Abstract

The molecular spectroscopy of a solution particle by structure resonance modulation spectroscopy is discussed [ S. Arnold and A. B. Pluchino, “ Infrared Spectrum of a Single Aerosol Particle by Photothermal Modulation of Structure Resonances,” Appl. Opt. 21, 4194 ( 1982); S. Arnold et al., “ Molecular Spectroscopy of a Single Aerosol Particle,” Opt. Lett. 9, 4 ( 1984)]. Analytical equations are derived for time dependence of the particle radius as it interacts with a low intensity IR source (<20 mW/cm2). This formalism is found to be in good agreement with pulsed experiments. Working equations for the spectroscopy are derived for both constant and periodic IR excitation.

© 1985 Optical Society of America

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References

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  1. S. Arnold, A. B. Pluchino, “Infrared Spectrum of a Single Aerosol Particle by Photothermal Modulation of Structure Resonances,” Appl. Opt. 21, 4194 (1982).
    [CrossRef]
  2. S. Arnold, M. Neuman, A. B. Pluchino, “Molecular Spectroscopy of a Single Aerosol Particle,” Opt. Lett. 9, 4 (1984).
    [CrossRef] [PubMed]
  3. A. J. Campillo, C. J. Dodge, H.-B. Lin, “Aerosol Particle Absorption Spectroscopy by Photothermal Modulation of Mie Scattered Light,” Appl. Opt. 20, 3100 (1981).
    [CrossRef] [PubMed]
  4. A. Ashkin, J. M. Dziedzic, “Observation of Optical Resonances of Dielectric Spheres by Light Scattering,” Appl. Opt. 20, 1803 (1981).
    [CrossRef] [PubMed]
  5. P. Chylek, J. T. Kiehl, M. K. W. Ko, “Optical Levitation and Partial Wave Resonances,” Phys. Rev. A 18, 2229 (1978).
    [CrossRef]
  6. G. Sageev, J. H. Seinfeld, “Laser Heating of Aqueous Aerosol Particles,” Appl. Opt. 23, 4368 (1984).
    [CrossRef] [PubMed]
  7. L. D. Landau, E. M. Lifshitz, Fluid Dynamics (Pergamon, London, 1959).
  8. G. Mie, “Beitrage zur Optik tüber Medien Speziell Kolloidaler Metallosungen,” Ann. Phys. 25, 377 (1908).
    [CrossRef]
  9. P. W. Dusel, M. Kerker, D. D. Cooke, “Distribution of Absorption Centers Within Irradiated Spheres,” J. Opt. Soc. Am. 69, 55 (1979);A. B. Pluchino, “Photophoretic Force on Particles for Low Knudsen Number,” Appl. Opt. 22, 103 (1983);S. Arnold, M. Lewittes, “Size Dependence of the Photophoretic Force,” J. Appl. Phys. 53, 5314 (1982).
    [CrossRef] [PubMed]
  10. See, for example,E. A. Moelwyn-Hughes, Physical Chemistry (Pergamon, London, 1957), p. 823.
  11. M. B. Baker, “Energy Absorption by Volatile Aerosol Particles,” Atmos. Environ. 10, 241 (1976).
    [CrossRef]
  12. M. A. Philip, F. Gelbard, S. Arnold, “An Absolute Method for Single Aerosol Particle Mass Measurement,” J. Colloid Interface Sci. 91, 507 (1982).
    [CrossRef]
  13. S. Arnold, Y. Amani, A. Orenstein, “Photophoretic Spectrometer,” Rev. Sci. Instrum. 51, 1202 (1980).
    [CrossRef]
  14. B. F. Wishaw, R. H. Stokes, “Activities of Aqueous Ammonium Sulphate Solutions at 25°C,” Trans. Faraday Soc. 50, 952 (1954).
    [CrossRef]
  15. P. E. Wagner, “Aerosol Growth by Condensation,” in Aerosol Microphysics IIW. H. Marlow, Ed. (Springer, Berlin, 1982), Chap. 5, pp. 129–178.
    [CrossRef]

1984 (2)

1982 (2)

M. A. Philip, F. Gelbard, S. Arnold, “An Absolute Method for Single Aerosol Particle Mass Measurement,” J. Colloid Interface Sci. 91, 507 (1982).
[CrossRef]

S. Arnold, A. B. Pluchino, “Infrared Spectrum of a Single Aerosol Particle by Photothermal Modulation of Structure Resonances,” Appl. Opt. 21, 4194 (1982).
[CrossRef]

1981 (2)

1980 (1)

S. Arnold, Y. Amani, A. Orenstein, “Photophoretic Spectrometer,” Rev. Sci. Instrum. 51, 1202 (1980).
[CrossRef]

1979 (1)

1978 (1)

P. Chylek, J. T. Kiehl, M. K. W. Ko, “Optical Levitation and Partial Wave Resonances,” Phys. Rev. A 18, 2229 (1978).
[CrossRef]

1976 (1)

M. B. Baker, “Energy Absorption by Volatile Aerosol Particles,” Atmos. Environ. 10, 241 (1976).
[CrossRef]

1954 (1)

B. F. Wishaw, R. H. Stokes, “Activities of Aqueous Ammonium Sulphate Solutions at 25°C,” Trans. Faraday Soc. 50, 952 (1954).
[CrossRef]

1908 (1)

G. Mie, “Beitrage zur Optik tüber Medien Speziell Kolloidaler Metallosungen,” Ann. Phys. 25, 377 (1908).
[CrossRef]

Amani, Y.

S. Arnold, Y. Amani, A. Orenstein, “Photophoretic Spectrometer,” Rev. Sci. Instrum. 51, 1202 (1980).
[CrossRef]

Arnold, S.

S. Arnold, M. Neuman, A. B. Pluchino, “Molecular Spectroscopy of a Single Aerosol Particle,” Opt. Lett. 9, 4 (1984).
[CrossRef] [PubMed]

S. Arnold, A. B. Pluchino, “Infrared Spectrum of a Single Aerosol Particle by Photothermal Modulation of Structure Resonances,” Appl. Opt. 21, 4194 (1982).
[CrossRef]

M. A. Philip, F. Gelbard, S. Arnold, “An Absolute Method for Single Aerosol Particle Mass Measurement,” J. Colloid Interface Sci. 91, 507 (1982).
[CrossRef]

S. Arnold, Y. Amani, A. Orenstein, “Photophoretic Spectrometer,” Rev. Sci. Instrum. 51, 1202 (1980).
[CrossRef]

Ashkin, A.

Baker, M. B.

M. B. Baker, “Energy Absorption by Volatile Aerosol Particles,” Atmos. Environ. 10, 241 (1976).
[CrossRef]

Campillo, A. J.

Chylek, P.

P. Chylek, J. T. Kiehl, M. K. W. Ko, “Optical Levitation and Partial Wave Resonances,” Phys. Rev. A 18, 2229 (1978).
[CrossRef]

Cooke, D. D.

Dodge, C. J.

Dusel, P. W.

Dziedzic, J. M.

Gelbard, F.

M. A. Philip, F. Gelbard, S. Arnold, “An Absolute Method for Single Aerosol Particle Mass Measurement,” J. Colloid Interface Sci. 91, 507 (1982).
[CrossRef]

Kerker, M.

Kiehl, J. T.

P. Chylek, J. T. Kiehl, M. K. W. Ko, “Optical Levitation and Partial Wave Resonances,” Phys. Rev. A 18, 2229 (1978).
[CrossRef]

Ko, M. K. W.

P. Chylek, J. T. Kiehl, M. K. W. Ko, “Optical Levitation and Partial Wave Resonances,” Phys. Rev. A 18, 2229 (1978).
[CrossRef]

Landau, L. D.

L. D. Landau, E. M. Lifshitz, Fluid Dynamics (Pergamon, London, 1959).

Lifshitz, E. M.

L. D. Landau, E. M. Lifshitz, Fluid Dynamics (Pergamon, London, 1959).

Lin, H.-B.

Mie, G.

G. Mie, “Beitrage zur Optik tüber Medien Speziell Kolloidaler Metallosungen,” Ann. Phys. 25, 377 (1908).
[CrossRef]

Moelwyn-Hughes, E. A.

See, for example,E. A. Moelwyn-Hughes, Physical Chemistry (Pergamon, London, 1957), p. 823.

Neuman, M.

Orenstein, A.

S. Arnold, Y. Amani, A. Orenstein, “Photophoretic Spectrometer,” Rev. Sci. Instrum. 51, 1202 (1980).
[CrossRef]

Philip, M. A.

M. A. Philip, F. Gelbard, S. Arnold, “An Absolute Method for Single Aerosol Particle Mass Measurement,” J. Colloid Interface Sci. 91, 507 (1982).
[CrossRef]

Pluchino, A. B.

Sageev, G.

Seinfeld, J. H.

Stokes, R. H.

B. F. Wishaw, R. H. Stokes, “Activities of Aqueous Ammonium Sulphate Solutions at 25°C,” Trans. Faraday Soc. 50, 952 (1954).
[CrossRef]

Wagner, P. E.

P. E. Wagner, “Aerosol Growth by Condensation,” in Aerosol Microphysics IIW. H. Marlow, Ed. (Springer, Berlin, 1982), Chap. 5, pp. 129–178.
[CrossRef]

Wishaw, B. F.

B. F. Wishaw, R. H. Stokes, “Activities of Aqueous Ammonium Sulphate Solutions at 25°C,” Trans. Faraday Soc. 50, 952 (1954).
[CrossRef]

Ann. Phys. (1)

G. Mie, “Beitrage zur Optik tüber Medien Speziell Kolloidaler Metallosungen,” Ann. Phys. 25, 377 (1908).
[CrossRef]

Appl. Opt. (4)

Atmos. Environ. (1)

M. B. Baker, “Energy Absorption by Volatile Aerosol Particles,” Atmos. Environ. 10, 241 (1976).
[CrossRef]

J. Colloid Interface Sci. (1)

M. A. Philip, F. Gelbard, S. Arnold, “An Absolute Method for Single Aerosol Particle Mass Measurement,” J. Colloid Interface Sci. 91, 507 (1982).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Lett. (1)

Phys. Rev. A (1)

P. Chylek, J. T. Kiehl, M. K. W. Ko, “Optical Levitation and Partial Wave Resonances,” Phys. Rev. A 18, 2229 (1978).
[CrossRef]

Rev. Sci. Instrum. (1)

S. Arnold, Y. Amani, A. Orenstein, “Photophoretic Spectrometer,” Rev. Sci. Instrum. 51, 1202 (1980).
[CrossRef]

Trans. Faraday Soc. (1)

B. F. Wishaw, R. H. Stokes, “Activities of Aqueous Ammonium Sulphate Solutions at 25°C,” Trans. Faraday Soc. 50, 952 (1954).
[CrossRef]

Other (3)

P. E. Wagner, “Aerosol Growth by Condensation,” in Aerosol Microphysics IIW. H. Marlow, Ed. (Springer, Berlin, 1982), Chap. 5, pp. 129–178.
[CrossRef]

See, for example,E. A. Moelwyn-Hughes, Physical Chemistry (Pergamon, London, 1957), p. 823.

L. D. Landau, E. M. Lifshitz, Fluid Dynamics (Pergamon, London, 1959).

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Figures (6)

Fig. 1
Fig. 1

Back scattered intensity vs particle size for an incident wavelength of 5346 Å. The refractive index is 1.331.

Fig. 2
Fig. 2

SRMS spectrum taken on a single solution drop of (NH4)2SO4 about 10 μm in diameter.

Fig. 3
Fig. 3

Oscillogram of both scattered light modulation (above) and incident IR intensity (below) from a (NH4)2SO4 particle 5 μm in diameter. The frequency of the incident visible light was positioned on the low-wavelength side of a structure resonance.

Fig. 4
Fig. 4

Experimental setup for transient light scattering measurements.

Fig. 5
Fig. 5

Light scattering transient from a solution particle of (NH4)2SO4 with a radius of 6.2 μm and a water mole fraction of 0.89 ± 0.01. The lower trace shows the measured IR pulse.

Fig. 6
Fig. 6

Scattered light vs time after IR intensity is turned off. The solid lines are theoretical predictions based on Eq. (19). The pressure of N2 gas plus vapor was 200 Torr.

Equations (25)

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δ S s ( λ 2 ) / S = F s β ( λ 2 ) Q a ( λ 1 ) I ( λ 1 ) ,
δ S ω ( λ 2 ) / S ¯ = F ω β ( λ 2 ) Q a ( λ 1 ) I ( λ 1 ) .
β υ ~ 3 D a 2 β t ~ K g ρ C g a 2 ,
2 C = 2 T = 0
P a = ( K g T + LD C ) n ̂ ds .
P a = Q a π a 2 I .
C ( r ) = ( C s C ) a r + C T ( r ) = ( T s T ) a r + T ,
C s = [ 1 i ( 1 X w ) ] C p ,
δ C s = i C p δ X w + [ 1 i ( 1 X w ) ] δ C p .
δ C p = C p ( LM RT 1 ) δ T T ,
δ X w = 3 X w ( 1 X w ) f w δ a a ,
δ C s = C p { 3 i X w ( 1 X w ) f w δ a a + [ 1 i ( 1 X w ) ] ( LM RT 1 ) δ T T } .
dm dt = D C r = a n ̂ ds .
ρ p a a ˙ = D δ C s ,
ɛ = D C p ρ p a 0 { [ 1 i ( 1 X w ) ] ( LM RT 1 ) δ T T + 3 i X w ( 1 X w ) f w ɛ a 0 } .
δ T = 1 K g ( Q a 4 I a LD δ C s ) .
δ T ( 1 + LZ ) = 1 K g [ Q a I a 4 3 iLD C p X w ( 1 X w ) f w ɛ a 0 ] ,
Z = D C p K g T [ 1 i ( 1 X w ) ] ( LM RT 1 ) .
˙ = α I γ ɛ ,
α = ( Z LZ + 1 ) Q a 4 ρ p , γ = 3 D C p i ρ p a 0 2 f w X w ( 1 X w ) LZ + 1 + Q a IZ 4 a 0 ρ p ( LZ + 1 ) .
γ = β υ ( i C p ρ p f w ) · X w ( 1 X w ) LZ + 1 .
ɛ e = I α γ .
F s = Z a 0 f w 12 D C p i X w ( 1 X w ) .
ɛ 1 ( t ) = α I 1 ( ω 2 + γ 2 ) 1 / 2 exp [ j ( ω t + ϕ ) ] ,
F ω = z 4 a 0 ρ p ( ω 2 + γ 2 ) 1 / 2 ( LZ + 1 ) .

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