Zugl.: Freiburg (Breisgau), Univ., Diss., 2009

archives@tulane.edu / A block copolymer (BCP) consists of two or more covalently-bound chemically distinct homopolymer blocks. These macromolecules have emerging applications in energy storage, membrane separations, and nanolithography stemming from their propensity to self-assemble into regular nanoscale structures. For a pure BCP, this self-assembly is dictated entirely by the polymer’s degree of polymerization (N), chemistry (χ), composition (f), and chain architecture. Blending together different types of these polymers provides a simpler, synthesis-free method for tuning nanoscale morphology and feature size. This dissertation describes the use of dissipative particle dynamic (DPD) simulation to develop a fundamental understanding of phase behavior in BCP/homopolymer and cyclic-linear BCP blends. Block copolymer-homopolymer blends offer a simple method for tuning nanostructure sizes to meet application-specific demands. We systematically investigated morphology and feature size in ternary blends of symmetric linear copolymers and their constituent homopolymers (A-b-B/A/B), finding a close match between simulation results and known experimental behavior. Having established DPD simulation as a valid model, we used the simulation results to explore the relationship between polymer chain length, molecular packing, and the degree of lamellar swelling with homopolymer addition in ternary blends. A consensus of theoretical and simulation work suggests that cyclic BCPs form features up to 40% smaller than their linear analogues - while also exhibiting superior thin film stability and assembly dynamics – making them intriguing candidates for nanolithography. However, the complex syntheses required to produce these molecules mean that a need for pure cyclic BCPs would present a challenge to large-scale manufacturing. Thus, we aspired to understand the self-assembly of cyclic-linear copolymer blends. We first combined DPD simulation results and strong segregation theory to develop a scaling prediction for neat BCP feature size based on experimentally-tunable parameters (χ, N, f, and polymer architecture). The resulting Revised Scaling Law quantitatively predicts domain spacings over a wide range of BCP chain lengths, segregation strengths, and compositions and offers an explanation for the significant discrepancies between prior theoretical predictions and experimental results of cyclic BCP feature size. Next, we investigated the dimensions and interfacial roughness of nanofeatures formed by cyclic-linear BCP blends. For mixtures of symmetric cyclic and linear polymers of equivalent N, up to 10% synthetic impurity had minimal impact on cyclic BCP feature dimensions. On the other hand, we found that adding small amounts of cyclic BCP was an effective method for “fine-tuning” linear BCP feature sizes. We also analyzed our simulated blend domain spacings in the context of the revised scaling law, and found deviations between simulation and theory that arose from molecular-level packing motifs not included in theory. Finally, we investigated the impact of blending polymer architectures on the BCP order-disorder transition, finding that a mismatch in molecular size and architecture can strongly inhibit ordering. These insights into blend self-assembly will assist experimentalists in the rational design of BCP materials for advanced nanolithography applications. / 1 / Amy Dubetz Goodson

In this thesis we study various dissipative processes that are associated with the flow of an atomic Bose-Einstein condensate at zero temperature. In particular, we investigate the effect of a weak correlated disorder potential on the collective dipole motion of a harmonically-confined elongated condensate. By using an extension of the Harmonic Potential Theorem, we demonstrate that the dynamics of the system can be described equivalently in terms of a disorder potential oscillating relative to a stationary condensate. This latter point of view allows the application of linear response theory to determine the drag force experienced by the condensate and to evaluate the damping rate of the centre of mass oscillation. The density response function for the elongated condensate is determined with a new local density approximation that takes into account the tight radial confinement of the atomic cloud. Our linear response theory reveals the detailed dependence of the damping rate on various system parameters. A comparison with available experimental data is only partially successful and points to the need for additional experiments. In addition to disorder induced dissipation, we also consider a variety of other problems that can be addressed by means of linear response theory. For example, we study momentum transferred to a condensate by a Bragg pulse and the energy absorption of a gas in an optical lattice that is parametrically modulated in different ways. All of these applications demonstrate the utility of linear response theory in describing the dynamics of Bose-condensed systems which are subjected to weak perturbations. / Thesis (Ph.D, Physics, Engineering Physics and Astronomy) -- Queen's University, 2013-04-26 10:54:11.915

We study behavior for negative times t of the 2D periodic Navier-Stokes equations and Burgers' original model for turbulence. Both systems are proved to have rich sets of solutions that exist for all t - R and increase exponentially as t -> -(Infinity) However, our study shows that the behavior of these solutions as well as the geometrical structure of the sets of their initial data are very different. As a consequence, Burgers original model for turbulence becomes the first known dissipative system that despite possessing a rich set of backward-time exponentially growing solutions, does not display any similarities, as t -> -(Infinity), to the linear case.

Attachment of particles to one another due to action of certain inter-particle forces is called as particle agglomeration. It has applications ranging from efficient capture of ultra-fine particles generated in coal-burning boilers to effective discharge of aerosol sprays. Aerosol sprays have their application in asthma relievers, coatings, cleaning agents, air fresheners, personal care products and insecticides. There are several factors that cause particle agglomeration and based on the application, agglomeration or de-agglomeration is desired. These various factors associated with agglomeration include van derWaals forces, capillary forces, electrostatic double-layer forces, effects of turbulence, gravity and brownian motion. It is therefore essential to understand the underlying agglomeration mechanisms involved. It is difficult to perform experiments to quantify certain effects of the inter-particle forces and hence we turn to numerical simulations as an alternative. Simulations can be performed using the various numerical simulation techniques such as molecular dynamics, discrete element method, dissipative particle dynamics or other probabilistic simulation techniques. The main objective of this thesis is to study the geometric characteristics of particle agglomerates using dissipative particle dynamics. In this thesis, agglomeration is simulated using the features of dissipative particle dynamics as the simulation technique. Forces of attraction from the literature are used to modify the form of the conservative force. Agglomeration is simulated and the characteristics of the result ing agglomerates are quantified. Simulations were performed on a sizeable number of particles and we observe agglomeration behavior. A study of the agglomerates resulting from the different types of attractive forces is performed to characterize them methodically. Also as a part of this thesis, a novel, dynamic particle simulation technique was developed by interfacing MATLAB and our computational C program.

Electrostatic interactions between charged species play a prominent role in determining structures and states of physical system, leading to important technological and biological applications. In coarse-grained simulations, accurate description of electrostatic interactions is crucial in addressing physical phenomena at larger spatial and longer temporal scales. In this thesis, we implement ENUF method, an abbreviation for Ewald summation based on non-uniform fast Fourier transform technique, into dissipative particle dynamics (DPD) scheme. With determined suitable parameters, the computational complexity of ENUF-DPD method is approximately described as O(N logN). The ENUF-DPD method is further validated by investigating dependence of polyelectrolyte conformations on charge fraction of polyelectrolyte and counterion valency of added salts, and studying of specific binding structures of dendrimers on amphiphilic membranes. In coarse-grained simulations, electrostatic interactions are either explicitly calculated with suitable methods, or implicitly included in effective potentials. The effect of treatment fashion of electrostatic interactions on phase behavior of [BMIM][PF6] ionic liquid (IL) is systematically investigated. Our systematic analyses show that electrostatic interactions should be incorporated explicitly in development of effective potentials, as well as in coarse-grained simulations to improve reliability of simulation results. Detailed image of microscopic structures and orientations of [BMIM][PF6] at graphene and vacuum interfaces are investigated by using atomistic simulations. Imidazolium rings and alkyl side chains of [BMIM] lie preferentially flat on graphene surface. At IL-vacuum interface, ionic groups pack closely together to form polar domains, leaving alkyl side chains populated at interface and imparting hydrophobic character. With the increase of IL filmthickness, orientations of [BMIM] change gradually from dominant flat distributions along graphene surface to orientations where imidazolium rings are either parallel or perpendicular to IL-vacuum interface with tilted angles. The interfacial spatial ionic structural heterogeneity formed by ionic groups also contributes to heterogeneous dynamics in interfacial regions.

Nesta tese analisamos o comportamento dinâmico, no espaço elos parâmetros, ele duas versões elo circuito eletrônico Double Scroll, descritas por sistemas, não integráveis, de equações diferenciais lineares por partes. A diferença entre esses circuitos reside na curva característica ela resistência negativa, uma contínua e a outra descontínua. O circuito Double Scroll é conhecido por apresentar comportamento caótico associado à existência ele órbitas homoclínicas. Desenvolvemos métodos numéricos para identificar distintos atratores periódicos e caóticos nesses circuitos. Realizamos um estudo completo elas variedades que esses sistemas apresentam, onde demonstramos que o circuito descontínuo não pode formar órbitas homoclínicas. Desenvolvemos um método geral para obter órbitas homoclínicas e heteroclínicas em sistemas lineares por partes. Esse método foi utilizado no circuito contínuo para identificar famílias ele órbitas homoclínicas no espaço elos parâmetros. Fazemos um estudo teórico sobre as órbitas homoclínicas, baseado no teorema ele Shilnikov, e determinamos a lei ele escala geral que descreve as acumulações elas infinitas órbitas homoclínicas no espaço elos parâmetros. Utilizando o método ele detecção ele órbitas homoclínicas, comprovamos, em distintos tipos ele órbitas homoclínicas, a validade dessa lei para o circuito Double Scroll contínuo. Além do mais, através da geometria apresentada pelas famílias ele órbitas homoclínicas que identificamos e ela teoria que permitiu demonstrar a lei ele escala, mostramos a existência ele estruturas ele órbitas homoclínicas que explicam o cenário homoclínico do espaço elos parâmetros. Essas estruturas estão presentes em todos os sistemas para os quais o teorema ele Shilnikov se aplica. Finalmente, sugerimos três experimentos para verificar a existência dessas órbitas e a relação delas com a dinâmica elo sistema. / In this thesis we study the dynamic behavior, in the parameter space, of two versions of the Double Scroll electronic circuit, whose flows are represented by piecewise non integrable systems. The difference between these circuits is the characteristic curves of the negative resistance, one continuous and the other discontinuous. The Double Scroll circuit is known to present chaotic behavior associated to the existence of homoclinic orbits. We develop numerical methods to identify periodic and chaotic attractors in these circuits. We present a complete study of these systems manifolds and demonstrate that the discontinuous circuit cannot form homoclinic orbits. We develop a general method to obtain homoclinic and heteroclinic orbits in piecewise linear systems. This method was used in the continuous circuit to identify homoclinic orbit families in the parameter space. We develop a theoretical study about the homoclinic orbits based on the Shilnikov theorem, determining a general scaling law that describes the accumulations of the infinity homoclinic orbits in the parameter space. Using the detecting homoclinic orbits method, we show the validity of this law for the continuous Double Scroll circuit. Moreover, combining the geometry of the homoclinic or bit families with the scaling law, we show the existence of homoclinic orbits structures of the homoclinic orbits that explain the homoclinic scenario in the parameter space. These structures are present in all systems for which we can apply the Shilnikov theorem. Finally, we suggest three experiments to verify the existence of these orbits and their relation with the system dynamics.

This thesis studies quantum coherence in macroscopic and mesoscopic dissipative electrical circuits, including LC circuits, microwave resonators, and Josephson junctions. For the LC resonator and the terminated transmission line microwave resonator, second quantization is carried out for the lossless system and dissipation in modeled as the coupling to a bath of harmonic oscillators. Stationary states of the linear and nonlinear resonator circuits as well as the associated energy levels are found, and the time evolution of uncertainty relations for the observables such as flux, charge, current, and voltage are obtained. Coherent states of both the lossless and weakly dissipative circuits are studied within a quantum optical approach based on a Fokker-Plank equation for the P-representation of the density matrix which has been utilized to obtain time-variations of the averages and uncertainties of circuit observables. Macroscopic quantum tunneling is addressed for a driven dissipative Josephson resonator from its metastable current state to the continuum of stable voltage states. The Caldeira-Leggett method and the instanton path integral technique have been used to find the tunneling rate of a driven Josephson junction from a zero-voltage state to the continuum of the voltage states in the presence of dissipation. Upper and lower bounds are obtained for the tunneling rate at the intermediate loss and approximate closed form expressions are derived for the overdamped and underdamped limits.

In this study, the nanocomposite of graphene and PMMA at the different volume fractions was investigated by molecular dynamics and dissipative particle dynamics simulations. The MD simulation can be performed to simulate the nanocomposite system at different weight fractions to obtain the different repulsive parameters. After obtaining the repulsive parameters, the DPD simulation can be utilized to study the equilibrium phase of graphene and PMMA nanocomposite. From our result, all equilibrium phases at different volume fractions are cluster. However, it is difficult to enhance the property for nanocomposite material due to the aggregated graphene (cluster). Hence, we change the interaction repulsive parameters to stand for the different degrees of functionalized graphene. When the interaction repulsive parameter is smaller than 80, the equilibrium phase is dispersion. In addition, the different number of functionalized garphene bead per graphene was studied, and results show that the equilibrium phase is dispersion when all graphene beads per graphene are functionalized.

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