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A study of the solution crystallization of poly(ether ether ketone) using dynamic light scattering
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A study of the solution crystallization of poly(ether ether ketone) using dynamic light scattering
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A ST U D Y O F T H E SO L U T IO N C R Y ST A L L IZ A T IO N OF P O L Y (E T H E R E T H E R K E T O N E ) U SIN G D Y N A M IC L IG H T SC A T T E R IN G by Chevan Goonetilleke A Thesis Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree of Master of Science (Chemistry) August 1995 Copyright 1995 Chevan Goonetilleke UNIVERSITY O F SO U T H E R N CALIFORNIA T H E G R A D U A T E SC H O O L U N IV ER SITY PARK L O S A N G E L E S. C A L IF O R N IA 9 0 0 0 7 This thesis, written by Chevan Goonetilleke under the direction of h.ia Thesis Committee, and approved by all its members, has been pre sented to and accepted by the Dean of The Graduate School, in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Dean D ate . .22, _ _ 1995 Chairman ACKNOWLEDGMENTS I am grateful to Professor Eric Amis, my adviser during the graduate program, for creating and building my interest in the field of polymer physical chemistry that lead to this thesis. He was a source of encouragem ent and was very understanding and helpful especially, when it was needed most. I would like to thank both past and present colleagues in my research group who have encouraged me and given me the opportunity to engage in interesting scientific discussions during my graduate work. They include Dr. Qun Yu, Dr. Xinhao Gao, Dr. Ning Hu, Brett Ermi, Diane Valachovic and especially, W enjun Wu who has not only contributed to my scientific growth, but has also helped me immensely during the writing of my thesis. It is with a deep sense of gratitude that I acknowledge her support. A very special "thank you" goes halfway across the globe to my parents who have always been loving and very supportive. They have given me the resources and the moral support to finish my graduate studies. TABLE OF CONTENTS Page Acknowledgements ....................................................................................................ii Table of Contents........................................................................................................ iii A bstract......................................................................................................................... iv C hapter 1. Introduction 1 References......................................................................................................... 8 Chapter 2. Theory of Polymer Crystallization 9 Nature of Polymer crystals............................................................................... 9 Polymer Crystallization - A Theoretical Perspective..................................13 The Basic Model of Polymer Crystallization...............................................14 References C hapter 3. Principles of Dynamic Light Scattering 19 The Light Scattering Phenomenon................................................................19 DLS techniques................................................................................ 20 Historical Developments................................................................................ 21 The Theory of Dynamic Light Scattering.....................................................22 Correlation Functions......................................................................................25 Fluctuations and Time-Correlation Functions............................................. 27 The Relationship between the Correlation Function and the Spectrum of the scattered light............................................................................................ 31 The Instrument................................................................................................35 Data Analysis...................................................................................................36 References........................................................................................................ 37 Chapter 4. Experimental Aspects and Results 38 SamplePreparation.......................................................................................... 39 Results and Discussion....................................................................................40 References........................................................................................................43 A B S T R A C T Following the successes in our lab in investigating the solution crystallization kinetics of linear Polyethyleneoxide, an attempt was made to extend the study to semi-flexible polymers. The technologically im portant Polyetherketoketone (PEKK) which is a high performance engineering thermoplastic was chosen as the semi-rigid polymer. A high tem perature dynamic light scattering set up was used to measure the crystal growth rate of PEKK. The intensity-intensity autocorrelation functions generated by the scattered laser light was analyzed to extract translational diffusion rates. The hydrodynamic radii were then calculated using these diffusion coefficients and the Stokes-Einstein relationship. The results, however, did not show crystal growth that leads one to believe that seed crystals were not even formed in the first place. A few suggestions are made to overcome this problem. Chapter 1. Introduction The study of the growth of linear polymer crystals has created immense scientific interest not only in the purely intellectual sense of understanding the nature of polymer crystallization but also because of its im portance from a technological standpoint. Many synthetic polymers of technological value like nylon and polyethylene are linear and crystalline; and the nature of the crystals has a bearing on the ultimate bulk physical (and even chemical) properties of the polymer. Systems of biological origin are frequently polymeric in character, and some of these or their prototypes or derivatives behave in a similar way to linear polymers upon crystallization. For instance, natural rubber, cellulose triacetate and the salts o f poly(L-glutamic) acid undergo crystallization - with chain folding - resembling the manner in which linear polymers crystallize from solution^. The importance of studying polymer crystallization led to some extensive studies in the past few decades on the crystallization kinetics of polym er crystals grown from both the melt and solution. Most of the initial research on polymer crystallization was conducted on linear, flexible, crystalline polyethylene (PE). A few models had been proposed for the behaviour of PE crystals with respect to the kinetics of growth and the morphology of fully grown crystals. Currently, the most widely accepted theory of polymer crystallization is the surface nucleation theory with chain folding lamellae put forth by Lauritzann and Hoffmann. The work 1 presented here was an attem pt to extend the application of this theory from flexible polymers to semi-rigid polymers. Before the middle of this century, what was known of polymer crystallization was minimal. The subcell of some polymer crystals in the bulk phase was known to be the same as that for the corresponding molecules of low molecular weight. For example, experiments by Bunn^ showed that the unit subcell in PE was very nearly identical to that of the n-paraffins. It was also known that polymer crystals were small; X-ray diffraction studies gave a number on the order of a few hundred angstroms. Broad melting ranges were also observed for polymers and the existence of non-crystallizable polymers was a common fact. Many polymers were known to exhibit "semicrystallinity" through the existence of a temperature range where a part of the polymer would behave like a crystal and the rest of the polymer like a liquid. Although spherulitic crystals in bulk polymers were known to exist, the now well accepted concept of folded chains comprising of the spherulites were not even considered at the time. However, Point, Bunn and Alcock did point out the fact that the chain axes were perpendicular to the spherulite radius. In 1955, Keller obtained, for the first time, single crystals of PE from dilute solution. Based on his studies, he concluded that the polymer chains in the crystals folded back upon themselves. This conclusion as to the chain folding nature of polymer crystals was supported by independent work carried out by Fischer and Till. Most of the subsequent research on crystallization of linear polymers was carried out on PE. It was 2 shown that the kinetics of PE crystal growth, both from melt and from solution, followed the surface nucleation theory proposed by Lauritzan and Hoffman. Previous extensive work carried out in our laboratory showed that the morphology and the crystal growth rate of linear, flexible polyethyleneoxide (PEO) also follows the theory of chain folding lamellae. The crystal growth rate showed two regimes for the crystallization temperature range studied as was evident by the plot of Log G versus 1/T(T-Td), the supercooling factor. Here, G, denotes the growth rate of the crystal, T, the crystallization temperature and Td the equilibrium dissolution temperature of crystals in solution. It is extremely hard to obtain Td through experimental means. Therefore, the 1 alue of Td had to be estimated. The lowest molecular weight PEO samples (23K) showed Regime I kinetics while the ones with molecular weights of 450K and 556K showed both Regime I and Regime II features. The existence of three regimes was facilitated by the surface nucleation theory of Lauritzan and Hoffman. The break up of the crystallization growth into these three regimes has been explained before in terms of the dependence of the rate of nucleation (i) and the rate of substrate completion (g) on the supercooling factor. In regime I, i « g , in regime II i is approximately equal to g and in regime III, i » g . The concentration of PEO in solution was found to have a power law relationship with the crystal growth rate. The exponent ranges from 3 0.49 to 0.73 and decreased with respect to the molecular weight of the polymer. However, there was very little temperature dependence of the exponent. A slow increase instead of an abrupt change of the exponent is observed around the temperatures corresponding to regime transitions. A miscible blend of PEO and PMMA (which is isorefractive with toluene) in toluene has also been studied and preliminary results showed that the crystaliization rate had only a very small dependency on the concentration of PMMA. Given the increase in viscosity of the system due to the addition of another polymer, one would have expected a marked reduction in the crystal growth rate. However, these results showed that the diffusion rate of the bulk polymer was not a rate determining factor in the crystallization. The success of the dynamic light scattering technique in these studies was a driving force to carry out more investigations into the behaviour of polymeric systems of interest when they undergo crystallization from dilute solutions. Data from DLS studies have not been reported for solution crystallization of semi-rigid polymers as of yet. Semi-Crystalline Poly(etherketoneketone) (PEKK) was picked for the semi-rigid polymer in my study of polymer crystallization. PEKK belongs to the Polyetherketone (PEK) family of high temperature, high performance engineering thermoplastic polymers^ which were introduced in the early 1980s. PEKK is of technological interest because of its use in aircrafts as interior lamination to replace the more hazardous poly(carbonates)4. 4 O f the PEKs, PEKK is the m ost rigid with the highest keto content (67% Ketone). The PEKK repeat unit has only one flexible ether linkage. Two of its three linkages connecting phenyl rings are carbonyl groups that give the keto linkages a very high rotational conformation energy barrier^. This results in a semi-rigid polymer with two thirds of the bonds being fairly rigid. Therefore, it was not obvious that PEKK would follow the chain folding model that flexible polymers like PE and PEO did. However, the crystal growth rate of PEKK from the melt has shown some agreement with the Lauritzan and Hoffman model of chain folding lam ellae^. A regim e III to regime II transition was observed on the plot of crystal growth rate vs the supercooling factor. M ost of the crystallization experiments use microscopy to measure the growth of the crystals - be it from melt or from solution. Because of the optical anisotropy of many polymer crystals, melt grown crystals are usually measured by optical microscopy. The morphology and growth rate of crystals grown from solution are measured by transmission electron m icroscopy^. These techniques have been coupled with a hot stage and video image analysis software to obtain the necessary data. A shortfall of using microscopy stems from the fact that it is not performed under in situ conditions. Our laboratory has developed the non-perturbative dynamic light scattering technique to obtain kinetic information in situ and in real time. 5 The polymer samples used in my study had a molecular weight of 12,000 and a fairly wide m olecular weight distribution with a polydispersity index of 3. The next chapter in this thesis gives the theoretical background to the behaviour of polymer chains as they undergo crystallization from solution. It is now known that a polymer crystal with a spherulite morphology consists of many thin layers, called lamellae, which have a thickness of the order of 50-200 Angstroms. The connection between lamellae and the macroscopic picture of a spherulite was not understood until lamella single crystals were observed by Keller. Ever since, a couple of theoretical models have been put forth with the intention of explaining the morphology, kinetics and thermodynamics of polymer crystal growth. Although the morphology of m elt grown crystals can be quite different to the ones grown from solution, many of the kinetic theories applicable to melt crystallization are also relevant to solution crystallization. The earliest of these models was the fringed micelle model which was followed by the switchboard model which in turn was followed by the now widely accepted chain folding model with adjacent re-entry. The kinetics of solution crystallization was first theorized based on the Avrami equation used in metallurgy for crystallization of metals. This was eventually succeeded by the surface nucleation theory. In Chapter 3, the very convenient, less time- consuming, non- perturbative, in situ technique using the dynamic light scattering (DLS) principle will be discussed in depth. It is an excellent method to study 6 crystallization behaviour in dilute solution but is limited in the sense that only very dilute solutions of polymers can be analyzed with this technique. However, there are ongoing efforts to use DLS for polymer melts and they are still at a very early stage of advancement. The DLS instrument measures the intensity of the scattered light and computes an intensity-intensity autocorrelation function that is a function of the Diffusion coefficient of - the scatterers - the polymer crystals in solution which in turn is related to the hydrodynamic radius of the crystal. The correlation functions are obtained about one every minute until the crystals are grown completely. Thus, the hydrodynamic radius can be plotted against time and the growth rate of crystals found from the slope. With the advent of technologically advanced software, one is able to see very detailed and precise information on the kinetic parameters. The growth rate from the very m oment the crystals are grown can be obtained with the DLS technique. Although not needed in our system that was investigated, one could conceivably study relaxation behaviour of polymer chains even in the sub-micro second time scale with the newly developed digital correlator used in our experiments. The final chapter discusses the experimental techniques involved in seed preparation and the results of the DLS measurements on dilute solutions of PEKK in trichloroacetic acid. 7 R eferences 1. Hoffman, J.D. and Lauritzen, J.I., Treatise on Solid State Chemistry, Plenum, New York, 1976, p503 2. Ibid 3. Gardner, H.K. and Hsiao B.S. Polymer 1991, p0266 4. Hodd, K. Trends in Polymer Science, May 1993, V ol.l, No. 5, p i 32 5. Abraham, R.J. and Haworth, I.S. Polymer 1991,32, p i 21 6. Hsiao, B.S. and Gardner, K.H. ACS Polymer Preprint 1991 p259 7. Ni Ding, PhD dissertation, University of Southern California, 1990, p38. 8 Chapter 2. Polymer Crystallization The process of polymer crystallization can be simply stated as one of ordering where polymer chains exhibiting random motion settle in regular positions in the solid state. For a linear, flexible polymer chain this could mean a change from a random walk motion (drunkard's stagger) to an orderly arrangement of chains with a huge reduction in entropy. The lowering of the entropy has to be compensated by a large negative change in the enthalpy in order for a favourable free energy change to occur. A reduction in the enthalpy can be brought about by the alignment of symmetrical polymer chains that will allow for the regular close packing needed for crystal formation which would also facilitate strong interm olecular forces via suitable chain groups that would in turn result in the polymer attaining a much lower level of energy.1 Nature of Polymer Crystals - a comparison with small molecular crystals Small molecular crystals and polymer crystals do have a few things in common. Polymer crystals resemble molecular crystals with respect to the forces that hold the crystal intact since for both cases they are of the Van der W aals type. Usually, the crystal attraction energy involves London forces, with dipole-dipole interaction and hydrogen bonding present if the appropriate chemical groups are attached to the polymer backbone.2 9 The few similarities between polymer chains and small molecules undergoing crystallization are far outweighed by the myriad of differences that exist between them. Unlike for small molecular crystals, one cannot ascertain an exact melting point, a crystal dissolution temperature (for polymer crystals in solution) or a crystallization temperature for polymers. This stems from the fact that the polymers never attain perfect crystallinity. Instead, they contain amorphous regions and crystallites of varying size, the size of which would depend on the thermal history of the sample, vis-a- vis the level of undercooling during the crystallization. A large fraction (10%-70%) of the polymer consists of non-crystalline regions even after prolonged storage at a temperature where crystallization was initially rapid. This might seem like a violation of Gibbs' phase rule which is not encountered for small molecules undergoing crystallization. Actually, the rule does not apply to this system because it is not in equilibrium. Crystallization from the melt introduces further complications due to the fact that the polymer is very viscous at the crystallization temperature. This retards the movement of the polymer chains and results in a highly entangled system of chains. Therefore, the chains do not have sufficient time to diffuse into the three-dimensional order required for crystallite formation. Thus, rapid cooling from the melt usually prevents the development of significant crystallinity. However, in dilute solution crystallization of polymers, as was the case in my work, one does not encounter as many entanglements. Nevertheless, perfectly crystalline polymers are not known to exist, even if they are crystallized from a dilute solution. Given the length of the polymer chains and the long range order 10 required for perfect crystal formation, this should not come as a surprise. The broad melting range of a polymer gives an indication of the size and perfection of the crystallites. At high undercoolings, the nucleation density is high, segmental diffusion rates are low; as a result small imperfect crystalline regions are formed. Thus, the melting temperature ranges become broad for polymers crystallized at lower temperatures and narrow for higher crystallization temperatures. It follows that careful annealing at the appropriate temperature could produce samples with high crystallinity. An example in case, is the annealing of linear polyethylene for 40 days.3 There was a marked improvement in the level of crystallinity as was clear from the almost perfect first order phase transition at the melting temperature. The drop in the specific volume for the linear PE sample was an order of magnitude larger than that for a branched (low crystallinity) PE. The dimensional growth of polymer crystals is quite different to that of small molecular crystals. It is now a well known fact that linear polymers under a variety of conditions crystallize by chain folding forming very thin platelets of the order of 0.05 - 0.2nm thick while the two remaining dimensions are very large in comparison and increase in size as the crystals grow. This unique behaviour of polymer chains as they undergo crystallization has been - to say the least - quite a challenge to crystal growth theories. 1 1 For reasons that will be enunciated later in this chapter, chain folded polym er crystals break some of the usual "rules" followed by crystals in general. For example, screw dislocations play only a minor role in the crystal growth process; and there has been no known example where screw dislocations have been rate determining. Another interesting fact is that the highest energy surface in a polymer crystal - the chain folded surface - does not grow at all. Generally, the surface of a crystal with the highest energy would be growing the fastest. Another unique feature of polymer crystals have been made to use by experimentalists trying to measure the rate of polymer crystal growth. The optical anisotropy of the crystalline regions and the transparency of the uncrystallized regions in many polymers makes it possible to use an optical miroscope with crossed Nicol prisms together with a temperature- controlled hot stage for the relatively easy measuring of crystal growth rates. The cross polarization from the prisms will enable one to verify that the polymer crystals studied are single crystals. Because of the imperfect crystallinity and the broad melting range of polymer crystals, it is impossible to obtain some of the thermodynamic information required for a rigorous analysis. Even with carefully annealed polymer samples, the equilibrium melting temperature of the completely crystalline polymer, T°m , cannot be measured. The same goes for polymers in solution where T°<j, the equilibrium crystal dissolution temperature has to be estimated. 12 Polymer Crystallization - A Theoretical Perspective Unlike small molecules, the long chain nature of the polymer m olecules gives rise to a highly complex system of innumerous interactions and diverse growth forms. This gives the experimentalist a challenging task in analyzing and characterizing polymer crystal growth. The theories of crystallization have suffered endless debate due to this highly complex nature of polymeric systems. The modern era of polymer crystallization began with the discovery by Keller in 1959 that solution grown single crystals o f polyethylene are thin platelets, or lamellae as they are called so often now. Through Xray diffraction studies conducted on his samples, Keller found out that the polymer backbone lay along the thin dimension of the platelets. He concluded that the chains folded in a regular manner depositing on the crystal. Since the discovery of lamellae that crystallized through chain folding a vast and diverse set of opinions have been put out. Many points of dispute still remain. Although the theories put forth have varying assumptions, they have several features that are common. The basic premises as they pertain to polymer crystal growth will be discussed in the following section. The Basic Model of Polymer Crystallization The morphology of polymer crystals has been studied extensively by many. It was mentioned above that polymer single crystals take the 13 form of thin lamellae, which are large (submicron range) in two of the dimensions but extremely small (a few hundred Angstroms) in the third. Although the general structure of a single lamellae may be easily described, the resulting morphology is far from simple and includes rhombic and hexagonal shaped crystals, and many other variations depending on the polym er and on the crystallization conditions.^ However, the fact that the growth rate and the thickness of the lamellae can in general be described in terms of the temperature and the supercooling shows that the controlling factors are the same in all cases. It can also be inferred that the morphology does not affect the rate to a considerable extent in general. The basic model presented in this section is obviously a very simplified version of the real crystal which contains many defects, dislocations and entanglements. The model neglects the three-dimensional nature of the lamella which one may have thought to be important: the influence of the stacking of folds, which is commonly believed to lead to the pyramidal shapes is lost and the molecules are assumed to traverse the lamella perpendicular to the fold surface. These factors may influence any quantitative predictions through the physical parameters, however they must not be the fundamental reason for growth via chain folding in order for the crystalline model to be valid. Another important assumption in the model is that the predominant type of folding involves reentry of an emergent molecule into an adjacent position within the crystal. If the effects of 'loops' or 'cilia'(chain ends hanging off of the crystallographic phase) are considered at all it is as a 14 correction to the the predominantly adjacent re-entry growth. Supporting this assumption, Monte Carlo studies^, of chain folding has shown that adjacent and next-nearest neighbour re-entry always dominate. Neutron scattering and infrared studies have also confirmed this. Hoffman^ also showed that random re-entry (also called the switchboard model) which would have destroyed our assumption here would lead to an unphysical increase in density outside the crystallographic phase. Surface Nucleation Theory The surface nucleation theory put forth by Laurtzen and Hoffman has emerged as a promising framework for describing crystallization rates for linear polymers both in melt and in dilute solution. Extensive research carried out in our lab^ for linear PEO crystallization from dilute solution agreed well with this theory. Surface nucleation theory is based on the assumption that chain folding and lamellar formation are kinetically controlled. The thermodynamically stable crystal is an extended chain crystal with no folds that could be formed under pressure or when the chain length is short. The Gibbs free energy of a single chain-folded crystal can be expressed as AOcrystal = 4x 1 g + 2x^ae - x21(Af) where 1 is the thin dimension of the crystal, s the large dimension, Ge the folding surface free energy, o the lateral surface free energy and Af the 15 bulk free energy o f fusion. The value of Af can be approximated near the melting point by assuming that the heat of fusion is independent of temperature. Then we can write, A f = Ahf - TASf = Ahf - T(Ahf) / T °m = Ahf (AT) / T < > m Here Ahf is the heat of fusion per unit volume of crystal, T°m is the melting point of the extended chain crystal (the equilibrium melting temperature) and AT the undercooling T °m - T. At the crystal melting temperature, AOcrystal = 0. F o r x » l, Tm = T ° m [ l - 2 a e/Ahfl] This equation shows that the observed melting point T m for a thin platelet is depressed below that of an infinite crystal by an amount 2 T °mae/A h f 1 . If one plots experimental values of Tm against 1/1, and if the value of Ahf is known, Gq can be determined from the intercept and the slope of the plot. For the solution crystallization process, Tm and T °m are replaced by Td and T°d respectively. A plot of Tm versus T is linear to a fair approximation. The intersection with line Tm = Tc will occur at T ° m . The values obtained for T °m from a plot of Tm against 1/1 are close to these values. The kinetic theories of crystallization naturally predicted a temperature dependence of the crystal growth rate. Knowing the rate of nucleation of new layers at the crystal edge, one can obtain the rate of growth if the manner of completion of the substrate can be related to the nucleation process. There are three regimes of crystal growth which are 16 controlled by two com peting processes - nucleation rate (i) and the growth rate of substrate(g). The first regime, known as regime I, describes a single nucleation event per substrate length L, where the nucleation rate is slower than the substrate completion rate. The crystal growth rate is given by G l = biL, where b is the thickness of the crystalline stem. In the second regim e (regime II), multiple nucleation occurs on the growth surface as the nucleation rate becomes approximately equal to the substrate completion rate. The crystal growth rate is given by G n = b(2ig)]/2. The final regime, (regime III) is a state of rapid polynucleation growth where nucleation occurs so rapidly that the separation of two associated growth fronts, i.e. niches, on the substrate which characterizes regime II, approaches the width of a single stem. For crystals grown from solution, the crystal growth rate is expressed by the following equation. C Y - U * -K„(i) G : = ----- exp( )ex p ( — ) ' N a RT TAT where c is the polymer concentration with a y power dependence which depends on the regime, U* is the diffusion activation energy of the dissolved polymer, N is the degree of polymerization, a is approximately 0.5 for a snake-like polymer chain and Kg(i) is the nucleation constant for regime(i). The values of Kg(i) can be obtained from the relationships below. Kg(I) = 4 b a a eTom /(k A h f) 17 and Kg(I) = 2 Kg(II) = Kg(III) There have been some challenges to this surface nucleation theory and debates over the existence of the different regimes. However, with some re-estim ation of 1 by Hoffman and M iller^, these concerns have been dealt with. References 1. J.M .G. Cowie, Polymers'.chemistry &physics o f modern materials, John W iley & Sons, New York, 1991, pp229-230. 2. John Hoffman and G.T. Davis and J.I. Lauritzen, Treatise on Solid State Chemistry, Plenum, New York, 1976, Vol3, p 498. 3. George H. Stout and Lyle H. Jensen, X-Ray stucture determination, John W iley & Sons, New York, 2nd edition, 1989, p 78-9 4. K. Armitstead and G. Goldbeck-Wood, Polymer Crystallization Theories, Advances in Polymer Science, p 226. 5. M ansfield, M.S. Macromolecules 1983, 16,914 6. Hoffman J.D. Polymer 24,3 7. Ni Ding, PhD dissertation, University of Southern California, 1990 8. Hoffman, J.D. and Miller, R.L. Macromolecules, 1989, 22, 3502 18 Chapter 3. Dynamic Light Scattering The Light Scattering Phenomenon Light scattering can be thought of as a process where particles absorb energy from the incident light beam and re-emits the energy in the form of light. The scattering can be elastic, inelastic or quasielastic. Inelastic scattering usually refers to processes (eg. Raman scattering, fluorescence, and phosphorescence) where there is a well defined change in the quantum mechanical energy level of the material as a result of the scattering phenomena. Elastic scattering can be thought of as a special case of quasielastic scattering. In quasielastic light scattering the scattered intensities can be measured at different frequencies using a filter. The scattered intensity at the incident frequency is the quantity of interest in elastic scattering. Quasielastic scattering experiments on the other hand, measure the very small frequency shifts that the incident light undergoes as it is scattered from the particles in the sample. Quasielastic scattering is actually an older term used to describe what is now well known as dynamic light scattering (DLS). The term DLS came to use because the technique studies the dynamics of molecular motions as opposed to the static light scattering technique (SLS) which takes measurements under steady state or static conditions. More 19 specifically, in SLS, the scattered light is collected in time periods much longer than the time scale of motion of the particles. On the other hand, DLS measurements are done in time scales that correspond to the speeds of molecular motion. DLS Techniques There are two main classes of DLS techniques. Both categories essentially measure the frequency distribution of the scattered light. The older technique directly measures the frequency distribution by placing a monochromator ("filter") before the PMT detector. The more common approach now is to use a digital technique that uses photon correlation to measure the time dependence of the intensity of light scattered by the medium. The rate at which the intensity of the scattered light fluctuates about its average value depends on the rate of diffusion of particles in solution. One can rapidly and accurately obtain, in situ, a value for the diffusion coefficient. This value can be calculated from either the linewidth of the spectral density profile of the scattered light intensity or the autocorrelation function of the photo multipler tube (PMT) current. The latter method is employed in our analysis of the signal from the PMT. The technique of dynamic light scattering has emerged as such a strong experimental method that there are a number of variations of the DLS method that have been used for specific purposes. Electrophoretic light scattering or Doppler shift spectroscopy refers to the DLS experiment 2 0 where a square-wave electric field is applied across the sample. Laser Doppler velocimetry refers to the DLS technique in the presence of a laminar-flow field. Quasielastic light scattering is the term used to describe experiments that do not involve electric or hydrodynamic flow fields.^ And then, there is photon correlation spectroscopy - used in my work - which is actually a method of quasielastic light scattering with the use of a digital signal via photon counting. This replaced the now almost defunct method of using an analog signal to transfer data on scattered intensities to a correlator. Historical Developments The static light scattering technique has been used as a major method of polymer analysis by industry since 1944.1 W eight-average molecular weights, radii of gyration, virial coefficients and molecular conform ations in dilute solution were obtained through this steady state or static technique. However, the use of light scattering to study the dynamics of molecular motion in solution - the dynamic light scattering technique - did not emerge until about 20 years later. Now, the DLS technique is routinely used to measure diffusion rates, hydrodynamic radii and polydispersity of polymers in solution and is employed in the commercially available particle size analyzers. It has been known since the beginning of this century through the works of Smoluchowski (1908) and Einstein (1910) that fluctuations in the 21 density of particles in solution result in local inhomogeneities that lead to scattering of light at angles other than in the forward direction. In the ensuing research conducted over the next few decades, attempts were made to study the spectral density profile of the scattered light in order to extract vital information regarding the molecular dynamics. In 1964, Pecora showed that the frequency profile of the scattered electric field was broadened by the diffusion processes of polymers. He showed that the half-width at half-height of the central peak was a direct measure of the translational diffusion coefficient. In the same year, Cummings et al. published the first experimental report of using lasers as the source for the study of polymers in solution. Early applications of the DLS technique focused on determining the molecular weights and shapes. The highly successful results were a major contributor to the acceptance of the DLS method by the scientific community in the mid-1970s. Technological advances have helped in the building of better instruments which have given more accurate and precise data. Data analysis has been made rapid and easy with the use of com puter technology. For instance, the data acquisition and analysis in the DLS experiments that I carried out in our laboratory was completely automated. The intensity of the scattered light was measured by a PMT which transferred its signal to a Correlator Card(BI9000AT); the autocorrelation functions generated by the correlator software were then transferred to a curve fitting program that was installed in an IBM PC which plotted the translational diffusion coefficient versus time. 2 2 The Theory of Dynamic Light Scattering The concepts underlying the principle of dynamic light scattering can be presented in a very simplistic manner using a Doppler-shift description. Although clumsy for detailed calculations, it gives a general physical picture sufficient to grasp the fundamentals of light scattering spectroscopy. When a beam of light is incident upon a suspension of particles in solution, the particles will scatter light. We know that these particles are not stationary and that they continuously undergo Brownian motion. Therefore, when incident light with frequency co impinges on these particles travelling with a velocity v, the scattered light will have a shift in its frequency. This shift, commonly called the Doppler shift, is proportional to the velocity, vj, and the scattering vector, k, of the particles. Since k.vj is different for each particle, the frequency of the scattered light will be a symmetric spread Aco centered on (o. The frequency shift depends on the diffusion coefficient. Specifically, Aco is inversely proportional to the time required for a typical particle to diffuse through a distance of one light w avelength. The principles underlying the phenomenon of light scattering can be explained both classically and quantum mechanically (using quantum field theory). I will pursue the former less complicated explanation that uses classical electromagnetic theory. 23 Particle Motions that Lead to Fluctuations in the Intensity of the Scattered Light The intensity fluctuations that accompanies light scattering arise from the positions and motions of the scattering particles. The classical description of light scattering presented here is based on the Rayleigh- Gans-D ebye theory. The electric field of the incident light can be written as E(r,t) = E0 exp[i(q.r - cot)] (3.1) where r is the position of the particle, to is the incident frequency and q is the scattering vector given by q = (4 7t / A ,) sin (0/2) (3.2) The electric field of the scattered light from a suspension of N particles can be given as E(q,t) = E0 £ cxj exp[i(q.rj - cot)] (3.3) where Eo is the magnitude of the electric field, a j is the scattering efficiency of particle i. The intensity of the scattered light can be obtained by using the relationship I(t) = E(t) E(t) and equation (14) above. I(t) = IE0^I {X (i=l to N) a i^ + Z(i=l to N)L (j=l to N) a j a j exp(i q.(rj - rj)j (3.4) 24 On closer observation of the above equation for I(t), one could see the physical origin of the intensity fluctuations. These physical factors are: 1. Diffusion of the scattering particles that causes them to move with respect to each other which changes ri - rj and thus results in fluctuations in I(t). 2. The variation of the scattering amplitude oq with time. This effect is prominent in the "depolarized" or "VH" spectrum, in which the vertical light is polarized and the horizontal component of the scattered light is observed. This gives information on the rotational diffusion of the molecules. 3. The change in the number of particles in the scattering volume, N, because of Brownian motion of particles that will move in and out of the illuminated path. This effect, however, is very small because the relative changes in N are extremely small and they occur very slowly. The intensity fluctuations measured in a DLS experiment are then analyzed with the use of correlation functions. C o rrelatio n F unctions The need for it: W ave interference yields information on the particle size whenever the wavelength of the incident light is of the same order of magnitude as 25 the size of the scatterer. Before the advent of lasers, most scattering studies were done using the time-averaged scattered intensity. This average time is also called the correlation time of the intensity fluctuations of the scattered light. A light scattering spectrometer essentially measures these correlation times. It should be quite obvious that the slower the diffusion of the scatterer the longer the correlation time. (The correlation time is a direct measure of the translational diffusion coefficient.) The scattering intensity from say, a polymer solution fluctuates with time. Since the macromolecular particles move in solution, the scattered light contains a range of frequencies due to the well known Doppler broadening effect as was explained before. If the frequency of the incident light was coo and the intensity fluctuates over a time period on the order of x, then the scattered light must have a power spectrum with a frequency range c o q ± (27TU)'l. If the profile of the scattered intensity can be measured within this range o f frequencies then we have the necessary data to calculate the diffusion information. One might think that this is simply a matter of using a grating monochromator that would measure the intensities at different frequencies in the range under investigation. Unfortunately, the resolution required for such an experim ent is beyond any classical optical instruments. Let's see why this is the case. The frequency of visible light is around 5x10^4 Hz and the intensity fluctuations occur in the 1 to 10"8 second time scale. The scattered light therefore, must have a spectral line width of 0.2 to 0.2x10^ Hz. In order to measure this line width one needs a spectrometer with a 26 resolution of 3x10^ to 3 x 1 0 ^ . The lower end of the range is possible with a good interferometer. However, the higher end of resolution needed for an accurate study is impossible with classical optical spectroscopy. Given the experimental difficulties mentioned above, one could resort to an alternative approach of measuring the fluctuations in the scattering intensity versus time. Then with the use of the intensity- intensity correlation function one could effectively obtain diffusion rates as will be shown in the sections to follow. Fluctuations and Time-Correlation Functions Since its introduction by Wax in 1954, the theory of noise and stochastic processes has been used in many areas of statistical physics and spectroscopy. This has been done through the use of correlation functions. The scattered intensity values from light scattering experiments also fall into the catagory of time-dependent correlation functions and hence the use of them in analyzing data from DLS experiments. Since the system investigated in light scattering is at equilibrium, the measured intensity of the scattered light is a time average and thus can be expressed as: < I(to) > = Lim. (T-> oo) (1/T) Jto t o + T dt I(t) (3.5) It can be shown that the average of I(t0) is independent of to. Therefore, the average value of I(t) can be written as 27 = Lim. (T-> oo) (1/T) loT dt I(t) (3.6) In general, I(t) I(t+x). The values of I(t+x) become very close to I(t) when x is very small compared to the times that are typical of fluctuations in I(t). As x increases the deviation of I(t+x) from I(t) becomes greater. One can infer from this that I(t+x) is correlated with I(t) when x is small and that the correlation disappears as x gets large compared to the period of the fluctuations. A measure of this correlation can be expressed in terms of a correlation function of the scattered intensity which is given by = Lim. (T-> oo) (1/T) JoT dt I(t) I(t+x). (3.7) Since I(t+x) is only a delayed form of l(t), the relation is called autocorrelation. The autocorrelation function, , is a real quantity and can be measured in a standard DLS experiment. Now let us see how this autocorrelation function of the signal from the light scattering experiment behaves so that we could extract information on the dynamic properties at the microscopic level. The following discussion will show that this time-correlation function changes with time giving us vital information on the molecular motions. The ensuing analysis of the autocorrelation function is carried out by replacing the continuous integrals in the two equations above with a discrete notation for sake of clarity. The first step is to divide the time axis into intervals of At such that t = jAt; x = nAt; T = NAt. If At is picked to be very small we can assume safely that the value of I(t) does not change 28 appreciably. Now we can approximate the values on the R.H.S. of equations 3.6 and 3.7. = N-> oo Lim (1/N) X(j=l to N) Ij (3.8) = N-> oo Lim (1/N) X(j=l to N) Ij Ij+n (3.9) where Ij is the value of I(t) at the beginning of the jth interval. As one m ight expect the sums in the above two equations get closer to the infinite time averages in equations (3.6) and (3.7) as At -> 0. Note that many of the values of the Ij Ij+n terms in equation (3.9) are negative. Further, the Ij Ij terms are all positive and thus we can say that 10=1 toN) lj2 > £0=1 toN) lj Ij+n (3.10) or > . (3.11) This means that the autocorrelation function either remains constant at its initial value for all times x (true for a conserved quantity) or that it decays from its original value. For the case of scattered light from the DLS m easurements made in our laboratory, the latter is true. For times x large com pared to the time for the fluctuation of I, the intensity of scattered light, I(t) and I(t+x) become uncorrelated. This can be expressed as lim x->°o = < 1(0) > < I(x) > = 2 29 and thus the time-correlation function of I(t) decays from <I2> to 2 . The correlation time corresponding to this decay gives us the diffusion coefficient of the polymer chains. This relationship will be established later in this chapter. The correlation time of I(t) is defined as tc = lo°° dT (<8I(0) 8l(x)>) / <5I2> (3.12) where 5l(t) is the fluctuation in the scattered intensity, I(t) and is given by 8l(t) = I(t) - . (3.13) The autocorrelation function of many of the properties, including light scattered from monodispersed dilute polymer solutions in general, have single exponential decays and this can be expressed as = 2 + { <I2> - 2 ) exp(-T /xr) (3.14) or <81(0) 8I(t)> = <8I>2 exp (-x /xr) . (3.15) For this special case of single exponential decay, Xc is equal to Xr, the characteristic decay time, or what is often referred to as the "relaxation time". O f course, for non-exponential decay, the correlation time and the relaxation time become different. 30 The Relationship between the Correlation Function and the Spectrum of the Scattered Light The relationship between the correlation function and the molecular properties will be established in this section. Rotational and other internal molecular motions are not considered in this description. If I(t) is the scattered intensity at time t, then is the ensemble-averaged intensity-intensity correlation function for which we will use the symbol G(2)(t). G(2)(t) = < l(t) l(t+x)> = JoT dt I(t) I(t+x) (3.16) The electric field autocorrelation function of the scattered light, g O )(t) can be written as g O )(t) = <E(t)E(t+x)> (3.17) Since I(t) = <E(t)E*(t)> , using equations (3.16) and (3.17) we get G(2)(t) = l g O)(t) I2 + 2 (3.18) From equation (3.3) one can deduce that the electric field generated by the scattered light is proportional to the qth spatial Fourier component aq(t) of the concentration of scattering particles. aq(t) = E (i= l to N) aj exp[i(q.ri] (3.19) From equations (3.3) and (3.19) we have G O )(t) = I E q 2 I < aq(t) a-q(t+x) > (3.20) 31 As shown in equation (3.19), aq(t) is a sinusoidal concentration fluctuation. The Onsager regression hypothesis states that on average, a random fluctuation in a variable obeys the macroscopic relaxation equation for the decay of nonequilibrium values of the same variable. The relaxation of a macroscopic concentration gradient is described by Fick’s law; the Onsager regression hypothesis indicates that the microscopic concentration fluctuations produced by Brownian motion also decay in accordance with Fick's law. Fick's law of diffusion states that the diffusion flux is given by where D is the diffusion coefficient. The conservation equation is given as From equations (20) and (21) we see that the sinusoidal concentration distribution J = -D Vc (3.21) dc/dt = - V. J (3.22) c(r,t) = c0 + aq(t) cos(q.r) (3.23) decays as 0c(r,t)/5t = -D 0 k^ aq(t) cos(q.r) (3.24) The solution to this equation is aq(t) = aq(0) exp(-Dq2t) (3.25) From this result we can express g O )(t) as 32 GO)(t) = exp(-Dq2x) (3.26) where = lEo2 ! < aq(0)^ >. Therefore, G(2)(t) = A exp(-2Dq2x) + B (3.27) where A = <I2> - 2, and B = 2 According to the W iener-Khintchine theorem, the correlation function G (2 )(t) and the optical power spectrum S’ (co) are a Fourier transform pair, i.e., G(2)(t) = (1/2 7c) -0 0J 0 0 dco S'(co) exp[27ti(OTj (3.28) and S'(co) = -ooj°° dx G (2 )(t) exp[-27ti(ox] (3.29) If G(2)(t) is exponential, as is the case for macromolecules in dilute solution, the power spectrum becomes a Lorentzian: S'(co) = (1/re) [4 D q2 A / ( (O 2 + (2D q2 )2 ) ] (3.30) Here 2D q2 is sometimes referred to as the linewidth of the spectrum. Since the members of a Fourier transform pair contain the same information, G (2)(t) and S'(o)) are both referred to as the "spectrum" of the scattered light. 33 Figure 3.1 A simplified schematic of the high temperaute laser light scattering apparatus. (A) Argon laser; (B) and (D) mirrors, (C) He-Ne laser used for alignment; (E) and (I) adjustable apertures; (F) Focus lens; (G) scattering cell assembly, (H) beam stop; (J) photomultiplier tube; (K) correlator and computer 34 The Instrument In general all light scattering experiments contain the same components and it is only in the specific details that they may vary. A schematic diagram of our instrum ent is shown in Figure 3.2. The Ar ion laser is operated at a wavelength of 453.5 nm with the power output being around 200 to 400 mW. The laser light is directed to a focusing lens and then is further focused by an iris before it enters the index matching vat which is filled with polydimethylsiloxane (PDMS), commonly called silicone oil. The use of PDMS (instead of the more com m only used toluene) was necessitated by the high temperatures (upto 120 0C) that had to be maintained during the experiment. A temperature bath of ethylene glycol was used to maintain the high temperatures. The focused laser beam then enters a cylindrical scattering cell which is placed in the center of the vat. The scattered light is measured at a constant angle of 45^ and is focused with an iris before it hits the PMT detector (Thorn EMI 9863B). The signal from the PM T is then passed through an Amplifier-Discriminator that uses TTL logic to pass the small PM T output current into pulses that are in an acceptable form of input to a digital correlator. The digital correlator used in our instrument was a BI-9000AT correlator card that was capable of having 522 channels. However, because of overlapping I managed to obtain only a maximum of 463 channels which was still much more than the typical number of channels 35 needed for a successful analysis. One could also have the first channel at only 25 ns giving this correlator the ability to measure very fast relaxation processes although they were not relevant in my case. The correlator card was connected to an IBM PC compatible com puter with an 80386 processor which had a least squares fitting program called 'merge' that was used to obtain diffusion rates from the curve fits to the data. Data Analysis The software program 'merge' which is used to obtain curve fits to the intensity correlation fuctions is based on Koppel's cum ulant analysis^- Since the scattering angle was kept constant, the diffusion coefficient is obtained directly from the first cumulant. The diffusion coefficient is related to the hydrodynamic radius (Rh) through the Stokes-Einstein relation, i.e., 6TCT|Rh where k is the Boltzman constant, T is the temperature and r| is the solvent viscosity. Through the relationships established above, one can see how one could measure the increase in Rh by the use of correlation functions. This was the basis for the use of the DLS technique coupled with the use of the inensity-intensity autocorrelation function to obtain growth rates (changes in Rh) of polymer crystals in my experiments 36 References 1. Howard G. Barth and Jimmy W. Mays, Modern Methods of Polymer Characterization, p377, 1991. 2. Kenneth S. Schmitz, Dynamic Light Scattering by Macromolecules, p2, 1990. 3. Ibid.p8 4. Koppel, D.E., J.Chem. Ptiys. 1972, 57, 4814 5. Chu, B. Laser Light Scatteering', Academic, New York, 1974 6. Berne, B.J. and Pecora, R, Dynamic Light Scattering, Wiley, 1976 7. Ford, N .C ., Modern Methods of Polymer Characterization, Wiley, 1991, pp 20-25. 8. Flippen, R.B., Modern Methods of Polymer Characterization, Wiley, 1991, pp 379,383. 9. Phillies, G.D.J., Optical Methods of Analysis, pp 45-65 37 C hapter 4 E xp erim ental A spects and R esults In order to study the growth of cystals from solution, one needs to provide some nucleation sites for the polymer chains to deposit on. The samples used in the DLS experiments must be extra clean and free of dust. The scattering tubes have to be scratch free to avoid any unnecessary scattering. Thus one has to provide alternate nucleation sites since dust particles or scratches on the wall that usually tend to provide the necessary nucleation sites are absent. Therefore, seeds of PEKK had to be either simply added externally to the polymer sample in the scattering cell or created through heterogeneous nucleation in the sample itself so that it could undergo crystallization. There are three reported methods of preparing polymer seeds to act as nucleation sites for the solution crystal growth study. They are self-seeding, rapid quenching in liquid nitrogen and the droplet method. The first two of these were tried in my attempts of generating seed crystals of PEKK. The self-seeding method 1 is one of the oldest and most widely used methods for seed preparation. In this method, first, the polymer solution is brought to a crystallization temperature, Tc j . After the polymer chains are crystallized, the suspension is immersed in a thermal bath kept at a temperature above TC1 and below T<j, the crystal dissolution temperature to partially dissolve the crystals and leave suspended uniform seeds. Then the suspension is kept at a desired crystallization temperature, Tc2, where dissolved polymer chains will begin to deposit on the seed crystals. The 38 nuclei of these crystals are thought to be largely heterogeneous. A new technique was developed in our lab^ that produced uniform, small polymer crystal seeds of PEO. Instead of generating the seeds in the sample itself (as is the case in self-seeding), the seeds are made by rapidly quenching a polymer solution with liquid nitrogen and then allowing it to warm to a temperature above Tc but below Td. The suspension of seeds formed are very stable (for a couple of days at least), uniform and they can be made as small as 0.16 pm in diameter. Sample Preparation The M n and M w values for the samples of PEKK used were 10,100 and 23,800 respectively, which gave it a polydispersity index of 2.36. For any meaningful analysis of data from the DLS technique, one needs to obtain smooth correlation functions and for this it is important that the sample be extremely clean. Filtering the samples for dust had to be carried out at temperatures as high as 120 °C. This was neccessitated by the fact that the solvent crystallizes at 55 °C and that PEKK dissolved in the solvent at only 100 °C. The PEKK pellets were first placed in a scattering tube and hot (120 °C ) TCA was poured in through a filter funnel that had a 5 pm fritted glass disk. Since the filtration had to be done without crystallizing the solvent or filtering out the PEKK from solution, the filtration set up had to be put in an oven and maintained at around 120 °C during the filtration. Pressure had to be applied for the solvent to go 39 through the fritted disk at a reasonable rate. This was accomplished by placing the filter funnel in a metal chamber and pushing nitrogen through. The hot solution was filtered into a scattering tube that was free of scratches. The hot sample was then used to obtain the nucleation sites through self-seeding. The sample was first placed at about 70 °C in the vat for 5 minutes to allow for the seeds to form and then placed in a silicone oil temperature bath at 85 °C for about 5 minutes to partially dissolve the crystals. Finally, the sample was placed in the scattering cell at about 80 °C and correlation functions taken. Results and Discussion At the onset it must be emphasized that the experimental work done here is not com plete enough to come up with concrete statements as to the crystallization behaviour of PEKK from solution. Obtaining dust-free samples was quite a daunting task at these higher temperatures and in fact only a fraction of the samples were completely dust free to give meaningful intensity-intensity autocorrelarion functions. The correlation functions will usually have spikes that would indicate the presence of highly scattering dust particles in the PEKK polymer solution that did not get filtered. Since the hot filtration set up (mentioned in the previous section) did not consistently remove dust from the polymer samples an alternative method was tried. This entailed the use of a hot syringe and a 0.45 [im 40 polytetrafluoroethykene membrane. The PEKK pellets were first dissolved in TCA at 120 °C and then poured into the barrel of the syringe (maintained at 100 °C ) and filtered through the PTFE membrane into a scattering tube. Even this did not completely eliminate the dust problem. Initially, the self-seeding method was tried with samples kept for relatively short time periods (about 10 minutes) at the temperature where crystals were expected to be formed. No crystal growth was shown according to the data analysis and it was thought that seeds were probably not formed in the first place. Therefore, the PEKK samples were kept at the seeding temperature for very long periods of time (as long as 20 hours in some cases). The time periods for the other temperatures were unchanged. Obviously, we do not want to increase the time at which the seeds are partially dissolved for then we would end up dissolving all the seeds. However, even this does not seem to have helped in the formation of seeds. This prompted the rather drastic method (but sucessfully tried for linear polyethylene oxide) of creating the seeds by quenching the PEKK solution in liquid nitrogen. The whole sample froze and then it was allowed to warm to room temperature and kept for about four hours. The seeds were then placed at 68 °C for ten minutes to dissolve trichloroacetic acid and correlation functions were taken at 68 °C. The plots of 1/T versus time did not show any consistent increase in the Rh values that would have indicated crystal growth. The diffusion coefficients for the PEKK samples could however be calculated since the 41 value of 1/r was slightly scattered around a value of 5 ms. Using the relationships among T, D and Rh, the value of the hydrodynamic radius was calculated to be around 0.2 Jim. The values for the hydrodynamic radii for PEKK obtained under the different conditions mentioned above are consistent and plausible. Given the apparently constant values obtained for Rh even at the "initial stages of growing" crystals (at the very beginning of taking scattered intensity measurement), it is not ludicrous to suggest that polymer seeds were not formed in the first place, i.e., even at the supposed seeding temperature of 70 °C . However, the lack of any change in the Rh values shows that crystal growth was not observed. In order to make any firm statements on the nature of PEKK crystallization from solution, further in depth investigations have to be carried out. Obtaining polymer seeds seem to be the biggest problem faced during my investigations. A successful seeding technique is very important to the success of a crystallization study. There could be a number of reasons why crystal seeds were not formed. The absence of dust or other foreign particles (in the samples where successful correlation functions were obtained) from the solution and the scratch-free nature of the scattering tubes make the creation of nucleation sites very hard. Further, the solvent, TCA, might have very strong interactions with the PEKK chains thus reducing the probability of strong polymer-polymer interactions needed for crystal seed formation. There are reported cases of polymers not crystallizing even at 40 °C below its crystal dissolution 42 temperature (Td) under conditions mentioned above (i.e. typical DLS experimental conditions inside a scattering tube). With the lack of nucleation sites they become supercooled solutions. This could well be the case for PEKK in the TCA solvent. If PEKK remains as a supercooled solution as much as 45 °C below Td (Td is around 100 °C) then it would never crystallize because the frozen solvent at temperatures below 55 °C (m.p. of TCA) would not allow for PEKK chains to diffuse and form crystals. There are a few more experiments that one could try. A use of a different solvent might help in the formation of polymer seeds that would create the necessary nucleation sites for crystal growth. In this regard, trifluorophenol has been suggested. Further variation in the seed preparation methods might result in the successful obtaining of polymer seeds. For instance, one could try varying the temperatures and their time periods in the time-temperature cycle in the self seeding method. Obtaining uniform and stable polymer seeds seems to be a key to the study of polymer crystal growth and thus cannot be overemphasized. References 1. Blundell, D.J., Keller, A. Polym. Lett. 1966,4,481 2. Ni Ding PhD dissertation, University of Southern California, 1990 pp 42- 63 43 INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. 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The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand comer and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the back of the book. Photographs included in the original manuscript have been reproduced xerographically in this copy. 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Goonetilleke, Chevan
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A study of the solution crystallization of poly(ether ether ketone) using dynamic light scattering
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1995-08
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