Abstract

Quasi-elastic light scattering of Carnauba wax in the liquid phase is done in a homodyne setup and is interpreted as due partially to polarized clusters. A dynamics model is proposed, and effective parameters are obtained in the 85–130°C temperature range. Some evidence exists that the local field seen by a polarized cluster is much higher than the applied static electric field.

© 1983 Optical Society of America

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References

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  1. Encyclopedia of Chemical Technology, Vol. 22 (Wiley, New York, 1970).
  2. R. J. Phelan, R. J. Mahler, A. R. Cook, Appl. Phys. Lett. 19, 337 (1971); T. Furukawa, G. E. Johnson, Appl. Phys. Lett. 38, 1027 (1981).
    [CrossRef]
  3. G. T. Davis, M. G. Broadhurst, International Symposium on Electrets and Dielectrics (Academia Brasileira de Ciências, Rio de Janeiro, 1977).
  4. B. Gross, Phys. Rev. 66, 26 (1944); B. Gross, Endeavour 30, No. 11 (Sept.1971).
    [CrossRef]
  5. H. Z. Cummins, E. R. Pike, Eds., Photon Correlation and Light Beating Spectroscopy (Plenum, New York, 1973).
  6. H. Z. Cummins, F. D. Carlson, T. J. Herbert, G. Woods, Biophys. J. 9, 518 (1969); D. W. Schaefer, G. B. Benedek, P. Schofield, E. Bradford, J. Chem. Phys. 55, 3884 (1971).
    [CrossRef] [PubMed]
  7. P. Debye, Polar Molecules (Dover, New York, 1929).
  8. D. E. Koppel, J. Chem. Phys. 57, 4814 (1972).
    [CrossRef]
  9. G. A. Barbosa, R. Russi, A. S. T. Pires, O. N. Mesquita, Appl. Phys. Lett. 38, 236 (1981).
    [CrossRef]

1981

G. A. Barbosa, R. Russi, A. S. T. Pires, O. N. Mesquita, Appl. Phys. Lett. 38, 236 (1981).
[CrossRef]

1972

D. E. Koppel, J. Chem. Phys. 57, 4814 (1972).
[CrossRef]

1971

R. J. Phelan, R. J. Mahler, A. R. Cook, Appl. Phys. Lett. 19, 337 (1971); T. Furukawa, G. E. Johnson, Appl. Phys. Lett. 38, 1027 (1981).
[CrossRef]

1969

H. Z. Cummins, F. D. Carlson, T. J. Herbert, G. Woods, Biophys. J. 9, 518 (1969); D. W. Schaefer, G. B. Benedek, P. Schofield, E. Bradford, J. Chem. Phys. 55, 3884 (1971).
[CrossRef] [PubMed]

1944

B. Gross, Phys. Rev. 66, 26 (1944); B. Gross, Endeavour 30, No. 11 (Sept.1971).
[CrossRef]

Barbosa, G. A.

G. A. Barbosa, R. Russi, A. S. T. Pires, O. N. Mesquita, Appl. Phys. Lett. 38, 236 (1981).
[CrossRef]

Broadhurst, M. G.

G. T. Davis, M. G. Broadhurst, International Symposium on Electrets and Dielectrics (Academia Brasileira de Ciências, Rio de Janeiro, 1977).

Carlson, F. D.

H. Z. Cummins, F. D. Carlson, T. J. Herbert, G. Woods, Biophys. J. 9, 518 (1969); D. W. Schaefer, G. B. Benedek, P. Schofield, E. Bradford, J. Chem. Phys. 55, 3884 (1971).
[CrossRef] [PubMed]

Cook, A. R.

R. J. Phelan, R. J. Mahler, A. R. Cook, Appl. Phys. Lett. 19, 337 (1971); T. Furukawa, G. E. Johnson, Appl. Phys. Lett. 38, 1027 (1981).
[CrossRef]

Cummins, H. Z.

H. Z. Cummins, F. D. Carlson, T. J. Herbert, G. Woods, Biophys. J. 9, 518 (1969); D. W. Schaefer, G. B. Benedek, P. Schofield, E. Bradford, J. Chem. Phys. 55, 3884 (1971).
[CrossRef] [PubMed]

Davis, G. T.

G. T. Davis, M. G. Broadhurst, International Symposium on Electrets and Dielectrics (Academia Brasileira de Ciências, Rio de Janeiro, 1977).

Debye, P.

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

Gross, B.

B. Gross, Phys. Rev. 66, 26 (1944); B. Gross, Endeavour 30, No. 11 (Sept.1971).
[CrossRef]

Herbert, T. J.

H. Z. Cummins, F. D. Carlson, T. J. Herbert, G. Woods, Biophys. J. 9, 518 (1969); D. W. Schaefer, G. B. Benedek, P. Schofield, E. Bradford, J. Chem. Phys. 55, 3884 (1971).
[CrossRef] [PubMed]

Koppel, D. E.

D. E. Koppel, J. Chem. Phys. 57, 4814 (1972).
[CrossRef]

Mahler, R. J.

R. J. Phelan, R. J. Mahler, A. R. Cook, Appl. Phys. Lett. 19, 337 (1971); T. Furukawa, G. E. Johnson, Appl. Phys. Lett. 38, 1027 (1981).
[CrossRef]

Mesquita, O. N.

G. A. Barbosa, R. Russi, A. S. T. Pires, O. N. Mesquita, Appl. Phys. Lett. 38, 236 (1981).
[CrossRef]

Phelan, R. J.

R. J. Phelan, R. J. Mahler, A. R. Cook, Appl. Phys. Lett. 19, 337 (1971); T. Furukawa, G. E. Johnson, Appl. Phys. Lett. 38, 1027 (1981).
[CrossRef]

Pires, A. S. T.

G. A. Barbosa, R. Russi, A. S. T. Pires, O. N. Mesquita, Appl. Phys. Lett. 38, 236 (1981).
[CrossRef]

Russi, R.

G. A. Barbosa, R. Russi, A. S. T. Pires, O. N. Mesquita, Appl. Phys. Lett. 38, 236 (1981).
[CrossRef]

Woods, G.

H. Z. Cummins, F. D. Carlson, T. J. Herbert, G. Woods, Biophys. J. 9, 518 (1969); D. W. Schaefer, G. B. Benedek, P. Schofield, E. Bradford, J. Chem. Phys. 55, 3884 (1971).
[CrossRef] [PubMed]

Appl. Phys. Lett.

R. J. Phelan, R. J. Mahler, A. R. Cook, Appl. Phys. Lett. 19, 337 (1971); T. Furukawa, G. E. Johnson, Appl. Phys. Lett. 38, 1027 (1981).
[CrossRef]

G. A. Barbosa, R. Russi, A. S. T. Pires, O. N. Mesquita, Appl. Phys. Lett. 38, 236 (1981).
[CrossRef]

Biophys. J.

H. Z. Cummins, F. D. Carlson, T. J. Herbert, G. Woods, Biophys. J. 9, 518 (1969); D. W. Schaefer, G. B. Benedek, P. Schofield, E. Bradford, J. Chem. Phys. 55, 3884 (1971).
[CrossRef] [PubMed]

J. Chem. Phys.

D. E. Koppel, J. Chem. Phys. 57, 4814 (1972).
[CrossRef]

Phys. Rev.

B. Gross, Phys. Rev. 66, 26 (1944); B. Gross, Endeavour 30, No. 11 (Sept.1971).
[CrossRef]

Other

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

G. T. Davis, M. G. Broadhurst, International Symposium on Electrets and Dielectrics (Academia Brasileira de Ciências, Rio de Janeiro, 1977).

Encyclopedia of Chemical Technology, Vol. 22 (Wiley, New York, 1970).

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

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Figures (10)

Fig. 1
Fig. 1

Experimental homodyne setup. The geometry is chosen to make E//q.

Fig. 2
Fig. 2

Time correlation spectra under applied electric field. Scattering angle is 20°. Temperature control is better than 0.1°C.

Fig. 3
Fig. 3

Time correlation spectra for scattering angles of 20, 40, and 60°.

Fig. 4
Fig. 4

Coordinate systems adequate to write the diffusion equations. Pure translational motion is written in x,y,z rotating system while rotational motions are written in X,Y,Z laboratory coordinate system.

Fig. 5
Fig. 5

Average translational diffusion coefficient D ¯ in function of temperature. Solid line represents D ¯ = D 0 + A D s / L with D0 = 2.5 × 10−10 cm2/sec, A = 4.5 Å. Ds and L are, respectively, the solvent self-diffusion coefficient and cluster length.

Fig. 6
Fig. 6

Rotational diffusion coefficient DR as a function of temperature. The straight line represents DR = CTC) − D2, with C = 9.9 × 10−2 Hz/°C and D2 = 5.9 Hz.

Fig. 7
Fig. 7

Cluster effective length L vs temperature. Straight line represents L = L0αT(°C) with L0 = 3.2 × 104 Å and α = 230 Å/°C.

Fig. 8
Fig. 8

Solvent self-diffusion coefficient Ds vs temperature. Straight line represents Ds = BT(°C) − D1, with B = 1.8 × 10−8 cm2/sec °C and D1 = 1.5 × 10−6 cm2/sec.

Fig. 9
Fig. 9

Scattering densities as represented by Eq. (9) as a function of temperature. ρc is the scattering density for the clusters and ρs for the solvent.

Fig. 10
Fig. 10

Typical time correlation data (dots) compared with theoretical fitted dashed line [Eq. (9)] and with a best fit (solid line) obtained from a single relaxation time [Eq. (8)].

Equations (12)

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P t + · J p = 0 ,
r · J transl . = [ D 2 z 2 + D ( 2 x 2 + 2 y 2 ) ] P ( x , y , z system ) ,
· J B . rot . · ( D R P ) = D R [ l ( 1 l 2 ) l ] P ( X , Y , Z system ) ,
· J E = d E k T D R [ l ( 1 l 2 ) ] P ( X , Y , Z system ) .
p τ = q 2 D ¯ [ 1 + μ ( l 2 1 3 ) ] p + D R [ l ( 1 l 2 ) l + l ( 1 l 2 ) ] p ,
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 | 0 , l 0 ) × exp [ i q · ( R R 0 ) ] .
C 1 ( q , t ) = E * s ( t ) E s ( t + τ ) 2 N ( n E s ) 2 exp ( i ω L τ ) 1 1 d l p ( q , l , 0 ) p ( q , l , τ ) ,
p = m A m ( q , τ ) P m ( l ) ,
C 1 ( q , τ ) = exp ( q 2 D ¯ τ ) ( b 0 2 2 + b 0 2 10 exp ( 6 D R τ ) + b 0 b 2 2 10 { [ 1 exp ( 6 D R τ ) ] 3 [ exp ( 2 D R τ ) exp ( 6 D R τ ) ] 2 } ) ,
b 0 = 2 q L 0 q L / 2 j 0 ( x ) d x , b 2 = 10 q L 0 q L / 2 j 2 ( x ) d x .
C 2 ( τ ) = A exp ( τ / τ 0 ) + B
C ( τ ) = [ ρ c C 1 ( τ ) + ρ s exp ( q 2 D s τ ) ] / [ ρ c C 1 ( 0 ) + ρ s ] ,

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