Charge and excitation-energy transfer in time-dependent density functional theory
- Learning about and understanding the mechanisms and pathways of charge and excitation-energy transfer of natural molecular complexes is a promising approach for the tailored design of new artificial energy-converting materials. Therefore, next to extensive experimental investigations, a theoretical method that is able to reliably describe and predict these phenomena from first principles is of practical relevance. In principle, density functional theory (DFT) and time-dependent density functional theory (TDDFT) appear as natural choices to study the relevant sizable molecules on a first-principles scale at bearable computational cost. However, the application of standard local and semilocal density functional approximations suffers from well-known deficiencies, in particular, as far as the simulation of charge-transfer phenomena is concerned. The present thesis approaches charge and excitation-energy transfer with the objective of improving the predictive power and extending the range of applicability of (TD)DFT.
The deficiencies of standard density functional approximations have been related to self-interaction. Hence, one major aspect of this work is the extension of the self-interaction correction in Kohn-Sham DFT that is based on the generalized optimized effective potential to TDDFT using a real-time propagation approach. The multiplicative Kohn-Sham potential allows for a transparent analysis of the exchange-correlation potential during time evolution. It reveals frequency-dependent field-counteracting behavior and step structures that appear in dynamic charge-transfer situations. The latter are important for the proper description of charge transfer. Self-interaction correction allows to access many cases that are difficult for standard TDDFT ranging from chain-like systems over excitonic excitations in semiconductor nanoclusters to short- and long-range charge-transfer excitations. At the same time, it does not spoil the reasonable accuracy that already (semi)local functionals exhibit for local excitations. Moreover, the TDDFT perspective on self-interaction correction sheds new light also on the ground-state formalism. Complex degrees of freedom in the energy-minimizing transformation of the generalized optimized effective potential approach yield smoother orbital densities that appear more reasonable when inserted into approximate functionals in the self-interaction correction formalism. This work provides new insight into the use of different functional approximations. Last but not least, the influence of spin-symmetry breaking and step structures of the potential on the preference to transfer integer units of the elementary electric charge between largely separated donor and acceptor moieties is illustrated when static external electric fields are applied. This work has been reported in three publications and one submitted manuscript.
In the field of excitation-energy transfer, recent discoveries of quantum coherence effects shed new light on the mechanisms behind energy-transfer rates. The latter are affected by a number of different properties of the isolated molecules, but involve also effects due to the environment of the system. This thesis addresses excitation-energy transfer phenomena from two perspectives. First, I use real-time propagation TDDFT to investigate the intermolecular coupling strength and the coupling mechanism between single fragments of supermolecular setups. These investigations base on standard closed quantum system TDDFT and exploit the coherent oscillation of excitation energy between separated molecules after the initial excitation process. Second, I use open quantum system ideas in the framework of TDDFT to study the influence of the system’s environment on the energy-transfer time scales and pathways in a circular arrangement of molecules using an effective energy-dissipation mechanism. The first part of these results is published. The second part is presented in this thesis and includes work in progress.
Polyelectrolyte Coatings with Internal Hierarchy
- The results presented in this thesis are focused on the surface modification by polyelectrolytes and polyelectrolyte copolymers. The internal structural hierarchy originate thereby from the self-assembly processes at different length scales. To generate different levels of hierarchy, the coatings were constructed by using either the layer-by-layer (LbL) deposition method (lateral chemical structure), the adsorption of supramolecular aggregates (lateral topographycal structure), or the combination of both. Using these techniques, one can control the properties of the coatings by varying the chemical structure of the polyelectrolytes, for instance, their charge density, thus providing a convenient way for their functionalization and the ability to tune properties of the surface. Therefore, we were working with systems which have variable charge densities. With this approach, we were able to produce thin and ultrathin nanostructured films with tunable properties and functionality.
Synthesis and Combinatorial Optimization of Novel Star-Shaped Resist Materials for Lithographic Applications
- Gordon Earle Moore predicted in the mid-1960s the cost-efficient doubling of transistors’ number on integrated circuits every two years – known as Moore’s Law. Leading companies orientates by the development of integrated circuits on this Moore’s Law and contributed to this prediction to come true up to the present. In so doing, the semiconductor industry drafts every two years aims to fulfill this prediction summarized in the so-called International Technology Roadmap for Semiconductors (ITRS). The ITRS lists guidelines for cost-effective progresses in performance of integrated circuits, e.g. design of integrated circuits, advancements of exposure tools and exposure techniques, and closely correlated resist materials. This thesis deals with the development of new resist materials and their combinatorial investigation concerning the performance in lithographic patterning.
The lithographic patterning procedure is a sequence of multiple processing steps and thus this procedure involves many processing variables interacting strongly with each other. For understanding and comprehensive investigation of such multi-variable dependent systems the development and implementation of combinatorial approaches were in the focus of this thesis. Furthermore this thesis is focused on the synthesis of new tailored resist materials for lithographic patterning. Star topology was the selected polymer architecture of this new resist material realized via the core-first atom transfer radical polymerization (ATRP) technique. The lithographic performance of electron beam lithography patterning was investigated for the resulting randomly distributed star terpolymers and star block copolymers by combinatorial libraries in view of features’ quality.
The first chapter deals with developed, adapted, and improved combinatorial techniques for thin film investigations in general and utilized for lithographic patterning investigations in particular. The lithographic patterning procedure of chemically amplified resist systems consists of various steps: film preparation, post apply bake (PAB) to remove residual solvent, exposure, post exposure bake (PEB) to activate the catalytic reaction, and development. For this rather complex process variable gradients were developed and adapted for each processing step to investigate and optimize the performance of especially new resist systems. For the film preparation a method was developed to prepare an internal material composition gradient. This was realized by a gradient extrudate prepared using two individual controllable syringe pumps and subsequent doctor-blading. The material composition gradient was verified by high performance liquid chromatography. The second (PAB) and also the fourth (PEB) processing step are both annealing processes of the resist film although they serve different purposes. For the investigation of such annealing processes temperature gradients were prepared adjustable in temperature range and temperature slope. This adjustability is ensured by the active heating and the active cooling source and also by the gap and the type of metal plate. For the third step exposure methods were developed to realize defined exposure dose gradients in very small areas of the resist film. Different exposure dose gradients were designed for photolithography as well as for electron beam lithography. For the latter case this dose gradient was programmed in the pattern design using the software which controls the electron beam during the exposure process. The dose gradient for photolithography investigations was realized by a special designed shadow mask. For the last processing step development a preliminary screening of the dissolubility conditions of the resist film was established utilizing quartz crystal microbalances. Based on this measured dissolubility behavior the time frame was set for development time gradients performed by a stepwise or continuously immersion of the resist films. Lastly two to three variable gradients were combined to binary or ternary combinatorial libraries, respectively. The ternary combinatorial libraries allow the investigation of three variables of the lithographic patterning process in one experiment. Thus it is possible to optimize a resist material system fast and efficiently in respect to resist performance.
In the second chapter a star-shaped teroligomer is reported as new high potential resist type for lithographic patterning purposes. The polymerization was carried out via the core-first ATRP route using a functionalized saccharose with eight initiating sites as core. Four star-shaped teroligomers were synthesized with varying target arm lengths. In addition a saccharose molecule was synthesized with an average number of 3.5 initiating sites and thus a star oligomer was realized with a reduced arm number but an identical core and similar arm length. As reference resist material a linear model oligomer was synthesized using ethyl 2-bromoisobutyrate as initiator. For all polymers narrow monomodal distributions were detected with polydispersity index values of lower than 1.1. Based on calibration polymerizations runs the monomer feed of the three used monomers was adapted to achieve targeted monomer incorporations for all teroligomers. The targeted monomer incorporation was copied from a currently industrially used linear teroligomer. One star oligomer was selected as proof of principle for the utilization of the star architecture for lithographic purposes. This new resist material was combinatorial investigated in a ternary library and thus optimized in one experiment concerning exposure dose, PEB temperature, and development time. The optimized patterns with a feature size of 100 nm and an excellent line edge roughness (LER) value of 3.1 nm were observed.
The last chapter of this thesis demonstrates the straight forward advancement of the star-shaped resist material reported in chapter two. The statistical monomer incorporation was exchanged by the introduction of the tailored star block copolymer architecture. This architecture was synthesized for the first time via the core-first ATRP route by full conversion of a first polar monomer and in-situ polymerization of additionally added nonpolar monomer. The successful syntheses were indicated by contact angle measurements showing increased hydrophobicity of star block copolymers in contrast to random star copolymers with the same monomer incorporation. The star block copolymers exhibited also enhanced dissolubility behavior characterized by quartz crystal microbalance measurements. Furthermore they demonstrated an up to eight times increased sensitivity at their lithographic application in contrast to the synthesized reference linear copolymer. The most promising star block copolymer was selected to investigate its lithographic performance. The optimization was performed in a ternary combinatorial library based on the gradient variables exposure dose and feature size, PEB temperature, and development time. The optimized pattern of clear lines and a feature size of 66 nm was observed with a LER value of 6 nm.
To conclude, different tailored star-shaped terpolymers were synthesized using the ATRP core-first route and successfully applied in the lithographic patterning process for the first time. In addition the combinatorial optimization offers the absolutely promising potential of utilizing these star shaped resist materials by the demonstrated brilliant LER values, the achieved extremely high sensitivity, and the fast and efficient development of clear 66 nm lines.
Single-Particle Orbit Tracking - Setup, Characterisation and Application
- In this thesis, the development and experimental realisation of an optical setup which records the 2-dimensional trajectories of single fluorescently labeled polystyrene beads, either 20nm or 50nm in diameter, with a high spatial and temporal resolution is introduced. Combining single molecule fluorescence techniques with a new method called single-particle orbit tracking the spatial position of the beads could be determined with an accuracy of less than 10nm at a time resolution of 4 ms. The idea is to manipulate the excitation light spatially and temporally to locate a particle. In order to do so, special optics which deflect a laser beam and guide it on a circular path were used. Subsequently, this rotating beam is projected by a microscope into the sample with the diffusing particles. Due to the spatially and periodically modulated excitation light, the emission signal of the bead is modulated with the frequency of the rotation of the laser focus. The amplitude of the modulated emission signal depends on the position of the particle within the excitation orbit. An ingeniously developed algorithm calculates the position of the particle with respect to the centre of the orbit by demodulating the emission signal and restores the particle back to the orbit centre. Applying this method successively, the trajectory of the diffusing bead can be reconstructed. Besides the experimental realisation, the characterisation of the setup in terms of the spatial and temporal accuracy as well as the experimental shortcomings that influences the measured trajectories and hence, the interpretation of the data, were also the main topics of this work. For this purpose a reference sample of 20nm sized beads in glycerol was used. The accuracies were studied mainly by computer simulations and the artifacts by experiments. The technical details of the setup and the characterisation results were published (publication P1).
The recorded trajectories were analysed with various methods, among which the commonly used mean squared displacement (MSD) yields the results with highest information. The diffusion coefficient as well as the diffusion behaviour could be quantified. With this method the obtainable accuracy in measuring the diffusion coefficient by the acquisition of single-particle trajectories was studied as a function of the length of the trajectories and as a function of the number of fitting points that were used for a linear fit to the experimentally determined MSD-curves. As expected, the relative error of the determined diffusion coefficient gets better for longer trajectories. Further, an optimal number of fitting points for the linear approximation to the MSD-curves was found, which yields the most exact values for the diffusion coefficients and which is independent of the trajectory length. For the first time, experimental results on that issue were compared with theoretical predictions, where a good agreement was found. These findings were published (publication P2). By the use of the Stokes-Einstein relation the diffusion coefficients could further be converted to particle radii. A closer examination of these radii emphasises the influence of the afore mentioned number of fitting points. For the optimal value, significantly precise radii could be determined.
Finally, an application of the new setup is presented. In cooperation with the chair of experimental physics I (group of Prof. Dr. M. Weiss) of the University of Bayreuth, the diffusion behaviour of single nanoparticles in a complex fluid was studied. Background hereto is the investigation of biochemical reactions in a biological cell, whose kinetic is given by the diffusion of the corresponding reaction partners. Due to the high crowding of the cell compartments the diffusion is hindered. The diffusion behaviour in these systems is called anomalous and more exactly subdiffusive. Several theoretical models have been developed to explain this phenomenon, but yet without experimental verifications. Here, the diffusion of 50nm sized polymer beads in the model system dextran (a highly branched biopolysaccaride) is investigated experimentally with high spatial and temporal resolution. The data were analysed in the group of the cooperation partner which yields a very good agreement with the model of “fractional Brownian motion”. These results were also published (publication P3).
Jahresbericht 2010-11 zum Förderprojekt 01879 Untersuchung der Veränderung der Konzentration von Luftbeimengungen und Treibhausgasen im hohen Fichtelgebirge 2007 – 2014
- no abstract
Polymer Melts Investigated by Field Cycling NMR Relaxometry: From Simple Liquid to Reptation Dynamics
- The focus of this thesis is the investigation of linear polymer melts by applying Field Cycling Nuclear Magnetic Resonance (FC NMR) relaxometry. The objective is to understand their microscopic dynamics and its dependence on the molecular mass (M) of the polymer chains.
With the commercial availability of FC NMR relaxometers, the method gained attraction for studying dynamics of soft condensed matter due to its ability to detect both the structural or alpha-relaxation (identified with the segmental dynamics) and slower collective dynamics. In the case of polymer melts the latter is described most often by the Rouse model for non-entangled chains and the Doi/Edwards tube-reptation model for entangled polymers. Since 2004 a commercial relaxometer by Stelar has been operated in the Rössler group. Its capability to rapidly switch between different magnetic fields allows to measure the spin-lattice relaxation time in the proton frequency range from 10 kHz to 20 MHz. In previous works by the Rössler group the pioneering works by Kimmich and co-workers have been extended in order to combine the results of a broad temperature range: Frequency-temperature superposition is applied to construct master curves in the susceptibility representation. The key benefits are: the susceptibility is scaled by time constant of segmental dynamics and an "isofrictional" representation is achieved; the accessible frequency range is significantly increased; the time constants are provided and compared with those obtained by other techniques; the regimes of glassy and polymer dynamics can be easily distinguished; finally, the dipolar correlation function is obtained directly by Fourier transform.
In this thesis by employing the above approach, the dipolar correlation function of polybutadienes (PB) melts is presented and comprises - depending on M - glassy, Rouse and entanglement dynamics. The latter two relaxation regimes can be described by different power-laws, which are compared to the predictions of the tube-reptation model. A good agreement is found for the Rouse regime (I). For the constrained Rouse regime (II) at long times, a highly protracted crossover to completely established reptation dynamics is discovered. That is, the exponent depends on M and reaches 0.32 only at M=441000, which is in accord with Double Quantum (DQ) 1H NMR results by Saalwächter and co-workers and very close to 0.25 predicted for regime II of the tube-reptation model. This is only achieved by additional relaxation experiments in cooperation with the Fujara group at TU Darmstadt, since their home-built FC NMR relaxometer is equipped with an active stray field compensation, which allows to reach extremely low frequencies down to 200 Hz. Consequently, the frequency range is extended by two decades toward lower frequencies with respect to the commercial spectrometer and the obtained correlation function stretches over 10 decades in time and 8 in amplitude for molecular masses up to 220 Me. This establishes FC 1H NMR also at long times as competitive with DQ 1H NMR.
The analyses of the dipolar correlation function appear to support the applicability of the tube-reptation model. However, intramolecular and intermolecular relaxation contributions have to be discriminated and up to now the dominance of the first has been assumed implicitly. Therefore, isotopic blends of high-M protonated and deuterated PB are investigated, which allows to decompose the 1H master curves into intramolecular and intermolecular relaxation contributions. They reflect reorientational and translational dynamics, respectively. It is demonstrated that at long times or low frequencies the intermolecular contribution dominates. Consequently, the reorientational correlation function obtained from the intramolecular part exhibits a faster decay with the long-time exponent 0.49. This is ascertained by the FC 2H NMR relaxation of completely deuterated PB, which detects reorientational dynamics only. The observed exponent is significantly larger than 0.25 of regime II of the tube reptation model. Concomitantly, the segmental mean square displacement is attained from the intermolecular part following an approach by Kimmich and Fatkullin. The predicted power-laws of the tube-reptation model for the Rouse and constrained Rouse regimes are identified for the first time by FC NMR: a transition between the power-laws t^ 0.49 and t^0.19 is revealed, respectively. Thus, NMR relaxometry is designated as a method comparable to neutron scattering to study subdiffusion in polymer melts. In conclusion, the power-law predictions of the tube-reptation model are disclosed by the segmental mean square displacement, yet not by the reorientational correlation function. Thus, the simple tube-reptation model does not completely describe the microscopic dynamics of polymer melts.
Impact of extreme hydrological conditions on belowground carbon cycling and redox dynamics in peat soils from a northern temperate fen
Cristian Estop Aragonés
- Peatlands have an important role in the global carbon cycle and constitute the largest pool of carbon stored in terrestrial ecosystems due to their disproportionally high areal soil carbon density. This globally relevant carbon stock is the result of a process mostly initiated after the last glaciation period. A key factor for this long term carbon accumulation is the relative low decomposition of organic matter in these predominantly water logged ecosystems. Hydrological conditions play thus a fundamental role in peatlands and the feedback of carbon cycling in these ecosystems in response to climate change is under debate. Peatlands are important CO2 sinks but also constitute global sources of CH4. The atmospheric exchange and production rates of these greenhouse gases are strongly influenced by the hydrological regime. An increased frequency of extreme meteorological conditions resulting in drying and flooding events is predicted to occur in the future.
The major issue regarding the climate change debate at the global scale is how rapid these greenhouse gases are being released to the atmosphere. Despite the general consensus regarding the broad effects of drying and flooding on CO2 and CH4 exchange, belowground processes producing such greenhouse gases and their response to water table dynamics is underrepresented and usually simplified or overgeneralized. Temperature, moisture, oxygen content and nutrient content are among the major environmental controls for organic matter decomposition rates in peat soils. Another important and intrinsic control is peat quality or humification degree of organic matter. The interrelation and relevance of all these factors vary among sites and with hydrological condition in a temporal and spatial scale.
This work presents investigations focusing on belowground redox processes aiming to witness the dynamic interrelation of soil physical and chemical (soil gas and pore water chemistry) variables, and evaluates the relevance of some controls of organic matter decomposition during a wide range of hydrological conditions. Most of this work shows information under in situ conditions and complementary laboratory experiments were performed minding the in situ observations. The findings contribute to general knowledge by providing raw data in fen peats under fluctuating and contrasting water table conditions in a relatively high spatiotemporal resolved scale. Dryings led to increased air filled porosity, O2 intrusion, CO2 degassing, inhibition of methanogenesis and renewal of electron acceptors. The opposite trend occurred upon rewetting with pulses of iron and sulphate reduction and delayed methane production to a variable extent. Upon flooding, continued anaerobic conditions stimulated the accumulation of reduced products, methanogenic precursors (acetate and hydrogen) and CH4.
The general assumption that the water table directly controls the oxygen content in peat was relativized. This work shows that such relation is greatly influenced by peat physical properties, which partially control the changes in moisture. Based on these findings, the mineral content and the degree of compaction in organic soils can be implemented to more accurately represent the dynamics of aeration in peats upon water table changes. Another general assumption is that drying events, i.e. temporary decline of water table below mean position, lead to increased CO2 production and emission from peat soils to the atmosphere. Such statement was also relativized and must account for the depth distribution of respiration rates in relation to the mean water table of the peat deposit. Based on these findings, the high relative contribution of upper peat layers already exposed above the water table mask the effects of increased CO2 production in deeper peat upon water table drop. Additionally, the role of moisture was shown to be little for aerobic respiration. This work also evaluates the importance of drought severity by accounting for the post drought effects on methane production. More intense and prolonged drying events led to a greater regeneration of electron acceptors in peat soil, which broadly suppressed or limited methane production upon rewetting. This relation was not simple and several factors such as water table position, post drought water table fluctuations, temperature and organic matter content contributed to the recovery of methane production after drying. The provision of substrates by fermentation processes limited peat respiration during shallow water table and drying. In contrast, accumulation of acetate and hydrogen was observed during flooding indicating a decoupling of fermentation from terminal metabolism and favouring the co-occurrence of iron reduction, sulphate reduction and methanogenesis.
Monte Carlo Simulation Methods for Studying the Thermodynamics of Ligand Binding & Transfer Processes in Biomolecules
R. Thomas Ullmann
- The binding and transfer of ligands is of central
importance for the function of many biomolecular
systems. The main topic of this thesis is the
development and application of Monte Carlo (MC)
simulation methods for studying complex ligand
binding equilibria which can also involve
conformational changes. The simulated systems
were described by microstates within a continuum
electrostatics/molecular mechanics (CE/MM) model
of the receptor-ligand system. The CE/MM modeling
methodology was improved. The improvements led to
more detailed molecular models that enable a more
realistic reproduction of system properties and
environmental conditions. The developed simulation
methods were applied to biomolecular systems whose
function involves aspects that are important for
the understanding of bioenergetic energy
transduction. The results of this thesis are
presented in five articles that are published in
peer reviewed scientific journals.
Manuscript A presents the Monte Carlo simulation
software GMCT which was largely developed in this
thesis. The software offers a variety of different
simulation methods that allow the user to harness
the full potential of CE/MM models in the simulation
of complex receptor systems.
Manuscript B presents a novel theoretical framework
for free energy calculations with the free energy
perturbation method. The novel framework is more
broadly applicable and can lead to more efficient
simulations than previous formulations. The
derivation of the formalism also led to interesting
insights into general statistical mechanics. The
formalism was implemented in GMCT and could already
be used fruitfully for the free energy calculations
presented in Manuscripts C and D.
Manuscript C demonstrates the application of free
energy measures of cooperativity to study the
coupling of protonation, reduction and conformational
change in azurin from Pseudomonas aeruginosa (PaAz).
Such a coupling is prototypic for bioenergetic systems
because it forms the thermodynamic basis of their
energy transducing function. PaAz is an experimentally
well characterized, small electron transport protein.
For this reason, PaAz was used here as model system
to demonstrate the usefulness of cooperativity free
energies in detecting and quantifying thermodynamic
coupling between events in complex biomolecular
systems. The results of this study led to new insight
that could help to determine the still enigmatic
physiological role of PaAz.
In Manuscript D, free energy calculations were
applied to study the thermodynamics of transport
through the ammonium transporter Amt-1 from
Archaeoglobus fulgidus (AfAmt-1). Ammonium is the most
directly utilizable nitrogen source for plants and
microorganisms. AfAmt-1 and its homologues facilitate
the transport of ammonia/ammonium across biological
membranes in living beings from all domains of life.
It is intensely debated how these proteins perform
their function and whether ammonia or its protonated
form ammonium is actually transported. The study
extended upon previous theoretical studies by
including the effects of substrate concentration,
electrochemical transmembrane gradients,
proton-coupled binding equilibria and competitive
binding of different ligand species. It was found
that the transported species is most likely the
ammonium ion. An ammonia/proton symport mechanism
that involves a pair of coplanar histidine residues
at the center of the transmembrane pore as transient
proton acceptor is made plausible by the high
genetic conservation of these residues.
Manuscript E presents a first application of the
microstate description within a CE/MM model to the
simulation of the non-equilibrium dynamics of a
molecular system. We simulated the re-reduction
kinetics of the primary electron donor in the
photocycle of the bacterial photosynthetic reaction
center from Blastochloris viridis. The simulation
results are in very good agreement with
experimentally measured data.
Budget and fluxes of nitrogen in mountainous agroecosystems in a summer monsoonal climate under intensive land use
- A balanced nitrogen (N) cycle in intensively managed ecosystems is necessary as it underpins other ecosystem services. This study evaluated the agricultural practices in a typical mountainous catchment in South Korea in respect to N dynamics and their potential effect on water quality with the aim to develop options for a more sustainable catchment management.
In the 1st study, we used two approaches to calculate N budgets for the 5 key crops of the basin at the field scale. The gross and net N budgets for all crop types were found to be positive. Based on the small differences between the results of the two approaches we identified fertilizer N as well as soil Nmin as the dominant N input sources. As fertilizer N application was the major N input source (>50%), its reduction is the major scope of action for N savings at the field scale. A closely linked action is the synchronization of fertilizer N with soil Nmin. The large amount of fertilizer that is applied prior to planting (>60%) at the beginning of the monsoon season revealed that split applications could help reducing the fertilizer N additions and increase the low N use efficiencies (NUE). Based on the significant differences between gross and net N surplus for rice and bean fields, we identified the high amount of plant residues remaining after harvesting (>100 kg N ha-1) as a further factor for potential N savings. The 5 main crops accounted for over 80% of the total catchment N surplus (>400 Mg), even though their contribution to the area was only around 20%. A land use shift to perennial crops with lower N inputs was therefore found to be a possible but spatially limited chance to reduce N surpluses at the catchment scale. The comparison of catchment N surplus with stream N export revealed that 73-86% of the agricultural N surpluses were transported to water bodies in the catchment by either leaching or surface runoff.
In the 2nd study, we followed the fate of fertilizer N in a ridge and furrow (R/F) cultivation with polyethylene (PE) mulch by using 15N tracer. N leaching was simulated with Hydrus 2D. The comparison of 4 N fertilization levels (0, 150, 250 and 350 kg N ha-1) revealed that already 150 kg N ha-1 is sufficient to reach the maximal yield of radishes. Based on the low results of fertilizer N use efficiency (FNUE), we recommend two applications during the first 25 days of growth and a further application around day 50. These split applications adjusted to the plants’ needs increase the FNUE of the radish and decrease the fertilizer N losses during the growing season. However, split applications might be impractical in plastic covered R/F cultivations because mechanical equipment to apply fertilizer under the PE mulch is required. Based on the finding that 15N retention in soil and nitrate concentration in seepage water decreased similarly for ridges and furrows during the entire growing season, we conclude that the PE mulch had no significant effect on 15N retention in soil and on nitrate concentration in seepage water and did therefore not effectively protect the fertilizer in the ridges from percolation. Based on the simulation results, we found that the ridges and furrows contributed approximately an equal amount of leached N to the total amount. We therefore conclude that the PE mulch provided little protection for the fertilizer N in the ridges during heavy rainfall. N leaching amounts were further found to increase linearly with an increase in N addition rate as it is well known for R/F cultivations without PE mulch. The PE mulch did therefore not prevent the linear increase in leaching with an increase in fertilizer N addition. We summarize that without the use of additional measures such as split applications of fertilizer, the application of PE mulch in a summer monsoon climate with heavy rainfall events does not positively influence the N leaching rates.
In the 3rd study, we monitored soil water dynamics in the field and used this data set to simulate the influence of PE mulch on water fluxes with Hydrus 2D. We simulated soil water dynamics in 1) conventional flat tillage (CT); 2) R/F cultivation without PE mulched ridges (RT); and 3) R/F cultivation with PE mulched ridges (RTpm). The comparison of the simulated pressure heads during dry and wet periods revealed that the PE mulch induced significant soil moisture patterns only during the dry periods. During monsoon events, the effect of the PE mulch was dependent on the soil texture and the hydraulic conductivity. Summarizing the advantages and disadvantages of the R/F cultivation with PE mulch on sloped fields, the practice was observed to have the lowest amount of drainage water, the lowest evaporation rates but also the highest surface runoff rates. Hence, PE mulching might be assessed as a tool to reduce percolating water, but it concurrently increases water contribution to the river network by surface runoff.
The Integrated Size and Price Optimization problem
- We present the Integrated Size and Price Optimization Problem (ISPO)
for a fashion discounter with many branches. Based on a two-stage
stochastic programming model with recourse, we develop an exact
algorithm and a production-compliant heuristic that produces small
optimality gaps. In a field study we show that a distribution of
supply over branches and sizes based on ISPO solutions is
significantly better than a one-stage optimization of the
distribution ignoring the possibility of optimal pricing.