Assessment of the characterization of nonabsorbing nanoparticles in suspension from effective optical properties

R. Márquez-Islas; C. Sánchez-Pérez; A. García-Valenzuela

doi:10.1364/AO.54.009082

Applied Optics
Vol. 54,
Issue 31,
pp. 9082-9092
(2015)
•https://doi.org/10.1364/AO.54.009082

Assessment of the characterization of nonabsorbing nanoparticles in suspension from effective optical properties

R. Márquez-Islas, C. Sánchez-Pérez, and A. García-Valenzuela

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R. Márquez-Islas, C. Sánchez-Pérez, and A. García-Valenzuela, "Assessment of the characterization of nonabsorbing nanoparticles in suspension from effective optical properties," Appl. Opt. 54, 9082-9092 (2015)

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- Instrumentation, Measurement, and Metrology
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About this Article
History
- Original Manuscript: August 6, 2015
- Revised Manuscript: September 27, 2015
- Manuscript Accepted: September 27, 2015
- Published: October 21, 2015

Abstract

We analyze a method recently proposed to retrieve the size, refractive index, and concentration of particles in nonabsorbing nanofluids from measurements of the complex effective refractive index of two dilutions of the nanofluid [Opt. Lett. 39, 559 (2014) [CrossRef] ]. The method uses simple formulas to retrieve the particles’ parameters. First, we discuss precautions needed with the new method when inferring the refractive index of the particles from measurements of the imaginary part of the effective refractive index of two dilutions of the original nanofluid. Then we analyze the use of this methodology to obtain some average radius in the size of polydisperse suspensions and in the case of suspensions of weakly absorbing particles. We also perform an error analysis considering fixed errors in measurements and calculating the errors in the retrieved size, refractive index, and concentration of particles. Finally, we characterize experimentally nanofluids of polymeric particles fabricated of poly(methyl-methacrylate) (PMMA) and polystyrene (PS) for which we achieved an uncertainty of $5 \times 10^{- 3}$ and $1 \times 10^{- 2}$ in the determination of the particle refractive index, respectively, and a precision better than 3% in the determination of their radii.

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$σ$	$a_{v}$ (nm)	$a_{app}$ (nm)	$δ a$ (%)
1.1	1.01 $a_{p 0}$	1.04 $a_{p 0}$	2.7
1.2	1.05 $a_{p 0}$	1.16 $a_{p 0}$	10.0
1.3	1.11 $a_{p 0}$	1.36 $a_{p 0}$	23.0
1.4	1.18 $a_{p 0}$	1.66 $a_{p 0}$	40.0

Particle	$n_{p}$	$\bar{n_{p}}$	$Δ n_{eff, m 1}^{''}$	$a_{p, ret}$ (nm)	$\bar{a_{p, ret}}$ (nm)	$a_{p, m}$ (nm)	$δ a_{p} / a_{p, m}$ (%)	$f_{ret} \times 10^{- 3}$ (%)	$\bar{f} \times 10^{- 3}$ (%)
${PS}_{23 - 1}$	1.516	$1.52 \pm 0.01$	0.0015	25.7	23.7	23.0	3.0	6.1	$7.3 \pm 1.2$
${PS}_{23 - 2}$	1.532		0.0019	23.6				10.0	$10.0 \pm 0.2$
${PS}_{23 - 3}$	1.527		0.0023	21.9				13.0	$15.0 \pm 2.3$
${PMMA}_{54 - 1}$	1.469	$1.473 \pm 0.005$	0.0010	60.6	54.6	54.0	1.1	6.8	$7.0 \pm 0.4$
${PMMA}_{54 - 2}$	1.477		0.0015	51.4				10.7	$10.5 \pm 0.5$
${PMMA}_{54 - 3}$	1.468		0.0020	51.9				15.0	$15.0 \pm 0$
${PMMA}_{22 - 1}$	1.476	$1.482 \pm 0.006$	0.0052	24.5	23.9	22.5	3.0	37.0	$39.6 \pm 0.5$
${PMMA}_{22 - 2}$	1.488	$1.482 \pm 0.006$	0.0062	23.3	23.9	22.5	3.0	41.0	$45.3 \pm 0.5$

$σ$	$a_{v}$ (nm)	$a_{app}$ (nm)	$δ a$ (%)
1.1	1.01 $a_{p 0}$	1.04 $a_{p 0}$	2.7
1.2	1.05 $a_{p 0}$	1.16 $a_{p 0}$	10.0
1.3	1.11 $a_{p 0}$	1.36 $a_{p 0}$	23.0
1.4	1.18 $a_{p 0}$	1.66 $a_{p 0}$	40.0

Particle	$n_{p}$	$\bar{n_{p}}$	$Δ n_{eff, m 1}^{''}$	$a_{p, ret}$ (nm)	$\bar{a_{p, ret}}$ (nm)	$a_{p, m}$ (nm)	$δ a_{p} / a_{p, m}$ (%)	$f_{ret} \times 10^{- 3}$ (%)	$\bar{f} \times 10^{- 3}$ (%)
${PS}_{23 - 1}$	1.516	$1.52 \pm 0.01$	0.0015	25.7	23.7	23.0	3.0	6.1	$7.3 \pm 1.2$
${PS}_{23 - 2}$	1.532		0.0019	23.6				10.0	$10.0 \pm 0.2$
${PS}_{23 - 3}$	1.527		0.0023	21.9				13.0	$15.0 \pm 2.3$
${PMMA}_{54 - 1}$	1.469	$1.473 \pm 0.005$	0.0010	60.6	54.6	54.0	1.1	6.8	$7.0 \pm 0.4$
${PMMA}_{54 - 2}$	1.477		0.0015	51.4				10.7	$10.5 \pm 0.5$
${PMMA}_{54 - 3}$	1.468		0.0020	51.9				15.0	$15.0 \pm 0$
${PMMA}_{22 - 1}$	1.476	$1.482 \pm 0.006$	0.0052	24.5	23.9	22.5	3.0	37.0	$39.6 \pm 0.5$
${PMMA}_{22 - 2}$	1.488	$1.482 \pm 0.006$	0.0062	23.3	23.9	22.5	3.0	41.0	$45.3 \pm 0.5$

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Applied Optics