Structural analysis of nanoparticles by small angle X-ray scattering

Structural Analysis of Nanoparticles by Small Angle X-ray Scattering Dissertation Zur Erlangung des akademischem Grades eines Doktors der Naturwissenschaften (Dr. rer. Nat.) in Fach Chemie der Fakult¨at f¨ur Biologie, Chemie und Geowissenschaften der Universit¨at Bayreuth vorgelegt von Christophe N. Rochette, M. Sc. geboren in Bordeaux, Frankreich Bayreuth, Donnerstag den 17. November 2011 Die vorliegende Arbeit wurde in der Zeit von November 2005 bis November 2009 am Lehrstuhl f¨ur Physikalische Chemie I der Universit¨at Bayreuth unter Betreuung von Herrn Prof. Dr. Matthias Ballauff angefertigt. Vollst¨andiger Abdruck der von der Fakult¨at f¨ur Biologie, Chemie und Geowissenschaften der Universit¨at Bayreuth genehmigten Dissertation zur Erlangung des akademischen Grades eines Doktors der Naturwissenschaften (Dr. rer. nat.). Dissertation eingereicht am: 17.11.2011 Zulassung durch die Pr¨ufungskommission: 15.12.2011 Wissenschlaftliches Kolloquiums: 14.05.2012 Amtierender Dekan: Prof. Dr. Beate Lohnert Pr¨ufungsausschuss: Prof. Dr. M. Ballauff (Erstgutachter) Prof. Dr. St. F¨orster (Zweigutachter) Prof. Dr. A. M¨uller (Vorsitz) Prof. Dr. B. Weber 2 This work is dedicated to Jean de Bertier, my Grandfather. 3 4 Contents 1 Introduction 8 2 Theory of SAXS 10 2.1 BasisofSAXStheory.............................. 10 2.2 Scattering function of monodisperse particles . . . . . . . . . . . . . . . . . 12 2.2.1 Spherical particles . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2.2 Disk-like particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2.3 Localfluctuations............................ 13 2.3 Polydispersity.................................. 13 2.4 Interparticle interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.4.1 Aggregation............................... 14 2.4.2 Polymer Reference Interaction Site Model - PRISM . . . . . . . . . 15 2.5 ContrastVariation ............................... 15 3 Generalities 17 3.1 Calcification................................... 17 3.2 Polybutadiene.................................. 21 3.3 Polyethylene................................... 22 4 Study of the early stage of calcification 26 4.1 Investigation of the early stage . . . . . . . . . . . . . . . . . . . . . . . . . 26 4.1.1 Materials ................................ 27 4.1.2 Experimental .............................. 28 4.2 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 4.2.1 Nucleation................................ 29 4.2.2 Structural effect of Fetuin-A onto the CPPs . . . . . . . . . . . . . 33 5 Polybutadiene 41 5.1 Experimental .................................. 41 5.2 Theoreticalmodeling.............................. 42 5.3 Results and Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 5.3.1 Cryo-TEM................................ 43 5 5.3.2 SAXS .................................. 44 5.4 Conclusion.................................... 46 6 Polyethylene 48 6.1 Experimental .................................. 48 6.2 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 6.2.1 Cryo-TEM................................ 49 6.2.2 SAXS .................................. 50 6.3 Variation of annealing temperature . . . . . . . . . . . . . . . . . . . . . . 53 7 Experimental 58 7.1 SAXS ...................................... 58 7.1.1 Kratky-Compact-Camera . . . . . . . . . . . . . . . . . . . . . . . . 58 7.1.2 ID02................................... 58 7.2 Dynamic Light Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 7.3 Densitometry .................................. 59 8 Summary 61 8.1 Calcification................................... 61 8.2 Polybutadiene.................................. 62 8.3 Polyethylene................................... 63 9 Zusammenfassung 64 9.1 Calcifizierung .................................. 64 9.2 Polybutadien .................................. 65 9.3 Polyethylen ................................... 66 Appendices 67 A Theory of SAXS 68 A.1 Effectofpolydispersity............................. 68 A.2 C++ programs.................................. 69 A.2.1 form factor of homogenous spherical polydisperse particles . . . . . 69 A.2.2 structure factor of the aggregation of spherical particles . . . . . . . 71 A.3 Modified hamburger model . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 B Additional experimental information 76 B.1 TEM pictures of calcium phosphate complexes . . . . . . . . . . . . . . . . 76 B.1.1 Without addition of Fetuin-A . . . . . . . . . . . . . . . . . . . . . 77 B.1.2 With 30 µMofFetuin-A........................ 78 B.2 WAXS signal of calcium phosphate complexes . . . . . . . . . . . . . . . . 79 6 B.3 Synthesis of the polyethylene nanoparticles . . . . . . . . . . . . . . . . . . 80 B.4 Influence of the annealing process on N V.................... 81 B.5 ContrastseriesofPL78............................. 82 B.5.1 Original system - PL78 . . . . . . . . . . . . . . . . . . . . . . . . . 82 B.5.2 System annealed at 90◦C........................ 83 B.5.3 System annealed at 105◦C ....................... 84 B.5.4 System annealed at 115◦C ....................... 85 B.6 SynthesisofsPB ................................ 86 B.7 X-ray diffraction of BK280 . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 B.8 DLSofBK280.................................. 88 B.9 Models investigated for the SAXS-CV of BK280 . . . . . . . . . . . . . . . 89 7 Chapter 1 Introduction During the last decades, Small Angle X-ray Scattering (SAXS) became a powerfull technique in colloidal science for the determination of shape, size and internal structures of nanoscale objects in the size range of few nanometers [1] up to about 300 nm [2]. Calcified particles have been extensively studied within the last decades [3–5]. Their formations are of importance for clinical reasons and are investigated from the second part of last century [6–8]. Amorphous calcium phosphate formation has been the subject of numerous investigations in the past concerning their structure [9,10], stability [9] and transformation into other crystalline phases [11]. However, the evolution of these complexes remains poorly understood. Few years ago, the formation of calcium carbonate precursor particles have been successfully presented by Time-Resolved-SAXS (TR-SAXS) [12] and it has been shown that a double hydrophilic block-copolymer is responsible of the slow down of the aggregation of these particles [13]. The authors of reference [12,13] demonstrated that the formation of calcified objects can be monitored and investigated as well by the help of TR-SAXS experiments. Lately, the interaction between proteins and calcium phosphate particles has been discovered [14,15] but no study investigated the earliest stage of calcium-phosphate formation up to that time [16,17]. The first part of this thesis is to investigate the formation at the earliest stage of calcium phosphate particles and to study the effect of a protein called Fetuin-A onto the calcification process. TR-SAXS by using a Synchrotron source was used to explore this formation. Polybutadiene is one of the most synthesized polymer system which is found for instances in tyres [18,19]. Since the Second World War, new syntheses in bulk of these sys8 2.5 Contrast Variation Theory of SAXS Ndenotes here the total number of particles. g(r) is the particle pair-correlation function and describes the probability of having two particles separated by a distance 2rfrom each other. By taking into account the size ξof the cluster, the pair-correlation function is rendered as: g(r) = A rd−dfe−r/ξ (2.19) where Ais a constant. Using the relation in equation 2.18 and performing a Fourier transform result to: S(q) = 1 + S0 [1 + q2ξ2](df−1)/2 sin[(df−1) tan−1(qξ)] (df−1)qξ (2.20) with S0defines as: S0=C(df−1)Γ(df−1)ξdf(2.21) where Γ(x) = ∞ Z 0 tx−1e−tdt (2.22) and C is a constant. Since lim x→0 sin(tan−1(x)) x= 1 (2.23) S(0)=1+S0defines the number of particles per aggregate. 2.4.2 Polymer Reference Interaction Site Model - PRISM The PRISM theory is derived from the Reference Interaction Site Model (RISM) developped by Chandler and co-workers [40–44]. In this part, only the general aspect behind the RISM will be describe. The PRISM bases on liquid state integral equation theory which was originally developped for atomic and small molecule fluids [45]. Given an interparticle potential, the theory provides an interparticle pair correlation function. This pair correlation function is connected with the structure factor S(q) measured in SAXS by Fourier transform. In the particular case of this study, the PRISM describes the equilibrium structure and properties of polymers in bulk solution. The main approximation thereby is that all sides of a particle are equivalent. Thus the particle interaction problem is reduce to a simple problem. More information about the PRISM theory and application could be found in references [45,46]. 2.5 Contrast Variation The scattered intensity I(q) of an ensemble of N particles of volume VPin a volume V is given by: 15 2.5 Contrast Variation Theory of SAXS I(q) = N V(∆ρ)2V2 PP(q)S(q) (2.24) with ∆ρ=ρs-ρmwhere ρsand ρmdefine the mean electron density of the system and the medium. According to equation 2.24, varying the electron density of the medium ρm lead to different resulting intensities. Figure 2.3 displays a schematic view of the contrast variation technique: changing the electron density of the solvent corresponds to a change of the color of the background. There are two extreme cases: infinite contrast and zero contrast. At a contrast of ±∞ (case a and e in figure 2.3), only information about the overall size and shape could be obtained. When the electron density of the solvent is equal to one the mean electron density of the particle, then only the derivations, due to different internal contrast, are visible. Measuring the same system with different contrast lead to a complete investigation of the structure of heterogenous systems. In praxis, contrast variation is not often used in conventional SAXS due to the difficulty to change only the electron contrast ρmof the medium without modifying the structure of the investigated system in the same time. Figure 2.3: Schematic representation of the contrast variation. Different electron densities of the solvent help to detect substructures of the system. This method permits then to study the total structure and the different phases present in the analyzed particles in detail. ∆ρdefines the electron contrast of the studied system relative to the medium. 16 Chapter 3 Generalities 3.1 Calcification Calcification is the process in which the mineral calcium builds up in soft tissue, causing it to harden. The first appearance of biomineralization in History is documented in the Precambrian invertebrate Cloudina [47], a shelly tube-like fossil. In order to control this mineralization, potent inhibitors of spontaneous calcification must exist. The multiplicity of the existing phases of calcium phosphate complexes (see table 3.1) is as well an important parameter in the complexity of the chemical equilibrium engaged. Vertebrates, including Human, contain these phases which are found mostly eveywhere in the body (bones, ligaments and even muscles) but at different concentrations. The mechanism of regulation of calcium and phosphate concentration in the Vertebrates is really far from being completely understood. Phase Acronym Empirical formula Ksp Amorphous calcium phosphate ACP Ca3(PO4)2·xH2O - Dicalcium phosphate dihydrate DCPD CaHPO4·2H2O 1.87 ×10−7M2 Dicalcium phosphate anhydrous DCPA CaHPO49.2 ×10−7M2 β-tricalcium phosphate TCP Ca3(PO4)29.2 ×10−29 M5 Octacalcium phosphate OCP Ca8H2(PO4)6·5H2O 2.5 ×10−99 M8 Hydroxyapatite HAP Ca10(PO4)6(OH)25.5 ×10−118 M9 Table 3.1: Different phases of calcium phosphate complexes and their respective solubility products Ksp.Munit is mol/L. Data obtained from reference [48]. The understanding of the formation of calcium phosphate complexes is hardly investigated especially since the middle of last century. In 1967, Walton and co-authors demonstrated that Hydroxyapatite and Octacalcium phosphate may not be the initial phase of calcium phosphate complexes [49]. There is no doubt about the nature of precipitation of these ions at early stage of calcification but this initial product is still not precisely known and depends mainly on parameters such as temperature, pH or solvent. It is now generally 17 3.1 Calcification Generalities recognized that the first compound formed from soluble salts is a metastable precursor phase [48]. This precursor phase, also called Amorphous Calcium Phosphate (ACP), has been widely studied by changing the calcium to phosphate ratio [50], their initial molar product [6] or the experimental temperature [51]. Kinetic studies of the structuration of calcium phosphate complexes has been performed recently [52]. These authors mixed Dicalcium Phosphate DiHydrate (DCPD) with Calcium Oxide (CaO) and detected the formation of nanoHydroxyApatite (nano-HA) particles within few hours by the combination of X-Ray Diffraction (XRD) and Differential Scanning Calorimetry (DSC) measurements. The structuration of the initial calcium phosphate complexes (DCPD) is very similar to ACP according to the present study (see page 29 in chapter Calcification at early stage). Vascular calcification (VC), that is deposition of calcium phosphate mineral in cardiovascular tissues including arteries, heart valves and cadriac muscles, is often encountered in the developpment of artherosclerotic intimal lesions and is a common consequence of aging [53]. VC is positively correlated with increased risk of myocardial infarction and of dissection after angioplasty [54]. In 2000, Jono and coworkers demonstrated that different levels of phosphate regulates human smooth muscle cell calcification through a sodiumdependent phosphate transporter-sensitive mechanism and implicate this mechanism in the developpment of ectopic calcification in vivo [55]. Kinetically and structurally speaking, the formation of the precursor particles of calcium phosphates complexes leading to the precipitation of the ions is unclear. A huge number of scientific articles are proposing Monte-Carlo simulations in order to better interpret such a behaviour (see for instance references [56, 57]). Authors of reference [57] demonstrated that the solution may be divided into three regimes: the first one presents invidual monomers in solution, in the second regime, small clusters of monomers are forming and in the last case, large particles are formed. However, the calcification process is far much more complicated and it is evident that additional molecules play a significant role in the formation of teeth or bones [58]. The formation of calcium phosphate complexes has been investigated by using functionalized macromolecules as templates. For instance, Holt and coworkers [59] used β-casein phosphopeptides as stablising agent and demonstrated that the peptide covered nanoparticles of calcium phosphate. Enlow et al. [60] created an organized network of 20 nm diameter calcium phosphate nanospheres by the help of copolymers, Li [61] showed that β-cyclodextrin is the only macromolecule of this family which is able to stabilize the amorphous phase of ACP. In 2002, Combes and Rey studied the growth of calcium phosphate complexes in presence of BSA proteins and proposed a schematical representation of crystalline OCP covered by an adsorbed layer of BSA to prevent further growth of the nanoparticles [62]. The long way to understand the complexity of calcification is far from being achieved. 18 3.1 Calcification Generalities Figure 3.1: Model of the three domains of Fetuin-A. D1 and D2 remain of the Cystatin Superfamily while D3 has a structural homolgy with an insertion domain. Picture taken from reference [63]. Since some years, the properties of a particular protein are of remarkable interest in the field of mineralization: α2-HS-glycoprotein (ahsg) also called Fetuin-A (see structural model of the protein in figure 3.1). The name α2-HS-glycoprotein refers to the fact that this protein migrates with the α2fraction of serum proteins upon traditional cellulose acetate paper based electrophoresis. H and S reminds of Heremans [65] and Schmid [66], Figure 3.2: Hypothetical model of a calciprotein particle (CPP) consisting of aggregated calcium-phosphate-Fetuin complexes. Figure taken from reference [64]. 19 3.1 Calcification Generalities Figure 3.3: Radiological analysis of 9-months-old mice. The mouse in the right is genetically deficient in Fetuin-A production while the one on the left is a wild type mouse. The lack of Fetuin-A is characterized by a strong calcification in extracelular space. Picture taken from reference [72]. the co-discovers of this protein in humans [67]. The name Fetuin is coming from the latin word fetus and has been given to this protein for its abundance in fetal calf serum [68]. Finally, this glycoprotein is called Fetuin-A after the recent discovery of a second Fetuin, Fetuin-B [69]. The abundance of Fetuin-A in bone suggests that the glycoprotein may have a role in bone formation or remodeling. In 1996, Schinke and coworkers [70] were the first to suggest a possible role of inhibitor in mineralization for this protein. In the following years, it has been shown that Fetuin-A acts as a systemic inhibitor of calcification [15,71] and that Fetuin-A is responsible of the formation of a Fetuin-mineral complex called calciprotein particle (CPP [64]). An hypothetical model of CPP is displayed in figure 3.2. A recent work [72] showed that mice genetically modified not to synthesize Fetuin-A displayed after 4 months a severe systemic calcification phenotype (see figure 3.3). The first part of this thesis will present a study of the influence of Fetuin-A onto the earliest stage of calcification by the combination of time-resolved SAXS measurements, dynamic light scattering and transmission electron microscopy. 20 3.2 Polybutadiene Generalities 3.2 Polybutadiene Depending on the structural variations of the components in the polymeric materials, the chemical structures of polymers is subject to change. Polybutadiene (PB) consists of three isomeric units: cis-1,4, trans-1,4 and 1,2-vinyl. Furthermore, the 1,2-vinyl structure has three possible sequence arrangements along the backbone chain: isotactic-, syndiotactic and atactic-1,2 units [73,74]. Other catalyst systems that can produce syndiotactic polymers with controllable constitution and configuration have been used and some works on synthesis, thermal behavior, crystallization, structure and morphology of syndiotactic polybutadiene (sPB) have been published [75–79]. sPB is a thermoplastic elastomer of industrial interest due to its properties of both plastics and rubbers. This polymer may be found in “packaging breathing” items for fruits, vegetables and seafood because of its higher carbon oxide gases and oxygen permeability and better resistance against wetting and slippage, in molding application such as molded bottles, adhesive, oil paint, photosensitive resin, plastic materials, tire treadings in adhesives or in footwears for instance [80, 80, 81]. The adjective syndiotactic means that crystalline sPB has a stereoregular structure in which the side-chain vinyl groups are located alternatively on the opposite sides in relation to the polymeric main chain. Figure 3.4 presents a schematical representation of sPBD. Figure 3.4: Schematical representation of syndiotactic 1,2-poly(1,3-butadiene). We note a regular alternation of the CH-CH2bond behind and before the plane of the acyl chain. sPB was first synthesized by Natta [82] in 1955 and its structure was determined one year after by the help of X-ray diffraction [83]: orthorhombic packing (Pacm, a=10.98 ˚ A, b=6.60 ˚ Aand c=5.14 ˚ A). Such polymers samples are now synthesized with a purity of 1,2 content of 97% (see e. g. reference [84]). Up to now, little attention has been paid to the structuration of nanoparticles of sPB [74,85,86]. Using an in-situ cobalt catalyst [87], very small semicrystalline nanoparticles of sPB could be synthesized (see synthesis of these nanoparticles in appendix page 86). These particles have a diameter of the order of 14 nm and do present a crystallisation percentage around 50% [20]. The second part of this thesis is to present the structural analysis of these sPB nanoparticles by using the combination of SAXS and cryo-TEM experiments. 21 3.3 Polyethylene Generalities 3.3 Polyethylene Crystallization of polyethylene (PE) is among the classical subjects of polymer science. In 1957, Till [88], Fisher [89] and Keller [90] independently demonstrated that PE crystallizes by chain folding leading to a lamellar structure. In order to initiate the spontaneous formation of chain-folded lamellae, the crystallization temperature needs to be high enough to permit the requisite molecular motions. In the special case of surface nucleation, the lateral surface free energy σcould be written as [91,92]: σ=T∆hf Tm a0 2 lb lu 1 C∞ (3.1) where ∆hfis the heat of fusion, Tmthe melting point, a0the width of the chain, lbthe bond length, luthe C-C distance and C∞is an empirical parameter determined to 6.7 for the special case of polyethylene [93]. Two different types of folds are described in the literature [93]: sharp-fold and tight-fold. The sharp-fold is defined as an emergent chain that executes a transit to an adjacent where it re-enters the lamella of origin. The tight-fold is described as one emergent chain that re-enters within the lamella of origin with a mimal traverse length with little amorphous contribution (See the schematical representations in figure 3.5). Figure 3.5: Schematical representation of sharpand tight-folded chains of crystalline polymers. The kinetic of the growth of the crystallites along the lateral axis depends mainly of the reptation in the melt. The reptation refers to the deformation of the chains so as to create the fold itself. This reptation highly depends on the viscosity ηwithin the amorphous phase of the polymer and thus on the molecular weight of the polymer. For the case of polymers with high molecular weight, the reptation may occur on different parts of one chain and, after a critical period of time, the resulted structures may be removed leading to a decrease of the kinetic of the growth of the cristallites. The reader may refer to part II of reference [93] for more details about the reptation. 22 3.3 Polyethylene Generalities Solution-grown crystals of PE usually have lateral dimensions of the order of some micrometers and are difficult to handle. At low temperature, PE crystals precipitate on cooling to form platelets which have the appearance of a lozenge [94]. Such a morphology could be explain as shown in figure 3.6 [95–99]: The faces 100 disappear as they grow faster than the 110 resulting to a lozenge shape. In the literature, the crystalline thickness of PE varies between 10 and 20 nm and a correlation between the inverse of this thickness and the temperature of the synthesis has been found [100]. Figure 3.6: Schematic growth of a nascent PE nanocrystal. The faces 100 disappear as they grow faster than the 110 (left), resulting to a lozenge shape (right). The letter G refers to the growth along the face. During the last decades, the mechanism of recrystallization of lamellar PE crystals after melting has been extensively studied [101,102]. However, the process in which recrystallization occurs is not yet fully understood. In 1975, Windle analyzed the annealing of multi-lamellar PE crystallized in solution by an X-ray diffraction study and suggested an asymmetric step-like thickening of the crystalline phase [103]. Twenty years ago, Sadler and Spells demonstrated by the combination of neutron scattering and infrared spectroscopy that a localized solid-state transformation is involved during heating close to the melting temperature [104, 105]. In 1997, Rastogi and coworkers showed that PE crystalline lamellae are doubling in size during annealing and explained it by stacking of crystalline adjacent lamellae [106]. In 2001, microscopic studies [107] show that the annealing process may occur at temperature slightly above the crystallization temperatures and far below the melting temperatures of the crystals. However, none of these studies explain the morphology of swiss-cheese-like shapes observed after the annealing of lozenge-like crystalline PE particles [101]. Most of the previous studies so far have been performed on PE bulk or by means of macroscopic PE crystals. Up to the end of last century, polymer latexes were polymerized exclusively by freeradical processes [108,109]. Since the begining of the 21st century, a new route of polymer23 3.3 Polyethylene Generalities ization of PE particles emerged: catalytic polymerization in aqueous dispersion [30–32]. Stable aqueous dispersions of surfactant-stabilized polymer nanoparticles in the range of 50 to 500 nm diameter are obtained. In 2007, Weber and coworkers [33] presented a complete analysis of these PE nanoparticles by using a combination of cryo-TEM and SAXS experiments. These particles consist of a remarkably thin crystalline single layer of PE (6.5 nm) sandwiched between two amorphous polymer sheets (“nano-hamburgers”). Thermodynamically, the formation of the polymer crystallites had become of a strong interest in the last few years [110,111]. In 2009, Strobl proposed an hypothetical scheme (see figure 3.7), depending exclusively on the temperature T and on the number of structure unit per crystalline chain n, that might explain the formation and recrystallization of polymer crystalline particles [34]: A precursor formation of a mesomorphic inner structure (point (1) in figure 3.7) occurs and polymer chains rearrange themselves to quasi-stretched conformations but not close enough to each other to form a density equivalent to the crystal itself (between points (1) and (2)). Once the stretched chains reach a certain limit, the layers thicken to form the native crystalline phase (point (2)). The passage from the crystallization line up to the recrystallization one is still matter of debate. In 2005, Strobl assumed that no elongation of the crystalline thickness occurs during the annealing while, Figure 3.7: Thermodynamic scheme of polymer crystals proposed in literature [34]. n defines the number of structure unit per crystalline chain, see text for further explanations. This scheme is still under debate especially the pathway from point 2 to 3. 24 4.2 Results and discussion Calcification at early stage size around 100 nm. Due to the experimental procedure, the earliest DLS measurements were achieved ca. 30 seconds after the mixing process. No change in the size of the formed particles were visible during the first four hours after the mixing process. Thus, DLS measurements do not permit to detect the nucleation of the primary particles. Figure 4.4: Evolution of the SAXS intensities with time in the abscence of Fetuin-A at the very early stage. The growth in intensity is characteristic of the nucleation phase, id est, the formation of the first precursor particles. The time point of measurement is reported in the legend. Time-resolved SAXS experiments by using a synchrotron source have been used in order to detect the formation of calcium-phosphate complexes. Figure 4.4 presents the scattered intensities recorded for the sample containing no Fetuin-A at the very early calcification stage, during the first 0.05 second. There are two main points: a growth in intensity at all q-values which is characteristic of a growth of the number of particles. And there is absolutely no change in the shape of the scattered intensities, which means that the morphology and the size of the particles do not evolve. At q-values below 0.15 nm−1, the three earliest scattered intensities overlap themselves. This is attributed to the remaining flow in the capillary (quasi steady state not reached). This creates artefacts in the signal. No further change in intensity were seen for longer times meaning that the number of particles per volume stays constant. This shows the very fast kinetic of the nucleation of calcium phosphate particles. As well, no oscillation of the scattered intensities could be seen which is typical for a very high polydispersity in size of the system. The scattered intensities in figure 4.4 were obtained by changing the initial so-called dead-time, that is the time between the end of the mixing process and the time corresponding to the first measurement. The intensity I(q) is proportional to the number of particles per volume N V, to the square of the electron contrast of the system ∆ρand to the square of the volume of the particle VP(see equation 2.24 page 16). In the special case of nucleation, the 31 4.2 Results and discussion Calcification at early stage size of the system and its density are constant and the structure factor S(q) is equal to unity. The scattered intensity is then directly proportionnal to the number of particles per volume N V. The time-evolution of the scattered intensity at a certain q-value permits then to qualitatively study the nucleation process. At q-values below 0.15 nm−1, artefacts appear and they are attributed to the remaining flow in the capillary (figure 4.4). Data at q-values higher than ca. 0.45 nm−1are more subject to noise and these intensities will be later on attributed mainly to the density fluctuation of the amorphous system. It results that the nucleation of this system could be studied by following the scattered intensities recorded between 0.15 and 0.45 nm−1. Figure 4.5: Time-evolution of the intensities collected at q=0.25 nm−1for the earliest SAXS intensities collected. The formation of the primary particles follows a kinetic of first order. The kinetic constant k is directly proportionnal to the slope and is decreasing with the amount of Fetuin-A. Data collected for the system without added protein (blue) is compared to the systems including 1 µM (red), 5 µM (black) and 15 µM (green) of Fetuin-A. Considering as first step the formation of dicalcium phosphate dihydrate (DCPD), and since the molar ratio used implies more calcium ions, the limiting ion during the formation of the precursor phase is HPO2− 4. Thus, the nucleation is directly proportional to the initial phosphate concentration and to the kinetic constant kof the first order. SAXS intensities at q=0.25 nm−1have been followed for each sample at the very early stage of calcification during the first 0.05 second and are displayed in figure 4.5. The constant k is directly proportionnal to the slope of these sets of data. Within the limit of error, it seems evident that Fetuin-A has an influence from the very begining of the nucleation process: The lower the kinetic constant, the higher amount of the glycoprotein (see figure 4.5). 32 4.2 Results and discussion Calcification at early stage Figure 4.6: Influence of Fetuin-A onto the size of the CPPs. The DLS setup was thermostated at 37◦C and 1.8 mL of calcium solution (with the appropriate concentration of Fetuin-A) was inserted in a glass cell. A solution of phosphate ions was as well thermostated at 37◦C and 0.2 mL of this solution were inserted in the cell. The solution was then mixed by hand and the DLS measurements started ca. 30 seconds after the mixing process. The final concentration of calcium and phosphate ions was respectively 10 mM and 6 mM. The system without added protein (dark blue) is compared to the ones with 1µM (red), 5 µM (black), 15 µM (green) and 30 µM (light blue) of Fetuin-A. 4.2.2 Structural effect of Fetuin-A onto the CPPs In this part, a comparison between the results obtained in reference [17] and the data recorded in presence of different amounts of Fetuin-A from 1 µM up to 15 µM, the latter corresponding to a physiological concentration of the protein, will be realized. Size of CPPs in presence of Fetuin-A In this paragraph, the ionic concentration of calcium and phosphate are the same than in the work of Heiss [17]. The effect of the overall size of the CPPs have been investigated by using DLS measurements and is presented in figure 4.6 page 33. A drastical change in the size of the particles is observed. None of the experiments involving 10 mM of Ca2+ and 6 mM of PO3− 4led to a mean hydrodynamic radius of less than 20 nm. Table 4.1 presents the different mean value of the hydrodynamic radii obtained when 11.1 mM of calcium and 60 mM of phosphate ions are mixed (volume ratio 9:1 to get a calcium-to-phosphate ratio of 10/6) in presence of different concentrations of the glycoprotein. The sizes reported in this table correspond to the ones once the first equilibirum state is reached, ca. 60 seconds after the mixing process. As expected by the work of Heiss and coworkers [17], there is a decrease of the sizes of the formed particles with the 33 4.2 Results and discussion Calcification at early stage increase of the concentration of Fetuin-A. Studies about the size of the primary particles is missing in literature. Additional experiments by DLS have been investigated in order to estimate this size. Single particles Figure 4.7: DLS measurements of CPPs obtained by mixing 10 mM of Ca2+ with 6 mM of PO3− 4. The influence of the addition of 4 µM of Fetuin-A (red) is well highlighted compared to the system without added protein (blue). In this paragraph, lower concentrations of calcium and phosphate ions have been used but the calcium-to-phosphate-ratio is kept at 10/6. As previously shown in figure 4.3 page 30, the weight fraction of calcium and phosphate ions have a strong importance onto the aggregation process. Several attempts of DLS measurements were realized by using different amounts of Fetuin-A. As an example, figure 4.7 presents the results of DLS measurements performed by mixing 10 mM of calcium ions with 6 mM of phosphate ions without any glycoprotein and with 4 µM of Fetuin-A. [Fetuin-A] (µM) RH(nm) 0>1000 1 150 5 90 15 70 30 45 Table 4.1: Hydrodynamic radius of the particles formed depending on the concentration of the glycoprotein. The mix was realized at 37◦C by using solutions of 11.1 mM of calcium (1.8 mL) and 60 mM of phosphate (0.2 mL). 34 4.2 Results and discussion Calcification at early stage At the exception of the system without any addition of protein, all measurements including 1 µM of FetuinA lead to a mean hydrodynamic radius of ca. 10 nm at room temperature and at 37◦C. These results are in agreement with TEM micrographs which were taken at room temperature for the systems without and with 30 µM of Fetuin-A (figure 4.8). Figure 4.8: TEM micrograph of a sample obtained by mixing 20 mM of Ca2+ with 12 mM of HPO2− 4without addition of Fetuin-A (left) and in presence of 15 µM of the glycoprotein (right). The left part of figure 4.8 presents a TEM micrograph of the system without any addition of Fetuin-A. Aggregates of spherical-like particles are observed. The spherical subparticles have a size of the order of ca. 10 nm and the size of the aggregate is of the order of ca. 50 nanometers. Some aggregates of more than one micrometer were as well observed on other areas of the grid (see in the appendix page 77). The right part of figure 4.8 presents a TEM micrograph of a sample obtained by mixing 20 mM of Ca2+ and 12 mM of HPO2− 4in presence of 15 µM of the glycoprotein. The general observation was the presence of single spherical-like particles with a mean size of the order of 10 to 20 nm. A very low number of aggregates of 2 or 3 spherical particles was found. They were suspected to be formed during the blotting of the excess solution by the help of a filter paper. Quantitative analysis SAXS experiments have been performed in order to quantitatively study the aggregation process highlighted by the help of DLS and TEM measurements. The top part of figure 4.9 presents the evolution of the scattered intensities of the sample containing no addition of Fetuin-A. A weak minimum around 0.3 nm−1and the abscence of oscillation in these intensities are characteristic of the high polydispersity of the system. This is in agreement with both DLS and TEM experiments. Scattering patterns older than 0.26 35 4.2 Results and discussion Calcification at early stage s did not present any change in the shape or in intensity (measurements realized up to 145 seconds). This demonstrates the very fast kinetic of mineralization of calcium and phosphate ions. Figure 4.9: Evolution of the SAXS intensities with time in the abscence of Fetuin-A. Later SAXS intensities did not show any evolution of the shape or the intensity. This underlines the very fast kinetic of early calcification leading to the first equilibrium phase of calcium phosphate particles. Time point of measurements are: 0.035 s (blue), 0.255 s (red) and 1.355 s (green) after the mixing process. Measurements realized by adding the glycoprotein gave similar data at q-values bigger than 0.3 nm−1. As an example, the figure 4.10 presents the evolution of the SAXS intensities recorded for the sample containing 15 µM of the glycoprotein, that is at physiological concentration. The main difference as compared to figure 4.9 in the trend of the scattered intensities is situated at small q-values. However, it is of course necessary to fit the SAXS intensities in order to get quantitative piece of information for the role of Fetuin-A onto the early stage of calcification. The fitting procedure was realized by assuming the primary particles as homogenous spheres by using equation 2.6 page 12 as expected from the work of A. Heiss using TEM experiments [64]. The polydispersity in size of the primary particles was taken into account by assuming a normalized Gaussian distribution. Due to the presence of an amorphous system (WAXS measurements in solution were realized and did not show any Bragg peak, see figure B.2 page 79 in appendix), it is necessary to add an additional term to simulate the thermal fluctuations according to the theory of Ornstein-Zernike (see reference [38]). This has been taken into account by the use of the equation 2.12 page 13. The up-turn at small q-values was quantified by the help of the structure factor (equation 2.23 page 36 4.2 Results and discussion Calcification at early stage Figure 4.10: Evolution of the SAXS intensities with time in the abscence (top) and in presence of 15 µM (bottom) of Fetuin-A. Later SAXS intensities did not show any evolution of the shape or the intensity. This demonstrates the very fast kinetic of early calcification leading to the first equilibrium phase of calcium phosphate particles. Time point of measurements are: 0.035 s (blue circles), 0.255 s (red squares), 0.695 s (black triangles) and 6.415 s (blue squares) after the mixing process. 15). The electron contrast of the calcium phosphate complex and of the Fetuin-A are determined respectively to 536 and ca. 50 e/nm3. Thus, it is assumed that the scattered intensities is only due to the calcium-phosphate complex. The resulting theoretical equation that has been used in order to fit the experimental scattered intensities I(q) is then: I(q) = N V(∆ρ)2V2 pS(q)[I0(q) + Ifluc(q)] (4.3) Figure 4.11 presents the scattered intensities collected 0.89 s after the mixing process for all samples studied. No additional structure factor was needed in order to fit the data of the sample involving 15 µM of Fetuin-A. Figure 4.12 present the structure factors S(q) resulting from the modelling of the SAXS data recorded 0.89 s after the mixing process. The figure 4.13 presents the evolution of the radius of the primary spherical particles Rpsp for all studied samples. A very fast kinetic is detected for all studied samples since within one second, the primary particles do not grow anymore. However, this kinetic is too fast to get a quantitative analysis of the growth of the primary particles. Quantitatively, the different radii of the primary particles are interesting: the higher the concentration of Fetuin-A, the bigger the primary particles. Such a result could not be determined just by the help of DLS or microscopic measurements. The figure 37 4.2 Results and discussion Calcification at early stage Figure 4.11: Experimental data of measured samples and their respective fits 0.89 second after the mixing process. The points represent the experimental data. For the sake of clarity, only one out of two points is reproduced. The dashed lines exhibit the theoretical fits of polydisperse homogenous non interacting spheres, including the thermal fluctuations and the full lines reflect the complete fit when the structure factor is needed. The graphic shows the different concentrations studied: 0 µM, 1 µM, 5 µM and 15 µM of Fetuin-A from bottom to top. Figure 4.12: Evolution of the structure factor S(q) obtained from the modelling of the SAXS data recorded 0.89 s after the mixing process. The up-turn at small q-values characterizes the aggregation of the nanoparticles. Mixes contain 0 µM (blue), 1 µM (red), 5 µM (black) and 15 µM (green) of Fetuin-A. 38 4.2 Results and discussion Calcification at early stage Figure 4.13: Time-evolution of the radius of the primary spherical particles of calcium phosphate as a function of the concentration of the protein. The primary spherical particles grow with a very fast kinetic within 1 s for all samples studied. The dashed lines are guide lines for the evolution of the radius of the primary spherical particles. Data involving a concentration of 1 µM of Fetuin-A are not reproduced for the sake of clarity and is intermediate to the one of 0 and 5 µM. Figure 4.14: Time-evolution of the number of primary spherical particles per aggregate (S(0)+1). The main effect of Fetuin-A is seen here: inhibition of the aggregation. The dashed lines are guide lines for the evolution of the parameters. Mixes contain 0 µM (blue), 1 µM (red), 5 µM (black) and 15 µM (green) of Fetuin-A. 39 4.2 Results and discussion Calcification at early stage 4.14 presents the time-evolution of the number of primary paricles per aggregate. This plot permits to better understand the role of Fetuin-A onto the calcification at early stage. As demonstrated by figures 4.11 and 4.12, there were no need to simulate any interparticle interactions in order to fit the system involving a physiological concentration of the protein (15 µM). The results obtained from the other studied concentrations of the glycoprotein show that the lower the amount of Fetuin-A, the bigger the number of particles per aggregate. This is the proof that α2-HS-glycoprotein/Fetuin-A is inhibiting the aggregation of the primary spherical particles of calcium phosphate and is stabilising these particles from the earliest stage of mineralization. According to the results found in this study and to previous work in literature [17], an hypothetical model of the formation of calcium phosphate particles induced by the presence of Fetuin-A could be described as follow: During the nucleation process, FetuinA has a weak effect until the primary particles grow to ca. 10 nm in radius. Once the nucleation process is ended, Fetuin-A may cover the calcium-phosphate particles and act as a shield to prevent aggregation. According to Heiss [64], the glycoprotein interacts with 6 different calcium ions (see figure 4.15), which is probably the way for the protein to create a layer of itself onto the calcified particles. Figure 4.15: Binding of the D1 domain of Fetuin-A onto the surface of hydroxyapatite. The positive charges of Ca2+ are marked in blue and the negative phosphate charges are represented in red. Figure taken from reference [63]. 40 5.4 Conclusion Polybutadiene of the different phases (crystalline, amorphous sPB and SDS) were let free. The best theoretical intensities were achieved with an electron density of the crystalline layer corresponding to a weight density of 0.962 g/cm3. This value is, according to Natta [83], the weight density of crystalline sPB. The electron density of the surfactant’s phase (SDS) was of the same order as the one determined for the polyethylene study (see next chapter). This underlines and confirms the veracity of the results obtained. The number of polymer chain per particle has been as well determined by the help of equation 5.4 page 43 and it resulted to only two polymer chains which is drastically lower than for the PE system studied in reference [33] where an average of 14 polymer chains were constituting each nanoparticle. 47 Chapter 6 Polyethylene 6.1 Experimental For this study (collaboration with Dr. Qiong Tong from the group of Proff Mecking, Konstanz), two different PE systems PL39 and PL78 were investigated due to the limited amount of each sample. The samples PL39 and PL78 contain 1.7 wt% and 1.6 wt% PE, respectively. The surfactant sodium dodecyl sulfate (SDS) is needed to stabilize the PE particles against coagulation. The weight fractions of SDS are 0.87 wt% for PL39 and 0.36 wt% for PL78. Hence, the amount of SDS in PL39 has been increased as compared to the previous study [33]. The PE systems differ in the labile ligand of the catalyst used during the synthesis (TPPTS for PL39, NH2-PEG for PL78, see additional piece of information in the appendix page 80). The longer lifetime of the catalyst with the NH2-PEG ligand results in the different amount of SDS during synthesis. This does not have a significant influence on either the molecular weight or in molecular structure of the obtained PE chains. Annealed samples were produced by placing a 5 mL glass bottle containing the original system onto a metal box heated at the annealed temperature for 20 minutes. PE nanoparticles annealed for longer time (up to 60 minutes) did not reveal any further increase of the thickness of the crystal. The annealed systems were slightly more concentrated since evaporation could not be completely avoided. Dynamic Light Scattering measurements were performed with an ALV/DLS/SLS-5000 compact goniometer system (ALV Langer) equipped with a He-Ne laser (632.8 nm) and a thermostat (Rotilabo, ±0.1◦C) at 25◦C. Diluted samples (0.0013 wt%) were analyzed from 30 to 80◦. According to the Stoke-Einstein equation, the hydrodynamic radius of each sample was determined respectively to 11.2 ±0.2 nm and 11.4 ±0.2 nm for the original and annealed sample. These light scattering experiments did not permit to detect any 48 6.2 Results and discussion Polyethylene difference before and after the annealing process. In order to have a better understanding of the morphology of the particles studied, cryogenic transmission electron microscopy experiments have been performed. 6.2 Results and discussion 6.2.1 Cryo-TEM Specimens for cryo-TEM experiments were prepared at room temperature as explained on page 42. The concentration used here was higher by a factor of 10 leading to 0.3 wt%. Figure 6.1 presents typical overviews of the cryo-TEM micrographs recorded of the Figure 6.1: Typical cryo-TEM micrographs of the original PL39 system (top) and of the annealed PL39 sample (bottom). Insets in each micrograph presents a single particle in which the direction of the main axis is orhthogonal and parallel to the direction of the electron beam. The annealing process was carried at 125◦C for 20 minutes. For both micrographs, the weight percentage studied is 0.3 wt%. 49 6.2 Results and discussion Polyethylene original system (top) and of the annealed one (bottom). These particles are well dispersed in the solution. Different morphologies could be remarked and this comes from the angle between the main axis of the particle and the one of the electron beam. The difference of contrast between one particle and another is related to different angles between the normal of the platelets and the direction of the electron beam. This is more prononced in the top-inset where the main axis of a single particle is parallel to the electron beam. Such particles appear as dark rods. At the opposite, the bottom-inset present a single particle in which the main axis is orthogonal to the direction of the beam. These particles appear as lighter hexagons. This hexagonal shape agrees well with the theoretical growth of PE nanoparticles (figure 3.6). The annealed nanoparticles (bottom micrograph in figure 6.1) present the same morphology as shown in the inset. However, a change appeared in the dimensions (radius and thickness) of the system. Derived from the image analysis of 20 particles with their normal oriented perpendicular to the electron beam, the height of the platelets was determined to 7 ±1 nm before and 13 ±2 nm after annealing and the platelet radii decreased from 14 ±4 nm to 9 ±2 nm respectively. One has to take into account that it is not possible to detect the amorphous layer of these PE nanoparticles because its electron density is very similar to the one of the surrounding medium (low density amorphous ice, [33]; light gray in the background represents the low density amorphous ice). In order to elucidate the shape and structure of the PE particles in more details, the systems have been investigated using SAXS and contrast variation technique. 6.2.2 SAXS SAXS experiments were performed at the ID02 beamline at ESRF, Grenoble, France and in Bayreuth by using a Kratky Compact Camera. Figure 6.2 presents the scattered intensities of the PL39 PE nanoparticles before (top) and after (bottom) the annealing process. The volume fraction of the contrast agent varies from 0% (blue points), 4% (red points), 10% (black points) up to 14% (green points), while the volume fraction of the nanoparticles decrease: 2.5, 2.4, 2.3, 2.2 vol% for the original system (top) and 2.6, 2.5, 2.3 and 2.2 vol% for the annealed sample (bottom) respectively. The three lowermost intensities are divided by factors of 10, 102and 103for sake of clarity. The theroretical SAXS intensities have been modelled by using equations 5.1 to 5.3 and are presented in figure 6.2. The solid lines represent the result of the non-interacting polydisperse disks. The short dashed lines (q<0.14 nm−1) are obtained using the PRISM integral theory. PRISM theory is well known to account for interactions of anistropic particles and surface charges. The difference between the dashed and the solid lines reflect the intermolecular interactions between the nanoparticles. The modelling including the interparticle interaction was realized by Priv.-Doz. Dr. Ludger Harnau. 50 6.2 Results and discussion Polyethylene Figure 6.2: Normalized scattered intensities of the PL39 PE system before (top) and after (bottom) the annealing procedure. All intensities are normalized by the volume fraction of the sample. The volume fraction of the contrast agent varies from 0 (blue points), 0.04 (red points), 0.10 (black points) up to 0.14 (green points), while the volume fraction of the nanoparticles decrease: 2.5, 2.4, 2.3, 2.2 vol% for the original system (top) and 2.6, 2.5, 2.3 and 2.2 vol% for the annealed sample (bottom) respectively. The three lowermost intensities are divided by factors of 10, 102and 103for sake of clarity. The vertical gray dashed lines show the q-value below which the structure factor is needed. For the sake of clarity, only one out of 5 points is shown. The dashed lines represents the result of the modeling of the SAXS data assuming a dispersion of non-interacting polydisperse platelets. The solid lines represent the scattering intensity calculated for a dispersion of interacting polydisperse platelets. 51 6.2 Results and discussion Polyethylene Evidently, and as expected by the cryo-TEM micrographs (figure 6.1), the annealing process changed the structure of the original system. There are more oscillations in the scattered intensities of the annealed system than in the one of the original PE nanoplatelets (see figure 6.2). One can note that the structure factor S(q) intervene only at long distances, i.e. small magnitudes of the scattering vector q, below 0.14 nm−1. This defines the average distance dbetween two particles with the equation d= 2π/q= 45 nm. This value remains constant before and after the annealing process. This demonstrates that the number of particles per volume is constant, thus no fusion of the particles occur during the annealing process. This is further confirmed by the fact that I(q=0)/[φ(∆ρ)2] is constant for the original and annealed system (see figure B.4 in the appendix page 81). The change of the morphology of the nanoplatelets can directly be seen by the SAXS data: the location of the side maxima and minima shift to lower qvalues after annealing. System Original Annealed R [nm] 10.0 ±3.0 7.5 ±3.0 Lc[nm] 6.5 ±1.0 13.0 ±1.0 La[nm] 3.1 ±0.8 3.8 ±1.0 Table 6.1: Parameters obtained from adapting equations 5.1 to 5.3 to the experimental data. Lcand Ladefine the overall crystalline and amorphous thickness of the particle. Table 6.1 resumes the parameters obtained by adjusting equations 5.1 to 5.3 to the experimental data of the original and annealed system (see figure 6.2). The thickness of the crystalline layer increases by a factor of 2 (from 6.5 to 13 nm respectively for the original and annealed system). The thickness of the amorphous layer remains nearly constant (respectively 3.1 nm and 3.8 nm). Within the limit of error, the radius decreases from 10 nm to 7.5 nm. By using a Gaussian polydispersity during the fitting of the SAXS data, the average number of polymer chain nchains has been determined according to equation 5.4 (ρcri=339 e.u./nm3and ρamo=302 e.u./nm3). This average number of polymer chains was determined to nchains=8 before and after the annealing process. The combination of the cryo-TEM experiments and of the SAXS contrast variation data permit to demonstrate that annealing the sample PL39 at 125◦C for 20 minutes leads to a doubling of the crystalline thickness (6.5 nm to 13 nm). In the literature, two scenarios of the thickening process are proposed. The first one is an unlooping of the polymer chains within one crystalline platelet (figure 6.3 (a), references [120,121]). Increasing the temperature leads to an increase of the chain mobility and to cooperative motion of the monomer units. This hypothesis leads to a surface of the crystalline phase divided by two as compared to the original system and to the same number of particles. The second model 52 6.3 Variation of annealing temperature Polyethylene explains the thickening by the stacking of two adjacent crystalline layers into one of the same surface and double thickness (figure 6.3 (b) and references [106,122]). Such a model is valid for systems in which the crystalline phases are connected by amorphous regions and lead to a number of particles divided by two. From the fitting parameters, there is a doubling of the thickness of the crystalline phase. Moreover, the number of particles per volume remains constant before and after the annealing process. This behaviour is characteristic of the unlooping model proposed by references [120,121]. Thus model (b) in figure 6.3 is ruled out. Figure 6.3: 2D-model of the unlooping process expected by some authors [106,120–122]. (a): The full unlooping process of one single crystalline nanoparticle lead to a doubling of the crystalline thickness of the same particle. (b): The stack of two crystalline particles lead to one particle with a doubled crystalline thickness. 6.3 Variation of annealing temperature The study of the effect of the annealing process has been presented in the previous section. Well-defined nanoparticles of polyethylene have been subject to a thermic treatment for 20 minutes at 125◦C, that is just below the melting temperature Tm=128◦C according to DSC measurements. The last section demonstrated that, during the annealing process, no fusion occurs and a simple unfolding of the crystalline chains is responsible of the doubling of the crystalline thickness. The PE nanoparticles are then particularly interesting to better understand the annealing process of PE crystalline phase. These experiments have been pushed forward by varying the annealing temperature to lower temperatures. The annealing process was carried at 90◦C, 105◦C and 115◦C for 20 minutes by using the sample PL78 due to the lack of sample PL39. Cryo-TEM experiments have been performed onto these samples by using the same setup as the system PL39 and the growth of the overall thickness is highlighted (see figure 6.4). A very broad polydispersity over the radius of the particles is observed as expected by the synthesis (use of a catalyst leading to a longer lifetime and stronger polydispersity, see appendix). Thus, cryo-TEM 53 6.3 Variation of annealing temperature Polyethylene micrographs only permit to insure that the nanoparticles are well-defined. Figure 6.4: Cryo-TEM micrographs of PL78 sample (original and different annealed temperatures). The black bar represents 50 nm. Figure 6.5: Two-dimensional schematical representation of partial unlooping of PE chains within a nanoparticle. A partial unlooping leads to a very small decrease of the radius R of the platelet, probably a decrease too small to be detected by SAXS experiments. However, it seems evident that the thickness of the crystalline phase increases with 54 6.3 Variation of annealing temperature Polyethylene the annealing temperature as expected. Because of these very small dimensions and this high polydispersity, the resolution of the SAXS experiments do not allow to determine precisely these radii. In the previous section, for the system PL39, the nanoparticles were fully annealed (the thickness of the crystalline phase fully doubled). Due to partial annealing, it is impossible to determine the precise location and amount of unlooped PE chains (figure 6.5). In combination with the given polydispersity of radius Rand the limited resolution of SAXS, the exact determination of the radius is impossible. Thus, for this system, a radius of 6 nm was kept constant during fitting routine. Nevertheless, it is still kept in mind that the number of particles per volume is constant and that the radius of each particle must slightly decrease with the annealing temperature. SAXS measurements have been performed by the same approach than for the PL39 system. Figure 6.6 presents the experimental data of the samples PL78 in water and their corresponding fits according to equations 5.1, 5.2 and 5.3 including the interparticular interactions given by S(q). The differences between the measured scattering intensities of the original sample PL39 (lower symbol in the top graphic of figure 6.2) and the original sample PL78 (lower symbols in figure 6.6) is due to the different amount of SDS added. Crystalline thicknesses of 6.5 ±1 nm, 8.5 ±1.4 nm, 10.2 ±1.4 nm and 11.8 ±1.4 nm resulted for the original system and the ones annealed at 90◦C, 105◦C and 115◦C respectively. The data of the whole contrast series are displayed in the appendix page 82 to 85. Figure 6.6: Experimental data and corresponding fits of the original sample PL78 dispersed in pure water (blue circles). The volume fractions of the systems are: 2.1 vol%, 1.6 vol%, 2.4 vol% and 2.6 vol% respectively for the original system (bottom) and the ones annealed at 90◦C (red squares), 105◦C (black triangles) and 115◦C (green circles). 55 6.3 Variation of annealing temperature Polyethylene Figure 6.7: Experimental data of the reciprocal of the crystalline thickness depending on the annealing temperature. The data with triangular and square symbols have been obtained from micron crystalls originally crystallized at T=85◦C and T=95◦C respectively [123]. The blue circles represent the data of this study (nanocrystals freely suspended). Figure 6.7 displays a plot of the annealing temperature against the reciprocal of the crystalline thickness Lcresulted from the fits of the SAXS data. As suggested by the thermodynamic equation 3.3 page 25, these data (blue circles) describe a linear dependency against the reciprocal of the crystalline thickness. As a comparision, experimental data of micron crystals on substrate are plotted [123]. By extrapolation, all data lead to a crystalization temperature of an infinite crystal of the order of T∞ c=182◦C. This behaviour may seem intriguing for the case of two different systems, but by extrapolating at an infinite crystal, the susbtrate effect and the SDS molecules can be neglected. It is also interesting to compare the results to the thermodynamic scheme of polymers proposed in literature (see figure 3.7 page 24). This leads to figure 6.8 which presents the recrystallization line obtained from this study (red square), the thicknesses of crystalline lamella of PE collected from melt (blue circle [94]) and post-thickened crystalline PE lamella as determined by electron microscopy (green filled circles [123]). The resulting recrystallization line defines a linear relationship between the annealing temperature and the reciprocal of the crystalline lamellar layer. As expected by the corresponding thermodynamic equations 3.2 and 3.3 page 25, the extrapolation of the crystallization and recrystallization lines at an infinite crystalline thickness lead to the same temperature T∞ c≈182◦C. According to figure 6.7, this T∞ ccorrespond to the melting temperature of 56 8.3 Polyethylene Summary 8.3 Polyethylene Finally, in contrast to recent literature on bulk polyethylene (PE), this thesis investigated freely suspended nanoparticles of PE. As suggested by Weber and coworkers [33], the combination of SAXS and cryo-TEM has been used for this study. The structure of individual PE nanocrystals has been determined in detail and an improved model of the form factor (SAXS) has been developped in close collaboration with Priv.-Doz. Dr. Ludger Harnau. The second part of this thesis mainly deals with the annealing of these PE particles. For the first time, it is shown that the effect of the annealing process results in a doubling of the crystalline layer of the PE nanoparticles. This behaviour could be traced back to the unlooping of the PE chains. In addition, a linear relationship between the reciprocal of the crystalline layer and the annealing temperature has been experimentally drawn. This line was predicted by the Gibbs-Thomson equation according to the literature [34]. This result is important because it allows to control the crystalline thickness and physical properties of the system, by the temperature. Figure 8.2 is a sketch of the obtained results on the PE nanocrystals: The original semicrystalline PE nanoparticles have a very thin crystalline lamella. By annealing at a temperature far below the melt, a thickening of the lamella occurs. This behaviour ends up at the melting line. Figure 8.2: Schematical resume of the experiments realized onto the PE nanoparticles annealed at different temperatures. T is the temperature and n is the number of monomer units in the crystalline thickness. 63 Chapter 9 Zusammenfassung Das Ziel dieser Arbeit war, durch eine Kombination von Kleinwinkelr¨ontgenstreuung (SAXS), Elektronenmikroskopie (TEM und Kryo-TEM) und dynamischer Lichtstreuung (DLS) Teilchen mit Gr¨oßen im Nanometerbereich im Detail zu analysieren. Dazu wurden zwei Systeme mit sehr unterschiedlicher Morphologie und Zusammensetzung untersucht: Kugelf¨ormige Teilchen von Calciumphosphat-Protein-Komplexen und heterogene Scheibchen von Polyethylen/Polybutadien. 9.1 Calcifizierung Die Arbeiten ¨uber Calciumphosphat-Protein-Komplexen befassten sich mit dem Einfluss des Proteins Fetuin-A, auch AHSG genannt, auf die Calcifizierung zu fr¨uhen Zeitpunkten. Dazu wurden Calciumund Phosphationen mit und ohne Fetuin-A in einer Pufferl¨osung mit pH = 7,4 gemischt. In einem ersten Schritt wurden DLS-Messungen durchgef¨uhrt, um den Einfluss der absoluten Gewichtsanteile der Ca2+ und PO3− 4-Ionen besser zu verstehen. Durch diese Experimente wurde herausgefunden, dass ohne Zugabe von AHSG die gebildeten Teilchen mit kleinerem Gewichtsanteil dieser Ionen kleiner sind. In weiteren Experimenten wurde der Einfluss von Fetuin-A auf den Prozess der Calcificierung w¨ahrend der ersten Minute untersucht. Die fr¨uhe Bildung von CalciumphosphatKomplexen konnte erfolgreich mit TR-SAXS verfolgt werden. Dabei wurde eine schnelle Nukleierung von Nanopartikeln innerhalb einer Sekunde beobachtet. Zum ersten Mal konnte die Rolle des Glycoproteins Fetuin-A in der sehr fr¨uhen Phase der Calcifizierung qualitativ beschrieben werden: AHSG verhindert die Aggregation der CalciumphosphatTeilchen. Fetuin-A spielt demnach eine wichtige Rolle im f¨otalen Serum in der Vorbildung des Skelets von Wirbeltieren. Die Untersuchung hat ferner gezeigt, dass eine physiologische Konzentration von 15 µM dieses Glycoproteins ausreicht, um die Aggregation der Calciumphosphat-Teilchen vollst¨andig zu verhindern. In Abbildung 9.1 sind die Ergebnisse zusammengefasst. Die TEM-Aufnahmen auf der rechten Seite zeigen das System ohne Protein (unten) und mit 15 µM AHSG (oben), 64 9.2 Polybutadien Zusammenfassung der physiologischen Konzentration. Im fr¨uhen Stadium der Calcificierung zeigt sich die Nukleierung der Calciumphosphat-Teilchen. Wenn diese Teilchen eine bestimmte Gr¨oße erreicht haben, wirkt Fetuin-A, wenn es in der L¨osung vorhanden ist, als Abschirmung und umh¨ullt die calcifizierten Teilchen, um so eine weitere Aggregation zu verhindern. Systeme ohne Protein oder mit einer geringen Konzentration von Fetuin-A weisen Aggregation auf. Figure 9.1: Vorgeschlagenes Modell des Einflusses von Fetuin-A (rot) auf die Bildung von Calciumphosphat-Teilchen (orange). Die Bilder auf der rechten Seite zeigen TEMAufnahmen der Calciumphosphat-Komplexen, die ohne (unten) und mit 15 µM Fetuin-A (oben) gebildet wurden. 9.2 Polybutadien Es wurden frei suspendierte Nanopartikel aus syndiotaktischem Polybutadien untersucht. Mittels einer Kombination aus cryo-TEM und SAXS wurde gezeigt, daß die Partikel eine bemerkenswert d¨unne kristalline Polymerlamelle besitzen. Verschiedene Modelle f¨ur homogene und heterogene Nanopartikel (mit zwei oder drei verschiedenen Streul¨angendichten innerhalb eines Teilchens) wurden miteinander verglichen um eine optimale theoretische Beschreibung der experimentellen R¨ontgenkleinwinkelstreudaten zu erhalten. Das Vorliegen von amorphem und kristallinem Polybutadienbereichen wurde mittels R¨ontgendiffraktion gezeigt. Die Notwendigkeit einer zus¨atzlichen SDS-Schicht bei der Modellierung ist auf den SDS-¨ Uberschuß w¨ahrend der Synthese der Polybutadienpartikel (Gewichtanteil ca. 1:1) zu erkl¨aren. Eine Beschreibung der theoretischen R¨ontgenkleinwinkelstreuintensit¨aten ist ungen¨ugend wenn die Anwesenheit von SDS nicht ber¨ucksichtigt wird. Die Bildung von semikristallinen PE-Nanopartikeln erm¨oglicht eine neue Syntheseroute zu Nanopolymeren mit interessanten physikalisch-chemischen Eigenschaften wie sie in Halbleitern oder photovoltaische Komponenten gefunden werden. 65 9.3 Polyethylen Zusammenfassung 9.3 Polyethylen Im Gegensatz zur neueren Literatur ¨uber Polyethylen (PE) im Bulk wurden in dieser Arbeit frei suspendierte PE-Nanopartikel untersucht. Wie von Weber et al. [33] vorgeschlagen, wurde dazu eine Kombination aus SAXS und Kryo-TEM verwendet. Die Struktur von einzelnen kristallinen PE-Nanoteilchen wurde im Detail beschrieben und ein verbessertes Model f¨ur den Formfaktor f¨ur SAXS in enger Zusammenarbeit mit Priv.-Doz. Dr. Ludger Harnau entwickelt. Der zweite Teil der Arbeit besch¨aftigt sich mit dem Tempern dieser PE-Teilchen. Zum ersten Mal wurde gezeigt, dass der Temperungsprozess eine Verdopplung der kristallinen Schichtdicken der PE-Nanopartikel bewirkt. Dieses Verhalten kann auf ein Entfalten der PE-Polymerketten zur¨uckgef¨uhrt werden. Zus¨atzlich wurde experimentell eine lineare Beziehung zwischen der Reziproken der kristallinen Schichtdicke und der Tempertemperatur hergestellt. Diese Linie wurde auf Basis der Gibbs-ThomsonGleichung in der Literatur [34] vorausgesagt. Dieses wichtige Ergebnis zeigt, dass die kristalline Dicke und physikalischen Eigenschaften des Systems durch die Temperatur kontrolliert werden kann. Abbildung 9.2 zeigt schematisch die Ergebnisse ¨uber die PE-Nanokristalle: Die kristalline Lamelle der urspr¨unglich semikristallinen PE-Nanopartikel ist sehr d¨unn. Durch Tempern bei Temperaturen weit unterhalb der Schmelze findet eine Verdickung der Lamelle statt. Dieses Verhalten endet an der Schmelzkurve. Figure 9.2: Schematische Zusammenfassung der Experimente mit PE-Nanopartikeln und verschiedenen Tempertemperaturen. 66 Appendices 67 Appendix A Theory of SAXS A.1 Effect of polydispersity Effect of the polydispersity onto the scattering intensity of an ensemble of non-interacting spherical particles of mean radius R0=10 nm. Polydispersities used here are 5%, 10% and 20% in gaussian distribution (corresponding respectively to 0.5 (red square), 1.0 (black triangle) and 2.0 nm (blue circles) for their standard deviations σ). ∆ρis here equals to 1 e.u.nm−3and N Vis equal to unity. The intensity at q=0 grow with the polydispersity. At high polydispersity, the first peak is hardly visible and thus piece of information are lost. 68 A.2 C++ programs Appendix A.2 C++ programs A.2.1 form factor of homogenous spherical polydisperse particles 69 A.2 C++ programs Appendix 70 A.2 C++ programs Appendix A.2.2 structure factor of the aggregation of spherical particles 71 A.3 Modified hamburger model Appendix A.3 Modified hamburger model 72 B.2 WAXS signal of calcium phosphate complexes Appendix B.2 WAXS signal of calcium phosphate complexes The previous figure presents WAXS signal of the calcium-phosphate complexes without (blue full line) and in presence of 15µM of Fetuin-A (red bold line). Due to the abscence of crystalline peak, the systems have been assumed as amorphous. 79 B.3 Synthesis of the polyethylene nanoparticles Appendix B.3 Synthesis of the polyethylene nanoparticles The synthesis of the nanoparticles were realized in Konstanz, Germany, by Dr. Qiong Tong. Dispersion synthesis was carried out in a 300 mL stainless steel mechanically stirred (1000 rpm) pressure reactor equipped with a heating/cooling jacket supplied by a thermostat controlled by a thermocouple dipping into the polymerization mixture. To a mixture of 750 mg of SDS (Fluka, 98%) and 10 µmol of the Ni(II)-complex in a 250 mL Schlenk flask was added 100 mL of distilled and degassed water at room temperature. The resulting homogenous solution was then cannula-transferreed to the argon flushed reactor cooled at 12◦C. The reactor was pressurized to a constant ethylene pressure of 40 bar while the temperature was adjusted at 15◦C. After 30 min reaction time, ethylene feeding was interrupted, the reactor was carefully depressurized, and the obtained dispersion was filtrated through a plug of glass wool. The left molecule is the catalyst used for the synthesis of PL39. The right molecule is the catalyst used for the synthesis of PL78. 80 B.4 Influence of the annealing process on N VAppendix B.4 Influence of the annealing process on N V Normalized scattered intensities of the PE systems before (blue) and after (red) the heating procedure bathing in the highest glucose solutions. All intensities are normalized by the volume fraction of the sample: respectively 6.26 vol% and 6.96 vol% for the original and annealed particles. The volume fraction of the added D+-glucose are 14.25 vol% and 14.29 vol% respectively. The equality of the scattered intensities at low scattering vectors demonstrate that the number of particles per volume is constant before and after the annealing process. 81 B.5 Contrast series of PL78 Appendix B.5 Contrast series of PL78 B.5.1 Original system - PL78 Experimental contrast variation SAXS data of the original PL78 system and their respective theoretical intensities according to equations 5.2 and 5.3 page 42. The volume percentages of the systems are from bottom to top: 2.1 vol%, 1.9 vol%, 1.8 vol% and 1.7 vol% and their respective volume percentages of added glucose are: 0.0 vol%, 4.4 vol%, 9.9 vol% and 15.0 vol%. The mean crystalline thickness measures here 6.5 nm. 82 B.5 Contrast series of PL78 Appendix B.5.2 System annealed at 90◦C Experimental contrast variation SAXS data of the PL78 system annealed at 90◦C and their respective theoretical intensities according to equations 5.2 and 5.3 page 42. The volume percentages of the systems are from bottom to top: 1.6 vol%, 1.5 vol%, 2.0 vol% and 1.9 vol% and their respective volume percentages of added glucose are: 0.0 vol%, 4.4 vol%, 9.9 vol% and 14.9 vol%. The mean crystalline thickness measures here 8.5 nm. 83 B.5 Contrast series of PL78 Appendix B.5.3 System annealed at 105◦C Experimental contrast variation SAXS data of the PL78 system annealed at 105◦C and their respective theoretical intensities according to equations 5.2 and 5.3 page 42. The volume percentages of the systems are from bottom to top: 2.4 vol%, 2.2 vol%, 2.1 vol% and 2.0 vol% and their respective volume percentages of added glucose are: 0.0 vol%, 4.4 vol%, 9.9 vol% and 15.1 vol%. The mean crystalline thickness measures here 10.2 nm. 84 B.5 Contrast series of PL78 Appendix B.5.4 System annealed at 115◦C Experimental contrast variation SAXS data of the PL78 system annealed at 115◦C and their respective theoretical intensities according to equations 5.2 and 5.3 page 42. The volume percentages of the systems are from bottom to top: 2.6 vol%, 2.4 vol%, 2.3 vol% and 2.1 vol% and their respective volume percentages of added glucose are: 0.0 vol%, 4.4 vol%, 9.9 vol% and 14.9 vol%. The mean crystalline thickness measures here 11.8 nm. 85 B.6 Synthesis of sPB Appendix B.6 Synthesis of sPB The synthesis of the nanoparticles were realized in Konstanz, Germany, by Dr. Brigitte Korthals. A toluene solution (5 ml) of cobalt(II) 2-ethylhexanoate (1.60 mmol) was introduced under argon to a mechanically stirred 10 ml pressure glass reactor equipped with a heating/cooling jacket controlled by a temperature sensor dipping into the reaction mixture. After evaporating of toluene in vacuum, 32.5 g of butadiene were condensed at -5◦C. An ethanol solution (15 ml) of sodium borohydride (3.55 mmol) was added, affording a solution of the precatalyst [Co(C8H13)(C4H6)]. An aqueous solution of surfactant (46.5 g SDS/ 20 g pentanol and 400 g H2O) was then transferred to the reactor by means of a pump under stirring (1000 rpm) and the temperature was set to 20◦C, affording a transparent butadiene/precatalyst microemulsion. A toluene solution of carbon disulfide (1.6 mmol, [CS2] / [Co] = 1) was pumped into the reactor, which was then rapidly heated to the desired temperature (T = 40◦C). After 3h the reaction was stopped by cooling and releasing residual gas pressure, affording a light brown transparent latex. 86 B.7 X-ray diffraction of BK280 Appendix B.7 X-ray diffraction of BK280 X-ray diffraction of the polybutadiene system BK280 (blue full line) and of the glas susbtrate (red bold line). X-ray diffraction of the polybutadiene system BK280 alone. This data were obtained by subtracting the signal of the glas and of the amorphous part. The hkl peak of the crystalline syndiotactic 1,2-polybutadiene (Pacm, a=10.98 ˚ A, b=6.60 ˚ Aand c=5.14 ˚ A) are reported when visible. 87 B.8 DLS of BK280 Appendix B.8 DLS of BK280 Figure B.1: DLS data of the polybutadiene system. The diffusion coefficient was determined to 3.81×10−23 m2/s leading to an hydrodynamic radius of 6.4 nm. The system was diluted in water at a concentration of 0.00013 wt%. 88 LIST OF FIGURES Appendix 4.14 Time-evolution of the number of primary spherical particles per aggregate (S(0)+1). The main effect of Fetuin-A is seen here: inhibition of the aggregation. The dashed lines are guide lines for the evolution of the parameters. Mixes contain 0 µM (blue), 1 µM (red), 5 µM (black) and 15 µM (green) ofFetuin-A.................................... 39 4.15 Binding of the D1 domain of Fetuin-A onto the surface of hydroxyapatite. The positive charges of Ca2+ are marked in blue and the negative phosphate charges are represented in red. Figure taken from reference [63]. . . . . . . 40 5.1 Hamburger model used in this study. Two additional sheets of SDS have to be taken into account to model the structure. Lt, L=Lc+Laand Lc represent the thicknesses of the whole particle, of the polymer and of the crystalline phase respectively, while R is the radius of the disk. . . . . . . . 43 5.2 Cryo-TEM image of the nanoparticle of polybutadiene. The concentration was 0.03 wt%. The scale bar of the main micrograph represents 50 nm while the ones in the insets represent 10 nm. . . . . . . . . . . . . . . . . . 44 5.3 Normalized scattering intensities of the polybutadiene nanoparticles. For the sake of clarity, the four lowermost scattered intensities were divided by factor of 101, 102, 103and 104. From bottom to top, the concentration of glucose (and of the sample) in solution was 0.0 (1.19), 3.2 (1.23), 6.5 (1.24), 9.8 (1.24) and 17.3 (1.32) vol%. . . . . . . . . . . . . . . . . . . . . . . . . 45 5.4 Plot of the temperature as a function of the reciprocal of the crystalline thickness of syndiotactic polybutadiene systems. The red squares are obtained from reference [119] and the blue circle represents this study. The bold red and blue lines are guide-lines for the recrystallization and crystallization lines respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 6.1 Typical cryo-TEM micrographs of the original PL39 system (top) and of the annealed PL39 sample (bottom). Insets in each micrograph presents a single particle in which the direction of the main axis is orhthogonal and parallel to the direction of the electron beam. The annealing process was carried at 125◦C for 20 minutes. For both micrographs, the weight percentage studied is 0.3 wt%. . . . . . . . . . . . . . . . . . . . . . . . . . 49 95 LIST OF FIGURES Appendix 6.2 Normalized scattered intensities of the PL39 PE system before (top) and after (bottom) the annealing procedure. All intensities are normalized by the volume fraction of the sample. The volume fraction of the contrast agent varies from 0 (blue points), 0.04 (red points), 0.10 (black points) up to 0.14 (green points), while the volume fraction of the nanoparticles decrease: 2.5, 2.4, 2.3, 2.2 vol% for the original system (top) and 2.6, 2.5, 2.3 and 2.2 vol% for the annealed sample (bottom) respectively. The three lowermost intensities are divided by factors of 10, 102and 103for sake of clarity. The vertical gray dashed lines show the q-value below which the structure factor is needed. For the sake of clarity, only one out of 5 points is shown. The dashed lines represents the result of the modeling of the SAXS data assuming a dispersion of non-interacting polydisperse platelets. The solid lines represent the scattering intensity calculated for a dispersion of interacting polydisperse platelets. . . . . . . . . . . . . . . . . . . . . . . . 51 6.3 2D-model of the unlooping process expected by some authors [106,120–122]. (a): The full unlooping process of one single crystalline nanoparticle lead to a doubling of the crystalline thickness of the same particle. (b): The stack of two crystalline particles lead to one particle with a doubled crystalline thickness. .................................... 53 6.4 Cryo-TEM micrographs of PL78 sample (original and different annealed temperatures). The black bar represents 50 nm. . . . . . . . . . . . . . . . 54 6.5 Two-dimensional schematical representation of partial unlooping of PE chains within a nanoparticle. A partial unlooping leads to a very small decrease of the radius Rof the platelet, probably a decrease too small to be detected by SAXS experiments. . . . . . . . . . . . . . . . . . . . . . . 54 6.6 Experimental data and corresponding fits of the original sample PL78 dispersed in pure water (blue circles). The volume fractions of the systems are: 2.1 vol%, 1.6 vol%, 2.4 vol% and 2.6 vol% respectively for the original system (bottom) and the ones annealed at 90◦C (red squares), 105◦C (black triangles) and 115◦C (green circles). . . . . . . . . . . . . . . . . . . 55 6.7 Experimental data of the reciprocal of the crystalline thickness depending on the annealing temperature. The data with triangular and square symbols have been obtained from micron crystalls originally crystallized at T=85◦C and T=95◦C respectively [123]. The blue circles represent the data of this study (nanocrystals freely suspended). . . . . . . . . . . . . . . 56 96 LIST OF FIGURES Appendix 6.8 Experimental thermodynamic scheme obtained by the help of data in reference [124] (blue circles) and from the present study (red squares). The blue, red and black lines represent respectively the crystallization, recrystallization and melting lines of the thermodynamic scheme proposed in litterature [29,94]. The bold green line is a guide line for the post-thickened experimental data points [123]. . . . . . . . . . . . . . . . . . . . . . . . . 57 7.1 Schematic representation of the USAXS/SAXS/WAXS equipment at the ERSF in Grenoble, France. Picture taken from http://www.esrf.eu/Users AndScience/Experiments/SoftMatter/ID02/BeamlineLayout on Jully, the 1st 2009...................................... 59 7.2 Determination of the density of a calcium phosphate system in buffer solution. From the slope, ρis determined to 1.67 ±0.05 g/cm3. ....... 60 8.1 Hypothetical model of the influence of Fetuin-A (red) onto the formation of calcium phosphate complexes (orange). Black and white images on the right present TEM micrographs of calcium-phosphate particles formed without (bottom) and in presence of 15 µM of Fetuin-A (top). . . . . . . . 62 8.2 Schematical resume of the experiments realized onto the PE nanoparticles annealed at different temperatures. T is the temperature and n is the number of monomer units in the crystalline thickness. . . . . . . . . . . . . 63 9.1 Vorgeschlagenes Modell des Einflusses von Fetuin-A (rot) auf die Bildung von Calciumphosphat-Teilchen (orange). Die Bilder auf der rechten Seite zeigen TEM-Aufnahmen der Calciumphosphat-Komplexen, die ohne (unten) und mit 15 µM Fetuin-A (oben) gebildet wurden. . . . . . . . . . . . 65 9.2 Schematische Zusammenfassung der Experimente mit PE-Nanopartikeln und verschiedenen Tempertemperaturen. . . . . . . . . . . . . . . . . . . . 66 B.1 DLS data of the polybutadiene system. The diffusion coefficient was determined to 3.81×10−23 m2/s leading to an hydrodynamic radius of 6.4 nm. The system was diluted in water at a concentration of 0.00013 wt%. . . . . 88 97 LIST OF FIGURES Appendix B.2 Theoretical SAXS signal of the different structural models. The intensities resulting from models B and C do not lead to any drastical change of the SAXS intensities while the model used in this study as well as the corebishell model do lead to a stronger change in intensities at small q-values. For the model used in this study, ”model PE/sPB”, the parameters used are: R = 12.0 ±2.0 nm, Lc= 6.5 ±0.4 nm, La= 3.1 ±0.8 nm and Lsds = 2.0 nm. For model B: R = 12.0 ±2.0 nm, Ra= R-2.0 nm (Radenotes the radius of the amorphous phase alone), Rc= Ra-1 2La(Rcdenotes the radius of the crystalline phase alone) Lc= 6.5 ±0.4 nm, La= 3.1 ±0.8 nm and Lsds = 2.0 nm. For model C: R = 12.0 ±2.0 nm, Ra= R-2.0 nm (Rpdenotes the radius of the polymer phase alone), Lc= 6.5 ±0.4 nm, La= 3.1 ±0.8 nm and Lsds = 2.0 nm. For the core bi-shell model: Rc = 6.5 ±0.4 nm, ha= 3.1 ±0.8 nm and hsds = 2.0 nm. For all models in this appendix, the electron densities have the following values: 333.57 e.u.nm−3, 339 e.u.nm−3, 302 e.u.nm−3and 397 e.u.nm−3respectively for the solvent, crystalline, amorphous and sds phase. . . . . . . . . . . . . . . 91 98 Acknowledgements First of all, I would like to express my deepest gratitude to Prof. Dr. M. Ballauff for giving me the interesting subjects that I have been investigating. I would like to thank him for being very helpful for the publications and this thesis. I am very grateful to Prof. Dr. W. Jahnen-Dechent and Prof. Dr. S. Mecking for their helpful discussions and for kindly providing samples during our collaborations. Many thanks are given to Dr. Sabine Rosenfeldt for her critical readings of my works and especially this thesis. I give my acknowlegement to Dr. Alexander Heiss for all valuable discussions about the calcification project and to Priv.-Doz. Dr. Ludger Harnau for his oustanding contribution to the simulation work on interparticle interactions of the polyethylene nanoparticles. Dr. Markus Drechsler is acknowledged for his great investigations by electron microscopies on the different samples that I studied. I am very grateful to Dr. J´erˆome Crassous for his daily good mood and for our valuable discussions at any time. I would like to thank him as well for the very interesting project that we have been investigating together. I am grateful to all my colleagues who have constructed a very friendly atmosphere for working. I give my acknowledgements especially to Adriana and Sergio Mihut for their help during the study of the polyethylene nanoparticles and for giving me some piece of advice for the programming of the fitting programs respectively. I would like to thank, Dr. Katja Henzler for realizing the SAXS experiments of the first polyethylene sample at the ESRF, Grenoble, France. A very big thanks is given to Dr. Theyencheri Narayanan for providing beam time at the Synchrotron source for all studied systems. Qiong Tong is greatly thanked for the synthesis of the PE nanoparticles and for all important discussions for a better understanding of these objects. I treasure my friendship with my colleagues Frank Polzer, Christian Schneider, Michael Zeiser, Dr. Yan Lu, Dr. Alexander Wittemann, Miriam Siebenb¨urger and Dr. Sreenath Bolisetty. I thank Elisabeth D¨ungfelder for her bureaucratic work with a lot of patience and kindness and Karlheinz Lautenbach for his availibility and technical support. My special thanks goes to my family. My parents have encouraged me and shown their appreciations for my every progress in these works. I am very grateful too to my brothers for kindly giving me the opportunity to use unix servers for simulating SAXS theoretical intensities and for their encouragements. 99 Financial support by the Deutsche Forschungsgemeinschaft, SFB 481, Bayreuth, and by the Marie Curie Research Training Network (POLYAMPHI) are gratefully acknowledged. 100 Bibliography [1] Fajun Zhang, Maximilian W. A. Skoda, Robrt M. J. Jacob, Richard A. Martin, Christopher M. Martin, and Frank Schreiber. 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Harnau: Annealing of single lamella nanoparticles of polyethylene Macromolecules, 44(12), 4845-4851, 2011. 112 Curriculum Vitae Private: Name: Christophe Nicolas Rochette Address: 5 rue de Savoie 33600 Pessac FRANCE Marital status: Single Schools: 1984-1988: Ecole primaire de la Glaci`ere, M´erignac, France 1988-1990: Ecole primaire de Cap de Bos, Pessac, France 1990-1994: Coll`ege Ladonne, Pessac, France 1994-1995: Lyc´ee Pape Cl´ement, Pessac, France 1995-1998: Lyc´ee Sainte Marie Grand Lebrun, Bordeaux, France Scientific studies: 1998-2000: Institute of Technology, Physical Measurements, Talence, France 2000: Research assistant: ”Studies of the poluttant effect of aluminium ions on sunflowers”, TAMK, Tampere, Finland - Supervisor: Prof. Dr. Marjukka Dyer 2000-2004: Master of Chemistry, University of Bordeaux 1, Talence, France 2003: Research assistant: ”Membrane structure and interactions of antibiotic peptides from Australian tree frogs”, School of Chemistry, University of Melbourne, Victoria, Australia - Thesis supervisor: Prof. Dr. Frances Separovic 2004: Research assistant: ”Study of the confinement of anionic peptides onto cationic amphiphiles”, European Institute of Chemistry and Biology, University of Bordeaux 1, France - Thesis supervisor: Prof. Dr. Reiko Oda PhD: Since November 2005: ”Structural Analysis of Nanoparticles by Small Angle X-ray Scattering”, Bayreuth Center for Colloids and Interface Science, University of Bayreuth, Germany - Thesis supervisor: Prof. Dr. Matthias Ballauff 113 Erkl¨arung Hiermit erkl¨are ich, dass die Arbeit selbst¨andig verfasst und keine anderen als die von mir angegebenen Quellen und Hilfsmittel benutzt habe. Ferner erkl¨are ich, dass die anderweitig mit oder ohne Erfolf nicht versucht habe, diese Dissertation einzureichen. Ich habe keine gleichartige Doktorpr¨ufung an einer anderer Hochschule endg¨ultig nicht bestanden. Bayreuth, Christophe N. Rochette 114