Advertisement

The Analysis of Polydisperse Scattering Data

  • E. R. Pike
Part of the NATO Advanced Study Institutes Series book series (NSSB, volume 73)

Abstract

There will be no need at this school for a lengthy introduction to the problem outlined in my title. It is well-known that light scattering from a suspension of macromolecules undergoing Brownian motion can be used to gain information about their size and shape. In particular, for spherical monodisperse particles the normalised “self-beat” photon correlation function, g(2)(τ), of the scattered light has the simple exponential form
$${g^{\left( 2 \right)}}\left( \tau \right) = 1 + C{\left| {{g^{\left( 1 \right)}}\left( \tau \right)} \right|^2} = 1 + C{e^{ - 2{D_T}{K^2}\tau }}$$
(1)
where K is the scattering wave vector, C is an experimental constant, g(1)(τ) is the first-order correlation function (the Fourier transform of the optical spectrum) and DT is the linear translational diffusion coefficient, related to the particle radius, a, by the Stokes-Einstein relation
$$ {\text{D = }}\frac{{{\text{kT}}}}{{{\text{6}}\pi \eta {\text{a}}}} $$
(2)
η is the kinematic viscosity of the medium, T the temperature and k, Boltzmann’s constant.

Keywords

Parameter Inversion Error Ellipsoid Unshaded Region Scatter Wave Vector Exponential Sampling 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Photon Correlation and Light Beating Spectroscopy, H. Z. Cummins and E. R. Pike, eds. (Plenum, New York, 1974).Google Scholar
  2. 2.
    Photon Correlation Spectrometry and Velocimetry, H. Z. Cummins and E. R. Pike, eds. (Plenum, New York, 1977).Google Scholar
  3. 3.
    M. Bertero, C. de Mol, and G. A. Viano, Inverse Scattering Problems in Optics, H. P. Baltes, ed. (Springer, Berlin, 1980).Google Scholar
  4. 4.
    J. G. McWhirter and E. R. Pike, J. Phys. A: Math. Gen. 11: 1729 (1978).MathSciNetADSCrossRefGoogle Scholar
  5. 5.
    A Tikhonov and V. Arsenine, Methodes de Resolution des Problèmes Mal Posés (Mir, Moscow, 1976).Google Scholar
  6. 6.
    G. F. Miller, Numerical Solution of Integral Equations, L. M. Delves and J. Walsh, eds. (Clarendon Press, Oxford, 1974).Google Scholar
  7. 7.
    S. Twomey, J. Franklin Inst. 279: 95 (1965).MathSciNetCrossRefGoogle Scholar
  8. 8.
    J. G. McWhirter, Optica Acta 27: 83 (1980).ADSCrossRefGoogle Scholar
  9. 9.
    B. Chu, Es Gulari, and Er Gulari, Physica Scripta 19: 476 (1979).ADSCrossRefGoogle Scholar
  10. 10.
    E. Jakeman, E. R. Pike, and S. Swain, J. Phys. A: Gen. Phys. 4: 517 (1971).ADSCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1981

Authors and Affiliations

  • E. R. Pike
    • 1
  1. 1.Royal Signals and Radar EstablishmentMalvernUK

Personalised recommendations