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In the first part of my work I have investigated the ageing properties of the first passage time distributions in a one-dimensional subdiffusive continuous time random walk with power law distributed waiting times of the form $\psi(\tau) \sim \tau^{-1-\alpha}$ with $0<\alpha<1$ and $1<\alpha<2$. The age or ageing time $t_a$ is the time span from the start of the stochastic process to the start of the observation of this process (at $t=0$). I have calculated the results for a single target and two targets, also including the biased case, where the walker is driven towards the boundary by a constant force. I have furthermore refined the previously derived results for the non-ageing case and investigated the changes that occur when the walk is performed in a discrete quenched energy landscape, where the waiting times are fixed for every site. The results include the exact Laplace space densities and infinite (converging) series as exact results in the time space. The main results are the dominating long time power law behavior regimes, which depend on the ageing time. For the case of unbiased subdiffusion ($\alpha < 1$) in the presence of one target, I find three different dominant terms for ranges of $t$ separated by $t_a$ and another crossover time $t^{\star}$, which depends on $t_a$ as well as on the anomalous exponent $\alpha$ and the anomalous diffusion coefficient $K_{\alpha}$. In all three regimes ($t \ll t_a$, $t_a \ll t \ll t^{\star}$, $t \gg t^{\star}$) one finds power law decay with exponents depending on $\alpha$. The middle regime only exists for $t_a \ll t^{\star}$. The dominant terms in the first two regimes (ageing regimes) come from the probability distribution of the forward waiting time, the time one has to wait for the stochastic process to make the first step during the observation. When the observation time is larger than the second crossover time $t^{\star}$, the first passage time density does not show ageing and the non-ageing first passage time dominates. The power law exponents in the respective regimes are $-\alpha$ for strong ageing, $-1-\alpha$ in the intermediate regime, and $-1-\alpha/2$ in the final non-ageing regime. A similar split into three regimes can be found for $1<\alpha<2$, only with a different second crossover time $t^*$. In this regime the diffusion is normal but also age-dependent. For the diffusion in quenched energy landscapes one cannot detect ageing. The first passage time density shows a quenched power law $^\sim t^{-(1+2\alpha)/(1+\alpha)}$. For diffusion between two target sites and the biased diffusion towards a target only two scaling regimes emerge, separated by the ageing time. In the ageing case $t \ll t_a$ the forward waiting time is again dominant with power law exponent $-\alpha$, while the non-ageing power law $-1-\alpha$ is found for all times $t \gg t_a$. An intermediate regime does not exist. The bias and the confinement have similar effects on the first passage time density. For quenched diffusion, the biased case is interesting, as the bias reduces correlations due to revisiting of the same waiting time. As a result, CTRW like behavior is observed, including ageing. Extensive computer simulations support my findings.
The second part of my research was done on the subject of ageing Scher-Montroll transport, which is in parts closely related to the first passage densities. It explains the electrical current in an amorphous material. I have investigated the effect of the width of a given initial distribution of charge carriers on the transport coefficients as well as the ageing effect on the emerging power law regimes and a constant initial regime. While a spread out initial distribution has only little impact on the Scher-Montroll current, ageing alters the behavior drastically. Instead of the two classical power laws one finds four current regimes, up to three of which can appear in a single experiment. The dominant power laws differ for $t \ll t_a, t_c$, $t_a \ll t \ll t_c$, $t_c \ll t \ll t_a$, and $t \gg t_a,t_c$. Here, $t_c$ is the crossover time of the non-aged Scher-Montroll current. For strongly aged systems one can observe a constant current in the first regime while the others are dominated by decaying power laws with exponents $\alpha -1$, $-\alpha$, and $-1-\alpha$. The ageing regimes are the 1st and 3rd one, while the classical regimes are the 2nd and the 4th. I have verified the theory using numerical integration of the exact integrals and applied the new results to experimental data.
In the third part I considered a single file of subdiffusing particles in an energy landscape. Every occupied site of the landscape acts as a boundary, from which a particle is immediately reflected to its previous site, if it tries to jump there. I have analysed the effects single-file diffusion a quenched landscape compared to an annealed landscape and I have related these results to the number of steps and related quantities. The diffusion changes from ultraslow logarithmic diffusion in the annealed or CTRW case to subdiffusion with an anomalous exponent $\alpha/(1+\alpha)$ in the quenched landscape. The behavior is caused by the forward waiting time, which changes drastically from the quenched to the annealed case. Single-file effects in the quenched landscape are even more complicated to consider in the ensemble average, since the diffusion in individual landscapes shows extremely diverse behavior. Extensive simulations support my theoretical arguments, which consider mainly the long time evolution of the mean square displacement of a bulk particle.
Interplay of coupling and common noise at the transition to synchrony in oscillator populations
(2016)
There are two ways to synchronize oscillators: by coupling and by common forcing, which can be pure noise. By virtue of the Ott-Antonsen ansatz for sine-coupled phase oscillators, we obtain analytically tractable equations for the case where both coupling and common noise are present. While noise always tends to synchronize the phase oscillators, the repulsive coupling can act against synchrony, and we focus on this nontrivial situation. For identical oscillators, the fully synchronous state remains stable for small repulsive coupling; moreover it is an absorbing state which always wins over the asynchronous regime. For oscillators with a distribution of natural frequencies, we report on a counter-intuitive effect of dispersion (instead of usual convergence) of the oscillators frequencies at synchrony; the latter effect disappears if noise vanishes.
In this Thesis, the properties of aqueous hemicellulose polysaccharides are investigated using computer simulations. The high swelling capacity of materials composed of these molecules allows the generation of directed motion in plant materials entirely controlled by water uptake.
To explore the molecular origin of this swelling capacity, a computational model with atomistic resolution for hemicellulose polysaccharides is build and validated in comparison with experiments. Using this model, simulations of small polysaccharides are employed to gain an understanding of the interactions of these molecules with water, the influence of water on their conformational freedom, and the swelling capacity quantified in terms of osmotic pressure. It is revealed that the branched hemicellulose polysaccharides show different hydration characteristics compared to linear polysaccharides.
To study swelling properties on length and time scales that exceed the limitations imposed by atomistic simulations, a procedure to obtain transferable coarse-grain models is developed. The transferability of the coarse-grain models over both different degrees of polymerization as well as different solute concentrations is demonstrated. Therefore, the procedure allows the construction of large coarse-grained systems based on small atomistic reference systems. Finally, the coarse-grain model is applied to demonstrate that linear and branched polysaccharides show a different swelling behavior when coupled to a water bath.
Can the statistical properties of single-electron transfer events be correctly predicted within a common equilibrium ensemble description? This fundamental in nanoworld question of ergodic behavior is scrutinized within a very basic semi-classical curve-crossing problem. It is shown that in the limit of non-adiabatic electron transfer (weak tunneling) well-described by the Marcus–Levich–Dogonadze(MLD) rate the answer is yes. However, in the limit of the so-called solvent-controlled adiabatic electron transfer, a profound breaking of ergodicity occurs. Namely, a common description based on the ensemble reduced density matrix with an initial equilibrium distribution of the reaction coordinate is not able to reproduce the statistics of single-trajectory events in this seemingly classical regime. For sufficiently large activation barriers, the ensemble survival probability in a state remains nearly exponential with the inverse rate given by the sum of the adiabatic curve crossing (Kramers) time and the inverse MLD rate. In contrast, near to the adiabatic regime, the single-electron survival probability is clearly non-exponential, even though it possesses an exponential tail which agrees well with the ensemble description. Initially, it is well described by a Mittag-Leffler distribution with a fractional rate. Paradoxically, the mean transfer time in this classical on the ensemble level regime is well described by the inverse of the nonadiabatic quantum tunneling rate on a single particle level. An analytical theory is developed which perfectly agrees with stochastic simulations and explains our findings.
We introduce azobenzene-functionalized polyelectrolyte multilayers as efficient, inexpensive optoacoustic transducers for hyper-sound strain waves in the GHz range. By picosecond transient reflectivity measurements we study the creation of nanoscale strain waves, their reflection from interfaces, damping by scattering from nanoparticles and propagation in soft and hard adjacent materials like polymer layers, quartz and mica. The amplitude of the generated strain ε ∼ 5 × 10−4 is calibrated by ultrafast X-ray diffraction.
The title compounds, [(1R,3R,4R,5R,6S)-4,5-bis(acetyloxy)-7-oxo-2-oxabicyclo-
[4.2.0]octan-3-yl]methyl acetate, C14H18O8, (I), [(1S,4R,5S,6R)-5-acetyloxy-7-
hydroxyimino-2-oxobicyclo[4.2.0]octan-4-yl acetate, C11H15NO6, (II), and
[(3aR,5R,6R,7R,7aS)-6,7-bis(acetyloxy)-2-oxooctahydropyrano[3,2-b]pyrrol-5-
yl]methyl acetate, C14H19NO8, (III), are stable bicyclic carbohydrate derivatives.
They can easily be synthesized in a few steps from commercially available
glycals. As a result of the ring strain from the four-membered rings in (I) and
(II), the conformations of the carbohydrates deviate strongly from the ideal
chair form. Compound (II) occurs in the boat form. In the five-membered
lactam (III), on the other hand, the carbohydrate adopts an almost ideal chair
conformation. As a result of the distortion of the sugar rings, the configurations
of the three bicyclic carbohydrate derivatives could not be determined from
their NMR coupling constants. From our three crystal structure determinations,
we were able to establish for the first time the absolute configurations of all new
stereocenters of the carbohydrate rings.
The goal of the presented work is to explore the interaction between gold nanorods (GNRs) and hyper-sound waves. For the generation of the hyper-sound I have used Azobenzene-containing polymer transducers. Multilayer polymer structures with well-defined thicknesses and smooth interfaces were built via layer-by-layer deposition. Anionic polyelectrolytes with Azobenzene side groups (PAzo) were alternated with cationic polymer PAH, for the creation of transducer films. PSS/PAH multilayer were built for spacer layers, which do not absorb in the visible light range. The properties of the PAzo/PAH film as a transducer are carefully characterized by static and transient optical spectroscopy. The optical and mechanical properties of the transducer are studied on the picosecond time scale. In particular the relative change of the refractive index of the photo-excited and expanded PAH/PAzo is Δn/n = - 2.6*10‐4. Calibration of the generated strain is performed by ultrafast X-ray diffraction calibrated the strain in a Mica substrate, into which the hyper-sound is transduced. By simulating the X-ray data with a linear-chain-model the strain in the transducer under the excitation is derived to be Δd/d ~ 5*10‐4.
Additional to the investigation of the properties of the transducer itself, I have performed a series of experiments to study the penetration of the generated strain into various adjacent materials. By depositing the PAzo/PAH film onto a PAH/PSS structure with gold nanorods incorporated in it, I have shown that nanoscale impurities can be detected via the scattering of hyper-sound.
Prior to the investigation of complex structures containing GNRs and the transducer, I have performed several sets of experiments on GNRs deposited on a small buffer of PSS/PAH. The static and transient response of GNRs is investigated for different fluence of the pump beam and for different dielectric environments (GNRs covered by PSS/PAH).
A systematic analysis of sample architectures is performed in order to construct a sample with the desired effect of GNRs responding to the hyper-sound strain wave. The observed shift of a feature related to the longitudinal plasmon resonance in the transient reflection spectra is interpreted as the event of GNRs sensing the strain wave. We argue that the shift of the longitudinal plasmon resonance is caused by the viscoelastic deformation of the polymer around the nanoparticle. The deformation is induced by the out of plane difference in strain in the area directly under a particle and next to it. Simulations based on the linear chain model support this assumption. Experimentally this assumption is proven by investigating the same structure, with GNRs embedded in a PSS/PAH polymer layer.
The response of GNRs to the hyper-sound wave is also observed for the sample structure with GNRs embedded in PAzo/PAH films. The response of GNRs in this case is explained to be driven by the change of the refractive index of PAzo during the strain propagation.
The strong adhesion of sub-micron sized particles to surfaces is a nuisance, both for removing contaminating colloids from surfaces and for conscious manipulation of particles to create and test novel micro/nano-scale assemblies. The obvious idea of using detergents to ease these processes suffers from a lack of control: the action of any conventional surface-modifying agent is immediate and global. With photosensitive azobenzene containing surfactants we overcome these limitations. Such photo-soaps contain optical switches (azobenzene molecules), which upon illumination with light of appropriate wavelength undergo reversible trans-cis photo-isomerization resulting in a subsequent change of the physico-chemical molecular properties. In this work we show that when a spatial gradient in the composition of trans- and cis- isomers is created near a solid-liquid interface, a substantial hydrodynamic flow can be initiated, the spatial extent of which can be set, e.g., by the shape of a laser spot. We propose the concept of light induced diffusioosmosis driving the flow, which can remove, gather or pattern a particle assembly at a solid-liquid interface. In other words, in addition to providing a soap we implement selectivity: particles are mobilized and moved at the time of illumination, and only across the illuminated area.