Abstract

In this paper we study the possibility of analyzing solutions of mixtures of spherical and cylindrical macromolecules, impinging on them with laser light and measuring the normalized second-order factorial moment, n(2)(T), of the scattered light. With this method we intend to determine the quotient of concentrations of the two solute fractions or the molecular weight of one of the components. The errors in these measurements are studied by means of a computer simulation method. The validity of the simulation method is experimentally proved with a mixture of two kinds of spherical particles of different size.

© 1982 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. E. Koppel, J. Chem. Phys. 57, 4814 (1972).
    [CrossRef]
  2. P. N. Pusey, in Photon Correlation and Light Beating Spectroscopy, H. Z. Cummins, E. R. Pike, Eds. (Plenum, London, 1974).
  3. Y. Tagami, R. Pecora, J. Chem. Phys. 51, 3293 (1969).
    [CrossRef]
  4. R. Pecora, Y. Tagami, J. Chem. Phys. 51, 3298 (1969).
    [CrossRef]
  5. S. R. Aragón, R. Pecora, J. Chem. Phys. 64, 2395 (1976).
    [CrossRef]
  6. A. P. Chaikovskii, Opt. Spectrosc. 40, 76 (1976).
  7. H. Z. Cummins, in Photon Correlation and Light Beating Spectroscopy, H. Z. Cummins, E. R. Pike, Eds. (Plenum, London, 1974).
  8. B. Saleh, Photoelectron Statistics (Springer, Berlin, 1978).
  9. J. C. Abad, M. A. Rebolledo, Spectrosc. Lett. 14, 123 (1981).
    [CrossRef]
  10. C. B. Bargeron, J. Chem. Phys. 60, 2516 (1974).
    [CrossRef]
  11. F. C. Chen, W. Tscharnuter, D. Schmidt, B. Chu, J. Chem. Phys. 60, 1675 (1974).
    [CrossRef]
  12. M. Corti, V. Degiorgio, M. Giglio, A. Vendramini, Opt. Commun. 23, 282 (1977).
    [CrossRef]
  13. S. B. Dubin, Ph.D. Thesis, MIT (1970).
  14. N. C. Ford, Chem. Scr. 2, 193 (1972).
  15. C. B. Bargeron, Appl. Phys. Lett. 23, 379 (1973).
    [CrossRef]
  16. J. Newman, H. L. Swinney, Biopolymers 15, 301 (1976).
    [CrossRef] [PubMed]
  17. R. Pecora, J. Chem. Phys. 48, 4126 (1968).
    [CrossRef]
  18. T. A. King, A. Knox, J. D. G. McAdam, Biopolymers 12, 1917 (1973).
    [CrossRef] [PubMed]

1981 (1)

J. C. Abad, M. A. Rebolledo, Spectrosc. Lett. 14, 123 (1981).
[CrossRef]

1977 (1)

M. Corti, V. Degiorgio, M. Giglio, A. Vendramini, Opt. Commun. 23, 282 (1977).
[CrossRef]

1976 (3)

S. R. Aragón, R. Pecora, J. Chem. Phys. 64, 2395 (1976).
[CrossRef]

A. P. Chaikovskii, Opt. Spectrosc. 40, 76 (1976).

J. Newman, H. L. Swinney, Biopolymers 15, 301 (1976).
[CrossRef] [PubMed]

1974 (2)

C. B. Bargeron, J. Chem. Phys. 60, 2516 (1974).
[CrossRef]

F. C. Chen, W. Tscharnuter, D. Schmidt, B. Chu, J. Chem. Phys. 60, 1675 (1974).
[CrossRef]

1973 (2)

C. B. Bargeron, Appl. Phys. Lett. 23, 379 (1973).
[CrossRef]

T. A. King, A. Knox, J. D. G. McAdam, Biopolymers 12, 1917 (1973).
[CrossRef] [PubMed]

1972 (2)

N. C. Ford, Chem. Scr. 2, 193 (1972).

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

1969 (2)

Y. Tagami, R. Pecora, J. Chem. Phys. 51, 3293 (1969).
[CrossRef]

R. Pecora, Y. Tagami, J. Chem. Phys. 51, 3298 (1969).
[CrossRef]

1968 (1)

R. Pecora, J. Chem. Phys. 48, 4126 (1968).
[CrossRef]

Abad, J. C.

J. C. Abad, M. A. Rebolledo, Spectrosc. Lett. 14, 123 (1981).
[CrossRef]

Aragón, S. R.

S. R. Aragón, R. Pecora, J. Chem. Phys. 64, 2395 (1976).
[CrossRef]

Bargeron, C. B.

C. B. Bargeron, J. Chem. Phys. 60, 2516 (1974).
[CrossRef]

C. B. Bargeron, Appl. Phys. Lett. 23, 379 (1973).
[CrossRef]

Chaikovskii, A. P.

A. P. Chaikovskii, Opt. Spectrosc. 40, 76 (1976).

Chen, F. C.

F. C. Chen, W. Tscharnuter, D. Schmidt, B. Chu, J. Chem. Phys. 60, 1675 (1974).
[CrossRef]

Chu, B.

F. C. Chen, W. Tscharnuter, D. Schmidt, B. Chu, J. Chem. Phys. 60, 1675 (1974).
[CrossRef]

Corti, M.

M. Corti, V. Degiorgio, M. Giglio, A. Vendramini, Opt. Commun. 23, 282 (1977).
[CrossRef]

Cummins, H. Z.

H. Z. Cummins, in Photon Correlation and Light Beating Spectroscopy, H. Z. Cummins, E. R. Pike, Eds. (Plenum, London, 1974).

Degiorgio, V.

M. Corti, V. Degiorgio, M. Giglio, A. Vendramini, Opt. Commun. 23, 282 (1977).
[CrossRef]

Dubin, S. B.

S. B. Dubin, Ph.D. Thesis, MIT (1970).

Ford, N. C.

N. C. Ford, Chem. Scr. 2, 193 (1972).

Giglio, M.

M. Corti, V. Degiorgio, M. Giglio, A. Vendramini, Opt. Commun. 23, 282 (1977).
[CrossRef]

King, T. A.

T. A. King, A. Knox, J. D. G. McAdam, Biopolymers 12, 1917 (1973).
[CrossRef] [PubMed]

Knox, A.

T. A. King, A. Knox, J. D. G. McAdam, Biopolymers 12, 1917 (1973).
[CrossRef] [PubMed]

Koppel, D. E.

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

McAdam, J. D. G.

T. A. King, A. Knox, J. D. G. McAdam, Biopolymers 12, 1917 (1973).
[CrossRef] [PubMed]

Newman, J.

J. Newman, H. L. Swinney, Biopolymers 15, 301 (1976).
[CrossRef] [PubMed]

Pecora, R.

S. R. Aragón, R. Pecora, J. Chem. Phys. 64, 2395 (1976).
[CrossRef]

Y. Tagami, R. Pecora, J. Chem. Phys. 51, 3293 (1969).
[CrossRef]

R. Pecora, Y. Tagami, J. Chem. Phys. 51, 3298 (1969).
[CrossRef]

R. Pecora, J. Chem. Phys. 48, 4126 (1968).
[CrossRef]

Pusey, P. N.

P. N. Pusey, in Photon Correlation and Light Beating Spectroscopy, H. Z. Cummins, E. R. Pike, Eds. (Plenum, London, 1974).

Rebolledo, M. A.

J. C. Abad, M. A. Rebolledo, Spectrosc. Lett. 14, 123 (1981).
[CrossRef]

Saleh, B.

B. Saleh, Photoelectron Statistics (Springer, Berlin, 1978).

Schmidt, D.

F. C. Chen, W. Tscharnuter, D. Schmidt, B. Chu, J. Chem. Phys. 60, 1675 (1974).
[CrossRef]

Swinney, H. L.

J. Newman, H. L. Swinney, Biopolymers 15, 301 (1976).
[CrossRef] [PubMed]

Tagami, Y.

Y. Tagami, R. Pecora, J. Chem. Phys. 51, 3293 (1969).
[CrossRef]

R. Pecora, Y. Tagami, J. Chem. Phys. 51, 3298 (1969).
[CrossRef]

Tscharnuter, W.

F. C. Chen, W. Tscharnuter, D. Schmidt, B. Chu, J. Chem. Phys. 60, 1675 (1974).
[CrossRef]

Vendramini, A.

M. Corti, V. Degiorgio, M. Giglio, A. Vendramini, Opt. Commun. 23, 282 (1977).
[CrossRef]

Appl. Phys. Lett. (1)

C. B. Bargeron, Appl. Phys. Lett. 23, 379 (1973).
[CrossRef]

Biopolymers (2)

J. Newman, H. L. Swinney, Biopolymers 15, 301 (1976).
[CrossRef] [PubMed]

T. A. King, A. Knox, J. D. G. McAdam, Biopolymers 12, 1917 (1973).
[CrossRef] [PubMed]

Chem. Scr. (1)

N. C. Ford, Chem. Scr. 2, 193 (1972).

J. Chem. Phys. (7)

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

R. Pecora, J. Chem. Phys. 48, 4126 (1968).
[CrossRef]

Y. Tagami, R. Pecora, J. Chem. Phys. 51, 3293 (1969).
[CrossRef]

R. Pecora, Y. Tagami, J. Chem. Phys. 51, 3298 (1969).
[CrossRef]

S. R. Aragón, R. Pecora, J. Chem. Phys. 64, 2395 (1976).
[CrossRef]

C. B. Bargeron, J. Chem. Phys. 60, 2516 (1974).
[CrossRef]

F. C. Chen, W. Tscharnuter, D. Schmidt, B. Chu, J. Chem. Phys. 60, 1675 (1974).
[CrossRef]

Opt. Commun. (1)

M. Corti, V. Degiorgio, M. Giglio, A. Vendramini, Opt. Commun. 23, 282 (1977).
[CrossRef]

Opt. Spectrosc. (1)

A. P. Chaikovskii, Opt. Spectrosc. 40, 76 (1976).

Spectrosc. Lett. (1)

J. C. Abad, M. A. Rebolledo, Spectrosc. Lett. 14, 123 (1981).
[CrossRef]

Other (4)

P. N. Pusey, in Photon Correlation and Light Beating Spectroscopy, H. Z. Cummins, E. R. Pike, Eds. (Plenum, London, 1974).

H. Z. Cummins, in Photon Correlation and Light Beating Spectroscopy, H. Z. Cummins, E. R. Pike, Eds. (Plenum, London, 1974).

B. Saleh, Photoelectron Statistics (Springer, Berlin, 1978).

S. B. Dubin, Ph.D. Thesis, MIT (1970).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Scheme of the variable angle scattering system consisting of two optical benchs (B1, B2), a laser (L), two mirrors (M1, M2), a scattering cell (C), a linear polarizer (P), two diaphragms (D1, D2), and the detection system (D).

Fig. 2
Fig. 2

Diagram of the detection and data processing system consisting of a shielded and refrigerated photomultiplier (PH), an amplifier–discriminator (AD), a counter (C), a signal synthesizer (S), and a minicomputer (COM).

Fig. 3
Fig. 3

Relative error (·) in percent in the determination of α for the ten mixtures of spheres of the last column in Table II. The full line was obtained from a least-squares fit to the experimental points and corresponds to the equation: error (%) = 0.3545/(D/Di − 1) + 0.05128.

Fig. 4
Fig. 4

Relative errors (·) in obtaining α vs α for the most representative case. The full line was obtained from a least-squares fit to the experimental points and corresponds to the equation: error = 0.9292 × 10−2 − 0.448 × 10−3X + 0.997 × 10−3X2 − 0.371 × 10−4X3 + 0.124 × 10−3X4.

Tables (3)

Tables Icon

Table I Agreement Between the Values Obtained for the Error in α from Fast Simulation and Experimentally

Tables Icon

Table II Errors in Percent Obtained in the Determination of α from Ten Series and 108 Samples in Each Series

Tables Icon

Table III Coefficients for the Calculation of the Error fiin α from the Error f obtained from the Curve In Fig. 4 (fi= a + bf)

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

g ( 2 ) ( τ ) = 1 + C [ g 1 ( 1 ) ( τ ) 2 ( 1 + α ) 2 + g 2 ( 1 ) ( τ ) 2 ( 1 + α - 1 ) 2 + 2 g 1 ( 1 ) ( τ ) g 2 ( 1 ) ( τ ) ( 1 + α ) ( 1 + α - 1 ) ] ,
α = I 2 / I 1 .
c 2 c 1 = α [ M 1 P 1 ( θ ) ( d n / d c ) 1 2 M 2 P 2 ( θ ) ( d n / d c ) 2 2 ] = constant · α ,
2 T 2 [ T 2 n ( 2 ) ( T ) ] = 2 g ( 2 ) ( T ) ,
σ 2 [ n ( 2 ) ] 2 n ( 2 ) N { [ n ( 2 ) - 1 ] [ n ( 2 ) - 1 + 2 n ¯ ] + 1 n ¯ 2 } ,
n ( 2 ) ( T ) = 1 + C { F ( γ 1 ) ( 1 + α ) 2 + F ( γ 2 ) ( 1 + α - 1 ) 2 + 2 F ( γ 1 + γ 2 ) / 2 ( 1 + α ) ( 1 + α - 1 ) } , γ i = Γ i T ,             F ( γ ) = γ - 1 - γ - 2 / 2 + γ - 2 · exp ( - 2 γ ) / 2 , Γ i = 16 π n 2 sin 2 ( θ / 2 ) K B t 6 η λ 2 r i ,
n ( 2 ) ( T ) = 1 + C · { F ( γ s ) ( 1 + α ) 2 + b 0 2 F ( γ 0 r ) + b 1 2 F ( γ 1 r ) + 2 b 0 b 1 F [ ( γ 0 r + γ 1 r ) / 2 ] ( 1 + α - 1 ) 2 + 2 b 0 F [ ( γ s + γ 0 r ) / 2 ] + 2 b 1 F [ ( γ s + γ 1 r ) / 2 ] ( 1 + α ) ( 1 + α - 1 ) 2 } = 1 + C · f ( α , T ) , γ s = Γ s · T , γ 0 r = Γ 0 r · T , γ 1 r = Γ 1 r · T , Γ s = D T s · K 2 , Γ 0 r = D T r K 2 , Γ 1 r = D T r · K 2 + 6 D R r , α = I r / I s , b i = B i / B , B = i ( B i ) ,
R = 0.92 , dispersion in R = 7.9 % .
R = 0.69 , dispersion in R = 44 % .
R = 0.50 , dispersion in R = 54 % .

Metrics