Mie Model Research Articles

Microwave Scattering and Medium Characterization for Terrestrial Snow With QCA–Mie and Bicontinuous Models: Comparison Studies

Comparison studies are made between the QCA–Mie model and the bicontinuous model in microwave scattering from terrestrial snow. Both the scattering properties and the medium characterization are compared. For QCA, we use the multisize and the sticky particle models. For the bicontinuous model, we use the probability distribution function for the wavenumber. We compare the scattering rate and the angular distribution of scattering using the mean cosine of scattering and show that the two models have similar properties. In medium characterization, we use the pair distribution functions used in QCA to derive the correlation functions. We show that both the Percus–Yevick pair functions and the bicontinuous model have tails in the correlation functions that are distinctly different from the traditional exponential correlation functions. The methodologies of using ground measurements of grain size distributions and correlation functions to obtain model parameters are addressed.

Light scattering microscopy measurements of single nuclei compared with GPU-accelerated FDTD simulations

Single cell nuclei were investigated using two-dimensional angularly and spectrally resolved scattering microscopy. We show that even for a qualitative comparison of experimental and theoretical data, the standard Mie model of a homogeneous sphere proves to be insufficient. Hence, an accelerated finite-difference time-domain method using a graphics processor unit and domain decomposition was implemented to analyze the experimental scattering patterns. The measured cell nuclei were modeled as single spheres with randomly distributed spherical inclusions of different size and refractive index representing the nucleoli and clumps of chromatin. Taking into account the nuclear heterogeneity of a large number of inclusions yields a qualitative agreement between experimental and theoretical spectra and illustrates the impact of the nuclear micro- and nanostructure on the scattering patterns.

A closure study of aerosol optical properties at a regional background mountainous site in Eastern China

There is a large uncertainty in evaluating the radiative forcing from aerosol–radiation and aerosol–cloud interactions due to the limited knowledge on aerosol properties. In-situ measurements of aerosol physical and chemical properties were carried out in 2012 at Mt. Huang (the Yellow Mountain), a continental background mountainous site in eastern China. An aerosol optical closure study was performed to verify the model outputs by using the measured aerosol optical properties, in which a spherical Mie model with assumptions of external and core–shell mixtures on the basis of a two-component optical aerosol model and high size-segregated element carbon (EC) ratio was applied. Although the spherical Mie model would underestimate the real scattering with increasing particle diameters, excellent agreement between the calculated and measured values was achieved with correlation coefficients above 0.98. Sensitivity experiments showed that the EC ratio had a negligible effect on the calculated scattering coefficient, but largely influenced the calculated absorption coefficient. The high size-segregated EC ratio averaged over the study period in the closure was enough to reconstruct the aerosol absorption coefficient in the Mie model, indicating EC size resolution was more important than time resolution in retrieving the absorption coefficient in the model. The uncertainties of calculated scattering and absorption coefficients due to the uncertainties of measurements and model assumptions yielded by a Monte Carlo simulation were ±6% and ±14% for external mixture and ±9% and ±31% for core–shell mixture, respectively. This study provided an insight into the inherent relationship between aerosol optical properties and physicochemical characteristics in eastern China, which could supplement the database of aerosol optical properties for background sites in eastern China and provide a method for regions with similar climate.

Aerosol optical properties and mixing state of black carbon in the Pearl River Delta, China

Aerosols contribute the largest uncertainty to the total radiative forcing estimate, and black carbon (BC) that absorbs solar radiation plays an important role in the Earth's energy budget. This study analysed the aerosol optical properties from 22 February to 18 March 2014 at the China Meteorological Administration Atmospheric Watch Network (CAWNET) station in the Pearl River Delta (PRD), China. The representative values of dry-state particle scattering coefficient (σsp), hemispheric backscattering coefficient (σhbsp), absorption coefficient (σabsp), extinction coefficient (σep), hemispheric backscattering fraction (HBF), single scattering albedo (SSA), as well as scattering Ångström exponent (α) were presented. A comparison between a polluted day and a clean day shows that the aerosol optical properties depend on particle number size distribution, weather conditions and evolution of the mixing layer. To investigate the mixing state of BC at the surface, an optical closure study of HBF between measurements and calculations based on a modified Mie model was employed for dry particles. The result shows that the mixing state of BC might be between the external mixture and the core-shell mixture. The average retrieved ratio of the externally mixed BC to the total BC mass concentration (rext-BC) was 0.58 ± 0.12, and the diurnal pattern of rext-BC can be found. Furthermore, considering that non-light-absorbing particles measured by a Volatility-Tandem Differential Mobility Analyser (V-TDMA) exist independently with core-shell and homogenously internally mixed BC particles, the calculated optical properties were just slightly different from those based on the assumption that BC exist in each particle. This would help understand the influence of the BC mixing state on aerosol optical properties and radiation budget in the PRD.

SATURN’S G AND D RINGS PROVIDE NEARLY COMPLETE MEASURED SCATTERING PHASE FUNCTIONS OF NEARBY DEBRIS DISKS

The appearance of debris disks around distant stars depends upon the scattering/phase function (SPF) of the material in the disk. However, characterizing the SPFs of these extrasolar debris disks is challenging because only a limited range of scattering angles are visible to Earth-based observers. By contrast, Saturn's tenuous rings can be observed over a much broader range of geometries, so their SPFs can be much better constrained. Since these rings are composed of small particles released from the surfaces of larger bodies, they are reasonable analogs to debris disks and so their SPFs can provide insights into the plausible scattering properties of debris disks. This work examines two of Saturn's dusty rings: the G ring (at 167,500 km from Saturn's center) and the D68 ringlet (at 67,600 km). Using data from the cameras onboard the Cassini spacecraft, we are able to estimate the rings' brightnesses at scattering angles ranging from 170 to 0.5 degrees. We find that both of the rings exhibit extremely strong forward-scattering peaks, but for scattering angles above 60 degrees their brightnesses are nearly constant. These SPFs can be well approximated by a linear combination of three Henyey-Greenstein functions, and are roughly consistent with the SPFs of irregular particles from laboratory measurements. Comparing these data to Fraunhofer and Mie models highlights several challenges involved in extracting information about particle compositions and size distributions from SPFs alone. The SPFs of these rings also indicate that the degree of forward scattering in debris disks may be greatly underestimated.

Characterization of submicron aerosols and effect on visibility during a severe haze-fog episode in Yangtze River Delta, China

Particle size, composition and optical properties were measured at a regional atmosphere background station in the Yangtze River Delta (YRD) to understand the formation and evolution of haze-fog episodes in Jan. 2013. The peak of particle number size distribution was in the size range of 80–100 nm during the measurements. PM1 mass concentration contributed 84% to the total particle mass (PM10). Based on visibility and ambient relative humidity, three types of weather conditions (i.e., clear, haze and fog) were classified in this study. The extinction coefficients of PM1 and PM10 under dry conditions were simulated by the Mie model. Under dry conditions, PM1 was found to contribute approximately 91% to the light extinction coefficient of PM10. However, the PM1 with the assumption of dry state was found to contribute approximately 85% to the ambient extinction coefficient of PM10 during clear conditions, 58% during haze conditions and approximately 41% during fog conditions. The variation of the dry PM1 contribution was related to the water uptake of particles under different relative humidity conditions.A severe haze-fog event on Jan. 14–17 was discussed in more detail as a case study. Two episodes were chosen to show that nitrate and organics dominated the aerosol component during the severe haze-fog episode and were related to secondary aerosol formation and air mass origin. Nitrate played a more dominant role than sulfate in heavy haze formation in the YRD region, which was different from the North China Plain region.

The development of unlike induced association-site models to study the phase behaviour of aqueous mixtures comprising acetone, alkanes and alkyl carboxylic acids with the SAFT-γ Mie group contribution methodology

Providing accurate predictions of the thermodynamic properties of highly polar and hydrogen bonding compounds and their mixtures is challenging from a theoretical perspective. The combination of an equation of state (EoS) based on the statistical associating fluid theory (SAFT) with a group contribution (GC) methodology offers both accuracy and predictive capability for the thermodynamic properties of mixtures. In our current work, the SAFT-γ Mie equation of state is used to capture the underlying complexity of systems in which specific interactions (e.g. hydrogen bonding, dipolar interactions, chemical association) play an important role, by incorporating highly versatile association-site schemes to model mixtures in which unlike induced association interactions occur; this is done by assigning to the functional groups a number of association sites that are inactive in the pure fluid, but become active in certain mixtures. We refer to this type of association mechanism as “unlike induced” association and to the sites involved in this interaction as “unlike induced” association sites. The concept of unlike induced association sites is applied here to develop reliable SAFT-γ Mie group contribution models to describe the properties of acetone, alkyl carboxylic acids, and their mixtures with water and n-alkanes. The parameter table of available SAFT-γ Mie models is expanded to incorporate the corresponding group interaction parameters for acetone, which is treated as a molecular group, the carboxyl group COOH, and their unlike interaction group parameters with water, and the methyl CH3, methanediyl CH2, and methanetriyl CH alkyl groups. In particular, one unlike induced site is used with the acetone model to mediate hydrogen bonding of the acetone oxygen in mixtures containing hydrogen bond donors, and two pairs of unlike induced sites are included on the COOH group to mediate hydrogen bond formation in mixtures of carboxylic acids and hydrogen bond donors. The models developed allow for the successful description of the complex fluid-phase behaviour of the relevant binary and ternary mixtures, including accurate predictions of systems which have not been used to determine the model parameters.

Corresponding states law for a generalized Lennard-Jones potential.

It was recently shown that vapor-liquid coexistence densities derived from Mie and Yukawa models collapse to define a single master curve when represented against the difference between the reduced second virial coefficient at the corresponding temperature and that at the critical point. In this work, we further test this proposal for another generalization of the Lennard-Jones pair potential. This is carried out for vapor-liquid coexistence densities, surface tension, and vapor pressure, along a temperature window set below the critical point. For this purpose, we perform molecular dynamics simulations by varying the potential softness parameter to produce from very short to intermediate attractive ranges. We observed all properties to collapse and yield master curves. Moreover, the vapor-liquid curve is found to share the exact shape of the Mie and attractive Yukawa. Furthermore, the surface tension and the logarithm of the vapor pressure are linear functions of this difference of reduced second virial coefficients.

Seeded Growth Synthesis of Composition and Size-Controlled Gold–Silver Alloy Nanoparticles

We propose a novel methodology to synthesize monodisperse gold–silver alloy nanoparticles (NPs) with fine control of size and composition. The synthesis is based on a combination of the coreduction of gold and silver salts for the formation of alloys and the seeded growth approach for the formation of size-controlled NPs. While the simple use of coreduction gives alloy NPs limited to ∼30 nm, the combination of both methods yields spherical alloy NPs with a size that can be controlled between ∼30 and ∼150 nm, with a coefficient of variation smaller than 15%. The alloy NPs can be synthesized to any composition between pure silver and pure gold. We also show that the alloy composition is nonhomogeneous, with a gold-rich core and a silver-rich surface. The transition in the alloy composition is gradual from the core to the surface, resulting in optical properties very similar to the optical properties of a homogeneous alloy, except for the smaller (∼30 nm) NPs. A multilayer Mie model has been introduced to st...

Nanoparticle analysis of cancer cells by light transmission spectroscopy

We have measured the optical properties of cancer and normal whole cells and lysates using light transmission spectroscopy (LTS). LTS provides both the optical extinction coefficient in the wavelength range from 220 to 1100nm and (by spectral inversion using a Mie model) the particle distribution density in the size range from 1 to 3000nm. Our current work involves whole cells and lysates of cultured human oral cells in liquid suspension. We found systematic differences in the optical extinction between cancer and normal whole cells and lysates, which translate to different particle size distributions (PSDs) for these materials. Specifically, we found that cancer cells have distinctly lower concentrations of nanoparticles with diameters less than 100nm and have higher concentrations of particles with diameters from 100 to 1000nm—results that hold for both whole cells and lysates. We also found a power-law dependence of particle density with diameter over several orders of magnitude.

The effect of complex black carbon microphysics on the determination of the optical properties of brown carbon

AbstractAssessment of the impacts of brown carbon (BrC) requires accurate determination of its physical properties, but a model must be invoked to derive these from instrument data. Ambient measurements were made in London at a site influenced by traffic and solid fuel (principally wood) burning, apportioned by single particle soot photometer data and optical properties measured using multiwavelength photoacoustic spectroscopy. Two models were applied: a commonly used Mie model treating the particles as single‐coated spheres and a Rayleigh‐Debye‐Gans approximation treating them as aggregates of smaller‐coated monomers. The derived solid fuel BrC parameters at 405 nm were found to be highly sensitive to the model treatment, with a mass absorption cross section ranging from 0.47 to 1.81 m2/g and imaginary refractive index from 0.013 to 0.062. This demonstrates that a detailed knowledge of particle morphology must be obtained and invoked to accurately parameterize BrC properties based on aerosol phase measurements.

Consideration of adsorbate vibrations and their phase states in porous systems

The phase state of adsorbate in porous systems is considered, in which the walls are characterized by interaction potential with adsorbate: from strong attraction to absence of attraction. The equations are based on discrete distribution functions (the lattice gas model) taking into account the contribution of the vibration motions of adsorbate. The vibration motion of molecules is taken into account in the modified quasi-dimer Mie model. Molecular distributions are calculated in the quasi-chemical approximation reflecting the effects of direct correlations of interacting particles using the Lennard-Jones potential. Conditions of express estimates of vibration frequencies are discussed in which vibration frequencies weakly affect molecular distributions in the case of strong adsorption. It is found that consideration of vibrations results in a shift in adsorption isotherms in the coordinates of chemical potential-density to higher values of vapor pressure in the range of high fillings. This is related to the necessity of additional vapor “compression” for its transition into the adsorbed state characterized by higher kinetic energy.

Effect of adsorbate vibrations on adsorption isotherms in slit-like pores

A molecular model of adsorbate melting in slit-like pores [1] is used to calculate adsorption isotherms with regard to the contribution from vibrational motions of the adsorbate. The equations are based on discrete distribution functions (the lattice gas model). Molecular distributions are calculated in a quasi-chemical approximation reflecting the effects of direct correlations of interacting particles using the Lennard-Jones potential. The vibrational motion of molecules is taken into account using a modified quasi-dimer Mie model. It is shown that considering vibrations shifts the adsorption isotherms in the chemical potential-density coordinates to higher vapor pressures in the region of high filling. This is due to the need for additional compression of the vapor to transfer it into the adsorbed state with increased kinetic energy.

An alternative method for estimating hygroscopic growth factor of aerosol light-scattering coefficient: a case study in an urban area of Guangzhou, South China

Abstract. A method was developed to estimate hygroscopic growth factor (f(RH)) of aerosol light-scattering coefficient (bsp), making use of the measured size- and chemically resolved aerosol samples. In this method, chemical composition of the measured aerosol samples were first reconstructed using the equilibrium model ISORROPIA II. The reconstructed chemical composition, which varies with relative humidity (RH), was then employed to calculate bsp and hygroscopic growth factor of bsp (fsp(RH)) using the Mie model. Furthermore, the calculated fsp(RH) was fitted with an empirical curve. To evaluate the applicability of fsp(RH), the curve of fsp(RH) was used to correct the long-term records of the measured bsp from the values under comparative dry conditions to the ones under ambient RH conditions. Compared with the original bsp data, the fsp(RH)-corrected bsp had a higher linear correlation with, and a smaller discrepancy from, the bsp derived directly from visibility and absorption measurements. The fsp(RH) determined here was further compared with that reported in previous studies. The method described in this manuscript provides an alternative approach to derive credible fsp(RH) with high accuracy and has many potential applications in aerosol-related research.

Seasonal variation of aerosol water uptake and its impact on the direct radiative effect at Ny-Ålesund, Svalbard

Abstract. In this study we investigated the impact of water uptake by aerosol particles in ambient atmosphere on their optical properties and their direct radiative effect (ADRE, W m−2) in the Arctic at Ny-Ålesund, Svalbard, during 2008. To achieve this, we combined three models, a hygroscopic growth model, a Mie model and a radiative transfer model, with an extensive set of observational data. We found that the seasonal variation of dry aerosol scattering coefficients showed minimum values during the summer season and the beginning of fall (July-August-September), when small particles (< 100 nm in diameter) dominate the aerosol number size distribution. The maximum scattering by dry particles was observed during the Arctic haze period (March-April-May) when the average size of the particles was larger. Considering the hygroscopic growth of aerosol particles in the ambient atmosphere had a significant impact on the aerosol scattering coefficients: the aerosol scattering coefficients were enhanced by on average a factor of 4.30 ± 2.26 (mean ± standard deviation), with lower values during the haze period (March-April-May) as compared to summer and fall. Hygroscopic growth of aerosol particles was found to cause 1.6 to 3.7 times more negative ADRE at the surface, with the smallest effect during the haze period (March-April-May) and the highest during late summer and beginning of fall (July-August-September).

Tropospheric aerosol scattering and absorption over central Europe: a closure study for the dry particle state

Abstract. This work analyses optical properties of the dry tropospheric aerosol measured at the regional Global Atmosphere Watch (GAW) observation site Melpitz in East Germany. For a continuous observation period between 2007 and 2010, we provide representative values of the dry-state scattering coefficient, hemispheric backscattering coefficient, absorption coefficient, single scattering albedo, and scattering Ångström exponent. Besides the direct measurement, the aerosol scattering coefficient was alternatively computed from experimental particle number size distributions using a Mie model. Within pre-defined limits, a closure could be achieved with the direct measurement. The achievement of closure implies that such calculations can be used as a high-level quality control measure for data sets involving multiple instrumentation. All dry-state optical properties show pronounced annual and diurnal variations, which are attributed to the corresponding variations in the regional emission fluxes, the intensity of secondary particle formation, and the mixing layer height. Air mass classification shows that atmospheric stability is a major factor influencing the dry aerosol properties at the GAW station. In the cold season, temperature inversions limit the volume available for atmospheric mixing, so that the dry-state aerosol optical properties near the ground proved quite sensitive to the geographical origin of the air mass. In the warm season, when the atmosphere is usually well-mixed during daytime, considerably less variability was observed for the optical properties between different air masses. This work provides, on the basis of quality-checked in situ measurements, a first step towards a climatological assessment of direct aerosol radiative forcing in the region under study.

From Mie to Fresnel through effective medium approximation with multipole contributions

The Mie theory gives the exact solution to scattering from spherical particles while the Fresnel theory provides the solution to optical behavior of multilayer thin film structures. Often, the bridge between the two theories to explain the behavior of materials such as nanoparticles in a host dielectric matrix, is done by effective medium approximation (EMA) models which exclusively rely on the dipolar response of the scattering objects. Here, we present a way to capture multipole effects using EMA. The effective complex dielectric function of the composite is derived using the Clausius–Mossotti relation and the multipole coefficients of the approximate Mie theory. The optical density (OD) of the dielectric slab is then calculated using the Fresnel approach. We have applied the resulting equation to predict the particle size dependent dipole and quadrupole behavior for spherical Ag nanoparticles embedded in glass matrix. This dielectric function contains the relevant properties of EMA and at the same time predicts the multipole contributions present in the single particle Mie model.

Quantum and dielectric confinements of sub-10 nm gold in dichroic phosphate glass nanocomposites

Blue shifts of the surface plasmon resonance band of sub-10 nm gold in dichroic phosphate glass nanocomposites are observed with increase in both size of gold nanoparticles and refractive index of the medium, which are contrary to the common trends. These phenomena have been enlightened with the electrodynamics theories (Mie and Drude models) and happened due to quantum and dielectric confinements. Nanocomposites have been synthesized by in-situ thermochemical reduction technique in reducing phosphate glass matrices. The plasmon bands are characterized by the UV–vis spectrophotometer, and shape and size of the nanogold by the transmission electron microscopy. All the nanocomposites are dichroic in nature.

A universal description of a solid crystal and liquid using discrete distribution functions

The numerical implementation of a crystallization/melting theory that has two branches of isotherms for liquids and solids as in Landau’s theory within the general self-consistent theory of condensed states is discussed. Equations are based on discrete distribution functions (the lattice gas model). Molecular distributions are calculated to a quasi-chemical approximation reflecting the effects of direct correlations between interacting particles. the interaction between particles is described by the Lennard-Jones potential, while the vibrational motion of molecules is included using a modified quasi-dimer Mie model. The effect of the vibrations of atoms on lateral interactions between nearest and next nearest neighbors is considered, along with a scheme for considering the displacement of particles in a liquid that modify such lateral interactions. Examples of calculations describing a defective crystal and vapor-liquid system are given.

Characteristics of atomic vibrational motion in a one-component defective crystal

Vibrations of atoms in a defective argon crystal are considered. Frequencies are calculated in the harmonic approximation and Mie and Einstein approximations. The vibrations are calculated for a set of local clusters differing in the position of a vacancy at different distances from a selected atom. Probabilities for these clusters are calculated within a quasichemical approximation of the lattice gas model. It is shown that when combined contributions from lateral interactions and vibrational motions are allowed for in the free crystal energy, there is an increase in the lattice constant upon a rise in temperature in all approximations. It is found that the frequencies calculated using the Mie model become closer to the frequency distribution in the harmonic approximation as the degree of crystal defectiveness increases.