Abstract

Quasi-elastic light scattering of carnauba wax in the liquid phase is obtained in a heterodyne setup, and dynamic processes are analyzed through electrophoresis. Nonspherical polar clusters are found, containing a net electrical charge. An applied square-wave electric field induces drift and rotation of these clusters. These effects are dependent on strength and frequency of the applied electric field. At 373 K and in the low frequency limit the local electric field strength is approximately 70 times the strength of the applied one. This enhancement is believed to be caused by collective orientation of the clusters. The electrophoretic mobility is 1.1 × 10−12 m2/V sec in the high frequency limit and 7.4 × 10−11 m2/V sec in the low frequency limit. The electric dipole moment is 6.3 × 10−16N−1/2 m−1/2 where N is the cluster density/cubic meter and the net charge is about one or two elementary charges.

© 1983 Optical Society of America

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References

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  1. G. A. Barbosa, R. Russi, A. S. T. Pires, O. N. Mesquita, Appl. Phys. Lett. 38, 239 (1981).
    [CrossRef]
  2. L. Fonseca, G. A. Barbosa, Appl. Opt. 22, 1409 (1983).
    [CrossRef] [PubMed]
  3. B. Gross, An. Acad. Bras. Ciênc 17, 219 (1945).
  4. B. Gross, J. Chem. Phys. 17, 866 (1949).
    [CrossRef]
  5. H. Z. Cummins, F. D. Carlson, T. J. Herbert, G. Woods, Biophys. J. 9, 518 (1969).
    [CrossRef] [PubMed]
  6. D. W. Shaefer, G. B. Benedeck, P. Schofield, E. Bradford, J. Chem. Phys. 55, 3884 (1971).
    [CrossRef]
  7. G. Uhlenbeck, L. S. Orstein, Phys. Rev. 36, 823 (1930).
    [CrossRef]
  8. A. Einstein, Investigation on the Theory of Brownian Movement (Dover, New York, 1967).
  9. H. Z. Cummins, E. R. Pike, Photon Correlation and Light Beating Spectroscopy (Plenum, New York, 1973), p. 216.
  10. P. Debye, Polar Molecules (Dover, New York, 1929).
  11. J. H. Van Vleck, The Theory of Electric and Magnetic Susceptibilities (Lowe & Brydone, London, 1966).

1983

1981

G. A. Barbosa, R. Russi, A. S. T. Pires, O. N. Mesquita, Appl. Phys. Lett. 38, 239 (1981).
[CrossRef]

1971

D. W. Shaefer, G. B. Benedeck, P. Schofield, E. Bradford, J. Chem. Phys. 55, 3884 (1971).
[CrossRef]

1969

H. Z. Cummins, F. D. Carlson, T. J. Herbert, G. Woods, Biophys. J. 9, 518 (1969).
[CrossRef] [PubMed]

1949

B. Gross, J. Chem. Phys. 17, 866 (1949).
[CrossRef]

1945

B. Gross, An. Acad. Bras. Ciênc 17, 219 (1945).

1930

G. Uhlenbeck, L. S. Orstein, Phys. Rev. 36, 823 (1930).
[CrossRef]

Barbosa, G. A.

L. Fonseca, G. A. Barbosa, Appl. Opt. 22, 1409 (1983).
[CrossRef] [PubMed]

G. A. Barbosa, R. Russi, A. S. T. Pires, O. N. Mesquita, Appl. Phys. Lett. 38, 239 (1981).
[CrossRef]

Benedeck, G. B.

D. W. Shaefer, G. B. Benedeck, P. Schofield, E. Bradford, J. Chem. Phys. 55, 3884 (1971).
[CrossRef]

Bradford, E.

D. W. Shaefer, G. B. Benedeck, P. Schofield, E. Bradford, J. Chem. Phys. 55, 3884 (1971).
[CrossRef]

Carlson, F. D.

H. Z. Cummins, F. D. Carlson, T. J. Herbert, G. Woods, Biophys. J. 9, 518 (1969).
[CrossRef] [PubMed]

Cummins, H. Z.

H. Z. Cummins, F. D. Carlson, T. J. Herbert, G. Woods, Biophys. J. 9, 518 (1969).
[CrossRef] [PubMed]

H. Z. Cummins, E. R. Pike, Photon Correlation and Light Beating Spectroscopy (Plenum, New York, 1973), p. 216.

Debye, P.

P. Debye, Polar Molecules (Dover, New York, 1929).

Einstein, A.

A. Einstein, Investigation on the Theory of Brownian Movement (Dover, New York, 1967).

Fonseca, L.

Gross, B.

B. Gross, J. Chem. Phys. 17, 866 (1949).
[CrossRef]

B. Gross, An. Acad. Bras. Ciênc 17, 219 (1945).

Herbert, T. J.

H. Z. Cummins, F. D. Carlson, T. J. Herbert, G. Woods, Biophys. J. 9, 518 (1969).
[CrossRef] [PubMed]

Mesquita, O. N.

G. A. Barbosa, R. Russi, A. S. T. Pires, O. N. Mesquita, Appl. Phys. Lett. 38, 239 (1981).
[CrossRef]

Orstein, L. S.

G. Uhlenbeck, L. S. Orstein, Phys. Rev. 36, 823 (1930).
[CrossRef]

Pike, E. R.

H. Z. Cummins, E. R. Pike, Photon Correlation and Light Beating Spectroscopy (Plenum, New York, 1973), p. 216.

Pires, A. S. T.

G. A. Barbosa, R. Russi, A. S. T. Pires, O. N. Mesquita, Appl. Phys. Lett. 38, 239 (1981).
[CrossRef]

Russi, R.

G. A. Barbosa, R. Russi, A. S. T. Pires, O. N. Mesquita, Appl. Phys. Lett. 38, 239 (1981).
[CrossRef]

Schofield, P.

D. W. Shaefer, G. B. Benedeck, P. Schofield, E. Bradford, J. Chem. Phys. 55, 3884 (1971).
[CrossRef]

Shaefer, D. W.

D. W. Shaefer, G. B. Benedeck, P. Schofield, E. Bradford, J. Chem. Phys. 55, 3884 (1971).
[CrossRef]

Uhlenbeck, G.

G. Uhlenbeck, L. S. Orstein, Phys. Rev. 36, 823 (1930).
[CrossRef]

Van Vleck, J. H.

J. H. Van Vleck, The Theory of Electric and Magnetic Susceptibilities (Lowe & Brydone, London, 1966).

Woods, G.

H. Z. Cummins, F. D. Carlson, T. J. Herbert, G. Woods, Biophys. J. 9, 518 (1969).
[CrossRef] [PubMed]

An. Acad. Bras. Ciênc

B. Gross, An. Acad. Bras. Ciênc 17, 219 (1945).

Appl. Opt.

Appl. Phys. Lett.

G. A. Barbosa, R. Russi, A. S. T. Pires, O. N. Mesquita, Appl. Phys. Lett. 38, 239 (1981).
[CrossRef]

Biophys. J.

H. Z. Cummins, F. D. Carlson, T. J. Herbert, G. Woods, Biophys. J. 9, 518 (1969).
[CrossRef] [PubMed]

J. Chem. Phys.

D. W. Shaefer, G. B. Benedeck, P. Schofield, E. Bradford, J. Chem. Phys. 55, 3884 (1971).
[CrossRef]

B. Gross, J. Chem. Phys. 17, 866 (1949).
[CrossRef]

Phys. Rev.

G. Uhlenbeck, L. S. Orstein, Phys. Rev. 36, 823 (1930).
[CrossRef]

Other

A. Einstein, Investigation on the Theory of Brownian Movement (Dover, New York, 1967).

H. Z. Cummins, E. R. Pike, Photon Correlation and Light Beating Spectroscopy (Plenum, New York, 1973), p. 216.

P. Debye, Polar Molecules (Dover, New York, 1929).

J. H. Van Vleck, The Theory of Electric and Magnetic Susceptibilities (Lowe & Brydone, London, 1966).

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Figures (4)

Fig. 1
Fig. 1

Heterodyne setup.

Fig. 2
Fig. 2

Time correlation data (dots) taken in a homodyne setup in the liquid phase (T = 373 K) of carnauba wax (λ = 6328 Å), with a static electric field and 60° scattering angle. Continuous line is the best fit obtained from a single relaxation time.

Fig. 3
Fig. 3

Correlation spectra taken in a heterodyne setup in the liquid phase (T = 373 K) of carnauba wax (λ = 6328 Å). The applied square-wave electric field frequency is 20 Hz.

Fig. 4
Fig. 4

Drift velocity as a function of applied square-wave electric field frequency.

Equations (15)

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P t + J = 0 ,
J = D T P + v P D R R P + ω × R P ,
m v ˙ = f T v + Z e E F ( t ) ,
I ω ˙ = f R ω + d × E + G ( t ) ,
υ = Z e k T D T E ,
ω = ε D R ( 1 l 2 ) 1 / 2 ,
[ τ + D T q 2 i q v τ D R l ( 1 l 2 ) ( l ε ) ] p ( q , l , τ ) = 0 ,
p ( q , l , τ ) 1 2 1 1 d l 0 a ( q , l 0 ) υ d 3 ( r r 0 ) P ( r r 0 , l , τ l 0 , 0 ) × exp i q ( r r 0 ) ;
a ( q , l j ) = υ d 3 r j ρ ( r j ) exp i q r j .
C ( τ ) = E s * ( t ) E s ( t + τ ) = 2 N ( n E s ) 2 × exp ( i ω 0 τ ) 1 1 dlp ( q , l , τ ) p ( q , l , 0 ) ,
g 2 H ( τ ) = E * ( t ) E ( t ) E * ( t + τ ) E ( t + τ ) E * ( t ) E ( t ) = 1 + 2 n ̅ ( 1 + n ̅ ) 2 g 1 ( τ ) + 1 ( 1 + n ̅ ) 2 | g 1 ( τ ) | 2 ,
g 2 H ( τ ) = 1 + 2 n ̅ ( 1 + n ̅ ) 2 [ exp ( D T q 2 τ ) R ] cos ( q v τ ) + 1 ( 1 + n ̅ ) 2 [ exp ( D T q 2 τ ) R ] 2 ,
R = 1 1 + 5 b 2 { 1 + 5 b 2 exp ( 6 D R τ ) b ε 2 × [ 1 exp ( 6 D R τ ) 3 exp ( 2 D R τ ) exp ( 6 D R τ ) 2 ] } ,
b = 0 q L / 2 j 2 ( x ) d x / 0 q L / 2 j 0 ( x ) d x ; j n ( x )
E = E a + P 3 ε 0 = E a + 1 3 ε 0 ( N d 2 3 k T ) E ,

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