El conocimiento de la teoría lógica de Bolzano permite apreciar las aportaciones de su artículo m... more El conocimiento de la teoría lógica de Bolzano permite apreciar las aportaciones de su artículo matemático sobre la "demostración puramente analítica..." a la filosofía de la ciencia. Esta obra sirve como ejemplo de la productividad de su antipsicologismo en lógica, supone un argumento en apoyo de su rechazo de las tesis kantianas sobre la verdad matemática, y pone de manifiesto la relación entre lógica, matemáticas y filosofía en la tarea de fundamentación de la ciencia que emprendió.
Transient Photoluminescence Microscopy (TPLM) allows for the direct visualization of carrier tran... more Transient Photoluminescence Microscopy (TPLM) allows for the direct visualization of carrier transport in semiconductor materials with sub nanosecond and few nanometer resolution. The technique is based on measuring changes in the spatial distribution of a diffraction limited population of carriers using spatiotemporal detection of the radiative decay of the carriers. The spatial resolution of TPLM is therefore primarily determined by the signal-to-noise-ratio (SNR). Here we present a method using cylindrical lenses to boost the signal acquisition in TPLM experiments. The resulting asymmetric magnification of the photoluminescence emission of the diffraction limited spot can increase the collection efficiency by more than a factor of 10, significantly reducing acquisition times and further boosting spatial resolution.
Gold nanoparticles moving in aqueous solution under a optical vortex lattice are shown to present... more Gold nanoparticles moving in aqueous solution under a optical vortex lattice are shown to present a complex collective optofluidic dynamics. Above a critical field intensity and concentration the system presents a spontaneous transition towards synchronised motion, driven by nonconservative optical forces, thermal fluctuations and hydrodynamic pairing. The system exhibits a rich assortment of collective dynamics such as strong unidirectional currents of nanoparticles at speeds of centimetres per second. This relatively simple optofluidic setup offers an alternative way to control mass and heat transport at the nanoscale, which has been so far elusive.
Campisi, Zhan, Talkner and Hänggi have recently proposed a novel Hamiltonian thermostat which the... more Campisi, Zhan, Talkner and Hänggi have recently proposed a novel Hamiltonian thermostat which they claim may be used both in simulations and experiments. We show, however, that this is not possible due to the length and time scales involved, which depend exponentially on the total energy of the system. The implementation suggested by Campisi et alii implies equilibration times greater than the age of the universe for systems with more than a few dozen particles. 1 Campisi, Zhan, Talkner and Hänggi have recently proposed the use of the logarithmic oscillator as a novel Hamiltonian thermostat [1] and have claimed that "it may be implemented not only in a computer but also with real-world experiments". Unfortunately, this is not possible in most practical applications, because of the length and time scales involved, which depend exponentially on the total energy of the system (which in turn should be set to a large value, according to [1]). Consider the implementations suggested in [1]: an ion in a two-dimensional Coulomb potential generated by a thin oppositely charged wire (or a laser beam) that interacts through
Transient microscopy is of vital importance in understanding the dynamics of optical excited stat... more Transient microscopy is of vital importance in understanding the dynamics of optical excited states in optoelectronic materials, as it allows for a direct visualization of the movement of energy carriers in space and time. Important information on trap‐state dynamics can be obtained using this technique, typically observed as a slow‐down of energy transport as carriers are trapped at defect sites. To date, however, studies of the trap‐state dynamics have been mostly limited to phenomenological descriptions of the early time‐dynamics. Here, it is shown how long‐acquisitiontime transient photoluminescence microscopy can be used to provide a detailed map of the trapstate landscape in 2D perovskites, in particular when used in combination with transient spectroscopy. An anomalous evolution of the studied exciton distribution is observed, which cannot be explained with existing models for trap limited exciton transport that only account for a single trap type. Instead, using a continuous...
Two-dimensional layered perovskites are attracting increasing attention as more robust analogues ... more Two-dimensional layered perovskites are attracting increasing attention as more robust analogues to the conventional three-dimensional metal-halide perovskites for both light harvesting and light emitting applications. However, the impact of the reduced dimensionality on the optoelectronic properties remains unclear, particularly regarding the spatial dynamics of the excitonic excited state within the two-dimensional plane. Here, we present direct measurements of exciton transport in single-crystalline layered perovskites. Using transient photoluminescence microscopy, we show that excitons undergo an initial fast diffusion through the crystalline plane, followed by a slower subdiffusive regime as excitons get trapped. Interestingly, the early intrinsic diffusivity depends sensitively on the choice of organic spacer. A clear correlation between lattice stiffness and diffusivity is found, suggesting exciton–phonon interactions to be dominant in the spatial dynamics of the excitons in ...
The analytical theories derived here for the acoustic load impedance measured by a quartz crystal... more The analytical theories derived here for the acoustic load impedance measured by a quartz crystal microbalance (QCM), due to the presence of layers of different types (rigid, elastic, and viscous) immersed in a fluid, display generic properties, such as "vanishing mass" and positive frequency shifts, which have been observed in QCM experiments with soft-matter systems. These phenomena seem to contradict the well-known Sauerbrey relation at the heart of many QCM measurements, but here, we show that they arise as a natural consequence of hydrodynamics. We compare our one-dimensional immersed plate theory with three-dimensional simulations of rigid and flexible submicron-sized suspended spheres and with experimental results for adsorbed micron-sized colloids, which yield a "negative acoustic mass". The parallel behavior unveiled indicates that the QCM response is highly sensitive to hydrodynamics, even for adsorbed colloids. Our conclusions call for a revision of existing theories based on adhesion forces and elastic stiffness at contact, which should, in most cases, include hydrodynamics.
Despite being a fundamental tool in soft matter research, quartz crystal microbalance (QCM) analy... more Despite being a fundamental tool in soft matter research, quartz crystal microbalance (QCM) analyses of discrete macromolecules in liquid so far lack a firm theoretical basis. Currently, acoustic signals are qualitatively interpreted using ad-hoc frameworks based on effective electrical circuits, effective springs and trapped-solvent models with abundant fitting parameters. Nevertheless, due to its extreme sensitivity, the QCM technique pledges to become an accurate predictive tool. Using unsteady low Reynolds hydrodynamics we derive analytical expressions for the acoustic impedance of adsorbed discrete spheres. Our theory is successfully validated against 3D simulations and a plethora of experimental results covering more than a decade of research on proteins, viruses, liposomes, massive nanoparticles, with sizes ranging from few to hundreds of nanometers. The excellent agreement without fitting constants clearly indicates that the acoustic response is dominated by the hydrodynamic...
Using unsteady hydrodynamics theory, this work derives parameter-free analytic relations which qu... more Using unsteady hydrodynamics theory, this work derives parameter-free analytic relations which quantitatively agree with QCM experiments of either light of heavy adsorbed particles ranging between 5 and 200 nm in size.
A thesis rarely comes into being without the help of many people. First, I would like to thank my... more A thesis rarely comes into being without the help of many people. First, I would like to thank my advisor, Pep Español, for his patience. I do not think he realises how much the discussion we had in our first meeting shaped all the work that I have carried out since. I would also like to thank my colleagues and friends at the university. They often lent me a hand, especially with keeping spirits high. William G. Hoover read some sections in Chapter 4 and made many helpful comments, for which I am very grateful. Finally, I must thank my family, to whom I dedicate these pages. My mother braved through the whole text hunting for typographical errors and suggesting many improvements. Thank you very much, mother. Foremost, I would like to say thank you to Emma, who patiently accepted that I had little time to play with her during the summer, and thank you to Ana: without your constant support and encouragement I would have never written this book. iv To my family, especially Ana, Emma and Eric.-This is not poetry, but it does praise beauty. propuesto recientemente es ineficiente debido a que sus propiedades termodinámicas se aplican a escalas temporales mucho más grandes que aquellas sobre las que se supone que debe actuar como termostato. Terminamos con comentarios sobre cómo estimar la importancia de los efectos de memoria.
Halide mixing is one of the most powerful techniques to tune the optical bandgap of metal-halide ... more Halide mixing is one of the most powerful techniques to tune the optical bandgap of metal-halide perovskites. However, halide mixing has commonly been observed to result in phase segregation, which reduces excited-state transport and limits device performance. While the current emphasis lies on the development of strategies to prevent phase segregation, it remains unclear how halide mixing may affect excited-state transport even if phase purity is maintained. Here, we study exciton transport in phase pure mixed-halide 2D perovskites of (PEA) 2 Pb(I 1−x Br x) 4. Using transient photoluminescence microscopy, we show that, despite phase purity, halide mixing inhibits exciton transport. We find a significant reduction even for relatively low alloying concentrations. By performing Brownian dynamics simulations, we are able to reproduce our experimental results and attribute the decrease in diffusivity to the energetically disordered potential landscape that arises due to the intrinsic random distribution of alloying sites.
We show that distribution functions of nonequilibrium steady states (NESS) evolving under a slowl... more We show that distribution functions of nonequilibrium steady states (NESS) evolving under a slowly varying protocol can be accurately obtained from limited data and the closest known detailed state of the system. In this manner, one needs to perform only a few detailed experiments to obtain the nonequilibrium distribution function for the entire gamut of nonlinearity. We achieve this by maximizing the relative entropy functional (MaxRent), which is proportional to the Kullback-Leibler distance from a known density function, subject to constraints supplied by the problem definition and new measurements. MaxRent is thus superior to the principle of maximum entropy (MaxEnt), which maximizes Shannon's informational entropy for estimating distributions but lacks the ability of incorporating additional prior information. The MaxRent principle is illustrated using a toy model of φ 4 thermal conduction consisting of a single lattice point. An external protocol controlled position-dependent temperature field drives the system out of equilibrium. Two different thermostatting schemes are employed: the Hoover-Holian deterministic thermostat (which produces multifractal dynamics under strong nonlinearity) and the Langevin stochastic thermostat (which produces phase space-filling dynamics). Out of the 80 possible states produced by the protocol, we assume that 4 states are known to us in detail, one of which is used as input into MaxRent at a time. We find that MaxRent accurately approximates the phase space density functions at all values of the protocol even when the known distribution is far away. MaxEnt, however, is unable to capture the fine details of the phase space distribution functions. We expect this method to be useful in other external protocol driven nonequilibrium cases as well, making it unnecessary to perform detailed experiments for all the values of the protocol when one wishes to obtain approximate distributions.
The maximum entropy formalism developed by Jaynes determines the relevant ensemble in nonequilibr... more The maximum entropy formalism developed by Jaynes determines the relevant ensemble in nonequilibrium statistical mechanics by maximising the entropy functional subject to the constraints imposed by the available information. We present an alternative derivation of the relevant ensemble based on the Kullback-Leibler divergence from equilibrium. If the equilibrium ensemble is already known, then calculation of the relevant ensemble is considerably simplified. The constraints must be chosen with care in order to avoid contradictions between the two alternative derivations. The relative entropy functional measures how much a distribution departs from equilibrium. Therefore, it provides a distinct approach to the calculation of statistical ensembles that might be applicable to situations in which the formalism presented by Jaynes performs poorly (such as non-ergodic dynamical systems).
El conocimiento de la teoría lógica de Bolzano permite apreciar las aportaciones de su artículo m... more El conocimiento de la teoría lógica de Bolzano permite apreciar las aportaciones de su artículo matemático sobre la "demostración puramente analítica..." a la filosofía de la ciencia. Esta obra sirve como ejemplo de la productividad de su antipsicologismo en lógica, supone un argumento en apoyo de su rechazo de las tesis kantianas sobre la verdad matemática, y pone de manifiesto la relación entre lógica, matemáticas y filosofía en la tarea de fundamentación de la ciencia que emprendió.
Transient Photoluminescence Microscopy (TPLM) allows for the direct visualization of carrier tran... more Transient Photoluminescence Microscopy (TPLM) allows for the direct visualization of carrier transport in semiconductor materials with sub nanosecond and few nanometer resolution. The technique is based on measuring changes in the spatial distribution of a diffraction limited population of carriers using spatiotemporal detection of the radiative decay of the carriers. The spatial resolution of TPLM is therefore primarily determined by the signal-to-noise-ratio (SNR). Here we present a method using cylindrical lenses to boost the signal acquisition in TPLM experiments. The resulting asymmetric magnification of the photoluminescence emission of the diffraction limited spot can increase the collection efficiency by more than a factor of 10, significantly reducing acquisition times and further boosting spatial resolution.
Gold nanoparticles moving in aqueous solution under a optical vortex lattice are shown to present... more Gold nanoparticles moving in aqueous solution under a optical vortex lattice are shown to present a complex collective optofluidic dynamics. Above a critical field intensity and concentration the system presents a spontaneous transition towards synchronised motion, driven by nonconservative optical forces, thermal fluctuations and hydrodynamic pairing. The system exhibits a rich assortment of collective dynamics such as strong unidirectional currents of nanoparticles at speeds of centimetres per second. This relatively simple optofluidic setup offers an alternative way to control mass and heat transport at the nanoscale, which has been so far elusive.
Campisi, Zhan, Talkner and Hänggi have recently proposed a novel Hamiltonian thermostat which the... more Campisi, Zhan, Talkner and Hänggi have recently proposed a novel Hamiltonian thermostat which they claim may be used both in simulations and experiments. We show, however, that this is not possible due to the length and time scales involved, which depend exponentially on the total energy of the system. The implementation suggested by Campisi et alii implies equilibration times greater than the age of the universe for systems with more than a few dozen particles. 1 Campisi, Zhan, Talkner and Hänggi have recently proposed the use of the logarithmic oscillator as a novel Hamiltonian thermostat [1] and have claimed that "it may be implemented not only in a computer but also with real-world experiments". Unfortunately, this is not possible in most practical applications, because of the length and time scales involved, which depend exponentially on the total energy of the system (which in turn should be set to a large value, according to [1]). Consider the implementations suggested in [1]: an ion in a two-dimensional Coulomb potential generated by a thin oppositely charged wire (or a laser beam) that interacts through
Transient microscopy is of vital importance in understanding the dynamics of optical excited stat... more Transient microscopy is of vital importance in understanding the dynamics of optical excited states in optoelectronic materials, as it allows for a direct visualization of the movement of energy carriers in space and time. Important information on trap‐state dynamics can be obtained using this technique, typically observed as a slow‐down of energy transport as carriers are trapped at defect sites. To date, however, studies of the trap‐state dynamics have been mostly limited to phenomenological descriptions of the early time‐dynamics. Here, it is shown how long‐acquisitiontime transient photoluminescence microscopy can be used to provide a detailed map of the trapstate landscape in 2D perovskites, in particular when used in combination with transient spectroscopy. An anomalous evolution of the studied exciton distribution is observed, which cannot be explained with existing models for trap limited exciton transport that only account for a single trap type. Instead, using a continuous...
Two-dimensional layered perovskites are attracting increasing attention as more robust analogues ... more Two-dimensional layered perovskites are attracting increasing attention as more robust analogues to the conventional three-dimensional metal-halide perovskites for both light harvesting and light emitting applications. However, the impact of the reduced dimensionality on the optoelectronic properties remains unclear, particularly regarding the spatial dynamics of the excitonic excited state within the two-dimensional plane. Here, we present direct measurements of exciton transport in single-crystalline layered perovskites. Using transient photoluminescence microscopy, we show that excitons undergo an initial fast diffusion through the crystalline plane, followed by a slower subdiffusive regime as excitons get trapped. Interestingly, the early intrinsic diffusivity depends sensitively on the choice of organic spacer. A clear correlation between lattice stiffness and diffusivity is found, suggesting exciton–phonon interactions to be dominant in the spatial dynamics of the excitons in ...
The analytical theories derived here for the acoustic load impedance measured by a quartz crystal... more The analytical theories derived here for the acoustic load impedance measured by a quartz crystal microbalance (QCM), due to the presence of layers of different types (rigid, elastic, and viscous) immersed in a fluid, display generic properties, such as "vanishing mass" and positive frequency shifts, which have been observed in QCM experiments with soft-matter systems. These phenomena seem to contradict the well-known Sauerbrey relation at the heart of many QCM measurements, but here, we show that they arise as a natural consequence of hydrodynamics. We compare our one-dimensional immersed plate theory with three-dimensional simulations of rigid and flexible submicron-sized suspended spheres and with experimental results for adsorbed micron-sized colloids, which yield a "negative acoustic mass". The parallel behavior unveiled indicates that the QCM response is highly sensitive to hydrodynamics, even for adsorbed colloids. Our conclusions call for a revision of existing theories based on adhesion forces and elastic stiffness at contact, which should, in most cases, include hydrodynamics.
Despite being a fundamental tool in soft matter research, quartz crystal microbalance (QCM) analy... more Despite being a fundamental tool in soft matter research, quartz crystal microbalance (QCM) analyses of discrete macromolecules in liquid so far lack a firm theoretical basis. Currently, acoustic signals are qualitatively interpreted using ad-hoc frameworks based on effective electrical circuits, effective springs and trapped-solvent models with abundant fitting parameters. Nevertheless, due to its extreme sensitivity, the QCM technique pledges to become an accurate predictive tool. Using unsteady low Reynolds hydrodynamics we derive analytical expressions for the acoustic impedance of adsorbed discrete spheres. Our theory is successfully validated against 3D simulations and a plethora of experimental results covering more than a decade of research on proteins, viruses, liposomes, massive nanoparticles, with sizes ranging from few to hundreds of nanometers. The excellent agreement without fitting constants clearly indicates that the acoustic response is dominated by the hydrodynamic...
Using unsteady hydrodynamics theory, this work derives parameter-free analytic relations which qu... more Using unsteady hydrodynamics theory, this work derives parameter-free analytic relations which quantitatively agree with QCM experiments of either light of heavy adsorbed particles ranging between 5 and 200 nm in size.
A thesis rarely comes into being without the help of many people. First, I would like to thank my... more A thesis rarely comes into being without the help of many people. First, I would like to thank my advisor, Pep Español, for his patience. I do not think he realises how much the discussion we had in our first meeting shaped all the work that I have carried out since. I would also like to thank my colleagues and friends at the university. They often lent me a hand, especially with keeping spirits high. William G. Hoover read some sections in Chapter 4 and made many helpful comments, for which I am very grateful. Finally, I must thank my family, to whom I dedicate these pages. My mother braved through the whole text hunting for typographical errors and suggesting many improvements. Thank you very much, mother. Foremost, I would like to say thank you to Emma, who patiently accepted that I had little time to play with her during the summer, and thank you to Ana: without your constant support and encouragement I would have never written this book. iv To my family, especially Ana, Emma and Eric.-This is not poetry, but it does praise beauty. propuesto recientemente es ineficiente debido a que sus propiedades termodinámicas se aplican a escalas temporales mucho más grandes que aquellas sobre las que se supone que debe actuar como termostato. Terminamos con comentarios sobre cómo estimar la importancia de los efectos de memoria.
Halide mixing is one of the most powerful techniques to tune the optical bandgap of metal-halide ... more Halide mixing is one of the most powerful techniques to tune the optical bandgap of metal-halide perovskites. However, halide mixing has commonly been observed to result in phase segregation, which reduces excited-state transport and limits device performance. While the current emphasis lies on the development of strategies to prevent phase segregation, it remains unclear how halide mixing may affect excited-state transport even if phase purity is maintained. Here, we study exciton transport in phase pure mixed-halide 2D perovskites of (PEA) 2 Pb(I 1−x Br x) 4. Using transient photoluminescence microscopy, we show that, despite phase purity, halide mixing inhibits exciton transport. We find a significant reduction even for relatively low alloying concentrations. By performing Brownian dynamics simulations, we are able to reproduce our experimental results and attribute the decrease in diffusivity to the energetically disordered potential landscape that arises due to the intrinsic random distribution of alloying sites.
We show that distribution functions of nonequilibrium steady states (NESS) evolving under a slowl... more We show that distribution functions of nonequilibrium steady states (NESS) evolving under a slowly varying protocol can be accurately obtained from limited data and the closest known detailed state of the system. In this manner, one needs to perform only a few detailed experiments to obtain the nonequilibrium distribution function for the entire gamut of nonlinearity. We achieve this by maximizing the relative entropy functional (MaxRent), which is proportional to the Kullback-Leibler distance from a known density function, subject to constraints supplied by the problem definition and new measurements. MaxRent is thus superior to the principle of maximum entropy (MaxEnt), which maximizes Shannon's informational entropy for estimating distributions but lacks the ability of incorporating additional prior information. The MaxRent principle is illustrated using a toy model of φ 4 thermal conduction consisting of a single lattice point. An external protocol controlled position-dependent temperature field drives the system out of equilibrium. Two different thermostatting schemes are employed: the Hoover-Holian deterministic thermostat (which produces multifractal dynamics under strong nonlinearity) and the Langevin stochastic thermostat (which produces phase space-filling dynamics). Out of the 80 possible states produced by the protocol, we assume that 4 states are known to us in detail, one of which is used as input into MaxRent at a time. We find that MaxRent accurately approximates the phase space density functions at all values of the protocol even when the known distribution is far away. MaxEnt, however, is unable to capture the fine details of the phase space distribution functions. We expect this method to be useful in other external protocol driven nonequilibrium cases as well, making it unnecessary to perform detailed experiments for all the values of the protocol when one wishes to obtain approximate distributions.
The maximum entropy formalism developed by Jaynes determines the relevant ensemble in nonequilibr... more The maximum entropy formalism developed by Jaynes determines the relevant ensemble in nonequilibrium statistical mechanics by maximising the entropy functional subject to the constraints imposed by the available information. We present an alternative derivation of the relevant ensemble based on the Kullback-Leibler divergence from equilibrium. If the equilibrium ensemble is already known, then calculation of the relevant ensemble is considerably simplified. The constraints must be chosen with care in order to avoid contradictions between the two alternative derivations. The relative entropy functional measures how much a distribution departs from equilibrium. Therefore, it provides a distinct approach to the calculation of statistical ensembles that might be applicable to situations in which the formalism presented by Jaynes performs poorly (such as non-ergodic dynamical systems).
Los fasores son números complejos que rotan alrededor del origen con velocidad angular uniforme. ... more Los fasores son números complejos que rotan alrededor del origen con velocidad angular uniforme. Tienen muchı́simas aplicaciones en matemáticas, fı́sica e ingenierı́a. Como veremos, se pueden utilizar para representar oscilaciones y facilitan la resolución de muchas ecuaciones diferenciales lineales. Se utilizan como herramienta de manera habitual en electromagnetismo, óptica, acústica, mecánica de vibraciones, teorı́a de circuitos y mecánica cuántica, entre otros campos.
Los fasores extienden la sencilla fórmula de Euler,
exp(iθ) = cos(θ) + i sin(θ),
para permitir que el argumento θ cambie con el tiempo. Por tanto, para leer este libro hace falta estar familiarizado con la aritmética de números complejos y las propiedades de la exponencial. Haremos derivadas sencillas y algunas integrales, por lo que conviene haber estudiado cálculo o análisis matemático.
This article presents a peculiar type of logical fallacy. I have decided to call it the modal fal... more This article presents a peculiar type of logical fallacy. I have decided to call it the modal fallacy because it emerges from an unjustified disregard for the accessibility relations in modal logic. A closely related fallacy (also known as the modal fallacy or, sometimes, modal scope fallacy), involves an inappropriate change in the scope of a modal operator and, therefore, amounts to a syntactical error analogous to the invalid inference of ∃y∀xPxy from ∀x∃yPxy. In contrast, the fallacy considered here constitutes a valid argument from the point of view of logical syntax, but involves an implicit shift in the accessibility relations. This marks the problem as a characteristically modal phenomenon. Towards the end of this paper, we will turn to two simple applications of the insight gained from our diagnosis.
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Papers by marc melendez
Los fasores extienden la sencilla fórmula de Euler,
exp(iθ) = cos(θ) + i sin(θ),
para permitir que el argumento θ cambie con el tiempo. Por tanto, para leer este libro hace falta estar familiarizado con la aritmética de números complejos y las propiedades de la exponencial. Haremos derivadas sencillas y algunas integrales, por lo que conviene haber estudiado cálculo o análisis matemático.