Abstract

A photoelectric polarization photometer is described for the measurement of the polarization of the fluorescence of solutions. This instrument uses the principle that the linearly polarized component of the fluorescence vibrating in the direction of propagation of the exciting light is independent of the plane of polarization of the excitation and may be used to give a reference signal against which the signal given by the fluorescence component in the direction of vibration of the excitation may be compared. Positive and negative polarizations may be measured and actual measurements of solutions with p=0.003 to p=0.44 show the standard deviation of a measurement to be Δp=±0.001. Analysis of the systematic errors involved indicates an absolute precision of equal magnitude. The absorption and re-emission of the fluorescence by the solutions results in changes of the polarization with concentration which are easily detected in the case of glycerol and water solutions of xanthydrol derivatives, where conditions are particularly favorable.

© 1956 Optical Society of America

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References

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  1. P. Soleillet, Ann. phys. 12, 23 (1929).
  2. F. Perrin, Ann. phys. 12, 169 (1929).
  3. P. Selenyi, Phys. Rev. 56, 477 (1939).
    [Crossref]
  4. S. Freed and S. I. Weisman, Phys. Rev. 60, 440 (1941).
    [Crossref]
  5. L. A. Tumerman, Doklady Akad. Nauk. S.S.S.R. 58, 1945 (1947), [cf. Phys. Abs., 198 (1949)].
  6. H. Wille, Optik 9, 84 (1952).
  7. J. S. Hall, J. Opt. Soc. Am. 41, 963 (1952).
    [Crossref]
  8. S. I. Wavilov, Z. Physik 32, 721 (1925); B. Lyot, Annals de l’observatoire de Paris (sec. de Meudon) 7, 8, 31, 100 (1926).
    [Crossref]
  9. C. R. Singleterry and L. A. Weinberger, J. Am. Chem. Soc. 73, 4574 (1951).
    [Crossref]
  10. G. Kortüm and H. Meier, Z. Naturforsch. 8a, 235 (1953).
  11. K. W. Keohane and W. K. Metcalf, J. Sci. Instr. 32, 259 (1955).
    [Crossref]
  12. E. P. Clancy, J. Opt. Soc. Am. 42, 357 (1952).
    [Crossref]
  13. W. H. Steel, J. Opt. Soc. Am. 41, 223 (1951).
    [Crossref]
  14. J. B. Birks, Scintillation Counters (McGraw-Hill Book Company, Inc., New York, 1953).
  15. A. Schmillen, Z. Physik 135, 294 (1953).
    [Crossref]
  16. E. A. Bailey and G. K. Rollefson, J. Chem. Phys. 21, 1315 (1953).
    [Crossref]
  17. J. B. Birks and W. A. Little, Proc. Phys. Soc. (London) A66, 921 (1953).
  18. P. P. Pheofilov and B. Sveshnikoff, J. Phys. (U.S.S.R.) 3, 493 (1940).
  19. L. Grisebach, Z. Physik 101, 13 (1936).
    [Crossref]
  20. Th. Förster, Fluoresenz Organisches Verbindungen (Vandenhoeck and Ruprecht, Göttingen, 1951), Chap. IX.
  21. G. Weber, Trans. Faraday Soc. 44, 185 (1948).
    [Crossref]
  22. J. Burch, Biochem. J. 59, 97 (1955).

1955 (2)

K. W. Keohane and W. K. Metcalf, J. Sci. Instr. 32, 259 (1955).
[Crossref]

J. Burch, Biochem. J. 59, 97 (1955).

1953 (4)

G. Kortüm and H. Meier, Z. Naturforsch. 8a, 235 (1953).

A. Schmillen, Z. Physik 135, 294 (1953).
[Crossref]

E. A. Bailey and G. K. Rollefson, J. Chem. Phys. 21, 1315 (1953).
[Crossref]

J. B. Birks and W. A. Little, Proc. Phys. Soc. (London) A66, 921 (1953).

1952 (3)

1951 (2)

C. R. Singleterry and L. A. Weinberger, J. Am. Chem. Soc. 73, 4574 (1951).
[Crossref]

W. H. Steel, J. Opt. Soc. Am. 41, 223 (1951).
[Crossref]

1948 (1)

G. Weber, Trans. Faraday Soc. 44, 185 (1948).
[Crossref]

1947 (1)

L. A. Tumerman, Doklady Akad. Nauk. S.S.S.R. 58, 1945 (1947), [cf. Phys. Abs., 198 (1949)].

1941 (1)

S. Freed and S. I. Weisman, Phys. Rev. 60, 440 (1941).
[Crossref]

1940 (1)

P. P. Pheofilov and B. Sveshnikoff, J. Phys. (U.S.S.R.) 3, 493 (1940).

1939 (1)

P. Selenyi, Phys. Rev. 56, 477 (1939).
[Crossref]

1936 (1)

L. Grisebach, Z. Physik 101, 13 (1936).
[Crossref]

1929 (2)

P. Soleillet, Ann. phys. 12, 23 (1929).

F. Perrin, Ann. phys. 12, 169 (1929).

1925 (1)

S. I. Wavilov, Z. Physik 32, 721 (1925); B. Lyot, Annals de l’observatoire de Paris (sec. de Meudon) 7, 8, 31, 100 (1926).
[Crossref]

Bailey, E. A.

E. A. Bailey and G. K. Rollefson, J. Chem. Phys. 21, 1315 (1953).
[Crossref]

Birks, J. B.

J. B. Birks and W. A. Little, Proc. Phys. Soc. (London) A66, 921 (1953).

J. B. Birks, Scintillation Counters (McGraw-Hill Book Company, Inc., New York, 1953).

Burch, J.

J. Burch, Biochem. J. 59, 97 (1955).

Clancy, E. P.

Förster, Th.

Th. Förster, Fluoresenz Organisches Verbindungen (Vandenhoeck and Ruprecht, Göttingen, 1951), Chap. IX.

Freed, S.

S. Freed and S. I. Weisman, Phys. Rev. 60, 440 (1941).
[Crossref]

Grisebach, L.

L. Grisebach, Z. Physik 101, 13 (1936).
[Crossref]

Hall, J. S.

Keohane, K. W.

K. W. Keohane and W. K. Metcalf, J. Sci. Instr. 32, 259 (1955).
[Crossref]

Kortüm, G.

G. Kortüm and H. Meier, Z. Naturforsch. 8a, 235 (1953).

Little, W. A.

J. B. Birks and W. A. Little, Proc. Phys. Soc. (London) A66, 921 (1953).

Meier, H.

G. Kortüm and H. Meier, Z. Naturforsch. 8a, 235 (1953).

Metcalf, W. K.

K. W. Keohane and W. K. Metcalf, J. Sci. Instr. 32, 259 (1955).
[Crossref]

Perrin, F.

F. Perrin, Ann. phys. 12, 169 (1929).

Pheofilov, P. P.

P. P. Pheofilov and B. Sveshnikoff, J. Phys. (U.S.S.R.) 3, 493 (1940).

Rollefson, G. K.

E. A. Bailey and G. K. Rollefson, J. Chem. Phys. 21, 1315 (1953).
[Crossref]

Schmillen, A.

A. Schmillen, Z. Physik 135, 294 (1953).
[Crossref]

Selenyi, P.

P. Selenyi, Phys. Rev. 56, 477 (1939).
[Crossref]

Singleterry, C. R.

C. R. Singleterry and L. A. Weinberger, J. Am. Chem. Soc. 73, 4574 (1951).
[Crossref]

Soleillet, P.

P. Soleillet, Ann. phys. 12, 23 (1929).

Steel, W. H.

Sveshnikoff, B.

P. P. Pheofilov and B. Sveshnikoff, J. Phys. (U.S.S.R.) 3, 493 (1940).

Tumerman, L. A.

L. A. Tumerman, Doklady Akad. Nauk. S.S.S.R. 58, 1945 (1947), [cf. Phys. Abs., 198 (1949)].

Wavilov, S. I.

S. I. Wavilov, Z. Physik 32, 721 (1925); B. Lyot, Annals de l’observatoire de Paris (sec. de Meudon) 7, 8, 31, 100 (1926).
[Crossref]

Weber, G.

G. Weber, Trans. Faraday Soc. 44, 185 (1948).
[Crossref]

Weinberger, L. A.

C. R. Singleterry and L. A. Weinberger, J. Am. Chem. Soc. 73, 4574 (1951).
[Crossref]

Weisman, S. I.

S. Freed and S. I. Weisman, Phys. Rev. 60, 440 (1941).
[Crossref]

Wille, H.

H. Wille, Optik 9, 84 (1952).

Ann. phys. (2)

P. Soleillet, Ann. phys. 12, 23 (1929).

F. Perrin, Ann. phys. 12, 169 (1929).

Biochem. J. (1)

J. Burch, Biochem. J. 59, 97 (1955).

Doklady Akad. Nauk. S.S.S.R. (1)

L. A. Tumerman, Doklady Akad. Nauk. S.S.S.R. 58, 1945 (1947), [cf. Phys. Abs., 198 (1949)].

J. Am. Chem. Soc. (1)

C. R. Singleterry and L. A. Weinberger, J. Am. Chem. Soc. 73, 4574 (1951).
[Crossref]

J. Chem. Phys. (1)

E. A. Bailey and G. K. Rollefson, J. Chem. Phys. 21, 1315 (1953).
[Crossref]

J. Opt. Soc. Am. (3)

J. Phys. (U.S.S.R.) (1)

P. P. Pheofilov and B. Sveshnikoff, J. Phys. (U.S.S.R.) 3, 493 (1940).

J. Sci. Instr. (1)

K. W. Keohane and W. K. Metcalf, J. Sci. Instr. 32, 259 (1955).
[Crossref]

Optik (1)

H. Wille, Optik 9, 84 (1952).

Phys. Rev. (2)

P. Selenyi, Phys. Rev. 56, 477 (1939).
[Crossref]

S. Freed and S. I. Weisman, Phys. Rev. 60, 440 (1941).
[Crossref]

Proc. Phys. Soc. (London) (1)

J. B. Birks and W. A. Little, Proc. Phys. Soc. (London) A66, 921 (1953).

Trans. Faraday Soc. (1)

G. Weber, Trans. Faraday Soc. 44, 185 (1948).
[Crossref]

Z. Naturforsch. (1)

G. Kortüm and H. Meier, Z. Naturforsch. 8a, 235 (1953).

Z. Physik (3)

A. Schmillen, Z. Physik 135, 294 (1953).
[Crossref]

S. I. Wavilov, Z. Physik 32, 721 (1925); B. Lyot, Annals de l’observatoire de Paris (sec. de Meudon) 7, 8, 31, 100 (1926).
[Crossref]

L. Grisebach, Z. Physik 101, 13 (1936).
[Crossref]

Other (2)

Th. Förster, Fluoresenz Organisches Verbindungen (Vandenhoeck and Ruprecht, Göttingen, 1951), Chap. IX.

J. B. Birks, Scintillation Counters (McGraw-Hill Book Company, Inc., New York, 1953).

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Figures (2)

Fig. 1
Fig. 1

Plan of photoelectric polarization photometer.

Fig. 2
Fig. 2

Coordinates for the derivation of systematic errors in the alignment. i1=plane of vibration of polarizer G3; i2=actual direction of observation; I3=direction of excitation; I1=direction of electric vector of exciting wave; I2=normal to the plane of I1 and I3, is the ideal direction of observation.

Tables (2)

Tables Icon

Table II Polarizations of xanthydrol derivatives in water at 18°C.

Tables Icon

Table III Polarizations of miscellaneous substances in water at 18°. Exciting wavelength: 366 mμ Hg.a

Equations (59)

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p = I - I I + I .
S r = f r I + D r ,
S v = f v I + D v .
S r - S v = ( f r - f v ) I .
S v = f v ( I cos 2 θ + I sin 2 θ ) cos 2 θ
I = I cos 4 θ + I sin 2 θ cos 2 θ ,
p = 1 - ( I / I ) 1 + ( I / I ) = sin 2 θ 1 + cos 2 θ cos 2 θ ,             ( p 0 )
1 p = 1 + 2 cos 2 θ tan 2 θ .
S r = f r I ,             S v = f v I .
S r = f v I .
S v = f v I cos 2 θ ,
I / I = cos 2 θ ,
p = - sin 2 θ 1 + cos 2 θ ,             ( p 0 ) .
I + 2 I = I ( 3 - p 1 - p ) = I ( 3 - p 1 + p ) .
i cos 2 θ ( 3 - p 1 - p )
i 1 = I 1 cos 2 δ + I 2 sin 2 δ cos 2 α + I 3 sin 2 δ sin 2 α , I 2 = I 1 sin 2 δ + I 2 cos 2 δ cos 2 α + I 3 cos 2 δ sin 2 α , i 3 = I 2 sin 2 α + I 3 cos 2 α .
S r = f r i 3 = f r ( I 2 sin 2 α + I 3 cos 2 α )                     = f r ( I sin 2 α + I cos 2 α ) , S v = f v i 1 = f v ( I 1 cos 2 δ + I 2 sin 2 δ cos 2 α + I 3 sin 2 δ sin 2 α ) , = f v ( I cos 2 δ + I sin 2 δ cos 2 α + I sin 2 δ sin 2 α ) .
S r = f r I , S v = f v [ ( I cos 2 δ + I sin 2 δ ) cos 4 θ + I sin 2 θ cos 2 θ ] .
f v [ I ( cos 2 δ + sin 2 α sin 2 δ ) + I cos 2 α sin 2 δ ] · f r I f r ( I sin 2 α + I cos 2 α ) .
f v I [ 1 + 2 p 1 - p sin 2 δ cos 2 α / 1 + 2 p 1 - p sin 2 α ] f v I [ 1 + ( 2 p 1 - p ) ( sin 2 δ - sin 2 α ) ]
f v I [ 1 + 2 p 1 - p ( sin 2 δ - sin 2 α ) ] = f v [ I cos 4 θ + I sin 2 θ cos 2 θ - I 2 p 1 - p sin 2 δ cos 4 θ ] .
p sin 2 θ + 2 p 1 - p [ sin 2 δ - sin 2 α + ( 1 - p 1 + p ) sin 2 δ cos 4 θ ] / 1 + cos 2 θ cos 2 θ + ( 2 p 1 - p ) × [ sin 2 δ - sin 2 α - 1 - p 1 + p sin 2 δ cos 4 θ ] .
S a = [ I cos 2 ( θ a + h ) + I sin 2 ( θ a + h ) ] cos 2 θ a S c = [ I cos 2 ( θ c - h ) + I sin 2 ( θ c - h ) ] cos 2 θ c } θ a < θ c ,
cos 2 ( θ ± h ) = cos 2 θ sin 2 θ · h , sin 2 ( θ ± h ) = sin 2 θ ± sin 2 θ · h .
S a = I ( cos 4 θ a - cos 2 θ a sin 2 θ a · h ) + I ( sin 2 θ a cos 2 θ a - cos 2 θ a sin 2 θ a · h ) , S c = I ( cos 4 θ c + cos 2 θ c sin 2 θ c · h ) + I ( sin 2 θ c cos 2 θ c + cos 2 θ c sin 2 θ c · h ) .
θ c = θ ¯ - Δ ;             θ a = θ ¯ + Δ .
cos 4 ( θ ¯ ± Δ ) = cos 4 θ ¯ 2 cos 2 θ ¯ sin 2 θ ¯ · Δ . cos 2 ( θ ¯ ± Δ ) sin 2 ( θ ¯ ± Δ ) = sin 2 θ ¯ cos 2 θ ¯ ± sin 2 θ ¯ cos 2 θ ¯ · Δ . cos 2 ( θ ¯ ± Δ ) sin 2 ( θ ¯ ± Δ ) = cos 2 θ ¯ sin 2 θ ¯ ± cos 2 θ ¯ cos 2 θ ¯ · Δ sin 2 2 θ ¯ · Δ .
S a = I ( cos 4 θ ¯ + 2 cos 2 θ ¯ sin 2 θ ¯ · Δ ) + I ( cos 2 θ ¯ - cos 4 θ ¯ + sin 2 θ ¯ · Δ - 2 cos 2 θ ¯ sin 2 θ ¯ · Δ ) - ( I + I ) h · ( sin 2 θ ¯ · cos 2 θ ¯ + sin 2 2 θ ¯ · Δ - 2 cos 2 θ ¯ cos 2 θ ¯ · Δ ) , S c = I ( cos 4 θ ¯ - 2 cos 2 θ ¯ sin 2 θ ¯ · Δ ) + I ( cos 2 θ ¯ - cos 4 θ ¯ - sin 2 θ ¯ · Δ + 2 cos 2 θ ¯ sin 2 θ ¯ · Δ ) + ( I + I ) h ( cos 2 θ ¯ sin 2 θ ¯ - sin 2 2 θ ¯ · Δ + 2 cos 2 θ ¯ · cos 2 θ ¯ · Δ ) ,
S a - S c = 0 = I ( 4 cos 2 θ ¯ sin 2 θ ¯ · Δ ) + I ( 2 sin 2 θ ¯ - 4 cos 2 θ ¯ sin 2 θ ¯ · Δ ) - ( I + I ) 2 h · sin 2 θ ¯ cos 2 θ ¯ .
h = [ 1 + p + ( 1 - p ) 1 - 2 cos 2 θ ¯ 2 cos 2 θ ¯ ] Δ .
h [ tan 2 θ ¯ + sec 2 θ ¯ tan 2 θ ¯ + 2 cos 2 θ ¯ ] Δ .
p a = sin 2 θ a 1 + cos 2 θ a · cos 2 θ a ;             p c = sin 2 θ c 1 + cos 2 θ c cos 2 θ c ,
p = I - I I + I = sin 2 θ c - cos 2 θ c sin 2 θ c · 2 h 1 + cos 2 2 θ c cos 2 θ c = sin 2 θ a + cos 2 θ a sin 2 θ a · 2 h 1 + cos 2 2 θ a cos 2 θ a = p c ( 1 - cos 2 θ c sin 2 θ c sin 2 θ c · 2 h ) = p a ( 1 + cos 2 θ a sin 2 θ a sin 2 θ a · 2 h ) .
p = 1 2 ( p a + p c ) + ( cos 2 θ a sin 2 θ a sin 2 θ a - cos 2 θ c sin 2 θ c sin 2 θ c ) · h .
p = 1 2 ( p a + p c ) + [ 1 + sin 2 θ ¯ 1 - ( 4 cos 2 θ ¯ / sin 2 θ ¯ ) Δ 2 ] · h Δ ,
p - 1 2 ( p a + p c ) < 6 h Δ .
p a + p c 2 = p ( θ ¯ + Δ ) + p ( θ ¯ - Δ ) 2 = ( sin 2 θ ¯ 1 + cos 2 θ ¯ cos 2 θ ¯ ) × [ 1 + sin 2 2 θ ¯ ( 6 cos 2 θ ¯ - 1 ) Δ 2 sin 2 θ ¯ ( 1 + cos 2 θ ¯ cos 2 θ ¯ ) 1 - sin 2 2 θ ¯ ( 6 cos 2 θ ¯ - 1 ) Δ 2 ( 1 + cos 2 θ ¯ cos 2 θ ¯ ) 2 ] .
p ( θ ¯ ) = ( p a + p c ) / 2 = p .
p t p ,
α = exp - ( k ¯ c v 1 3 ) ,
k ¯ = 0 k ( λ ) I ( λ ) d λ 0 I ( λ ) d λ ,
F 2 / F 1 = q · α = q · exp ( - k ¯ c v 1 3 ) .
E i i - E i j E i i + E i j = p F ;             E i j = E i i 1 - p F 1 + p F             ( i j ) ;
q I i α = E i 1 + E i 2 + E i 3 = E i i + 2 E i j ,
E i i = α q I i 1 + p F 3 - p F ;             E i j = α q I i 1 - p F 3 - p F .
S r = I 3 ( 1 - α ) + E 13 + E 23 + E 33 ,
S r = ( 1 - α ) I 3 + α q [ ( I 1 + I 2 ) ( 1 - p F 3 - p F ) + I 3 ( 1 + p F 3 - p F ) ] ,
S v = ( 1 - α ) I 1 + α q [ ( 1 + p F 3 - p F ) I 1 + ( I 2 + I 3 ) ( 1 - p F 3 - p F ) ] .
S r = ( 1 - α ) I + α q ( I + I ) ( 1 - p F 3 - p F ) + α q I ( 1 + p F 3 - p F ) = i .
S v = ( 1 - α ) I + α q I ( 1 + p F 3 - p F ) + 2 α q I ( 1 - p F 3 - p F ) = i .
p t = i - i i + i , p t = p 1 - α [ 1 - ( 2 q p F / 3 - p F ) ] 1 - α ( 1 - q [ 1 - p ( 1 - p F / 3 - p F ) ] ) .
p t p ( 1 - α / 2 ) ,
p t p ( 1 - α ) .
Δ I = I - I = I 2 p ( 1 - p ) .
Δ i i Δ I I = 2 p 1 - p ,
p 3 2 δ ¯ i .
2 3 δ ¯ Δ i < Δ p p < δ ¯ Δ i .
δ ¯ / Δ i 5.10 - 3 .
1 p · d p d θ = - d d θ [ 2 cos 2 θ tan 2 θ ] 1 + 2 ( cos 2 θ / tan 2 θ ) , Δ p p - 4 tan θ ( 1 + sin 2 θ tan 2 θ + 2 cos 2 θ ) Δ θ .