Nonlocality, Superposition, and Time in the 4+1 Formalism.

The field of quantum gravity struggles with several problems related to time, quantum measurement, nonlocality, and realism. To address these issues, this study develops a 4+1 formalism featuring a flat 4D spacetime evolving with a second form of time, τ, worldlines that locally conserve momentum, and a hypersurface representing the present. As a function of τ, worldlines can spatially readjust and influences can travel backward or forward in the time dimension along these worldlines, offering a physical mechanism for retrocausality. Three theoretical models are presented, elucidating how nonlocality in an EPR experiment, the arrival time problem, and superposition in a Mach-Zehnder interferometer can be understood within this 4+1 framework. These results demonstrate that essential quantum phenomena can be reproduced in the 4+1 formalism while upholding the principles of realism, locality, and determinism at a fundamental level. Additionally, there is no measurement or collapse problem, and a natural explanation for the quantum-to-classical transition is obtained. Furthermore, observations of a 4D block universe and of the flow of time can be simultaneously understood. With these properties, the presented 4+1 formalism lays an interesting foundation for a quantum gravity theory based on intuitive principles and compatible with our observation of time.

Single Elementary Charge Fluctuations on Nanoparticles in Aqueous Solution.

100 years ago, in 1923, the Nobel prize in physics was awarded for measurement of the unit charge. In addition to a profound impact on contemporary physics, this discovery has reshaped our understanding of charge-based interactions in chemistry and biology, ranging from oxidation and ionization to protein folding and metabolism. In a liquid, the discrete nature of the electric charge becomes prominent at the nanoscale when a charge carrier is exchanged between a molecule or a nanoparticle and the surrounding medium. However, our ability to observe the dynamics of such interactions at the level of a single elementary charge is limited due to the abundance of ions in water. Here, we report on the observation of single binding-unbinding events with elementary charge resolution at the surface of a nanoparticle suspended in water. Discrete steps in the electrical charge are revealed by analyzing the motion of optically trapped nanoparticles under the influence of an applied sinusoidal electric field. The measurements are sufficiently fast and long to observe individual (dis)charging events that occur on average every 3 s. Our results offer prospective routes for studying the dynamics of diverse chemical and biological phenomena on the nanoscale with elementary charge resolution.

Uni- and Bidirectional Rotation and Speed Control in Chiral Photonic Micromotors Powered by Light.

Liquid crystalline polymers are attractive materials for untethered miniature soft robots. When they contain azo dyes, they acquire light-responsive actuation properties. However, the manipulation of such photoresponsive polymers at the micrometer scale remains largely unexplored. Here, uni- and bidirectional rotation and speed control of polymerized azo-containing chiral liquid crystalline photonic microparticles powered by light is reported. The rotation of these polymer particles is first studied in an optical trap experimentally and theoretically. The micro-sized polymer particles respond to the handedness of a circularly polarized trapping laser due to their chirality and exhibit uni- and bidirectional rotation depending on their alignment within the optical tweezers. The attained optical torque causes the particles to spin with a rotation rate of several hertz. The angular speed can be controlled by small structural changes, induced by ultraviolet (UV) light absorption. After switching off the UV illumination, the particle recovers its rotation speed. The results provide evidence of uni- and bidirectional motion and speed control in light-responsive polymer particles and offer a new way to devise light-controlled rotary microengines at the micrometer scale.

Single-particle electrophoresis for studying the adsorption of cationic polymers onto anionic particles.

Understanding the adsorption of polymers onto particles is crucial for many technological and biomedical applications. Even though polymer adsorption on particles is a dynamic process, most experimental techniques can only study the adsorption indirectly, in equilibrium and on the ensemble level. New analysis methods are required to overcome these limitations. We investigated the use of single-particle electrophoresis to study the adsorption kinetics of cationic polymers onto anionic particles and compared the resulting data to a theoretical model. In this approach, the electrophoretic mobility of single polystyrene (PS) particles, exposed to different concentrations of poly(2-guanidinoethyl methacrylate), was measured as a function of time. The polymer adsorption leads to an electrophoretic mobility change of the PS particle over time, from the initial negative value to a positive value at equilibrium. By fitting the kinetics data to the Langmuir model, the adsorption rate, desorption rate and equilibrium constant were determined. Finally, the adsorption kinetics of several other polymers was investigated. This showed that the presented technique enables direct analysis and comparison of the kinetics of polymer adsorption on the single-particle level.

Measurement of the amplitude and phase of the electrophoretic and electroosmotic mobility based on fast single-particle tracking.

The electrophoretic mobility of micron-scale particles is of crucial importance in applications related to pharmacy, electronic ink displays, printing, and food technology as well as in fundamental studies in these fields. Particle mobility measurements are often limited in accuracy because they are based on ensemble averages and because a correction for electroosmosis needs to be made based on a model. Single-particle approaches are better suited for examining polydisperse samples, but existing implementations either require multiple measurements to take the effect of electroosmosis into account or are limited in accuracy by short measurement times. In this work, accurate characterization of monodisperse and polydisperse samples is achieved by measuring the electrophoretic mobility on a particle-to-particle basis while suppressing electroosmosis. Electroosmosis can be suppressed by measuring in the middle of a microchannel while applying an AC voltage with a sufficiently high frequency. An accurate measurement of the electrophoretic mobility is obtained by analyzing the oscillating particle motion for 1.5s per particle with a high-speed camera measuring at 850Hz , synchronized to the applied electric field. Attention is paid to take into account the effect of the rolling shutter and the non-uniform sampling in order to obtain the accurate amplitude and phase of the electrophoretic mobility. The accuracy of method is experimentally verified and compared with a commercial apparatus for polystyrene microspheres in water. The method is further demonstrated on a range of particle materials and particle sizes and for a mixture of positively and negatively charged particles.

Waveguiding of Photoluminescence in a Layer of Semiconductor Nanoparticles.

Semiconductor nanoparticles (SNPs), such as quantum dots (QDs) and core/shell nanoparticles, have proven to be promising candidates for the development of next-generation technologies, including light-emitting diodes (LEDs), liquid crystal displays (LCDs) and solar concentrators. Typically, these applications use a sub-micrometer-thick film of SNPs to realize photoluminescence. However, our current knowledge on how this thin SNP layer affects the optical efficiency remains incomplete. In this work, we demonstrate how the thickness of the photoluminescent layer governs the direction of the emitted light. Our theoretical and experimental results show that the emission is fully outcoupled for sufficiently thin films (monolayer of SNPs), whereas for larger thicknesses (larger than one tenth of the wavelength) an important contribution propagates along the film that acts as a planar waveguide. These findings serve as a guideline for the smart design of diverse QD-based systems, ranging from LEDs, where thinner layers of SNPs maximize the light outcoupling, to luminescent solar concentrators, where a thicker layer of SNPs will boost the efficiency of light concentration.

Correction: Space charge limited release of charged inverse micelles in non-polar liquids.

Correction for 'Space charge limited release of charged inverse micelles in non-polar liquids' by Manoj Prasad et al., Phys. Chem. Chem. Phys., 2016, 18, 19289-19298, DOI: .

Correction: Electrokinetics and behavior near the interface of colloidal particles in non-polar dispersions.

Correction for 'Electrokinetics and behavior near the interface of colloidal particles in non-polar dispersions' by Manoj Prasad et al., Soft Matter, 2017, 13, 5604-5612, DOI: .

Polarity-Dependent Adsorption of Inverse Micelles.

The adsorption of charged inverse micelles at the electrode-liquid interface has an important effect on field screening and on the voltage drop over diffuse double layers. Recently, we analyzed the behavior of inverse micelles in a nonpolar liquid close to this electrode-liquid interface. For the fluorocarbon/surfactant system under study, we are in the limit of slow adsorption and negligible desorption of inverse micelles on the electrodes. Upon applying a voltage step, this results in a measurable Stern layer buildup in the time range of hours clearly distinguishable from the diffuse double layer buildup, which happens in less than 1 s. This Stern layer buildup manifests itself by a shift in the voltage drop from the diffuse double layer to the Stern layer until the voltage drop over the Stern layers reaches the applied voltage, leaving a zero bulk field without the diffuse double layer. New measurements of the transients of Stern layer buildup show that the buildup of charges in the Stern layer is more complex. We explain the observed transient behavior by introducing an asymmetry in the adsorption rate of charged inverse micelles. We provide an equivalent electrical network, an analytical solution to explain the behavior in more detail, and simulations within the diffuse double layer limit for a range of adsorption rates.

Axial electrokinetic trapping of anisotropic particles.

Anti-Brownian electrokinetic trapping is a method for trapping single particles in liquid based on particle position measurements and the application of feedback voltages. To achieve trapping in the axial direction, information on the axial particle position is required. However, existing strategies for determining the axial position that are based on measuring the size of the first diffraction ring, theory fitting, advanced optical setups or pre-determined axial image stacks are impractical for anisotropic particles. In this work, axial electrokinetic trapping of anisotropic particles is realized in devices with planar, transparent electrodes. The trapping algorithm uses Fourier-Bessel decomposition of standard microscopy images and is learning from the correlation between applied voltages and changes in the particle appearance. No previous knowledge on the particle appearance, theory fitting or advanced optical setup is required. The particle motion in the trap and the influence of screening of the electric field on this motion are analyzed. The axial trapping method opens new possibilities for measuring properties of anisotropic or isotropic particles and forces acting on such particles.

Electric field induced charging of colloidal particles in a nonpolar liquid.

HYPOTHESIS: Colloidal particles in a pure nonpolar solvent are expected to be in a state of dynamic equilibrium where a particle's charge fluctuates around a stable mean value. However, we find that PHSA-coated PMMA microparticles in dodecane gain positive charge over time. We hypothesize that this phenomenon is prompted by the high electric field (∼1 V/µm) that is applied in these measurements. Hence, we expect the reaction rate at which charge builds up on the particle to change when modifying the measurement parameters. EXPERIMENTS: Single elementary charging and discharging events can be resolved by measuring the charge of PHSA-coated PMMA particles with optical trapping electrophoresis. With this technique, the influence of the electric field amplitude and frequency, particle size, electrode material and acquired charge can be investigated. FINDINGS: The rate of the charging phenomenon is proportional to the amplitude of the applied electric field and the charging stops when the voltage is switched off. We propose a reaction mechanism where the particle sheds negatively charged ions. This mechanism can account for all the experimental observations of the electric field induced charging phenomenon.

Low coherence digital holography microscopy based on the Lorenz-Mie scattering model.

We demonstrate the use of low spatial and temporal coherence holography microscopy, based on the Lorenz-Mie model, using the standard tungsten-halogen lamp present in an inverted microscope. An optical model is put forward to incorporate the effect of spectral width and different incidence angles of the incident light determined by the aperture at the back focal plane of the condenser lens. The model is validated for 899 nm diameter polystyrene microspheres in glycerol, giving a resolution of 0.4% for the index of refraction and 2.2% for the diameter of the particles.

Charge transport by inverse micelles in non-polar media.

Charged inverse micelles play an important role in the electrical charging and the electrodynamics of nonpolar colloidal dispersions relevant for applications such as electronic ink displays and liquid toner printing. This review examines the properties and the behavior of charged inverse micelles in microscale devices in the absence of colloidal particles. It is discussed how charge in nonpolar liquids is stabilized in inverse micelles and how conductivity depends on the inverse micelle size, water content and ionic impurities. Frequently used nonpolar surfactant systems are investigated with emphasis on aerosol-OT (AOT) and poly-isobutylene succinimide (PIBS) in dodecane. Charge generation in the bulk by disproportionation is studied from measurements of conductivity as a function of surfactant concentration and from generation currents in quasi steady-state. When a potential difference is applied, the steady-state situation can show electric field screening or complete charge separation. Different regimes of charge transport are identified when a voltage step is applied. It is shown how the transient and steady-state currents depend on the rate of bulk generation, on insulating layers and on the sticking or non-sticking behavior of charged inverse micelles at interfaces. For the cases of AOT and PIBS in dodecane, the magnitude of the generation rate and the type of interaction at the interface are very different.

Electrokinetics and behavior near the interface of colloidal particles in non-polar dispersions.

The electrokinetics and charging of nonpolar colloidal dispersions subjected to a voltage are investigated by electric current and optical measurements. From electric current measurements in response to an alternating triangular voltage with a peak value of a few hundred volts, we find that polystyrene toner particles are compacted near the electrodes and their charge increases by more than a factor of 20. The important increase of charge is interpreted by a mechanism in which counter charges, which are originally at the particle surface, are desorbed. Optical measurements performed under a dc voltage of the order of a few hundred volts demonstrate that the charge of the particles can again decrease or even be inverted. These phenomena are attributed to the movement of counter charged species from the interface layers onto the surface of the particles. The findings of this study are relevant for electrophoretic displays and liquid toner printing.

Space charge limited release of charged inverse micelles in non-polar liquids.

Charged inverse micelles (CIMs) generated during a continuous polarizing voltage between electrodes in the model system of polyisobutylene succinimide in dodecane do not populate a diffuse double layer like CIMs present in equilibrium (regular CIMs), but instead end up in interface layers. When the applied voltage is reversed abruptly after a continuous polarizing voltage step, two peaks are observed in the transient current. The first peak is due to the release of regular CIMs from the diffuse double layers formed during the polarizing voltage step, which is understood on the basis of the Poisson-Nernst-Planck equations. The second peak is due to the release of a small fraction of generated negative CIMs from the interface layer. A model based on space charge limited release of the generated negative CIMs from the interface layer is presented and the results of the model are compared with several types of measurements. For the situation in which the bulk is deprived of regular CIMs and neutral inverse micelles, the results of the model are in agreement with the experimental results. However, for the situation in which regular CIMs and neutral inverse micelles are present, the model shows discrepancies with the experiment for high voltages and high charge contents. These discrepancies are attributed to electrohydrodynamic flow caused by local variations in the electric field at the vicinity of the electrodes, which occur during the reversal voltage. Also the long term decrease of the amount of released generated CIMs is studied and it is found that the presence of regular CIMs and neutral inverse micelles speeds up the decrease. This study provides a deeper insight in the electrodynamics of CIMs and is relevant for various applications in non-polar liquids.

Different Types of Charged-Inverse Micelles in Nonpolar Media.

Over the last few years, the electrodynamics of charged inverse micelles (CIMs) in nonpolar liquids and the generation mechanism and properties of newly generated CIMs have been studied extensively for the model system of polyisobutylene succinimide in dodecane. However, the newly generated CIMs, which accumulate at the electrodes when a continuous voltage is applied, behave differently compared to the regular CIMs present in equilibrium in the absence of a field. In this work, we use transient current measurements to investigate the behavior of the newly generated CIMs when the field is reduced to zero or reversed. We demonstrate that the newly generated CIMs do not participate in the diffuse double layer near the electrode formed by the regular CIMs but form an interface layer at the electrode surface. A fraction of the newly generated negative CIMs can be released from this interface layer when the field there becomes zero. The findings of this study provide a better understanding of fundamental processes in nonpolar liquids and are relevant for applications such as electronic ink displays and liquid toner printing.

Charging Dynamics of Aerosol OT Inverse Micelles.

Aerosol OT (AOT) is a commonly used surfactant and charging agent in nonpolar liquids. Properties such as the conductivity of AOT suspensions in nonpolar liquids and the behavior of charged AOT inverse micelles at interfaces have been studied recently, but still little is known about the generation dynamics of charged AOT inverse micelles. In this article, the generation dynamics of charged AOT inverse micelles in dodecane are investigated with transient current measurements. At low applied voltages, the generation rate is sufficiently fast to maintain the equilibrium concentration of charged inverse micelles, such that the current scales proportionally with the applied voltage. However, above a threshold voltage the current becomes limited by the generation of charged inverse micelles. Al2O3-coated electrodes are used to achieve these high-voltage current measurements while reducing surface generation currents. The dependency of the resulting generation-limited currents with the micelle concentration and the liquid volume is compatible with a bulk disproportionation mechanism. The measured currents are analyzed using a model based on drift, generation, and recombination of charged inverse micelles and the corresponding generation and recombination rates of charged AOT inverse micelles have been determined.

Switching of charged inverse micelles in non-polar liquids.

The electrodynamics of micellar ions in nonpolar liquids are well understood for the case that a voltage is applied or switched off. In this work, the electrodynamics of charged inverse micelles (CIMs) are studied when the applied voltage is switched to the opposite polarity, which is relevant for applications such as electrophoretic displays and liquid toner printing. Transient current measurements are used to characterize the switching of CIMs formed in a solution of surfactant polyisobutylene succinimide in n-dodecane. For reverse voltages with amplitude below 10V the measurements are in good agreement with a drift and diffusion model, confirming the established understanding of CIMs in nonpolar liquids. When the charge content is high, the reversal current shows a characteristic peak which is explained on the basis of dynamic space-charge effects. However, for reverse voltages larger than 10V, the transient currents are influenced by electrohydrodynamic flow in the liquid causing the CIMs to switch faster than predicted by the model. The occurrence of electrohydrodynamic flow is verified by optical tracking of tracer particles. Also, when the polarizing voltage is applied for longer times, an additional current peak emerges which is due to the accumulation of newly generated charges at the electrodes.

Joule heating monitoring in a microfluidic channel by observing the Brownian motion of an optically trapped microsphere.

Electric fields offer a variety of functionalities to Lab-on-a-Chip devices. The use of these fields often results in significant Joule heating, affecting the overall performance of the system. Precise knowledge of the temperature profile inside a microfluidic device is necessary to evaluate the implications of heat dissipation. This article demonstrates how an optically trapped microsphere can be used as a temperature probe to monitor Joule heating in these devices. The Brownian motion of the bead at room temperature is compared with the motion when power is dissipated in the system. This gives an estimate of the temperature increase at a specific location in a microfluidic channel. We demonstrate this method with solutions of different ionic strengths, and establish a precision of 0.9 K and an accuracy of 15%. Furthermore, it is demonstrated that transient heating processes can be monitored with this technique, albeit with a limited time resolution.

Characterizing generated charged inverse micelles with transient current measurements.

We investigate the generation of charged inverse micelles in nonpolar surfactant solutions relevant for applications such as electronic ink displays and liquid toners. When a voltage is applied across a thin layer of a nonpolar surfactant solution between planar electrodes, the generation of charged inverse micelles leads to a generation current. From current measurements it appears that such charged inverse micelles generated in the presence of an electric field behave differently compared to those present in equilibrium in the absence of a field. To examine the origin of this difference, transient current measurements in which the applied voltage is suddenly increased are used to measure the mobility and the amount of generated charged inverse micelles. The mobility and the corresponding hydrodynamic size are found to be similar to those of charged inverse micelles present in equilibrium, which indicates that other properties determine their different behavior. The amplitude and shape of the transient currents measured as a function of the surfactant concentration confirm that the charged inverse micelles are generated by bulk disproportionation. A theoretical model based on bulk disproportionation with simulations and analytical approximations is developed to analyze the experimental transient currents.