9 research outputs found
Dynamics of Classical Scattering in a Periodic Lattice
No full textThis project concerns the analysis of mathematical model of classical scattering. I consider a 2-dimensional model of a particle that is scattered through a symmetric lattice and interact through the Lennard-Jones potential. The model is investigated as a Hamiltonian system and simulations are done in the context of molecular dynamics. The analysis is done following the formalism of chaotic scattering. In particular, the fractal dimension d_c of the scattering function and the mean exit time tau from the scattering region are computed. By increasing the lattice size from 2-by-2 to 4-by-4, I find an increase in both tau and d_c. This is an indication of an increase in the positive Lyapunov exponent chi_1 with increasing lattice size.This project concerns the analysis of mathematical model of classical scattering. I consider a 2-dimensional model of a particle that is scattered through a symmetric lattice and interact through the Lennard-Jones potential. The model is investigated as a Hamiltonian system and simulations are done in the context of molecular dynamics. The analysis is done following the formalism of chaotic scattering. In particular, the fractal dimension d_c of the scattering function and the mean exit time tau from the scattering region are computed. By increasing the lattice size from 2-by-2 to 4-by-4, I find an increase in both tau and d_c. This is an indication of an increase in the positive Lyapunov exponent chi_1 with increasing lattice size
Structural Changes in Cylinder-Forming PS-b-PB Thin Films During Solvent Vapor Annealing
No full textThe orientational changes of cylinders in Polystyrene-b-Polybutadiene (PS-b-PB) diblock copolymer thin films during solvent vapor annealing (SVA) was investigated using White- Light Interferometry (WLI) and time-resolved grazing-incidence small-angle x-ray scattering (GISAXS). The SVA procedure was performed with three different solvents of varying selec- tivity to the two blocks: Ethyl Acetate (EAC), Toluene (TOL) and Cyclohexane (CHX). A change from standing to lying cylinders was found using all three solvents. The orientational change appears to depend on the minimal polymer volume fraction phi_min of the film, and different threshold values were found for each solvent: phi_min,EAC = 0.66, phi_min,TOL = 0.63, phi_min,CHX = 0.49. In one experiment with CHX, the switch from standing to lying cylin- ders happens through a disordered phase spanning 15 minutes. This, along with other circumstantial evidence, hints at the timescales of structural changes.The orientational changes of cylinders in Polystyrene-b-Polybutadiene (PS-b-PB) diblock copolymer thin films during solvent vapor annealing (SVA) was investigated using White- Light Interferometry (WLI) and time-resolved grazing-incidence small-angle x-ray scattering (GISAXS). The SVA procedure was performed with three different solvents of varying selec- tivity to the two blocks: Ethyl Acetate (EAC), Toluene (TOL) and Cyclohexane (CHX). A change from standing to lying cylinders was found using all three solvents. The orientational change appears to depend on the minimal polymer volume fraction phi_min of the film, and different threshold values were found for each solvent: phi_min,EAC = 0.66, phi_min,TOL = 0.63, phi_min,CHX = 0.49. In one experiment with CHX, the switch from standing to lying cylin- ders happens through a disordered phase spanning 15 minutes. This, along with other circumstantial evidence, hints at the timescales of structural changes
Oxygen Dynamics in the High-Temperature Superconductor LSCO+O
No full textUnderstanding the mechanisms of high-temperature superconductivity in the cuprates remains one of the great unsolved questions of condensed matter physics. Hole-doping the Mott-insulator La2CuO4 with various chemical species creates a superconductor with a transition temperature Tc that depends heavily on the amount and type of doped species. While the amount of hole-dopingtypically dictates the phase diagram, there are certain situations where superconductivity can be suppressed or enhanced due to structural modifications caused by the dopant species. In this thesis, I investigate these structural modifications and, in particular, related dynamics in order to better understand any possible relationship to superconductivity. A particular interesting sample in this context is La2−xSrxCuO4+δ (LSCO+O), where doping can be performed with two distinct chemical species, Sr and O. Doping with Sr is ‘quenched’, meaning that Sr has a fixed, random distribution on La sites. On the other hand, doping with O is performed after crystal growth using electrochemical methods. Oxygen dopants are ‘annealed’ in the sense that they sit on interstitial sites and are mobile at room temperature. In addition, doping with O creates a superconductor with slightly better Tc that is equipped with a number of unique phenomena such as electronic phase separation and complex superstructures. In thisthesis, various aspects of phonon dynamics in LSCO+O are investigated through a combination of theoretical and experimental methods. Density functional theory and molecular dynamics is used to numerically estimate the phonon band structure and density of states. Inelastic neutron scattering is used to probe phonon dynamics and the two methods are compared. Despite the fact that Density Functional Theory is known to struggle with the electronic structure of the cuprates, excellent agreement between phonon dynamical simulations and experiments are found. An analysis of this relationship reveals unique dynamics of octahedral tilt patterns due to interstitial oxygen. We speculate that these tilt patterns may assist in relieving the inherent frustration between magnetism and superconductivity in LSCO+O. Finally, anomalous features in the Cu-O bond stretching phonon of two different LSCO+O samples is observed with neutron scattering. This ‘phonon anomaly’ is suspected to be a signature of charge density fluctuations that might be important for superconductivity. While previously observed in Sr-doped La2−xSrxCuO4, this result rules out a phonon anomaly caused by structural mechanism related to the specific dopant type
Karakterisering af vesikler ved dynamisk lysspredning
No full textFormålet med projektet er at undersøge alkohols indvirkning på brudstyrken (lysis ten- sion) af DMPC-vesikler. Ved at ekstrudere multilamellare vesikler opnår vi en monodis- pers opløsning af unilamellere vesikler. Ved at variere mængden af alkohol i membranen forventer vi en ændring af brudstyrken. En model for ekstruderingsprocessen foreslår, at denne ændring vil give anledning til en ændret størrelse af de ekstruderede vesikler. Vi måler den hydrodynamiske radius af vesiklerne med dynamisk lysspredning. Da vi har haft eksperimentelle problemer med systematiske fejl og usikkerheder, er vi ud fra vores resultater ikke i stand til at sige noget generelt om alkohols betydning for brud- styrken. Vi er derfor ikke i stand til at eftervise den foreslåede model. Vi diskuterer, på baggrund af vores eksperimentelle vanskeligheder, fejlkilder og usikkerheder med det formål at videregive erfaringer om forsøg med dynamisk lysspredning.Formålet med projektet er at undersøge alkohols indvirkning på brudstyrken (lysis ten- sion) af DMPC-vesikler. Ved at ekstrudere multilamellare vesikler opnår vi en monodis- pers opløsning af unilamellere vesikler. Ved at variere mængden af alkohol i membranen forventer vi en ændring af brudstyrken. En model for ekstruderingsprocessen foreslår, at denne ændring vil give anledning til en ændret størrelse af de ekstruderede vesikler. Vi måler den hydrodynamiske radius af vesiklerne med dynamisk lysspredning. Da vi har haft eksperimentelle problemer med systematiske fejl og usikkerheder, er vi ud fra vores resultater ikke i stand til at sige noget generelt om alkohols betydning for brud- styrken. Vi er derfor ikke i stand til at eftervise den foreslåede model. Vi diskuterer, på baggrund af vores eksperimentelle vanskeligheder, fejlkilder og usikkerheder med det formål at videregive erfaringer om forsøg med dynamisk lysspredning
Dynamikken ved opvarmning og nedkølning: The dynamics of heating and cooling
No full textDette projekt vil belyse, om der er nogen problemer forbundet med at anvende gennemsnitstemperaturer over større tidsintervaller, fremfor præcise data over kortere intervaller, indenfor modellering af varmetransport gennem en væg. Dette gøres gennem teoretisk analyse af principperne bag varmeledning og computersimuleringer ud fra modeller opstillet på baggrund af denne teori. Som en del af simuleringerne, betragtes temperaturvariationen i Danmark ud fra et helt års detaljeret vejrdata. Konklusionen er, at den fejl der opstår ved brug af gennemsnitstemperaturer, i forhold til varierende temperaturer, er ubetydelig. Denne konklusion er gældende både for realistiske danske temperaturvariationer og for helt urealistiske og kunstige variationer. På trods af denne fejls ubetydelighed, er der alligevel en tendens til, at den stiger ved brug af større tidsinterval. Grunden til dette er ikke sikker, men meget tyder på, at væggens bufferkapacitet er afgørende for den lille fejl.Dette projekt vil belyse, om der er nogen problemer forbundet med at anvende gennemsnitstemperaturer over større tidsintervaller, fremfor præcise data over kortere intervaller, indenfor modellering af varmetransport gennem en væg. Dette gøres gennem teoretisk analyse af principperne bag varmeledning og computersimuleringer ud fra modeller opstillet på baggrund af denne teori. Som en del af simuleringerne, betragtes temperaturvariationen i Danmark ud fra et helt års detaljeret vejrdata. Konklusionen er, at den fejl der opstår ved brug af gennemsnitstemperaturer, i forhold til varierende temperaturer, er ubetydelig. Denne konklusion er gældende både for realistiske danske temperaturvariationer og for helt urealistiske og kunstige variationer. På trods af denne fejls ubetydelighed, er der alligevel en tendens til, at den stiger ved brug af større tidsinterval. Grunden til dette er ikke sikker, men meget tyder på, at væggens bufferkapacitet er afgørende for den lille fejl
Barkaner - Sammenstød og Stabilitet
No full textBarkaner er en type sandklitter, som bevæger sig langs vindretningen. Modeller af enkelte barkaner, viser at disse burde være ustabile, på trods af at de observeres i stort antal i store, homogene felter. Det er derfor interessant at undersøge hvad der fører til denne stabilitet. Gennem et nedskaleret forsøg med barkaner, beskriver vi sammenstød mellem barkaner, hvorefter resultaterne implementeres i en simpel model. Denne model simulerer udviklingen af et virkeligt barkanfelt. Igennem vores forsøg, finder vi at centrale sammenstød fører til, at barkaner effektivt passerer igennem hinanden, men at der ved decentrale sammenstød kan forekomme mere komplekse resultater, som dannelse af nye barkaner. Ud fra vores simulering har vi fundet, at den observerede sammenstødstype fra vores forsøg, kan være en medvirkende faktor til stabiliteten i barkanfelter. På baggrund af vores og andres resultater, mener vi, at sammenstød har en indvirkning på stabiliteten af barkanfelter.Barkaner er en type sandklitter, som bevæger sig langs vindretningen. Modeller af enkelte barkaner, viser at disse burde være ustabile, på trods af at de observeres i stort antal i store, homogene felter. Det er derfor interessant at undersøge hvad der fører til denne stabilitet. Gennem et nedskaleret forsøg med barkaner, beskriver vi sammenstød mellem barkaner, hvorefter resultaterne implementeres i en simpel model. Denne model simulerer udviklingen af et virkeligt barkanfelt. Igennem vores forsøg, finder vi at centrale sammenstød fører til, at barkaner effektivt passerer igennem hinanden, men at der ved decentrale sammenstød kan forekomme mere komplekse resultater, som dannelse af nye barkaner. Ud fra vores simulering har vi fundet, at den observerede sammenstødstype fra vores forsøg, kan være en medvirkende faktor til stabiliteten i barkanfelter. På baggrund af vores og andres resultater, mener vi, at sammenstød har en indvirkning på stabiliteten af barkanfelter
Solvent Vapor Annealing of a Diblock Copolymer Thin Film with a Nonselective and a Selective Solvent:Importance of Pathway for the Morphological Changes
No full textDiblock copolymer thin films of polystyrene-block-poly(dimethyl siloxane)(PS-b-PDMS) featuring PDMS cylinders in a PS matrix are investigated duringsolvent vapor annealing with mixtures of n-heptane (which is strongly selectivefor PDMS) and toluene (which is close to nonselective for both blocks).Swelling in the vapor of one of the pure solvents and exchanging it stepwise bythe vapor of the other solvent is compared to swelling in a given binary solventvapor mixture for a prolonged time. The resulting structural changes, such asordering of the cylinders on a hexagonal lattice and their transition into lamellae, are followed using in situ, real-time grazing-incidence small-angle X-ray scattering (GISAXS). In three runs, the sequence of solvent vapor swelling and vapor exchange is varied. Compiling the resulting morphologies in a diagram of states in dependence on the solvent content in the film and in the minority nanodomains allows insight into the role of the glass transition of the PS matrix for the ordering processes and their time scales. Based on these findings, a protocol is suggested to efficiently obtain an order-to-order transition from the cylindrical morphology with random domain orientation to the oriented lamellar state.Diblock copolymer thin films of polystyrene‐block‐poly(dimethyl siloxane) (PS‐b‐PDMS) featuring PDMS cylinders in a PS matrix are investigated during solvent vapor annealing with mixtures of n‐heptane (which is strongly selective for PDMS) and toluene (which is close to nonselective for both blocks). Swelling in the vapor of one of the pure solvents and exchanging it stepwise by the vapor of the other solvent is compared to swelling in a given binary solvent vapor mixture for a prolonged time. The resulting structural changes, such as ordering of the cylinders on a hexagonal lattice and their transition into lamellae, are followed using in situ, real‐time grazing‐incidence small‐angle X‐ray scattering (GISAXS). In three runs, the sequence of solvent vapor swelling and vapor exchange is varied. Compiling the resulting morphologies in a diagram of states in dependence on the solvent content in the film and in the minority nanodomains allows insight into the role of the glass transition of the PS matrix for the ordering processes and their time scales. Based on these findings, a protocol is suggested to efficiently obtain an order‐to‐order transition from the cylindrical morphology with random domain orientation to the oriented lamellar state
Multiple scattering camouflaged as magnetic stripes in single crystals of superconducting (La,Sr)<sub>2</sub>CuO<sub>4</sub>
No full textNeutron diffraction has been a very prominent tool to investigate high-temperature superconductors, in particular through the discovery of an incommensurate magnetic signal known as stripes. We here report the findings of a neutron diffraction experiment on the superconductor (La,Sr)2CuO4, where a spurious signal appeared to be magnetic stripes. The signal strength was found to be strongly dependent on the neutron energy, peaking at E = 4.6 meV. We therefore attribute the origin of this signal to be a combination of multiple scattering and crystal twinning. A forward calculation of the scattering intensity including these two effects almost completely recovers our experimental observations. We emphasize the need for employing such analysis when searching for ways to avoid spurious scattering signals.</p
Nature of the magnetic stripes in fully oxygenated La<sub>2</sub>CuO<sub>4+y</sub>
No full textWe present triple-axis neutron scattering studies of static and dynamic magnetic stripes in an optimally oxygen-doped cuprate superconductor, La2CuO4+y, which exhibits a clean superconducting transition at Tc=42K. Polarization analysis reveals that the magnetic stripe structure is equally represented along both of the tetragonal crystal axes and that the fluctuating stripes display significant weight for in-plane as well as out-of-plane spin components. Both static magnetic order as well as low-energy fluctuations are fully developed in zero applied magnetic field and the low-energy spin fluctuations at ω=0.3-10meV intensify on cooling. We interpret this as an indication that superconductivity and low-energy spin fluctuations coexist microscopically in spatial regions which are separated from domains with static magnetic order. </p
