

1.8

0.6

0.8

1.0

1.2

1.4

1.6

1.8

26 59 81

50 40

σ / MPa

0.4

30 20 10 0 0.0 80

0.2

23 38 50

70 60

σ / MPa

0.4

50 40 30 20 10 0 0.0

0.2

0.4

εH

Figure 4.1: True stress-strain curves, measured at a constant Hencky strain rate of 5 10 3s 1 at the temperatures indicated in the plot for HDPE (top), LDPE33 (center) and PEVA18 (bottom).

A closer look at the low deformation region (Figure 4.3) shows the same temperature independence for the two other transition points A and B. At A, associated with the onset of individual slip processes, for the rst time irreversible strains H;b arise. Then, at point B, a strong increase in the dierential compliance is observed. It is caused by both increases of the recoverable and the permanent part. For all temperatures we nd point A at a strain H 0:03 and point B at H 0:13.

44

CHAPTER 4.


1.4

total base cyclic

1.2

1.0

C

εH

0.8

0.6

0.4

0.2

0.0 0

5

10

15

20

25

1.4

1.2

1.0

C

εH

0.8

0.6

0.4

0.2

0.0 0

5

10

15

20

1.4

1.2

1.0

C

εH

0.8

0.6

0.4

0.2

0.0 0

5

10

15

σ / MPa

Figure 4.2: Total strain, base part and cyclic strain component as a function of imposed stress, derived for PEVA18 from step-cycle tests under variation of the temperature. 23 Æ C (top), 38 Æ C (center) and 50 Æ C (bottom).

Figures 4.4 and 4.5 show data from analogous experiments carried out for LDPE33. It is obvious that the general results agree with PEVA18, even if the data are less

4.1.

45


0.30

total base cyclic

0.25

εH

0.20

B

0.15

0.10

A

0.05

0.00 0

2

4

6

8

0.30

0.25

εH

0.20

B

0.15

0.10

A 0.05

0.00 0

1

2

3

4

5

0.30

0.25

εH

0.20

B

0.15

0.10

A

0.05

0.00 0

1

2

3

σ / MPa

Figure 4.3: PEVA18 at dierent temperatures: (23 Æ C (top), 38 Æ C (center) and 50 Æ C (bottom)) Partitioning of the total strain into the cyclic and the base component for small strain values (enlarged view from Figure 4.2).

accurate. Independent of the temperature we nd three critical strains, located at H 0:03 (A), H 0:13 (B) and H 0:6 (C). The HDPE sample has much smaller recoverable strain components than the copoly-

46

CHAPTER 4.


1.6

total base cyclic

1.4 1.2

εH

1.0

C

0.8 0.6 0.4 0.2 0.0 0

5

10

15

20

25

30

35

1.6 1.4 1.2

εH

1.0

C

0.8 0.6 0.4 0.2 0.0 0

5

10

15

20

4

6

8

1.0

0.8

C εH

0.6

0.4

0.2

0.0 0

2

σ / MPa

Figure 4.4: Total strain, base part and cyclic component as a function of imposed stress, derived for LDPE33 from step-cycle tests under variation of the temperature (26 Æ C (top), 59 Æ C (center) and 80 Æ C (bottom)).

mer, which makes it diÆcult to detect the characteristic points in a step-cycle run. Here we employed the free shrinkage experiment and determined the strain H;r remaining after a sudden unloading. It comes near to the base part in the step-cycle test, i.e. H;r H;b . Figure 4.6 shows H;r plotted as a function of the total strain. Al-

4.1.

47


0.30

total base cyclic

0.25

εH

0.20

B

0.15

0.10

A

0.05

0.00 0

2

4

6

8

10

12

14

0.30

0.25

εH

0.20

B

0.15

0.10

A

0.05

0.00 0

1

2

3

4

5

0.30

0.25

εH

0.20

B

0.15

0.10

A

0.05

0.00 0

1

2

3

σ / MPa

Figure 4.5: LDPE33 at dierent temperatures (26 Æ C (top), 59 Æ C (center) and 80 Æ C (bottom)): Partitioning of the total strain into the cyclic and the base component for small strain values (enlarged view from Figure 4.4).

though heating results in higher retracting forces, which could in principle reduce the

48

CHAPTER 4.


1.0

0.60 0.55 0.50

0.8

0.45 0.40

24 50 70 110

0.35 0.30

C

εH,i

εH,r

0.6

0.25

0.4

23 70 110

0.20 0.15

0.2

0.10

D

A,B

0.05 0.0 0.0

0.00 0.2

0.4

0.6

0.8

1.0

1.2

εH

Figure 4.6: Persisting strain after sudden unloading in a free shrinkage experiment at several temperatures (H;r ) and after heating the sample up to its melting point (H;i) for HDPE as a function of the total deformation.

remaining strain, this is not observed. Permanent deformations arise from H ' 0:1, in the range of the points A and B, and at C a break is seen, located for all temperatures at H 0:6. Finally, when the free shrinkage experiment is combined with a heating up to the melting point, one can detect the fourth transition point, D, where disentangling leads to a true plastic deformation. Here, dierent from the critical strains A, B, C, we do see a temperature eect. One observes a tendency to a lowering of the related strain with increasing temperature, down to the location of point C. The gures in this section give an impression of the accuracy of the data. As always in deformation tests, this accuracy is not too high, and one nds corresponding variations when repeating the experiments taking another sample. In spite of that, the existence of critical points, where the yielding process changes, shows up clearly, and their locations are quite well determined.

4.1.

49


4.1.2 Eect of strain rate on deformation behaviour To study the in uence of the deformation rate on the mechanical behaviour, videocontrolled tensile tests at several constant strain rates were performed. Figure 4.7 shows 200 -2

1*10

-3

3.5*10

-3

1*10

150

-4

3.5*10

-4

σ / MPa

1*10

100

B 50

0 0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

50

40

5*10

-4

5*10

-3

5*10

-2

σ / MPa

30

20

B

10

0 0.0 50

0.2 5*10 5*10

40

5*10

-4 -3 -2

σ / MPa

30

20

B 10

0 0.0

0.2

εH

Figure 4.7: Strain rate dependence of true stress-strain curves at room temperature for HDPE (top), LDPE33 (center) and PEVA18 (bottom). Strain rate unit in the legend is s 1 .

50

CHAPTER 4.


the true stress-strain curves for both materials, obtained for constant local strain rates in the range of _H =10 2 s 1 to 10 4 s 1 . For the HDPE sample there is a pronounced eect, as decreasing the strain rate remarkably lowers the stresses at all strains. For the copolymer the dierence in stress for the various strain rates is smaller, although still observable. As pointed out previously (compare Figure 5 in Hiss [21]), for HDPE the stress-strain rate dependence as observed in the plateau after the yield point is indicative for an Eyring process. Now we note in addition, that although yield stresses increase with rate, the yield strains as given by the location with the largest change in the dierential compliance do not change. They are always in the range H 0:120:02. Figure 4.8 shows cyclic and base strain components determined by the step-cycle test in the case of PEVA18, carried out for dierent strain rates. One nds that the total strain H at point C does not change, while the related stress increases with strain rate. Figure 4.9 depicts analogous data for LDPE33, leading to the same result. Figure 4.10 shows for HDPE the results of free shrinkage experiments, carried out after deformations with various strain rates, plotting the remaining part H;r as a function of total strain. Data points for all strain rates fall onto one line, beginning with the activation of the slip processes at points A and B and showing a break at H = 0:6, i.e. at point C associated with the beginning of brillation. Obviously, not only the critical total strain does not change with strain rate, but also the partitioning into cyclic and base component is independent, too. For the truly plastic deformation, as given by the irreversible part of the strain remaining even after heating, one nds for HDPE no strain rate dependence.

4.1.3

Discussion

The observed eects of temperature and strain rate at the stresses during a stretching show the expected tendencies: Decreasing strain rate and increasing temperature generally result in a lowering of the stress needed to reach a given strain. Although for PEVA18 and LDPE33 heating also results in a lower content of crystalline material, in the case of HDPE crystallinity is not much changed in the given temperature range. We therefore must conclude that the stresses and, in particular, those at the critical points B and C show in addition to the known eect of the crystallinity an explicit dependence on temperature. In a global view, the yielding behaviour of polyethylene may be addressed as the deformation of the network set up by the entanglements under conditions of a high internal viscosity. Variation of the temperature, the strain rate and, caused by the partial melting, the crystallinity changes only the internal friction component. Physically this friction comes from inter- and intralamellar shear processes. It increases with the volume fraction of the sheared crystalline material, because the area of the slipping surfaces is increased, and with strain rate as a consequence of a higher local deformation speed. Heating facilitates rearranging of the texture, as the viscosity of the

4.1.

51


1.4

total base cyclic

1.2

1.0

εH

0.8

C

0.6

0.4

0.2

0.0 0

5

10

15

20

25

5

10

15

20

25

1.4

1.2

1.0

0.8

εH

C

0.6

0.4

0.2

0.0 0 1.4

1.2

1.0

0.8

εH

C

0.6

0.4

0.2

0.0 0

5

10

15

20

25

σ / MPa

Figure 4.8: Total strain, base part and cyclic strain component as a function of imposed stress, derived from step-cycle tests for PEVA18 under variation of the strain rate(5 10 2 =s(top), 5 10 3 =s(center) and 5 10 4 =s (bottom)).

amorphous intercrystalline layers decreases. For the copolymer, it additionally results in a lower volume content of crystallites, which further supports the stress lowering eect.

52

CHAPTER 4.

1.6


total base cyclic

1.4 1.2

εH

1.0

C

0.8 0.6 0.4 0.2 0.0 0

5

10

15

20

25

30

35

40

5

10

15

20

25

30

35

40

5

10

15

20

25

30

35

40

1.6 1.4 1.2

εH

1.0

C

0.8 0.6 0.4 0.2 0.0 0

1.6 1.4 1.2

εH

1.0

C

0.8 0.6 0.4 0.2 0.0 0

σ / MPa

Figure 4.9: Total strain, base part and cyclic strain component as a function of imposed stress, derived from step-cycle tests for LDPE33 under variation of the strain rate(5 10 2 =s(top), 5 10 3 =s(center) and 5 10 4 =s (bottom)).

The shear processes induced by the stretching change the amorphous-crystalline texture in step-wise fashion, rst locally, then by rearrangement of the whole lamellar

4.1.

53


1.0

0.30

0.25 0.8

0.20 5*10

0.6

5*10 1*10

-4 -3 -2

εH,r 0.4

1*10

-2

5*10

-3

5*10

-4

εH,i

0.15

C

0.10

0.2 0.05

A,B

0.0 0.0

D

0.2

0.4

0.6

0.8

1.0

0.00 1.2

εH

Figure 4.10: Persisting strain after sudden unloading in a free shrinkage experiment H;r and after heating the sample up to its melting point (H;i) as a function of the total deformation, observed for dierent strain rates for HDPE.

structure, after that by breaking up the lamellae and forming brils and lastly by disentanglement, which nally leads to fracture of the sample. The transition points A, B, C and D where the material behaviour changes show up clearly, also under variation of temperature and strain rate: Directly in the stress-strain curve as an increase in the dierential compliance at the yield point (Figures 4.1 and 4.7), in the step-cycle experiment as changes in the (linear) dependence of the cyclic strain component and the base part on the total strain (Figures 4.2, 4.3, 4.4, 4.5, 4.8 and 4.9) and in the rst occurrence of a truly plastic deformation persisting after a heating (Figures 4.6 and 4.10). In contrast to the stresses at the transition points A, B and C, which greatly vary, the critical strains at these points are not aected by changes in the temperature and the strain rate. This is an important nding. It complements and ts with

54

CHAPTER 4.


the previously observed independence on the crystallinity. As long as the underlying entanglement network is not destroyed, activation of the dierent deformation steps during stretching is only strain dependent. Neither sample crystallinity nor mechanical or thermal history change the critical strain values at the transition points, which means that in order to reach a given strain the sample texture has to change in a well-de ned manner. As discussed previously this is only possible, if there were at least ve slip systems to enable the amorphous-crystalline system to react to the imposed stress. At each critical strain the deformation limit that can be realized through a certain shear process is reached, so the next step in the sequence of deformation processes has to start. 10

25

8

F/A0 / MPa

42 6

60 4

78

2

0 0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

ε

Figure 4.11: LDPE33: Engineering load-extension curves measured at the indicated temperatures. As the only exception, opposite to points A, B and C, at point D heating shows an eect: Figure 4.6 depicts the truly irreversible strain H;i which persist in the free shrinkage experiment even after a heating to the melting point as a function of total deformation for a range of temperatures. One can see a tendency that at higher deformation temperatures true plastic deformation sets in at lower strains. The behaviour is conceivable. The disentangling process, which is related to this characteristic strain,

4.2.

EXPERIMENTS ON SYNDIOTACTIC POLYPROPYLENE

55

becomes easier at high temperatures and thus may set in already at a lower strain, because the mobility of the chains increased. In comparison, as shown by the strain rate independence of the strain at point D, the deformation time does not play a role in the onset of this process for the strain rates used here. As we see, neither the partitioning of the total strain into an elastic and a remaining component nor the irreversible part are aected by the alteration of the strain rate. This means that inter- and intralamellar slips as well as fragmentation and disentangling have to take place fast enough, so that no retardation occurs. Decisive for the nding of the critical strain laws is the determination of true stressstrain curves for constant strain rates, as obtained employing the video-control. The normal engineering stretching curves registered with constant cross-head speed cannot provide these results. Indeed, load-extension curves measured for necking samples like HDPE and LDPE change their shape with temperature, as shown in Fig.4.11 for the case of LDPE33. There is no longer the systematic variation of the true stress-strain curves showing up in Fig.4.1. In particular, the engineering yield point, as given by the load maximum, may well shift in strain with temperature, as is reported, for example, in a recent paper on HDPE of Brooks et al [46]. In fact, in contrast to point B, which can be associated with the collective onset of slip processes, the engineering yield point, although of technical importance, has no simple physical background. Its location depends on the shape of the true stress-strain curve in a larger range above B, the change of stresses with the strain rate and the variations with time of the acting force.

4.2 Experiments on syndiotactic polypropylene In the last section, we have discussed the eect of temperature and strain rate on the deformation behavior of polyethylenes, and it has been illustrated that a critical strain law holds. This simple strain controlled deformation behaviour is attributed to the blocky substructure of lamellar crystals inside the semi-crystalline polymers. Only if the block coarse slip is generally activated during the tensile deformation process, samples can react easily on each imposed strain in a well de ned way. This conclusion implies that as long as the blocky substructure of lamellae exists, we would expect that the critical strain law is valid for other semi-crystalline polymers too. For this purpose, we investigated another typical semi-crystalline polymer, namely syndiotactic polypropylene. This selection is based on two points: 1. Syndiotactic polypropylene is de nitively dierent from polyethylene from the molecular motion point of view. It is well known that the chain longitudinal sliding diusion of polyethylene does not happen for syndiotactic polypropylene. 2. The crystallization process of this polymer is well studied in our group, and it follows a simple scheme (see chapter 3).

56

CHAPTER 4.

4.2.1


Tensile deformation behavior

Studies of the mechanical properties of s-PP are rare and mostly based on engineering measurements [47, 48]. Engineering stress (nom ) versus elongation (L=L0 ) curves for sPP95 under a constant cross-head speed (1.95 mm/min) for dierent temperatures are given in gure 4.12.

16

14

25

12

σnom. / MPa

10

8

6

4

105 2

0 -0.5

0.0

0.5

1.0

1.5

2.0

∆ L/L0

Figure 4.12: Engineering stress-extension curves for sPP95 at dierent stretching temperatures. The continuous line connects the engineering yield points, the dotted line shows the positions of the yield points deduced from true stress-strain measurements. Generally, one nds a yield maximum after a nearly linear region at low deforma-

4.2.


30 51 70 96

0.2

0.4

0.6

0.8

1.0

57

tions, followed by a necking and the growth of the neck indicated by a stress plateau. The engineering yield points denoted in gure 4.12 by the black dots change with temperature in such a manner that the yield stress greatly decreases, accompanied by some shift of the yield strain. In fact, the formation of the neck complicates the analysis of the deformation behavior [4]; for a better knowledge the true stress-strain curve is needed. We therefore carried out video-controlled tensile tests. 35

30

25

20

15

10

5

0 0.0

εH

Figure 4.13 shows the temperature dependence of the true stress-strain curves obtained under a constant strain rate (H_ = 5 10 3 s 1 ). As one notes, the stress maximum has disappeared. Under these conditions one can choose the point with the largest curvature on the stress-strain curve as the yield point. Comparing the dierent curves obtained for dierent drawing temperatures, one nds that in spite of the large changes in the stresses the strains at the yield points remain constant. These points are also included in gure 4.12, as the dotted line in the low deformation range. As we see, the yield strain derived from true stress-strain curve is smaller than that deduced from engineering stress extension measurement. This result again agrees with observations in the previous studies on polyethylene in section 4.1. More insight on the deformation process can be obtained from the recovery test.

Figure 4.13: True stress-strain curves, measured at a constant Hencky strain rate of 5 10 3 s 1 at dierent temperatures for sPP95.

σ / MPa

58

4.2.2

CHAPTER 4.


Strain recovery - critical points of deformation

As the rst recovery test we carried out the step-cycle test. The experimental results enable the total strain to be split into two parts, a recovered one, H;c , describing the strain associated with the cycle, and a remaining `base' part, H;b , as given by the strain in the moment of complete unloading. Results of the decomposition, taken from numerous step-cycle runs, are shown in gures 4.14 and 4.16, where H , H;c , and H;b are shown as a function of the true stress. The experiments refer to two dierent samples (sPP95 and sPP110), which were deformed at dierent temperatures (30 Æ C , 51 Æ C , 70 Æ C , and 96 Æ C ). The deformation behavior at the beginning, i.e. at low stresses is given in gures 4.15 and 4.17. For all tests, a purely Hookean elasticity can be seen in the low deformation range up to a strain of H 0:04 which is denoted in the plots as point `A'. From there on, irreversible strains H;b arise. A second transition point occurs at a point `B'. As shown in the plots there an increase in the dierential compliance takes place. As a comparison shows, point B agrees with the yield point as given by the point with the maximum curvature in the true stress-strain curves in gure 4.13. Its location remains essentially constant at H 0:12 for all testes. On further increasing the stress and strain, a third transition point, `C', shows up. At rst, both, the cyclic and the base component increase with the increasing stress. Then, however, as shown in the plots of gures 4.14and 4.16, for the cyclic part this increase comes to an end, and a maximum plateau value is reached. This occurs when the total strain reaches H 0:4, which determines C. This strain is common for all samples and temperatures, dierent from the stress which shows large variations. The experimental results tell us that the deformation behavior is controlled by critical strains rather than critical stresses. In other words, there again exists a critical strain law as it was already found for polyethylene. The physical background of the behavior should be the same one as for the polyethylenes. At point A, individual inter- and intralamellar slip sets in; at point B, the slip-processes then change into a collective activity. Finally, at larger deformations beginning at point C, the lamellar crystals fragment and brils are formed. The critical strains observed for s-PP are independent of structural parameters and the temperature, again in agreement with the ndings for polyethylene. As shown in the previous section, sPP95 and sPP110 show a similar crystallinity but dierent crystal thicknesses, 4.4nm and 5.8nm respectively. Temperature greatly changes the stresses at the critical points, for sPP110 at point C from 20MPa to 7.8MPa when going from 30 Æ C to 96 Æ C . This large change in stress, however, does not aect the critical strain value, which is constantly at H = 0:4. As a second recovery test, free shrinkage experiments were carried out at room temperature. Figure 4.18 shows a result. The reversible part, H;s , reaches a plateau value at a total strain of 0.4; simultaneously, the irreversible part shows a change in dierential compliance. Figure 4.18 demonstrates the independence of critical strains

4.2.

59


total base cyclic

1.0 0.8 0.6

εH

C

0.4 0.2 0.0 0

5

10

15

20

25

30

35

1.0 0.8 0.6

εH

C

0.4 0.2 0.0 0

5

10

15

20

25

30

1.0 0.8 0.6

εH

C

0.4 0.2 0.0 0

5

10

15

20

σ / MPa

Figure 4.14: Total strain, base part and cyclic component as a function of imposed stress, derived for sPP95 from step-cycle tests under variation of the temperature (30 Æ C (top), 51 Æ C (center) and 70 Æ C (bottom)).

on the structure, i.e., the crystal thicknesses. The result corroberates the ndings of the step-cycle tests.

60

CHAPTER 4.


0.30

total base cyclic

0.25

εH

0.20

B

0.15

0.10

A

0.05

0.00 0

5

10

15

20

0.30

0.25

εH

0.20

0.15

B

0.10

A

0.05

0.00 0

2

4

6

8

10

12

14

0.30

0.25

εH

0.20

0.15

B

0.10

0.05

A

0.00 2

4

6

8

10

12

σ / MPa

Figure 4.15: Total strain, base part and cyclic component as a function of imposed stress, derived for sPP95 from step-cycle tests at small strains under variation of the temperature (30 Æ C (top), 51 Æ C (center) and 70 Æ C (bottom)).

4.2.3

Orientational Changes during Deformation

As indicated in chapter 2, there exist four crystalline forms of s-PP: helical forms I, II and III [25, 26], and trans-planar form IV [27, 28]. The helical conformation is the most

4.2.

61


1.0

total base cyclic

0.8

εH

0.6

C

0.4 0.2 0.0 0

10

20

30

40

1.0 0.8

εH

0.6

C

0.4 0.2 0.0 0

5

10

15

20

25

1.0 0.8

εH

0.6

C

0.4 0.2 0.0 0

2

4

6

8

10

12

14

σ / MPa

Figure 4.16: Total strain, base part and cyclic component as a function of imposed stress, derived for sPP110 from step-cycle tests under variation of the temperature (30 Æ C (top), 51 Æ C (center) and 96 Æ C (bottom)).

stable one and always obtained when crystallizing from the isotropic melt. Crystalline conformational phase transitions during tensile deformations are of interest for some authors. Loos et.al. [24] and Zhang and Yang [49] showed that after necking the

62

CHAPTER 4.

0.30

total base cyclic

0.25 0.20

εH


B

0.15 0.10

A

0.05 0.00 0.30

0

5

10

15

20

0.25

εH

0.20

B

0.15 0.10

A

0.05 0.00 0

5

10

15

0.30 0.25

εH

0.20

B

0.15 0.10

A

0.05 0.00 0

2

4

6

8

σ / MPa

Figure 4.17: Total strain, base part and cyclic component as a function of imposed stress, derived for sPP110 from step-cycle tests at small strains under variation of the temperature (30 Æ C (top), 51 Æ C (center) and 96 Æ C (bottom)).

crystalline phase completely transforms into a trans-planar form. Figure 4.19 collects some wide angle X-ray scattering diagrams registered for sPP95 at dierent stages of deformation (other samples yield similar results). Both patterns under load (upper) and in the unloaded state (lower) are given always at equal Hencky strains. Samples were rst exposed at certain end strain during stretching, and then the stresses were

4.2.

63


0.6

εH,r εH,s

0.4

C

0.2

0.0 0.0

0.2

0.4

0.6

0.8

1.0

0.6

0.8

1.0

0.6

0.4

C

0.2

0.0 0.0

0.2

0.4

εH

Figure 4.18: Results of free shrinkage experiments carried out for sPP95 (top) and sPP110 (bottom) : Partitioning of the total strain H into the amount of shrinkage, H;s , and the remaining part, H;r .

released to get the unloaded WAXS pattern. In all cases only the helical crystalline form was obtained which is in agreement with the reported behaviour. Guadagno et.al., when studying the polymorphism of oriented s-PP, found that only for draw ratio above about = 6 , the transformation from helical form to trans-planar conformation took place [50]. In our study the strain was limited to draw ratio below = 4. The three circles in the WAXS patterns are associated with a scattering of 200(inner circle), 020-(middle circle), and 121-(outer circle) lattice planes. The broad halo

64

CHAPTER 4.


Figure 4.19: sPP95: Selected WAXS diagrams measured for the indicated local Hencky strains, both under stretching(upper) and unloaded(lower) patterns are included.Drawing was performed horizontally.

near to the 020-re ection is associated with the amorphous regions. The azimuthal intensity distributions along the circles re ect the orientational distribution of the crystals and amorphous chains. We put the focus on the 200-re ection and the amorphous halo. Starting in the non-deformed state with the isotropic intensity distribution, the rst visible changes in WAXS pattern occur for H 0:1 0:2.Four maxima at oblique angles show up for 200-re ection; for the amorphous halo two maxima appear at the equator. Deforming the sample further to H > 0:4, both the 200-re ections and the amorphous halo show maxima at the equator. More clear results are presented in gures 4.20a and 4.20b, which give the azimuthal scans of the intensity distribution of the 200-re ection and amorphous halo. In both plots the background intensity is substracted. An orientational order parameter is often used to express quantitatively degrees of orientation in uniaxially oriented samples. It is de ned by (3 < cos2 > 1) S= 2 where denotes the angle enclosed by the axis of interest and the unique axis. The values for S200 and Samorphous can be derived from the azimuthal intensity distribution

4.2.


65

4000

a b 0

4000

0

3000

0.1 3000

Intensity [arb. units]

Indensity [arb. units]

0.1

2000

0.2

0.2

2000

0.3 0.4

0.3 1000

1000

0.4

0.6 0.6

1.0 1.0

0 -50

0

0 50

100

150

200

θ

250

300

350

400

-50

0

50

100 150 200 250 300 350 400 θ

Figure 4.20: Intensity orientational distribution of 200-lattice planes (a) and amorphous halo (b) at indicated Hencky strains.

function I () along the respective circles by using of the Polanyi equation 3.13. The results of two order parameters are given in gure 4.21 as a function of true strain S (H ). Note that for a perfect orientation of the lattice plane, with its normal in the plane of equator, the order parameter would be S = 0:5. This limiting value is not reached. The changes of the texture at low and moderate deformations, up to point C, are induced by slip processes. Two kinds of slip processes exist while the sample is stretched, known as inter- and intralamellar slip processes. However, these two slip processes lead to opposite changes of the value of the order parameter [21]. Interlamellar shear leads a location of the 200-re ections on the meridian, and thus to an order parameter S > 0. On the other hand, for the intralamellar slip, i.e., block slip within the lamellae, the chain axis changes its direction towards the meridian. As a consequence, the intensity maxima of 200-re ections shift towards the equator, leading to order order parameters S < 0. According to our observations, at rst, within deformation range H 0:1 0:2, a four maxima pattern shows up, with a nearly constant order parameter S200 0 . This result indicates that both slip processes are activated in this range, and the order parameter results from a superposition of interlamellar shear and intralamellar slip. When the sample is further stretched, to H > 0:2, a rapid decrease occurs for S200 , indicating the intralamellar slip becoming dominant.

66

CHAPTER 4.


GXULQJ VWUHWFKLQJ XQORDGHG

6

ε+ GXULQJ VWUHWFKLQJ XQORDGHG

6DPRUSKRXV

ε+ Figure 4.21: Orientational order parameters associated with the 200- and amorphous as a function of strain.

Dierent from the crystal orientation, the amorphous orientational order parameter decreases from the beginning, indicating that the amorphous chains orient during the deformation constantly towards the stretching direction, which comes as expected. Another noteworth feature in the plots is that the orientational order parameters of under load and unloaded samples do not overlap each other. This result indicates that the deformation of crystalline lamellae is irreversible when the imposed strain over passes the critical strains. The clearest comparison is S200 (H = 0:2) for both the under load

4.3.

SUMMARY

67

and the unload samples. For the under load sample, S200 (H = 0:2) is closed to zero, and for the unloaded sample, which was rst stretched to about H = 0:4 then released to H = 0:2, we obtained a large order parameter, S200 = 0:27.

4.3 Summary In this chapter, we have discussed the tensile deformation behaviour of a series polyethylenes and syndiotactic polypropylene based on a video-controlled true stress-true strain measurement. Polyethylene and syndiotactic polypropylene are considered as model samples for semi-crystalline polymers. Experimental results clearly indicate a critical strain law for both types of samples. Changing of the experimental parameters like temperature, strain rate, crystalline lamellar thicknesses and so on may vary the stress greatly. However, there always exist critical strains where the elastic properties and dierential compliance of the true stress-true strain curves change. These critical strains generally keep constant with the variation of other parameters. The common scheme for describing the deformation behaviour of polyethylenes and syndiotactic polypropylene can be explained by the blocky substructure of lamellar crystals. Only if the coarse block slip is generally activated during the deformation process, the critical strain law holds. Studies in this chapter also indicate that the critical strain behaviour may appear not only on those samples we have looked at, but also, more generally, on those semi-crystalline polymers which crystallized from their melt states at normal crystallization rate. In that case, a blocky substructure feature will govern the deformation process via block slips.

Chapter 5 Young's modulus and yield stress It is well known that room temperature elastic moduli and yield stresses of exible chain polymers are related to the crystalliniy [51, 52]. Considering a simple two-phase model, the dependence of the elastic modulus on the crystallinity is understandable. Semi-crystalline polymers can be considered as crystals lying embedded in a liquid-like rubbery matrix. The elastic modulus of the system should be a combination of both crystalline and amorphous moduli. An increase of the modulus with the crystallinity is thus obvious. However, how this combination has to be theoretically treated is uncertain. Calculations of the modulus cannot be accomplished without some arbitrary assumptions[53, 54]. The yielding needs irreversible slips within the crystallites. This plasticity has been regarded as a thermal activated process involving nucleation and propagation of screw dislocations under the eect of an applied shear stress [55, 56]. Support for this view was provided by evidence of intralamellar slips in the electron microscopy and in X-ray diraction studies [12, 13, 14, 15]. Darras and Seguela [57] arrive at the conclusion that the yield stress depends on the crystalline thickness rather than the crystallinity. As we have discussed in last chapter, the critical strain B has a much more clear physical background than the traditional yield point obtained from the engineering stress extension curves. We thus will study the yielding properties based on a true stress-strain measurement and take the stress at B as the yield stress in this chapter. Although crystallinity plays an important role on the modulus and the yielding properties, it is the purpose of this chapter to show the unsubstituted eect of temperature on both elastic modulus and yield stress.

5.1 The eect of temperature Studies mostly concerned the mechanical properties at room temperature. The few attempts to interpret the variations with temperature were not too successful. In one paper, Crist et al. [54] calculated the temperature dependence of the yield stress based 68

5.1.

69

THE EFFECT OF TEMPERATURE

on the screw dislocation model. Comparison with the experimental results was not very satisfactory. The eect of temperature on Young's modulus and yield stress is huge as shown in gures 5.1 and 5.2. The lines in both plots just follow an empirical knowledge [54] that the room temperature yield stress and Young's modulus of polyethylene can be linearly represented versus crystallinity in a semilogrithmic plot. Looking at the data of PE27 as an example we nd large drops in both the yield stress and the Young's modulus when the crystallinity does not change much, but the drawing temperature is increased. 40

PEVA18 LDPE33 PEII27

20

σB / MPa

10 8 6 4

2

1 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Crystallinity

Figure 5.1: Yield stress in dependence of crystallinity of PE27, LDPE33 and PEVA18. Line denotes the room temperature relationship. Data taken from the last chapter from measurements obtained at dierent temperatures. In the majority of basic studies, polyethylene was chosen as a model polymer. Due to its simple chemical structure a simple behavior is expected . However, polyethylene has unusual properties. The high chain mobility in the crystallites leads to ongoing structure changes like crystal thickening and surface melting [4]. A polymer like s-PP which has a stable semi-crystaline structure may be more suitable for basic studies. Its behavior during crystallization and a subsequent heating is exactly analysed and follows some simple laws. To draw conclusions from temperature dependent mechanical

70

CHAPTER 5.

YOUNG'S MODULUS AND YIELD STRESS

800 600

PEVA18 LDPE33 PEII27

400

E / MPa

200

100 80 60 40

20

10 8 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Crystallinity

Figure 5.2: Young's modulus in dependence of crystallinity of PE27, LDPE33 and PEVA18. Line denotes the room temperature relationship. Data taken from the last chapter from measurements obtained at dierent temperatures.

experiments then is more easy. Let us consider the results. Figures 5.3 and 5.4 display the temperature dependence of the Youngs modulus and the yield stress for dierent sPP samples. Obviously, a large drop both in the elastic modulus and the yield stress occurs when the temperature is increased. On the other hand, the eects of the structure variations achieved by dierent crystallization conditions (dierent crystal thicknesses, dierent amounts of secondary crystallization during cooling) are negligible within the melt crystallized series and still moderate for the sample crystallized from the glassy state. Hence, we nd an explicite temperature eect as a major property in the mechanics and have to ask about its origin. In a global view, deformation of a semicrystalline polymer may be understood as the stretching of two interpenetrating networks, one built up by the entangled uid parts and the other by the crystallites. At low deformations below the yield point the force is mainly transmitted via the crystallites. The elastic modulus and also the yield stress then are determined by their coupling. In view of the blocky substructure of the crystalline lamellae it is clear that the coupling of the blocks is of

5.1.

71

THE EFFECT OF TEMPERATURE

350 spp95

300

spp100 spp105 spp110

250

qspp24

E / MPa

qspp24a90

200

150

100

50

0 20

40

60

80

100

120

T / °C

Figure 5.3: Temperature dependence of the Youngs modulus E of sPPs crystallized at dierent conditions.

primary importance. Increasing the temperature may lead to a successive decoupling of blocks, which would reduce the number of routes of force transmission and thus the stiness. It appears that the secondary crystallites formed during cooling are rather inactive in the force transmission. As shown by gure 5.4, all melt crystallized samples follow the same curve. Even weaker is the eect on the elastic modulus, as shown by gure 5.3. At low temperatures, the quenched and then crystallized sample shows a similar modulus as the other samples. It thus seems that the crystal network formed during the isothermal crystallization is the decisive one. The crystallinity after the isothermal crystallization is constant (chapter 3 gure 3.10), and correspondingly the stiness doesn't change either.

72

CHAPTER 5.


spp95

spp105

qspp24

spp100

spp110

qspp24a90

σ %03D

7&

Figure 5.4: Temperature dependence of the stress at critical strain B of sPPs crystallized at dierent conditions.

5.2 The relationship between modulus and yield stress It has been seen in last section that the Young's modulus is determined by the coupling of blocks and, the yield stress is the stress which causes a collective activity of the block slips. Both quantities are tightly related with the blocky lamellar substructure of semicrystalline polymers. It is thus reasonable to ask about the relationship between them. Empirically, the yield stress is always written as y ' Ey : (5.1) It is clear that as soon as the slip process occurs the structure is starting to be changed and thus the Young's modulus. This happens at point A already. However, the yield strain B as we have shown in last chapter remains small and constant for all testing condition. This gives y = Constant, and from equation 5.1 we have y E . It is thus reasonable to use equation 5.1 to study the relationship between y and E. If equation 5.1 holds, we would expect a plot of y versus E follows a line. Figures 5.5 and 5.6 give the results.

5.2.

THE RELATIONSHIP BETWEEN MODULUS AND YIELD STRESS

30

73

P E 27 LD P E 33

25

P E V A 18

σ B / MPa

20

15

10

5

0 0

100

200

300

400

500

600

E / MPa

Figure 5.5: The relationship between the yield stress and the Young's modulus E of PE27, LDPE33 and PEVA18. Data from gures 5.1 and 5.2.

We have illustrated in last chapter by studying the elastic recovery properties and structure analysis that the deformation of semi-crystalline polymers obeys a general critical strain law. It has been also demonstrated that this critical strain behaviour is determined by the blocky substructure of lamellae. The block slip is generally activated at the same strain value for a certain type of crystallite. It does not depend on how much crystallites the system has. The eects of crystallinity and temperature on the stiness and yield stress are clearly shown in gures 5.1 and 5.2. As we have discussed that the same deformation mechanism was found for all PEs at all testing conditions, we thus expect that the equation 5.1 holds for all PEs. It is exactly the case as indicted in gure 5.5. Data from three distinctly dierent polyethylenes and testing temperatures follow a same line. Figure 5.6 gives the same results. Here, data from sPPs crystallized at dierent conditions follow a same linear track. The derivation happens only for the quenched sample when the testing temperature is lower than 50 Æ C where E has a value of about 150 MPa (see gure 5.3). It is due to the large amount of secondary crystallinity which is rather active for Young's modulus but not for the yield stress. As the testing temperature is larger than 50 Æ C , all data fall

74

CHAPTER 5.


20 spp95 spp100 spp105

15

spp110

σ B / MPa

qspp24 qspp24a90 10

5

0 0

50

100

150

200

250

300

E / MPa

Figure 5.6: The relationship between the yield stress and the Young's modulus E of sPP. Data from gures 5.3 and 5.4.

onto a single line. The crystallinity changes the number of blocks on the one side and, the temperature changes the viscosity of the block-slip process on the other side. And both are strongly related with the mechanical properties. However, as demonstrated in gures 5.5 and 5.6, both factors aect the relation between the Young's modulus and yield stress in a same way. This is clearly illustrated in gure 5.5 when we look at for example the data of PE27. The shift of the data point to lower value is mainly due to the change of the temperature. Within the testing temperature, only a small amount of crystallinity is changed. Those high testing temperature data points are at the positions of the data from low crystallinity sample at low testing temperatures.

5.3 summary In this chapter, we have discussed the origin of the Young's modulus and the yield stress in semi-crystalline polymer systems. It has been demonstrated that both quantities are determined by the coupling of blocks inside the lamellar crystallites. When this block coupling and block slip process are taken into account, we can easily explain the large

5.3.

SUMMARY

75

variance in both Young's modulus and the yield stress while the testing temperature is changed. They are attributed to the successive decoupling of blocks when the testing temperature increases. A simple linear relationship between Young's modulus and yield stress is found to hold for all samples at all testing temperatures.

Chapter 6 The relaxation of s-PP In chapter 4, we studied the yielding behavior of semi-crystalline polymers under a uniaxial tensile forces in measurements of true stress-true strain curves. Experiments were rst carried out for a series of linear, branched and copolymerized polyethylenes with various crystallinities and then also for syndiotactic polypropylene. The results of the mechanical tests and accompanying WAXS texture determinations demonstrated that the deformation behavior under tensile stress follows a general scheme. There exist always four critical points where the dierential compliance, the recovery properties and the strain induced texture variations change simultaneously. As an important fact it turned out that the strains at the critical points A, B, C are invariant. For polyethylene it was found that the (Hencky-) strains at the critical points A, B and C were constantly at H 0.03, 0.1 and 0.6, independent of the crystallinity which varied between 80% and 10%, the temperature which was changed between ambient and a few degrees below the nal melting,and the strain rate with values between 10 4 s 1 and 10 2s 1 . In the case of syndiotactic polypropylene we investigated one commercial sample under variation of the temperature and the strain rate and found again constant critical strains, now located at H 0:04; 0:12 and 0.4. Dierent from the invariant strains, the stresses at the critical points change greatly. They may decrease by more than one order of magnitude on lowering the crystallinity, heating samples up to the region of nal melting or choosing a lower deformation rate. The ndings rst of all indicate that tensile deformations of semi-crystalline polymers like polyethylene and polypropylene are strain-controlled. The crystal texture in the sample reacts in well-de ned manner to the externally imposed strain. This simple strain controlled, which implies purely geometric, reaction is hard to understand if semicrystalline polymers are viewed as being composed of stacks of laterally extended, internally rigid crystal lamellae. It becomes, however, conceivable if one recognizes that the lamellar crystallites possess an internal blocky substructure. This property is well-known and generally accepted since long time for copolymerized or short-chain branched polymers (compare for example the electron microscopic pictures presented 76

6.1.

ISOTROPIC S-PP

77

in Michler's book [58] or in the work of Minick et al [59]). But recent works, as shown in chapter 2, in particular observations with atomic force microscopes [18, 60] now indicate that the blockiness of crystal lamellae is not a peculiarity of non-perfect chains, but most probably a general phenomenon. As it appears now, it is a consequence of a multiple stage route generally followed in the formation of polymer crystallites [39, 20]. Given the blocky substructure of the lamellae, block-slips provide an easy process for plastic deformations. If there exists a suÆciently large number of independent slip modes, and each block provides three slip planes with two slip directions for each one, it becomes possible to realize any external deformation. In fact, one nds examples in the literature which show these block motions directly, for example, in an earlier work of Yang and Geil [61] on deformed poly-1-butene, where transmission electron micrographs show the blocks and their motion, and now in a recent study of Godehard et al [62], who use the atomic force microscope during the deformation of polyethylene. If block-slips represent the dominant general mechanism of yielding up to the point of bril formation one would expect to observe these motions not only during large deformations but already in the linear response regime in measurements of the dynamic Young's modulus. A contribution of block-slips to the dynamic mechanical behavior in the linear range is, of course, not a new idea. It was raised already long ago, maybe at rst by Iwayanagi [63], and then also by Takayanagi [64], who assigned one part of the -process in polyethylene to this kind of motion. In polyethylene the process is superposed by a second part which is, according to a common view, controlled by single chain diusions through the crystallites, rather than a block motion [65]. Both, the block motion and the single chain diusion enable further deformations of the amorphous interlamellar regions to be realized when they become activated. In s-PP chains are xed within the crystallites and cannot carry out longitudinal diusions, but block slips can still exist. We therefore searched in s-PP for the occurrence of block slips in linear response and, indeed, found a process with corresponding properties. As is described in this chapter it can be observed at elevated temperatures. We determined the relaxation rate of the process and found an unusual temperature dependence, qualitatively dierent from both, Arrhenius- and WLF-behavior, but as we think, conceivable for block slips. Two kinds of samples are used to check the assignment of this relaxation process. They are isotropic and oriented s-PP lm. In the following sections, we will show the occurrence of the -process in both isotropic and oriented s-PP lms, and discuss how block slips could illustrate this relaxation process clearly.

6.1 Isotropic s-PP Figure 6.1 presents the frequency dependence of the real part E 0 of the Young's modulus measured at various temperatures during a step-wise heating from room temperature to 110 Æ C . The sample was isothermally crystallized at 95 Æ C , annealed at 110 Æ C and

78

CHAPTER 6.

THE

RELAXATION OF S-PP

1 10°C

6 0°C

2 0°C

then cooled slowly. As determined by DSC in chapter 3, the crystallinity was 0.25 after completion of the isothermal crystallization and then during cooling increased somewhat, reaching nally at ambient temperature a value of 0.28. A look at the curves shows two noteworthy features. First, one observes a pronounced drop of E 0 with temperature. It appears impossible to relate it to the small change in the crystallinity. What we nd here is an explicit temperature dependence. An explanation has already been given in last chapter dealing with the mechanical properties of s-PP. In a situation where the crystallinity remains essentially constant, a drop in the stiness indicates, generally speaking, a change in the modes of force transmission or more precisely

ORJI+]

Figure 6.1: s-PP, isothermally crystallized at 95 Æ C , annealed at 110 Æ C and cooled to room temperature: Youngs' modulus (real part) as a function of frequency, measured at the indicated temperatures during a stepwise heating

ORJ( 3D

6.1.

79

ISOTROPIC S-PP

speaking a change in the mechanical coupling of the force-transmitting rigid crystalline objects. In our understanding these are the blocks which set up the lamellar crystallites. We therefore consider the decrease of the Young's modulus with increasing temperature as being due to a weakening of the contact forces between the blocks, following from a mobilization and maybe also an extension of the non-crystalline regions separating adjacent blocks in the lamellae.

& & & & &

WDQδ

ORJI+]

Figure 6.2: s-PP, same sample as in gure 6.1: Frequency dependent loss-tangent measured at the indicated temperatures during a stepwise heating up to 60 Æ C Secondly, one nds always, for all temperatures, an increase of E 0 with the frequency. For 60 Æ C this increase in linear, but for low temperatures and high temperatures one nds characteristic deviations. The measurements at the lowest temperatures show an upward curvature at the high frequency end. Its origin is obvious, as being caused by the dynamical glass process. The new feature comes up at the highest temperatures where the frequency dependence of the Young's modulus shows a downward curvature on decreasing the frequency. The behavior is indicative for an approach to another relaxation process which is slower than the dynamical glass transition. For semi-crystalline polymers the occurrence of such a process, located at the high temperature- or low frequency- side of the glass transition, is an often observed

80

CHAPTER 6.

THE

RELAXATION OF S-PP

phenomenon [66]. If it is observed, the dynamical glass transition is conventionally addressed as -process and the additional slower process then as -process. To our knowledge, so far there are no reports about the occurrence of such a process in s-PP. As we see now, it exists, as is indicated by Figure 6.1, and further results will be presented in the following.

& & & & & &

WDQδ

ORJI+]

Figure 6.3: Frequency dependent loss tangent measured during a further heating up to 110 Æ C Figures 6.2 and 6.3 give the results of the same experiment in terms of the loss tangent, tan Æ , split up in two ranges, the temperatures below 60 Æ C which are aected by the -process, and the higher temperatures above 60 Æ C , where the in uence of the -process comes up. The existence of the -process is demonstrated rather clearly. As it appears, for 110 Æ C the loss maximum is just reached at the lowest frequency. An even more convincing proof for the occurrence of an -process is provided in gure 6.4. It represents a master-curve composed of the single measurements at dierent temperatures in gure 6.3 after appropriate shifts along the log f -axis, i.e. in horizontal direction only. The curve refers to the relaxation behavior at 60 Æ C ; all the curves given in gure 6.3, measured at higher temperatures, where shifted to lower frequencies until an overlap. As one notes, the construction works perfectly. One obtains a smooth

6.1.

81

ISOTROPIC S-PP

curve representing a relaxation process with a maximum at the lower frequency end at f = 10 3:5 Hz. & & & & & &

WDQδ

ORJI+]

Figure 6.4: Master curve constructed from horizontal shifts of the curves of gure 6.3 until an overlap in the low frequency range. The curve for 60 Æ C is kept at its place When carrying out the shift, the uprises on the high frequency side towards the process do obviously not fall on a common line. This means, that the shift factors for the -process and the -process dier from each other. As we did it for the -process, one can also try to establish a master-curve for the -process. The result obtained is shown in gure 6.5. This master-curve now is set up of the curves given in gure 6.2. We choose again 60 Æ C as the reference temperature. The master-curve shows that although the construction seems to work at the high frequency end, deviations are found in the intermediate frequency range. They indicate the occurrence of further contributions to the relaxation behavior, but dierent from the - and -process, its strength is temperature-dependent. It is absent at the higher temperatures, 50 Æ C and 60 Æ C , and comes only up during cooling. Hints about its possible origin can be found in publications of Lu and Cebe [67], Schick et al [68] and Schwarz et al [69]. For many semi-crystalline polymers it is found in DSC measurements that the step-wise increase of the speci c heat at the glass transition

82

CHAPTER 6.

THE

RELAXATION OF S-PP

& & & & &

WDQδ

ORJI+]

Figure 6.5: Master curve constructed from horizontal shifts of the curves of gure 6.2 until an overlap in the high frequency range. The curve for 60 Æ C is kept at its place

is smaller than expected on the basis of the crystallinity derived from the heat of fusion. The nding indicates that not all of the non-crystallized material achieves at the glass transition already the full uid-like mobility. The result is usually expressed by introducing a third (`rigid amorphous') phase which, although non-crystalline, has a greatly reduced mobility. Lu and Cebe for poly(ethylene therephtalate) and Schick et al for samples of polycarbonate and poly(3-hydroxybutyrate) showed, employing temperature modulated DSC that this phase becomes mobilized during the heating process. Schwarz et al in studies of s-PP found out that this mobilization has in fact a mechanical eect, leading to a drop in the stiness. We therefore feel that the temperature-dependent contribution in the intermediate part of the loss tangent could well arise from this eect. At low temperatures the third phase with reduced mobility shows up as a contribution at the low frequency wing of the -process which then disappears on heating. It is another interesting observation that the construction of the master-curve which works so perfectly for the loss tangent cannot be applied to the real part of the Young's modulus. gure 6.6 shows the results when the same shifts as for the loss tangent,

6.1.

83

ISOTROPIC S-PP

&

ORJ( 3D

&

&

ORJI+]

Figure 6.6: Result of applying the shifts performed in the construction of the master curves in gures 6.4 and 6.5 on the curves in gure 6.1

dierent ones for the high and low temperature region, are carried out for E 0 . The explicit temperature-dependence of its magnitude is not at all removed. What does this mean? The answer is simple [4] and leads us also to another conclusion. The loss tangent expresses a ratio, that between the stored and dissipated energy. If both the stored and the dissipated energy refer to the amorphous regions only then the ratio becomes independent of the crystallinity and of the coupling conditions active between the blocks. Both the - and the -process produce shear deformations of the

84

CHAPTER 6.

THE

RELAXATION OF S-PP

amorphous interlamellar regions. For the -process this takes place with essentially rigid lamellae. The -process then leads to a further deformation. It is mediated by the block slips which cause a deformability of the lamellae which has as consequence that the shearing of the amorphous regions can increase a second time.

α β

SURFHVV SURFHVV

∆ ORJI+]

A β =51.6 K J/m ol

A α =150.2 K J/m ol

7 .

Figure 6.7: Shift factors log f used in the construction of the master curves in gures 6.4 and 6.5 Next, we have a look at the shift factors. These are shown in gure 6.7 for both the - and the -process. For the -process we obtain in the limited temperature range a quasi-Arrhenius behavior, but the high activation energy indicates that we deal here with an apparent value which would increase on further approaching the glass transition temperature. Interesting is the nding for the -process. We nd an even larger slope in the Arrhenius diagram, corresponding to a huge apparent activation energy. Noteworthy, in addition, is a curvature which is not that of a WLF-curve, going just the other way round. One observes an acceleration of the relaxation process with increasing temperature, rather than an increasing retardation with a decreasing temperature as in the WLF-case. Indeed, such a behavior is expected for block slips, if the contact forces between the blocks in the lamellae are weakened when the sample is heated. This could arise from a softening of the lateral surfaces of the crystal blocks,

6.1.

85

ISOTROPIC S-PP

& & &

WDQδ

ORJI+]

Figure 6.8: s-PP, isothermally crystallized at 95 Æ C and annealed at 110 Æ C : Frequency dependent loss tangent obtained with the Rheometrix Solid Analyzer at the indicated temperatures

so that grain boundaries existing at low temperatures are transformed into uid-like inter-block regions, or a mobilization and growth of the latter ones. Better than a knowledge of the shift factors only is, of course, a determination of the temperature dependence of the relaxation rate of the -process. To achieve it, we have to pick up the location of the relaxation maximum for some temperatures. Using the Rheometrics Solid Analyzer we were successful, and gure 6.8 depicts the results. The expansion of the frequency range to lower values carries us over the loss maximum. Using the thus determined relaxation rates at three high temperatures together with the shift factors already measured for the lower temperatures yields the temperature dependence of the frequency at the -process, shown in gure 6.9. We observe again the characteristic upward curvature related with an increase in temperature.

86

CHAPTER 6.

THE

RELAXATION OF S-PP

-0.5 -1.0

log10(f/Hz)

-1.5 -2.0 -2.5 -3.0 -3.5 2.6

2.7

2.8 -1

2.9 -3

3.0

-1

T / 10 K

Figure 6.9: s-PP, isothermally crystallized at 95 Æ C : Temperature dependence of the relaxation frequency of the -process following from the results shown in gures 6.7 and 6.8 Hence, we have clear evidence for the existence of an -process in syndiotactic polypropylene at the high temperature side of the dynamical glass transition. The temperature dependence of the relaxation rate is at rst unusual, but looks conceivable when we assign the process to block slips. In any case, independent of this tentative assignment it is obvious that the -process produces a second further deformation of the amorphous regions, in addition to that produced at the glass transition. It becomes activated together with a second retarded response of the assembly of the crystalline parts in the structure. For block slips one expects an eect, namely a retardation of the -process with increasing crystal thickness. As we discussed in chapter 3, it is possible to vary the crystallite thickness by the choice of the crystallization temperature, and this in a well-de ned way. Figures 6.10 and 6.11 concern the thickness dependence of the relaxation processes in s-PP. We compared the relaxation properties of two samples, one crystallized at 95 Æ C and the other at 110 Æ C . We know from chapter 3, where we also carried out small angle X-ray scattering measurements, that the structure parameters at these

6.1.

87

ISOTROPIC S-PP

V33 V33

WDQδ

ORJI+]

Figure 6.10: Two samples of s-PP, isothermally crystallized at 95 Æ C and 110 Æ C : Master curves representing the respective -processes at 60 Æ C

temperatures are as follows

Tc = 95 Æ C : Tc = 110 Æ C :

dc = 4:3 nm; L = 14:4 nm dc = 5:6 nm; L = 18 nm

Note that although the length scales of the structures are dierent, both have the same linear crystallinity, l = 0:30 (which is above the mass fraction crystallinity determined by DSC, an indication for the presence of amorphous regions within the lamellar crystallites). With regard to the eect of the crystal thickness one nds a dierence between the - and the -process. There is no eect at all for the dynamic glass transition, however, a retardation of the -process of the thicker crystals relative to the thinner ones. Even more clear than the results in gure 6.10, which could be either addressed as a shifting towards lower frequencies for the thicker crystals or as a decrease in the magnitude of the loss tangent, is the plot of the shift factors for the two samples presented in gure 6.12. Here the change in the relaxation rates is obvious.

88

CHAPTER 6.

THE

RELAXATION OF S-PP

spp110 spp95

WDQδ

ORJI+]

Figure 6.11: sPP, same samples as Fig.6.10: Master curves representing the -process at 60 Æ C s-P P 95

2.5

s-P P 110

∆ log 10 (f/H z)

2.0

1.5

1.0

0.5

0.0 2.6

2.7

2.8

T

-1

2.9 -3

/ 10 K

3.0

-1

Figure 6.12: Shift factors used in the construction of the two master curves in gure 6.10

6.2.

ORIENTED S-PP

89

6.2 Oriented s-PP As was demonstrated in particular by Ward [70] in numerous works carried out primarily for polyethylene, measurements on oriented samples can be used to analyze the orientational properties of relaxation processes. This often helps in the assignment, and we followed this route.

Figure 6.13: Oriented lm of sPP, produced by an uniaxial drawing to = 5 at 90 Æ C : Wide angle X-ray scattering diagram. The arrow indicates the drawing direction The anisotropy studies were carried out for the oriented sample. The texture achieved by the drawing process can be seen in the WAXS diagram of gure 6.13. The drawing- and chain-direction is indicated by the arrow. In order to see also the orientation of the lamellae we measured the small angle X-ray scattering curves with a Kratky camera, and the results are shown in gure 6.14. One curve was measured with the slit-like primary beam perpendicular to the drawing direction (0Æ ) and the other parallel to it (90Æ ). The results are indicative for a two-point scattering pattern, i.e. the existence of lamellae with normals parallel to the drawing direction. Figure 6.15 presents the frequency dependence of E 0 at 90 Æ C for three dierent samples. They were all cut out of the oriented lm, rectangularly shaped, with the long side, along which the tensile stress was applied, chosen in three dierent directions, parallel and perpendicular to the drawing direction, or inclined under an angle of 45Æ . At rst we note that the values of E 0 clearly dier between the three samples which demonstrates the global anisotropy in the stiness of the sample. On the other hand,

90 800 600 400 200 100 80 60 40 20 10 8 6 4 2 1 0.0 0.2 -1

0.6

CHAPTER 6.

0.4

s / nm

THE

1.0

90°

0°

RELAXATION OF S-PP

0.8

the decrease of E 0 with decreasing frequency, being caused by the activity of the process, does not show much variations. The relaxation strength, which shows up in the decrease, is apparently very similar for the 90Æ - and 45Æ -sample and, maybe, slightly smaller for the 0Æ -sample. The similar result is also shown in gure 6.16 where the tanÆ values of the same samples as in gure 6.15 are given. In gure 6.16, an obvious isotropic behaviour is found. Which conclusions can be drawn from the observations? The global anisotropy with a minimum stiness for the 45Æ -sample is caused by the -process. For frequencies above that of the dynamic glass transition one would expect agreement between all three samples (chains in crystalline s-PP have a helical con rmation, and the crystallites then possess internally only a small mechanical anisotropy). The largest drop introduced by the -process occurs for 45Æ , because the resolved shear stress acting along the lamellar surfaces then takes on its maximum value. On the other hand, block slips are much less directionally restricted. There are no restrictions with regard to the slip direction, and this goes together with an isotropic distribution of the block surface planes. For this reason one expects for a block-slip mediated relaxation process not much anisotropy, which would agree with the observation.

Figure 6.14: Oriented lm of sPP: Small angle X-ray scattering curves measured with a Kratky-camera with the slit perpendicular ( 0Æ ) and parallel ( 90Æ ) to the drawing direction

Intensity / a. u.

6.2.

91

ORIENTED S-PP

ORJ( 3D

ORJI+]

Figure 6.15: Samples cut out of the oriented lm with the long edge parallel, 45Æ and perpendicular (90Æ ) to the direction of drawing : Frequency dependent Young's modulus showing the orientational dependence of the mechanical properties

WDQδ

ORJI+]

Figure 6.16: Same samples as in gure 6.15: Frequency dependent tanÆ showing the orientational dependence of the mechanical relaxation.

92

CHAPTER 6.

THE

RELAXATION OF S-PP

6.3 Summary In summary, we have discussed the occurrence of the process in both the isotropic and oriented syndiotactic polypropylene lms. Due to the fact that the molecular chains of syndiotactic polypropylene inside the crystallites are xed, we assign this high temperature relaxation as the block motions. This assignment nds supports in the unusual temperature dependency of relaxation frequency and, the isotropy of the associated mechanical relaxation strength in an oriented sample. The nding of the process in syndiotactic polypropylene also indicates that the block motion based mechanical relaxation process is a general phenomenon in melt crystallized polymers.

Chapter 7 The in uence of the molecular weight In the previous chapters, we have shown that the deformation behavior of PEs and s-PP follows a critical strain law. It is considered as a result of the lamellae blocky substructure of semicrystalline polymers. Only if the block coarse slip is generally activated during the deformation process, the system possesses enough degrees of freedom to react on any imposed strain in a well de ned way. Because of the interpenetrating network built up by both crystallites and the entangled uid the reaction of the semicrystalline polymers upon stretching is in uenced by both portions. The relative weight changes with the deformation stage. At low deformation below yield the force is transmitted via the crystallites. As the strain increases, the force generated from the entangled uid becomes more and more important. From this point of view, the dierent critical strains could re ect dierent properties of the two portions. It is the purpose of this chapter to illustrate the physical background of the critical strains by analyzing the crystallinity dependence of the elastic plateau strain of the PEs, and by an ideal experiment via introducing an ideal sample; it will be shown that the critical strain C represents mainly a property of the entangled uid portion. We will then discuss a special knots-network model in case of linear PEs. This special network proposed rst by R. Bayer shows a strong molecular weight dependence. It is the aim of this chapter to study the in uence of the molecular weight on the critical strains to demonstrate the existence of a critical molecular weight for the formation of the knots network.

7.1 The plateau elastic strain As was demonstrated in chapter 4, the total strain is composed by an elastic and a plastic component which were derived via the step-cycle test and the free shrinkage measurement. Both components increase with increasing total strain. However, when 93

94

CHAPTER 7.

THE INFLUENCE OF THE MOLECULAR WEIGHT

0.7

PE

plateau elastic strain εH

0.6

0.5

0.4

0.3

0.2

0.1

0.0 0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

crystallinity

Figure 7.1: Crystallinity dependence of plateau elastic strains as derived from data of chapter 4 and ref. [21].

a critical strain H = 0:6 is reached, the elastic part arrives at a maximum value. An elastic strain plateau is thus formed. In gure 7.1, this plateau elastic strain is plotted as a function of the crystallinity for the PEs studied in this and previous works [21]. The linear dependence of the plateau elastic strain H;P on the crystallinity c is described by the relation H;P = 0:6 (1 c). Apart from this linear dependence, two more important informations can be obtained from the limiting situations of the samples. Considering a sample with 100% crystallinity, one may conclude that it has no elasticity at all which means that the slip of blocks is irreversible due to the absence of the amorphous entangled uid, which generally provides the restoring network force. Decreasing the crystallinity results in a linear increase of the elastic plateau. This increase, however, is limited as the crystallinity tends to zero. Then maximum plateau elastic strain becomes identical with the critical strain at C, H;P = H (C ) = 0:6. This nding leads us to the conclusion that the critical strain C is a property of the entangled

uid portion only. For a better understanding we carry out a `Gedankenexperiment '. Let us consider a set of semicrystalline PEs with dierent crystallinity. Two special samples are needed: On the one hand, a fully crystallized PE with still the blocky

7.1.

95

THE PLATEAU ELASTIC STRAIN

substructure presents the ideal solid behavior; on the other hand, we imagine a sample without crystallinity but still keeping the structural feature of lamellae. In the latter case, the lamellar feature can be regarded as a certain number of zero thickness sheets which are still forming a percolation network. The sheets react on the imposed strain exactly in the same way as the real lamellae. They can be divided into smaller pieces at small strain, and slip out of each other while they are stretched further, and become fragmented like the blocks in the real case when the imposed strain reaches the critical strain at point C . The only dierence will be that in the ideal sample the sheet-like lamellae exist without any volume fraction. The assumption makes our ideal sample dierent from a real polymer melt and an ideal rubber. How would such an ideal sample react on the imposed strain? Figure 7.2 gives the answer. Following a step-cycle test, we split the total strain into a cyclic (elastic) H;c part and a base (plastic) H;b part. We plot the cyclic and the base strain as a function of the total strain. a

b

εH,c

εH,b

αc=100%

α c=0

εH(C)

εH(C)

αc decrease

ideal rubber

αc=0

αc decrease

εH(C)

εH

εH(C)

εH

Figure 7.2: Results of ideal step-cycle tests for samples with dierent crystallinity: a.the cyclic strain H;c as a function of total strain H ; b. the base strain H;b as a function of total strain H Figure 7.2a presents the dependence of cyclic strains on imposed total strains, and gure 7.2b gives the behavior of the base part correspondingly. It can be seen that the cyclic and base strains show a general tendency on stretching. The critical strain is observed at H (C ) where the elastic plateau appears and, the plastic strain increases in a more pronounced manner correspondingly. First, let us consider the base strain of the fully crystallized sample in gure 7.2b. Due to the absence of amorphous entangled

uid, this sample looses the critical strain behavior. Generally we get H;b = H in this case. No elasticity should be expected because we assumed that this ideal sample

96

CHAPTER 7.


deforms via a block slip process only. The samples with a certain crystallinity react as in the real case. As the crystallinity decreases to the other limiting situation, c = 0 , a unique behaviour of the ideal sample shows up. In gure 7.2a, the ideal sample reacts like an ideal rubber if the total strain is less than the critical strain H (C ), When the total strain is larger than H (C ) it shows a maximum elasticity, i.e. the plateau of the cyclic strain, which is accompanied by the linear increase of the base part from H (C ) on ( gure 7.2b). For a better understanding of this special behaviour we make a simple calculation. From the nding of a critical strain law governing the deformation process, we may conclude that a homogeneous strain situation is always obtained when a semi-crystalline polymer is deformed. We have

H (Cry:) = H (Amor:) = H

(7.1)

where H (Cry:), H (Amor:) and H denote the strain in the crystalline region, amorphous region and for the sample as a whole respectively. We denote the length of the whole sample, and the fold length of the trajectories through crystalline and amorphous phases are L, LC and LA . It follows from the de nition of Hencky strain and equation 7.1 that L + L C L + LA L + LC + LA ln C = ln A = ln (7.2) LC LA L where LC and LA are the extensions of the crystalline and the amorphous phase trajectories respectively. The deformation of the crystalline phase is accomplished by the slip process and thus irreversible. Hence, the elasticity of the sample is given by the deformed amorphous part LA . In the step-cycle experiment we have the cyclic strain as L + LC + LA LA H;c = ln = ln(1 + ) (7.3) L + LC L + LC and the base part as L + LC H;b = ln : (7.4) L According to equation 7.2 we have L (7.5) LC = LA C : LA It follows from equations 7.3 and 7.5 that LA 1 H;c = ln(1 + ) = ln(1 + L (7.6) LC ) : L C L + LA LA LA + LA Equation 7.6 gives the relationship between the cyclic strain of the sample and the deformation of amorphous part. It keeps true only if the strain is homogeneous distributed, i.e. equation 7.2 holds. In general, the cyclic strain H;c increases with the

7.1.

THE PLATEAU ELASTIC STRAIN

97

increasing of the deformation of amorphous LA as well as the total imposed strain according to equation 7.2. The value of H;c changes with the crystallinity through the ratio LLCA . In the two limiting cases LC = 0 and LC = L we have L + LA H;c = ln = H (7.7) L and 1 H;c = ln(1 + L )=0 (7.8) + 1 LA respectively. The above two equations correctly describe the behaviour of the two ideal samples shown in gure 7.2 in the range of H H (C ). Equation 7.6 no longer makes sense when the imposed strain is larger than H (C ) which means that the homogeneous strain situation is getting to be lost. How can this special behaviour be understood? It has been discovered for the PEs and s-PP by the measurements of the wide angle X-ray scattering patterns that at C the crystallites begin to be destroyed and new crystallites, namely brils, start to be formed. The physical background of critical point C could be interpreted based on these results. Along a stretching process, one can nd rst isolated slips being activated at the end of a Hookean elasticity region (A), followed by a collective activity of the slips (B), then the fragmentation of crystallites accompanied by the formation of brils (C), and nally, before fracture a chain disentanglement (D). All these transitions show up in step-cycle tests in changes of recovery properties. However, as we mentioned above, for an ideal sample with zero crystallinity neither point A nor point B shows up in the recovery properties. It reacts like an ideal rubber for strains below H (C )( gure 7.2). From H (C ) on, the ideal sample no longer follows the behavior of the ideal rubber, but shows an irreversible deformation. How can this be true? The answer is the formation of brils. For this formation process, the destruction of crystallites, by a strain induced melting process, is necessary. This view is supported by the experimental observations that the crystalline thickness of semi-crystalline polymer deformed at elevated temperatures is only related with the deformation temperature. The higher the deformation temperature is the thicker are the crystalline thickness. It is thus necessary to melt the previously existing crystalline lamellae before the formation of brils. In general, a critical stress is needed to destruct a crystal. The existence of the de ned critical strain C means that a critical stress is always generated when the sample is stretched to a strain of H (C ). In principle, this stress is created by the orientation of the amorphous part according to the stress-optical rule (see [4] chapter 7).It follows from the stress-optical rule that S (7.9) where S is the orientational order parameter of chains in amorphous portion. The orientation of the chains under a certain strain is determined by the entanglement

98

CHAPTER 7.


density. The denser the entanglements are located the higher is the orientation. In this sense we arrive at the conclusion that the entanglement density is the same for all samples we studied since they all show the same critical strain C. It should be mentioned that the brils form not only out of the previously existing lamellae but may also include deformed amorphous parts. The brils provide also the irreversible deformation in the ideal sample. A stretching above C leads to an increase of the amount of brils only, and the elasticity does not change any more. The process may also lead to a reorganization of the network within the sample.

7.2 Higher order entanglement-The knots model

Figure 7.3: left: Schematic representation of a mesh of knots. circles: volumes of an entanglement mesh; right: The simplest form of a knots (Magni cation of the square in the left gure).( from R. Bayer [72]) In the last section, we discussed the physical origin of the limitation of the recoveribility by considering both real and ideal experimental results. According to the interpretation given in the last section, the critical strain at C represents a property of the entangled uid in the semicrystalline polymers. The type of the entanglement will aect the mechanical respond. R. Bayer, in a series of papers [71, 72, 73], suggests a knots model for linear polyethylene by studying the structure transfer from a polyethylene melt to the solid state. He postulates the formation of knots from linear polyethylene when the molecular weight is large enough. These knots could form a special network when the molecular weight reaches a critical value. Physically, the

7.3.

99

THE TRANSITION IN THE YIELD PROPERTIES

knots are like an entanglement, but they are not formed by the chain molecule itself, but by the superstructure which a chain forms with its entanglements. They can be regarded as a super structure of entanglements. The left part of gure 7.3 shows a schematic representation of a mesh of knots. Based on both experimental results and theoretical calculations, Bayer predicts a critical molecular weight Mc0 of about 105 . Below Mc0 , isolated knots may be formed, and its number increases with the increasing of molecular weight. As Mc0 is reached, a percolation of these knots occurs. Above Mc0 , the number of knots per chain increase with molecular weight but the density of knots does not change and ,the knot mesh maintains its mean diameter.

7.3 The transition in the yield properties Following the discussion in last section, a molecular weight dependent transition in the yield properties of linear polyethylene can be expected due to the knots network formation above Mc0 . Thus, experiments of the true stress-strain behavior and the free shrinkage as well as the shrikage under heating were carried out for a series of linear polyethylene with dierent molecular weight. Figure 7.4 displays the true stress-strain curves of several linear polyethylenes. PEΙΙ5 PEΙΙ8 PEΙΙ26 PEΙΙ12

200

σ / MPa

150

100

50

0 0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

εH

Figure 7.4: Selected true stress-strain relations for four LPEs with dierent molecular weight, obtained by a video-controlled stretching experiment at a constant strain rate H_ = 5 10 3 s 1 .

100

CHAPTER 7.


1.0 24 50 70 110

1.2

24 50 85 105

0.8 1.0

0.6

εH,r

εH,r

0.8

0.6

C

0.4

C

0.4

0.2

0.2

A,B

0.0 0.0

A,B

0.2

0.4

0.6

0.8

εH

1.0

1.2

1.4

0.0 0.0

0.2

0.4

0.6

0.8

1.0

εH

Figure 7.5: Comparison of results from the free shrinkage measurements at dierent temperature between sample PE27 (left) which has a molecular weight larger than Mc0 and sample PE8 (right) which has a molecular weight lower than Mc0 . Their molecular weight covers a large range from 5104 to 106 . Samples were prepared by pressing the powder materials at 160 Æ C into sheet form. They were then either slowly cooled down to room temperature inside the pressure plates (PE8, PE12 and PE26) or rapidly quenched into ice water from melt (PE5 only). The quenching procedure was introduced because the slowly cooled PE5 was very brittle and, could not be drawn. Considering the plots, one rst nds that the yield strain for all samples remains unchanged. The dierence in the yield stress is due to the dierence of crystallinity. This result con rms our argument that the yield point is mainly determined by the coupling of crystallites. However, a molecular weight in uence appears when the deformation becomes larger. In the large deformation stage (H > 1), the eect of crystallinity is hidden by the eect of the molecular weight. The higher the molecular weight the larger the true stress. It will be shown in gure 7.7 that the disentangling sets in much earlier for low molecular weight samples than for the high molecular weight materials. We believe that the stress dierence among dierent molecular weight samples in gure 7.4 is attributed to this disentangling eect. For lower molecular weight samples in the large strain range the entanglement density is far lower than the one with higher molecular weight. It then appears a low stress at large strains.

7.3.

101


0.8

0.7

ε H (C )

0.6

0.5

0.4

0.3

0.2 10

4

10

5

10

6

10

7

Mη

Figure 7.6: Molecular weight dependence of critical strain C.

To determine the other critical points, C and D, was diÆcult based on the true stress-strain curves. Thus, the free shrinkage test as well as the shrinkage upon heating was performed. In gure 7.5 we select two typical results for a comparison. The two molecular weight samples, PE27 and PE8, represent two classes of polyethylenes. The two plots show some general properties: The irreversible strain denoted H;r ,at rst appears at small imposed strain, followed by a continued increase of the plasticity (A,B). A change in the dierential compliance then shows up at a certain strain C. For each sample, the critical strain keeps constant when the temperature is varied. The system shows more elasticity at higher temperature, but the characteristic change of the dierential compliance does not move in position; the critical strain law still holds, for each sample separately. However, the value of the critical strain at C does change. For the sample with lower molecular weight (< Mc0 ), a smaller value of the critical strain C is observed. The yielding point, representing the beginning of the plasticity, denoted as A and B in the plots, remains the same value for both samples. This result also agrees with the true stress-strain measurements in gure 7.4. A collection of data on the molecular weight dependence of the critical strain C is thus given in gure 7.6. Samples with dierent molecular weight were also used to determine point D from a

102

CHAPTER 7.


1.0 0.9 0.8 0.7

εH (D)

0.6 0.5 0.4 0.3

M c'

0.2 0.1 0.0 3 10

Mc 10

4

10

5

10

6

Mη

Figure 7.7: Molecular weight dependence of critical strain D

measurement of heating the sample to the melt after the free shrinkage test. Data are presented in gure 7.7. Clear enough, an abrupt change is found at similar molecular weights for both critical strains, C and D. The critical molecular weight is similar with the one Bayer proposed. In gure 7.6, the strain at point C is smaller when the molecular weight is lower than Mc0 , then increases rapidly within a narrow range of the molecular weight, to nally reach a constant value of H (C ) = 0:6. The result supports the Bayer model. As we know from 7.1, the critical strain C sets the limit of the elasticity of a sample. It is associated with the behavior of the entangled uid part in a semicrystalline polymer. Only if the network properties of this uid part are changed, a dierent response on the imposed strain can arise. According to the Bayer model, when the molecular weight is lower than Mc0 , the knots exist in an isolated manner thus do not play a major role when the network is stretched. The situation changes as soon as a network, built up by the knots, is formed in a percolating way when the molecular weight is larger than Mc0 . This network starts to govern the whole system. Because the density of the knots does not change upon increasing the molecular weight, a constant elasticity limitation of H (C ) = 0:6 is obtained for samples with a molecular weight larger than Mc0 .

7.3.

103


Reasonable results can also be seen in gure 7.7 where the disentangling strain is plotted as a function of molecular weight. Generally this disentangling point does not keep constant over the molecular weight range studied, but increases with molecular weight as we may easily imagine. However, this increase does not follow a single track but shows a sudden break at the critical molecular weight Mc0 . If there are no entanglements in the system, point D will decrease to zero strain which means that the truly irreversible strain sets in as soon as a stretching is imposed. Therefore extrapolating the disentangling point for the low molecular weights to zero strain should give us the critical molecular weight for entanglements. Indeed, we arrive at a value of about 4000 which well agrees with the critical molecular weight Mc for the beginning of the entangling of linear polyethylene. An abrupt increase appears together with the formation of the knots network. This special, superposed network enhances the stability of the system against the disentangling process under stretching. Before nishing this section, we have a look at the texture of the crystallites to see the in uence of the uid part. As an example, gure 7.8 shows a comparison of

I sinθ / a.u.

sample εH PE27 1.25 bayerb 0.8

-40

-20

0

20

40

60

80

100

120

140

160

180

200

220

θ

Figure 7.8: A comparison of the orientational distribution of the 110-lattice planes I ()sin for two dierent molecular weight samples measured during stretching. ( is the angle between the lattice plane normal and the tensile axis)

104

CHAPTER 7.


the orientational distribution of the crystalline 110-lattice planes of two samples with dierent molecular weights, which is lower( for bayerb) and higher(for PE27) than Mc0 . Samples were stretched to dierent strains as indicated in the plot. A pronounced dierence shows up between the two samples. The maximum at = 90Æ is indicative for brillar crystallites with the orientation of chains along the tensile stretching direction. Even for a lower strain the low molecular weight sample shows much more brils than the high molecular weight sample. This result is what we expect, since the two systems have dierent types of network and thus provide the critical forces necessary to destruct the crystallites at dierent strains.

7.4 Summary In this chapter, we discussed the physical basis of the critical strain C based on both real and ideal experimental results. It is shown that this critical strain is the property of the entangled uid portion in the semicrystalline polymeric system. At point C the homogeneous distribution of strain in the samples is starting to be lost. The system changes from the slip dominant deformation mechanism to a destruction (melt) and restruction (recrystallinzation) mechanism. The special network model proposed by R.Bayer shows that knots form only when the molecular weight is larger than a critical one Mc0 for a linear polymer. We then investigated the deformation property of a series of linear polyethene during tensile stretching to illustrate this molecular weight eect. Experimental results support the Bayer's knots model.

Chapter 8 Conclusions - Zusammenfassung Melt crystallized polymeric systems represent a semi-crystalline lamellar structure. In the recent years, more and more evidence have been found which show that the structure of the crystalline lamellae are not continuous but constructed of small building units with thin boundary in between [18, 19, 20]. In general, the physical properties of such semi-crystalline polymer systems should be tightly related with this blocky substructure feature of lamellae. In this work, we investigated the mechanical response of a range of polyethylene and syndiotactic polypropylene samples as models of semi-crystalline polymer systems for both small (linear response) and large deformation ranges. The uniaxial tensile deformation behaviours of a series of polyethylene samples with dierent crystallinities under dierent temperatures and strain rates and syndiotactic polypropylene samples with dierent lamellar thicknesses were studied. Splitting the total tensile deformation into elastic and plastic parts shows four characteristic points (A,B,C and D) from the true stress-true strain curves, where the dierential compliance and recovery property change. Plastic strains start to take place at point A. At point B, a strong change in the dierential compliance on the true stress-strain curve is obtained. Both elastic and plastic strains increase with the increasing of the total imposed strain. However, this increase is limited for the elastic part. The elastic strain always reaches a maximum plateau value at point C. Further increase of the total deformation only leads to an increase in the plastic strain. The last transition point appears at point D. Before reaching point D, all plastic deformation can be removed when the sample is heated to its melting temperature. Point D thus denotes the position at which the topological structure of the system starts to be destroyed, i.e. the disentangling process sets in. The stress at each point may vary greatly according to dierent samples or the testing temperature and the strain rate. However, the strains at points A,B and C remain constant in all cases. Point D may shift to lower strains while the deformation temperature is increased. These ndings agree with the results previously obtained for a series polyethylenes with dierent crystallinity at room temperature [21]. The 105

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CONCLUSIONS - ZUSAMMENFASSUNG

critical strain behaviour can be only understood if the coarse block slips of lamellae are generally activated during the deformation process. The study of the crystallinity dependence of the plateau elastic recovery strains and the eects of molecular weight on critical strains led us to a better understanding of the physical basis of each critical strain. It can be concluded that

the critical strains at the points A and B are mainly due to the crystalline phase representing the coupling and slips of blocks as well as lamellae.

the critical strain at C re ects a property of the amorphous phase. It is the maximum elasticity of the ideal semi-crystalline polymer system. At point C, a critical stress is reached which destroys the lamellar crystallites, followed by a formation of brils. Dierent crystallinity and testing conditions do not change the entanglement state of the amorphous regions and thus the critical stains.

the critical strain D is related to the molecular weight, the molecular chain structure and the testing temperature. It is thus a property of the polymer chain itself.

Intralamellar coarse slip mechanisms provide suÆcient degrees of freedom to accomplish a homogeneous strain distribution between crystalline and amorphous phase. It is the basic consequence of the critical strain law. However, the situation changes at point C. When the deformation is larger than the strain at point C, the strain distribution is no longer homogeneous and the dominant deformation mechanism changes to a destruction(melt) and construction (recrystallization) process. The transitions of the critical points C and D at a critical molecular weight of about 2105 for linear polyethylene shows the existence of higher order entanglements. After the formation of the knots network, the system represents a lower entanglement density state, leading to a higher strain at the critical stress necessary to destroy the crystallites. The blocky substructure of the lamellae allows us to understand the behaviours of the yield stress and the elastic modulus of semi-crystalline polymers easily, especially their dependence on temperature. The coupling between the blocks and lamellae provides the physical basis of the modulus and the yield stress in a semi-crystalline polymer system. The investigations of the dynamic mechanical relaxation show the existence of an process in syndiotactic polypropylene. Due to the fact that the molecular chains of syndiotactic polypropylene inside the crystallites are xed, this high temperature relaxation process can only be understood in terms of the block slip motions inside the lamellar crystallites. This assignment nds supports in the unusual activation behaviour and the low orientational dependence of the relaxation process. The discovery of the process in syndiotactic polypropylene also leads to the conclusion that melt crystallized polymers always show a high temperature mechanical relaxation due to the block slip motions.

107 Our experimental results clearly indicate that the mechanical response of a semicrystalline polymer system like polyethylene and syndiotactic polypropylene can be readily understood if the blocky substructure of lamellae is taken into account. It can be generally concluded that as long as polymers are crystallized from the melt to from lamellae with a blocky substructure they would react to an external stress in the way described in this work.

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Aus der Schmelze kristallisierte Polymersysteme zeigen eine teilkristalline lamellenformige Struktur. In den letzten Jahren ist mehr und mehr gezeigt worden, da die Struktur der kristallinen Lamellen nicht kontinuierlich ist, sondern aus kleinen Einheiten mit dunnen Grenzbereichen dazwischen aufgebaut ist. [18, 19, 20]. Allgemein sollten die physikalischen Eigenschaften solcher teilkristalliner Polymersysteme eng mit dieser blockartigen Unterstruktur der Lamellen verbunden sein. In dieser Arbeit wurde die mechanische Antwort einer Auswahl von Polyethylenund syndiotaktischen Polypropylenproben als Modelle teilkristalliner Polymersysteme auf kleine (lineare Antwort) und groe Deformationen untersucht. Die uniaxiale Zugdeformation bei verschiedenen Temperaturen und Dehnraten wurde an einer Reihe von Polyethylen-Proben mit unterschiedlicher Kristallinitat und an syndiotaktischen Polypropylen-Proben mit unterschiedlicher lamellarer Dicke untersucht. Die Auftrennung der Gesamtdeformation in elastische und plastische Teile zeigt vier charakteristische Punkte (A, B, C und D) in den Spannungs-Dehnungs-Kurven, an denen sich dierentielle Nachgiebigkeit und Erholungseigenschaften andern. Plas tische Deformationen setzen bei Punkt A ein. Am Punkt B wird eine starke Anderung der dierentielle Nachgiebigkeit in den Spannungs-Dehnungs-Kurven erhalten. Sowohl elastische als auch plastische Deformationen nehmen mit zunehmender Gesamtsdeformation zu. Fur den elastischen Anteil ist jedoch dieser Anstieg begrenzt. Die elastische Deformation erreicht immer einen maximalen Plateauwert an Punkt C. Daruber hinaus fuhrt eine weitere Erhohung der Gesamtdeformation nur zu einer Erhohung der plastis chen Deformation. Der letzte Ubergang passiert bei Punkt D. Vor dem Erreichen von Punkt D kann die plastische Deformation vollstandig ruckgangig gemacht werden, wenn die Probe auf ihre Schmelztemperatur erhitzt wird. D zeigt so den Punkt an, ab dem die topologische Struktur des Systems beginnt zerstort zu werden. Die Spannungen an jedem dieser Punkte variieren stark von Probe zu Probe und mit der Metemperatur und der Dehnrate. Die Dehnungen an den Punkten A, B und C bleiben in allen Fallen konstant. Punkt D kann sich bei Erhohung der Deformationstemperatur zu kleineren Dehnungen verschieben. Diese Resultate stimmen uberein mit Ergebnissen, die fruher fur eine Reihe von Polyethylenen mit unterschiedlicher Kristallinitat bei Raumtemperatur erhalten wurden [21]. Das Verhalten entsprechend einer kritischen Dehung kann nur verstanden werden, wenn das Abgleiten von Lamellenblocken wahrend des Deformationsprozesses generell aktiviert ist. Die Untersuchung der Abhangigkeit der elastischen Plateau-Dehnungen vom Kristallinitatsgrad fuhrte zu einem verbesserten Verstandnis der physikalischen Grundlagen jeder kritischen Dehnung. Zusammengefat kann festgestellt werden, da

die kritischen Dehnungen an den Punkten A und B hauptsachlich auf die kristalline Phase zuruckzufuhren sind, die die Kopplung und das Abgleiten der Blocke und Lamellen darstellen.

die kritische Dehnung bei C eine Eigenschaft der amorphen Phase widerspiegelt.

109 Es ist die maximale Elastizitat des idealen teilkristallinen Polymersystems. An Punkt C wird ein kritisches Spannung erreicht, welche die lamellaren Kristallite zerstort, worauf die Bildung von Fibrillen folgt. Unterschiedliche Kristallinitat und Untersuchungsbedingungen verandern den Verschlaufungszustand der amorphen Gebiete und so die kritischen Dehnungen nicht.

die kritische Dehnung D mit dem Molekulargewicht, der molekularen Kettenstruktur und der Untersuchungstemperatur in Beziehung steht. Sie ist deshalb eine Eigenschaft der Polymerkette selbst.

Intralamellare Abgleitmechanismen stellen genugend Freiheitsgrade bereit, um zwischen kristalliner und amorpher Phase eine homogene Verteilung der Dehnung zu erreichen. Es ist die grundlegende Folge des Gesetzes der kritischen Dehnung. Die Situation andert sich jedoch bei Punkt C. Wenn die Deformation groer als die Dehnung bei Punkt C ist, ist die Verteilung der Dehnung nicht mehr homogen und der dominierende Deformationsmechanismus wechselt zu einem Proze von Zerstorung (Schmelzen) und Aufbau (Rekristallisation). Die Uberg ange der kritischen Punkte C und D bei einem kritischen Molekulargewicht von etwa 2105 fur lineare Polyethylene zeigt die Existenz von Verschlaufungen hoherer Ordnung. Nach der Bildung des Knotennetzwerkes besitzt das System einen Zustand niedrigerer Verschlaufungsdichte, was zu einer hoheren Dehnung bei der kritischen Spannung fur die Zerstorung der Kristallite fuhrt. Die blockartige Unterstruktur der Lamellen erlaubt das Verhalten der Fliespannung und des Elastizitatsmoduls teilkristallener Polymere, insbesondere ihre Temperaturabhangigkeit, einfach zu verstehen. Die Kopplung zwischen Blocken und Lamellen ist die physikalische Grundlage des Moduls und der Fliespannung eines teilkristallenen Polymersystems. Die Untersuchungen der dynamischmechanischen Relaxation zeigt die Existenz eines -Prozesses in syndiotaktischem Polypropylen. Aufgrund der Tatsache, da die Ketten von syndiotaktischem Polypropylen im Kristalliten xiert sind, kann der Hochtemperaturrelaxationsproze nur in Hinsicht auf ein Blockabgleiten in den lamellenformigen Kristalliten verstanden werden. Diese Zuordnung ndet Unterstutzung im auergewohnlichen Aktivierungsverhalten und in der niedrigen Orientierungsabhangigkeit des Relaxationsprozesses. Die Entdeckung des -Prozesses in syndiotaktischem Polypropylen fuhrt auerdem zu dem Schlu, da aus der Schmelze kristallisierten Polymere immer eine mechanische Hochtemperaturrelaxation aufgrund des Blockabgleitens zeigen. Unsere experimentellen Ergebnisse zeigen eindeutig, da die mechanische Antwort eines teilkristallenen Polymersystems wie Polyethylen und syndiotaktischem Polypropylen verstanden werden kann, wenn die blockartiger Unterstruktur der Lamellen berucksichtigt wird. Es kann allgemein geschlossen werden, da immer wenn Polymere aus der Schmelze unter Bildung von Lamellen mit einer blockartigen Unterstruktur

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kristallisieren, sie in der in dieser Arbeit beschriebenen Weise auf eine externe Spannung reagieren wurden.

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Acknowledgement I would like to thank all persons who have helped me on this work in the last three years. My special thanks are due to Prof.Dr. Gert Strobl for providing me this interesting topic, for his many suggestions and a lot of constructive discussions and for being so patient to correct the English mistakes in this work. Prof. Bingzheng Jiang (Changchun Institute of Applied Chemistry(CIAC), Chinese Academy of Sciences(CAS)) who rst introduced me into the eld of polymers, and give me continuous encourages. BASF AG(Shanghai) for the contribution on my rst traveling cost from Beijing to Freiburg. Mrs. Christina Skorek for her kind helps in many aspects including both my private and the academic matters. Dr. Sven Hobeika for showing me how the Instron and the WAXD instruments work. Mrs. Barbara Heck for many helps in the SAXS and DSC experiments and for improving my spoken German skill. Dr. Werner Stille for many helps on the computer problems and many helpful advises on the experimental setup of DMA, and for his kind help in improving the German grammar in the chapter 8. Mrs. Silvia Siegenfuhr for helps in chemical experiments and some of the DSC measurements. Dr. Massanori Iijima and Dr. Jurgen Schmidtke for improving my oral German skill when we were drinking beer together many times. Prof.Dr. Qiang Fu and Dr. Wenbing Hu for many helpful discussions. Dr. Mahmoud Al-Hussein for correcting the English mistakes in part of this work. PD.Dr. Christin Friedrich and Mr. Wolfgang Schmioneck (the Freiburger Materialforschungszentrum(FMF)) for the assistance and a lot of helpful discussions on the rheological experiments. PD.Dr. R. Bayer (the University of Kassel) for calling our attention on the molecular weight dependence in the deformation behavior of linear PEs, and providing us several PE samples. The mechanical workshop in our faculty for the helps in building up the oven for the DMA instrument and other devices. The Graduiertenkolleg `Strukturbildung in Makromolekularen Systemen' for their nancial support which covers my living cost during this work. All other persons in the group of Prof. Strobl for the pleasant working atmosphere. Finally, I wish to express my special thanks to my wife, Yuqing Lai, for her understanding on my work, especially in the rst one and half years when she was not with me.

Curriculum Vitae

Yongfeng Men Born: 22 Sep. 1973 in Keyouqianqi China Status: Married

Basic education: 09/1980-07/1983 09/1983-07/1984 09/1984-07/1985 09/1985-07/1988 09/1988-07/1991

Yangjiatun primary school, Keyouqianqi China Tiexi 2nd primary school, Wulanhaote China Honglian primary school, Wulanhaote China No.5 Junior middle school, Wulanhaote China No.4 High middle school, Wulanhaote China

High education: 09/1991-07/1995 Physics department Southeast University, Nanjing China B.S. degree was awarded in July 1995 Supervisor: Prof.Dr. Ming Zhu and Prof. Feng Qian Thesis:Mobilition of Organic Modi ed F e2 O3 Nanocluster in Mimic Biomembrance 09/1995-07/1998 Polymer physics laboratory Changchun Institute of Applied Chemistry Chinese Academy of Sciences, Changchun China M.S. degree was awarded in July 1998 Supervisor: Prof. Bingzheng Jiang Thesis: Hybrid Organic/Inorganic Materials -Synthesis and their Physical properties from 09/1998

Polymer physics department Faculty of physics, University of Freiburg, Germany Ph.D Degree will be awarded in October 2001 Supervisor: Prof.Dr. Gert Strobl Thesis:Understanding of the mechanical response of semi-crystalline polymers based on the block-like substructure of crystalline lamellae