Abstract

An anomalous increase of the forward light scattering in liquid sulfur is reported to occur in the 158–169°C in which other physical properties of the liquid also show an anomalous behavior. The light scattering increases abruptly between 158°C and 161°C and then decreases and disappears at 169°C, paralleling the behavior of the viscosity and the specific heat. The anomalous scattering effect is explained in terms of composition fluctuations generated at the onset of the ring–chain equilibrium transition which produce dielectric constant fluctuations. Following the theoretical model of polymerization developed by Tobolsky, it is proposed that these composition fluctuations may be produced by the peculiar dependence of the polymerization process on the temperature. The effect of thermal gradients is taken into account to explain the spatial distribution of the observed light scattering. It is shown how the anomalous light scattering can apparently increase the measured value of the absorption coefficient of the liquid. It is also discussed how it can be used to measure the polymerization temperature of liquid sulfur or similar systems.

© 1976 Optical Society of America

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References

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  1. J. A. Poulis, C. H. Messen, Elemental Sulfur, B. Meyer, Ed. (Interscience, New York, 1965), p. 109.
  2. J. Schenk, Physica 23, 325 (1957).
    [CrossRef]
  3. R. F. Bacon, R. Fanelli, J. Am. Chem. Soc. 65, 639 (1943).
    [CrossRef]
  4. E. D. West, J. Am. Chem. Soc. 81, 29 (1959).
    [CrossRef]
  5. G. Gee, Trans. Faraday Soc. 48, 515 (1952); F. Fairbrother, G. Gee, G. T. Merrall, J. Polymer Sci. 16, 459 (1955).
    [CrossRef]
  6. A. V. Tobolsky, A. Eisenberg, J. Am. Chem. Soc. 81, 780 (1959); J. Colloid Sci. 17, 49 (1962). A. V. Tobolsky, W. J. MacKnight, in Polymeric Sulfur and Related Polymers (Interscience, New York, 1965).
    [CrossRef]
  7. A. Eisenberg, A. V. Tobolsky, J. Polymer Sci. 46, 19 (1960).
    [CrossRef]
  8. J. E. van Aken, Physica 39, 107 (1968).
    [CrossRef]
  9. J. A. Poulis, V. Derbyshire, Trans. Faraday Soc. 59, 559 (1963). J. A. Poulis, C. H. Massen, P. V. D. Leeden, Trans. Faraday Soc. 58, 474 (1962).
    [CrossRef]
  10. J. C. Koh, W. Klement, J. Phys. Chem. 74, 4280 (1970).
    [CrossRef]
  11. A. T. Ward, M. B. Meyers, J. Phys. Chem. 73, 1374 (1969).
    [CrossRef]
  12. M. Zanini, J. Tauc, to be published.
  13. W. Klement, J. Polym. Sci. Polym. Phys. Ed. 12, 815 (1974).
    [CrossRef]
  14. A. M. Bass, J. Chem. Phys. 21, 80 (1953); M. A. Gilleo, J. Chem. Phys. 19, 1291 (1951).
    [CrossRef]
  15. B. Meyer, T. V. Oommen, D. Jensen, J. Phys. Chem. 75, 912 (1970).
    [CrossRef]
  16. B. Meyer, Elemental Sulfur (Interscience, New York, 1965); Chem. Rev. 64, 429 (1964).
  17. G. C. Vezzoli, P. J. Kisatsky, L. W. Doremus, P. J. Wash, Appl. Opt. 15, 327 (1976).
    [CrossRef] [PubMed]
  18. M. E. Bauer, D. A. Horsma, J. Phys. Chem. 78, 1670 (1974).
    [CrossRef]
  19. H. Patel, L. B. Borst, J. Chem Phys. 54, 822 (1971).
    [CrossRef]
  20. C. W. Tompson, N. S. Gingrich, J. Chem. Phys. 31, 1598 (1959).
    [CrossRef]

1976 (1)

1974 (2)

M. E. Bauer, D. A. Horsma, J. Phys. Chem. 78, 1670 (1974).
[CrossRef]

W. Klement, J. Polym. Sci. Polym. Phys. Ed. 12, 815 (1974).
[CrossRef]

1971 (1)

H. Patel, L. B. Borst, J. Chem Phys. 54, 822 (1971).
[CrossRef]

1970 (2)

B. Meyer, T. V. Oommen, D. Jensen, J. Phys. Chem. 75, 912 (1970).
[CrossRef]

J. C. Koh, W. Klement, J. Phys. Chem. 74, 4280 (1970).
[CrossRef]

1969 (1)

A. T. Ward, M. B. Meyers, J. Phys. Chem. 73, 1374 (1969).
[CrossRef]

1968 (1)

J. E. van Aken, Physica 39, 107 (1968).
[CrossRef]

1963 (1)

J. A. Poulis, V. Derbyshire, Trans. Faraday Soc. 59, 559 (1963). J. A. Poulis, C. H. Massen, P. V. D. Leeden, Trans. Faraday Soc. 58, 474 (1962).
[CrossRef]

1960 (1)

A. Eisenberg, A. V. Tobolsky, J. Polymer Sci. 46, 19 (1960).
[CrossRef]

1959 (3)

A. V. Tobolsky, A. Eisenberg, J. Am. Chem. Soc. 81, 780 (1959); J. Colloid Sci. 17, 49 (1962). A. V. Tobolsky, W. J. MacKnight, in Polymeric Sulfur and Related Polymers (Interscience, New York, 1965).
[CrossRef]

E. D. West, J. Am. Chem. Soc. 81, 29 (1959).
[CrossRef]

C. W. Tompson, N. S. Gingrich, J. Chem. Phys. 31, 1598 (1959).
[CrossRef]

1957 (1)

J. Schenk, Physica 23, 325 (1957).
[CrossRef]

1953 (1)

A. M. Bass, J. Chem. Phys. 21, 80 (1953); M. A. Gilleo, J. Chem. Phys. 19, 1291 (1951).
[CrossRef]

1952 (1)

G. Gee, Trans. Faraday Soc. 48, 515 (1952); F. Fairbrother, G. Gee, G. T. Merrall, J. Polymer Sci. 16, 459 (1955).
[CrossRef]

1943 (1)

R. F. Bacon, R. Fanelli, J. Am. Chem. Soc. 65, 639 (1943).
[CrossRef]

Bacon, R. F.

R. F. Bacon, R. Fanelli, J. Am. Chem. Soc. 65, 639 (1943).
[CrossRef]

Bass, A. M.

A. M. Bass, J. Chem. Phys. 21, 80 (1953); M. A. Gilleo, J. Chem. Phys. 19, 1291 (1951).
[CrossRef]

Bauer, M. E.

M. E. Bauer, D. A. Horsma, J. Phys. Chem. 78, 1670 (1974).
[CrossRef]

Borst, L. B.

H. Patel, L. B. Borst, J. Chem Phys. 54, 822 (1971).
[CrossRef]

Derbyshire, V.

J. A. Poulis, V. Derbyshire, Trans. Faraday Soc. 59, 559 (1963). J. A. Poulis, C. H. Massen, P. V. D. Leeden, Trans. Faraday Soc. 58, 474 (1962).
[CrossRef]

Doremus, L. W.

Eisenberg, A.

A. Eisenberg, A. V. Tobolsky, J. Polymer Sci. 46, 19 (1960).
[CrossRef]

A. V. Tobolsky, A. Eisenberg, J. Am. Chem. Soc. 81, 780 (1959); J. Colloid Sci. 17, 49 (1962). A. V. Tobolsky, W. J. MacKnight, in Polymeric Sulfur and Related Polymers (Interscience, New York, 1965).
[CrossRef]

Fanelli, R.

R. F. Bacon, R. Fanelli, J. Am. Chem. Soc. 65, 639 (1943).
[CrossRef]

Gee, G.

G. Gee, Trans. Faraday Soc. 48, 515 (1952); F. Fairbrother, G. Gee, G. T. Merrall, J. Polymer Sci. 16, 459 (1955).
[CrossRef]

Gingrich, N. S.

C. W. Tompson, N. S. Gingrich, J. Chem. Phys. 31, 1598 (1959).
[CrossRef]

Horsma, D. A.

M. E. Bauer, D. A. Horsma, J. Phys. Chem. 78, 1670 (1974).
[CrossRef]

Jensen, D.

B. Meyer, T. V. Oommen, D. Jensen, J. Phys. Chem. 75, 912 (1970).
[CrossRef]

Kisatsky, P. J.

Klement, W.

W. Klement, J. Polym. Sci. Polym. Phys. Ed. 12, 815 (1974).
[CrossRef]

J. C. Koh, W. Klement, J. Phys. Chem. 74, 4280 (1970).
[CrossRef]

Koh, J. C.

J. C. Koh, W. Klement, J. Phys. Chem. 74, 4280 (1970).
[CrossRef]

Messen, C. H.

J. A. Poulis, C. H. Messen, Elemental Sulfur, B. Meyer, Ed. (Interscience, New York, 1965), p. 109.

Meyer, B.

B. Meyer, T. V. Oommen, D. Jensen, J. Phys. Chem. 75, 912 (1970).
[CrossRef]

B. Meyer, Elemental Sulfur (Interscience, New York, 1965); Chem. Rev. 64, 429 (1964).

Meyers, M. B.

A. T. Ward, M. B. Meyers, J. Phys. Chem. 73, 1374 (1969).
[CrossRef]

Oommen, T. V.

B. Meyer, T. V. Oommen, D. Jensen, J. Phys. Chem. 75, 912 (1970).
[CrossRef]

Patel, H.

H. Patel, L. B. Borst, J. Chem Phys. 54, 822 (1971).
[CrossRef]

Poulis, J. A.

J. A. Poulis, V. Derbyshire, Trans. Faraday Soc. 59, 559 (1963). J. A. Poulis, C. H. Massen, P. V. D. Leeden, Trans. Faraday Soc. 58, 474 (1962).
[CrossRef]

J. A. Poulis, C. H. Messen, Elemental Sulfur, B. Meyer, Ed. (Interscience, New York, 1965), p. 109.

Schenk, J.

J. Schenk, Physica 23, 325 (1957).
[CrossRef]

Tauc, J.

M. Zanini, J. Tauc, to be published.

Tobolsky, A. V.

A. Eisenberg, A. V. Tobolsky, J. Polymer Sci. 46, 19 (1960).
[CrossRef]

A. V. Tobolsky, A. Eisenberg, J. Am. Chem. Soc. 81, 780 (1959); J. Colloid Sci. 17, 49 (1962). A. V. Tobolsky, W. J. MacKnight, in Polymeric Sulfur and Related Polymers (Interscience, New York, 1965).
[CrossRef]

Tompson, C. W.

C. W. Tompson, N. S. Gingrich, J. Chem. Phys. 31, 1598 (1959).
[CrossRef]

van Aken, J. E.

J. E. van Aken, Physica 39, 107 (1968).
[CrossRef]

Vezzoli, G. C.

Ward, A. T.

A. T. Ward, M. B. Meyers, J. Phys. Chem. 73, 1374 (1969).
[CrossRef]

Wash, P. J.

West, E. D.

E. D. West, J. Am. Chem. Soc. 81, 29 (1959).
[CrossRef]

Zanini, M.

M. Zanini, J. Tauc, to be published.

Appl. Opt. (1)

J. Am. Chem. Soc. (3)

R. F. Bacon, R. Fanelli, J. Am. Chem. Soc. 65, 639 (1943).
[CrossRef]

E. D. West, J. Am. Chem. Soc. 81, 29 (1959).
[CrossRef]

A. V. Tobolsky, A. Eisenberg, J. Am. Chem. Soc. 81, 780 (1959); J. Colloid Sci. 17, 49 (1962). A. V. Tobolsky, W. J. MacKnight, in Polymeric Sulfur and Related Polymers (Interscience, New York, 1965).
[CrossRef]

J. Chem Phys. (1)

H. Patel, L. B. Borst, J. Chem Phys. 54, 822 (1971).
[CrossRef]

J. Chem. Phys. (2)

C. W. Tompson, N. S. Gingrich, J. Chem. Phys. 31, 1598 (1959).
[CrossRef]

A. M. Bass, J. Chem. Phys. 21, 80 (1953); M. A. Gilleo, J. Chem. Phys. 19, 1291 (1951).
[CrossRef]

J. Phys. Chem. (4)

B. Meyer, T. V. Oommen, D. Jensen, J. Phys. Chem. 75, 912 (1970).
[CrossRef]

J. C. Koh, W. Klement, J. Phys. Chem. 74, 4280 (1970).
[CrossRef]

A. T. Ward, M. B. Meyers, J. Phys. Chem. 73, 1374 (1969).
[CrossRef]

M. E. Bauer, D. A. Horsma, J. Phys. Chem. 78, 1670 (1974).
[CrossRef]

J. Polym. Sci. Polym. Phys. Ed. (1)

W. Klement, J. Polym. Sci. Polym. Phys. Ed. 12, 815 (1974).
[CrossRef]

J. Polymer Sci. (1)

A. Eisenberg, A. V. Tobolsky, J. Polymer Sci. 46, 19 (1960).
[CrossRef]

Physica (2)

J. E. van Aken, Physica 39, 107 (1968).
[CrossRef]

J. Schenk, Physica 23, 325 (1957).
[CrossRef]

Trans. Faraday Soc. (2)

G. Gee, Trans. Faraday Soc. 48, 515 (1952); F. Fairbrother, G. Gee, G. T. Merrall, J. Polymer Sci. 16, 459 (1955).
[CrossRef]

J. A. Poulis, V. Derbyshire, Trans. Faraday Soc. 59, 559 (1963). J. A. Poulis, C. H. Massen, P. V. D. Leeden, Trans. Faraday Soc. 58, 474 (1962).
[CrossRef]

Other (3)

J. A. Poulis, C. H. Messen, Elemental Sulfur, B. Meyer, Ed. (Interscience, New York, 1965), p. 109.

M. Zanini, J. Tauc, to be published.

B. Meyer, Elemental Sulfur (Interscience, New York, 1965); Chem. Rev. 64, 429 (1964).

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Figures (4)

Fig. 1
Fig. 1

Anomalous light scattering in liquid sulfur occurring around the polymerization transition. The figures correspond to (a) a heating cycle and (b) a cooling cycle, performed one after the other at a rate of 1.2°/°C between 149°C and 170°C; (c) a heating cycle and (d) a cooling cycle, between 149°C and 170°C at a rate of about 40°/min. In (c) and (d) the time elapsed from the moment at which the temperature was changed is given for each picture. The laser beam cross section was ~1 mm2. The exposure is the same for all the pictures.

Fig. 2
Fig. 2

Anomalous scattering effect observed with an enlarged beam of ~70 mm2: (a) a heating cycle; (b) a cooling cycle performed one after the other at a rate of 1.2°/min between 149°C and 170°C. The exposure is the same for all the pictures.

Fig. 3
Fig. 3

The absorption coefficient of liquid sulfur plotted as a function of the temperature for three wavelengths in the low absorption edge region. The continuous part of the curve corresponds to (a) a heating cycle from 146°C to 171°C, (b) a cooling cycle from 171°C to 146°C. The temperature was changed at a rate of 1.2°/min on both cycles. The dashed part corresponds to a constant temperature equal to the final temperature on each cycle. The arrow corresponds to 160°C in (a) and to 152.5°C in (b).

Fig. 4
Fig. 4

Light scattered from a He–Ne ~1-mm2 laser beam at 90 degrees as a function of the temperature; in (a) the temperature is increased at a rate of 1.2°/min, and the arrow corresponds to 161°C; (b) the temperature is decreased at the same rate, and the arrow corresponds to 152.5°C.

Equations (4)

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S 8 k S 8 * initiation S 8 + ( S 8 * ) n - 1 ( S 8 * ) n propagation ,
W = k M / ( 1 - k M ) 2 ,
P = ( 1 - k W ) - 1 .
ln k = - Δ H / R T + Δ S / R             ln k = - Δ H / R T + Δ S / R ,

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