The crystallization and melting behavior of linear polyethylene and of a series of random ethylene/styrene copolymers was investigated using a combination of classical and temperature modulated differential scanning calorimetry. In the case of linear polyethylene and low styrene content copolymers, the temporal evolutions of the melting temperature, degree of crystallinity, and excess heat capacity were studied during crystallization. The following correlations were established: 1) the evolution of the melting temperature with time parallels that of the degree of crystallinity, 2) the excess heat capacity increases linearly with the degree of crystallinity during primary crystallization, reaches a maximum during the mixed stage and decays during secondary crystallization, 3) the rates of shift of the melting temperature and decay of the excess heat capacity lead to apparent activation energies that are very similar to these reported for the crystal ac relaxation by other techniques. Strong correlations in the time domain between the secondary crystallization and the evolution of the excess heat capacity suggest that the reversible crystallization/melting phenomenon is associated with molecular events in the melt-crystal fold interfacial region. In the case of higher styrene content copolymers, the multiple melting behavior at high temperature is investigated through studies of the overall crystallization kinetics, heating rate effects and partial melting. Low melting crystals can be classified into two categories according to their melting behavior, superheating and reorganization characteristics. Low styrene content copolymers still exhibit some chain folded lamellar structure. The shift of the low melting temperature with time in this case is tentatively explained in terms of reorganization effects. Decreasing the crystallization temperature or increasing the styrene content leads to low melting crystals more akin to fringed-micelles. These crystals exhibit a lower tendency to reorganize during heating. The shift of their melting temperature with time is attributed to a decrease in the conformational entropy of the amorphous fraction as a result of constraints imposed by primary and secondary crystals. To further understand the mechanism of formation of low melting crystals, quasi-isothermal crystallization experiments were carried out using temperature modulation. The evolution of the excess heat capacity was correlated with that of the melting behavior. On the basis of these results, it is speculated that the generation of excess heat capacity at high temperature results from reversible segmental exchange on the fold surface. On the other hand, the temporal evolution of the excess heat capacity at low temperature for high styrene content copolymers is attributed to the reversible segment attachment and detachment on the lateral surface of primary crystals. The existence of different mechanisms for the generation of excess heat capacity in different temperature ranges is consistent with the observation of two temperature regimes for the degree of reversibility inferred from quasi-isothermal melting experiments. In a second project, the chain length and temperature dependences of spherulitic growth rates were studied for a series of narrow fractions of poly(ethylene oxide) with molecular weight ranging from 11 to 917 kg/mol. The crystal growth rate data spanning crystallization temperatures in regimes I and II was analyzed using the formalism of the Lauritzen-Hoffman (LH) theory. Our results are found to be in conflict with predictions from LH theory. The Kg ratio increases with molecular weight instead of remaining constant. The chain length dependence of the exponential prefactor, G0, does not follow the power law predicted by Hoffman and Miller (HM). On this basis, the simple reptation argument proposed in the HM treatment and the nucleation regime concept advanced by the LH model are questioned. We proposed that the observed I/II regime transition in growth rate data may be related to a transition in the friction coefficient, as postulated by the Brochard-de Gennnes slippage model. This mechanism is also consistent with recent calculations published by Toda in which both the rates of surface nucleation and substrate completion processes exhibit a strong temperature dependence. / Ph. D.

Le phénomène de condensation d’un gaz de bosons lorsqu’il est refroidi à zéro degrés Kelvin futdécrit par Einstein en 1925 en s’appuyant sur des travaux de Bose. Depuis lors, de nombreux physiciens,mathématiciens et numériciens se sont intéressés au condensat de Bose-Einstein et à son caractère superfluide. Nous proposons dans cette étude des méthodes numériques ainsi qu’un code informatique pour la simulation d’un condensat de Bose-Einstein en rotation. Le principal modèle mathématique décrivant ce phénomène physique est une équation de Schrödinger présentant une non-linéarité cubique,découverte en 1961 : l’équation de Gross-Pitaevskii (GP). En nous appuyant sur le logiciel FreeFem++,nous nous servons d’une discrétisation spatiale en éléments-finis pour résoudre numériquement cette équation. Une méthode d’adaptation du maillage à la solution et l’utilisation d’éléments-finis d’ordre deux nous permet de résoudre finement le problème et d’explorer des configurations complexes en deux ou trois dimensions d’espace. Pour sa version stationnaire, nous avons développé une méthode de gradient de Sobolev ou une méthode de point intérieur implémentée dans la librairie Ipopt. Pour sa version instationnaire, nous utilisons une méthode de Time-Splitting combinée à un schéma de Crank-Nicolson ou une méthode de relaxation. Afin d’étudier la stabilité dynamique et thermodynamique d’un état stationnaire, le modèle de Bogoliubov-de Gennes propose une linéarisation de l’équation de Gross-Pitaevskii autour de cet état. Nous avons élaboré une méthode permettant de résoudre ce système aux valeurs et vecteurs propres, basée sur un algorithme de Newton ainsi que sur la méthode d’Arnoldi implémentée dans la librairie Arpack. / The phenomenon of condensation of a boson gas when cooled to zero degrees Kelvin was described by Einstein in 1925 based on work by Bose. Since then, many physicists, mathematicians and digitizers have been interested in the Bose-Einstein condensate and its superfluidity. We propose in this study numerical methods as well as a computer code for the simulation of a rotating Bose-Einstein condensate.The main mathematical model describing this phenomenon is a Schrödinger equation with a cubic nonlinearity, discovered in 1961: the Gross-Pitaevskii (GP) equation. By using the software FreeFem++ and a finite elements spatial discretization we solve this equation numerically. The mesh adaptation to the solution and the use of finite elements of order two allow us to solve the problem finely and to explore complex configurations in two or three dimensions of space. For its stationary version, we have developed a Sobolev gradient method or an internal point method implemented in the Ipopt library. .For its unsteady version, we use a Time-Splitting method combined with a Crank-Nicolson scheme ora relaxation method. In order to study the dynamic and thermodynamic stability of a stationary state,the Bogoliubov-de Gennes model proposes a linearization of the Gross-Pitaevskii equation around this state. We have developed a method to solve this eigenvalues and eigenvector system, based on a Newton algorithm as well as the Arnoldi method implemented in the Arpack library.