Abstract

An optical technique to characterize the accretion of material by microparticles is described. Experiments on the absorption of water vapor by single levitated polystyrene microparticles are reported as examples of an application of the technique. The optical resonant frequencies of the microparticles are perturbed by the accretion of material and the observed shifts are used to characterize the growth. This technique, resonant ellipsometry, makes use of the polarization character of optical resonant modes to distinguish particle swelling from surface layer formation. The experimental results indicate that water vapor absorbed by polystyrene microparticles diffuses primarily into the particle bulk.

© 1992 Optical Society of America

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References

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  1. L. M. Folan, S. Arnold, “Determination of molecular orientation at the surface of an aerosol particle by morphology dependent photoselection,” Opt. Lett. 13, 1–3 (1988).
    [CrossRef] [PubMed]
  2. L. M. Folan, S. Arnold, T. R. O’Keeffe, D. E. Spock, L. B. Schein, A. F. Diaz, “A microparticle electrometer for repeated charge exchange measurements between a microparticle and a surface,” J. Electrostatics 25, 155–163 (1990).
    [CrossRef]
  3. J. A. Lock, “Interference enhancement of the internal fields at structure scattering resonances of a coated sphere,” Appl. Opt. 29, 3180–3187 (1990); R. L. Hightower, C. B. Richardson, “Resonant Mie scattering from a layered sphere,” Appl. Opt. 27, 4850–4855 (1988); A. B. Pluchino, “Surface waves and the radiative properties of micron-sized particles,” Appl. Opt. 20, 2986–2992 (1981).
    [CrossRef] [PubMed]
  4. R. L. Hightower, C. B. Richardson, H-B. Lin, J. D. Eversole, A. J. Campillo, “Measurements of scattering of light from layered microspheres,” Opt. Lett. 13, 946–948 (1988).
    [CrossRef] [PubMed]
  5. S. Arnold, “Spectroscopy of single levitated micron sized particles,” in Optical Effects Associated with Small Particles, P. W. Barber, R. K. Chang, eds. (World Scientific, Singapore, 1988).
  6. E. Marx, G. W. Mulholland, “Size and refractive index determination of single polystyrene spheres,” J. Res. Natl. Bur. Stand. 88, 321–338 (1983).
    [CrossRef]
  7. A. Ashkin, J. M. Dziedzic, “Observation of optical resonances of dielectric spheres by light scattering,” Appl. Opt. 20, 1803–1814 (1981).
    [CrossRef] [PubMed]
  8. G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. 25, 377–445 (1908).
    [CrossRef]
  9. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  10. Convergence criteria have been discussed by several authors including W. J. Wiscombe, “Improved Mie scattering algorithms,” Appl. Opt. 19, 1505–1509 (1980). For a review, see Ref. 9, Appendix A. The criterion chosen in this research is slightly more conservative than that used in Ref. 9.
    [CrossRef] [PubMed]
  11. H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), Chap. 12.
  12. A. L. Aden, M. Kerker, “Scattering of electromagnetic waves from two concentric spheres,” J. Appl. Phys. 22, 1242–1246 (1951).
    [CrossRef]
  13. Ref. 9, Chap. 8.
  14. Computer program listings are provided for homogeneous spheres, layered spheres, and infinite circular cylinders in the appendices of Ref. 9. Computer programs to calculate elastic scattering by a variety of homogeneous particles are provided on disks with the recently published book: P. W. Barber, S. C. Hill, “Light scattering by particles: computational methods” in Advanced Series in Applied Physics (World Scientific, Singapore, 1990), Vol 2.
  15. R. Bhandari, “Tiny core or thin layer as a perturbation in the scattering by a single-layered sphere,” J. Opt. Soc. Am. A 3, 319–328 (1986).
    [CrossRef]
  16. These expressions differ slightly from those in Ref. 15. To be consistent with the definitions of Ref. 9, a factor of -m2, which appears in both the numerator and denominator of the coefficients in Ref. 15, was divided out. The equivalent expression for DnL in Ref. 15 [Eq. (40)] contains m2, multiplying only the homogeneous term and not the first-order correction, which we suspect is a typographic error.
  17. E. J. Davis, “Single aerocolloidal particle instrumentation and measurement,” in Surface and Colloid Science, E. Matijevic, ed. (Plenum, New York, 1987), Vol 14.
    [CrossRef]
  18. L. B. Schein, Electrophotography and Development Physics, (Springer-Verlag, Berlin, 1988), Chap. 4.
    [CrossRef]
  19. A. G. Day, “Water sorption in dielectrics,” Trans. Faraday Soc. 59, 1218–1224 (1963).
    [CrossRef]
  20. R. C. Weast, ed., Handbook of Chemistry and Physics, 51st ed. (CRC, Cleveland, Ohio, 1970), p. D-148.
  21. H. M. Lai, P. T. Leung, K. Young, “Limitations on the photon storage lifetime in electromagnetic resonances of highly transparent microdroplets,” Phys. Rev. A 41, 5199–5204 (1990); S. Arnold, D. E. Spock, L. M. Folan, “Electric-field-modulated light scattering near a morphological resonance of a trapped aerosol particle,” Opt. Lett. 15, 1111–1113 (1990).
    [CrossRef] [PubMed]
  22. T. R. Lettieri, E. Marx, “Resonance light scattering from a liquid suspension of microspheres,” Appl. Opt. 25, 4325–4331 (1986).
    [CrossRef] [PubMed]

1990

L. M. Folan, S. Arnold, T. R. O’Keeffe, D. E. Spock, L. B. Schein, A. F. Diaz, “A microparticle electrometer for repeated charge exchange measurements between a microparticle and a surface,” J. Electrostatics 25, 155–163 (1990).
[CrossRef]

J. A. Lock, “Interference enhancement of the internal fields at structure scattering resonances of a coated sphere,” Appl. Opt. 29, 3180–3187 (1990); R. L. Hightower, C. B. Richardson, “Resonant Mie scattering from a layered sphere,” Appl. Opt. 27, 4850–4855 (1988); A. B. Pluchino, “Surface waves and the radiative properties of micron-sized particles,” Appl. Opt. 20, 2986–2992 (1981).
[CrossRef] [PubMed]

H. M. Lai, P. T. Leung, K. Young, “Limitations on the photon storage lifetime in electromagnetic resonances of highly transparent microdroplets,” Phys. Rev. A 41, 5199–5204 (1990); S. Arnold, D. E. Spock, L. M. Folan, “Electric-field-modulated light scattering near a morphological resonance of a trapped aerosol particle,” Opt. Lett. 15, 1111–1113 (1990).
[CrossRef] [PubMed]

1988

1986

1983

E. Marx, G. W. Mulholland, “Size and refractive index determination of single polystyrene spheres,” J. Res. Natl. Bur. Stand. 88, 321–338 (1983).
[CrossRef]

1981

1980

1963

A. G. Day, “Water sorption in dielectrics,” Trans. Faraday Soc. 59, 1218–1224 (1963).
[CrossRef]

1951

A. L. Aden, M. Kerker, “Scattering of electromagnetic waves from two concentric spheres,” J. Appl. Phys. 22, 1242–1246 (1951).
[CrossRef]

1908

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. 25, 377–445 (1908).
[CrossRef]

Aden, A. L.

A. L. Aden, M. Kerker, “Scattering of electromagnetic waves from two concentric spheres,” J. Appl. Phys. 22, 1242–1246 (1951).
[CrossRef]

Arnold, S.

L. M. Folan, S. Arnold, T. R. O’Keeffe, D. E. Spock, L. B. Schein, A. F. Diaz, “A microparticle electrometer for repeated charge exchange measurements between a microparticle and a surface,” J. Electrostatics 25, 155–163 (1990).
[CrossRef]

L. M. Folan, S. Arnold, “Determination of molecular orientation at the surface of an aerosol particle by morphology dependent photoselection,” Opt. Lett. 13, 1–3 (1988).
[CrossRef] [PubMed]

S. Arnold, “Spectroscopy of single levitated micron sized particles,” in Optical Effects Associated with Small Particles, P. W. Barber, R. K. Chang, eds. (World Scientific, Singapore, 1988).

Ashkin, A.

Barber, P. W.

Computer program listings are provided for homogeneous spheres, layered spheres, and infinite circular cylinders in the appendices of Ref. 9. Computer programs to calculate elastic scattering by a variety of homogeneous particles are provided on disks with the recently published book: P. W. Barber, S. C. Hill, “Light scattering by particles: computational methods” in Advanced Series in Applied Physics (World Scientific, Singapore, 1990), Vol 2.

Bhandari, R.

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Campillo, A. J.

Davis, E. J.

E. J. Davis, “Single aerocolloidal particle instrumentation and measurement,” in Surface and Colloid Science, E. Matijevic, ed. (Plenum, New York, 1987), Vol 14.
[CrossRef]

Day, A. G.

A. G. Day, “Water sorption in dielectrics,” Trans. Faraday Soc. 59, 1218–1224 (1963).
[CrossRef]

Diaz, A. F.

L. M. Folan, S. Arnold, T. R. O’Keeffe, D. E. Spock, L. B. Schein, A. F. Diaz, “A microparticle electrometer for repeated charge exchange measurements between a microparticle and a surface,” J. Electrostatics 25, 155–163 (1990).
[CrossRef]

Dziedzic, J. M.

Eversole, J. D.

Folan, L. M.

L. M. Folan, S. Arnold, T. R. O’Keeffe, D. E. Spock, L. B. Schein, A. F. Diaz, “A microparticle electrometer for repeated charge exchange measurements between a microparticle and a surface,” J. Electrostatics 25, 155–163 (1990).
[CrossRef]

L. M. Folan, S. Arnold, “Determination of molecular orientation at the surface of an aerosol particle by morphology dependent photoselection,” Opt. Lett. 13, 1–3 (1988).
[CrossRef] [PubMed]

Hightower, R. L.

Hill, S. C.

Computer program listings are provided for homogeneous spheres, layered spheres, and infinite circular cylinders in the appendices of Ref. 9. Computer programs to calculate elastic scattering by a variety of homogeneous particles are provided on disks with the recently published book: P. W. Barber, S. C. Hill, “Light scattering by particles: computational methods” in Advanced Series in Applied Physics (World Scientific, Singapore, 1990), Vol 2.

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Kerker, M.

A. L. Aden, M. Kerker, “Scattering of electromagnetic waves from two concentric spheres,” J. Appl. Phys. 22, 1242–1246 (1951).
[CrossRef]

Lai, H. M.

H. M. Lai, P. T. Leung, K. Young, “Limitations on the photon storage lifetime in electromagnetic resonances of highly transparent microdroplets,” Phys. Rev. A 41, 5199–5204 (1990); S. Arnold, D. E. Spock, L. M. Folan, “Electric-field-modulated light scattering near a morphological resonance of a trapped aerosol particle,” Opt. Lett. 15, 1111–1113 (1990).
[CrossRef] [PubMed]

Lettieri, T. R.

Leung, P. T.

H. M. Lai, P. T. Leung, K. Young, “Limitations on the photon storage lifetime in electromagnetic resonances of highly transparent microdroplets,” Phys. Rev. A 41, 5199–5204 (1990); S. Arnold, D. E. Spock, L. M. Folan, “Electric-field-modulated light scattering near a morphological resonance of a trapped aerosol particle,” Opt. Lett. 15, 1111–1113 (1990).
[CrossRef] [PubMed]

Lin, H-B.

Lock, J. A.

Marx, E.

T. R. Lettieri, E. Marx, “Resonance light scattering from a liquid suspension of microspheres,” Appl. Opt. 25, 4325–4331 (1986).
[CrossRef] [PubMed]

E. Marx, G. W. Mulholland, “Size and refractive index determination of single polystyrene spheres,” J. Res. Natl. Bur. Stand. 88, 321–338 (1983).
[CrossRef]

Mie, G.

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. 25, 377–445 (1908).
[CrossRef]

Mulholland, G. W.

E. Marx, G. W. Mulholland, “Size and refractive index determination of single polystyrene spheres,” J. Res. Natl. Bur. Stand. 88, 321–338 (1983).
[CrossRef]

O’Keeffe, T. R.

L. M. Folan, S. Arnold, T. R. O’Keeffe, D. E. Spock, L. B. Schein, A. F. Diaz, “A microparticle electrometer for repeated charge exchange measurements between a microparticle and a surface,” J. Electrostatics 25, 155–163 (1990).
[CrossRef]

Richardson, C. B.

Schein, L. B.

L. M. Folan, S. Arnold, T. R. O’Keeffe, D. E. Spock, L. B. Schein, A. F. Diaz, “A microparticle electrometer for repeated charge exchange measurements between a microparticle and a surface,” J. Electrostatics 25, 155–163 (1990).
[CrossRef]

L. B. Schein, Electrophotography and Development Physics, (Springer-Verlag, Berlin, 1988), Chap. 4.
[CrossRef]

Spock, D. E.

L. M. Folan, S. Arnold, T. R. O’Keeffe, D. E. Spock, L. B. Schein, A. F. Diaz, “A microparticle electrometer for repeated charge exchange measurements between a microparticle and a surface,” J. Electrostatics 25, 155–163 (1990).
[CrossRef]

van de Hulst, H. C.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), Chap. 12.

Wiscombe, W. J.

Young, K.

H. M. Lai, P. T. Leung, K. Young, “Limitations on the photon storage lifetime in electromagnetic resonances of highly transparent microdroplets,” Phys. Rev. A 41, 5199–5204 (1990); S. Arnold, D. E. Spock, L. M. Folan, “Electric-field-modulated light scattering near a morphological resonance of a trapped aerosol particle,” Opt. Lett. 15, 1111–1113 (1990).
[CrossRef] [PubMed]

Ann. Phys.

G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,” Ann. Phys. 25, 377–445 (1908).
[CrossRef]

Appl. Opt.

J. Appl. Phys.

A. L. Aden, M. Kerker, “Scattering of electromagnetic waves from two concentric spheres,” J. Appl. Phys. 22, 1242–1246 (1951).
[CrossRef]

J. Electrostatics

L. M. Folan, S. Arnold, T. R. O’Keeffe, D. E. Spock, L. B. Schein, A. F. Diaz, “A microparticle electrometer for repeated charge exchange measurements between a microparticle and a surface,” J. Electrostatics 25, 155–163 (1990).
[CrossRef]

J. Opt. Soc. Am. A

J. Res. Natl. Bur. Stand.

E. Marx, G. W. Mulholland, “Size and refractive index determination of single polystyrene spheres,” J. Res. Natl. Bur. Stand. 88, 321–338 (1983).
[CrossRef]

Opt. Lett.

Phys. Rev. A

H. M. Lai, P. T. Leung, K. Young, “Limitations on the photon storage lifetime in electromagnetic resonances of highly transparent microdroplets,” Phys. Rev. A 41, 5199–5204 (1990); S. Arnold, D. E. Spock, L. M. Folan, “Electric-field-modulated light scattering near a morphological resonance of a trapped aerosol particle,” Opt. Lett. 15, 1111–1113 (1990).
[CrossRef] [PubMed]

Trans. Faraday Soc.

A. G. Day, “Water sorption in dielectrics,” Trans. Faraday Soc. 59, 1218–1224 (1963).
[CrossRef]

Other

R. C. Weast, ed., Handbook of Chemistry and Physics, 51st ed. (CRC, Cleveland, Ohio, 1970), p. D-148.

S. Arnold, “Spectroscopy of single levitated micron sized particles,” in Optical Effects Associated with Small Particles, P. W. Barber, R. K. Chang, eds. (World Scientific, Singapore, 1988).

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

These expressions differ slightly from those in Ref. 15. To be consistent with the definitions of Ref. 9, a factor of -m2, which appears in both the numerator and denominator of the coefficients in Ref. 15, was divided out. The equivalent expression for DnL in Ref. 15 [Eq. (40)] contains m2, multiplying only the homogeneous term and not the first-order correction, which we suspect is a typographic error.

E. J. Davis, “Single aerocolloidal particle instrumentation and measurement,” in Surface and Colloid Science, E. Matijevic, ed. (Plenum, New York, 1987), Vol 14.
[CrossRef]

L. B. Schein, Electrophotography and Development Physics, (Springer-Verlag, Berlin, 1988), Chap. 4.
[CrossRef]

Ref. 9, Chap. 8.

Computer program listings are provided for homogeneous spheres, layered spheres, and infinite circular cylinders in the appendices of Ref. 9. Computer programs to calculate elastic scattering by a variety of homogeneous particles are provided on disks with the recently published book: P. W. Barber, S. C. Hill, “Light scattering by particles: computational methods” in Advanced Series in Applied Physics (World Scientific, Singapore, 1990), Vol 2.

H. C. van de Hulst, Light Scattering by Small Particles (Dover, New York, 1981), Chap. 12.

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Figures (5)

Fig. 1
Fig. 1

Squares indicate the calculated change in the resonant wavelength by using the complete electromagnetic treatment. The solid lines represent the results of the approximate treatment described in the text.

Fig. 2
Fig. 2

Schematic of the experimental apparatus. PMT, photomultiplier tube.

Fig. 3
Fig. 3

Measured fractional change in the dc voltage needed to balance the particle’s weight as a function of the RH in the levitator.

Fig. 4
Fig. 4

Set of four experimental and two theoretical elastic scattering spectra. The upper panel shows the parallel spectra S 90 Para, and the lower panel shows the perpendicular spectra S 90 Perp. Each panel contains three spectra: one taken of a particle in vacuum, another at 93% RH, and a theoretical spectrum for a particle with a radius of 4.653 μm and a refractive index of 1.59.

Fig. 5
Fig. 5

Shift in a pair of TM modes of a particle as the RH in the levitator was raised.

Equations (7)

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E θ , s = i exp ( ikr ) E 0 cos ϕ k r n = 1 n c 2 n + 1 n ( n + 1 ) [ a n τ n ( cos θ ) + b n π n ( cos θ ) ] ,
E ϕ , s = exp ( ikr ) E 0 sin ϕ i k r n = 1 n c 2 n + 1 n ( n + 1 ) [ a n τ n ( cos θ ) + b n π n ( cos θ ) ] ,
C n L = C n H ( m 1 x 2 ) + ( m 2 2 - m 1 2 ) ψ n ( m 1 x 2 ) ξ n ( x 2 ) ,
D n L = D n H ( m 1 x 2 ) + ( m 2 2 - m 1 2 ) × { ψ n ( m 1 x 2 ) ξ n ( x 2 ) + [ n ( n + 1 ) m 1 m 2 2 x 2 2 ] ψ n ( m 1 x 2 ) ξ n ( x 2 ) } ,
Δ X TE ( m 1 2 - m 2 2 ) ( m 1 2 - 1 )             Δ X TM = ( m 1 2 - m 2 2 ) ( m 1 2 - 1 ) [ ( m 2 2 α + 1 ) m 2 2 ( α + 1 ) ] ,
α = m 1 x 1 2 n ( n + 1 ) [ ψ n ( m 1 x 1 ) χ n ( x 1 ) ψ n ( m 1 x 1 ) χ n ( x 1 ) ] ,
Δ λ TE λ ( m 2 2 - 1 ) ( m 1 2 - 1 ) t a ,             Δ λ TM λ ( α + m 1 2 / m 2 2 α + 1 ) ( m 2 2 - 1 ) ( m 1 2 - 1 ) t a ,

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