Ballistic Particle-cluster Aggregation Research Articles

Influence of porosity on the Umov effect in silicate and organic refractory aggregates

This study investigates the influence of porosity on the Umov effect, a phenomenon observed in the scattering of light from celestial objects. The Umov effect describes an inverse relationship between the degree of linear polarization and the object’s reflectance (geometric albedo). To study the dependence of porosity on the Umov effect, a wide range of porosity (i.e., from 0.64 to 0.99) is considered. Four types of aggregates, ballistic cluster-cluster aggregate (BCCA), ballistic particle cluster aggregate (BPCA) or ballistic agglomeration (BA), ballistic agglomeration with one migration (BAM1), and ballistic agglomeration with two migrations (BAM2) each having porosity 0.99, 0.87, 0.74, and 0.64 are considered in this study. The multi-sphere T-matrix code is utilized to calculate the linear polarization and geometric albedo (A) considering silicate and organic refractory compositions for monodisperse aggregates. The results are reported for six different wavelengths, ranging from near-ultraviolet to the visible spectrum. When the polarization maximum (Pmax) is plotted against the geometric albedo (A) on a logarithmic scale, an inverse relation is observed. This relation exhibits non-linear changes, fitted by a second-degree polynomial equation, as the porosity changes from 0.64 to 0.99. This finding constitutes one of the interesting results of our study. In addition, the study explores the effect of porosity (P) on the ratio between log(Pmax) and log(A), showing a non-linear relationship. A comparison is drawn between the results obtained from organic refractory compositions and amorphous silicate compositions, emphasizing the importance of porosity and wavelength in regulating the Umov effect. In addition, the research investigates how mixing affects the results at different wavelengths, assuming the aggregates are blends of organic refractory and amorphous silicate compositions. The computations have also been performed for polydisperse aggregates (considering BCCA, BA, BAM1, and BAM2 structures) at a wavelength of 0.45 μm for silicate compositions, which also showed a non-linear dependence as observed in the case of monodisperse aggregates.

Impact of internal structure on aggregate collisions

ABSTRACT Granular-mechanics simulations are used to study collisions between granular aggregates. We compare the collision outcomes for three different types of aggregate: (i) aggregates constructed by a ballistic particle–cluster aggregation (BPCA) process, and two homogeneous spherical aggregates which differ by their grain coordination. All aggregates contain the same number of grains and (central) filling factor. We find that BPCA aggregates have a slightly decreased growth velocity for central impacts. After scaling the collision velocities to the growth velocity for central impact and the impact parameter to the gyration radius, our collision results show a remarkable degree of agreement for the aggregates studied. Also, the collision-induced compaction as well as the size of fluctuations during the collision process are identical for all aggregate types. Even at glancing collisions, the larger extension and rough surface of BPCA aggregates do not cause major changes as compared to homogeneous aggregates with a well-defined and smooth surface. However, monomer ejection during the collision is enhanced for BPCA aggregates. This study thus shows that details of the internal aggregate structure are of little importance in collisions of granular aggregates, except for grain ejection.

Supramolecular Fractal Growth of Self-Assembled Fibrillar Networks.

Complex morphologies, as is the case in self-assembled fibrillar networks (SAFiNs) of 1,3:2,4-Dibenzylidene sorbitol (DBS), are often characterized by their Fractal dimension and not Euclidean. Self-similarity presents for DBS-polyethylene glycol (PEG) SAFiNs in the Cayley Tree branching pattern, similar box-counting fractal dimensions across length scales, and fractals derived from the Avrami model. Irrespective of the crystallization temperature, fractal values corresponded to limited diffusion aggregation and not ballistic particle–cluster aggregation. Additionally, the fractal dimension of the SAFiN was affected more by changes in solvent viscosity (e.g., PEG200 compared to PEG600) than crystallization temperature. Most surprising was the evidence of Cayley branching not only for the radial fibers within the spherulitic but also on the fiber surfaces.

Effects of monomer shape on the formation of aggregates from a power law monomer distribution

The coagulation of dust aggregates is an important process in many physical systems such as the Earth's upper atmosphere, comet tails and protoplanetary discs. Numerical models which study the aggregation in these systems typically involve spherical monomers. There is evidence, however, via the polarization of sunlight in the interstellar medium, as well as optical and LIDAR observations of high-altitude particles in Earth's atmosphere (70–100 km), which indicate that dust monomers may not necessarily be spherical. This study investigates the influence of different ellipsoidal monomer shapes on the morphology of aggregates given various distributions of monomer sizes. Populations of aggregates are grown from a single monomer using a combination of ballistic particle–cluster aggregation and ballistic cluster–cluster aggregation regimes incorporating the rotation of monomers and aggregates. The resulting structures of the aggregates are then compared via the compactness factor, geometric cross-section and friction time.

Aggregates in the strength and gravity regime: Particles sizes in Saturn’s rings

Particles in Saturn’s main rings range in size from dust to kilometer-sized objects. Their size distribution is thought to be a result of competing accretion and fragmentation processes. While growth is naturally limited in tidal environments, frequent collisions among these objects may contribute to both accretion and fragmentation. As ring particles are primarily made of water ice attractive surface forces like adhesion could significantly influence these processes, finally determining the resulting size distribution. Here, we derive analytic expressions for the specific self-energy Q and related specific break-up energy Q★ of aggregates. These expressions can be used for any aggregate type composed of monomeric constituents. We compare these expressions to numerical experiments where we create aggregates of various types including: regular packings like the face-centered cubic (fcc), Ballistic Particle Cluster Aggregates (BPCA), and modified BPCAs including e.g. different constituent size distributions. We show that accounting for attractive surface forces such as adhesion a simple approach is able to: (a) generally account for the size dependence of the specific break-up energy for fragmentation to occur reported in the literature, namely the division into “strength” and “gravity” regimes and (b) estimate the maximum aggregate size in a collisional ensemble to be on the order of a few tens of meters, consistent with the maximum particle size observed in Saturn’s rings of about 10m.

DUST IN COMET C/2007 N3 (LULIN)

We report optical imaging, optical and near-infrared polarimetry, and Spitzer mid-infrared spectroscopy of comet C/2007 N3 (Lulin). Polarimetric observations were obtained in R (0.676 micron) at phase angles from 0.44 degrees to 21 degrees with simultaneous observations in H (1.65 micron) at 4.0 degrees, exploring the negative branch in polarization. Comet C/2007 N3 (Lulin) shows typical negative polarization in the optical as well as a similar negative branch near-infrared wavelengths. The 10 micron silicate feature is only weakly in emission and according to our thermal models, is consistent with emission from a mixture of silicate and carbon material. We argue that large, low-porosity (akin to Ballistic Particle Cluster Aggregates) rather absorbing aggregate dust particles best explain both the polarimetric and the mid-infrared spectral energy distribution.

Polarisation properties of comet NEAT C/2001 Q4

Comets exhibit high (up to 25 %) amount of optical polarization when they are observed through ground based or space telescopes. These polarizations are caused due to the scattering of cometary dust. The observed linear polarisation of comets is generally a function of the wavelength of incident light (λ), the scattering angle (θ), the geometrical shape and size of the particle and the composition of dust particles in terms of the complex values of the refractive index. The scattering properties of cometary dust will help to know the nature of cometary dust. In the present work, the observed linear polarization data of Comet NEAT are studied through simulations using Ballistic Particle-Cluster Aggregate (BPCA) and Ballistic Cluster-Cluster Aggregate (BCCA). Using Superposition T-matrix code, the best-fitting values of complex refractive indices are calculated which can well fit the observed polarization data of Comet NEAT C/2001 Q4. The best fitting values of complex refractive indices coming out from the present analysis correspond to mixture of both silicates and organics.

Aggregate dust model to study the polarization properties of comet C/1996 B2 Hyakutake

The observed linear polarization data of comet Hyakutake are studied at wavelengths λ = 0.365 μm, λ = 0.485 μm and 0.684μm through simulations using Ballistic Particle–Cluster Aggregate and Ballistic Cluster–Cluster Aggregate aggregates of 128 spherical monomers. We first found that the size parameter of the monomer, x ∼ 1.56–1.70, turned out to be the most suitable which provides the best fits to the observed dust scattering properties at three wavelengths: λ = 0.365 μm, 0.485 μm and 0.684 μm. Thus, the effective radius of the aggregate (r) lies in the range 0.45 μm ≤ r ≤ 0.49 μm at λ = 0.365 μm; 0.60 μm ≤ r ≤ 0.66 μm at λ = 0.485 μm and 0.88 μm ≤ r ≤ 0.94 μm at λ = 0.684 μm. Now using superposition t-matrix code and the power-law size distribution, n(r) ∼ r−3, the best-fitting values of complex refractive indices are calculated for the observed polarization data at the above three wavelengths. The best-fitting complex refractive indices (n, k) are found to be (1.745, 0.095) at λ = 0.365 μm, (1.743, 0.100) at λ = 0.485 μm and (1.695, 0.100) at λ = 0.684 μm. The refractive indices derived from the present analysis correspond to a mixture of both silicates and organics, which are in good agreement with the in situ measurement of comets by different spacecraft.

COLLISIONAL GROWTH CONDITIONS FOR DUST AGGREGATES

Collisions between dust aggregates are the key to understand the formation of planetesimals because the collision inevitably takes place in protoplanetary disks. To clarify whether or not dust aggregates can grow through their mutual collisions at relatively high velocities, we carry out more than 4000 runs of three-dimensional numerical simulations of collisions between icy equal-mass clusters formed under ballistic particle–cluster aggregation (BPCA) as well as those of ballistic cluster–cluster aggregation, including offset collisions with various values of the impact parameter. Since our BPCA clusters have a fractal dimension of 3 and a relatively compact structure, their results enable us to determine the criteria for growth and disruption of compressed aggregates at their collisions in protoplanetary disks. The results show that ice dust aggregates are able to grow at collisions with velocities up to 50 m s−1, in spite of their initial structures and impact parameters. We also find that the mass of ejecta relative to the total mass of colliding aggregates decreases with increasing the size of the aggregates. These results demonstrate the feasibility of growth and survival for dust aggregates through their mutual collisions with relatively high velocities in protoplanetary disks.

Aggregate dust model to describe polarization properties of Comet Hale-Bopp

In this work, the observed linear-polarization data of Comet Hale–Bopp are studied at wavelengths λ= 0.485 and 0.684 μm through simulations using Ballistic Particle–Cluster Aggregate and Ballistic Cluster–Cluster Aggregate. Using superposition t-matrix code, the best-fitting values of complex refractive indices are calculated which can well match the observed polarization data at the above two wavelengths. It is found from our analysis that there is not a single value of the monomer radius (am) that can simultaneously fit the observed polarization data at two wavelengths 0.485 and 0.684 μm. However, for different am in the two wavelengths, corresponding to similar size parameter of the monomer (x≈ 1.56), better fit can be achieved. The best-fitting complex refractive indices (n, k) coming out from this analysis are found to be (1.778, 0.059) at λ= 0.485 μm when am= 0.12 μm and (1.755, 0.080) at λ= 0.684 μm when am= 0.17 μm. The above values of refractive index show silicate behaviour as the values are close to amorphous olivine. Thus, it can be concluded that the silicate composition can best match the observed polarization data of Comet Hale–Bopp at λ= 0.485 and 0.684 μm. Finally, the polarization properties of Comet Hale–Bopp are compared with Comet Levy 1990XX.

Aggregate model of cometary dust: an application to comet Levy 1990XX

In the present work, the light-scattering properties of comet Levy 1990XX are studied through simulations using Ballistic Particle-Cluster Aggregation (BPCA) or Ballistic Cluster-Cluster Aggregation (BCCA) aggregates of up to 128 spherical monomers of different compositions (e.g. silicates, carbonaceous materials etc.) and the best-fitting theoretical polarization curve is generated using the SUPERPOSITION T-MATRIX code. The best-fitting refractive indices coming out from the present analysis show silicate behaviour when monomer radius is a m = 0.12 μm and provide excellent results on the maximum and negative degrees of linear polarization at a single wavelength λ = 0.485 μm for BCCA aggregates.

Aggregation with fractal trajectories of changing dimensionality

The fractal dimension of a particle–cluster aggregate depends on the space dimensionality, the geometric characteristic of the particle trajectory and on the progress of the process. The asymptotic values of fractal dimension are characteristic for large aggregates. The influence is analyzed of the step size of random walk on the structure of aggregates built by the successive addition of monomers to a growing cluster. Increasing the step size it is possible to obtain more and more compact structures [Phys. Rev. A 36 (1987) 4518] changing from that characteristic for diffusion-limited process to that observed for ballistic particle–cluster aggregation. Moreover, the trajectory fractal dimension increases as the aggregation proceeds due to the aggregate growth and the constancy of the step size of random walk. It is shown that aggregation act equation models such aggregation processes well.

Extended calculation of polarization and intensity of fractal aggregates based on rigorous method for light scattering simulations with numerical orientation averaging

The intensity and polarization of fractal aggregates have been investigated using both rigorous and approximate methods for light scattering simulations. However, previous studies using the analytical orientation averaging version of the rigorous method were generally limited to a few hundred monomers when the monomer size parameter was around 1.7. In this study, we propose using numerical orientation averaging instead of analytical orientation averaging. The numerical averaging is performed together with a fixed orientation version of the rigorous T-matrix method for clusters of spheres. This approach enables increasing the number of monomers by a factor of 2–7 or the size of monomers by a factor of 8–10 compared to the analytical orientation averaging version. We investigated the influence of monomer size and the number of monomers on the light scattering of silicate aggregates (refractive index m = 1.68 + 0.03 i ) for incident light with a wavelength of 0.6 μ m . We considered ballistic particle–cluster aggregates (BPCA) and ballistic cluster–cluster aggregates (BCCA) composed of 128, 256, 512, and 1024 monomers with radii between 0.11 and 0.17 μ m . Our results show that the size of monomers plays an important role in reproducing the negative polarization branch for all the BPCA and BCCA. Silicate aggregates with the monomer radius of less than 0.17 μ m contribute to reproducing the negative polarization branch, while aggregates with monomers larger than 0.17 μ m do not have the negative polarization branch. Polarization oscillation with scattering angle occurs for larger monomers (i.e., monomer radius ⩾ 0.3 μ m ). The maximum polarization decreases for increasing monomer radius between 0.11 and 0.17 μ m . However, the negative polarization branch is generally enhanced for monomer radii up to around 0.15 μ m , and reduced for further increase of monomer size. The number of monomers also has a large influence on the negative polarization branch in the case of BPCA. The increase in the number of monomers from 128 to 1024 shifts the scattering angle of minimum polarization to larger angles for BPCA. In addition, the increase in the number of monomers reduces the values of negative polarization for BPCA while the variation with the number of monomers for BCCA is small and is not monotonic.

Efficient numerical orientation averaging of light scattering properties with a quasi-Monte-Carlo method

We studied numerical orientation averaging with three methods for selection of orientations: lattice-grid division, crude Monte-Carlo (CMC) method, and quasi-Monte-Carlo (QMC) method. Numerical orientation averaging with these methods are carried out with a fixed orientation version of the T-matrix method for clusters of spheres. The errors of numerical orientation averaging as a function of number of orientations are investigated by comparison with results from analytical orientation averaging of the T-matrix method. We studied four types of aggregates: a bisphere, ballistic cluster–cluster aggregates of 4 and 128 monomers (BCCA4 and BCCA128), and a ballistic particle–cluster aggregate of 128 monomers (BPCA128). We studied convergence of the scattering efficiency Q sca , absorption efficiency Q abs , asymmetry parameter g, intensity 4 S 11 / x v 2 , and degree of linear polarization P = - S 12 / S 11 . For the polarization, scattering angles of maximum ( Θ max ) and minimum ( Θ min ) polarization in results of analytical orientation averaging are considered. For the intensity, in addition to Θ max and Θ min , forward scattering angle ( Θ = 10 ∘ ) is also considered. Q sca , Q abs and g of bisphere, BCCA4, and BPCA128 can be obtained accurately with smallest number of orientations by using QMC among three methods. Errors in Q sca , Q abs and g of BCCA128 were already small for smaller number of orientations (e.g., 100) with all the three methods. P ( Θ min ) generally shows slow convergence requiring several thousands of orientations to have errors less than 1%. There are also cases where convergence of P ( Θ min ) within 1% error is not attained even for largest number of orientations studied in this paper (i.e., BCCA4 with lattice-grid, BCCA128 with lattice-grid, BCCA128 with CMC). Intensity of Θ = 10 ∘ , Θ max and Θ min , and polarization of Θ max generally show convergence within 1% error for several hundreds to 1000 orientations with three methods for selection of orientation angles. Among three methods, QMC requires smallest number of orientations for intensity and polarization. We also investigated convergence of Θ max and Θ min . Convergence of Θ max and Θ min is generally attained for 100–1000 orientations. We also described the application of the method to the discrete dipole approximation. In these calculations, we considered three shape models with different number of dipoles and different dipole representations to describe BCCA4. The results show that scattering and absorption efficiencies, and asymmetry parameter can generally be obtained within 1% errors for all the three shape models. On the other hand, errors are larger for intensity (up to 10%) and polarization (up to 50–70%).

Optical properties of aerosols in Titan's atmosphere

In the frame of fractal modeling of tholin aggregates we made a systematic analysis of their optical properties. Ballistic particle–cluster aggregation (BPCA) and diffusion-limited aggregation (DLA) of spherical primary particles (monomers) identical in material composition were considered. Aggregates composed of identical particles (monodisperse cluster), as well as of size-distributed particles (polydisperse cluster), were simulated. To calculate the light-scattering models, the code based on the superposition T-matrix method is used. Orientationally averaged properties of light scattering by model particles were extracted, and the normalized phase function and the degree of linear polarization were calculated as functions of scattering angle. We concluded that: (a) aggregation mechanism as well as specific internal structure of the clusters play only a minor role, and for the future it is not necessary to investigate aggregates of different types; (b) the intensity is very sensitive both to the size parameter of forming particles x and to the size parameter of the aggregates X; (c) characterization of the aggregates by the number of monomers is insufficient to retrieve physical properties of aggregates from optical measurement; and (d) it is very desirable to include into the analysis polarization data calculated for the different clusters.

Porous irregular aggregates of sub-micron sized grains to reproduce cometary dust light scattering observations

The present study intends to interpret some of the characteristic features of the light scattered by cometary dust, such as phase angle and wavelength dependence of its polarization, through simulations using Ballistic Cluster-Cluster Aggregation (BCCA) or Ballistic Particle-Cluster Aggregation (BPCA) aggregates of up to 128 sub-micron sized grains (spherical and spheroidal with a possible size distribution) of various composition (silicates, organics, silicates core with organics mantle). The dependence of the linear polarization with the size parameter is shown to depend highly on the size and composition of the constitutive grains. Internal interactions induced by shape or orientation averaging of the grains may lessen this dependence, leading to results comparable to those observed on cometary dust for fluffy aggregates of grains with a size parameter in the 1.3–1.8 range. A size distribution of realistically shaped particles (aggregates of spheroids and larger spheroids) following a power law size distribution with a power index of - 3 , the smallest grains radius by 0.03– 0.2 μ m and the largest spheroids effective radius by 20 μ m , gives a very good fit to the Hale-Bopp observed phase curves. The best silicates–organics ratio ranges from about 50–75% organics and 25–50% silicates in volume considering the eventual presence of core-mantle grains.

Aggregation of interstellar dust grains: effects on optical properties and dynamical behaviour

We exploit the transition matrix technique, based on the multipole expansions of the electromagnetic fields, to calculate the optical properties of interstellar dust, modelled as composite, irregularly shaped particles. We consider two diffrent mechanisms of aggregation leading to clusters with a diffrent structure and degree of fluffiness: ballistic particle-cluster aggregation and ballistic cluster-cluster aggregation. We study how the morpholgy and chemical composition of such aggregates might affect their dynamical behaviour, leading to the removal of dust from the circumstellar radiation field or to the possibility of confining it in stable regions where gravitational and radiation forces balance.

Optical Properties of Composite Interstellar Grains: A Morphological Analysis

In the framework of the transition matrix approach, we calculate the relevant optical properties of cosmic dust grains of amorphous carbon and astronomical silicates, modeled as aggregates of spherical monomers. Two mechanisms of aggregation were considered, producing clusters with different structure and degree of fluffiness: ballistic particle-cluster aggregation (BPCA) and ballistic cluster-cluster aggregation (BCCA). Our results are very different from those obtained through computational approaches based on effective medium theories and might have major implications both on the modeling procedure and on the dust-mass balance in the interstellar medium.

Radiation pressure cross section for fluffy aggregates

—We apply the discrete dipole approximation (DDA) to estimate the radiation pressure cross section for fluffy aggregates by computing the asymmetry parameter and the cross sections for extinction and scattering. The ballistic particle–cluster aggregate and the ballistic cluster–cluster aggregate consisting of either dielectric or absorbing material are considered to represent naturally existing aggregates. We show that the asymmetry parameter perpendicular to the direction of wave propagation is maximized where the wavelength is comparable to the aggregate size, which may be characterized by the area-equivalent radius or the radius of gyration rather than the volume-equivalent radius. The asymmetry parameter for the aggregate depends on the morphology of the particle, but not on the constituent material. Therefore, the dependence of the radiation pressure cross section on the material composition arises mainly from that of the extinction and scattering cross sections, in other words, the single-scattering albedo. We find that aggregates consisting of high-albedo material show a large deviation of radiation pressure from the direction of incident radiation. When the aggregates are illuminated by blackbody radiation, the deviation of the radiation pressure increases with increasing temperature of the blackbody. Since the parallel component of the radiation pressure cross section for the aggregates is smaller than that for the volume-equivalent spheres at the size parameter close to unity, the Planck-mean radiation pressure cross section for the aggregates having radius comparable to the effective wavelength of radiation shows a lower value, compared with the volume-equivalent sphere. Consequently, the slope of the radiation pressure force per mass of the particle as a function of particle mass shows a lower maximum for the aggregates than for compact spherical particles.

Statistical method to calculate extinction by small irregularly shaped particles

A statistical approach is presented for calculation of the extinction of light by small, irregularly shaped particles in the framework of the strong-permittivity fluctuations theory. To this end the Dyson equation in the bilocal approximation is solved. The method, which is applicable even for particles with large optical constants, is used in the determination of the extinction cross section of interstellar dust particles in the visible and infrared region. The particles are assumed to be aggregates of the ballistic particle cluster aggregation type. A strong enhancement of the extinction in the far infrared is found. For moderate optical constants the results agree with Bruggeman’s effective-medium theory.