Semiclassical model for the absorption or emission of a photon by a charged particle in an intense static electric field

Quantum simulations made using Floquet methods show that a charged particle can exchange energy with an oscillating potential barrier in discrete quanta , where is the frequency of oscillation. However, this exchange is classically forbidden because no other mass is included in the model, so that energy and momentum could not both be conserved in the absorption or emission of a photon. We define a semiclassical mechanism for these inelastic processes in which a photon may be absorbed by a charged particle moving against an intense static electric field, or emitted when the particle moves with this field. In this model, the particle has an energy loss Q in photon absorption, and an energy gain Q in photon emission. Then the particle travels a short distance at constant momentum until the energy increment Q is made up by the interaction with the static electric field, after which the particle resumes classical motion with the initial energy plus or minus exactly one quantum. We use the energy–time uncertainty relation to determine the minimum value for the static electric field that is required for this process, and this value is typical of the experimental conditions for laser-assisted scanning tunneling microscopy and laser-assisted field emission where the exchange of quanta is found to occur.     

Atomic Force Microscopy,Transmission Electron Microscopy,and Photon Correlation Spectroscopy: Three Techniques for Rapid Characterization of Optimized Self-Nanoemulsiying Drug Delivery System of Glibenclamide,Carvedilol, and Lovastatin

This article looks at atomic force microscopy as an important aid to characterize the self-nanoemulsifying formulation of glibenclamide, lovastatin, and carvedilol in conjunction with other sophisticated technique, viz., transmission electron microscopy and photon correlation spectroscopy. Sizes obtained by processing the atomic force microscopy (AFM) image are comparable with those obtained from transmission electron microscope. Although in the present study, the mean particle size obtained from photon correlation spectroscopy does not correlate to the findings of atomic force microscopy and transmission electron microscopy, but the poly-disperse index values correlate well with the findings of AFM and transmission electron microscopy where uniform particle size was observed in aqueous dispersion of self-nanoemulsifying formulation of glibenclamide, lovastatin, and carvedilol.     

Basics of optical force

Light possesses momentum, and hence, force is exerted on materials if they absorb and/or scatter light. Laser techniques that use optical forces are currently attracting considerable attention. Optical manipulation for trapping, transporting small particles, and measuring the interparticle force is a representative technique. In addition, photoinduced force microscopy is a promising scanning type of microscopy using optical force. Optical force techniques have recently been used in various fields of research, such as molecular bioscience, organic photochemistry, materials engineering, and molecular fluid dynamics. In these techniques, several types of optical forces such as scattering, absorption, and gradient forces play their respective roles. In this article, we summarize the basics of optical forces and present their elementary expressions for using simplified models of light and matter systems. This will help the readers of this Special Issue to understand how different types of forces are distinguished in the basic expressions used for analyzing the optical force phenomena that appear depending on the light geometry and matter systems. After observing simplified cases of scattering and absorption forces, we introduce general formulae for the optical force and then discuss how different components appear in particular cases of laser geometry and materials.     

Friction and diffusion of a Brownian particle in a mesoscopic solvent

The friction and diffusion coefficients of a massive Brownian particle in a mesoscopic solvent are computed from the force and the velocity autocorrelation functions. The mesoscopic solvent is described in terms of free streaming of the solvent molecules, interrupted at discrete time intervals by multiparticle collisions that conserve mass, momentum, and energy. The Brownian particle interacts with the solvent molecules through repulsive Lennard-Jones forces. The decays of the force and velocity autocorrelation functions are analyzed in the microcanonical ensemble as a function of the number N of solvent molecules and Brownian particle mass and diameter. The simulations are carried out for large system sizes and long times to assess the N dependence of the friction coefficient. The decay rates of these correlations are confirmed to vary as N(-1) in accord with earlier predictions. Hydrodynamic effects on the velocity autocorrelation function and diffusion coefficient are studied as a function of Brownian particle mass and diameter.     

Low-Knudsen-number photophoresis of aerosol spheroids

The photophoretic motion of a freely suspended aerosol spheroid exposed to a radiative heat flux that is oriented arbitrarily with respect to its axis of revolution is analytically studied. The Knudsen number is assumed to be so small that the fluid flow can be described by a continuum model with a thermal slip at the particle surface. In the limit of small Peclet and Reynolds numbers, the appropriate energy and momentum equations are solved using the bifocal-coordinate transformations. Expressions for the photophoretic velocity and force are obtained in closed form for various cases of prolate and oblate spheroidal particles. The average photophoretic velocity and force for an ensemble of identical, noninteracting spheroids with random orientation distribution are also determined. The results indicate that the aspect ratio and relative thermal conductivity of a spheroidal particle and its orientation with respect to the incident light can have significant effects on its photophoretic behavior.     

A density functional representation of quantum chemistry. III. Rigorous realization of the program in lattice space

A mathematically rigorous reformulation of molecular quantum mechanics in terms of the particle density operator and a canonically conjugated phase field is given. Using a momentum cutoff, it is shown that the usual molecular Hamiltonian can be expressed in terms of the particle density operator and a rigorously defined phase operator. It is shown that this Hamiltonian converges strongly to the cutoff-free Hamiltonian. In spite of the fact that this Hamiltonian is of second order in the phase operators, all hitherto published expressions are not correct. Unfortunately, the correct formulation destroys the intuitive appeal of using the particle density operator as a coordinate for the many-body problems of quantum chemistry. Unless somebody provides an essential new and clever idea, we propose to resist the fascination of a local quantum field theory of molecular matter in terms of the particle density operator.     

Behavior of double emulsions in a cross-type optical separation system

The behavior of double emulsions in a cross-type optical particle separation system was studied for different combinations of refractive indices and different inner and outer layer radii. The radii and refractive indices of the double emulsions were easily adjusted by taking advantage of the coflowing geometry of a cross-type optical particle separation device. An analytical expression of the optical forces on a pair of concentric spheres was derived using the photon stream method in the ray optics regime. The predicted trajectories of the double emulsions by the optical force agreed well with the experimental data. This work has potential uses in cell separation by morphometry, drug delivery vehicle, and emulsion-based biomedical applications.     

Some Comments on the Matter Wave-light Wave Hypothesis

From the de Broglie matter wave hypothesis and Planck’s energy quantization law, and assuming conservation of energy in the absorption of a photon and its consequent conversion to kinetic energy of motion by a material particle initially at rest, one can deduce a simple mathematical relationship between the wavelength λ (or frequency ν), of the photon absorbed by the particle at rest, and the resulting de Broglie matter wave length, λ_D, of the particle with kinetic energy of motion of mv²/2. The relationship so deduced, λ_D∝√λ, suggests that visible wavelengths of light, from about 4000 ?, in the violet, to beyond about 7000 ?, in the red, on absorption by an electron at rest, lead to material electron wavelengths, λ_D, of the order of the size of the electron transfer proteins seen in the photosynthetic reaction centers of photosynthesizing organisms, at about a size of 50–100 ?. In addition to understanding the mechanism of photosynthesis as a material wave mediated phenomenon, further areas of importance of the relations pointed out in this paper are in the design of experiments to gain a deeper understanding of the basic tenets of wave mechanics, and in the use of tunable lasers to probe various properties of material waves, and to precisely control their properties for applications including lithography.     

A passive microfluidic device for continuous microparticle enrichment

A passive microfluidic device is reported for continuous microparticle enrichment. The microparticle is enriched based on the inertial effect in a microchannel with contracting‐expanding structures on one side where microparticles/cells are subjected to the inertial lift force and the momentum‐change‐induced inertial force induced by highly curved streamlines. Under the combined effect of the two forces, yeast cells and microparticles of different sizes were continuously focused in the present device over a range of Reynolds numbers from 16.7 to 125. ～68% of the particle‐free liquid was separated from the sample at Re = 66.7, and ～18 μL particle‐free liquid was fast obtained within 10 s. Results also showed that the geometry of the contracting‐expanding structure significantly influenced the lateral migration of the particle. Structures with a large angle induced strong inertial effect and weak disturbance effect of vortex on the particle, both of which enhanced the microparticle enrichment in microchannel. With simple structure, small footprint (18 × 0.35 mm), easy operation and cell‐friendly property, the present device has great potential in biomedical applications, such as the enrichment of cells and the fast extraction of plasma from blood for disease diagnose and therapy.     

Primary electroviscous effect in a suspension of charged porous spheres

Primary electroviscous effect for a dilute suspension of porous spheres with fixed volumetric charge density is investigated theoretically. In the absence of flow, the electrical potential and solution charge density are assumed to satisfy the linearized Poisson-Boltzmann equation. With incorporation of the electrical body force, the Brinkman equation and the Stokes equation are used to govern the fluid flow inside and outside a sphere. The theory is formulated by assuming weak deviation of the charge cloud from its equilibrium state. However, the electrical body force is not restricted to be small compared to the viscous force in the fluid momentum equation. The results show that the double layer distortion is increased with increasing particle permeability, thereby enhancing the relative importance of its stress contribution. Nonetheless, the intrinsic viscosity remains a decreasing function of permeability, similar to the case of uncharged particles.     

Statistical theory of endothermic reactions

The rate of unimolecular decomposition of an excited molecule is calculated from the statistical theory based on conservation of the total energy and total momentum. The limits of applicability of the quasiequilibrium theory are examined. Distribution functions are calculated for the dissociation products from photon capture and electron impact.     

Analytical applications of photon correlation spectroscopy for size distribution measurements of natural colloidal suspensions: capabilities and limitations

Particles are ubiquitous in all natural systems and play an important role in the control and fate of nutrients and pollutants. Currently, only limited information is available concerning particle number and size distributions, owing to the problems involved in their experimental determination. In the present paper, limitations and optimal conditions for particle size determinations of environmental samples using photon correlation spectroscopy are studied. The detection limit, the effects of polydispersity of the sample and the refractive index value are discussed based on results obtained with synthetic colloids. The photon correlation spectroscopic determination of particle size distributions in real aquatic systems is also presented in the second part of the paper.     

Non-equilibrium thermodynamics of photophoretic motion of colloidal particles

The behavior of electromagnetic radiation in colloidal systems is studied by non-equilibrium thermodynamics methods. Phenomenological equations of non-equilibrium thermodynamics are derived preliminarily for discontinuous systems where photon exchange occurs. Phenomenological equations describing the radiative transfer in absorbing medium are also considered. The equations responsible for the motion of particles in a nonuniform absorbing medium with the directed flux of electromagnetic radiation are derived. These equations describe thermo-and photophoretic motion of colloidal particles. The effect related to the radiation of electromagnetic waves by a colloidal particle moving in a uniform medium under the action of an external force is a cross effect with respect to photophoresis. The Onsager’s relations for kinetic coefficients are shown to be valid for all considered systems.     

Nanoparticle composition of a ferrofluid and its effects on the magnetic properties

Experiments were carried out on a water-based ferrofluid (gamma-Fe2O3 with carboxydextran shell) using photon correlation spectroscopy (PCS), atomic force microscopy, and magnetic nanoparticle relaxation measurements. The experiments were designed with the aim to relate the Néel signals that are in theory generated by large single core particles with nanoscopic properties, that is, particle size, particle size distribution, shell properties, and aggregation. For this purpose, the ferrofluid was fractionated by magnetic fractionation and size exclusion chromatography. Nanoparticles adsorbed onto positively charged substrates form a two-dimensional monolayer. Their mean core diameters are in the range of 6 to about 20 nm, and particles above 10 nm are mostly aggregates. The hydrodynamic particle diameters are between 13 and 80 nm. The core diameter of the smallest fraction is confirmed by X-ray reflectometry; the surface coverage is controlled by bulk diffusion. Comparison with the hydrodynamic radius yields a shell thickness of 3.8 nm. Considering the shell thickness to be constant for all particles, it was possible to calculate the apparent particle diameter in the original ferrofluid from the PCS signals of all fractions. As expected, the small cores yielded no Néel relaxation signals in freeze-dried samples; however, the fractions containing mostly aggregates yielded Néel relaxation signals.     

Use of optical tweezers for colloid science

A space-borne optical tweezer apparatus for use with colloidal crystallization experiments has been characterized. The trapping force has been measured as a function of index mismatch between colloidal microspheres and the surrounding fluid and as a function of particle size. This work also presents a method to determine the refractive index of a colloidal microsphere, which is then used to calculate the applied trapping force for the case of an arbitrary background fluid. This is useful for work with dense colloidal suspensions when the usual (e.g., Stokes flow) trap force measurement methods do not apply, as well as microrheological studies of complex soft matter.     

Second-order quantized Hamilton dynamics coupled to classical heat bath

Starting with a quantum Langevin equation describing in the Heisenberg representation a quantum system coupled to a quantum bath, the Markov approximation and, further, the closure approximation are applied to derive a semiclassical Langevin equation for the second-order quantized Hamilton dynamics (QHD) coupled to a classical bath. The expectation values of the system operators are decomposed into products of the first and second moments of the position and momentum operators that incorporate zero-point energy and moderate tunneling effects. The random force and friction as well as the system-bath coupling are decomposed to the lowest classical level. The resulting Langevin equation describing QHD-2 coupled to classical bath is analyzed and applied to free particle, harmonic oscillator, and the Morse potential representing the OH stretch of the SPC-flexible water model.     

Drag force acting on an evaporating particle immersed in a rarefied plasma flow

Analytical expressions are presented for the drag force acting on an evaporating or nonevaporating particle immersed in a plasma flow for the extreme case of free-molecule flow regime and thin plasma .sheath. It is shown that the drag force on a spherical particle is proportional to the square of the particle radius and to the relative velocity between the particle and the bulk plasma at low speed ratios. The existence of a relative velocity between the particle and the plasma results in a nonuniform heat flux distribution with its rnaximum value at the frontal stagnation point of tire sphere. This nonuniform distribution of the local heat fux density causes a nonuniforrn distribution of the local evaporated-mass flux and vapor reaction force around the surface of an evaporating particle, and thus induces an additional force on the particle. Consequently, the drag force acting on art evaporating particle is always greater than that on a nonevaporating one. This additional drag force due to particle evaporation is more significant for nonmetallic particles and for particle materials with lower latent heat of evaporation and lower vapor molecular mass. It increases with increasing plasma temperature and with decreasing gas pressure at the high plasma temperatures associated with appreciable gas ionization. The drag ratio increases with increasing electron/heavy-particle temperature ratio at high electron temperatures for a two-temperature plasma.     

Recent experimental studies of photon–atom scattering in the X-ray energy region

We present a review of our recent measurements of large angle elastic and inelastic scattering differential cross-sections in the photon energy range 14–88 keV (momentum transfer ranging 1.135 to 6.310 Å⁻¹ covering large number of elements in the atomic region Z=1–92, with special emphasis on the elements having K/Li shell/subshell binding energy in the vicinity of the incident photon energy. These measurements were performed using energy dispersive X-ray fluorescence (EDXRF) setup involving radioisotope as a photon source and a solid-state photon detector arranged in an annular geometry. The measured scattering differential cross-sections were compared with the theoretical values based on the state-of-art relativistic second order S-matrix calculations and those based on the form factor approximations in order to check their reliability. The KL and KM resonant Raman scattering (RRS) at 59.54 keV incident photon energy was also investigated for some heavy elements.     

Thermophoretic force acting on an evaporating particle suspended in a rarefied plasma

Analytical results of the thermophoretic force on an evaporating spherical particle immersed in a rarefied plasma with a large temperature gradient are presented for the extreme case of free-molecule regime and thin plasma sheath. It has been shown that the existence of a temperature gradient in the plasma causes a nonuniform distribution of the local heat flux density on the sphere surface with its maximum value at the fore-stagnation point of the sphere, although the total heal flux to the whole particle is independent of the temperature gradient existing in the plasma. This nonuniform-distribution of the local heat flux density causes a nonuniform distribution of the. local evaporated-mass flux and related reaction force around the surface of an evaporating particle, and thus causes an additional force on the particle. Calculated results show that the thermophoretic force on an evaporating particle may substantially exceed that on a nonevaporating one, especially for the case of a metallic particle (with infinite electric conductivity). The effect of evaporation on the thermophoretic force is more pronounced as the evaporation latent heat of the particle material is comparatively low and as high plasma temperatures are involved.