Dissertations / Theses on the topic 'Random polymers'

After a brief introduction to the problem of directed polymers in a random medium, several aspects of the problem are addressed in more detail. It is possible to show that, in high enough dimension and above a certain temperature, a phase exists in which the free energy is given by the annealed free energy, with probability one. The proof of this statement is extended to obtain upper and lower bounds on the temperature transition between this phase and a low temperature phase and hence prove the existence of the phase transition. The mean field solution is reviewed and a method of obtaining high dimension expansions around it is presented. The method uses the idea of 'n-tree approximations' as a systematic way of including the correlations present in finite dimensions. Using this approach 1/d expansions are obtained for the free energy, transition temperature, transverse fluctuations and overlaps. The results are consistent with the existence of a finite upper critical dimension above which the behaviour is of a mean field nature. Directed polymers are then considered on disordered hierarchical lattices. On these lattices the problem reduces to the study of the stable laws that occur when one combines random variables in a nonlinear way. Recursion relations for various properties of the system are obtained which are studied using numerical and analytical techniques. It is possible to obtain a perturbative expansion for the free energy, overlaps and non-integer moments of the partition function. Finally, a generalisation of the standard directed polymer problem is considered, in which one allows the walks to contribute positive and negative weights to the partition sum. The solution of the mean field limit of this problem is obtained indirectly, by using the relationship between the mean field directed polymer problem, the random energy model (REM) and the generalised random energy model (GREM). Numerical simultions are presented which give good confirmation of the analytical predictions. It is observed that in solving this generalised polymer problem one has also obtained a formula for the largest Lyapounov exponent of a product of large, sparse random matrices.

Thesis (PhD)--Stellenbosch University, 2002.
ENGLISH ABSTRACT: Most polypropylene copolymers commercially available have ethylene, and to a lesser degree t-butene as comonomers. Commercially available higher a-olefins, mostly even-numbered, are seldom used for the production of pp copolymers, probably due to cost. Sasol's Fischer- Tropsch oil-from-coal process produces many linear and branched a-olefins as by-products that can be isolated and purified by a relatively cheap refinery process, including the odd-numbered 1- pentene olefin. Sasol's gas-phase Novolen pp plant at Secunda, South Africa is ideally suited to the manufacture of high quality pp random copolymers. As such an opportunity was identified to research the use of higher a-olefins, and more specifically 1-pentene, in the gas-phase production of pp random copolymers. Different methods to produce propylene / 1-pentene random copolymers in the slurry phase on bench-scale were investigated. A procedure was subsequently developed to produce propylene / 1-pentene random copolymers in the gas-phase in 10 litre autoclaves. It was found that commercially available fourth generation supported catalysts successfully incorporated the bulky 1-pentene monomer into the propylene backbone, both during slurry and gas-phase polymerisations. Software modelling was employed to determine the dew points of selected gas mixtures typically found during the production of pp random copolymers. The results indicated that typical process conditions could be employed during the gas-phase polymerisation of propylene and 1-pentene without the risk of condensation taking place inside the reactor. Propylene / 1-pentene random copolymers were subsequently successfully produced on the 800 litre BASF pilot plant in Germany followed by the first commercial production of the copolymer on Sasol's 50m3 Novolen gas-phase plant at Secunda. Using commercially available software the impact of introducing 1-pentene as comonomer during the production of random copolymers on the condenser cooling capacity was evaluated. Feasible and safe plant operating conditions were established for the production of propylene / 1-pentene random copolymers. The relationship between operating pressure and powder morphology was investigated to optimise process conditions. Operating at higher pressure in the gas-phase increases the monomer concentration in the reactor and as such improves the space/time/yield ratio of the 50m3 reactors. It was shown that higher operating pressures could be employed through the introduction of 1-pentene as comonomer during the production of PP random copolymer. The dramatic increase in catalyst productivity observed during the 800 litre pilot plant trials, up to a comonomer ratio of about 5%, supported the results obtained from a kinetic study carried out in bench-scale autoclaves. A comprehensive study was undertaken to compare the rheological, thermal, crystallisation, physical and mechanical properties of propylene / 1-pentene random copolymers with those of commercially available pp random copolymers. A series of propylene homo- and random copolymers with 1-pentene and ethylene as comonomers respectively, was prepared. NMR and IR techniques were developed to facilitate the determination of copolymer composition for the new family of 1-pentene random copolymers. The effect of comonomer content, molecular weight and temperature on the properties of the series of polymers was investigated. The propylene / 1-pentene random copolymers show unique rheological behaviour associated with the short propyl branches in the polymer backbone with minimum zero shear viscosity at about 2% 1-pentene content. The effect of molecular structure changes with comonomer content were analysed by the calculation of square average end-toend distance, packing length, tube diameter, molecular mass between entanglements and critical molecular mass. The viscosity of the 1-pentene random copolymers shows higher shear and temperature sensitivity compared to propylene homo- and ethylene random copolymers. The thermodynamic melting point of the propylene / 1-pentene random copolymers showed a significant decrease with increasing comonomer content in the 0 to 5% range. A wider melting range and higher peak melting point depression rate was observed compared to ethylene random copolymers at similar and increasing comonomer content measured on a weight % basis. It was found that the crystal structure of the propylene / 1-pentene random copolymers contains both the Q- and the y-modifications with the ratio of the respective crystal forms a function of both comonomer content and crystallisation temperature. The glass temperature decreased slightly with increasing comonomer (1-pentene) content. It is proposed that the short branch (propyl) "defects" in the polymer backbone are .incorporated into the crystal lattice resulting in increased rate of melting point depression with increasing (wt%) comonomer content compared to other random copolymers while maintaining relative high stiffness. The propylene / 1-pentene random copolymers exhibit the lowest haze values compared to all commercially available pp random copolymers at corresponding levels of comonomer content on a wt% basis. The stiffness to haze ratio of propylene / 1-pentene random copolymers are unique for all the members of the pp family. An inverse relationship between comonomer content and the measured tensile yield strength and modulus is observed. Application studies conducted on the propylene / 1-pentene random copolymers highlighted several interesting characteristics. Films produced from these copolymers exhibited very low haze and xylene soluble values while maintaining mechanical integrity. In the BOPP application the combination of processability and premium film properties presents a unique opportunity for the family of propylene / 1-pentene random copolymers. Blow moulding and injection moulding trials highlighted several advantages of product properties manufactured with propylene / 1-pentene random copolymers if compared to other commercially available random copolymers. The 1-pentene randoms presented lower in-mould as well as total shrinkage than ethylene based random copolymers. Stabilisation and nucleation studies conducted on the propylene / 1-pentene random copolymers showed that a typical combination antioxidant package and nucleating agent, at normal loading levels, could be used. In the larger pp random copolymer family 1-pentene imparts a better balance of properties than other comonomers. The combination of low melting point and xylene solubles with high stiffness and clarity is unique to propylene / 1-pentene random copolymers.
AFRIKAANSE OPSOMMING: Die oorgrote meerderheid van kommersieel beskikbare polipropileen (PP) kopolimere het etileen, en tot 'n mindere mate buteen, as komonomeer. Die relatief hoë koste van kommersieel beskikbare hoër alfa-olefiene is moontlik die rede waarom hulle selde gebruik word vir die vervaardiging van PP kopolimere. Die Sasol Fischer-Tropsch proses, waartydens olie uit steenkool vervaardig word, lewer verskeie liniêre en vertakte alfa-olefiene as neweprodukte wat geïsoleer en gesuiwer kan word in 'n relatiewe goedkoop rafineringsproses. Dit sluit ook die onewe-koolstofgetal 1-penteen-olefien in. Sasol se gasfase Novolen PP aanleg in Secunda, Suid-Afrika, is besonder geskik vir die vervaardiging van hoë standaard PP statistiese kopolimere. Voortvloeiend hieruit is die geleentheid geidentifiseer om die gebruik van hoër alfa-olefiene, en meer spesifiek 1-penteen, na te vors tydens die gasfaseproduksie van PP statistiese kopolimere. Verskeie metodes om propeleen / 1-penteen statistiese kopolimere in 'n koolwaterstofoplosmiddel op laboratoriumskaal te produseer, is ondersoek. 'n Prosedure is daarna ontwikkel om propileen / 1-penteen statistiese kopolimere ook in die gasfase te vervaardig in 10-liter drukvate. Die bevinding was dat kommersieel beskikbare vierde-generasie ondersteunde kataliste die swaarder 1-penteenmonomeer suksesvol geïnkorporeer het in die propileenketting tydens beide die koolwaterstof oplosmiddel- en gasfase polimerisasiereaksies. Rekenaargebaseerde modellering is gebruik om die kondensasiekondisies van tipiese gasmengsels, teenwoordig tydens die produksie van PP statistiese kopolimere, te bepaal. Die resultate het aangedui dat normale proseskondisies tydens die gasfasepolimerisasie van propileen en 1-penteengeen risiko van kondensasie in die reaktor inhou nie. Propileen / 1-penteen statistiese kopolimere is gevolglik met groot sukses vervaardig by die 800-liter BASF loodsaanleg in Duitsland, gevolg deur die eerste kommersiële vervaardiging van die kopolimeer op die Sasol50m3 Novolen gasfase-aanleg in Secunda. Deur gebruik te maak van kommersieel beskikbare sagteware, is die impak van 1-penteen as komonomeer tydens die vervaardiging van statistiese kopolimere op die verkoelingskapasiteit van die kondensator bepaal. Veilige en uitvoerbare aanlegkondisies is uitgestip vir die vervaardiging van propileen /1-penteen statistiese kopolimere. Die verhouding tussen die reaktordruk en poeiermorfologie is ondersoek om die prosestoestande te optimiseer. Vervaardiging van kopolimere in die gasfase by hoër drukke lei tot verhoogde monomeerkonsentrasie in die reaktor en gevolglik hoër produksiedeursette. Daar is bewys dat tydens die produksie van PP statistiese kopolimere, met 1-penteen as komonomeer, hoër reaktordruk ingespan kan word. Die dramatiese toename in katalisproduktiwiteit waargeneem tydens die 800- liter loodsaanleg proefloop, tot en met 'n komonomeer inhoud van ongeveer 5%, word ondersteun deur die resultate van 'n kinetiese studie uitgevoer in laboriumskaal drukvate. 'n Omvattende studie, om die reologiese, termiese, kristallyne, fisiese en meganiese eienskappe van propileen / 1-penteen statistiese kopolimere te vergelyk met kommersieel beskikbare PP statistiese kopolimere, is uitgevoer. 'n Reeks propileen homo- en statistiese kopolimere, met 1-penteen en etileen as komonomere onderskeidelik, is berei. KMR- en IR- tegnieke is ontwikkel om die bepaling van komonomeersamestelling vir die nuwe familie van 1- penteen statistiese kopolimere te fasiliteer. Die invloed van komonomeersamestelling, molekulere gewig en temperatuur op die eienskappe van die reeks polimere is ondersoek. Die propoleen / 1- penteen statistiese kopolimere toon unieke reologiese eienskappe wat geassosieer kan word met die propielsykettings in die polimeerruggraat. Die viskositeit van die propileen / 1-penteen statistiese kopolimere toon 'n hoër wrywings- en temperatuursensitiwiteit in vergelyking met propileen homo- en etileen statistiese kopolimere. 'n Drastiese verlaging in die termodinamiese smeltpunt van die propileen / 1- penteen statistiese kopolimere met 'n toename in komonomeerinhoud is waargeneem tot en met 'n 5% komonomeerinhoud. Die propileen / 1-penteen statistiese kopolimere toon 'n breër smeltgebied en 'n hoër tempo in die piek smeltpuntafname in vergelyking met etileen statistiese kopolimere met soortgelyke komonomeer inhoud, gemeet op 'n massabasis. Daar is bewys dat die kristalstruktuur van die propileen / 1-penteen statistiese kopolimere beide die alfa en gamma modifikasies bevat. Die verhouding van die onderskeie kristalvorms is 'n funksie van komonomeerinhoud en kristalisasietemperatuur. 'n Afname in die glastemperatuur met verhoogde komonomeer inhoud is waargeneem. Die aanname dat die kort propielsykettings in die polimeerruggraat in die kristalstruktuur geïnkorporeer word, is gemaak. Dit verklaar die hoë afname in die tempo van die smeltpunt met toenemende komonomeer inhoud relatief tot ander statistiese kopolimere, met die handhawing van hoë moduluswaardes. Die besondere deursigtigheid van die propileen / 1-penteen statistiese kopolimere tesame met relatief hoë modulus waardes is uniek. 'n Omgekeerde verhouding tussen komonomeer inhoud en treksterkte asook moduluswaardes is waargeneem. 'n Toepassingstudie uitgevoer met die propileen / 1-penteen statistiese kopolimere het verskeie interessante resultate gelewer. Films vervaardig van hierdie kopolimere toon besonderse deursigtigheid en lae waarde van xileenoplosbaarheid, terwyl meganiese integriteit gehandhaaf word. Voordele in die vervaardigingsproses van BOPP-films asook bogemiddelde filmeienskappe hou unieke moontlikhede vir propileen / 1-penteen statistiese kopolimere in. Verskeie voordele tydens blaas- en spuitvormingsprosesse is waargeneem relatief tot ander beskikbare statistiese kopolimere. Die 1-penteen statistiese kopolimere toon 'n laer in-vorm sowel as totale krimping relatief tot etileen- gebaseerde kopolimere. 'n Studie het aangetoon dat tipiese bymiddelpakette by normale toevoegingsvlakke geskik is vir propileen / 1-penteen statistiese kopolimere. Gesien in die groter pp statistiese kopolimeer familie toon 1-penteen 'n beter balans van eienskappe as ander komonomere. Die kombinasie van laer smeltpunt en xileen-oplosbares met hoë moduluswaardes en helderheid is uniek aan propileen /1-penteen statistiese kopolimere.

We grow AB₂ random hyperbranched polymer structures in different ways and using different simulation methods. In particular we use a method of ad hoc construction of the connectivity matrix and the bond fluctuation model on a 3D lattice. We show that hyperbranched polymers split into two universality classes depending on the growth process. For a “slow growth” (SG) process where monomers are added sequentially to an existing molecule which strictly avoids cluster–cluster aggregation the resulting structures share all characteristic features with regular dendrimers. For a “quick growth” (QG) process which allows for cluster–cluster aggregation we obtain structures which can be identified as random fractals. Without excluded volume interactions the SG model displays a logarithmic growth of the radius of gyration with respect to the degree of polymerization while the QG model displays a power law behavior with an exponent of 1/4. By analyzing the spectral properties of the connectivity matrix we confirm the behavior of dendritic structures for the SG model and the corresponding fractal properties in the QG case. A mean field model is developed which explains the extension of the hyperbranched polymers in an athermal solvent for both cases. While the radius of gyration of the QG model shows a power-law behavior with the exponent value close to 4/5, the corresponding result for the SG model is a mixed logarithmic–power-law behavior. These different behaviors are confirmed by simulations using the bond fluctuation model. Our studies indicate that random sequential growth according to our SG model can be an alternative to the synthesis of perfect dendrimers.

We introduce and study four $q$-randomized Robinson--Schensted--Knuth (RSK) insertion tableau dynamics. Each of them is a discrete time Markov dynamics on two-dimensional interlacing particle arrays (these arrays are in a natural bijection with semistandard Young tableaux). For $0Mathematics

We are interested in two probabilistic models of a process interacting with a random environment. Firstly, we consider the model of directed polymers in random environment. In this case, a polymer, represented as the path of a simple random walk on a lattice, interacts with an environment given by a collection of time-dependent random variables associated to the vertices. Under certain conditions, the system undergoes a phase transition from an entropy-dominated regime at high temperatures, to a localised regime at low temperatures. Our main result shows that at high temperatures, even though a central limit theorem holds, we can identify a set of paths constituting a vanishing fraction of all paths that supports the free energy. We compare the situation to a mean-field model defined on a regular tree, where we can also describe the situation at the critical temperature. Secondly, we consider the parabolic Anderson model, which is the Cauchy problem for the heat equation with a random potential. Our setting is continuous in time and discrete in space, and we focus on time-constant, independent and identically distributed potentials with polynomial tails at infinity. We are concerned with the long-term temporal dynamics of this system. Our main result is that the periods, in which the profile of the solutions remains nearly constant, are increasing linearly over time, a phenomenon known as ageing. We describe this phenomenon in the weak sense, by looking at the asymptotic probability of a change in a given time window, and in the strong sense, by identifying the almost sure upper envelope for the process of the time remaining until the next change of profile. We also prove functional scaling limit theorems for profile and growth rate of the solution of the parabolic Anderson model.

Les dispersions colloïdales ont beaucoup d’applications technologiques importantes. A cause du mouvement brownien, les particules ont des collisions fréquentes entre elles. Les forces d’attraction de van der Waals,dérivant de potentiels à longue portés, conduisent à l’agrégation et à la précipitation des particules. Plusieurs méthodes ont été proposées pour diminuer ou contrebalancer l’effet d’attraction de van der Waals et augmenter la stabilité colloïdale. Par exemple, le choix du solvant possédant l’indice de réfraction le plus proche possible de celui des particules peut diminuer les forces de van der Waals. D'autres facteurs influencent la stabilité comme les interactions électrostatiques et les interactions spécifiques liées aux chaînes de polymères. Dans le cas des polymères, les chaînes peuvent être greffées à la surface des particules ou être dissoutes dans le solvant (chaînes libres). Dans ce travail de thèse, nous avons étudié l’effet de la stabilisation par déplétion dans le cas des chaînes de polymères libres (FPI, "free polymer induced interaction"). Des modèles théoriques précédents portent un caractère trop simplifié et utilisent des approximations sans vérification. De plus, l’influence des paramètres de la solution, c’est-à-dire, de la structure de polymères et de son interaction avec la surface de particule, n’a pas été étudiée.Les chaînes polymères libres ont été modélisées comme des marches aléatoires dans un champ moléculaire auto-cohérent qui satisfait à l'équation intégro-différentielle de diffusion. Pour le domaine moléculaire, nous avons utilisé un potentiel chimique qui, pour la solution de polymère semi-dilué, peut être représenté comme une expansion du viriel où nous n’avons pris en considération que les deuxième et troisième coefficients du viriel de la solution de polymère. En variant des paramètres tels que la rigidité du polymère, la longueur du polymère, la concentration en polymère et le régime du solvant (comme le solvant thêta), que ce soit pour une surface colloïdale purement répulsive, pour une surface adsorbée ou pour la surface d'une couche de polymère greffé, nous avons été en mesure d'améliorer la barrière répulsive due aux polymères libres entre les particules et donc nous avons trouvé des conditions de la stabilisation cinétique du système
Stable colloidal dispersions with evenly distributed particles are important for many technological applications. Due to Brownian motion colloidal particles have constant collisions with each other which often lead to their aggregation driven by the long range van der Waals attraction. As a result the colloidal systems often tend to precipitate. A number of methods have been devised to minimize the effect of long-range van der Waals attraction between colloidal particles or to override the influence of the attraction in order to provide the colloidal stability.In the PhD thesis we investigated the colloidal stabilization in solutions of free polymers which is commonly referred to as depletion stabilization. Previous theoretical studies of free-polymer induced (FPI) stabilization were based on oversimplified models involving uncontrolled approximations. Even the most basic features of the depletion stabilization phenomenon were unknown. It was unclear how the PI repulsion depends on the solution parameters, polymer structure and monomer/surface interactions.The free polymer chains were modeled as random walks in a self-consistent molecular field that satisfied to diffusion-like integro-differential equation. As the molecular field we used the chemical potential that for semi-dilute polymer solution can be represented as a virial expansion where we took into account only second and third virial coefficients of the polymer solution. Varying the parameters like polymer stiffness, polymer length, polymer concentration and solvent regime (like theta solvent) whether it is for purely repulsive colloidal surface, adsorbed surface or surface with grafted polymer layer we were able to enhance the repulsive barrier due to the free polymers between the particles and therefore found conditions for kinetic stabilization of the system

Polymeric and biological disordered materials are characterized by unique dynamical features. Although the details of the physical dynamical mechanisms are different, the disorder seems to be a common cause for non-exponential relaxation in these materials. The numerous experimental results which reveal a rather universal form of relaxation, namely a KWW or stretched exponential type function ( e-t/tb , beta < 1) have not yet been adequately explained by a unified theory. Such a disordered polymeric system is studied in this thesis and its relaxation is analysed in the framework of the well known Rouse model. This model allows for exact solutions and different types of disorder are analysed here. Exact solution and a good control over the disorder provide us with a fundamental description of the transition towards KWW behaviour. Our results favor a theory of relaxation based on parallel relaxation modes. The second part of the thesis focuses on the elasticity of a single polymer chain. The correct statistical mechanical ensemble associated with an experimental measurement probing single chain properties is an issue of great interest given the breakthroughs in the development of methods which can directly probe single chain mechanics. The complicated force-extension expressions obtained for a chain subjected to spatial constraints are available only as approximations, even for ideal models. The use of such relations in theoretical studies as well as in computer simulations is cumbersome and time consuming. A systematic method to construct simpler but still accurate expressions for the force function is given. As we demonstrate, these approximations can provide expressions with an arbitrary degree of accuracy and the proper mean statistical properties.

In this thesis, we study the expected mean of the torsion angle of an n-stepequilateral random walk in 3D. We consider the random walk is generated within a confining sphere or without a confining sphere: given three consecutive vectors →e1 , →e2 , and →e3 of the random walk then the vectors →e1 and →e2 define a plane and the vectors →e2 and →e3 define a second plane. The angle between the two planes is called the torsion angle of the three vectors. Algorithms are described to generate random walks which are used in a particular space (both without and with confinement). The torsion angle is expressed as a function of six variables for a random walk in both cases: without confinement and with confinement, respectively. Then we find the probability density functions of these six variables of a random walk and demonstrate an explicit integral expression for the expected mean torsion value. Finally, we conclude that the expected torsion angle obtained by the integral agrees with the numerical average torsion obtained by a simulation of random walks with confinement.

Disordered systems are among the most difficult and most fascinating problems in statistical mechanics. One speaks of disordered (or complex) system when the dynamics, or the structures that appears within the system, exhibits a rich variety of behaviours, while the microscopic entities the system is made of, and the interactions among these entities, are a priori simple. In this thesis we consider two famous examples of these systems: spin glasses and directed polymers in random environments. In the first part of the thesis we study a variant of the Sherrington-Kirkpatrick (SK) model, the SK model with ferromagnetic interactions. More precisely the Hamiltonian that describes the model is a combination of a SK and Curie-Weiss Hamiltonian. Our aim is to extend the well known results obtained in the SK model, trying to describe this new model in the high temperature region. The main result is that the two key parameters, the magnetization and the overlap, are asymptotically close to constants ? and q, That are the unique solutions of the so-called replica symmetric equations of this model. We then use this result to study the thermodynamical limit of the free energy and the behaviour of the Gibbs measure. In the second part of the thesis we consider two models of directed polymers in random environment. First of all we consider a Brownian polymer in a Gaussian environment, fully determined by its covariance function. In this case it is known that the thermodynamical limit of the free energy exists and it is expected that the polymer is in the strong disorder regime for low temperatures. We give a better estimate of the limit of the free energy in order to quantify how far we are from the weak disorder regime. Then we modify the hypothesis on the covariance of the environment, to determine if one ever leaves the strong disorder regime. After this we consider a continuous time random walk in a white noise potential, making a link between the last result and this new model.

Thesis (Ph.D.)--Chemistry and Biochemistry, Georgia Institute of Technology, 2009.
Committee Chair: Marcus Weck; Committee Member: Bunz, Uwe; Committee Member: Collard, David; Committee Member: Jones, Christopher; Committee Member: Payne, Christine

The synthesis and preliminary optoelectronic properties of a series of donor-acceptor (DA) type polymers differing by the acceptor units in the polymer backbone were investigated. Polymers CoP1, CoP2 and CoP3 were designed to yield alternating DA segments with randomly distributed different acceptor units along polymer backbone. The combination of neutral state red colored and neutral state green colored materials resulted in different neutral state colors with respect to their additional acceptor unit. 5,8-Dibromo-2,3-bis(4-tert-butylphenyl) quinoxaline, 5,8-dibromo-2,3-di(thiophen-2-yl)quinoxaline and 4,7-dibromobenzo[c][1,2,5]selenadiazole units were perceived as additional acceptor units and these constituents were combined with the 4,7-dibromo-2-dodecyl-2H-benzo[d][1,2,3]triazole unit and the 2,5-bis(tributylstannyl)thiophene moiety via Stille coupling. The resultant donor acceptor type random copolymers indicated that possessing 5,8-dibromo-2,3-di(thiophen-2-yl)quinoxaline as an extra electron deficient with 4,7-dibromo-2-dodecyl-2H-benzo[d][1,2,3]triazole unit on the same polymer backbone originated a neutral state black colored copolymer along with spanning the entire visible spectrum.

The commercialization of proton exchange membrane (PEM) fuel cells depends largely upon the development of PEMs whose properties are enhanced over current perfluorinated sulfonic acid PEMs. Understanding how a PEMâ s molecular weight and morphology affect its relevant performance properties is essential to this effort. Changes in molecular weight were found to have little effect on the phase separated morphologies, water uptake, and proton conductivities of random copolymers. Changes in block length, however, have a pronounced effect on multiblock copolymers, affecting surface and bulk morphologies, water uptake, proton conductivity, and hydrolytic stability, suggesting that multiblock copolymer PEM properties may be optimized by changes in morphology. A major goal of current proton exchange membrane fuel cell research involves developing high temperature membranes that can operate at ~120 °C and low humidites. Multiblock copolymers synthesized from 100% disulfonated poly(arylene ether sulfone) (BPSH100) and naphthalene polyimide (PI) oligomers may be an alternative. At block lengths of ~15 kg/mol they displayed no morphological changes up to 120 °C or even higher. Water desorption was observed to decrease with increasing block length. The copolymers exhibited little to no water loss during a 200 °C isotherm in contrast to random BPSH copolymers and Nafion. A BPSH100-PI multiblock copolymer with large block length appears to have morphological stability and retain water at temperatures exceeding 120 °C, suggesting its candidacy as a high temperature PEM. A growing number of alternative PEM research efforts involve multiblock copolymer chemistries, but little emphasis is placed on the methods used to couple the oligomers. Fluorinated linkage groups can help increase block efficiency during coupling, but their effect on a PEM is not well-known. The choice of linkage type, hexafluorobenzene (HFB) vs. decafluorobiphenyl (DFBP), appears to have small but observable influences on multiblock copolymers with disulfonated and unsulfonated poly(arylene ether sulfone) oligomers. DFBP linkages promote greater phase separation than HFB linkages, resulting in increased stiffness, decreased ductility, and increased proton conductivity at low humidities. DFBP linkages also promote more surface enrichment of fluorine, causing changes in surface morphology and slightly increased water desorption, but determining the impact on actual fuel cell performance requires further research.
Ph. D.

Le modèle d'accrochage de polymère décrit le comportement d'une chaîne de Markov en interaction avec un état donné. Cette interaction peut attirer ou repousser la chaîne de Markov et elle est modulée par deux paramètres, h et β. Quand β = 0 on parle de modèle homogène, qui est complètement solvable. Le modèle désordonné, i.e. quand β > 0, est mathématiquement le plus intéressant. Dans ce cas, l'interaction dépend d'une source d'aléa extérieur indépendant de la chaîne de Markov, appelée désordre. L'interaction est réalisée en modifiant la loi originelle de la chaîne de Markov par une mesure de Gibbs et la probabilité obtenue définit le modèle d'accrochage de polymère. Le but principal est d'étudier et de comprendre la structure des trajectoires typiques de la chaîne de Markov sous cette nouvelle probabilité. Le premier sujet de recherche concerne le modèle d'accrochage de polymère où le désordre est à queues lourdes et où le temps de retour de la chaîne de Markov suit une distribution sous-exponentielle. Dans notre deuxième résultat nous étudions le modèle d'accrochage de polymère avec un désordre à queues légères et le temps de retour de la chaîne de Markov avec une distribution à queues polynomiales d'exposant α > 0. On peut démontrer qu'il existe un point critique, h(β). Notre but est comprendre le comportement du point critique quand β -> 0. La réponse dépend de la valeur de α. Dans la littérature on a des résultats précis pour α < ½ et α > 1. Nous montrons que α ∈ (1/2, 1) le comportement du modèle dans la limite du désordre faible est universel et le point critique, opportunément changé d'échelle, converge vers la même quantité donnée par un modèle continu
The pinning model describes the behavior of a Markov chain in interaction with a distinguished state. This interaction can attract or repel the Markov chain path with a force tuned by two parameters, h and β. If β = 0 we obtain the homogeneous pinning model, which is completely solvable. The disordered pinning model, i.e. when β > 0, is most challenging and mathematically interesting. In this case the interaction depends on an external source of randomness, independent of the Markov chain, called disorder. The interaction is realized by perturbing the original Markov chain law via a Gibbs measure, which defines the Pinning Model. Our main aim is to understand the structure of a typical Markov chain path under this new probability measure. The first research topic of this thesis is the pinning model in which the disorder is heavy-tailed and the return times of the Markov chain have a sub-exponential distribution. In our second result we consider a pinning model with a light-tailed disorder and the return times of the Markov chain with a polynomial tail distribution, with exponent α > 0. It is possible to show that there exists a critical point, h(β). Our goal is to understand the behavior of the critical point when β -> 0. The answer depends on the value of α and in the literature there are precise results only for the case α < ½ et α > 1. We show that for α ∈ (1/2, 1) the behavior of the pinning model in the weak disorder limit is universal and the critical point, suitably rescaled, converges to the related quantity of a continuum model

Da un punto di vista chimico e fisico, un polimero è una lunga catena di unità ripetute, chiamate monomeri, quasi identiche nella struttura, ma che possono differire tra loro per il grado di affinità rispetto ad alcuni solventi. Questa caratteristica permette di avere delle interazioni tra il polimero e l’ambiente in cui esso si trova. Tale interazione può dare luogo a fenomeni di localizzazione e concentrazione ed è possibile osservare una transizione di fase. Nel caso in cui questa regione è un punto o una linea si parla di modello di pinning, che rappresenta il principale oggetto di studio di questa tesi. Matematicamente il modello di pinning descrive il comportamento di una catena di Markov in interazione con uno suo stato dato. Questa interazione può attirare o respingere il cammino della catena di Markov con una forza modulata da due parametri, h e β. Quando β = 0 si parla di modello omogeneo, che è completamente risolubile. Il modello disordinato, i.e., β > 0, è matematicamente più interessante. In questo caso l'interazione dipende da un parametro aleatorio esterno, indipendente dalla catena di Markov, chiamato disordine. L’interazione è realizzata modificando la legge originale della catena di Markov attraverso una misura di Gibbs (dipendente dal disordine, h e β). L’obiettivo principale è comprendere la struttura della catena di Markov rispetto a questa nuova probabilità. Il primo lavoro di ricerca di questa tesi riguarda il modello di pinning in cui si considera un disordine a code pesanti e il tempo di ritorno della catena di Markov avente una distribuzione sub-esponenziale. Noi dimostriamo che l’insieme dei tempi in cui la catena di Markov visita lo stato dato, opportunamente riscalato, converge in legge verso un insieme limite, dipendente unicamente dal disordine. Dimostriamo inoltre che esiste una transizione di fase con un punto critico aleatorio sotto il quale l’insieme limite è banale. In un secondo lavoro consideriamo il modello di pinning con un disordine a code leggere e il tempo di ritorno della catena di Markov con una distribuzione a code polinomiali di esponente 0 < α < 1. Sotto queste ipotesi si può dimostrare che esiste un’interazione non banale tra i parametri h e β che dà origine a un punto critico, h_c (β), dipendente unicamente dalle leggi del disordine e della catena di Markov. Se h > h_c (β), allora la catena di Markov è localizzata attorno allo stato dato e lo visita un numero infinito di volte. Altrimenti, se h < h_c (β), la catena di Markov è delocalizzata. Un problema molto interessante riguarda il comportamento del modello nel limite del disordine debole: più precisamente vogliamo comprendere il comportamento del punto critico h_c(β) quando β → 0. Nel caso 1/2 < α < 1, in letteratura non esistono stime precise sull’asintotica di h_c (β) per β → 0. Aver trovato l’asintotica precisa rappresenta il risultato più importante di questa tesi.
A polymer is a long chain of repeated units (monomers) that are almost identical, but they can differ in their degree of affinity for certain solvents. Such property allows to have interactions between the polymer and the external environment. This interaction can attract or repel the polymer, giving rise to localization and concentration phenomena. It is then possible to observe the existence of a phase transition. Whenever such region is a point or a line, then we talk about pinning model, which represents the main subject of this thesis. From a mathematical point of view, the pinning model describes the behavior of a Markov chain in interaction with a distinguished state. This interaction can attract or repel the Markov chain path with a force tuned by two parameters, h and β. If β = 0 we obtain the homogeneous pinning model, which is completely solvable. The disordered pinning model, which corresponds to β > 0, is most challenging and mathematically interesting. In this case the interaction depends on an external source of randomness, independent of the Markov chain, called disorder. The interaction is realized by perturbing the original Markov chain law via a Gibbs measure, which depends on the disorder, hand β. Our main aim is to understand the structure of the Markov chain under this new probability measure. The first research topic of this thesis is the pinning model in which the disorder is heavy-tailed and the return times of the Markov chain have a sub-exponential distribution. We prove that the set of the times at which the Markov chain visits the distinguished state, suitably rescaled, converges in distribution to a limit random set which depends only on the disorder. We show that there exists a phase transition with a random critical point, below which the limit set is trivial. In the second part of the thesis We consider a pinning model with a light-tailed disorder and the return times of the Markov chain with a polynomial tail distribution, with exponent 0 < α < 1. It is possible to show that there exists a non-trivial interaction between the parameters h and β. Such interaction gives rise to a critical point, hc (β), depending only on the law of the disorder and of the Markov chain. If h > hc (β), then the Markov chain visits infinitely many times the distinguished state and we say that it is localized. Otherwise, if h < hc (β), then the Markov chain visits such state only a finite number of times. Therefore the critical behavior of the model is deeply connected with the structure of hc (β). A very challenging problem is to describe the behavior of the pinning model in the weak disorder regime. To be more precise, one wants to understand the behavior of the critical point when β → 0. In the case of 1/2 < α < 1, in the literature there are non-matching estimates about the asymptotics of hc (β) as β → 0. Getting the exact asymptotics for hc (β) represents the most important result of this thesis.

Com o intuito de melhorar a eficiência dos dispositivos emissores de luz poliméricos uma das técnicas utilizadas é o confinamento da conjugação, diminuindo as perdas de energia em sítios de extinção, como fins de cadeia, defeitos ou armadilhas. Além disso, o confinamento quântico permite o controle do comprimento de onda emissivo desses materiais. Um dos mecanismos para o confinamento é a copolimerização, por meio da qual bloco conjugados são inseridos como grupos laterais na cadeia principal ou espaçadores nãoconjugados são inseridos ao longo da cadeia principal conjugada, limitando o comprimento da conjugação. O presente trabalho visou sintetizar e estudar as propriedades de copolímeros estatísticos derivados do PPV contendo segmentos com diferentes graus de conjugação distribuídos aleatoriamente na cadeia e limitados por segmentos não conjugados, e o estudo do comportamento desses materiais como camada ativa em dispositivos emissores de luz (PLEDs). Para a obtenção dos copolímeros randômicos poli[bis-(fenilenovinileno)-stat-(1,8-bis- (2,6-dioximetano-1,4- fenilenovinileno)-dioxioctano)-1,4-fenileno) (RBPV-DODM-PPV) utilizou-se a rota de Wittig, a partir dos monômeros: tereftaldeído (um dialdeído completamente conjugado), 1,8 bis (4 formil 2,6 dimetoxifenoxi) octano (um dialdeído interespaçado por uma cadeia saturada de oitometilenos) e o dicloreto de 1,4 bis (trifenilfosfôniometil) benzeno. Três razões molares x:y dos monômeros dialdeídos foram utilizadas para sintetizar os polímeros randômicos, obtendo-se diferentes proporções e tamanhos de segmentos conjugados distribuídos aleatoriamente nas cadeias poliméricas. Os materiais foram caracterizados por espectroscopia de ressonância magnética nuclear (RMN), no infravermelho, UV-visível, e fluorescência. A técnica de GPC foi utilizada para obtenção das massas moleculares e medidas de Tg foram realizadas por meio de DSC. As propriedades físico-químicas desses materiais foram analisadas em função das razões molares x:y utilizadas nas sínteses. E um estudo estatístico foi realizado para verificar as probabilidades de distribuição dos diferentes segmentos conjugados ao longo da cadeia em função dessas razões. Um estudo da morfologia e espessura dos filmes poliméricos em função dos parâmetros de deposição foi realizado a fim de descobrir as melhores condições para se obter filmes homogêneos e com espessuras da ordem de 20 a 60nm, necessários para alcançar melhores eficiências nos diodos emissores de luz poliméricos (PLEDs). Para a fabricação dos PLEDs foram utilizados ITO e Al como anodo e catodo, respectivamente, e uma camada de 20nm do polímero estatístico como matriz ativa e eletroluminescente. Para facilitar o transporte de portadores de cargas, camadas de PEDOT:PSS e BPBD foram colocadas entre o filme polimérico e os eletrodos. Também foram realizados testes com filmes da molécula Alq-3 como camada transportador-injetora de elétrons. Os dispositivos apresentaram eletroluminescência EL em quase toda a faixa do espectro visível, com máximos na região do ciano, para o copolímero R55 e na região do verde, para o copolímero p37. Baseado no mecanismo de Forster de transferência de energia, concluímos que os filmes desses polímeros estatísticos comportam-se como sistema hospedeiro-hóspede, devido a sobreposição parcial dos espectros de absorção e emissão dos polímeros, ocorrendo a transferência dos excitons-singletos dos segmentos de maior gap para os de menor gap, e, assim, o deslocamento dos centros emissivos para o vermelho e o aumento da eficiência dos dispositivos.
In order to improve the efficiency of polymeric light-emitting devices one of the techniques used is the conjugation confinement, decreasing the losses of energy in quenching sites, such as chain ends, defects or impurities. Moreover, the quantum confinement allows control the emissive wavelength of these materials. One of the confinement mechanisms is the copolymerization, which conjugated blocks are inserted as side groups in the main chain or non-conjugated spacers are inserted along the conjugated main chain, limiting the conjugation length. This study aimed synthesize and study the properties of random copolymers containing segments with different conjugation degrees randomly distributed in the chain and limited by no conjugated segments, and the study of the behaviour of these materials as active layer in a light emitting devices (PLEDs). To obtain random copolymers of poly [bis (fenilenovinileno)-stat-(1,8-bis-(2,6-dioximetano- 1, 4 - fenilenovinileno)-dioxioctano) -1,4-phenylene) (RBPV-DODM - PPV) have been used the Wittig route, from monomers: terephtaldeyde (a dialdeyde completely conjugated), 1.8 - bis (4 - formyl - 2.6 - dimethoxiphenoxi) octane (a dialdeyde interspaced by a saturated chain of eight methylene) and dichloride of 1.4 - a (triphenylphosphoniomethil) benzene. Three molars reasons x: y of dialdeydes monomers were used to synthesize the random polymers, obtaining various proportions and sizes of conjugated segments randomly distributed in the polymer chains. Infrared (IR) and ultravioletvisible (UVvis)spectroscopies, hydrogen nuclear magnetic resonance (1HNMR) spectrometry and differential scanning calorimetry(DSC) were used to characterize the prepared copolymersstructures. Polymers molecular weights were determined by gel permeation chromatography (GPC). The physical-chemical properties of these materials were analyzed by the molars reasons x: y used in the synthesis. And a statistical study was conducted to ascertain the probability of distribution of the various conjugated segments along the chain by these reasons. A study of the morphology and thickness of the polymer films as a function of the parameters of deposition was conducted in order to find out the best conditions to obtain homogeneous films with thickness in the order of 20 to 60 nm, necessary to achieve the best efficiencies in the polymer light emitting diode (PLEDs). For the manufacture of PLEDs ITO and Al were used as anode and cathode respectively, and a layer of 20nm of the statistical polymer as active matrix and electroluminescent. To facilitate the transport of charge carriers, layers of PEDOT: PSS and BPBD were placed between the film and polymer electrodes. Tests were also carried out with films of the molecule Alq-3 as layer electron carrier / injector. The devices had electroluminescence EL in almost the entire range of the visible spectrum, with maximum in the region of cyan, for the copolymer R55 and in the green, for the copolymer p37. Based on the Forster mechanism of energy transfer, we find that the films of these statistical polymers behave themselves as host-guest system, due to partial overlap of absorption and emission spectra of the polymers, occurring the transfer of excitons-singletes of the segments with largest gap for the smaller gap, and thus the displacement of the emission centers for the red.

Cette thèse est consacrée à l’étude des liens entre les polymères dirigés en milieu aléatoire,l’équation de la chaleur stochastique avec bruit multiplicatif (SHE) et l’équation Kardar-Parisi-Zhang (KPZ), en différentes dimensions d’espace. En dimension d = 1, l’équation KPZ et l’équation SHE font partie d’une classe de modèle possédant des coefficients d’échelle et des limites d’échelle non-standards, appelée la classe d’universalité KPZ. Il est possible de montrer que certains modèles particuliers de polymères, dits exactement solubles, font partie de la même classe, mais un des problèmes ouverts du domaine est de montrer l’universalité de ce résultat pour des modèles généraux de polymères dirigés. Toutefois, sous un changement d’échelle diffusif, on peut montrer que la fonction de partition point-à-point des polymères généraux converge vers la solution de l’équation de la chaleur stochastique, montrant un résultat d’universalité KPZ faible des modèles de polymères. En dimension supérieure, il n’est pas encore certain que les équations KPZ et SHE soient bien posées. Pour étudier ces équations en dimension supérieure, l’approche que l’on considérera consiste à régulariser les équations KPZ et SHE avec un bruit moyenné en espace, puis à regarder la limite des solutions lorsque la régularisation est dissipée. Il se trouve que dans un certain régime de paramètres, les solutions de ces équations régularisées sont reliées aux fonctions de partition d’un modèle de polymère dirigé, et l’on peut mettre à profit les techniques et résultats de la littérature des polymères pour les étudier
This thesis is dedicated to the study of the links between directed polymers in random environment, the stochastic heat equation with multiplicative noise (SHE) and the Kardar-Parisi-Zhang equation (KPZ), under different space dimensions. In dimension d= 1, the KPZ equation and the SHE equation belong to a particular class of models which feature non-standard scaling coefficients and non-standard scaling limits. This class is called the KPZ universality class. It is possible to prove that some specific polymer models, which are called exactly solvable models, belong to this class, but one of the open problems in this field is to show that this result should be universal, that is that polymer models should belong to the KPZ universality class for very general types of environment. Nevertheless, one can prove that under a scaling limit, the point-to-point partition function of general polymer models converges towards the solution of the SHE equation, which can be seen as a weak universality result for the polymer models. In higher space dimension, it is not clear whether the KPZ and SHE equations should be well-posed. In order to study these equations in higher dimension, we will consider them with a noise that is be regularized in space (in this case, the solutions of the equations are well-defined) and try to look at the limiting behaviour of the solutions when the regularization is removed. It turns out that for a certain choice of parameters, the solutions of the regularized equations are linked to the partition functions of a directed polymer model, and one can use standard polymer techniques to study the asymptotic behaviour of the solutions

It is generally accepted that in random styrene ionomers the ion-pairs tend to associate to form small aggregates termed multiplets which are embedded in the polymer and act as crosslinks. At sufficiently high ion-contents, ion-rich regions termed clusters are believed to phase-separate from the polymer matrix. In this study, the dynamic mechanical properties of random styrene ionomers containing various concentrations of alkali-metal methacrylate groups were measured over a range of temperatures at several different frequencies. Two peaks are evident in the loss tangent (tan $ delta)$ vs. temperature curves, indicating that the materials are phase-separated, with each tan $ delta$ peak resulting from the glass transition (T$ sb{ rm g})$ of a separate phase. This hypothesis is supported by the magnitudes of the apparent activation energies determined in this study for each transition. The relative heights and areas of the tan $ delta$ peaks indicate that the cluster phase becomes dominant at ion contents above ca. 6 mol %, and that complete phase inversion occurs at relatively low ion-contents. This finding, together with the results of small-angle X-ray studies performed elsewhere, led to the development of a new model for the morphology of random styrene ionomers. The model is based on aggregation of ion-pairs to form multiplets. Each ion-pair in a multiplet effectively anchors the polymer chain to which it is attached, thereby forming a layer of polymer with restricted mobility surrounding the multiplet. Isolated multiplets act as large crosslinks, thus increasing the glass transition temperature of the material. As the ion content is increased, the regions of restricted mobility surrounding each multiplet overlap to form larger contiguous regions of restricted mobility. When these regions become sufficiently large, they exhibit phase-separated behaviour and are termed clusters. The model is in good agreement with a very wide range of experimentally observed p

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2005.
Includes bibliographical references (p. 112-124).
In Part I of the thesis, a general physical framework describing the kinetics of protein- DNA interaction is developed. Recognition and binding of specific sites on DNA by proteins is central for many cellular functions such as transcription, replication, and recombination. In the process of recognition, a protein rapidly searches for its specific site on a long DNA molecule and then strongly binds this site. Earlier studies have suggested that rapid search involves sliding of the protein along the DNA. I treat sliding as a one-dimensional diffusion in a sequence-dependent rough energy landscape. I demonstrate that, despite the landscape's roughness, rapid search can. be achieved if one-dimensional sliding is accompanied by three-dimensional diffusion. I estimate the range of the specific and nonspecific DNA-binding energy required for rapid search and suggest experiments that can test the proposed mechanism. It appears that realistic energy functions cannot provide both rapid search and strong binding of a rigid protein. To reconcile these two fundamental requirements, a search-and-fold mechanism is proposed that involves the coupling of protein binding and partial protein folding. In this regard, I propose an effective energy landscape that incorporates longitudinal (sliding) and transversal (folding) dynamics. I also study the influence of finite correlation length in the binding potential profile on the one-dimensional diffusion. The proposed mechanism has several important biological implications for search in the presence of other proteins and nucleosomes, simultaneous search by several proteins, etc.
(cont.) In Part II, I analyze the behavior of random walks in presence of smooth manifolds. First, I treat a random walk (or gaussian polymer) confined to a half-space using a field-theoretic approach. Using path integrals, I derive basic scaling relations and the probability distribution function for arbitrary coupling strength between the polymer and the manifold. Next, I consider self-avoiding polymers attached to the tip of an impenetrable probe. The scaling exponents [gamma] ₁ and [gamma]₂, characterizing the number of configurations for the attachment of the polymer by one end, or at its midpoint, are shown to vary continuously with the tip's angle. These apex exponents are calculated analytically by [epsilon]-expansion and compared to numerical simulations in three dimensions. I find that when the polymer can move through the attachment point, it typically slides to one end; the apex exponents quantify the entropic barrier to threading the eye of the probe.
by Michael Slutsky.
Ph.D.

The aim of this study was to explore the effects of a range of variables on the properties of ionomers, and also to investigate the structure-morphology-property relationships in these materials in order to advance our understanding in the light of the EHM model. In the first part of the work, the influence of variables such as sample preparation conditions, molecular weight and degree of neutralization on the dynamic mechanical properties of ionomers were studied.
In the second part, the effects of surfactant addition and chemical structure of ionomers were investigated. Sodium sulfonated polystyrene ionomers were mixed with the surfactant sodium p-dodecylbenzene sulfonate. This surfactant molecule has a head group identical to the ionic group of the polymer chain. Therefore, the head group resides in the multiplets, and tail group in the restricted mobility region surrounding the multiples. This results in a dramatic decrease in the cluster $T sb{ rm g}$ as a function of the amount of added surfactant. In the next project, the contact surface area of the chain and its effect on multiplet size was studied. An inverse relationship between contact surface area and size of multiplet was found; if the size of multiplet is decreased, the cluster $T sb{ rm g}$ increases and the ionic plateau is also higher and longer. Furthermore, when the pendant group of the polymer is replaced by a bulkier group, the chain becomes stiffer. As a result, the two $T sb{ rm g}$s shift to higher temperatures. In still another part of the study, the dynamic mechanical properties of poly(styrene-co-sodium methacrylate) ionomers were re-investigated in detail. Discontinuities in the plots of various parameters obtained from the tan $ delta$ vs temperature and modulus vs temperature curves as a function of the ion contents were found. These discontinuities suggest that there are two morphological changes in the system as a function of the ion contents, one at ca. 4-6 and the other at ca. 12-14 mol % of ions. In addition, the data were interpreted using filler and percolation concepts. The Guth equation for modulus vs filler content is applicable up to 30 volume % of the clusters. The Halpin-Tsai equation for the regular system is also applicable at low ion contents. For the percolation approach, the percolation threshold was found at 5.4 mol % of ions. The critical exponent and critical volume fraction of clusters were found to be 1.31 and 0.64, respe

Thesis (PhD (Chemistry and Polymer Science))--University of Stellenbosch, 2006.
Propylene/1-pentene random copolymers are a relatively new family of random copolymers being prepared by Sasol Polymers and reveals high impact strength, good tensile properties, excellent optical properties, good rheological properties and a large pool of processing possibilities. These commercial copolymers are being prepared with stereospecific heterogeneous Ziegler-Natta catalytic systems containing multiple active sites and therefore producing copolymers with a varying degree of stereoregularity. Two different groups of propylene/1-pentene random copolymers were received by Sasol Polymers and investigated in this project. The first group (Group 1, Polymers A - F) consisted of six totally different batches of commercial propylene/1-pentene copolymers which were produced by different catalyst systems. All had different melt flow indices (MFIs) and different 1-pentene contents and all of the copolymers, except for one, were nucleated. The second group (Group 2, Polymers G - J) were produced by the same catalyst, but with varying donor:catalyst ratios and also differing in their 1-pentene content. Investigation of the Group 1 copolymers was used in order to construct a “molecular toolbox” which was then used to study the Group 2 copolymers. The original commercial copolymers were all studied by various analytical techniques: high-temperature carbon thirteen nuclear magnetic resonance spectroscopy (13C-NMR), high-temperature gel permeation chromatoghraphy (HT-GPC), crystallization analysis fractionation (CRYSTAF), differential scanning calorimetry (DSC), wide angle X-ray diffraction (WAXD) and positron annihilation lifetime spectroscopy (PALS). The random copolymers were all fractionated by preparative TREF and the fractions analyzed utilizing the following analytical techniques: 13C-NMR, HT-GPC, CRYSTAF and DSC. The results of these analyses were used to investigate inter alia the distribution of 1-pentene in the copolymers. In order to investigate the low molecular weight material of the copolymers, which were part of the room temperature fraction during TREF, solvent extractions were carried out using different solvents and different extraction techniques. A complete structural analysis study was carried out on the extracts. The percentages of xylene-solubles were also determined during the quantitative xylene extraction study of the copolymers. Characterization of the xylene non-soluble material was carried out using 13C-NMR, HT-GPC, CRYSTAF, DSC and WAXD in order to compare the properties of the unextracted copolymers with the material after removal of the xylene soluble fraction. Positron annihilation lifetime spectroscopy (PALS) was used as an alternative investigation method for the Group 1 copolymers and their XNS fractions in order to determine what type of information this novel analytical method could generate and how the results compared with those of previous PALS studies on poly-olefins. A new fractionation technique, preparative solution fractionation (SF), was developed and evaluated. The commercial propylene/1-pentene copolymers were fractionated using this novel technique, the fractions were analyzed by 13C-NMR, HT-GPC, CRYSTAF and DSC and the results were compared with previously existing fractionation methods, namely TREF and CRYSTAF. A final study was done on the random copolymers by blending one of the commercial Ziegler-Natta catalyzed propylene/1-pentene copolymers with a tailored, low 1-pentene content, metallocene propylene/1-pentene copolymer in different ratios. The blends were analyzed by molecular weight, thermal and crystal phase analysis in order to investigate the effect of the tailored, highly isotactic propylene/1-pentene copolymer on the properties the commercial random copolymers. Throughout the project the influence of the 1-pentene as well as the donor:catalyst ratio on the copolymers was investigated. This study, in its entirety, therefore allow a better understanding of the effects that the commercial, heterogeneous, transition metal catalysts have on the make up of the copolymers and, by extension, the ultimate properties of the materials.

Modeling of polymer chains, that is long linear molecules made up of a sequence of simpler units called monomers, has, for a lot of time, received a lot of attention in physics, chemistry, biology, ... Mathematics belongs to this list too. For example, probabilistic models that naturally arise in statistical mechanics have been widely studied by mathematicians for the very challenging and novel problems that they pose. This is true to the extent that, in probability, the word polymer has become synonymous with self–avoiding walk, a basic and extremely difficult mathematical entity. The interaction of a polymer with the environment leads to even more challenging questions: these are often tackled in the framework of directed walks. Restricting attention to directed trajectories is a way of enforcing the self–avoiding constraint that leads to much more tractable models. Still, the interaction with the environment may quickly lead to extremely difficult questions. A particularly interesting situation is that of an inhomogeneous polymer (or copolymer) in the proximity of an interface between two selective solvents. The polymer is inhomogeneous in that its monomers may differ in some characteristics and, consequently, the interaction with the solvents and the interface may vary from monomer to monomer. In interesting cases there can be a phase transition between a state in which the polymer sticks very close to the interface (localized regime) and a state in which it wanders away from it (delocalized regime). The typical mechanism underlying such phase transitions is an energy/entropy competition. The main task of this Ph.D. thesis is to introduce and study random walk models of polymer chains with the purpose of understanding this competition in a deep and quantitative way. Since a random walk can be regarded as an example of an abstract polymer, the idea of modeling real polymers using random walks is quite natural and it has proved to be very successful. The models we are going to consider are modifications of a basic model intro- duced in the late eighties by T. Garel, D. A. Huse, S. Leibler and H. Orland that in turn had translated into the language of theoretical physics ideas that were developing in the applied sciences. Despite the fact that the definition of these models is extremely elementary, their analysis is not simple at all. For a number of interesting issues there is still no agreement in the physical literature. From a mathematical viewpoint it has taken quite a lot of time and effort to rigorously derive their basic properties, and several interesting questions are still open. In this Ph.D. thesis we present new results that answer some of these questions. The approach taken here is essentially probabilistic, and it is interesting to note how the analysis performed has required the application of a wide range of techniques in- cluding Large Deviations and Concentration Inequalities (Ch. 2), Perron–Frobenius Theory (Ch. 3), Renewal Theory (Ch. 4) and Fluctuation Theory for random walks (Ch. 5 and 6). A numerical and statistical study has also been performed (Ch. 2). Reciprocally, the study of the models stimulates the extension of these techniques, see, for instance, the Local Limit Theorem for random walks conditioned to stay positive presented in Chapter 6. The thesis is organized as follows. The definition of the models we consider is given in detail in Chapter 1, where we also give some motivation and we collect the known results from the literature. The following five chapters contain original results. A detailed outline of the thesis may be found in Section 5 of Chapter 1.

Candidate materials for low-loss optical waveguides based on poly(glycidyl methacrylate-ran-pentafluostyrene) (P(GMA-ran-PFS)) copolymers were synthesized by nitroxide mediated polymerization (NMP) initiated with BlocBuilder® (N-(2-methylpropyl)-N-(1-diethlphosphono-2,2-dimethylpropyl)-O-(2-carboxylprop-2-yl) hydroxylamine) bearing a succinimidyl ester group (NHS-BlocBuilder) at 90 oC in 1,4 dioxane. The copolymerizations yielded copolymers with low dispersity between 1.2-1.4. The core structure of single-mode channel waveguides was fabricated by direct UV lithographic patterning. The copolymers with low resulted in line width roughness (LWR) of about 0.16 μm, whereas LWR of copolymers with ~ 3.5 but similar compositions was about 0.5 μm. The improvement in microstructural control allotted by NMP permitted finer pattern replication for copolymers desired for optical waveguides, as suggested for photoresist polymers.
Les matériaux candidats pour des guides d'ondes optiques à faible perte à base de copolymères poly(méthacrylate de glycidyle-ran-pentafluostyrene) (poly(GMA-ran-SSP)) ont été synthétisés par la polymérisation médiée par nitroxyde (NMP) initiée avec BlocBuilder® (N-(2-méthylpropyl)-N-(1-diethlphosphono-2,2-diméthylpropyl)-O-(2-carboxylprop-2-yl) hydroxylamine) portant un groupe d'ester de succinimidyle (NHS-BlocBuilder) à 90 ° C dans du 1,4-dioxane. Les copolymérisations ont donné des copolymères à faible dispersité ( ) entre 1,2-1,4. La structure de base des guides d'ondes canaux monomodes a été fabriqué à l'aide de motifs lithographique par UV directe. Les copolymères de faible ont donné une rugosité à la largeur de ligne (LWR) d'environ 0,16 μm tandis que la LWR des copolymères avec ~3.5 mais de compositions similaires était d'environ 0,5 μm. L'amélioration du contrôle de microstructure attribué par NMP a permis la réplication des motifs plus fins pour les copolymères dont l'utilisation est souhaitée dans les guides d'ondes optiques, tel que suggéré pour les polymères photosensibles.

In this work of thesis is reported the synthesis and the optoelectronic characterization of a new family of random conjugated copolymers based on 9,9-bisalkylfluorene, thiophene and benzothiadiazole monomers unit synthesized by a palladium-catalyzed Suzuki cross-coupling reaction. The photophysical, thermal, electrochemical properties were investigated. The electronic structures of the copolymers were simulated via quantum chemical calculations. Bulk heterojunction solar cells based on these copolymers blended with fullerene, exhibited power conversion efficiency as high as 1% under illumination of 97 mW/cm2

We perform Monte-Carlo simulations of a binary, strongly separated mixture of A- and B-type homopolymers with some amount of random AB copolymers added. The interface is analyzed and the interface tension is calculated using the model of capillary waves. We can clearly demonstrate that random copolymers are localized at real, fluctuating interfaces between incompatible polymer species and micellization is not favored over adsorption. Our study proves that random copolymers are potential candidates for compatibilization of polymer-polymer mixtures. By simulating random copolymers in a one-component bulk and comparing their free energy to the copolymers adsorbed at the two-phase interface we show that the adsorption is thermodynamically stable. We use scaling arguments developed for ideal and non-fluctuating interfaces to rationalize the simulation results and we calculate the reduction of interface tension with increasing amount of the adsorbed copolymers.

The research presented in this dissertation furthers the state of the art for reliability-based design of composite structures subjected to high cycle variable amplitude (spectrum) fatigue loads. The focus is on fatigue analyses for axially loaded fiber reinforced polymer (FRP) composites that contain a significant proportion of fibers in the loading direction and thus have fiber-direction dominated failure. The four papers presented in this dissertation describe the logical progression used to develop an improved reliability-based methodology for fatigue-critical design. Throughout the analysis extensive experimental fatigue data on several material systems was used to verify the assumptions and suggest the path forward. A comparison of 12 fatigue model approaches from the literature showed that a simple linear residual strength approach (Broutman and Sahu) provides an improvement in fatigue life prediction compared to the Palmgren-Miner rule, while more complex residual strength models did not consistently improve on Broutman and Sahu. Evaluation of the effect of load history randomness on fatigue life was made using experimental results for spectra in terms of the first order autocorrelation of the stress events. For approximately reversed Rayleigh distributed fatigue loading, load sequence was not critical in the material behavior. Based on observations of empirical data and evaluation of the micro-mechanics deterioration and failure phenomena of FRP composites under fatigue loading, a new residual strength model for the tension and compression under any load history was proposed. Then this model was implemented in a stochastic framework and a method was proposed to enable calculation of the load and resistance factor design (LRFD) parameters for realistic reliabilities with relatively few computations. The proposed approach has significant advantages over traditional lifetime-damage-sum-based reliability analysis and provides a significant step toward enabling more accurate reliability-based design with composite materials.
Ph. D.

Une interface est une zone de l'espace qui sépare deux régions possédant des propriétés physiques différentes. La plupart des interfaces de la nature résultent d'un processus de croissance, mêlant une composante aléatoire et une dynamique déterministe régie par les symétries du problème. Le résultat du processus de croissance est un objet présentant des corrélations à longue portée. Dans cette thèse, nous nous proposons d'étudier la statistique d'extrême de différents types d'interfaces. Une première motivation est de raffiner la compréhension géométrique de tels objets, via leur maximum. Une seconde motivation s'inscrit dans la démarche plus générale de la statistique d'extrême de variables aléatoires fortement corrélées. A l'aide de méthodes analytiques d'intégrales de chemin nous analysons la distribution du maximum d'interfaces à l'équilibre, dont l'énergie es t purement élastique à courte portée. Nous attaquons ensuite le problème d'interfaces élastiques en milieu désordonné, principalement à l'aide de simulations numériques. Enfin nous étudierons une interface hors-équilibre dans son régime de croissance. L'équivalence de ce type d'interface avec le polymère dirigé en milieu aléatoire, un des paradigmes de la physique statistique des systèmes désordonnés, donne une portée étendue aux résultats concernant la statistique du maximum de l'interface. Nous exposerons les résultats que nous avons obtenus sur un modèle de mouvements browniens qui ne se croisent pas, tout en explicitant le lien entre ce modèle, l'interface en croissance et le polymère dirigé.

Le procédé d'injection soufflage est rendu accessible aux presses d'injection standard à travers le procédé d'injection soufflage cycle chaud, sans stockage puis réchauffe de la préforme. Le but étant de rendre accessible la production de petites séries de pièces creuses à des entreprises possédant un parc machine de presse à injecter. Les pièces sont réalisées en polypropylène et sont soufflées juste après avoir été injectées. Ce processus implique que la préforme se doit d'être suffisamment malléable pour être soufflée mais suffisamment visqueuse pour éviter de se rompre durant la phase de soufflage. Ces contraintes conduisent à une fenêtre de mise en oeuvre réduite, comprise entre la température de fusion du polymère et la température de cristallisation, soit le domaine ou le polypropylène est à l'état amorphe et suffisamment froid pour avoir une viscosité conséquente sans cristalliser. Ce procédé cycle chaud implique des gradients de température, de grands taux d'étirages et d'importantes cinétiques de refroidissement. Des mesures de rhéométrie à l'état fondu sont réalisées pour identifier le comportement de la matière dans la plage de température du procédé, de même que des tests de calorimétrie différentielle. L'observation du procédé et l'étude de la cristallisation du matériau permettent de supposer que ce dernier reste à l'état fondu durant la phase de soufflage. Un modèle rhéologique de Cross est utilisé, avec la dépendance thermique prise en compte par une loi d'Arrhénius. Le procédé est simulé à l'aide d'un logiciel de calcul par éléments finis dédié aux écoulements de fluides complexes (POLYFLOW) dans l'espace de travail ANSYS Workbench. La géométrie autorise une approche axisymétrique, facilitant ainsi la modélisation. Le calcul transitoire est lancé sous conditions anisothermes et l'auto-échauffement est considéré. Des études de sensibilité sont réalisées et révèlent l'influence de paramètres procédé tels que le comportement du matériau, la pression de soufflage et le champ de température initial. Des mesures d'épaisseurs sont réalisées en utilisant une méthode de traitement d'image permettant l'analyse des images numérisées de pièces découpées et des images issues de tomographie X des pièces. Les résultats simulés sont comparés aux mesures expérimentales. Le modèle présente les mêmes tendances que les mesures. L'existence de déformations élongationnelles, mais aussi par cisaillement lors du soufflage après contact avec le moule, est discutée. Une boucle d'optimisation est mise en place afin de déterminer numériquement la géométrie optimale de préforme. Des points de contrôle sont placés le long de la préforme et l'algorithme d'optimisation modifie les épaisseurs à ces points
Single stage injection blow molding process, without preform storage and reheat, could be run on a standard injection molding machine, with the aim of producing short series of specific hollow parts. The polypropylene bottles are blown right after being injected. The preform has to remain sufficiently malleable to be blown while being viscous enough to avoid being pierced during the blow molding stage. These constraints lead to a small processing window, and so the process takes place between the melting temperature and the crystallization temperature, where the polypropylene is in his molten state but cool enough to enhance its viscosity without crystallizing. This single stage process introduces temperature gradients, molecular orientation, high stretch rate and high cooling rate. Melt rheometry tests were performed to characterize the polymer behavior in the temperature range of the process, as well as Differential Scanning Calorimetry. A viscous Cross model is used with the thermal dependence assumed by an Arrhenius law. The process is simulated through a finite element code (POLYFLOW) in the Ansys Workbench framework. The geometry allows an axisymmetric approach. The transient simulation is run under anisothermal conditions and viscous heating is taken into account. Thickness measurements using image analysis are done and the simulation results are compared to the experimental ones. The experimental measurements are done by analizing tomography datas. The simulation shows good agreements with the experimental results. The existence of elongational strain as well as shear strain during the blowing after contact with the mold is discussed. An optimization loop is run to determine an optimal initial thickness repartition by the use of a Predictor/Corrector method to minimize a given objective function. Design points are defined along the preform and the optimization modifies the thickness at these locations. This method is compared to the Downhill Simplex Method and shows better efficiency

Copolymeres a base d'acrylate d'ethyle et porteurs de groupes lateraux zwitterionique de structure variee, soit par voie radicalaire soit par quaternarisation des precurseurs contenant une amine tertiaire. Complexation d'anion polarisable sur un homopolymere du type sulfopropylbetaine