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The effects of long chain branching on the rheological properties of polymers Giumanca, Radu 2002

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THE EFFECTS OF L O N G C H A I N BRANCHING ON THE  RHEOLOGICAL  PROPERTIES OF POLYMERS by RADU GIUMANCA Bachelor of Engineering (Chem. Eng.), City College of New York, 1999  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  M A S T E R OF APPLIED SCIENCE in the Faculty of Graduate Studies Department of Chemical and Biological Engineering  We accept this thesis as conforming to the required standard  T H E UNIVERSITY OF BRITISH C O L U M B I A June 2002 © 2002 Radu Giumanca  In  presenting  degree freely  this  at the  thesis  in  partial  fulfilment  of  University  of  British  Columbia,  I agree  available for  copying  of  department publication  this or of  reference  thesis by  this  for  his thesis  and study. scholarly  or for  her  I further  purposes  gain  shall  requirements that  agree  may  representatives.  financial  the  It not  the  that  Library  permission  be  granted  is  understood be  for  allowed  by  of  £HFM-tlAL- & MVjodtCA^  The University of British Vancouver, Canada  Date  DE-6 (2/88)  OC  \2G  lo?-  Columbia  for  that without  WEE* «^3  advanced  shall make  the  permission.  Department  an  it  extensive  head  of  my  copying  or  my  written  ABSTRACT  Long chain branching (LCB) is a very important feature in polymer science due to its influence on the rheological properties of polymers. It has been shown that long chain branching causes strain hardening behavior in the extensional flow of polymer, feature which is not seen in linear species. A great industrial interest has been shown in a method which would detect long chain branching by a simple, yet robust method. Fifteen different samples of polypropylene (PP) of varying molecular weights (MW) and branching structures were studied. The aim was to obtain linear viscoelastic measurements using a Rheometrics System IV rheometer and compare the results to determine the effects of backbone M W , branch M W , and number of branches on the polymers' viscoelastic properties. It was discovered that the samples exhibit drastic thermal degradation, even under inert atmosphere. An antioxidant (Irganox 1010) was found to have no effect. A comparison of linear viscoelastic data yielded questionable results, perhaps suggesting a higher than expected polydispersity. Samples of comb-structure polystyrene were also studied. Linear viscoelastic data was obtained for two different series of PS, differing in M W and branch M W . B y comparing with previously obtained data, it was discovered that time (-20 years) has had a small effect for most of the samples. Non-linear measurements were also obtained, and the results for the most part agree with published data. The differences, especially an extended plateau feature previously unpublished, are discussed.  it  TABLE OF CONTENTS  Abstract  List of Figures  List of Tables  Acknowledgements  Chapter 1: Introduction  Chanter 2: Long Chain Branching: General Review 2.1 Introduction 2.2 Viscoelasticity 2.3 The Relaxation Modulus of Molten Polymers 2.4 Small Amplitude Oscillatory Shear 2.5 Non-Linear Viscoelasticity 2.6 Effects of LCB on the Rheology of Polymers 2.7 Effects of Comb Structure on the Rheology of Polymers  Chapter 3: Scope of Work 1.1 Introduction 1.2 Thesis Objectives 1.3 Thesis Organization  Chapter 4: Experimental Work 4.1 Introduction 4.2 Experimental Equipment  in  4.2.1 Parallel Plate Geometry 4.2.2 Cone and Plate Geometry 4.2.3 Sources of Error 4.3 Operating Procedure 4.3.1 Linear Measurements 4.3.2 Non-Linear Measurements Chapter 5: Rheology of LCB Polypropylenes  24 25 26 27 27 28 29  5.1 Introduction 29 5.2 Samples Used 29 5.3 Results Obtained 31 5.3.1 Effect of Prolonged Exposure to Temperature; Degradation ... 31 5.3.1. A Effect of Temperature 31 5.3.1.B Effect of Stabilizer Irganox 1010 [CD3A Chemicals] . 34 5.3.1.C Temperature History Effect 38 5.3.2 Effect of Molecular Weight Increase 39 5.3.3 Effect of Increasing Number of Branches 42 5.4 Overall Conclusions 43  Chanter 6: Rheology of Comb Polystyrenes 6.1 Introduction 6.2 Samples Used 6.3 Results Obtained 6.3.1 Linear Viscoelastic Measurements 6.3.2 Non-Linear Stress Relaxation Experiments  Chapter 7: Conclusions and Recommendations 7.1 Introduction 7.2 Findings & Suggestions for Future Work on PP Project 7.3 Findings & Suggestions for PS Project  References  45 45 43 46 46 57  67 67 67 68  70  iv  LIST OF FIGURES  Chapter 1 Figure 1.1 (pg. 2): Comparison of Polymer Branching States Figure 1.2 (pg. 3): Comparison of L C B vs. Linear Polymer Behavior in Shear and Extensional Flows Figure 1.3 (pg. 5): Reptation Mechanism; Restricted motion in a Tube Figure 1.4 (pg. 6): Comparison of Various L C B Architectures  Chapter 2 Figure 2.1 (pg. 9): Comparison of Viscoelastic to Liquid and Solid Behavior Figure 2.2 (pg. 9): Illustration of Boltzmann Superposition Principle Figure 2.3 (pg. 10): A Typical Stress Relaxation Spectrum for a High and a Low M W Polymer Figure 2.4 (pg. 13): Dynamic Moduli Spectrum for sample c652, tested at Fo.R.T.H. Figure 2.5 (pg. 14): Stress Relaxation for a Comb Polystyrene Solution 30% in DEP, at various strains Figure 2.6 (pg. 15): Stress Relaxation Curves shown in Figure 2.5 shifted to determine the separation time  Figure 2.7 (pg. 15): Damping Function for Data Shown in Figure 2.5  Chapter 4 Figure 4.1 (pg. 25): Setup for Parallel - Plate Geometry Figure 4.2 (pg. 26): Setup for Cone and Plate Geometry  Chapter 5 Figure 5.1 (pg. 30): Illustration of PP Sample Structures Figure 5.2 (pg. 32): Effect of Prolonged Exposure to High Temperature for Sample Figure 5.3 (pg. 33): Thermal Degradation for Sample 13 Figure 5.4 (pg. 33): Differences between U B C and Fo.R.T.H. Data, Sample 13 Figure 5.5 (pg. 34): Decrease in Zero-Shear Rate Viscosity with Exposure Time Figure 5.6(a) (pg. 35): Effect of Stabilizer Irganox 1010 over Storage Modulus Figure 5.6(b) (pg. 37): Effect of Irganox 1010 over Complex Viscosity Figure 5.7 (pg. 37): Comparison of Degradation with or Without Irganox 1010 for Sample 3 Figure 5.8 (pg. 38): Comparison of Different Strategies Used for Sample 13 Figure 5.9 (pg. 40): Chain Length Increase Effect on Complex Viscosity, Linear Polymers Figure 5.10 (pg. 41): Effect of Backbone M W Increase for Branched PP's Figure 5.11 (pg. 41): Effect of Backbone M W Increase on Samples 11, 12 and 13 Figure 5.12 (pg. 42): Effect of Increasing Number of Branches  Chapter 6 Figure 6.1 (pg. 46): Illustration of Comb PS Samples Figure 6.2(a) (pg. 47): C6 Series Storage Moduli Figure 6.2(b) (pg. 47): C 6 Series Loss Moduli Figure 6.3(a) (pg. 48): C 7 Series Storage Moduli Figure 6.3(b) (pg. 48): C Series Loss Moduli 7  Figure 6.4(a) (pg. 49): C6 Series Complex Viscosities  vi  Figure 6.4(b) (pg. 49): C7 Series Complex Viscosities Figure 6.5 (pg. 51): Comparison of Zero-Shear Viscosities for C612 and C712 Figure 6.6(a) (pg. 52): Comparison of G \ G " curves from Roovers and at Fo.R.T.H., Series C612 Figure 6.6(b) (pg. 52): Comparison of G \ G " curves from Roovers and at Fo.R.T.H., C622 Figure 6.6(c) (pg. 53): Comparison of G ' , G " curves from Roovers and at Fo.R.T.H., C632 Figure 6.6(d) (pg. 53): Comparison of G ' , G " curves from Roovers and at Fo.R.T.H., C642 Figure 6.6(e) (pg. 54): Comparison of G ' , G " curves from Roovers and at Fo.R.T.H., C652 Figure 6.6(f) (pg. 54): Comparison of G \ G " curves from Roovers and at Fo.R.T.H., C722 Figure 6.6(g) (pg. 55): Comparison of G \ G " curves from Roovers and at Fo.R.T.H., C732 Figure 6.6(h) (pg. 55): Comparison of G ' , G " curves from Roovers and at Fo.R.T.H., C742 Figure 6.7(a) (pg. 58): Stress Relaxation for sample C752, 30% wt. in D E P Figure 6.7(b) (pg. 59): Shifted Curves from Figure 6.7(a), C752 30%wt. in D E P Figure 6.7(c) (pg. 59): Damping Function for C752, 30% wt. in DEP Figure 6.8(a) (pg. 60): Stress Relaxation for Sample C742, 30% wt. in DEP Figure 6.8(b) (pg. 60): Shifted Curves from Figure 6.8(a) Figure 6.9 (pg. 61): Comparison of C742 and C752 Damping Functions Figure 6.10(a) (pg. 62): Stress Relaxation for C652 20% in DEP Figure 6.10(b) (pg. 63): Shifted Curves for Figure 6.7(a) Figure 6.11 (pg. 63): Stress Relaxation for C642 20% wt. in DEP, Shifted Curves  Vll  Figure 6.12 (pg. 64): Comparison of C652 and C642 Damping Functions Figure 6.13 (pg. 65): Comparison of C642 30% and C642 20% solutions damping functions Figure 6.14 (pg. 66): Comparison of Linear PS Damping Function to Comb to DoiEdwards Prediction Figure 6.15 (pg. 66): Stress Relaxation Curves for a Linear Polystyrene 30% wt. in  viii  LIST OF TABLES  Chapter 5  Table 5.1 (pg. 30): Description of the 15 PP Samples used  Chapter 6 Table 6.1 (pg. 45): Specifics of Comb PS Samples Table 6.2 (pg. 57): Comparison of GN° values  IX  ACKNOWLEDGEMENTS  I wish to express my most heartfelt gratitude to my supervisor, Prof. Savvas G. Hatzikiriakos, for his guidance and utmost support during the course of this study.  I sincerely thank Dr. Dimitris Vlassopoulos for his mentorship, his many valuable suggestions during the course of my study and for inviting me to spend eight months to work on my thesis at the Foundation for Research and Technology - Hellas, in Crete, Greece. I am grateful to Dr. Vlassopoulos for the excellent hospitality that was extended to me during my stay in Crete, and for his financial support.  Thanks also to Ms. Eirini Chira for her invaluable support with the use of the rheometer, her expertise was appreciated. To Ms. Chira and everyone at Fo.R.T.H. who have aided me, I extend a heartfelt  "£V)(aplotco  TT O X v " .  M y colleagues, both at the U.B.C. RheoLab and at Fo.R.T.H., have helped me in various ways. I wish to thank Alfonsius Budi Ariawan, Philip Servio, and Peter Holmqvist for their helpfUl discussions and exchange of ideas.  Finally, I wish to extend a special note of thanks to my family. I would like to thank my mother for her never-ending love and support and for her faith in me, and my sisters, Ruxandra and Doina, who have been a source of strength and motivation for success. Thanks also go out to my father for his belief in me and perpetual pep talks.  x  CHAPTER 1 INTRODUCTION  Polymers are generally recognized as long chains of carbon atoms with varying architectures and molecular weights. A linear chain is one in which any carbon atom is chemically bonded to at most two other carbon atoms. Such a chain is known as a linear chain (see Figure 1.1). Any chains of carbon atoms which stem from carbon atoms that are already part of another chain, are known as branches. Long chain branches (as opposed to short ones) are those whose length is close to that of the distance between chain intersections in a polymer network. On the basis of diffusion measurements, Jordan et. al (1989) have indicated that polymers with branches of the order of 2M_ (average molecular weight between entanglements) behave as long-chain branched molecules. A lot of polymers contain what is known as side branches. Such structures influence to a great extent various aspects of the polymer rheology (Larson, 1999). The length of the branches is the primary factor that decides the extent of the differences. Branches can be introduced deliberately in order to alter the processability and/or mechanical properties of a certain polymer. Often times, however, they can occur as an undesired side reaction during polymerization in industrial processes. In such cases, even small changes in the reaction conditions can lead to great differences in the rheological behavior of the product. Metallocene catalysts are known to be able to synthesize polymers with relatively narrow molecular weight and comonomer distributions, which, combined with controlled amounts of long chain branching is claimed to lead to improved processability and enhanced mechanical properties (Hatzikiriakos, 2000).  1  Long Chain Branching  Short Chain Branching  Linear Chain (no branching)  Figure J.J: Comparison of Branching States  For polymer melts used in commercial applications, large differences  in their  processability and rheological behavior have been noticed between long-chain branched (LCB) polymers and linear ones. The differences are most clearly evident in flows involving extensional elements. Certain melts, such as low density polyethylene (LDPE), which are known to have an extensive amounts of irregularly spaced side long chain branches, exhibit a distinct "strain hardening" phenomenon in uniaxial extensional flows that is in direct contrast with results obtained in a similar experiment for linear polymers. In shearing flows, nevertheless, the behavior of long-chain branched polymers is qualitatively similar to that of linear ones, both exhibiting a highly "strain softening" behavior (McLeish, Larson et al, 1998). The only difference is that the presence of L C B increases the extent of the shear thinning or "shear softening". Strain softening and strain hardening behavior is illustrated by the relationship between the viscosity and strain rate. Figure 1.2 shows a typical schematic to illustrate this type of behavior. For example, in this situation, strain hardening behavior is equivalent to the fact that, for strains in the  2  nonlinear region, the viscosity values rise above those of the linear values of viscosity. Such behavior would certainly be of great interest to industrial applications that use extensive amounts of extensional flows, such as fiber spinning or film blowing. In addition, the viscosity at very low shear rates, known as zero-shear viscosity, has been discovered to grow exponentially with molecular weight. Berry and Fox (1968) performed a study of several nearly monodisperse polymers and found that their viscosity scales linearly with molecular weight up to a certain molecular weight they defined as critical (Mc), from which point viscosity scales as a power law, n - MW . 34  o  Shear Rate (radls) Figure 1.2: AdaptedfromMcLeish & Larson, 1997, comparison of LCB vs. Linear polymer behavior in extensional and shear flows  A plausible explanation for the above behavior exists in literature (Rouse, 1953). Rouse proposed a model that works well for unentagled polymers that emphasizes the friction between polymer chains as they glide past each other. The steeper slope above Mc. is caused by entanglements, which are restrictions to flow for a chain due to the physical presence of other chains, i.e. chains cannot pass through other chains. Due to  3  entanglements, a chain has only a limited path to go, and it is restricted in its motions perpendicular to its own molecular contour. Such constraints can be summed up as a restrictive tube that encapsulates each chain. As such, a molecule can only perform a snake-crawl-like motion along its tube, which is known as reptation (de Gennes, 1971). In the case of entangled chains, the Rouse theory needs to be supplemented by a model that takes into account the severe topological restrictions that are caused by the tight vicinity of the other molecules. The tube model of Doi and Edwards (1986) provides for such constraints. A molecule that is confined to a tube can only perform a reptative motion along its tube, the free chain ends being free to explore the melt without the constraints of this tube, as seen in Figure 1.3. The presence of branching brings about additional constraints for which new models have been created, the most significant of which is the Pom-Pom Model (McLeish, Larson 1998). All these peculiarities exhibited by L C B polymers lead to an increased industrial interest in the subject. More importantly, it is a challenging task to find a straightforward and effective means of detecting whether a polymer contains even small amounts of L C B . Rheology provides a good means for detecting even small amounts of L C B . The tell-tale signs that alert us to the presence of L C B , are as discussed above, an increase in zero-shear viscosity over linear chains, the onset of shear thinning behavior at smaller shear rates and also the ratio of the loss modulus over the storage modulus is reduced significantly (Yan, 1999).  4  Figure 1.3: Reptation Mechanism in a Tube (adaptedfrom http://www.kfajuelich. de/iff/personen/G. Schuetz/pictures/tube.jpg)  A likely reason for this, as discussed above, is because a branched polymer finds it a lot more difficult to navigate in a polymer network because of the additional constraints offered by the existence of the branches. We thus have the grounds for further investigation of LCB-containing polymers. Though a lot is known about these types of polymers, more insight is needed to be able to predict more accurately the presence and extent of branching. In addition, since polydispersity acts in the same direction as branching, only reasonably monodisperse samples need to be studied in order to single out solely the effect of long chain branching. In order to further investigate the effects of L C B , and how to detect their presence using linear viscoelastic measurements, a study of polypropylenes might be worthwhile. To this effect, nearly monodisperse samples of polypropylene were synthesized, with  5  varying molecular weights of the backbone, and of the arms. The samples' rheological behavior was analyzed, and the results are outlined in this thesis. A series of comb polystyrenes was also studied, in order to deepen our understanding of the effects of morphology and branching on the rheological behavior of polymers. A comb constitutes a special type of architecture for a L C B molecule, which is carefully synthesized in the laboratory, in order, to observe its behavior, and draw appropriate conclusions. Combs are used as an intermediary step, a "stepping stone" between "star" polymers and linear polymers, and can also be designed to test the effect of L C B . Figure 1.4 illustrates the differences between the aforementioned structures, as well as compares it to theoretical models such as the P O M - P O M and H-polymers.  Figure 1.4: Comparison of Various LCB Polymer Architectures and Theoretical Models Thus, carefully prepared nearly monodisperse comb polystyrenes of various molecular weights and arm lengths were tested Theologically. The aim of this particular study is to obtain linear and nonlinear measurements in order to find the effect of comb structure on their rheology. The larger purpose of studying comb polymers is to bridge the structure gap between randomly branched commercial polymers and model stars (Roovers, 1981). The results obtained are outlined in this thesis.  6  CHAPTER 2 LONG CHAIN BRANCHING: GENERAL REVIEW  2.1 Introduction Beginning as early as the first two decades of the 20  th  century, due to their  industrial usefulness, a great amount of attention has been paid to polymers in general. The industry's primary motivation was to optimize the quality of their product, and reduce costs, and to that effect they became very interested in polymers' physical and chemical properties. In this section, the key theoretical concepts behind polymer rheology are outlined. In addition, the latest outstanding research published in the literature is analyzed.  2.2 Viscoelasticity Polymers are materials which exhibit a behavior that lies between those of a fluid or a solid. Hooke's law accurately describes solid behavior, where the tensile stress in extension is directly proportional to the strain, or the relative length change. o (t) = G-y(t)  (2.1a)  E  The corresponding form of Hooke's law for simple shear is: c = G-y  (2.16)  where G is the shear modulus or modulus of rigidity. For fluids, Newton's law of viscosity accurately predicts that the force is directly proportional to the rate of strain. ° ( 0 = TI-YW  (-) 2  7  2  In these equations, a represents the shear stress, y(t) and y (t) the shear strain and strain rate, respectively, whereas n represents the viscosity of the fluid. An appropriate visual example that illustrates both types of behavior is "silly putty". When bounced against a hard surface, it rebounds, much like a solid, but when allowed to stand on a solid surface for an extended period of time, shows a liquid-like tendency to flow. For a viscoelastic substance, such as a polymeric one, the stress history becomes important. As pointed out in the "silly putty" example, the response varies from that of a solid-like behavior at very short times to that of a liquid-like behavior at long times. Such behavior is called viscoelasticity and fluids that follow it are referred to as viscoelastic fluids. Viscoelasticity can be demonstrated by several different simple experiments. For example, a stress relaxation experiment implies imposing a small shear strain yo at time 0, and then monitoring the stress while the strain is held fixed. The difference in response between a liquid, a solid and a viscoelastic fluid is shown in Figure 2.1. The ratio of stress to strain is then a linear viscoelastic property, G(t), called the shear stress relaxation modulus. G{t) = a{t)/y  (2.3)  0  When the imposed strain and strain rates are small enough, so that the molecules are not disturbed far away from their equilibrium state, the relaxation modulus is independent of the imposed strain or strain rate. Such behavior is called linear viscoelasticity. For such stresses, in the linear regime, the Boltzmann superposition principle states that the stress at any point is simply a sum of all previous stresses resulting from a series of N small strains. For example, Figure 2.2 illustrates a series of  8  strains imposed at different times. To calculate the shear stress at time t, one can use Equation 2.4:  i3  00 ^5  Time  0  (A) Liquid-like (B) Solid-like (C) Viscoelastic Figure 2.1: Liquid-like, solid-like and, respectively, viscoelastic response for a material with a structural time dependency G(0=£G('-O-5Y(O  (2.4)  In such a case, the viscosity of a viscoelastic material is related to the relaxation modulus: r) =]G{t)-dt  (2.5)  0  Fig 2.2: Sequence of Step Strains - Boltzmann Superposition Principle  9  2.3 The Relaxation Modulus ofMolten Polymers The primary characteristics of a typical G(t) plot are shown in Figure 2.3. As can be seen, G(t) exhibits a plateau region. The value of this plateau is a function of the polymeric structure. The plateau modulus GN° is a constant for a particular polymer species, and increasing the length of the chain (i.e. the molecular weight) only increases the width of the plateau region, but not the value at which it occurs. The plateau region separates the short time relaxation region, where the large scale chain architecture has little effect and the long-time relaxation region where factors like molecular weight, molecular weight distribution and long chain branching influence the values of G(t) greatly (Graessley, 1993).  Time  Figure 2.3: Typical Stress Relaxation Modulus Features for a High Molecular Weight Polymer The reason why the plateau region exists is due to the entanglements that occur in the polymer network. At high polymer concentrations, individual polymer chains have a hard time returning to their initial equilibrium orientations due to the physical presence of many other neighboring polymer chains, which restrict its range of movement. As shown 10  in Figure 2.3 and mentioned in the previous chapter, polymer chains are forced to undertake a snake-crawl like motion around the physical constraints offered by the presence of other chains through a restrictive tube, called reptation (De Gennes, 1971, Doi & Edwards, 1986). Naturally, the lower the molecular weight, the less constrictive the tube is. The molecular weight at which entanglements first occur is an important material property which is known asMc, the entanglement critical molecular weight.  2.4 Small Amplitude Oscillatory Shear - Relaxation Moduli Another important experiment which is employed for the characterization of polymers and was of great use for the development of this thesis is the small-amplitude oscillatory shear stress experiment. In such an experiment, the liquid is strained sinusoidally, and the in-phase and out-of-phase components of shear stress at steady state are measured as a function of the frequency, co. y(/) = y -sin(co/)  (2.6)  0  In this equation, y represents the strain amplitude. By differentiating, we obtain the shear 0  rate as a function of time: y(0 = Y ©cos(co^) = y cos(co^) 0  0  (2.7)  For the case of sufficiently small yo we can calculate the stress by using the Boltzmann superposition principle. Thus, it can be shown that the stress is sinusoidal in time and has the same frequency as the strain: c(t)=o  0  -sin(co/+ 5)  (2.8)  where go is the stress amplitude and S is a phase shift called the "mechanical loss angle". 11  In order to simplify things, it is customary to write Equation 2.8 as: o (0/Yo = G'(co )• sin (co r)+G"(o) • cos(co t)  (2.9)  G'(co) is known as the dynamic storage modulus, and is the component of G that is in phase with the strain. G"(a>) is known as dynamic loss modulus and it is the component of stress that is out of phase with the strain, but in phase with the rate of strain. For a low enough initial strain, these measurements can all be performed in the linear region. Thus, the behaviors of both G'(ou) and G"(co) are linked to G(t) through the Boltzmann superposition principle and the values for the zero-shear viscosity can be obtained from their properties in the low-frequency limit: T  io = l i m " ( » ) / G  f f l  (  2 1  °)  0)~>0  In addition, it is perhaps noteworthy to mention that the G(t) curve can also be obtained from G\ G" data simply by performing an inverse Fourier transform that converts G'(co) and G"(co) vs. co to G(t) vs. / data. A typical dynamic moduli spectrum is shown in Figure 2.4 for a nearly monodisperse polystyrene sample. The dynamic moduli, as seen in Figure 2.4, span over several orders of magnitude in the frequency domain. Unfortunately, no single experiment can cover this whole area, due to apparatus limitations. In fact, Figure 2.4 represents what is known as a master curve, which can be obtained based on the fact that the polymers used obey the timetemperature superposition principle. The time-temperature superposition principle states that a change in temperature shifts the viscoelastic functions along the modulus axis without changing their shape. Thus, measurements at many different temperatures can be  12  put together, spanning many more orders of magnitude than can be obtained by any single experiment (Dealy, 1990). C652 Tref170 041201 - MasterCurve  1 0  -3  10  2  10T  1  10°  10'  10  2  10  3 1 Q  4  Freq [rad/s]  Figure 2.4: Dynamic Moduli Spectrum for Polystyrene sample number C652, Master curve (from experiments performed by Giumanca at Fo.RT.H., Greece)  2.5 Non-Linear Viscoelasticity So far we have only discussed the behavior of fluids in the linear regime, where deformations are small and slow enough to allow the material to return to its equilibrium state. However, this is not the case when dealing with large deformations, the chains are displaced significantly from their equilibrium conformations and the Boltzmann superposition principle no longer applies. Furthermore, the relaxation modulus, G(t), is no longer independent of the strain: o(/,y) = y - G ( / , y )  13  (2.11)  However, for many polymeric liquids, stress relaxation following a sudden imposition of shear is factorizable into strain-dependent and time-dependent functions: o(t,y) = yh(y)-G(t)  (2.12)  where h(y) is known as the damping function. This is not normally observed at A L L times following step strain (Archer, 1999). Instead time-strain separability is only found after a characteristic separability time Ik that varies with polymer molecular weight, architecture, concentration, and temperature (Osaki, 1982). A plot of relaxation modulus vs.  time is shown in Figure 2.5, at different stresses, for a solution of nearly  monodisperse comb-architecture polystyrene in diethylphthalate (DEP).  r 1 1 1 h i — i — i — 1 1 1 1 1 i i — i  10"  2  i  1 1 1 1 n i  10"  10°  1  i  i  i * 11111  i  10  1  i  10  i 2  t(s)  Fig 2.5: Stress Relaxation for a Comb Polystyrene Solution 30% wt in DEP, at Different Strains Figure 2.6 represents the same data in Figure 2.5, but the data is shifted up to indicate the separation time.  14  C752 3 0 %S o l u t i o n in D E P 280202  10° b-  D a s h e d Line represents Linear Data from D F S  10' fe-  Separation time X  ~  10  10  3  2  t-  i 11iii  i  i  *  i  10"'  _i  i  • i 11111  • • • • tti  10  10  i  i  11  10'  i  10'  t(s)  Figure 2.6: Shifted Curvedfor Stress Relaxation, Comb Polystyrene, from experiments by Giumanca. Vertical line indicates separation time, Xk.  A plot of the damping function is shown in Figure 2.7:  0.1  -i  1  I  i — j i i i  —i  0.1  i  i  i  i  ' i '  10  Figure 2.7 Damping Function for Comb Polystyrene  15  2.6 Effects of LCB on the Rheology of Polymers Due to increased interest in the rheological behavior of polymers, extensive work has been done on this subject and these results have been reported in the literature. Polyethylene (PE) has been a polymer that's been studied quite extensively in the past few decades. Vega et al. (1996) studied the rheological behavior of metallocene catalyzed HDPE's and compared to that of conventional HDPE's. The differences found for metallocene HDPE's include higher viscosities than their conventional counterparts, the existence of a power law dependence on M W with a power of 4.2, a lower crossover value for the storage and loss moduli, and a reported difficulty to process due to sharkskin and slip-stick effects. In a subsequent article, Vega et al (1998) studied the viscoelastic behavior of 23 noncommercial metallocene-catalyzed PE's in order to find a correlation between rheological behavior and small amounts of long-chain branching. Results point to the fact that the samples which they believe to contain L C B exhibit higher values for zero-shear viscosities, higher relaxation times, higher values of elastic modulus and a higher Arrhenius activation energy all when compared to other PE's of similar M W , polydispersity and amount of short-chain branching (SCB). Wood-Adams and Dealy (2000) investigated the effect of polydispersity, SCB and L C B on the linear viscoelastic behavior of polyethylenes. They found out that for metallocene polyethylene, L C B increased the zero-shear rate viscosity and also broadened the relaxation spectrum by adding a long time relaxation mode when compared to linear PE's of the same molecular weight. Hatzikiriakos (2000) investigated a means of detecting the presence of LCB  from linear viscoelastic measurements.  16  He discovered that, after plotting  atan(G'VG') vs. G* (Van Gurp plots), the area below the Van Gurp curves correlates with the extent of L C B and polydispersity. The rheological behavior of L C B polypropylene has also been studied, though significantly less extensively than PE. Kurzbeck et al. (1999) investigated two polypropylenes (PP) with different molecular structures, in shear and elongational flow. He confirmed the no strain-hardening behavior for the linear species, yet for the L C B species he found a more pronounced strain-hardening behavior than any other polyolefin studied up to date. He appropriates this behavior to the coexistence of a long chain branched structure and a high molecular weight component. Tsenoglou et al. (2001) studied the effect of introducing long chain branching on an initially linear PP. They developed a simple rheological method for estimating the degree of long chain branching (the fraction of branched chains or the average number of branches per chain) in a polymer melt undergoing the early stages of cross-linking. Due to the fact that polypropylene is less prominent than PE as far as industrial interest is concerned, it has been studied less extensively. However, due to its attractive physical properties (high melting point, low cost, high tensile stress, low density) and the inception of some novel methods of producing narrow molecular weight species, such as the metallocene catalyzed method, there has lately been an increased interest in PP. As such, a comprehensive rheological study that analyzes the effect of the number of branches, branch length and backbone length on a series of model polypropylenes would perhaps be of great interest. Such a study is attempted here. The degradation of polypropylene, which is related to this thesis, as will be evident below, has also been studied extensively. Tzoganakis (1988) studied the  17  controlled degradation of polypropylene. He splits degradative processes into two general categories: thermal degradation and peroxide promoted degradation. Thermal degradation is reported to occur over relatively long periods of time (1-24 hrs) at very high temperatures (>240°C), and to achieve relatively low degrees of M W reduction. Peroxide promoted degradation is described as a deliberate process, and it involves mixing an amount of peroxide into the PP melt before feeding it to an extruder. A description of the degradation mechanism is also provided. Curry and Jackson (1988) have studied the effects of controlled degradation. They had developed a control loop around the degradation system in order to maximize the desired results. Ibrahim and Seehra (1997) reported on sulphur as being a promoter of degradation in a PE/PP system. They employed electron spin resonance (ESR) spectroscopy in order to investigate the thermal and catalytic degradation of a sample of commingled plastics (CP) containing about 95% P E and 5% PP. They reported significant reductions in the depolymerization temperature of CP with added catalysts, which include sulphur, NiMo/Al 03, and zeolite HZSM-5. 2  Schoenberg (1996) reported on a process for increased peroxide efficiency in controlled rheology polypropylene resin. He has reported a decrease in M W and an increase in melt flow index of a controlled rheology polypropylene resin without exceeding a limit of 100 parts per million of tertiary butyl alcohol as a peroxide decomposition product. This is accomplished by adding small amounts of hexane and thioester. Watson et al (1975) reported on the economical and convenience benefits of injecting air (oxygen) into a melted polymer as it is processed within an extruder, towards the purpose of achieving controlled degradation of C?+ polyolefins, in particular polypropylene. In all these references, degradation of a polyolefin is meant to create a product of lower molecular  18  weight, but with more desirable rheological properties, such as viscosity and melt flow index, and lower polydispersity. In our case, degradation is an undesired side effect, and it occurs at much lower temperatures than what has been reported. Initially, it was not the purpose of this thesis to study the thermal degradation of polymers. However, as I proceeded with my study, it became evident that our samples degraded with temperature, to the point that they even hindered it. The results outlined above portray the benefits of a controlled degradation of polymers, whereas in our case degradation is an unintended and undesired side effect. In addition, none of the results report significant degradation at relatively low temperatures (~190-210°C), as is our case. Even more surprisingly, as discussed below, is that significant thermal degradation of the samples occurs despite adding an anti-oxidant (Irganox 1010 - C I B A Chemicals) and operating in an inert nitrogen atmosphere.  2.7 Effects of Comb Structure on the Nonlinear Rheology of Polymers A great range of literature is also available on the properties of model comb polymers. Comb architecture is a carefully produced model meant to be a link between linear polymers and randomly branched industrial polymers. Daniels et al. (2001) presented experiments and theory on the melt dynamics of monodisperse entangled comb polymers. They found data to be in good agreement with a tube-model theory which combines star polymer melt behavior at high frequency with modified linear polymer reptation at low frequencies. Qualitatively distinct features of comb polymers were then compared to simpler star and H-topologies. Roovers (1981) performed a study on two series of narrow molecular weight polystyrenes. He found the plateau modulus to be the  19  same for linear, star and comb polystyrenes of same backbone M W . The frequency dependence of the dynamic moduli was interpreted to be consistent with three relaxation mechanisms: movement of the whole molecule (reptation) at long times, movement of branches at intermediate times and the high frequency is identified with that found in the transition zone of linear and star polymers. Several nonlinear stress relaxation studies are also available. In a series of papers, Watanabe et al. (1996) examined the nonlinear stress relaxation behavior for blends of styrene-isoprene diblock copolymers in a homopolyisoprene matrix. For sufficiently small strains, he found G(y,t) to agree with linear values of G(t). He also found two distinct relaxation processes, a fast and a slow one, and he attributed the fast process to the relaxation of the individual corona blocks. Islam et. al (2001) studied non-linear step shear relaxation moduli in a series of polystyrene/diethylphtalate solutions in order to understand whether the shear damping function is universal for fluids in the class entangled liquids, and got a clear answer in the negative. They also found that with increasing entanglement densities, the damping function becomes progressively softer, and they explained these results through the prism of a tube model. Vrentas and Graessley (1982) obtained shear stress relaxation data for a range of shear strains on a series of entangled polymer liquids (linear and star polybutadienes of narrow M W D ) in order to test time-strain factorability and the Doi-Edwards predictions about strain dependence.  They observed some departures  from  time-strain factorability, but  nonsystematic and uncorrelated. They also observed some departures from Doi-Edwards behavior at higher entanglement densities, the causes of which they deemed to be unknown. Osaki (1993) reviewed published data on the damping function of the shear  20  relaxation modulus. He found most of the data to be in good agreement with the DoiEdwards prediction. He associated weaker damping with (1) comb branching, (2) lack of entanglement and (3) bimodal molecular weight distribution. For highly entangled systems (more than 50 entanglement points per molecule) he discovered the strain dependence to be stronger than predicted by Doi-Edwards, which he deemed possible to be due to slip, or an instability or deformation within the material. The aim of our thesis is to obtain the linear viscoelastic data for comb polymers, then run stress relaxation experiments and see how data compare for low strains. In addition, the shear damping function will be analyzed and compared to previous results and the Doi-Edwards prediction.  21  CHAPTER 3 SCOPE OF W O R K  3.1 Introduction Although there is a great commercial interest in the effect of long-chain branching on the rheological properties of a polymer, there is still much to be discovered about the properties of L C B polymers. In the long run, more knowledge on the subject will lead to process optimization, improved products and increased profits. Lately, there has been an increased interest in polypropylene, due to its attractive physical properties. However, a comprehensive rheological study of L C B propylene has yet to be published. Likewise, there is a need for a unifying theory that describes nonlinear rheology. Although much progress has been made lately, for example, the PomPom theory, more work needs to be done on nearly monodisperse model architectures, such as the comb structures.  3.2 Thesis Objectives This research project is fundamental in nature. Its scope is two-fold. First, a series of polypropylene samples are studied. The objectives of this work were: 1. To obtain linear viscoelastic measurements  for  15 samples  of nearly  monodisperse polypropylene, of different molecular weights and branching architectures. 2. To analyze the effect of molecular weight, branch length, and number of branches on the rheological properties of the polymers.  22  3. To attempt to rationalize the results through the prism of a complex theoretical model, i.e. the Pom-Pom model. Secondly, a series of comb polystyrenes were studied. The objectives of this study can be summarized as: 1. To obtain linear viscoelastic measurements on two series of nearly monodisperse comb-architecture polystyrenes and compare results to data obtained by Roovers et al. (1976). 2. To perform non-linear stress relaxation measurements, and compare the results obtained to the linear data in order to obtain the damping function. 3. To use a comprehensive theory, such as that of Daniels and McLeish (2001) to analyze the results obtained. 3.3 Thesis Organization The first chapter provides an introduction, a set of fundamental information on the features and importance of long-chain branching in polymers. The chapter also introduces the concept of comb architecture, and discusses its features. Chapter 2 presents a brief overview of the key theoretical concepts. In addition, it reviews the latest advances in the long-chain branched polymer field published in the literature. Chapter 4 provides a basic analysis of the equipment used. The rheology of 15 samples of polypropylene is discussed in Chapter 5. A through description of the samples is given, and the rheological results obtained for the 15 samples are also discussed in Chapter 5. Chapter 6 relates linear and non-linear viscoelastic experiments on 10 samples of monodisperse, combstructure polystyrenes. Chapter 7 presents the most important conclusions of the results presented in Chapters 5 and 6. Recommendations for future work are also given.  23  CHAPTER 4 EXPERIMENTAL WORK  4.1 Introduction This chapter describes the means by which the experimental results were obtained. The main equipment used in our quest is a parallel-plate rheometer. The concepts and design of such an apparatus are explained. Two sets of samples were used towards our goals, a set of 15 samples of L C B polypropylene, with varying molecular weights and architecture, and a set of comb polystyrene of increasing arm molecular weight. A detailed description of the two sets of samples is also given. Finally, a brief overview of the experimental procedure is presented here.  4.2 Experimental Equipment For the purpose of analyzing the rheological properties of polymers, a rheometer is a very useful piece of equipment. For the purpose of this study, two different parallelplate rheometers were used, located at U B C and Fo.R.T.H. (Greece). The non-linear stress-relaxation measurements were performed by means of cone-and plate geometry.  4.2.1 Parallel-Plate Geometry The parallel plate geometry utilized by a rheometer is shown schematically in Figure 4.1. For this type of geometry, the fluid is placed between the parallel plates, one of which rotates with a user-defined angular velocity. In order to determine the linear viscoelastic properties, one plate is oscillated with angular amplitude, <po, the torque amplitude is  24  measured, Mo, as well as its phase lag, 6, which is calculated from the stress signal. Then, the following relations can be used to calculate the linear viscoelastic moduli of polymer melts and solutions (Dealy, 1982):  Sample  Fixed Plate  Figure 4.1: Parallel Plate Geometry  G =  ~—coso %-R -<p  (  0  2-M -h  . sin 5  a  G =  (  n • R • (p  0  The software provided with the rheometer (Rheometric Scientific) performs these calculations automatically and outputs a set of G', G" vs. frequency (of) data.  4.2.2 Cone-and-Plate Geometry A different geometry that is used to determine viscoelastic properties is known as cone-and-plate.  A sketch of this geometry is shown in Figure 4.2. The principal  advantages of such geometry are that loading and cleaning are relatively easy, and the  25  shear rate is uniform for small angles. Thus, differentiation of data is not necessary to compute the relevant material functions.  Fixed Plate  Figure 4.2: Cone and Plate Geometry  4.2.3 Sources of Error in both Parallel-Plate and Cone-and-Plate Flows Viscous heating and temperature fluctuations within the sample can introduce significant errors into the measurements. This effect is, however, very small in comparison with the variations of temperature with time resulting from the operation of the temperature control system. These variations results in fluctuations in system geometry and sample density, which will be most severe in the case of highly viscous fluids. Another important source of error is edge effects. One of the assumptions used to derive the rheometrical equations is that the free surface is spherical with a radius of curvature equal to the cone radius. At large rotational speeds, the fluid deformation can cause a pronounced change in the shape of the free surface. The fluid tends to flow outwards near the walls of the plates. The torque decreases markedly and then fluctuates.  26  As speed is further increased, air bubbles may be entrapped when the speed is reduced again, making it impossible to reproduce low shear rate data when the shear rate is subsequently reduced. "Edge failure", as this phenomenon has come to be known, governs the maximum shear rate at which cone-and-plate can be used in the study of molten polymers (Hutton, 1963). Deviations in the flow geometry from that for a perfectly shaped, aligned and positioned plates will also lead to errors in the measured properties. First, for cone-and plate, the apex of the cone is assumed to be just touching the surface of the lower plate, and there are several mechanisms that can cause deviations from this ideal situation, for example, lack of care in calibrating the gap between the plates, or failure to account for plate expansion due to temperature. In addition, another mechanism that can alter the gap spacing once the rheometer has been put into operation is a deflection of the rheometer frame in response to a large imposed stress. To minimize this, the rheometer has to be sturdy enough and firmly set into the floor.  4.3 Operating Procedure  4.3.1 Linear Measurements The operating procedure we used consists of a series of different tests using a rheometer. Initially, a Dynamic Time Sweep (DTS), at a relatively low frequency (5 s" ) 1  and using a relatively low strain of 0.1 strain units, in the linear regime, at the initial starting temperature, which was between 150 and 170°C. The tests were run for anywhere  27  between 4 hours to 10 hours. This is done in order to test the chemical stability of the sample under the operating conditions. In case the DTS yielded positive results (no significant change in the viscoelastic functions with time), we moved on to what's known as a Dynamic Strain Sweep (DSS), where the frequency is held constant and strain is increased, typically from 0.1 strain units to 10 strain units, in order to determine the limits of the linear region. We ran several DSS's at various constant frequencies, to ensure that the linear region is determined for the whole frequency range of interest. At low strains, as previously discussed, the viscoelastic functions are not a function of the strain. As such, when the viscoelastic functions begin to decrease with increasing strain, its critical strain marks the onset of non-linear viscoelasticity. The ensuing test was a Dynamic Frequency Sweep (DFS) at constant strain, which was picked to be as high as possible, but well within the linear regime. This type of test was run at several temperatures, and the results were superimposed to yield a master curve (an example is given in Figure 2.4) using the time-temperature superposition principles already discussed.  4.3.2 Non-Linear Measurements Non-linear stress relaxation tests were also performed, on a series of comb polystyrenes. Stress relaxation tests were run for strains increasing in magnitude from 0.1 stress units (linear regime) up to 100 strain units. A typical set of results, plotted on the same set of axes, is shown in Figure 2.6.  28  CHAPTER 5 RHEOLOGY OF LCB POLYPROPYLENES  5.1 Introduction In this section, the main results obtained on the rheology of long chain branched polypropylenes are outlined. Overall, the results differ greatly from expectations, but still, valuable conclusions can be drawn. An attempt is made to rationalize the results, and analyze the reasons why expectations were not met. The effects of molecular weight, number of branches and thermal degradation upon the linear viscoelastic properties of polypropylene are analyzed.  5.2 Samples Used Since the effects of polydispersity and L C B have similar effects on the rheological properties of polymers, it was of paramount importance for this study to obtain samples having the narrowest possible molecular weight distribution. To this end, polypropylene samples were synthesized by Tzoganakis et al. (2001), with reportedly well defined L C B structures and low polydispersities. Samples used in this work are listed in Table 5.1. The zero-shear viscosities are obtained from the RSI Orchestrator software, which fits the viscosity curves using a mathematical model (Ellis model) and then extrapolates the curves to low shear rate values. The values are based on data obtained at U B C , when samples were tested Theologically for the first time. In order to illustrate the strategy behind studying the rheology of the samples, and the aim of this study, Figure 5.1 shows a schematic of how the samples were expected to  29  look like, in order to thoroughly test the effects of molecular weight, arm length (MW), and number of arms, on the rheological properties of polypropylene.  Comonomer  Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 Sample 6 Sample 7 Sample 8 Sample 9 Sample 10 Sample 11 Sample 12 Sample 13 Sample 14 Sample 15  Nominal (label)  MW from  MWn  GPC(x1000)  M. T e m p  Melt # 1(DSC) T e m p #2 (deg.C)  (DSC) ( d e g . C)  Zero Shear R ate Viscosity  Homo PP  -110K  113  154.88  155.03  3462.8  Homo PP  -170K  137  156.69  154.72  3257.6  Homo PP  -210K  215  147.1  147.12  5557.3  0.5% C8  -110K  129  150.12  148.45  3586.4  0.8% C8  -110K  102  147.08  145.38  5086.5  0.8% C8  -170K  158  142.73  142.99  6304.1  0.8% C8  -210K  194  141.53  NA  6181.7  2% C8  -170K  179  132.84  132.52  10766  135.34  133.64  4942.7  2% C8  -210K  214  0.5% C16  -110K  115  147  148.73  2481.6  0.8 % C16  -110K  144  141.78  140.47  4071.2  0.8% C16  -170K  170  144.76  141  3755.1  0.8% C16  -210K  212  142.69  139.94  6002.5  2% C16  -170K  188  131.55  132  6193.3  2% C16  -210K  206  127.56  127.4  5876.7  Table 5.1: Polypropylene Samples Synthesized by Tzoganakis et al. (2001)  Figure 5.1: Structures of PP Samples  30  5.3 Results Obtained As previously mentioned, the results did not meet our expectations. Following is a detailed account of the results obtained, and their comparison.  5.3. J Effect of Prolonged Exposure to Temperature; Degradation 5.3. LA Effect of Temperature This experimental program was initiated at U B C by studying the linear viscoelastic behavior of all samples listed in Table 5.1. Upon arrival to Fo.R.T.H. (Crete, Greece), an attempt was made to validate the results obtained at U.B.C. by reproducing them. However, we were quite unsuccessful in reproducing the values obtained at U.B.C. by testing amounts of sample which had already been exposed to high temperature through rheological testing. These samples had been collected off the rheometer fixtures for re-testing purposes. It was also noticed that the values of the moduli ( G ' , G") dropped (in some cases sharply) in consecutive experiments, using the same sample. From these results the conclusion was drawn that the available PP samples are unstable with prolonged exposure to temperature, as can be seen in Figure 5.2. The dynamic viscosity of sample 3 obtained by various runs and using two different parallel-plate rheometers at U B C and Fo.R.T.H is plotted. The numbering of runs coincides with the order the runs were carried out. Degradation was observed for all samples tested, but only sample 3 was tested extensively. Figure 5.3 shows the same effect for sample 13. At this time, an attempt was made to replicate the U.B.C. results by testing a previously unused amount of sample. The differences observed are illustrated in Figure 5.4. They are essentially too large to be deemed due to experimental error or rheometer  31  calibration. This is possibly due to polydispersity, which means differences in M W and as such leads to differences in rheological properties, which may have incurred during sample preparation, by using different thermal histories for different samples. For example, compression molding is used to. prepare the disks to be loaded onto the rheometer. This exposure might be critical to the stability of the sample.  # 1  10  J  •  D  Sample # 3 T = 170 C All FoRTH Measurements  •  h  #2 Q_  #3 0  O  O  O  S  °  10'  c  o  o  0  8 8  -l_  I  I  I  I  •  I  8  I  10  10  u  8  S  ?  10'  (o ( r a d / s )  Figure 5.2: Effect of Prolonged Exposure to High Temperature for Sample 3  The data presented in Figure 5.2 is also analyzed and a plot of zero-shear rate viscosity vs. time of exposure is shown in Figure 5.5. It appears that the sample stabilizes after -15 hours at high temperature. The sample undergoes thermal degradation, in spite of the experiment taking place under an inert nitrogen atmosphere.  32  • J—I—I  I I I 11  1  1 — I — I I I I 11  10°  1  1 — I —  10  I  10  1  I  1 I  10  2  3  a> (rad/s)  Figure 5.3: Thermal Degradation for Sample 13  Sample # 3 D  ° °oo D  ° o o  D |  T=170°C  ••r D  Q  o  ° o O 1(T  o  •  U B C Data  o  F o R T H Data  U  o  Q  •  o  D n  10' jj  10"  I  nil  I • • • • t tl  10  u  10'  _J  10'  •  I  • • • •  10  Figure 5.4: Differences between UBC and. Fo.R. T.H. Data for sample 3  33  3000 Sample # 3, No Irganox, Exposure T= 160 C  2500 h-  O  2000 h  w  03 •r  1500 h  1000 500 h-  a  "O-G--0--0  0 h _i  L  j  5  >  10  I  L  15  20  25  i  L  30  Time of Exposure (hrs)  Figure 5.5: Decrease of Zero-Shear Viscosity with Time of Exposure to Temperature  5.3. IB Effect of Stabilizer Irganox 1010 fCIBA Chemicals] It is believed that the degradation effect showed in the previous sub-section (continuous decrease of rjo with exposure to temperature) is due to chain-scission effects (Tzoganakis, 1988). Even though the experiments are performed in an inert nitrogen atmosphere, somehow (perhaps contained within the sample itself) free agent oxygen radicals manage to break up larger chains, thus causing the molecular weight to drop. This hypothesis can explain the observed reduction in the viscosity. In order to reduce this effect, it was suggested that an anti-oxidating stabilizing agent should be added to the samples, in a concentration of 0.1% by mass. The antioxidant suggested was Irganox 1010 (CIBA Chemicals). The addition of the stabilizing agent had only limited success in stabilizing the samples. One example is shown in  34  Figure 5.6(a). In this case, the G' values are plotted as obtained in successive runs. It is worthwhile mentioning that G', G" and 77* all follow the same trends, so plotting any of these is equivalent. Figure 5.6(b) plots n*, for example.  -  • •  :  O  •  •  •  •  rj  •  •  • •  m®  • &  •  • •  n  • •©•© © ©  •  •  D  #2  D  •  D  D  ••  #4  &  •  •® •® •® ®  •  r  * 10°  " " " " I  1  11 01  1  1  1 10  1 1 1 1  2  1  1  •  t  1 1 1 1  10  3  1  CD ( S ) 1  Figure 5.6(a): Effect of Stabilizer Irganox 1010 (CUBA Chemicals) for Sample 3  In this experiment, a previously unused sample was treated with Irganox 1010 (0.1% by mass), then tested at 170°C (#1), then left at 190°C for 3 hours and it was retested at 170°C. The sample was then allowed to rest for the night at 200°C and it was retested at 170°C (#4). Finally, after run #3, the sample was allowed to remain at 170°C for 3 hours and it was re-tested to see if the rheological functions can "rebound" to higher values (#5). The storage moduli for these experiments are compared in Figure 5.6(a). The storage modulus of the same sample tested at U.B.C. is also plotted on the same graph, for comparison purposes. It can be observed that the longer the sample is exposed to high temperatures, degradation continues to occur for periods of about 24 hours. It seems that  35  after -24 hours the sample has been stabilized (see #4 and #5). Tzoganakis (1988) reported thermal degradation of polypropylene over extended periods of time (1-24 hours) at relatively high temperatures (>240°C). However, in our case, degradation occurs at significantly lower temperatures (200°C, where the sample is allowed to rest) and that despite an inert nitrogen atmosphere, which was flushed through the testing chamber of the rheometer throughout the duration of the series of experiments. Ibrahim and Seehra (1997) reported on sulphur as being a promoter of degradation in a PE/PP system, but we have no sulphur in our system. Similarly, there are a number of references [Tzoganakis (1988), Schoenberg (1996)] that discuss various aspects of peroxidepromoted degradation, which does not apply in our case. Watson (1975) discusses an improvement in degradation with injection of oxygen into the system, which probably occurs with a similar mechanism to our case. The oxygen necessary for the thermal degradation is probably provided from within the samples, which may have small amounts of trapped air, or from the air provided when the rheometer chamber is opened for sample inspection, re-adjustment, gap changes, etc. However, in all cases presented above, degradation is an intended and desirable effect, whereas in our case it is an undesired side effect, and it hinders our study of the effect of L C B on the rheology of polypropylene. In Figure 5.7, the values of the zero-shear rate viscosity for sample 3 with Irganox are plotted vs. time of exposure. The no-Irganox results are also shown, for comparison purposes. It can be seen that the non-Irganox sample degrades faster, in spite of the fact that the Irganox sample rested at even higher temperature. However, the Irganox seems  36  seem to have only a limited effect in stabilizing the samples. In addition, it is noteworthy to point out that the two samples degrade to the same equilibrium value. #n #2.  10  J  ^ A y.  h  A  . A  •  .  A A  • A.  A  < A  S a m p l e #3 + 0.1% wt. Irganox 1010 Exposure T = 200°C A l l F o . R . T . H . Experiments  A  #4 #5 10"  h —I  10"  10  I  '  »  L .  10"  1  co (S- ) 1  Figure 5.6(b): Effect of Degradation on Complex Viscosity, Sample 3 o  2500  Sample 3, No Irganox, T 1  5  •  7  '  0  =160 C  Exposure  Sample 3, 0.1% Irganox, T '  r  o  >  c  =200°C  Exposure  2000  w crj Q_  1500  1000  500  o~-6~-"r5" 5  10  15  20  25  30  35  T i m e of Exposure (hrs)  Figure 5.7: Degradation of Sample 3 with Exposure to Temperature, with and without Antioxidant Irganox 1010 37  5.3. 1. C Temperature History Effect Since the results obtained are highly dependent on the thermal history of the samples, a means of "erasing" the thermal history was necessary to be found. We believed that by allowing the sample to rest at a very high temperature (i.e. 210°C) after each particular dynamic frequency sweep at a lower temperature, the differences would get smoothed out, and we would get comparable results. However, that didn't work out as expected, as shown in Figure 5.8.  10°  10  10  1  2  co (rad/s)  Figure 5.8: Different "Strategies" used, and the results they yield, Sample 13  Two different strategies were involved, one going in 5°C increments from low to high, and the other, as mentioned, allowed to rest for two minutes at 210°C between measurements. The results are very different, enforcing the notion that thermal history plays a very important role in determining the values of the moduli i.e. altering the rheology. Figure 5.8 displays the master curves (i.e. superposed data of many DFS from  38  150°C to 210°C) at the reference temperature of 170°C. The only difference between the two curves is that for the second master curve, two-minute exposure at 210°C was used between consecutive DFS measurements i.e. the sample spent two minutes at 210°C between the DFS at 180°C and the DFS at 185°C. This reinforces the idea that in order for results to be comparable, they must be obtained by use of the same strategy, i.e. they must undergo similar heat treatments.  5.3.2 Effect of Backbone Molecular Weight (Chain Length) Increase The following results are based solely on data obtained at U.B.C. for unused samples. These samples contained no antioxidant, but the strategy obtained was consistent for all samples, which should make these results comparable. As previously discussed, we would expect the complex viscosity to increase with molecular weight. Guy and Berry (1968) reported that no (the zero-shear viscosity) scales as MW  34  for 1 inear polymers. The results we obtained, however, do not agree with this  trend. Figure 5.9 depicts data for three different species of similar architecture and different molecular weight, samples 1, 2, and 3. In particular, Figure 5.9 compares the dynamic viscosity of three homopolymers (i.e. linear PP). Due to their linearity, one would expect no cross-over of the viscosity curves. The values for the zero-shear rate viscosity (listed in Table 5.1), which are obtained using Rheometrics Scientific software by extrapolation, indicate that sample # 1 (MW=113k) exhibits a higher value than sample 2 (MW=137k). This is perhaps because, due to rheometer limitations, a clear plateau has not reached in the viscosity curve to definitely determine the so-called zeroshear rate viscosity. It has been suggested that the differences in M W between the three  39  samples are relatively small, and that these differences coupled with polydispersity differences would make the comparison difficult. MW=215,000 (from GPC) - Sample 3 MW=113,000 (from GPC) - Sample 1  J  MW=137,000 (from GPC) - Sample 2  I A  ra  0_ 10" h A I  10  ..I 10  10  1  2  A •  A  A  I 10"  co (rad/s)  Figure 5.9: Chain Length Increase Effect on Viscosity (T=170°C)  Figure 5.10 shows a similar behavior when comparing samples 5, 6 and 7, which have backbone M W ' s increasing from sample 5 to 7. In the case of short branched polymers, zero-shear viscosity is supposed to increase with M W . However, in our case, the rj* curves almost coincide for samples 6 (MW=158k) and 7 (MW=194k), although the differences in M W are significant. This disparity is further echoed by the values of the zero-shear viscosity presented in Table 5.1. Once again, this is perhaps a result of higher-than-reported polydispersity. A possible reason for higher polydispersity may be the thermal treatment of the samples during synthesis. For example, if one of the samples spent a lot more time under high  40  temperatures (>190°C) than its counterparts, it would degrade more and yield different results. MW=158,000 (GPC) - Sample # 6 MW=194,000 (GPC.) Sample # 7  MW=102,000 (GPC) - Sample tt 5  03 5>  10  3  .j  10  10"  i  10  10  2  J  (i) (rad/s)  Figure 5. JO: Effect of backbone MW increase for Branched Polymers (Samples 5, 6, 7) T=170°C  A  A a  MW=212,000 (GPC) - Sample # 13  MW=170,000 (GPCV Sample #14  03  CL  B_  A  MW=144,000 (GPC) - Sample U 11 A  10° h  A ' . A ® • A  —I  10"  1  —I  t • In J , J.J  1 1 III Il  10  10"  1  co (rad/s)  I  I  I I I II IJ  10  J  Figure 5.11: Comparison of Samples 11, 12 and 13 (0.8% C16) T=J70°C  41  A similar comparison is presented in Figure 5.11 for samples 11, 12 and 13, which have increasing backbone M W ' s across the series, and even longer branches than samples 5, 6, and 7. Once again, the dynamic viscosity curves almost coincide for sample 11 (MW=144k) and sample 12 (MW=170k). This unexpected behavior is also reflected in the values for zero-shear rate viscosity tabulated in Table 5.1. In addition to polydispersity, a cause for this may be low torque at low frequencies, which causes a hitch in the viscosity curve for sample 11.  5.3.3 Effect of Increasing Number of Branches  A©|  a• ®«  / 0.5% C (by mass) - Sample 4  ®  8  >—i—  I  10°  i — i — i  i i i 111  1  1  10  i i i i 111  10  1  0  i 2  i  • * i i 111  10  3  co (S" ) 1  Figure 5.12: Effect of Increasing Number of Branches (T=170°C)  In this case it is very difficult to determine what the effect of increasing the number of short branches on rheology is. Ideally, we would expect that the viscosity will increase with added branches on the same backbone. Such a finding would be consistent  42  with the tube model of De Gennes (1971) and Doi and Edwards (1986). More branches would provide additional constraints, thus increasing its relaxation time and making it more resistant to flows. That in turn would increase the viscosity. Thus, we would expect that sample 5, with 0.8% concentration of Cg, to have the highest viscosity value, followed by the 0.5% Cg (Sample 4) and lastly the linear (Sample 1). In this case, it seems that the curves are tending towards the expected outcome. However, since we are limited by rheometer constraints (and sample melting temperature) we cannot obtain a clear value for the zero-shear viscosity. The values for zero-shear viscosity obtained by fitting the Ellis theoretical model, listed in Table 5.1, confirm our expectations. Sample 5, which has the largest amount of branches, exhibits the highest zero-shear viscosity, followed by sample 4 and lastly, sample 1, even though the difference between samples 1 and 4 is not very large.  5.4 Overall Conclusions Even though our aims for this study were not accomplished entirely, some interesting facts were discovered. The most important fact is perhaps the great dependence of the rheological functions upon the thermal history of the sample. As seen, even relatively small changes in procedure drastically alter the obtained results. Thus, for future studies, it is of paramount importance to ensure that all samples are treated exactly the same way as far as exposure to temperature. This is even more important in synthesizing the sample in the lab. Also, it is important to treat all samples the same way for testing purposes, i.e. use a consistent strategy for all. After testing, it is perhaps best to  43  discard the sample and not attempt to re-use it for further experiments, as results will most likely be meaningless. Secondly, even though cutting-edge technology was available to us, we were still unable to characterize the rheology of all samples as thoroughly and as accurately as we would have liked. For most samples, we were unable to achieve a clear value for the zero-shear rate viscosity, and we were also unable to measure it at a high enough frequency in order to determine the plateau region for G". This is of great importance when trying to rationalize valuable theoretical and physical constitutive models through, such as the Pom-Pom Model (McLeish, Larson, 1998). In addition, even though we had no control over the sample synthesis, from our rheological data obtained we can infer that it is likely the polydispersity of the samples is higher than initially reported (closer to 2). Thus, somehow, the synthesis process needs to be revamped and closer to monodisperse samples need to be produced. Also, perhaps a stronger stabilizing agent needs to be identified and added to the samples, in order to decrease its temperature-history dependence and make the results more reproducible.  44  CHAPTER 6 RHEOLOGY OF COMB POLYSTYRENES  6.1 Introduction In this section, the results of rheological testing upon different samples of comb architecture polystyrene (PS) will be discussed. Linear dynamic frequency sweeps, as well as non-linear stress relaxation experiments were performed. The results are compared to our prior expectations, and to the data available in the literature.  6.2 Samples Used MW  B r a n c h MW Nr. Br./ Mol. (Avg.)  C612  475000  6500  31  CG22  624000  11700  30  C632  913000  25700  25  C642  1630000  47000  29  C652  3130000  98000  29  C712  1055000  6500  30  C722  1190000  11700  28  C732  1530000  25700  26  C742  2230000  47000  29  C752  3620000  98000  28  Table 6.1: Specifics of Comb Polystyrene Samples Table 6.1 shows a list of the samples used for this study. The samples were synthesized by Dr. Jacques Roovers (Roovers, 1979). The samples are nearly mono disperse (MW/M„<1.06), and they are designed to have longer arm lengths across the  45  series, but the same backbone length. A schematic is shown in Figure 6.1. Table 6.1 lists their molecular weight (MW), the molecular weight of their branches (Branch M W ) , as well as average number of branches present per backbone [Nr. Br./Mol. (Avg.)]. C6 Series  Figure 6.1: Schematic of Comb Polystyrene Samples  6.3 Results Obtained 6.3.1 Linear Viscoelastic Measurements Initially, linear viscoelastic measurements were obtained by Dr. Jacques Roovers (Roovers, 1981). Using the same samples prepared by Dr. Roovers, an attempt was made to reproduce his results (linear viscoelastic measurements), in order to determine whether time has had any effect on the samples. The outcomes are compared qualitatively in order to determine whether time (-20 years) has had any effect on the samples. A picture of the G \ G" for the  series is shown in Figures 6.2(a) and 6.2(b).  Similarly, for the C7 series, the G' and G" are presented, respectively, in Figures 6.3(a) and 6.3(b). These results are based on testing the melts of the samples, under a range of temperatures.  46  10  k  6  10 fe5  rn ^  10 |r 4  10  40. ™  3  10'  F  i . i i j II ill  i 11 m i l l — i 11 m i l l  10"  10"  4  10"  3  2  I_LJ.LUIII  10'  1  • '»"'"I  10°  J  ' •"""I  10  10  1  2  10  « 3  •> i • M  10  1111  *  10  4  i t sum  10  5  6  to ( s ) 1  Figure 6.2(a): C<5 Series Storage Moduli plotted as Master Curves at a Reference Temperature of 170°C  10°  ~  10  3  0_  • ©  10  4  A  V O  10  C612 C622 C632 C642 C652  J  '  10"  4  *  '  10"  3  • " " " I  ul  10"  2  • • IIIIIII  10"  1  ml  10°  10  to  ,f \ i 1 1 '  "I  10  1  2  10  ' t i»iJ 3  10  ' 4  ' • IIIIJ  10  • • i 5  10  6  (S ) 1  Figure 6.2 (h): C$ Series Loss Moduli plotted as Master Curves at the reference temperature of 170°C  47  48  49  In Figures 6.4(a) and 6.4(b), the complex viscosities for series C6 and C7, respectively, are also plotted. Qualitatively, a careful inspection of all the graphs yields several important conclusions: 1. The dynamic moduli increase with increasing M W (i.e. increasing branch M W on same backbone) such that the sample with the highest branch M W exhibits the highest value for G', trend which is also echoed by the G" graph. 2. A plateau feature is present for the G" curves, which is more pronounced for higher molecular weight samples. For some of the higher M W samples, for example C652, there appear to be actually two plateaus. Daniels and McLeish (2001), describe comb polymer relaxation. Our results are consistent with their discussion, namely, two different relaxation processes, at early times stress will relax in any dangling arms by Rouse motion of the chain along its tube (star-like), while the effective tube diameter grows continuously, eventually allowing for backbone relaxation in the thus enlarged tubes at long times. 3. In analyzing the G" curves for both series, it is noteworthy to point out that series C612 and C622, as well as C712 and C722, exhibit much lower plateau values than their higher-branch-MW counterparts. This would be expected due to the fact the lengths of the branches of C632, C642, and C652 are 25,700, 47,000, and 98,000, respectively, all above the reported literature value for the entanglement M W (M ) of 18,000, whereas C612 and C622 branches are below M . E  E  4. An analysis of the dynamic viscosity curves for series C6 reveals that the highest arm M W species (C652) exhibits the highest zero-shear viscosity, followed by C642 and all the others in the order of decreasing M W , C612 exhibiting the  50  lowest zero-shear viscosity. This trend is hard to detect in Figure 6.4 (b), however, this is because the values for zero-shear viscosity are unclear from that picture due to the fact that we were unable to measure at low enough frequencies. It is perhaps worthwhile to compare quantitatively the zero-shear rate viscosities for the two species. In Figure 6.5 the zero-shear rate viscosities for two series of similar branching, but different backbone M W , are plotted vs. M W in a logarithmic plot. The slope of the line adheres to the findings of Berry and Fox (1968), namely that no scales as MW ' . 3 4  io  6 :  V  /  C712,!  0  Slope=3.465S5  o  io : 5  C612n  0  1  I  I  I  ,  10  6  Molecular Weight  Figure 6.5: Comparison of Zero-Shear Rate Viscosities for Series C612 and C712 The storage and loss moduli of the samples are plotted in Figures 6.6(a) thru 6.6(h). They are compared, on the same set of axes, to the curves obtained by Roovers (1981). The similarities and contrasts are subsequently discussed.  51  10  10" fe-  10  5  b o r  io r 4  CO  0_  C612 Roovers (1981) T =169.5 C 10*  •  10" 10'  C612 F o R T H . (2002) T =170 C e  I  10"  3  10''  2  • • • »""*  10°  '  1  1  10  10  1  h  1  ' I  '"I  10  2  10"  3  10  5  Figure 6.6(a): C612 Storage and Loss Moduli, obtained at FoRTH (2002), and by Roovers (1981)  10  10°  * CD  10°  CD 10  4  C622 Roovers (1981) T =169.5 C 10 t 3  • I—i  10"  3  10"  2  i imill—  10'  1  C622 Fo.R.T.H. (2002) Tref =170 °C nl—i  i i mill  10°  i  10  I  10  1  i i 11 mil 2  10  ' ' 3  I  'I  10"  10  5  co (S" ) 1  Figure 6.6(b): C622 Storage and Loss Moduli obtained at FoRTH (2002), and by Roovers (1981)  52  10  J  •  C632 Roovers (1981) T =169.5 C  •  C632 F o . R T . H . (2002) T =170 °C  ref  •'••I  10  10  10  10"  10  10  10  i i i t iiiri  • • ' '1'"*  1  10  2  3  i i • i mil  10  10  co (S" ) 1  Figure 6.6(c): C632 Storage and Loss Moduli, obtained at FoRTH (2002), and by Roovers (1981)  10  10° * co D_  CD  10  03 CL  10'  3  • •  ID 10" u  •  C642 Roovers (1981) T =169.5 C  •  C642 F o . R T . H . (2002) T = 1 7 0 ° C  e  e f  i uiul—i t m i n i — i _ i - L U i u J — i 1 1 1 m i l — i i i n m l — L I IIIIUI  10'"  10"  3  10"  2  10"  1  10°  10  10  1  ' 2  I  10  • • 3  • ••  10"  I  10  • • • ••• 5  10  6  co (S' ) 1  Figure 6.6(d): C642 Storage and Loss Moduli, obtained at FoRTH (2002), and by Roovers (1981)  53  CD  C652 Roovers (1981) T =169.5 C e  10 fcm i l l — i 11 mill—i i 11 mil—  10"  10""  5  C652 F 0 . R . T . H . (2002) Tref =170 C  •  J  10"  I  10"  3  10"  2  1  I  I  10°  10  A  10  1  i  10  2  I  10  3  10  4  5  CO  Figure 6.6(e): C652 Storage and Loss Moduli, obtained at FoRTH (2002), and by Roovers (1981)  10  7  i  10°  CO CD  ° *  10  5  CO D_ CD  . 10  •  C722 Roovers (1981) T = 1 6 9 . 5 C  •  C722Fo.R.T.H. (2002) T = 170 °C  e f  4  B  e f  i 111mil—L-IIIIIJJ—t-i.iuiuJ—i i i mill—i i 11mil—UJUUUI  \ 10' 10"" 10" 5  3  10'  2  10"  1  10°  • •  10  1  '  10  2  "*  10  i • 3  10  4  10  5  co (S )  Figure 6.6(f): C722 Storage and Loss Moduli obtained at FoRTH (2002), and by Roovers (1981)  54  10 fc* CO CL s  CD  10* ti  10"  5  10""  10'  3  •  C732 Roovers (1981) T = 169.5 C  •  C732 Fo.RT.H. (2002) T = 170 °C  ref  i 11 m i l  "•'•I  t i inn  10'  2  10"'  10°  10'  •*  » 1  10  2  ll .,1-JJ.mill— 1  10  3  10'  10  s  Figure 6.6(g): C732 Storage and Loss Moduli, obtained at FoRTH (2002), and by Roovers (1981)  55  From Figures 6.6 (a)-(h), we can draw several conclusions: 1. It appears that most samples have not undergone significant deterioration with time. However, some samples, C612, C722, C732, and to a lesser extent C632 and C742, exhibit large differences when compared to Roovers (1981) data. These measurements should be repeated to determine whether they are due to deterioration or experimental error. Some sources of error may be the use of a different rheometer, a half-degree difference in reference temperature and reasonable variation between experiments. Nevertheless, the samples are thus suitable for further study. 2. Roovers (1981) measured at lower temperatures (~140°C), which we were reluctant to do because this temperature is below the glass transition temperature of PS, which we measured to be ~150°C. 3. Upon comparison of samples increasing in branch length, it appears that the area between the moduli curves increases with increasing number of branches. This is consistent with the findings of Hatzikiriakos (2000). Furthermore, at low branch M W , i.e. C612 and C622, the curves echo almost a gel-like behavior, whereas at high branch M W ' s , there is a defined plateau in G". This can be explained through the prism of a tube reptation model; as branches increase in length, it becomes increasingly difficult for the backbone to reptate due to added constraints [Yurasova, McLeish (1994)]. 4. For high M W branches, i.e. C732 and C742, at intermediate frequencies, the two curves approach, but do not intersect. The reason for this is unknown.  56  The G', G" data obtained was subjected to an inverse Fourier transform, and thus G(t) data was produced. The G(t) curve was then fitted using the Rheometrics Scientific software, a first-order exponential decay function, to obtain values for the GN°, the plateau modulus. The results were compared to those obtained by Roovers (1981). However, Roovers used the area under the G'Vco curve to obtain the plateau modulus. Our method is less accurate due to no clear plateau, but power-law behavior. Nevertheless, the comparison, illustrated in Table 6.2, shows similar results, and any differences may be due to sample degradation with time and experimental errors. For a few of the samples, it was difficult to determine a clear-cut plateau region, and as such they are not listed in Table 6.2. Further investigations, such as perhaps a G'Vco fitting, would shed more light on the situation and determine whether samples have degraded with time. Sample  #  GnO  (Pa) J. R.  (1981)  GnO  (Pa)  (FORTH)  Error  (+/-)  f? 2 A  CS12  2.00E+05  1.56E+05  1.39E+04  0.998  C632  2.10E+05  2.61E+05  1.62E+04  0.999  C642  2.10E+05  4.26E+05  1.63E+04  0.999  C652  2.20E+05  3.43E+05  8.49E+03  0.999  C712  1.95E+05  2.56E+05  5.50E+03  0.999  C722  1.95E+05  2.03E+05  9.73E+03  0.998  Table 6.2: Comparison O/GN Values  6.3.2 Non-Linear Stress Relaxation Experiments In order to learn more about the rheological response of comb architecture, the samples were subjected to non-linear stress relaxation experiments. Solutions of comb  57  polystyrene in diethylphthalate (DEP [Aldrich]) were prepared, of various concentrations. Only the highest branch M W samples were used for this study, due to their high entanglements. The experiments were conducted at different strains, and the results were compared to the G(t) obtained from linear data. Figure 6.7(a) shows a typical set of curves obtained for G(t) at different strains. The data is then shifted to the curve with the lowest strain (i.e. in the linear regime), as shown in figure 6.7(b). The shift factor, which is the ratio between G(t) and G°(t) [at very low stress (i.e. linear)], is known as the damping function and it is a function of strain, h(y). The damping function is then plotted vs. the strain, as shown in Figure 6.7(c).  r 1 1 1 1 i i — i — i  10'  2  11111ii  i  i  i  10"  10°  1  i  • •  i  i  10  1  " i  10  i 2  t(s)  Figure 6.7(a): Imposition of sudden step strain experiments and their consequent stress relaxation at several strains (strains: 0.1-10 strain units) for C752  58  1  1 I I I ll  10'  2  1 1  I I  1.1,1.1  1  1  1I  10'  I I I ll  10°  1  1  1  I  L-i-J-l-LlJ  I  '  *  10  10  1  2  t(s)  Figure 6.7(b): Shifted Curves from Figure 6.4(a)  C752 30% wt in DEP, Damping Function  10"  1  10°  10  1  Y  Figure 6.7(c): Damping Function for C752 same experiment for series C742 is presented in Figure 6.8(a) and 6.8(b).  59  10"  2  10"  10°  1  10  1  t(s)  Figure 6.8(b): Shifted curves from Figure 6.5(a), C742  60  10  2  As can be seen from the two experiments, the G(t) presents an extended plateau feature, which expands with increasing strain. Our experiments were conducted beginning at a linear stress of 0.2 strain units and gradually progressing up to 10 strain units. The presence of the extensive plateau feature, which has not been detected in the literature, remains a question mark. We now proceed to comparing the damping functions of C742 and C752 (both in 30% wt solution in DEP) to determine the effect of increasing branch M W , as shown in Figure 6.9:  J  i  '  »  *  i  '  .  • I  10°  10"'  i  i  '  '  i  i  i  i L  10  1  Y  Figure 6.9: E.ffect of Increasing Branch MW on the Damping Function h(y) In Figure 6.9, we have plotted the damping functions for series C742 and C752, between which the only difference is the arm M W . On the same set of axes the damping function for a linear polymer as predicted by the Doi-Edwards theory is also plotted. As can be seen, both series exhibit higher values than the Doi-Edwards theory predicts, as should be expected of a branched polymer. In addition, the lower values for C742 as compared to C752 are as should be expected, since the branches of C742 are of lower M W .  61  The same behavior is illustrated by the C6 series counterparts. In Figure 6.10(a) and 6.10(b), the stress relaxation curves for a 20% by weight solution of C652 in DEP, at strains ranging from 0.1 to 10 strain units, are presented. Figure 6.11 displays the stress relaxation curves for a C642 sample solution (20% wt in DEP). In the case of C652 the linear and non linear data fail to coincide, for reasons so far undetermined. In comparing the C6 and C7 series, it is perhaps noteworthy to point out the far more pronounced plateau present in the C7 curves. This is due to larger backbone M W .  j  LJ  i  i  i  i  i  10'  i  i i_l  i  •  •  i  i  i  •  10'  2  1  T i m e (s)  Figure 6.10(a): Imposition of sudden step strain experiments for C652 and their consequent stress relaxation at several, strains (strains: 0.1-10 strain units) The stress relaxation figures for C642 and C652 exhibit a strange kink feature, previously unreported. The reason for this is unknown, but it might be due to experimental issues such as edge effects, sample slip at the wall, or edge fracture. This aspect needs to be investigated more thoroughly in future experiments.  62  C652 20% Wt. in DEP T=30°C  10  1  _J  I  10"'  I  I  '  ' ' I  -j  10-  1  *  I  I  I  i  i i i  10  u  Time (s)  Figure 6.11: Stress Relaxation for C642 20% Wt. Solution in DEP, shifted curves  63  Figure 6.12 compares the damping functions for the C642 and C652 series. Similarly to the C7 series, the lower arm M W species exhibits values closer to linear behavior, i.e. Doi-Edwards theory. The difference, however, is not as drastic as in the C7 series case (Figure 6.9), and there is even some overlapping. That is peculiar, and it is perhaps due to not enough points in the linear region.  V  10°  w  W  $  \  -  -  9 \  \  • \  V  • * \ • \ v  Doi-Edwards Theory •  C652w20wt.  v  C642w20wt  10''  10°  10  1  Y  Figure 6.12: Comparison of Damping Functions for C652 and C642 Series In order to further illustrate the effect of entanglements, a higher concentration (i.e. more entanglements) sample of C642 was tested. The damping functions for a 30% by weight solution of C642 in DEP and a 20% solution in DEP of C642 are compared in Figure 6.13. As expected, the higher entanglement species exhibits a higher value for the damping function.  64  Doi-Edwards •  C642w30wt  •  C642w20wt  T  .-1  10'  1—i—i—i—r—p  10° y  Figure 6.13: Comparison of Different Solution Concentrations; Effect of Entanglements It is perhaps worthwhile to test the Doi-Edwards theory against a linear polymer. Thus, a linear PS (Aldrich) of unidisperse M W of the order of the C6 series was tested. The damping function for the 30% solution of the linear polystyrene of comparable backbone M W (-250,000) in DEP is shown in Figure 6.14. As can be observed, the behavior exhibited by the linear polymer is very close to the predicted behavior of Doi and Edwards. The difference lies in the fact that this is a high M W compound, which leads to a higher number of entanglements. The damping function for the C752 series is included for visual comparison. The relaxation spectrum for the linear PS is shown in Figure 6.15.  65  Figure 6.15: Stress Relaxation for a Linear Polystyrene 30% Wt. Solution in DEP  66  CHAPTER 7 CONCLUSIONS AND RECOMMENDATIONS  7.1 Introduction In this final chapter, the most important findings of this project are summed up. The findings will be split up into two different sections. First, the results of the L C B polypropylene project, which is presented in Chapter 5, will be summed up. Secondly, the conclusions based on the comb PS presented in Chapter 6 will be shown. Recommendations for future work will be given in both cases.  7.2 Findings and Suggestions for Future Work for PP Project Even though many of the goals we set out to accomplish, outlined in Chapter 3, were not met, there are still a great many valuable conclusions that can be drawn from this rheological study of a series of varying structure PP. The most important conclusions are: 1. The 15 samples degrade drastically with extended exposure to temperature. 2.  Small amounts (0.1% wt.) of antioxidizer Irganox 1010 (CIBA Chemicals) have just a limited effect and do not stop degradation.  3. The rheological results on the samples are strongly related to a sample's previous thermal history. 4. For various reasons (polydispersity, differences in arm M W not large enough, etc.), the effect of M W , branch length, and number of branches increase cannot be determined from this study.  67  5. Due to rheometer limitations and polymer melting temperature, we are unable to measure far enough into the G" plateau region to be able to determine the value of GN°- This makes it difficult to evaluate our results through the prism of available mathematical models, i.e. the Pom-Pom model. Based on this, I suggest the following improvements should be made for a subsequent study: 1. More care needs to be taken during sample preparation to ensure low polydispersity and identical thermal treatment of all the samples. 2. Perhaps we need to synthesize polymers with more drastic differences in molecular structure, to be able to determine the effect of arm length increase, number of arms, etc. on the rheological properties of the polymers.  7.3 Findings and Suggestions for PS Project In this section, we will sum up the findings of the previous chapter on nonlinear rheology of certain PS samples: 1. Time-strain factorability for all samples involved is evident at long times, and it is confirmed by the G(t)h(y) plots (shifted curves). 2. As the strain is increased in the experiments, the shape of the G(t) curve becomes more complex, exhibiting two inflexion points, reflecting two different relaxation mechanisms.  According to the  Doi-Edwards theory,  the two relaxation  mechanisms are (a) retraction within the tube (contour length relaxation), which is a relaxation mechanism that has negligible effect on linear behavior, but becomes  68  very important in the case of large, rapid deformations, and (b) reptation in the tube at long times. 3. All samples exhibit weaker damping than predicted by the Doi-Edwards theory. This is consistent with findings by Osaki (1993), which reported weaker damping to be associated with comb structure. In addition, according to Osaki's denomination, our samples exhibit B type damping, and a kinked type of relaxation. 4. DEP is chosen to be a good solvent. Based on these conclusions, the following recommendations should be made: 1. Some of the linear experiments need to be repeated to confirm deterioration with time. 2. Future work may include a quantitative evaluation of the data using theoretical models available in the literature, such as the McLeish (2001) model. 3. A more thorough analysis of the plateau modulus might be beneficial, perhaps using a method similar to that of Roovers (1981). 4. Furthermore, perhaps more nonlinear experiments need to be performed at different stresses and different concentrations (i.e. entanglement densities) in order to be able to develop a quantitative prediction of how branch length in comb polymers affects rheological properties. 5. The peculiar kink observed in C642 and C652 needs to be further investigated. 6. The extensive plateau feature needs to be further investigated, and the causes thereof determined.  69  REFERENCES  Archer, L . A., J. RheoL, 1999, 6, 43 Beech, D R . , Booth, C , Dodgson, D.V., POLYMER, February 1972, 13, 73 Berry, G.C., Fox, T.G., Adv. Polym. Sci., 1968, 5, 261 Curry, J., Jackson, S., Chemical Engineering Progress, November 1988, 48 Daniels, D R . , McLeish, T.C.B.,MacromolecuJ.es, 2001, 34, 7025 Dealy, J.M., Rheometers for Molten Plastics, Van Nostrand Reinhold, New York 1982 Dealy, J.M., Wissbrun, K.F., Melt Rheology and its Role in Plastics Processing, Van Nostrand Reinhold, New York 1990 De Gennes, P.G., J. Chem. Phys., 1971, 55, 572 Doi, M . , Edwards, S.F., The Theory of Polymer Dynamics, Oxford University Press, New York 1986 Graessley, W.W., Physical Properties of Polymers, 2 Ed., Chapter 3, pg. 97, A C S 1993 nd  Hatzikiriakos, S.G., Polym. Eng. And Sci., 2000, 40, pg.2279 Hutton, J.F., Nature, 1963, 200, 646 Ibrahim, M . M . , Seehra, M.S., Energy & Fuels, 1997, 11, 926 Islam, M.T., Sanchez-Reyes, J., Archer, L . A . , . / . RheoL, 2001, 1, 45 Jordan, E.A., Donald, A . M . , Fetters, L.J., Klein, J., ACS Polym. Prepr., 1989, 30, 63 Kurzbeck, S., Oster, F., Munstedt, H., J. 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