Abstract

This paper deals with investigations of the electric birefringence of colloidal solutions in alternating fields; the most detailed measurements were carried out with monodisperse bentonite sols. In general the double refraction consists of a direct and an alternating part, both of which depend on field strength and frequency of the applied field, particle size, temperature, and concentration of the solution. The direct birefringence, which can be positive or negative, can reverse its sign with a change of any of the five parameters mentioned. The measurements are interpreted by means of a relaxation theory which can explain all phenomena connected with the vibrating component in a satisfactory way. Likewise this theory is capable of explaining the variations and the reversal of the direct birefringence with changes of the frequency, field strength, particle size, and temperature. The character of the dependence of the steady birefringence on concentration which has not hitherto been observed with other colloids was first discussed by H. Mueller. The changes and reversal of sign of the direct component with concentration are accounted for by the assumption that the micelles are surrounded by a compressed water hull; the pressure of the water hull depends on particle size and concentration. Direct and alternating birefringence have different relaxation times.

© 1945 Optical Society of America

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References

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  1. H. Mueller and B. W. Sakmann, J. Opt. Soc. Am. 32, 309 (1942).
    [Crossref]
  2. References of previous work on the subject are given in the first article referred to above. In addition to the publications previously quoted, a good bibliography can be found in an article by W. Heller, Rev. Mod. Phys. 14, 390 (1942). See also B. W. Sakmann, M. S. Thesis (1939) and Ph.D. Thesis (1941), Massachusetts Institute of Technology.
    [Crossref]
  3. M. Schwob and R. Lucas, Comptes rendus 194, 1729 (1932).
  4. J. Errera, W. Oostveen, and H. Sack, Rec, Trav, Chim. 57, 185 (1938).
    [Crossref]
  5. H. Mueller and H. H. Helm, J. Opt. Soc. Am. 32, 743A (1942).
  6. Q. Majorana, Acc. dei Lincei 11, 1o sem., 374, 463;2o sem.,  90, 139 (1902).
  7. M. Cotton and H. Mouton, Ann. Chim. Phys. 11, 145, 289 (1907).
  8. P. Langevin, Le radium 7, 233, 249 (1911); M. Born, Ann. d. Physik 55, 177 (1918).
    [Crossref]
  9. A. Peterlin and H. A. Stuart, Zeits. f. Physik 112, 129 (1939).
    [Crossref]
  10. H. Abraham and J. Lemoine. Comptes rendus 129, 206 (1899).
  11. P. Debye, Ber. d. D. Phys. Ges. 15, 777 (1913).
  12. J. H. Tummers, Dissertation, Utrecht (1914).
  13. D. Edwardes, Quart. J. Math. 26, 70 (1893).
  14. R. Gans, Ann. d. Physik 86, 652 (1928).
  15. F. Perrin, J. de phys. et rad. [5] 7, 497 (1934); see also A. Budó, E. Fischer, and S. Miyamoto, Physik. Zeits. 40, 337 (1939).
    [Crossref]
  16. E. A. Hauser and D. S. Le Beau, J. Phys. Chem. 42, 1031 (1938).
    [Crossref]
  17. T. H. Havelock, Proc. Roy. Soc. London 77, 178 (1906).

1942 (3)

H. Mueller and B. W. Sakmann, J. Opt. Soc. Am. 32, 309 (1942).
[Crossref]

References of previous work on the subject are given in the first article referred to above. In addition to the publications previously quoted, a good bibliography can be found in an article by W. Heller, Rev. Mod. Phys. 14, 390 (1942). See also B. W. Sakmann, M. S. Thesis (1939) and Ph.D. Thesis (1941), Massachusetts Institute of Technology.
[Crossref]

H. Mueller and H. H. Helm, J. Opt. Soc. Am. 32, 743A (1942).

1939 (1)

A. Peterlin and H. A. Stuart, Zeits. f. Physik 112, 129 (1939).
[Crossref]

1938 (2)

J. Errera, W. Oostveen, and H. Sack, Rec, Trav, Chim. 57, 185 (1938).
[Crossref]

E. A. Hauser and D. S. Le Beau, J. Phys. Chem. 42, 1031 (1938).
[Crossref]

1934 (1)

F. Perrin, J. de phys. et rad. [5] 7, 497 (1934); see also A. Budó, E. Fischer, and S. Miyamoto, Physik. Zeits. 40, 337 (1939).
[Crossref]

1932 (1)

M. Schwob and R. Lucas, Comptes rendus 194, 1729 (1932).

1928 (1)

R. Gans, Ann. d. Physik 86, 652 (1928).

1913 (1)

P. Debye, Ber. d. D. Phys. Ges. 15, 777 (1913).

1911 (1)

P. Langevin, Le radium 7, 233, 249 (1911); M. Born, Ann. d. Physik 55, 177 (1918).
[Crossref]

1907 (1)

M. Cotton and H. Mouton, Ann. Chim. Phys. 11, 145, 289 (1907).

1906 (1)

T. H. Havelock, Proc. Roy. Soc. London 77, 178 (1906).

1899 (1)

H. Abraham and J. Lemoine. Comptes rendus 129, 206 (1899).

1893 (1)

D. Edwardes, Quart. J. Math. 26, 70 (1893).

Abraham, H.

H. Abraham and J. Lemoine. Comptes rendus 129, 206 (1899).

Cotton, M.

M. Cotton and H. Mouton, Ann. Chim. Phys. 11, 145, 289 (1907).

Debye, P.

P. Debye, Ber. d. D. Phys. Ges. 15, 777 (1913).

Edwardes, D.

D. Edwardes, Quart. J. Math. 26, 70 (1893).

Errera, J.

J. Errera, W. Oostveen, and H. Sack, Rec, Trav, Chim. 57, 185 (1938).
[Crossref]

Gans, R.

R. Gans, Ann. d. Physik 86, 652 (1928).

Hauser, E. A.

E. A. Hauser and D. S. Le Beau, J. Phys. Chem. 42, 1031 (1938).
[Crossref]

Havelock, T. H.

T. H. Havelock, Proc. Roy. Soc. London 77, 178 (1906).

Heller, W.

References of previous work on the subject are given in the first article referred to above. In addition to the publications previously quoted, a good bibliography can be found in an article by W. Heller, Rev. Mod. Phys. 14, 390 (1942). See also B. W. Sakmann, M. S. Thesis (1939) and Ph.D. Thesis (1941), Massachusetts Institute of Technology.
[Crossref]

Helm, H. H.

H. Mueller and H. H. Helm, J. Opt. Soc. Am. 32, 743A (1942).

Langevin, P.

P. Langevin, Le radium 7, 233, 249 (1911); M. Born, Ann. d. Physik 55, 177 (1918).
[Crossref]

Le Beau, D. S.

E. A. Hauser and D. S. Le Beau, J. Phys. Chem. 42, 1031 (1938).
[Crossref]

Lemoine, J.

H. Abraham and J. Lemoine. Comptes rendus 129, 206 (1899).

Lucas, R.

M. Schwob and R. Lucas, Comptes rendus 194, 1729 (1932).

Majorana, Q.

Q. Majorana, Acc. dei Lincei 11, 1o sem., 374, 463;2o sem.,  90, 139 (1902).

Mouton, H.

M. Cotton and H. Mouton, Ann. Chim. Phys. 11, 145, 289 (1907).

Mueller, H.

H. Mueller and H. H. Helm, J. Opt. Soc. Am. 32, 743A (1942).

H. Mueller and B. W. Sakmann, J. Opt. Soc. Am. 32, 309 (1942).
[Crossref]

Oostveen, W.

J. Errera, W. Oostveen, and H. Sack, Rec, Trav, Chim. 57, 185 (1938).
[Crossref]

Perrin, F.

F. Perrin, J. de phys. et rad. [5] 7, 497 (1934); see also A. Budó, E. Fischer, and S. Miyamoto, Physik. Zeits. 40, 337 (1939).
[Crossref]

Peterlin, A.

A. Peterlin and H. A. Stuart, Zeits. f. Physik 112, 129 (1939).
[Crossref]

Sack, H.

J. Errera, W. Oostveen, and H. Sack, Rec, Trav, Chim. 57, 185 (1938).
[Crossref]

Sakmann, B. W.

Schwob, M.

M. Schwob and R. Lucas, Comptes rendus 194, 1729 (1932).

Stuart, H. A.

A. Peterlin and H. A. Stuart, Zeits. f. Physik 112, 129 (1939).
[Crossref]

Tummers, J. H.

J. H. Tummers, Dissertation, Utrecht (1914).

Acc. dei Lincei (1)

Q. Majorana, Acc. dei Lincei 11, 1o sem., 374, 463;2o sem.,  90, 139 (1902).

Ann. Chim. Phys. (1)

M. Cotton and H. Mouton, Ann. Chim. Phys. 11, 145, 289 (1907).

Ann. d. Physik (1)

R. Gans, Ann. d. Physik 86, 652 (1928).

Ber. d. D. Phys. Ges. (1)

P. Debye, Ber. d. D. Phys. Ges. 15, 777 (1913).

Comptes rendus (2)

H. Abraham and J. Lemoine. Comptes rendus 129, 206 (1899).

M. Schwob and R. Lucas, Comptes rendus 194, 1729 (1932).

J. de phys. et rad. [5] (1)

F. Perrin, J. de phys. et rad. [5] 7, 497 (1934); see also A. Budó, E. Fischer, and S. Miyamoto, Physik. Zeits. 40, 337 (1939).
[Crossref]

J. Opt. Soc. Am. (2)

H. Mueller and H. H. Helm, J. Opt. Soc. Am. 32, 743A (1942).

H. Mueller and B. W. Sakmann, J. Opt. Soc. Am. 32, 309 (1942).
[Crossref]

J. Phys. Chem. (1)

E. A. Hauser and D. S. Le Beau, J. Phys. Chem. 42, 1031 (1938).
[Crossref]

Le radium (1)

P. Langevin, Le radium 7, 233, 249 (1911); M. Born, Ann. d. Physik 55, 177 (1918).
[Crossref]

Proc. Roy. Soc. London (1)

T. H. Havelock, Proc. Roy. Soc. London 77, 178 (1906).

Quart. J. Math. (1)

D. Edwardes, Quart. J. Math. 26, 70 (1893).

Rec, Trav, Chim. (1)

J. Errera, W. Oostveen, and H. Sack, Rec, Trav, Chim. 57, 185 (1938).
[Crossref]

Rev. Mod. Phys. (1)

References of previous work on the subject are given in the first article referred to above. In addition to the publications previously quoted, a good bibliography can be found in an article by W. Heller, Rev. Mod. Phys. 14, 390 (1942). See also B. W. Sakmann, M. S. Thesis (1939) and Ph.D. Thesis (1941), Massachusetts Institute of Technology.
[Crossref]

Zeits. f. Physik (1)

A. Peterlin and H. A. Stuart, Zeits. f. Physik 112, 129 (1939).
[Crossref]

Other (1)

J. H. Tummers, Dissertation, Utrecht (1914).

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Figures (13)

Fig. 1
Fig. 1

Frequency dependence of direct and alternating components of double refraction and of phase angle between alternating field and vibrating birefringence for linear and quadratic effect. Curve A: vibrating component of linear effect; curve B: direct component of linear effect; curve C: vibrating component of quadratic effect; curve D: direct component of quadratic effect; curve E: phase angle for linear effect; curve F: phase angle for quadratic effect.

Fig. 2
Fig. 2

Direct and alternating components of birefringence for superposition of linear and quadratic effect b / k T : ( a / k T ) 2 = - 1 2. Curve A: direct component; curve B: alternating component.

Fig. 3
Fig. 3

Frequency dependence of direct and alternating component of birefringence of monodisperse bentonite sol of 110-mμ mean particle diameter and concentration 0.16 percent for different values of the electric field strength. Phase angle between electric field and vibrating double refraction. Direct part: ○; alternating part: ⊙; phase angle: x.

Fig. 4
Fig. 4

Frequency dependence of direct and alternating component of birefringence of monodisperse bentonite sol of 20-mμ mean particle diameter and concentration 0.33 percent for different values of the electric field strength. Direct part: ○; alternating part: x.

Fig. 5
Fig. 5

Frequency dependence of direct component of birefringence of monodisperse bentonite sol of 20-mμ mean particle diameter and concentration 1.16 percent for different values of the electric field strength.

Fig. 6
Fig. 6

Dependence of reversal frequency on concentration for two monodisperse bentonite sols of 20-mμ and 58-mμ mean particle diameter.

Fig. 7
Fig. 7

Frequency dependence of direct and alternating component of the birefringence of a monodisperse bentonite sol of 20-mμ mean particle diameter and concentration 1.16 percent for constant field strength of 40 volts/cm and different values of the temperature of the solution.

Fig. 8
Fig. 8

Reversal frequency in cycles per sec. versus inverse of viscosity in cm sec./g for monodisperse bentonite sol of 20-mμ mean particle diameter and concentration 1.16 percent.

Fig. 9
Fig. 9

Dependence of direct component of birefringence on concentration for monodisperse bentonite sol of 50-mμ mean particle diameter and for constant field strength of 85 volts/cm.

Fig. 10
Fig. 10

Dependence of direct component of birefringence on mean particle diameter in mμ for field strength of 86 volts/cm and concentration of 1.0 percent.

Fig. 11
Fig. 11

Inverse of reversal frequency of direct birefringence versus mean particle diameter in for concentration of 1.0 percent and field strength of 86 volts/cm.

Fig. 12
Fig. 12

Dependence of direct birefringence on field strength for monodisperse bentonite sol of 110-mμ mean particle diameter and concentration 0.14 percent.

Fig. 13
Fig. 13

Dependence of direct birefringence on field strength for monodisperse bentonite sol of 58-mμ mean particle diameter and concentration 0.77 percent.

Equations (32)

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n p - n n = a + b cos ( 2 ω t - φ ) .
ρ k T f t = 1 sin ϑ ϑ [ sin ϑ ( f ϑ - f M k T ) ] ,
τ = ρ / 2 k T .
τ = ρ / 6 k T .
ρ = 8 π η r 3 .
ρ = 32 3 η a 3 .
M = a E 0 cos ϑ cos ω t + b E 0 2 sin ϑ cos ϑ cos 2 ω t .
0 2 π 0 π f ( ϑ ) sin ϑ d ϑ d φ = N ,
f ( ϑ , t ) = N 4 π [ 1 - a E 0 k T cos ω t cos ϑ + E 0 2 2 cos 2 ω t ( cos 2 ϑ - 1 3 ) { b k T + ( a k T ) 2 } ] .
f ( ϑ , t ) = N 4 π [ 1 - a E 0 k T cos ϑ p ( t ) + E 0 2 2 ( cos 2 ϑ - 1 3 ) { b k T q ( t ) + ( a k T ) 2 r ( t ) } ] .
p ( t ) + τ d p d t = - cos ω t ,
q ( t ) + τ 3 d q d t = - 1 2 ( 1 + cos 2 ω t ) ,
r ( t ) + τ 3 d r d t = cos φ cos ω t cos ( ω t - φ ) .
p ( t ) = - cos φ cos ( ω t - φ ) ,
q ( t ) = 1 2 [ 1 + cos ψ cos ( 2 ω t - ψ ) ] ,
r ( t ) = 1 2 [ cos 2 φ + cos ψ cos φ × cos ( 2 ω t - φ - ψ ) ] ,
tan φ = τ ω ,
tan ψ = 2 3 τ ω .
f ( ϑ , t ) = N 4 π [ 1 + a E 0 k T cos ϑ p ( t ) + E 0 2 2 ( cos 2 ϑ - 1 3 ) { b k T q ( t ) + ( a k T ) 2 r ( t ) } ] .
n p - n n = 3 π n 0 ( α 1 - α 2 ) × 0 π f ( ϑ , t ) ( cos 2 ϑ - 1 3 ) sin ϑ d ϑ .
n p - n n = 2 15 N α 1 - α 2 n 0 E 0 2 × { b 2 k T [ 1 + cos ψ cos ( 2 ω t - ψ ) ] + 1 2 ( a k T ) 2 [ cos 2 φ + cos φ cos ψ × cos ( 2 ω t - φ - ψ ) ] } .
b / k T : ( a / k T ) 2 = - 1 2 .
n p - n n = C [ ( 1 - 2 cos 2 φ ) - cos ψ cos ( 2 ω t - 2 φ - ψ ) ] ,
C = 1 15 N α 1 - α 2 n 0 E 0 2 b k T .
( n p - n n ) = 1 15 N α 1 - α 2 n 0 E 0 2 b k T × ( 1 + 4 9 ω 2 τ 2 ) - 1 2 cos ( 2 ω t - ψ ) ,
tan ψ = 2 3 ω τ .
( n p - n n ) = 1 15 N α 1 - α 2 n 0 E 0 2 ( a k T ) 2 × ( 1 + 13 9 ω 2 τ 2 + 4 9 ω 4 τ 4 ) 1 2 cos ( 2 ω t - φ - ψ ) ,
tan φ = ω τ .
( n p - n n ) ω η T = f 1 ,
( n p - n n ) ω 2 η 2 T 2 = f 2 .
n = 3 k T 32 π a 3 1 η ,
i = i 0 [ sin 2 A 2 + B 2 sin A cos ( 2 ω t - χ ) ] ,