Size Distribution — Log-Normal Statistics
PDI, D10/D50/D90, and the difference between number-, volume-, and intensity-weighted distributions
Parameters
σ_g = 1.0 would be perfectly monodisperse (all particles the same size). A well-controlled synthesis typically gives σ_g ≈ 1.1–1.3.
Results (number-weighted)
Mean (arithmetic)
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D10
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D50 (median)
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D90
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PDI
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CV (%)
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Volume-weighted D50
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Intensity-weighted D50 (DLS)
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$$f(d)=\dfrac{1}{d\,\ln\sigma_g\sqrt{2\pi}}\exp\!\left(-\dfrac{(\ln d-\ln d_g)^{2}}{2(\ln\sigma_g)^{2}}\right)$$
Number vs Volume vs Intensity Distribution
Cumulative Distribution (number) — D10/D50/D90