Abstract

The method of cumulants is a standard technique used to analyze dynamic light-scattering data measured for polydisperse samples. These data, from an intensity–intensity autocorrelation function of the scattered light, can be described in terms of a distribution of decay rates. The method of cumulants provides information about the cumulants and the moments of this distribution. However, the method does not permit independent determination of the long-time baseline of the intensity correlation function and can lead to inconsistent results when different numbers of data points are included in the fit. The method is reformulated in terms of the moments about the mean to permit more robust and satisfactory fits. The different versions of the method are compared by analysis of the data for polydisperse-vesicle samples.

© 2001 Optical Society of America

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References

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  1. D. E. Koppel, “Analysis of macromolecular polydispersity in intensity correlation spectroscopy: the method of cumulants,” J. Chem. Phys. 57, 4814–4820 (1972).
    [CrossRef]
  2. B. J. Berne, R. Pecora, Dynamic Light Scattering (Krieger, Malabar, Fla., 1990).
  3. P. Stepanek, “Data analysis in dynamic light scattering,” in Dynamic Light Scattering, W. Brown, ed. (Oxford University, Oxford, UK, 1993), pp. 177–240.
  4. R. Pecora, Dynamic Light Scattering (Plenum, New York, 1985).
    [CrossRef]
  5. B. Chu, Laser Light Scattering: Basic Principles and Practice (Academic, Boston, 1991).
  6. K. Schätzel, “Single-photon correlation techniques,” in Dynamic Light Scattering, W. Brown, ed. (Oxford University, Oxford, UK, 1993), pp. 76–148.
  7. A. Stuart, J. K. Ord, Kendall’s Advanced Theory of Statistics (Wiley, New York, 1994), Chap. 4.
  8. P. N. Pusey, D. E. Koppel, D. W. Schaefer, R. D. Camerini-Otero, S. H. Koenig, “Intensity fluctuation spectroscopy of laser light scattered by solutions of spherical viruses,” Biochemistry 13, 952–960 (1974).
    [CrossRef] [PubMed]
  9. For details of extrusion methods for vesicle production as used in these experiments, please see B. J. Frisken, C. Asman, P. J. Patty, “Studies of vesicle extrusion,” Langmuir 16, 928–933 (2000), and references therein.

2000 (1)

For details of extrusion methods for vesicle production as used in these experiments, please see B. J. Frisken, C. Asman, P. J. Patty, “Studies of vesicle extrusion,” Langmuir 16, 928–933 (2000), and references therein.

1974 (1)

P. N. Pusey, D. E. Koppel, D. W. Schaefer, R. D. Camerini-Otero, S. H. Koenig, “Intensity fluctuation spectroscopy of laser light scattered by solutions of spherical viruses,” Biochemistry 13, 952–960 (1974).
[CrossRef] [PubMed]

1972 (1)

D. E. Koppel, “Analysis of macromolecular polydispersity in intensity correlation spectroscopy: the method of cumulants,” J. Chem. Phys. 57, 4814–4820 (1972).
[CrossRef]

Asman, C.

For details of extrusion methods for vesicle production as used in these experiments, please see B. J. Frisken, C. Asman, P. J. Patty, “Studies of vesicle extrusion,” Langmuir 16, 928–933 (2000), and references therein.

Berne, B. J.

B. J. Berne, R. Pecora, Dynamic Light Scattering (Krieger, Malabar, Fla., 1990).

Camerini-Otero, R. D.

P. N. Pusey, D. E. Koppel, D. W. Schaefer, R. D. Camerini-Otero, S. H. Koenig, “Intensity fluctuation spectroscopy of laser light scattered by solutions of spherical viruses,” Biochemistry 13, 952–960 (1974).
[CrossRef] [PubMed]

Chu, B.

B. Chu, Laser Light Scattering: Basic Principles and Practice (Academic, Boston, 1991).

Frisken, B. J.

For details of extrusion methods for vesicle production as used in these experiments, please see B. J. Frisken, C. Asman, P. J. Patty, “Studies of vesicle extrusion,” Langmuir 16, 928–933 (2000), and references therein.

Koenig, S. H.

P. N. Pusey, D. E. Koppel, D. W. Schaefer, R. D. Camerini-Otero, S. H. Koenig, “Intensity fluctuation spectroscopy of laser light scattered by solutions of spherical viruses,” Biochemistry 13, 952–960 (1974).
[CrossRef] [PubMed]

Koppel, D. E.

P. N. Pusey, D. E. Koppel, D. W. Schaefer, R. D. Camerini-Otero, S. H. Koenig, “Intensity fluctuation spectroscopy of laser light scattered by solutions of spherical viruses,” Biochemistry 13, 952–960 (1974).
[CrossRef] [PubMed]

D. E. Koppel, “Analysis of macromolecular polydispersity in intensity correlation spectroscopy: the method of cumulants,” J. Chem. Phys. 57, 4814–4820 (1972).
[CrossRef]

Ord, J. K.

A. Stuart, J. K. Ord, Kendall’s Advanced Theory of Statistics (Wiley, New York, 1994), Chap. 4.

Patty, P. J.

For details of extrusion methods for vesicle production as used in these experiments, please see B. J. Frisken, C. Asman, P. J. Patty, “Studies of vesicle extrusion,” Langmuir 16, 928–933 (2000), and references therein.

Pecora, R.

R. Pecora, Dynamic Light Scattering (Plenum, New York, 1985).
[CrossRef]

B. J. Berne, R. Pecora, Dynamic Light Scattering (Krieger, Malabar, Fla., 1990).

Pusey, P. N.

P. N. Pusey, D. E. Koppel, D. W. Schaefer, R. D. Camerini-Otero, S. H. Koenig, “Intensity fluctuation spectroscopy of laser light scattered by solutions of spherical viruses,” Biochemistry 13, 952–960 (1974).
[CrossRef] [PubMed]

Schaefer, D. W.

P. N. Pusey, D. E. Koppel, D. W. Schaefer, R. D. Camerini-Otero, S. H. Koenig, “Intensity fluctuation spectroscopy of laser light scattered by solutions of spherical viruses,” Biochemistry 13, 952–960 (1974).
[CrossRef] [PubMed]

Schätzel, K.

K. Schätzel, “Single-photon correlation techniques,” in Dynamic Light Scattering, W. Brown, ed. (Oxford University, Oxford, UK, 1993), pp. 76–148.

Stepanek, P.

P. Stepanek, “Data analysis in dynamic light scattering,” in Dynamic Light Scattering, W. Brown, ed. (Oxford University, Oxford, UK, 1993), pp. 177–240.

Stuart, A.

A. Stuart, J. K. Ord, Kendall’s Advanced Theory of Statistics (Wiley, New York, 1994), Chap. 4.

Biochemistry (1)

P. N. Pusey, D. E. Koppel, D. W. Schaefer, R. D. Camerini-Otero, S. H. Koenig, “Intensity fluctuation spectroscopy of laser light scattered by solutions of spherical viruses,” Biochemistry 13, 952–960 (1974).
[CrossRef] [PubMed]

J. Chem. Phys. (1)

D. E. Koppel, “Analysis of macromolecular polydispersity in intensity correlation spectroscopy: the method of cumulants,” J. Chem. Phys. 57, 4814–4820 (1972).
[CrossRef]

Langmuir (1)

For details of extrusion methods for vesicle production as used in these experiments, please see B. J. Frisken, C. Asman, P. J. Patty, “Studies of vesicle extrusion,” Langmuir 16, 928–933 (2000), and references therein.

Other (6)

B. J. Berne, R. Pecora, Dynamic Light Scattering (Krieger, Malabar, Fla., 1990).

P. Stepanek, “Data analysis in dynamic light scattering,” in Dynamic Light Scattering, W. Brown, ed. (Oxford University, Oxford, UK, 1993), pp. 177–240.

R. Pecora, Dynamic Light Scattering (Plenum, New York, 1985).
[CrossRef]

B. Chu, Laser Light Scattering: Basic Principles and Practice (Academic, Boston, 1991).

K. Schätzel, “Single-photon correlation techniques,” in Dynamic Light Scattering, W. Brown, ed. (Oxford University, Oxford, UK, 1993), pp. 76–148.

A. Stuart, J. K. Ord, Kendall’s Advanced Theory of Statistics (Wiley, New York, 1994), Chap. 4.

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Figures (1)

Fig. 1
Fig. 1

Sample data taken for POPC vesicles formed by extrusion through polycarbonate membranes. The curve through the data is a fit of Eq. (23) to the data. The dashed curve shows the weighted residuals: the difference of the fit from the data divided by the uncertainty in each point.

Tables (4)

Tables Icon

Table 1 Fit of Eq. (17) to DLS Data for POPC Vesicles Extruded through 200-nm Poresa

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Table 2 Fit of Eq. (18) to DLS Data for POPC Vesicles Extruded through 200-nm Poresa

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Table 3 Fit of Eq. (23) to DLS Data for POPC Vesicles Extruded through 200-nm Poresa

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Table 4 Comparison of the Robustness of the Fits of Model Function 2 [Eq. (18)] and Model Function 3 [Eq. (23)] to DLS Data for POPC Vesicles Extruded through 200-nm Poresa

Equations (24)

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g2τ=ItIt+τIt2,
g2τ=B+βg1τ2,
g1τ=EtE*t+τEtE*t,
q=4πnλ0sinθ2,
g1τ=0 GΓexp-ΓτdΓ,
0 GΓdΓ=1.
M-τ, Γ=0 GΓexp-ΓτdΓg1τ.
mmΓ=dmM-τ, Γd-τm-τ=0=0 GΓΓm exp-ΓτdΓ|-τ=0.
K-τ, Γ=lnM-τ, Γlng1τ,
κmΓ=dmK-τ, Γd-τm-τ=0.
κ1Γ=0 GΓΓdΓΓ¯,
κ2Γ=μ2,
κ3Γ=μ3,
κ4Γ=μ4-3μ22  ,
μm=0 GΓΓ-Γ¯mdΓ.
lng1τK-τ, Γ=-Γ¯τ+κ22! τ2-κ33! τ3+κ44! τ4.
lng2τ-1=lnβ2-Γ¯τ+κ2τ22!-κ3τ33!+.
g2=B+β exp-2Γ¯τ+κ2τ2-κ33 τ3.
exp-Γτ=exp-Γ¯τexp-Γ-Γ¯τ.
g1τ=exp-Γτ0 GΓexp-Γ-Γ¯τdΓ.
g1τ=exp-Γ¯τ0 GΓ1-Γ-Γ¯τ+Γ-Γ¯22! τ2-Γ-Γ¯33! τ3+dΓ.
g1τ=exp-Γ¯τ1+μ22! τ2-μ33! τ3+.
g2=B+β exp-2Γ¯τ1+μ22! τ2-μ33! τ32.
χ2=1N-mi=1Nyi-fi2σi2,

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