Abstract

Single micron-size sulfuric acid droplets are levitated in vacuum in a quadrupole trap through which passes the beam from a He–Ne laser. Scattered light is monitored by a fixed detector as cavity resonances are excited in the evaporating droplet. Mie-Debye theory is used to determine particle size, which, with kinetic theory, yields vapor pressure. Over the temperature range studied, −10 to +30°C, the vapor pressure of pure sulfuric acid is lnp(Torr) = (20.70 ± 1.74) − (9360 ± 499)/T(K).

© 1986 Optical Society of America

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References

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  1. H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
  2. M. Kerker, The Scattering of Light (AcademicNew York1969).
  3. C. E. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-InterscienceNewYork1983).
  4. A. Ashkin, J. M. Dziedzic, “Observations of Resonances in the Radiation Pressure on Dielectric Spheres,” Phys. Rev. Lett. 38, 1351 (1977).
    [CrossRef]
  5. R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, “Observation of Structure Resonances in the Fluorescence from Microspheres,” Phys. Rev. Lett. 44, 475 (1980).
    [CrossRef]
  6. A. Ashkin, J. M. Dziedzic, “Observation of Optical Resonances of Dielectric Spheres by Light Scattering,” Appl. Opt. 20, 1803 (1981).
    [CrossRef] [PubMed]
  7. R. Thurn, W. Kiefer, “Raman-Microsampling Technique Applying Optical Levitation by Radiation Pressure,” Appl. Spectrosc. 38, 78 (1984);R. E. Preston, T. R. Lettieri, H. G. Semerjian, “Characterization of Single Levitated Drops by Raman Spectroscopy,” Langmuir 1, 365 (1985);R. Thurn, W. Kiefer, “Structural Resonances Observed in the Raman Spectra of Optically Levitated Liquid Droplets,” Appl. Opt. 24, 1515 (1985).
    [CrossRef] [PubMed]
  8. R. F. Wuerker, H. Shelton, R. V. Langmuir, “Electrodynamic Containment of Charged Particles,” J. Appl. Phys. 30, 342 (1959).
    [CrossRef]
  9. F. H. Verhoff, J. T. Banchero, “A Note on the Equilibrium Partial Pressures of Vapors Above Sulfuric Acid Solutions,” Am. Inst. Chem. Eng. J. 18, 1265 (1972).
    [CrossRef]
  10. J. I. Gmitro, T. Vermeulen, “Vapor-Liquid Equilibria for Aqueous Sulfuric Acid,” Am. Inst. Chem. Eng. J. 10, 740 (1964).
    [CrossRef]
  11. W. F. Giaque, E. W. Hornung, J. E. Kunzler, T. R. Rubin, “The Thermodynamic Properties of Aqueous Sulfuric Acid Solutions and Hydrates from 15 to 300 K,” J. Am. Chem. Soc. 86, 62 (1960).
    [CrossRef]
  12. W. Roedel, “Measurement of Sulfuric Acid Saturation Vapor Pressure; Implications for Aerosol Formation by Heteromolecular Nucleation,” J. Aerosol Sci. 10, 375 (1979).
    [CrossRef]
  13. G. P. Ayers, R. W. Gillett, J. L. Gras, “On the Vapor Pressure of Sulfuric Acid,” Geophys. Res. Lett. 7, 433 (1980).
    [CrossRef]
  14. H. H. Blau, D. J. McCleese, D. Watson, “Scattering by Individual Transparent Spheres,” Appl. Opt. 9, 2522 (1970).
    [CrossRef] [PubMed]
  15. C. B. Richardson, C. A. Kurtz, “A Novel Isopiestic Measurement of Water Activity in Concentrated and Supersaturated Lithium Halide Solutions,” J. Am. Chem. Soc. 106, 6615 (1984).
    [CrossRef]
  16. A. R. Lacey, H. K. McPhail, Z. J. Trafalski, “A Simple Automatic Water Still for Surfactant-Free Pure Water,” J. Phys. E 18, 532 (1985).
    [CrossRef]
  17. G. W. Reischl, W. John, W. Devor, “Uniform Electric Charging of Monodisperse Aerosols,” J. Aerosol Sci. 8, 55 (1977).
    [CrossRef]
  18. W. J. Wiscombe, Mie Scattering Calculations: Advances in Technique and Fast Vector-Speed Codes, Document PB301388 (NTIS, Springfield, VA 22161, 1979).
  19. I. Langmuir, “The Vapor Pressure of Metallic Tungsten,” Phys. Rev. 2, 329 (1913).
    [CrossRef]

1985 (1)

A. R. Lacey, H. K. McPhail, Z. J. Trafalski, “A Simple Automatic Water Still for Surfactant-Free Pure Water,” J. Phys. E 18, 532 (1985).
[CrossRef]

1984 (2)

1981 (1)

1980 (2)

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, “Observation of Structure Resonances in the Fluorescence from Microspheres,” Phys. Rev. Lett. 44, 475 (1980).
[CrossRef]

G. P. Ayers, R. W. Gillett, J. L. Gras, “On the Vapor Pressure of Sulfuric Acid,” Geophys. Res. Lett. 7, 433 (1980).
[CrossRef]

1979 (1)

W. Roedel, “Measurement of Sulfuric Acid Saturation Vapor Pressure; Implications for Aerosol Formation by Heteromolecular Nucleation,” J. Aerosol Sci. 10, 375 (1979).
[CrossRef]

1977 (2)

A. Ashkin, J. M. Dziedzic, “Observations of Resonances in the Radiation Pressure on Dielectric Spheres,” Phys. Rev. Lett. 38, 1351 (1977).
[CrossRef]

G. W. Reischl, W. John, W. Devor, “Uniform Electric Charging of Monodisperse Aerosols,” J. Aerosol Sci. 8, 55 (1977).
[CrossRef]

1972 (1)

F. H. Verhoff, J. T. Banchero, “A Note on the Equilibrium Partial Pressures of Vapors Above Sulfuric Acid Solutions,” Am. Inst. Chem. Eng. J. 18, 1265 (1972).
[CrossRef]

1970 (1)

1964 (1)

J. I. Gmitro, T. Vermeulen, “Vapor-Liquid Equilibria for Aqueous Sulfuric Acid,” Am. Inst. Chem. Eng. J. 10, 740 (1964).
[CrossRef]

1960 (1)

W. F. Giaque, E. W. Hornung, J. E. Kunzler, T. R. Rubin, “The Thermodynamic Properties of Aqueous Sulfuric Acid Solutions and Hydrates from 15 to 300 K,” J. Am. Chem. Soc. 86, 62 (1960).
[CrossRef]

1959 (1)

R. F. Wuerker, H. Shelton, R. V. Langmuir, “Electrodynamic Containment of Charged Particles,” J. Appl. Phys. 30, 342 (1959).
[CrossRef]

1913 (1)

I. Langmuir, “The Vapor Pressure of Metallic Tungsten,” Phys. Rev. 2, 329 (1913).
[CrossRef]

Ashkin, A.

A. Ashkin, J. M. Dziedzic, “Observation of Optical Resonances of Dielectric Spheres by Light Scattering,” Appl. Opt. 20, 1803 (1981).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, “Observations of Resonances in the Radiation Pressure on Dielectric Spheres,” Phys. Rev. Lett. 38, 1351 (1977).
[CrossRef]

Ayers, G. P.

G. P. Ayers, R. W. Gillett, J. L. Gras, “On the Vapor Pressure of Sulfuric Acid,” Geophys. Res. Lett. 7, 433 (1980).
[CrossRef]

Banchero, J. T.

F. H. Verhoff, J. T. Banchero, “A Note on the Equilibrium Partial Pressures of Vapors Above Sulfuric Acid Solutions,” Am. Inst. Chem. Eng. J. 18, 1265 (1972).
[CrossRef]

Barber, P. W.

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, “Observation of Structure Resonances in the Fluorescence from Microspheres,” Phys. Rev. Lett. 44, 475 (1980).
[CrossRef]

Benner, R. E.

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, “Observation of Structure Resonances in the Fluorescence from Microspheres,” Phys. Rev. Lett. 44, 475 (1980).
[CrossRef]

Blau, H. H.

Bohren, C. E.

C. E. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-InterscienceNewYork1983).

Chang, R. K.

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, “Observation of Structure Resonances in the Fluorescence from Microspheres,” Phys. Rev. Lett. 44, 475 (1980).
[CrossRef]

Devor, W.

G. W. Reischl, W. John, W. Devor, “Uniform Electric Charging of Monodisperse Aerosols,” J. Aerosol Sci. 8, 55 (1977).
[CrossRef]

Dziedzic, J. M.

A. Ashkin, J. M. Dziedzic, “Observation of Optical Resonances of Dielectric Spheres by Light Scattering,” Appl. Opt. 20, 1803 (1981).
[CrossRef] [PubMed]

A. Ashkin, J. M. Dziedzic, “Observations of Resonances in the Radiation Pressure on Dielectric Spheres,” Phys. Rev. Lett. 38, 1351 (1977).
[CrossRef]

Giaque, W. F.

W. F. Giaque, E. W. Hornung, J. E. Kunzler, T. R. Rubin, “The Thermodynamic Properties of Aqueous Sulfuric Acid Solutions and Hydrates from 15 to 300 K,” J. Am. Chem. Soc. 86, 62 (1960).
[CrossRef]

Gillett, R. W.

G. P. Ayers, R. W. Gillett, J. L. Gras, “On the Vapor Pressure of Sulfuric Acid,” Geophys. Res. Lett. 7, 433 (1980).
[CrossRef]

Gmitro, J. I.

J. I. Gmitro, T. Vermeulen, “Vapor-Liquid Equilibria for Aqueous Sulfuric Acid,” Am. Inst. Chem. Eng. J. 10, 740 (1964).
[CrossRef]

Gras, J. L.

G. P. Ayers, R. W. Gillett, J. L. Gras, “On the Vapor Pressure of Sulfuric Acid,” Geophys. Res. Lett. 7, 433 (1980).
[CrossRef]

Hornung, E. W.

W. F. Giaque, E. W. Hornung, J. E. Kunzler, T. R. Rubin, “The Thermodynamic Properties of Aqueous Sulfuric Acid Solutions and Hydrates from 15 to 300 K,” J. Am. Chem. Soc. 86, 62 (1960).
[CrossRef]

Huffman, D. R.

C. E. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-InterscienceNewYork1983).

John, W.

G. W. Reischl, W. John, W. Devor, “Uniform Electric Charging of Monodisperse Aerosols,” J. Aerosol Sci. 8, 55 (1977).
[CrossRef]

Kerker, M.

M. Kerker, The Scattering of Light (AcademicNew York1969).

Kiefer, W.

Kunzler, J. E.

W. F. Giaque, E. W. Hornung, J. E. Kunzler, T. R. Rubin, “The Thermodynamic Properties of Aqueous Sulfuric Acid Solutions and Hydrates from 15 to 300 K,” J. Am. Chem. Soc. 86, 62 (1960).
[CrossRef]

Kurtz, C. A.

C. B. Richardson, C. A. Kurtz, “A Novel Isopiestic Measurement of Water Activity in Concentrated and Supersaturated Lithium Halide Solutions,” J. Am. Chem. Soc. 106, 6615 (1984).
[CrossRef]

Lacey, A. R.

A. R. Lacey, H. K. McPhail, Z. J. Trafalski, “A Simple Automatic Water Still for Surfactant-Free Pure Water,” J. Phys. E 18, 532 (1985).
[CrossRef]

Langmuir, I.

I. Langmuir, “The Vapor Pressure of Metallic Tungsten,” Phys. Rev. 2, 329 (1913).
[CrossRef]

Langmuir, R. V.

R. F. Wuerker, H. Shelton, R. V. Langmuir, “Electrodynamic Containment of Charged Particles,” J. Appl. Phys. 30, 342 (1959).
[CrossRef]

McCleese, D. J.

McPhail, H. K.

A. R. Lacey, H. K. McPhail, Z. J. Trafalski, “A Simple Automatic Water Still for Surfactant-Free Pure Water,” J. Phys. E 18, 532 (1985).
[CrossRef]

Owen, J. F.

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, “Observation of Structure Resonances in the Fluorescence from Microspheres,” Phys. Rev. Lett. 44, 475 (1980).
[CrossRef]

Reischl, G. W.

G. W. Reischl, W. John, W. Devor, “Uniform Electric Charging of Monodisperse Aerosols,” J. Aerosol Sci. 8, 55 (1977).
[CrossRef]

Richardson, C. B.

C. B. Richardson, C. A. Kurtz, “A Novel Isopiestic Measurement of Water Activity in Concentrated and Supersaturated Lithium Halide Solutions,” J. Am. Chem. Soc. 106, 6615 (1984).
[CrossRef]

Roedel, W.

W. Roedel, “Measurement of Sulfuric Acid Saturation Vapor Pressure; Implications for Aerosol Formation by Heteromolecular Nucleation,” J. Aerosol Sci. 10, 375 (1979).
[CrossRef]

Rubin, T. R.

W. F. Giaque, E. W. Hornung, J. E. Kunzler, T. R. Rubin, “The Thermodynamic Properties of Aqueous Sulfuric Acid Solutions and Hydrates from 15 to 300 K,” J. Am. Chem. Soc. 86, 62 (1960).
[CrossRef]

Shelton, H.

R. F. Wuerker, H. Shelton, R. V. Langmuir, “Electrodynamic Containment of Charged Particles,” J. Appl. Phys. 30, 342 (1959).
[CrossRef]

Thurn, R.

Trafalski, Z. J.

A. R. Lacey, H. K. McPhail, Z. J. Trafalski, “A Simple Automatic Water Still for Surfactant-Free Pure Water,” J. Phys. E 18, 532 (1985).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

Verhoff, F. H.

F. H. Verhoff, J. T. Banchero, “A Note on the Equilibrium Partial Pressures of Vapors Above Sulfuric Acid Solutions,” Am. Inst. Chem. Eng. J. 18, 1265 (1972).
[CrossRef]

Vermeulen, T.

J. I. Gmitro, T. Vermeulen, “Vapor-Liquid Equilibria for Aqueous Sulfuric Acid,” Am. Inst. Chem. Eng. J. 10, 740 (1964).
[CrossRef]

Watson, D.

Wiscombe, W. J.

W. J. Wiscombe, Mie Scattering Calculations: Advances in Technique and Fast Vector-Speed Codes, Document PB301388 (NTIS, Springfield, VA 22161, 1979).

Wuerker, R. F.

R. F. Wuerker, H. Shelton, R. V. Langmuir, “Electrodynamic Containment of Charged Particles,” J. Appl. Phys. 30, 342 (1959).
[CrossRef]

Am. Inst. Chem. Eng. J. (2)

F. H. Verhoff, J. T. Banchero, “A Note on the Equilibrium Partial Pressures of Vapors Above Sulfuric Acid Solutions,” Am. Inst. Chem. Eng. J. 18, 1265 (1972).
[CrossRef]

J. I. Gmitro, T. Vermeulen, “Vapor-Liquid Equilibria for Aqueous Sulfuric Acid,” Am. Inst. Chem. Eng. J. 10, 740 (1964).
[CrossRef]

Appl. Opt. (2)

Appl. Spectrosc. (1)

Geophys. Res. Lett. (1)

G. P. Ayers, R. W. Gillett, J. L. Gras, “On the Vapor Pressure of Sulfuric Acid,” Geophys. Res. Lett. 7, 433 (1980).
[CrossRef]

J. Aerosol Sci. (2)

W. Roedel, “Measurement of Sulfuric Acid Saturation Vapor Pressure; Implications for Aerosol Formation by Heteromolecular Nucleation,” J. Aerosol Sci. 10, 375 (1979).
[CrossRef]

G. W. Reischl, W. John, W. Devor, “Uniform Electric Charging of Monodisperse Aerosols,” J. Aerosol Sci. 8, 55 (1977).
[CrossRef]

J. Am. Chem. Soc. (2)

C. B. Richardson, C. A. Kurtz, “A Novel Isopiestic Measurement of Water Activity in Concentrated and Supersaturated Lithium Halide Solutions,” J. Am. Chem. Soc. 106, 6615 (1984).
[CrossRef]

W. F. Giaque, E. W. Hornung, J. E. Kunzler, T. R. Rubin, “The Thermodynamic Properties of Aqueous Sulfuric Acid Solutions and Hydrates from 15 to 300 K,” J. Am. Chem. Soc. 86, 62 (1960).
[CrossRef]

J. Appl. Phys. (1)

R. F. Wuerker, H. Shelton, R. V. Langmuir, “Electrodynamic Containment of Charged Particles,” J. Appl. Phys. 30, 342 (1959).
[CrossRef]

J. Phys. E (1)

A. R. Lacey, H. K. McPhail, Z. J. Trafalski, “A Simple Automatic Water Still for Surfactant-Free Pure Water,” J. Phys. E 18, 532 (1985).
[CrossRef]

Phys. Rev. (1)

I. Langmuir, “The Vapor Pressure of Metallic Tungsten,” Phys. Rev. 2, 329 (1913).
[CrossRef]

Phys. Rev. Lett. (2)

A. Ashkin, J. M. Dziedzic, “Observations of Resonances in the Radiation Pressure on Dielectric Spheres,” Phys. Rev. Lett. 38, 1351 (1977).
[CrossRef]

R. E. Benner, P. W. Barber, J. F. Owen, R. K. Chang, “Observation of Structure Resonances in the Fluorescence from Microspheres,” Phys. Rev. Lett. 44, 475 (1980).
[CrossRef]

Other (4)

H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).

M. Kerker, The Scattering of Light (AcademicNew York1969).

C. E. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley-InterscienceNewYork1983).

W. J. Wiscombe, Mie Scattering Calculations: Advances in Technique and Fast Vector-Speed Codes, Document PB301388 (NTIS, Springfield, VA 22161, 1979).

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Figures (5)

Fig. 1
Fig. 1

Apparatus scheme: Q = quadrupole trap; L = He–Ne laser; TMP = turbomolecular pump; MP = mechanical pump; TC = temperature controller; V1 = precision valve; V2 = high-conductance valve; V3 = vent valve; C = liquid nitrogen trap; Z = zeolite trap; D = Drierite column; AP = air pump.

Fig. 2
Fig. 2

Intensity of scattered light as a particle passes through a cavity resonance. Size is x = 2πr/λ. Index of refraction is n = 1.437, the sulfuric acid value.

Fig. 3
Fig. 3

Upper trace: portion of the record of intensity of light scattered 90° from a sulfuric acid droplet suspended in vacuum at T = 10.9°C. Lower trace: Theoretical intensity of scattering at 90° for size x between 23.5 and 18. The resonance peaks occur at r = 2.304, 2.153, 2.003, and 1.850 μm for λ = 0.6328 μm. The 2.304-μm peak is that shown in Fig. 2.

Fig. 4
Fig. 4

Radius of the particle of Fig. 3 vs time. The solid curve is the best-fitting polynomial r = a + bt + ct2 + dt3.

Fig. 5
Fig. 5

Summary of results. Points are measured values. Solid line is the best-fitting curve of form lnp = ab/T. Upper curve is that of Ayers et al. Lower curve is that of Gmitro and Vermeulen. Circle is measured value of Roedel.

Tables (1)

Tables Icon

Table I Summary of Evaporation Measurements

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

d m d t ( g s ) = 5.83 × 10 2 α M / T A p ,
ρ d r d t = 5.83 × 10 2 M / T p ,
p = 17.14 T / M ρ d r d t .
μ = μ 0 + 2 γ υ / r ,
p = p 0 exp 2 γ υ / rkT ,
μ = μ 0 q 2 υ / 8 π r 4 ,
p = p 0 exp ( 2 γ / r q 2 / 8 π r 4 ) υ / k T ,
r = r RL = ( q 2 / 16 π γ ) 1 / 3 / 4 .
P = 4 σ A T 3 δ T ,
δ T = ( l / 4 υ σ T 3 ) | d r d t | ,
p = 17.14 T / M ρ | d r d t | exp ( l 2 / 4 υ k σ T 5 ) | d r d t | .

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