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Laser scattering centrifugal liquid sedimentation method for the accurate quantitative analysis of mass-based size distributions of colloidal silica

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Abstract

This paper proposes a laser scattering centrifugal liquid sedimentation (LS-CLS) method for the accurate quantitative analysis of the mass-based size distributions of colloidal silica. The optics comprised a laser diode light source and multi-pixel photon-counting detector for detecting scattered light intensity. The unique optics can only detect the light scattered by a sample through the interception of irradiated light. The developed centrifugal liquid sedimentation (CLS) method comprised a light-emitting diode and silicon photodiode detector for detecting transmittance light attenuation. The CLS apparatus could not accurately measure quantitative volume- or mass-based size distribution of poly-dispersed suspensions, such as colloidal silica, because the detecting signal includes both transmitted and scattered light. The LS-CLS method exhibited improved quantitative performance. Moreover, the LS-CLS system allowed the injection of samples with concentrations higher than that permitted by other particle size distribution measurement systems with particle size classification units using size-exclusion chromatography or centrifugal field-flow fractionation. The proposed LS-CLS method achieved an accurate quantitative analysis of the mass-based size distribution using both centrifugal classification and laser scattering optics. In particular, the system could measure the mass-based size distribution of approximately 20 mg mL−1 poly-dispersed colloidal silica samples, such as in a mixture of the four mono-dispersed colloidal silica, with high resolution and precision, thereby demonstrating high quantitative performance. The measured size distributions were compared with those observed through transmission electron microscopy. The proposed system can be used in practical setups to achieve a reasonable degree of consistency for determining particle size distribution in industrial applications.

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Abbreviations

C A :

Absorption cross section of the light path (m2)

Cs :

Scattering cross section of the light path (m2)

F a (x):

Area-based size distribution (–)

F v (x):

Volume-based size distribution (–)

F m (x):

Mass-based size distribution (–)

h :

Sedimentation distance (m)

h r :

Distance from the rotation axis to the measurement zone (m)

h s :

Distance from the rotation axis to the liquid–air interface of the sample (m)

I A 0 :

Transmitted light intensity when the reference cell passes through the light path (–)

I A i :

Transmitted light intensity when the sample cell passes through the light path (–)

I S0 :

Scattered light intensity when the reference cell passes through the light path (–)

I Si :

Scattered light intensity when the sample cell passes through the light path (–)

k :

Optical coefficient (–)

l :

Light path length of the cell (m)

n i :

Particle number per mass unit for particle size xi (–)

Q A :

Absorption extinction coefficient (–)

Q E :

Extinction coefficient (–)

Q S :

Scattering extinction coefficient (–)

t :

Sedimentation time (s)

t 0 :

Sedimentation time at t = 0 (s)

t end :

Sedimentation time at the end of the sedimentation process (s)

t’ :

Sedimentation time at α = 0 (s)

v :

Terminal sedimentation velocity (m s−1)

x :

Stokes diameter (m)

x i :

Maximum diameter size of the sample (m)

α :

Centrifugal angular acceleration (rad s−2)

η 0 :

Liquid viscosity (Pa s)

ρ :

Particle density (kg m−3)

ρ 0 :

Liquid density (kg m−3)

ω :

Centrifugal angular velocity before t = t’, (rad s−1)

ω 0 :

Centrifugal angular velocity at t = 0 (rad s−1)

ω max :

Centrifugal angular velocity after t = t’ (rad s−1)

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Acknowledgements

The author thanks Dr. Yasushige Mori of Doshisha University for helpful technical discussions regarding the Mie scattering theory and results of the proposed system. Dr. Yasushige Mori also facilitated the procurement of both SP-300 and HF-50 samples from the Fine Chemicals Research Center of JGC Catalysts and Chemicals, Ltd. and Fuji Chemical Co. Ltd., respectively.

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  1. HORIBA, Ltd., 2 Miyanohigashi, Kisshoin, Minami, Kyoto, 601-8510, Japan

    Tetsuji Yamaguchi

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Correspondence to Tetsuji Yamaguchi.

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Yamaguchi, T. Laser scattering centrifugal liquid sedimentation method for the accurate quantitative analysis of mass-based size distributions of colloidal silica. ANAL. SCI. 39, 1115–1128 (2023). https://doi.org/10.1007/s44211-023-00321-9

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