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Introduction:Particle size measurement of fine particles

5.Analysis principle of dynamic light scattering method

From the autocorrelation function obtained by the photon correlation method, the average particle size d (hydrodynamic diameter) and polydispersity index are obtained by the cumulant method, and the particle size distribution is obtained by the histogram method.


●Autocorrelation function
The intensity autocorrelation function G2 (τ) obtained directly from the temporal change of scattering intensity is expressed by the following equation.

When the particles are monodispersed, G1 (τ) is a single exponential decay curve and is expressed as follows using the decay constant Γ.

Γ is expressed as follows using the translational diffusion coefficient D.
q: Scattering vector,
n0: Refractive index of solvent,
λ0: Wavelength of laser light

●Stokes-Einstein equation 
Using the Stokes-Einstein equation, the particle size (Stokes diameter) can be obtained from the diffusion coefficient.
d: Particle diameter (hydrodynamic diameter),
k: Boltzmann constant,
T: Absolute temperature,
η: Viscosity of solvent

●Cumulant method analysis 
The average particle size and dispersity index are obtained from the first and second order coefficients, respectively by the series expansion of cumulant generating function.
The cumulant average particle size is obtained from Γ. The polydispersity index is obtained by normalizing μ2 by the square ofΓ  (μ2 / Γ2) and indicates the degree of polydispersity of the particle size distribution.

●Histogram analysis
In the histogram method, the distribution is represented by a finite number of Γj and approximated using the nonlinear least squares method.
Each attenuation constant is converted into a particle size using equations (4) and (6). The particle size distribution can be obtained by displaying a histogram with this as the horizontal axis and the frequency obtained here as the vertical axis.


[Outline of dynamic light scattering method]

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