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Overview ‧The Coherence Area ‧The Estimation of The Detected Power

Light Scattering Apparatus*. Overview ‧The Coherence Area ‧The Estimation of The Detected Power ‧Getting The Autocorrelation Function. 2007-2-1. * Dynamic Light Scattering: Applications of Photon Correlation Spectroscopy edited by R. Pecora (1985). The Coherence Area.

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Overview ‧The Coherence Area ‧The Estimation of The Detected Power

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  1. Light Scattering Apparatus* Overview ‧The Coherence Area ‧The Estimation of The Detected Power ‧Getting The Autocorrelation Function 2007-2-1 *Dynamic Light Scattering: Applications of Photon Correlation Spectroscopy edited by R. Pecora (1985)

  2. The Coherence Area • The intensity fluctuations are not usually observed for two reasons: • Taking place on a time scale faster than many photometers will respond • Taking place only at a point FIG. Geometry for calculating the intensity of light scattered from two molecules. The scattered intensity will depend on θ and d The fluctuations will be substantially the same as they would be at a point if the detector area is one coherence area or less: The Coherence Area: [Jakeman et al. 1970]

  3. FIG. Effect of the number of coherence areas on the fluctuations in the scattered light intensity. ‧Sample: 0.085 μm polystyrene latex spheres ‧The averaged scattered intensity was the same in (A)-(D) (by adjusting the laser power) ‧Detector radius: (A) < (B) < (C) < (D) [Jakeman et al. 1970] The Intensity Correlation Function g(2)(τ) Is: If the detector has an area exceeding a single coherence area, then FIG. Dependence of f(Ncoh) on the number of coherence areas Ncoh

  4. Spherical scattering volume with radius a The detector radius isb The Coherence Area: [Jakeman et al. 1970]

  5. The Estimation of The Detected Power It can be seen for the above equation that the scattered power PS into a single coherence area may be increased by decreasing the focal length of the entrance lens

  6. Delay Time τ (μs) C(τ) . . . . . . . . . . Shouldn’t be smaller than 10K or greater than 500K, otherwise an error message will be given Remark: The cleanliness of the solvent can be checked by putting some in a cuvette and monitoring the count rate. The steady count rate should be no more than a certain value

  7. Getting The Autocorrelation Function 0.002 wt% PS latex suspension Particle diameter ~ 300 nm • Use of One DAQ Card 3,000 data points to be stored 3,000 data points to be stored ‧ ‧ ‧ ‧ ‧ ‧ 3,000 data points to be stored

  8. Use of Two DAQ Cards Fixed 3,000 data points to be stored Card 1 3,000 data points to be stored Card 2

  9. Interactions in Colloidal Particle Systems* R. H. OTTEWILL School of Chemistry, University of Bristol, Bristol BSB lTS, U.K. 2007-2-1 *Structure and Dynamics of Polymer and Colloidal Systems edited by R. Borsali and R. Pecora (2002)

  10. Interaction Pair Potentials Hard-sphere potential DLVO-Yukawa potential Equivalent hard- sphere potential Important for the stability of charged particles A deep close-range attractive well

  11. Characterization of Colloidal Particles • Small Angle Neutron Scattering • A Monodispers Dispersion of Non-Interacting Homogeneous Spherical Particles The number of neutrons scattered per unit solid angle per unit time for unit intensity, I(Q), is: (1) For spherical particles the shape factor P(Q) is given by: For small amounts of polydispersity:

  12. Weakly Interacting Charge-Stabilized Spherical Particles The close fit of the calculated curve was obtained using eq 1 and a log normal distribution function with a standard deviation of 9% on particle size gives excellent agreement with the experimental results

  13. Interacting Charge-Stabilized Spherical Particles In This System: (1) Long range interactions occur (2) Particles are constantly interacting (3) A degree of ordering occurs (depending on the number concentration & the strength of the repulsive interactions) The effects of particle-particle interaction have now to be included in eq 1 by introducing a structure factor S(Q) thus giving: Volume fraction withS(Q)given by S(Q) can be obtained from exptl. data:

  14. (see the next slide)

  15. Correlation of S(Q) with VR(r) • The RMSA (Rescaled Mean Spherical Approximation) Model • Applied to the system where the interaction is dominated by electrostatic repulsion The Electrostatic Repulsive Potential Energy S(Q) could be modelled using VR(r) in conjunction with the Ornstein-Zernike eq

  16. The EHS (Equivalent Hard Sphere) Model • The effective diameter of the particles, Deff,taking into account the electrostatic repulsion can be calculated using: The Effective Diameter of The Particle:

  17. The Radial Distribution Function g(r) The curve indicates clearly an excluded volume region and then g(r)  1 as r increases 。 A clear peak is visible at r=750A indicating a shell of particles around the reference particle at the origin The first peak has moved to a smaller r and increased in magnitude and is followed by a 2nd and 3rd peak indicating longer range diffuse shells Fourier transform from S(Q) to real space in terms of r gives:

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