Abstract

We performed experiments to study the extinction, scattering, and polarization of light by ensembles of fractal dust aggregates that consist of spherical monomers large compared with the wavelength. Extinction was measured on a homogeneous dust cloud. Scattering and polarization were measured on a collimated dust beam. We found that polarization and extinction are determined only by a small size scale that is defined by a monomer and its closest neighbors in an aggregate. The scattering function might also depend on the overall size of the aggregate or the total number of monomers in an aggregate.

© 2002 Optical Society of America

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  1. P. Meakin, “Fractal aggregates in geophysics,” Rev. Geophys. 29, 317–354 (1991).
    [CrossRef]
  2. G. Wurm, J. Blum, “Experiments on preplanetary dust aggregation,” Icarus 132, 125–136 (1998).
    [CrossRef]
  3. C. Oh, C. M. Sorensen, “Structure factor of diffusion-limited aggregation clusters: local structure and non-self-similarity,” Phys. Rev. E 57, 784–790 (1998).
    [CrossRef]
  4. C. M. Sorensen, J. Cai, N. Lu, “Light-scattering measurements of monomer size, monomers per aggregate, and fractal dimension for soot aggregates in flames,” Appl. Opt. 31, 6547–6557 (1992).
    [CrossRef] [PubMed]
  5. D. W. Schaefer, J. E. Martin, P. Wiltzius, S. Canell, “Fractal geometry of colloidal aggregates,” Phys. Rev. Lett. 52, 2371–2374 (1984).
    [CrossRef]
  6. J. E. Martin, D. W. Schaefer, A. J. Hurd, “Fractal geometry of vapor-phase aggregates,” Phys. Rev. A 33, 3540–3543 (1986).
    [CrossRef] [PubMed]
  7. P. Dimon, S. K. Sinha, D. A. Weitz, C. R. Safinya, G. S. Smith, W. A. Varady, H. M. Lindsay, “Structure of aggregated gold colloids,” Phys. Rev. Lett. 57, 595–598 (1986).
    [CrossRef] [PubMed]
  8. J. R. Bottiger, E. S. Fry, R. C. Thompson, “Phase matrix measurements for electromagnetic scattering by sphere aggregates,” in Light Scattering by Irregular Shaped Particles, D. Schuerman, ed., (Plenum, New York, 1980), pp. 283–290.
    [CrossRef]
  9. H. Kimura, “Light-scattering properties of fractal aggregates: numerical calculations by a superposition technique and the discrete-dipole approximation,” in Light Scattering by Non-Spherical Particles: Halifax Contributions, G. Videen, Q. Fu, P. Chylek, eds., (Army Research Laboratory, Adelphi, Md., 2000), pp. 241–244.
  10. A. C. Levasseur-Regourd, M. Cabane, J. C. Worms, V. Haudebourg, “Physical properties of dust in the solar system: relevance of a computational approach and of measurements under microgravity conditions,” Adv. Space Res. 20, 1585–1594 (1997).
    [CrossRef]
  11. F. Rouleau, “Electromagnetic scattering by compact clusters of spheres,” Astron. Astrophys. 310, 686–698 (1996).
  12. J. Blum, M. Schnaiter, G. Wurm, M. Rott, “The deagglomeration and dispersion of small dust particles principles and applications,” Rev. Sci. Instrum. 67, 589–595 (1996).
    [CrossRef]
  13. J. Blum, G. Wurm, “Experiments on sticking, restructuring, and fragmentation of preplanetary dust aggregates,” Icarus 143, 138–146 (2000).
    [CrossRef]
  14. G. Wurm, J. Blum, “An experimental study on the structure of cosmic dust aggregates and their alignment by motion relative to gas,” Astrophys. J. 529, L57–L60 (2000).
    [CrossRef]
  15. S. Wolf, Thüringer Landessternwarte Tautenberg, Sternwarte 5, D-07778 Tautenberg, Germany (personal communication, 1999).

2000 (2)

J. Blum, G. Wurm, “Experiments on sticking, restructuring, and fragmentation of preplanetary dust aggregates,” Icarus 143, 138–146 (2000).
[CrossRef]

G. Wurm, J. Blum, “An experimental study on the structure of cosmic dust aggregates and their alignment by motion relative to gas,” Astrophys. J. 529, L57–L60 (2000).
[CrossRef]

1998 (2)

G. Wurm, J. Blum, “Experiments on preplanetary dust aggregation,” Icarus 132, 125–136 (1998).
[CrossRef]

C. Oh, C. M. Sorensen, “Structure factor of diffusion-limited aggregation clusters: local structure and non-self-similarity,” Phys. Rev. E 57, 784–790 (1998).
[CrossRef]

1997 (1)

A. C. Levasseur-Regourd, M. Cabane, J. C. Worms, V. Haudebourg, “Physical properties of dust in the solar system: relevance of a computational approach and of measurements under microgravity conditions,” Adv. Space Res. 20, 1585–1594 (1997).
[CrossRef]

1996 (2)

F. Rouleau, “Electromagnetic scattering by compact clusters of spheres,” Astron. Astrophys. 310, 686–698 (1996).

J. Blum, M. Schnaiter, G. Wurm, M. Rott, “The deagglomeration and dispersion of small dust particles principles and applications,” Rev. Sci. Instrum. 67, 589–595 (1996).
[CrossRef]

1992 (1)

1991 (1)

P. Meakin, “Fractal aggregates in geophysics,” Rev. Geophys. 29, 317–354 (1991).
[CrossRef]

1986 (2)

J. E. Martin, D. W. Schaefer, A. J. Hurd, “Fractal geometry of vapor-phase aggregates,” Phys. Rev. A 33, 3540–3543 (1986).
[CrossRef] [PubMed]

P. Dimon, S. K. Sinha, D. A. Weitz, C. R. Safinya, G. S. Smith, W. A. Varady, H. M. Lindsay, “Structure of aggregated gold colloids,” Phys. Rev. Lett. 57, 595–598 (1986).
[CrossRef] [PubMed]

1984 (1)

D. W. Schaefer, J. E. Martin, P. Wiltzius, S. Canell, “Fractal geometry of colloidal aggregates,” Phys. Rev. Lett. 52, 2371–2374 (1984).
[CrossRef]

Blum, J.

G. Wurm, J. Blum, “An experimental study on the structure of cosmic dust aggregates and their alignment by motion relative to gas,” Astrophys. J. 529, L57–L60 (2000).
[CrossRef]

J. Blum, G. Wurm, “Experiments on sticking, restructuring, and fragmentation of preplanetary dust aggregates,” Icarus 143, 138–146 (2000).
[CrossRef]

G. Wurm, J. Blum, “Experiments on preplanetary dust aggregation,” Icarus 132, 125–136 (1998).
[CrossRef]

J. Blum, M. Schnaiter, G. Wurm, M. Rott, “The deagglomeration and dispersion of small dust particles principles and applications,” Rev. Sci. Instrum. 67, 589–595 (1996).
[CrossRef]

Bottiger, J. R.

J. R. Bottiger, E. S. Fry, R. C. Thompson, “Phase matrix measurements for electromagnetic scattering by sphere aggregates,” in Light Scattering by Irregular Shaped Particles, D. Schuerman, ed., (Plenum, New York, 1980), pp. 283–290.
[CrossRef]

Cabane, M.

A. C. Levasseur-Regourd, M. Cabane, J. C. Worms, V. Haudebourg, “Physical properties of dust in the solar system: relevance of a computational approach and of measurements under microgravity conditions,” Adv. Space Res. 20, 1585–1594 (1997).
[CrossRef]

Cai, J.

Canell, S.

D. W. Schaefer, J. E. Martin, P. Wiltzius, S. Canell, “Fractal geometry of colloidal aggregates,” Phys. Rev. Lett. 52, 2371–2374 (1984).
[CrossRef]

Dimon, P.

P. Dimon, S. K. Sinha, D. A. Weitz, C. R. Safinya, G. S. Smith, W. A. Varady, H. M. Lindsay, “Structure of aggregated gold colloids,” Phys. Rev. Lett. 57, 595–598 (1986).
[CrossRef] [PubMed]

Fry, E. S.

J. R. Bottiger, E. S. Fry, R. C. Thompson, “Phase matrix measurements for electromagnetic scattering by sphere aggregates,” in Light Scattering by Irregular Shaped Particles, D. Schuerman, ed., (Plenum, New York, 1980), pp. 283–290.
[CrossRef]

Haudebourg, V.

A. C. Levasseur-Regourd, M. Cabane, J. C. Worms, V. Haudebourg, “Physical properties of dust in the solar system: relevance of a computational approach and of measurements under microgravity conditions,” Adv. Space Res. 20, 1585–1594 (1997).
[CrossRef]

Hurd, A. J.

J. E. Martin, D. W. Schaefer, A. J. Hurd, “Fractal geometry of vapor-phase aggregates,” Phys. Rev. A 33, 3540–3543 (1986).
[CrossRef] [PubMed]

Kimura, H.

H. Kimura, “Light-scattering properties of fractal aggregates: numerical calculations by a superposition technique and the discrete-dipole approximation,” in Light Scattering by Non-Spherical Particles: Halifax Contributions, G. Videen, Q. Fu, P. Chylek, eds., (Army Research Laboratory, Adelphi, Md., 2000), pp. 241–244.

Levasseur-Regourd, A. C.

A. C. Levasseur-Regourd, M. Cabane, J. C. Worms, V. Haudebourg, “Physical properties of dust in the solar system: relevance of a computational approach and of measurements under microgravity conditions,” Adv. Space Res. 20, 1585–1594 (1997).
[CrossRef]

Lindsay, H. M.

P. Dimon, S. K. Sinha, D. A. Weitz, C. R. Safinya, G. S. Smith, W. A. Varady, H. M. Lindsay, “Structure of aggregated gold colloids,” Phys. Rev. Lett. 57, 595–598 (1986).
[CrossRef] [PubMed]

Lu, N.

Martin, J. E.

J. E. Martin, D. W. Schaefer, A. J. Hurd, “Fractal geometry of vapor-phase aggregates,” Phys. Rev. A 33, 3540–3543 (1986).
[CrossRef] [PubMed]

D. W. Schaefer, J. E. Martin, P. Wiltzius, S. Canell, “Fractal geometry of colloidal aggregates,” Phys. Rev. Lett. 52, 2371–2374 (1984).
[CrossRef]

Meakin, P.

P. Meakin, “Fractal aggregates in geophysics,” Rev. Geophys. 29, 317–354 (1991).
[CrossRef]

Oh, C.

C. Oh, C. M. Sorensen, “Structure factor of diffusion-limited aggregation clusters: local structure and non-self-similarity,” Phys. Rev. E 57, 784–790 (1998).
[CrossRef]

Rott, M.

J. Blum, M. Schnaiter, G. Wurm, M. Rott, “The deagglomeration and dispersion of small dust particles principles and applications,” Rev. Sci. Instrum. 67, 589–595 (1996).
[CrossRef]

Rouleau, F.

F. Rouleau, “Electromagnetic scattering by compact clusters of spheres,” Astron. Astrophys. 310, 686–698 (1996).

Safinya, C. R.

P. Dimon, S. K. Sinha, D. A. Weitz, C. R. Safinya, G. S. Smith, W. A. Varady, H. M. Lindsay, “Structure of aggregated gold colloids,” Phys. Rev. Lett. 57, 595–598 (1986).
[CrossRef] [PubMed]

Schaefer, D. W.

J. E. Martin, D. W. Schaefer, A. J. Hurd, “Fractal geometry of vapor-phase aggregates,” Phys. Rev. A 33, 3540–3543 (1986).
[CrossRef] [PubMed]

D. W. Schaefer, J. E. Martin, P. Wiltzius, S. Canell, “Fractal geometry of colloidal aggregates,” Phys. Rev. Lett. 52, 2371–2374 (1984).
[CrossRef]

Schnaiter, M.

J. Blum, M. Schnaiter, G. Wurm, M. Rott, “The deagglomeration and dispersion of small dust particles principles and applications,” Rev. Sci. Instrum. 67, 589–595 (1996).
[CrossRef]

Sinha, S. K.

P. Dimon, S. K. Sinha, D. A. Weitz, C. R. Safinya, G. S. Smith, W. A. Varady, H. M. Lindsay, “Structure of aggregated gold colloids,” Phys. Rev. Lett. 57, 595–598 (1986).
[CrossRef] [PubMed]

Smith, G. S.

P. Dimon, S. K. Sinha, D. A. Weitz, C. R. Safinya, G. S. Smith, W. A. Varady, H. M. Lindsay, “Structure of aggregated gold colloids,” Phys. Rev. Lett. 57, 595–598 (1986).
[CrossRef] [PubMed]

Sorensen, C. M.

C. Oh, C. M. Sorensen, “Structure factor of diffusion-limited aggregation clusters: local structure and non-self-similarity,” Phys. Rev. E 57, 784–790 (1998).
[CrossRef]

C. M. Sorensen, J. Cai, N. Lu, “Light-scattering measurements of monomer size, monomers per aggregate, and fractal dimension for soot aggregates in flames,” Appl. Opt. 31, 6547–6557 (1992).
[CrossRef] [PubMed]

Thompson, R. C.

J. R. Bottiger, E. S. Fry, R. C. Thompson, “Phase matrix measurements for electromagnetic scattering by sphere aggregates,” in Light Scattering by Irregular Shaped Particles, D. Schuerman, ed., (Plenum, New York, 1980), pp. 283–290.
[CrossRef]

Varady, W. A.

P. Dimon, S. K. Sinha, D. A. Weitz, C. R. Safinya, G. S. Smith, W. A. Varady, H. M. Lindsay, “Structure of aggregated gold colloids,” Phys. Rev. Lett. 57, 595–598 (1986).
[CrossRef] [PubMed]

Weitz, D. A.

P. Dimon, S. K. Sinha, D. A. Weitz, C. R. Safinya, G. S. Smith, W. A. Varady, H. M. Lindsay, “Structure of aggregated gold colloids,” Phys. Rev. Lett. 57, 595–598 (1986).
[CrossRef] [PubMed]

Wiltzius, P.

D. W. Schaefer, J. E. Martin, P. Wiltzius, S. Canell, “Fractal geometry of colloidal aggregates,” Phys. Rev. Lett. 52, 2371–2374 (1984).
[CrossRef]

Wolf, S.

S. Wolf, Thüringer Landessternwarte Tautenberg, Sternwarte 5, D-07778 Tautenberg, Germany (personal communication, 1999).

Worms, J. C.

A. C. Levasseur-Regourd, M. Cabane, J. C. Worms, V. Haudebourg, “Physical properties of dust in the solar system: relevance of a computational approach and of measurements under microgravity conditions,” Adv. Space Res. 20, 1585–1594 (1997).
[CrossRef]

Wurm, G.

G. Wurm, J. Blum, “An experimental study on the structure of cosmic dust aggregates and their alignment by motion relative to gas,” Astrophys. J. 529, L57–L60 (2000).
[CrossRef]

J. Blum, G. Wurm, “Experiments on sticking, restructuring, and fragmentation of preplanetary dust aggregates,” Icarus 143, 138–146 (2000).
[CrossRef]

G. Wurm, J. Blum, “Experiments on preplanetary dust aggregation,” Icarus 132, 125–136 (1998).
[CrossRef]

J. Blum, M. Schnaiter, G. Wurm, M. Rott, “The deagglomeration and dispersion of small dust particles principles and applications,” Rev. Sci. Instrum. 67, 589–595 (1996).
[CrossRef]

Adv. Space Res. (1)

A. C. Levasseur-Regourd, M. Cabane, J. C. Worms, V. Haudebourg, “Physical properties of dust in the solar system: relevance of a computational approach and of measurements under microgravity conditions,” Adv. Space Res. 20, 1585–1594 (1997).
[CrossRef]

Appl. Opt. (1)

Astron. Astrophys. (1)

F. Rouleau, “Electromagnetic scattering by compact clusters of spheres,” Astron. Astrophys. 310, 686–698 (1996).

Astrophys. J. (1)

G. Wurm, J. Blum, “An experimental study on the structure of cosmic dust aggregates and their alignment by motion relative to gas,” Astrophys. J. 529, L57–L60 (2000).
[CrossRef]

Icarus (2)

G. Wurm, J. Blum, “Experiments on preplanetary dust aggregation,” Icarus 132, 125–136 (1998).
[CrossRef]

J. Blum, G. Wurm, “Experiments on sticking, restructuring, and fragmentation of preplanetary dust aggregates,” Icarus 143, 138–146 (2000).
[CrossRef]

Phys. Rev. A (1)

J. E. Martin, D. W. Schaefer, A. J. Hurd, “Fractal geometry of vapor-phase aggregates,” Phys. Rev. A 33, 3540–3543 (1986).
[CrossRef] [PubMed]

Phys. Rev. E (1)

C. Oh, C. M. Sorensen, “Structure factor of diffusion-limited aggregation clusters: local structure and non-self-similarity,” Phys. Rev. E 57, 784–790 (1998).
[CrossRef]

Phys. Rev. Lett. (2)

P. Dimon, S. K. Sinha, D. A. Weitz, C. R. Safinya, G. S. Smith, W. A. Varady, H. M. Lindsay, “Structure of aggregated gold colloids,” Phys. Rev. Lett. 57, 595–598 (1986).
[CrossRef] [PubMed]

D. W. Schaefer, J. E. Martin, P. Wiltzius, S. Canell, “Fractal geometry of colloidal aggregates,” Phys. Rev. Lett. 52, 2371–2374 (1984).
[CrossRef]

Rev. Geophys. (1)

P. Meakin, “Fractal aggregates in geophysics,” Rev. Geophys. 29, 317–354 (1991).
[CrossRef]

Rev. Sci. Instrum. (1)

J. Blum, M. Schnaiter, G. Wurm, M. Rott, “The deagglomeration and dispersion of small dust particles principles and applications,” Rev. Sci. Instrum. 67, 589–595 (1996).
[CrossRef]

Other (3)

J. R. Bottiger, E. S. Fry, R. C. Thompson, “Phase matrix measurements for electromagnetic scattering by sphere aggregates,” in Light Scattering by Irregular Shaped Particles, D. Schuerman, ed., (Plenum, New York, 1980), pp. 283–290.
[CrossRef]

H. Kimura, “Light-scattering properties of fractal aggregates: numerical calculations by a superposition technique and the discrete-dipole approximation,” in Light Scattering by Non-Spherical Particles: Halifax Contributions, G. Videen, Q. Fu, P. Chylek, eds., (Army Research Laboratory, Adelphi, Md., 2000), pp. 241–244.

S. Wolf, Thüringer Landessternwarte Tautenberg, Sternwarte 5, D-07778 Tautenberg, Germany (personal communication, 1999).

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Figures (8)

Fig. 1
Fig. 1

Number-density distribution of polystyrene particles during the experiment as measured by a condensation nucleus counter. The times when particle injection was started with a 1:1000 per volume polystyrene/water suspension and when the ratio changed to a 1:100 suspension are marked. Each suspension was injected during the entire time for which its number concentration shows a rising slope. When the extinction spectrum was taken at approximately 13:30 h, the number density was 2100 cm-3. Note that the measurement makes no distinction between a monomer and an aggregate to account for one particle.

Fig. 2
Fig. 2

Particle-mass distribution, in arbitrary units, as measured by an optical particle counter. We assumed that the signal of the instrument (Palas Model PCS2000) is proportional to the surface area of the particles and that the ratio of this value to the surface area of a single particle is an approximate measure of the number of particles in an aggregate (labeled on the x axis). We took only one absolute value from this distribution: the ratio between monomers and all particles, which can be determined even if the exact aggregate sizes rely on the assumption above. The structure or size of a counted aggregate has no effect on counting; it registers as one particle. There is a clear distinction between a monomer and everything larger than a monomer. The ratio of monomer number to total particle number is 0.65. With this ratio and the particle number density measured (Fig. 1) we calculated the signal that is due to monomer extinction and subtracted it from the experimental data (Fig. 3). The data also show that the mean aggregate consists of more than 20 monomers, which is a low estimate of the real size but separates the size significantly from those of monomers or of small aggregates.

Fig. 3
Fig. 3

Extinction spectrum of the polystyrene particles. Top, experimental data; middle, corrected measurements, which show only the aggregate extinction when the monomer extinction has been subtracted; bottom, the calculations of an average CCA cluster consisting of four monomers. This curve does not fit the absolute values of the extinction coefficient but shows arbitrary units because of a lack of detailed knowledge about the aggregate structure.

Fig. 4
Fig. 4

Wavelength-dependent ratio η of measured extinction by the aggregates to extinction by independent monomers (bottom). The ratio between measured extinction by the aggregates and extinction by an average CCA cluster consisting of four monomers that represent the small-scale structure is also shown. Both curves have been normalized to 1 at 1000 nm. We regard the strong oscillations in the UV as artifacts that are due to subtraction and division of the measured data by the idealized calculations. It can also be seen that the small-scale structure totally determines the wavelength dependence of the extinction; no influence of larger aggregate structures can be seen.

Fig. 5
Fig. 5

Schematic of the setup for light-scattering measurements of particles in a dust beam. The dust beam is injected by a device perpendicular to the plane of view as a beam of small width (radius, ≈100 µm). As the aggregates are growing under low pressure, a vacuum chamber is required. A polished BK7 glass ring is part of the vacuum setup to permit measurements outside the chamber. The illuminating laser light (≈17-mW laser diode at 680 nm) is polarized at 45° to the scattering plane. The scattered light is focused on an avalanche photodiode, integrated over a scattering angle of ∼1.5°. The light is polarized horizontally and vertically to the scattering plane before detection in two subsequent experiments; the results are combined to give the polarization and intensity of the scattered light. The signals are normalized by the signal of a detector fixed at an ∼90° scattering angle.

Fig. 6
Fig. 6

Dependence of the average number of particles per aggregate on time (from Ref. 2 with some minor recalculations). Circles, measured mean masses from a sequence of long-distance microscope images. Solid curve, model CCA calculations with the first measurable size distribution after 1.7 s. For details see Ref. 2. The latest times when reasonable light-scattering measurements were obtained for all angles are marked.

Fig. 7
Fig. 7

Dependence of polarization on aggregate size. Solid curve, a guide for the eye for values related to the initial, mostly monodisperse dust beam. The positions of minima and maxima are constant at all aggregate sizes measured. There is no difference in the amplitudes for small and large aggregates. There is a significant increase in the amplitude that distinguishes monomers from aggregates, which we attribute to alignment of dust aggregates in the beam, with only minor influence from the aggregation process.

Fig. 8
Fig. 8

Dependence of intensity on aggregate size. Aggregates show a significant enhancement of scattering in the forward direction. A trend for this enhancement to continue for larger aggregates can be seen.

Equations (3)

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x=2πr/λ,
M  Rd.
p=po-pppo+pp,

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