Abstract

The various instrumental factors which affect both peak and integrated Raman band intensities in liquids are discussed. These factors include the refractive index, color, and temperature of the sample; slit function and spectral sensitivity of the spectrophotometer; and the convergence and line width of the exciting radiation. Procedures for applying corrections for these factors relative to the 459 cm−1 band of carbon tetrachloride are presented. These considerations will allow good relative band areas to be obtained and will facilitate the interchangability of peak intensity data between different laboratories.

© 1959 Optical Society of America

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References

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  1. White, Alpert, and de Bell, Opt Soc. Am. 45, 154 (1955).
    [CrossRef]
  2. H. H. Cary, J. Opt. Soc. Am. (to be published).
  3. H. J. Bernstein and G. Allen, J. Opt. Soc. Am. 45, 237 (1955).
    [CrossRef]
  4. Long, Milner, and Thomas, Proc. Roy. Soc. (London) 237A, 197 (1956).
  5. S. R. Polo and M. K. Wilson, J. Chem. Phys. 23, 2376 (1955).
    [CrossRef]
  6. W. C. Mallard and J. W. Straley, J. Chem. Phys. 27, 877 (1957).
    [CrossRef]
  7. L. A. Woodward and J. H. B. George, Proc. Phys. Soc. (London) 64, 780 (1951).
    [CrossRef]
  8. J. H. Jaffe and S. Kimel, J. Chem. Phys. 25, 374 (1956).
    [CrossRef]
  9. R. A. Russell and H. W. Thompson, J. Chem. Soc. 479 (1955).
  10. E. E. Ferguson, J. Chem. Phys. 26, 1265 (1957).
    [CrossRef]
  11. D. A. Ramsay, J. Am. Chem. Soc. 74, 72 (1952).
    [CrossRef]
  12. P. C. von Planta, J. Opt. Soc. Am. 47, 629 (1957).
    [CrossRef]
  13. Kh. E. Sterin, Izvest. Akad. Nauk. S.S.S.R. Ser. Fiz. 14, 411 (1950).
  14. G. Placzek, Handbuch der Radiologie VI (Leipzig, Germany, 1934), p. 2.
  15. D. H. Rank and R. E. Kagarise, J. Opt. Soc. Am. 40, 89 (1950).
    [CrossRef]
  16. D. R. J. Boyd (private communication).
  17. B. P. Stoicheff, Can. J. Phys. 32, 330 (1954).
    [CrossRef]
  18. Rosenbaum, Cerato, and Lauer, J. Opt. Soc. Am. 42, 670 (1952).
    [CrossRef]

1957 (3)

W. C. Mallard and J. W. Straley, J. Chem. Phys. 27, 877 (1957).
[CrossRef]

E. E. Ferguson, J. Chem. Phys. 26, 1265 (1957).
[CrossRef]

P. C. von Planta, J. Opt. Soc. Am. 47, 629 (1957).
[CrossRef]

1956 (2)

J. H. Jaffe and S. Kimel, J. Chem. Phys. 25, 374 (1956).
[CrossRef]

Long, Milner, and Thomas, Proc. Roy. Soc. (London) 237A, 197 (1956).

1955 (4)

S. R. Polo and M. K. Wilson, J. Chem. Phys. 23, 2376 (1955).
[CrossRef]

R. A. Russell and H. W. Thompson, J. Chem. Soc. 479 (1955).

H. J. Bernstein and G. Allen, J. Opt. Soc. Am. 45, 237 (1955).
[CrossRef]

White, Alpert, and de Bell, Opt Soc. Am. 45, 154 (1955).
[CrossRef]

1954 (1)

B. P. Stoicheff, Can. J. Phys. 32, 330 (1954).
[CrossRef]

1952 (2)

1951 (1)

L. A. Woodward and J. H. B. George, Proc. Phys. Soc. (London) 64, 780 (1951).
[CrossRef]

1950 (2)

Kh. E. Sterin, Izvest. Akad. Nauk. S.S.S.R. Ser. Fiz. 14, 411 (1950).

D. H. Rank and R. E. Kagarise, J. Opt. Soc. Am. 40, 89 (1950).
[CrossRef]

Allen, G.

Alpert,

White, Alpert, and de Bell, Opt Soc. Am. 45, 154 (1955).
[CrossRef]

Bernstein, H. J.

Boyd, D. R. J.

D. R. J. Boyd (private communication).

Cary, H. H.

H. H. Cary, J. Opt. Soc. Am. (to be published).

Cerato,

de Bell,

White, Alpert, and de Bell, Opt Soc. Am. 45, 154 (1955).
[CrossRef]

Ferguson, E. E.

E. E. Ferguson, J. Chem. Phys. 26, 1265 (1957).
[CrossRef]

George, J. H. B.

L. A. Woodward and J. H. B. George, Proc. Phys. Soc. (London) 64, 780 (1951).
[CrossRef]

Jaffe, J. H.

J. H. Jaffe and S. Kimel, J. Chem. Phys. 25, 374 (1956).
[CrossRef]

Kagarise, R. E.

Kimel, S.

J. H. Jaffe and S. Kimel, J. Chem. Phys. 25, 374 (1956).
[CrossRef]

Lauer,

Long,

Long, Milner, and Thomas, Proc. Roy. Soc. (London) 237A, 197 (1956).

Mallard, W. C.

W. C. Mallard and J. W. Straley, J. Chem. Phys. 27, 877 (1957).
[CrossRef]

Milner,

Long, Milner, and Thomas, Proc. Roy. Soc. (London) 237A, 197 (1956).

Placzek, G.

G. Placzek, Handbuch der Radiologie VI (Leipzig, Germany, 1934), p. 2.

Polo, S. R.

S. R. Polo and M. K. Wilson, J. Chem. Phys. 23, 2376 (1955).
[CrossRef]

Ramsay, D. A.

D. A. Ramsay, J. Am. Chem. Soc. 74, 72 (1952).
[CrossRef]

Rank, D. H.

Rosenbaum,

Russell, R. A.

R. A. Russell and H. W. Thompson, J. Chem. Soc. 479 (1955).

Sterin, Kh. E.

Kh. E. Sterin, Izvest. Akad. Nauk. S.S.S.R. Ser. Fiz. 14, 411 (1950).

Stoicheff, B. P.

B. P. Stoicheff, Can. J. Phys. 32, 330 (1954).
[CrossRef]

Straley, J. W.

W. C. Mallard and J. W. Straley, J. Chem. Phys. 27, 877 (1957).
[CrossRef]

Thomas,

Long, Milner, and Thomas, Proc. Roy. Soc. (London) 237A, 197 (1956).

Thompson, H. W.

R. A. Russell and H. W. Thompson, J. Chem. Soc. 479 (1955).

von Planta, P. C.

White,

White, Alpert, and de Bell, Opt Soc. Am. 45, 154 (1955).
[CrossRef]

Wilson, M. K.

S. R. Polo and M. K. Wilson, J. Chem. Phys. 23, 2376 (1955).
[CrossRef]

Woodward, L. A.

L. A. Woodward and J. H. B. George, Proc. Phys. Soc. (London) 64, 780 (1951).
[CrossRef]

Can. J. Phys. (1)

B. P. Stoicheff, Can. J. Phys. 32, 330 (1954).
[CrossRef]

Izvest. Akad. Nauk. S.S.S.R. Ser. Fiz. (1)

Kh. E. Sterin, Izvest. Akad. Nauk. S.S.S.R. Ser. Fiz. 14, 411 (1950).

J. Am. Chem. Soc. (1)

D. A. Ramsay, J. Am. Chem. Soc. 74, 72 (1952).
[CrossRef]

J. Chem. Phys. (4)

S. R. Polo and M. K. Wilson, J. Chem. Phys. 23, 2376 (1955).
[CrossRef]

W. C. Mallard and J. W. Straley, J. Chem. Phys. 27, 877 (1957).
[CrossRef]

J. H. Jaffe and S. Kimel, J. Chem. Phys. 25, 374 (1956).
[CrossRef]

E. E. Ferguson, J. Chem. Phys. 26, 1265 (1957).
[CrossRef]

J. Chem. Soc. (1)

R. A. Russell and H. W. Thompson, J. Chem. Soc. 479 (1955).

J. Opt. Soc. Am. (4)

Opt Soc. Am. (1)

White, Alpert, and de Bell, Opt Soc. Am. 45, 154 (1955).
[CrossRef]

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

L. A. Woodward and J. H. B. George, Proc. Phys. Soc. (London) 64, 780 (1951).
[CrossRef]

Proc. Roy. Soc. (London) (1)

Long, Milner, and Thomas, Proc. Roy. Soc. (London) 237A, 197 (1956).

Other (3)

H. H. Cary, J. Opt. Soc. Am. (to be published).

D. R. J. Boyd (private communication).

G. Placzek, Handbuch der Radiologie VI (Leipzig, Germany, 1934), p. 2.

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Figures (17)

Fig. 1
Fig. 1

Path of exciting radiation through cross section of Raman tube.

Fig. 2
Fig. 2

Path of exciting radiation through liquid cross section.

Fig. 3
Fig. 3

Positions in the Raman tube of the cylinder of liquid scattering and the cylinder in which exciting intensity is constant.

Fig. 4
Fig. 4

Optical effect for 60-ml tube.

Fig. 5
Fig. 5

Optical effect for 5-ml Pyrex tube.

Fig. 6
Fig. 6

Optical effect for 5-ml Kimble flint glass tube.

Fig. 7
Fig. 7

Internal field effect on integrated intensity of 459 cm−1 band of CCl4 in solutions of CCl4 in various solvents.

Fig. 8
Fig. 8

Spectrophotometer slit function for various slit widths.

Fig. 9
Fig. 9

Variation of spectral slit width with wave number shift.

Fig. 10
Fig. 10

Variation of observed band width with spectral slit width for benzene and cyclohexane bands.

Fig. 11
Fig. 11

Variation of observed band width with spectral slit width for 314 cm−1 band of CCl4.

Fig. 12
Fig. 12

Dependence of intensity on mechanical slit width for a continuous spectrum.

Fig. 13
Fig. 13

Dependence of peak intensity on spectral slit width for 992 cm−1 band of benzene, the contribution of the mechanical slit width, f(w,ν0), is factored out.

Fig. 14
Fig. 14

Dependence of peak intensity on spectral slit width for 802 cm−1 band of cyclohexane.

Fig. 15
Fig. 15

Dependence of peak intensity on spectral slit width for 314 cm−1 band of CCl4.

Fig. 16
Fig. 16

Dependence of intensity on absorbance of sample at Raman line, the absorbance is for a 1-cm path length in the liquid.

Fig. 17
Fig. 17

Dependence of intensity on absorbance of sample at exciting line, the aborbance is for a 1-cm path length in the liquid.

Tables (3)

Tables Icon

Table I Internal field effect (Rint)CCl4/Rint for the integrated (limits 415 cm−1 and 505 cm−1) area of the 459 cm−1 band of CCl4 in various solvents.

Tables Icon

Table II Temperature dependence of bands of 1,1,1-trichloroethane.

Tables Icon

Table III Dependence of the temperature correction on wave number shift and on temperature.

Equations (37)

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A liq A air = 1 n E ( n E 2 + 2 3 ) 2 ,
A sol A air = n 0 3 ( n 2 + 2 n 2 + 2 n 0 2 ) 2 ,
( 1 - R ) + R ( 1 - R ) + R 2 ( 1 - R ) + = ( 1 - R ) α = 0 R α = ( 1 - R ) 1 1 - R = 1.
sin i 1 = n E sin i 4 ,
I 0 cos i 1 d S d i 1 d C ,
d C = 2 ( 1 - r 2 x 2 sin 2 i 4 ) - 1 2 d x ,
cos i 1 d i 1 = n E cos i 4 d i 4 .
I eff d x d i 4 d S = I 0 2 ( 1 - r 2 x 2 sin 2 i 4 ) - 1 2 n E cos i 4 d i 4 d x d S .
for             x r < 1 n E : I eff d x d S = 2 π I 0 n E x r d x d S
x r > 1 n E : I eff d x d S = 4 I 0 n E x r sin - 1 r n E x d x d S .
x r < 1 n E : I eff d x d l = 4 π 2 I 0 n E x d x d l
x r > 1 n E : I eff d x d l = 8 π I 0 n E x sin - 1 r n E x d x d l .
I eff d x d l = I x 2 π x d x d l .
x r < 1 n E : I x = 2 π n E I 0 x r > 1 n E : I x = 4 n E I 0 sin - 1 r n E x .
1 / R opt = 1 / n ,
I obs = I corr / R opt R int ,
I obs ( I obs ) CCl 4 = I corr ( I corr ) CCl 4 ( R opt ) CCl 4 R opt ( R int ) CCl 4 R int .
I obs ( I obs ) CCl 4 = I corr ( I corr ) CCl 4 n CCl 4 n ( R int ) CCl 4 R int .
I corr ( I corr ) CCl 4 = V 100 ,
i obs ( ν ) = 0 S ( μ , ν ) i T ( μ ) d μ .
S ( ν , ν ) = f ( w , ν ) g ( ν , ν ) ,
0 g ( ν , ν ) d ν 1.
i obs ( ν 0 ) = f ( w , ν 0 ) 0 i T ( μ ) g ( μ , ν 0 ) d μ .
i T ( ν ) g ( μ , ν 0 ) d μ = i obs ( ν 0 ) f ( w , ν 0 ) .
lim s 0 g ( μ , ν 0 ) = δ ( ν 0 )
lim s 0 0 i T ( μ ) g ( μ , ν 0 ) d μ = i T ( ν 0 ) .
lim s 0 i obs ( ν 0 ) f ( w , ν 0 ) = i T ( ν 0 ) .
I obs ( Δ ν ) = I corr ( Δ ν ) T 1 ( A 0 ) T 2 ( A Δ ν ) ,
I obs = c I 0 T 1 ( c 0 ) T 2 ( c Δ ν ) .
ln 1 T 1 = a 1 ( 0 c ) + b 1 ( Δ ν c ) 2
ln 1 T 2 = a 2 ( Δ ν c ) + b 2 ( Δ ν c ) 2 .
2 ( b 1 0 2 + b 2 Δ ν 2 ) c opt 2 + ( a 1 0 + a 2 Δ ν ) c opt - 1 = 0.
I 1 1 - e - h c Δ ν / k T ,
I corr = I obs ( 1 + ρ obs ) ,
I obs = I + I .
I corr = I obs 1 + ρ obs = I + I 1 + ( I / I ) = I .
I corr = I obs ( 1 - e - h c Δ ν / k T ) .