Charge transport in disordered materials : simulations, theory, and numerical modeling of hopping transport and electron-hole recombination

Min avhandling behandlar hur oordnade material leder elektrisk ström. Bland materialen som studeras finns ledande polymerer, d.v.s. plaster som leder ström, och mer allmänt organiska halvledare. Av de här materialen har man kunnat bygga elektroniska komponenter, och man hoppas på att kunna trycka hela kretsar av organiska material. För de här tillämpningarna är det viktigt att förstå hur materialen själva leder elektrisk ström. Termen oordnade material syftar på material som saknar kristallstruktur. Oordningen gör att elektronernas tillstånd blir lokaliserade i rummet, så att en elektron i ett visst tillstånd är begränsad t.ex. till en molekyl eller ett segment av en polymer. Det här kan jämföras med kristallina material, där ett elektrontillstånd är utspritt över hela kristallen (men i stället har en väldefinierad rörelsemängd). Elektronerna (eller hålen) i det oordnade materialet kan röra sig genom att tunnelera mellan de lokaliserade tillstånden. Utgående från egenskaperna för den här tunneleringsprocessen, kan man bestämma transportegenskaperna för hela materialet. Det här är utgångspunkten för den så kallade hopptransportmodellen, som jag har använt mig av. Hopptransportmodellen innehåller flera drastiska förenklingar. Till exempel betraktas elektrontillstånden som punktformiga, så att tunneleringssannolikheten mellan två tillstånd endast beror på avståndet mellan dem, och inte på deras relativa orientation. En annan förenkling är att behandla det kvantmekaniska tunneleringsproblemet som en klassisk process, en slumpvandring. Trots de här grova approximationerna visar hopptransportmodellen ändå många av de fenomen som uppträder i de verkliga materialen som man vill modellera. Man kan kanske säga att hopptransportmodellen är den enklaste modell för oordnade material som fortfarande är intressant att studera. Man har inte hittat exakta analytiska lösningar för hopptransportmodellen, därför använder man approximationer och numeriska metoder, ofta i form av datorberäkningar. Vi har använt både analytiska metoder och numeriska beräkningar för att studera olika aspekter av hopptransportmodellen. En viktig del av artiklarna som min avhandling baserar sig på är att jämföra analytiska och numeriska resultat. Min andel av arbetet har främst varit att utveckla de numeriska metoderna och applicera dem på hopptransportmodellen. Därför fokuserar jag på den här delen av arbetet i avhandlingens introduktionsdel. Ett sätt att studera hopptransportmodellen numeriskt är att direkt utföra en slumpvandringsprocess med ett datorprogram. Genom att föra statisik över slumpvandringen kan man beräkna olika transportegenskaper i modellen. Det här är en så kallad Monte Carlo-metod, eftersom själva beräkningen är en slumpmässig process. I stället för att följa rörelsebanan för enskilda elektroner, kan man beräkna sannolikheten vid jämvikt för att hitta en elektron i olika tillstånd. Man ställer upp ett system av ekvationer, som relaterar sannolikheterna för att hitta elektronen i olika tillstånd i systemet med flödet, strömmen, mellan de olika tillstånden. Genom att lösa ekvationssystemet fås sannolikhetsfördelningen för elektronerna. Från sannolikhetsfördelningen kan sedan strömmen och materialets transportegenskaper beräknas. En aspekt av hopptransportmodellen som vi studerat är elektronernas diffusion, d.v.s. deras slumpmässiga rörelse. Om man betraktar en samling elektroner, så sprider den med tiden ut sig över ett större område. Det är känt att diffusionshastigheten beror av elfältet, så att elektronerna sprider sig fortare om de påverkas av ett elektriskt fält. Vi har undersökt den här processen, och visat att beteendet är väldigt olika i endimensionella system, jämfört med två- och tredimensionella. I två och tre dimensioner beror diffusionskoefficienten kvadratiskt av elfältet, medan beroendet i en dimension är linjärt. En annan aspekt vi studerat är negativ differentiell konduktivitet, d.v.s. att strömmen i ett material minskar då man ökar spänningen över det. Eftersom det här fenomenet har uppmätts i organiska minnesceller, ville vi undersöka om fenomenet också kan uppstå i hopptransportmodellen. Det visade sig att det i modellen finns två olika mekanismer som kan ge upphov till negativ differentiell konduktivitet. Dels kan elektronerna fastna i fällor, återvändsgränder i systemet, som är sådana att det är svårare att ta sig ur dem då elfältet är stort. Då kan elektronernas medelhastighet och därmed strömmen i materialet minska med ökande elfält. Elektrisk växelverkan mellan elektronerna kan också leda till samma beteende, genom en så kallad coulombblockad. En coulombblockad kan uppstå om antalet ledningselektroner i materialet ökar med ökande spänning. Elektronerna repellerar varandra och ett större antal elektroner kan leda till att transporten blir långsammare, d.v.s. att strömmen minskar.

Theory and numerical integration of subsurface light transport

En synthèse d’images, reproduire les effets complexes de la lumière sur des matériaux transluminescents, tels que la cire, le marbre ou la peau, contribue grandement au réalisme d’une image. Malheureusement, ce réalisme supplémentaire est couteux en temps de calcul. Les modèles basés sur la théorie de la diffusion visent à réduire ce coût en simulant le comportement physique du transport de la lumière sous surfacique tout en imposant des contraintes de variation sur la lumière incidente et sortante. Une composante importante de ces modèles est leur application à évaluer hiérarchiquement l’intégrale numérique de l’illumination sur la surface d’un objet. Cette thèse révise en premier lieu la littérature actuelle sur la simulation réaliste de la transluminescence, avant d’investiguer plus en profondeur leur application et les extensions des modèles de diffusion en synthèse d’images. Ainsi, nous proposons et évaluons une nouvelle technique d’intégration numérique hiérarchique utilisant une nouvelle analyse fréquentielle de la lumière sortante et incidente pour adapter efficacement le taux d’échantillonnage pendant l’intégration. Nous appliquons cette théorie à plusieurs modèles qui correspondent à l’état de l’art en diffusion, octroyant une amélioration possible à leur efficacité et précision.

Tractable molecular theory of transport of Lennard-Jones fluids in nanopores

We present here a tractable theory of transport of simple fluids in cylindrical nanopores, which is applicable over a wide range of densities and pore sizes. In the Henry law low-density region the theory considers the trajectories of molecules oscillating between diffuse wall collisions, while at higher densities beyond this region the contribution from viscous flow becomes significant and is included through our recent approach utilizing a local average density model. The model is validated by means of equilibrium as well nonequilibrium molecular dynamics simulations of supercritical methane transport in cylindrical silica pores over a wide range of temperature, density, and pore size. The model for the Henry law region is exact and found to yield an excellent match with simulations at all conditions, including the single-file region of very small pore size where it is shown to provide the density-independent collective transport coefficient. It is also shown that in the absence of dispersive interactions the model reduces to the classical Knudsen result, but in the presence of such interactions the latter model drastically overpredicts the transport coefficient. For larger micropores beyond the single-file region the transport coefficient is reduced at high density because of intermolecular interactions and hindrance to particle crossings leading to a large decrease in surface slip that is not well represented by the model. However, for mesopores the transport coefficient increases monotonically with density, over the range studied, and is very well predicted by the theory, though at very high density the contribution from surface slip is slightly overpredicted. It is also seen that the concept of activated diffusion, commonly associated with diffusion in small pores, is fundamentally invalid for smooth pores, and the apparent activation energy is not simply related to the minimum pore potential or the adsorption energy as generally assumed. (C) 2004 American Institute of Physics.

Transport of simple fluids in nanopores: Theory and simulation

A theory is discussed of single-component transport in nanopores, recently developed by Bhatia and coworkers. The theory considers the oscillatory motion of molecules between diffuse wall collisions, arising from the fluid-wall interaction, along with superimposed viscous flow due to fluid-fluid interaction. The theory is tested against molecular dynamics simulations for hydrogen, methane, and carbon tetrafluoride flow in cylindrical nanopores in silica. Although exact at low densities, the theory performs well even at high densities, with the density dependency of the transport coefficient arising from viscous effects. Such viscous effects are reduced at high densities because of the large increase in viscosity, which explains the maximum in the transport coefficient with increase in density. Further, it is seen that in narrow pore sizes of less than two molecular diameters, where a complete monolayer cannot form on the surface, the mutual interference of molecules on opposite sides of the cross section can reduce the transport coefficient, and lead to a maximum in the transport coefficient with increasing density. The theory is also tested for the case of partially diffuse reflection and shows the viscous contribution to be negligible when the reflection is nearly specular. (c) 2005 American Institute of Chemical Engineers AIChE J, 52: 29-38, 2006.

Nonlinear transport and oscillating magnetoresistance in double quantum wells

The nonlinear regime of low-temperature magnetoresistance of double quantum wells in the region of magnetic fields below 1 T is studied both experimentally and theoretically. The observed inversion of the magnetointersubband oscillation peaks with increasing electric current and splitting of these peaks are described by the theory based on the kinetic equation for the isotropic nonequilibrium part of electron distribution function. The inelastic-scattering time of electrons is determined from the current dependence of the inversion field.

Conservation laws, integrability, and transport in one-dimensional quantum systems

In integrable one-dimensional quantum systems an infinite set of local conserved quantities exists which can prevent a current from decaying completely. For cases like the spin current in the XXZ model at zero magnetic field or the charge current in the attractive Hubbard model at half filling, however, the current operator does not have overlap with any of the local conserved quantities. We show that in these situations transport at finite temperatures is dominated by a diffusive contribution with the Drude weight being either small or even zero. For the XXZ model we discuss in detail the relation between our results, the phenomenological theory of spin diffusion, and measurements of the spin-lattice relaxation rate in spin chain compounds. Furthermore, we study the Haldane-Shastry model where a conserved spin current exists.

Transport properties of strongly correlated metals: A dynamical mean-field approach

The temperature dependence of the transport properties of the metallic phase of a frustrated Hubbard model on the hypercubic lattice at half-filling is calculated. Dynamical mean-held theory, which maps the Hubbard model onto a single impurity,Anderson model that is solved self-consistently, and becomes exact in the limit of large dimensionality, is used. As the temperature increases there is a smooth crossover from coherent Fermi liquid excitations at low temperatures to incoherent excitations at high temperatures. This crossover leads to a nonmonotonic temperature dependence for the resistance, thermopower, and Hall coefficient, unlike in conventional metals. The resistance smoothly increases from a quadratic temperature dependence at low temperatures to large values which can exceed the Mott-Ioffe-Regel value ha/e(2) (where a is a lattice constant) associated with mean free paths less than a lattice constant. Further signatures of the thermal destruction of quasiparticle excitations are a peak in the thermopower and the absence of a Drude peak in the optical conductivity. The results presented here are relevant to a wide range of strongly correlated metals, including transition metal oxides, strontium ruthenates, and organic metals.

A new diffusion and flow theory for activated carbon from low pressure to capillary condensation range

In this paper, we develop a theory for diffusion and flow of pure sub-critical adsorbates in microporous activated carbon over a wide range of pressure, ranging from very low to high pressure, where capillary condensation is occurring. This theory does not require any fitting parameter. The only information needed for the prediction is the complete pore size distribution of activated carbon. The various interesting behaviors of permeability versus loading are observed such as the maximum permeability at high loading (occurred at about 0.8-0.9 relative pressure). The theory is tested with diffusion and flow of benzene through a commercial activated carbon, and the agreement is found to be very good in the light that there is no fitting parameter in the model. (C) 2001 Elsevier Science B.V. All rights reserved.

Kinetics of adsorption on activated carbon: application of heterogeneous vacancy solution theory

The kinetics of single component adsorption on activated carbon is investigated here using a heterogeneous vacancy solution theory (VST) of adsorption. The adsorption isotherm is developed to account for the adsorbate non-ideality due to the size difference between the adsorbate molecule and the vacant site, while incorporating adsorbent heterogeneity through a pore-width-related potential energy. The transport process in the bidisperse carbon considers coupled mass transfer in both macropore and micropore phases simultaneously. Adsorbate diffusion in the micropore network is modeled through effective medium theory, thus considering pore network connectivity in the adsorbent, with the activation energy for adsorbate diffusion related to the adsorption energy, represented by the Steele 10-4-3 potential for carbons. Experimental data of five hydrocarbons, CO2 and SO2 on Ajax carbon at multiple temperatures, as well as three hydrocarbons on Norit carbon at three temperatures are first fitted by the heterogeneous VST model to obtain the isotherm parameters, followed by application of the kinetic model to uptake data on carbon particles of different sizes and geometry at various temperatures. For the hydrocarbons studied, the model can successfully correlate the experimental data for both adsorption equilibrium and kinetics. However, there is some deviation in the fit of the desorption kinetics for polar compounds such as CO2 and SO2, due to the inadequacy of the L-J potential model in this case. The significance of viscous transport in the micropores is also considered here and found to be negligible, consistent with recent molecular simulation studies. (C) 2002 Elsevier Science Ltd. All rights reserved.

Object transportation by multiple mobile robots controlled by attractor dynamics: theory and implementation

Dynamical systems theory is used as a theoretical language and tool to design a distributed control architecture for teams of mobile robots, that must transport a large object and simultaneously avoid collisions with (either static or dynamic) obstacles. Here we demonstrate in simulations and implementations in real robots that it is possible to simplify the architectures presented in previous work and to extend the approach to teams of n robots. The robots have no prior knowledge of the environment. The motion of each robot is controlled by a time series of asymptotical stable states. The attractor dynamics permits the integration of information from various sources in a graded manner. As a result, the robots show a strikingly smooth an stable team behaviour.

The thickness of the transport layer in stratified geomorphic flows

River Flow 2010

An improved method for discovering link criticality in transport networks

Quantitatively assessing the importance or criticality of each link in a network is of practical value to operators, as that can help them to increase the network's resilience, provide more efficient services, or improve some other aspect of the service. Betweenness is a graph-theoretical measure of centrality that can be applied to communication networks to evaluate link importance. However, as we illustrate in this paper, the basic definition of betweenness centrality produces inaccurate estimations as it does not take into account some aspects relevant to networking, such as the heterogeneity in link capacity or the difference between node-pairs in their contribution to the total traffic. A new algorithm for discovering link centrality in transport networks is proposed in this paper. It requires only static or semi-static network and topology attributes, and yet produces estimations of good accuracy, as verified through extensive simulations. Its potential value is demonstrated by an example application. In the example, the simple shortest-path routing algorithm is improved in such a way that it outperforms other more advanced algorithms in terms of blocking ratio