Determination of Particle Mixture Composition by Visible Spectroscopy

Abstract

Limited methods exist to determine the composition of particle mixtures. This research presents a simple UV-vis-spectroscopy-based method for the separate quantification of particles mixtures considering the following: synthesized ferrihydrite, commercial Fe₂O₃, and natural allophane. Calibration curves and adsorption/scattering coefficients are determined for each particle at different wavelengths. This is the main input to solve equation systems and, ultimately, quantify particle concentration in binary mixtures. The limit of detection varies with wavelength and particle type, yielding values as low as 1.5, 0.2, and 1.6 mg L⁻¹ for ferrihydrite (500 nm), Fe₂O₃ (450 nm), and natural allophane (450 nm), respectively. This study provides a simple, low-cost and straightforward method, compared to atomic-spectroscopy- or chromatography-based techniques, for resolving the composition of binary particle mixtures in suspension.

1. Introduction

The quantification of particles in liquid suspension is a relevant aspect in the implementation of industrial solutions and crucial environmental impact studies. Despite its importance, the methods for particle quantification are often hard to implement and expensive. Depending on the particle composition, the most adequate method for quantification in liquid suspension could vary. For instance, atomic spectroscopies such as Flame Atomic Adsorption Spectroscopy (FAAS) [1] and Inductively Coupled Plasma Optical Emission Spectroscopy (ICP-OES) [2,3,4,5] are extensively used for metallic and metallic-oxide particles, requiring previous dissolution steps before quantification. Also, vibrational spectroscopies such as Fourier Transform Infrared Spectroscopy [6,7,8] and Raman Spectroscopy [9,10,11,12] are suitable to characterize carbon based nanomaterials such as carbon nanotubes, graphene, and micro- and nano-plastics. Although these methods do not require pre-steps, sometimes matrix interferences hinder proper quantification. Finally, molecular spectroscopies such as Fluorescence Spectroscopy and UV–visible light spectroscopy are suitable for all kinds of particulates, including quantum dots [11,12,13]. In particular, UV–visible light spectroscopy-based methods are extensively used to monitor the syntheses, stability, aggregation, and other features of particle suspensions [14] due to their low cost, feasible implementation, and decent sensitivity. Several researchers use UV-vis spectroscopy to calculate particle concentration during synthesis [15], liberation to natural media [16,17,18,19], deposition [20], transport [21,22], and functionalization [23].

Particles (including micro- and nanoparticles) are used in a range of applications and consumer products, including electronics, optics, medical devices, food packaging, sunscreens, cosmetics, paints, water treatment technologies, fuel cells, catalysts, biosensors, environmental remediation agents, and in agricultural production [24,25,26]. Engineered particles are man-made particles that are often produced in large amounts [26]. For example, iron oxide-based nanoparticles (IONPs) are used in many environmental applications involving remediation treatments and the recovery of inorganic, organic, and heavy metal contaminants from wastewater due to their higher sorption affinity and faster sorption rate compared to other sorbents [27,28,29,30,31]. While these remarkable properties of IONPs make them excellent candidates for the remediation of contaminated soil and water, the augmentation of any engineered particles requires regulation and monitoring to control unintended consequences on the environment and ultimately human health [29,32,33,34]. In contrast, natural particles are compatible with the local environment and its organisms [26]. One example is ferrihydrite (Fh, Fe₅HO₈·4H₂O), an iron oxide mineral present in diverse environments such as water springs, drainage lines, lake oxide precipitates, groundwater, river sediments, and oceans, where it plays a significant role in many biogeochemical processes [28,35,36]. Another interesting natural particle is the main component of the clay fraction of volcanic ash-derived soils, natural allophane (NA, Al₂O₃·2SiO₂·nH₂O), a low-range ordered aluminosilicate mineral that occurs widely in Andisols [37]. Due to the presence of Al and Si on its surface, NA generates a variable surface charge. Together along with the high specific surface area of NA, this property confers a high capacity for the specific and nonspecific adsorption of ions, cation and anion exchange, and water sorption [37,38,39]. Considering these characteristics, particles suspensions of natural and engineered particles are thought to form complex mixtures when IONPs such as commercial Fe₂O₃ are applied to remediate contaminated soil and water. Therefore, understanding the dynamics of these particle mixtures is critical to both the success of the remediation program and the mitigation of unintended consequences to environmental or human health. Thus, it is important to have handy low-cost methods to characterize the impact (environmental fate, consequences) of the intended particle augmentations and their disposal in the environment. Methods to characterize particle mixtures must consider the complexity of the matrix as well as the concentrations and characteristics of the particles [2,40].

In a UV-vis spectroscopy cell, incident radiation is scattered and absorbed by the suspended particles, decreasing the intensity of the light that passes through the optical path, b, which is used by the device to calculate the reading, ${\mathrm{R}}_{\lambda }$, a variation from Beer’s Law [41,42,43].

$${\mathrm{R}}_{\lambda }={\mathrm{A}}_{\lambda }+{\mathrm{S}}_{\lambda }=-\log \left({\displaystyle \raisebox{1ex}{$\mathrm{I}$}\!\left/ \!\raisebox{-1ex}{${\mathrm{I}}_0$}\right.}\right)={\mathrm{K}}_{\lambda }\mathrm{bC}$$

(1)

The reading, ${\mathrm{R}}_{\lambda }$, corresponds to the sum between the absorbed, ${\mathrm{A}}_{\lambda }$, and the scattered light, ${\mathrm{S}}_{\lambda }$; both magnitudes depend on the radiation wavelength, $\lambda$. Thus, following the same relationship with Beer’s law, the ${\mathrm{R}}_{\lambda }$ depends on the optical path, b, the particle concentration, C, and a constant, ${\mathrm{K}}_{\lambda }$. This constant is related to both the absorption, ${\mathrm{a}}_{\lambda }$, and the turbidity coefficient, ${\mathrm{k}}_{\lambda }$, that depend on the selected wavelength:

$${\mathrm{R}}_{\lambda }={\mathrm{A}}_{\lambda }+{\mathrm{S}}_{\lambda }={\mathrm{a}}_{\lambda }\mathrm{bC}+{\mathrm{k}}_{\lambda }\mathrm{bC}={(\mathrm{a}}_{\lambda }\mathrm{b}+{\mathrm{k}}_{\lambda }\mathrm{b})\mathrm{C}={\mathrm{K}}_{\lambda }\mathrm{bC}$$

(2)

Now, if in a colloidal suspension there is a mixture of different “n” particles, the reading could be determined considering the additivity properties of the different R_λn [44,45]. In n-component mixtures, one can determine the concentration, ${\mathrm{C}}_{\mathrm{n}}$, of each component if the total R_λ is measured at n different wavelengths and the K_λ constant is determined for each particle at n wavelengths. In this sense, all the relationships to determine the individual concentrations of n particle types in the mixture can be expressed by

$${\mathrm{R}}_{\lambda 1}={\mathrm{K}}_{1\lambda 1}\mathrm{b}{\mathrm{C}}_1+{\mathrm{K}}_{2\lambda 1}\mathrm{b}{\mathrm{C}}_2\dots +{\mathrm{K}}_{\mathrm{n}\lambda 1}\mathrm{b}{\mathrm{C}}_{\mathrm{n}}$$

(3)

$${\mathrm{R}}_{\lambda 2}={\mathrm{K}}_{1\lambda 2}\mathrm{b}{\mathrm{C}}_1+{\mathrm{K}}_{2\lambda 2}\mathrm{b}{\mathrm{C}}_2\dots +{\mathrm{K}}_{\mathrm{n}\lambda 2}\mathrm{b}{\mathrm{C}}_{\mathrm{n}}$$

(4)

$${\mathrm{R}}_{\lambda \mathrm{n}}={\mathrm{K}}_{1\lambda \mathrm{n}}\mathrm{b}{\mathrm{C}}_1+{\mathrm{K}}_{2\lambda \mathrm{n}}\mathrm{b}{\mathrm{C}}_2\dots +{\mathrm{K}}_{\mathrm{n}\lambda \mathrm{n}}\mathrm{b}{\mathrm{C}}_{\mathrm{n}}$$

(5)

where the K_λ values can be determined from calibration curves constructed for each particle at each n wavelengths considered.

Here, we report the use of an additivity property work protocol to solve particle mixtures in colloid suspensions. To do so, the stabilization of a particle suspension is a key factor to take care of. The quantification of particles in suspension is usually conducted for single-particle systems. In this research, we prove that visible light spectroscopy can be used for the design of a quantification method for particle mixtures in suspension. Particles were first characterized as a function of their composition and size distribution. Calibration curves were constructed at different wavelengths and the particle mixtures were resolved by means of equation systems analogous to Equations (2)–(5) from above. The stability through time and sensitivity of the method also were evaluated.

2. Materials and Methods

Three particles were considered for this research: synthetic ferrihydrite (Fh), a commercial dispersion of Fe₂O₃, and natural allophane (NA), extracted from a volcanic ash-derived soil. The Fe₂O₃ dispersion and all the reagents used for this research were purchased from Sigma-Aldrich (Burlington, MA, USA).

2.1. Synthesis of Ferrihydrite

Fh was prepared using the method described by Schwertmann and Cornell (1991) [46]. First, 40 g of Fe(NO₃)₃·9H₂O was added to 0.5 L of water, and the pH was adjusted to 7–8 using 0.1 M KOH. The resulting solid was washed with double-distilled water and separated by centrifugation for 30 min at 10,000 rpm. The washing of the particles was repeated four times. A stock suspension of 17.76 mg mL⁻¹ was brought to pH 3 with HCl to optimize the quality of dispersion. The particles were kept in suspension for a week, then the first 20 cm of suspension was separated and kept refrigerated. According to calculations made using Stoke’s law, after one week of settling there should have been no Fh particles with dimensions higher than 14 µm. This part of the suspension was used as the concentrated ferrihydrite suspension.

2.2. Extraction of Natural Allophane

The extraction of NA from soil involved the destruction of the organic matter by treatment with 30% H₂O₂ until no dark residues remained [47]. After this peroxide attack, the sample was suspended in 1.0 L of double-distilled water and dispersed with an ultrasonic probe. Material < 2 µm was removed with a siphon from a depth of 20 cm after a period of 30 h. This < 2 µm sample was then treated for iron oxide removal by the dithionite–citrate–bicarbonate (DCB) procedure [48]. After iron oxide removal, the sample was treated again with 30% H₂O₂ to eliminate the adsorbed organic compounds involved in iron removal treatment [49]. Finally, the resulting suspension was centrifuged for 30 min at 10,000 rpm and re-suspended in double-distilled water to wash the sample; this procedure was repeated four times.

2.3. Morphological and Elemental Composition of Particles

Particle morphology was observed using a Zeiss Scanning Electron Microscope EVO MA 10 model (Jena, Germany). High vacuum was maintained during characterization. Accelerating voltage varied between 8 and 20 kV depending on the sample. Also, the elemental composition of the particles was determined by energy dispersive spectrometry using a Penta FET Precision EDS detector (Oxford Instrument, Oxford, UK) coupled to the SEM. One drop of each particle suspension was placed on a silicon film and allowed to dry after characterization.

2.4. Particle Size Distribution

The particle size distribution measurements were carried out on a Malvern Zetasizer Nano ZS Dynamic Light Scattering (DLS) system (Almeno, The Netherlands) [50,51]. The device uses classical single-scattering methods to calculate particle sizes in a range from 0.3 nm to 10 μm with a 633 nm laser and detects the backscattered light at 173°. Measurements were made at 25 °C and represent the average of 10 runs of 10 s duration for a total of 100 s. The sample in the cuvette was diluted to avoid multiple scattering.

2.5. Suspended Particle Quantification by UV–Visible Spectroscopy

All R_λ measurements were carried out in a Thermo Electron Spectronic Helios Alpha Beta UV–Visible (Waltham, MA, USA) double-beam spectrophotometer with a wavelength step of 1 nm. After measurements, suspensions were stirred for 30 s in vortex to ensure repeatable outcomes. Measurements were made using a 1 cm optical path quartz cell, with bi-distilled water as blank. Room temperature was maintained during the measurements. Concentrated and stable particle suspensions were diluted to prepare different reference materials and, ultimately, calibration curve construction ionic strength was fixed using a 100 mM concentration of NaNO₃ as background electrolyte to prepare standards. Particle mass concentration for the reference materials was controlled by the gravimetric method. A set of three 5 mL beakers of known mass were used to deposit an exact volume of particle suspension and left to dry in lab oven at 85 °C until they reached constant mass. Mass gain from beakers was accounted as suspended particle max and related to a certain R_λ measurement for calibration curve point-by-point construction. Experimental pH was monitored during experiments. For the determination of K, calibration curves were constructed at 450, 500, and 550 nm wavelengths, using pure particle standards of different concentrations within the range of 0 to 1.5 mg mL⁻¹.

A set of 12 binary particle mixtures were prepared using different concentrations. The reading R_λ was measured for each prepared mix at 450, 500, and 550 nm. These mixes were prepared and measured in triplicate. To ensure reproducibility, standard deviations were evaluated. Analysis of variance (ANOVA) performed on the results showed that there were no effective statistical differences (95% confidence) between the repetitions.

Regardless of the outcomes, we proved stability through 1-week-old standards; to avoid source of error, it was important to vigorously stir the standards before any measurement.

2.6. Stability of Calibration Curves over Time

To assess the stability of the calibration suspensions over time, calibration curves were constructed from freshly made suspensions and after one week of storage under refrigeration. The concentrations of the particle mixtures were calculated and compared using calibration curve data from both fresh and stored calibration suspensions.

2.7. Analytical Quality Parameters

For the proposed method, analytical quality parameters were evaluated as the limit of detection (LOD) and limit of quantification (LOQ) [52], based on Equations (6) and (7):

$$LOD=3\times {\displaystyle \frac{{\sigma }_{blk}}{m}}$$

(6)

$$LOQ=10\times {\displaystyle \frac{{\sigma }_{blk}}{m}}$$

(7)

where ${\sigma }_{blk}$ and $m$ correspond to blank standard deviation and calibration curve slope, respectively. These parameters were calculated for each particle suspension at 450, 500, and 550 nm.

3. Results

3.1. Particle Characterization

The particle suspensions presented characteristic pH values of 1.9 ± 0.2, 3.5 ± 0.1, and 2.5 ± 0.5 for Fh, Fe₂O_3, and NA, respectively. The size distribution of the suspensions after DLS characterization is presented in Figure 1.

The size distribution reveals that more than the 90% of the synthesized Fh corresponded to nanoparticles with a mean diameter of 81 nm. In contrast, the other two materials exhibited a monodisperse signal, with 100% of particles measuring 83 nm for Fe₂O₃ and 206 nm for NA. This agrees with the Fe₂O₃ supplier’s description of a nanoparticle dispersion with less than 100 nm particle size. Also, the size distribution of NA agrees well with past reports on this natural particle that naturally forms sub-micro- and micro-sized aggregates [53].

The SEM micrographs (Figure S1) obtained revealed similar size distributions for the particles as were described after DLS characterization. While Fh presented a broader size-distribution, Fe₂O₃ and NA displayed more homogeneously sized particles. In addition, EDS characterization established that the Fh particles contained comparable amounts of Fe and O as their major constituents (Figure S1). Some K and Cl were also found, probably from their synthesis and acid–water rinses for particle-dispersion enhancement. For Fe₂O₃, oxygen and iron were found at the expected ratio of 3:2, while some amounts of C and N were detected due to the dispersing agent, as described by the provider. Finally, the major constituents of NA were Al, Si, and O in a 3:2:2 ratio. Additionally, some amounts of Cl, Na, and C were found in the NA samples, likely because of the extraction procedure. Other elements found in smaller proportion may belong to the natural mineral particles present in the volcanic soil samples used to extract the NA.

3.2. Determination of Particle Mixtures Using UV–Visible Spectroscopy

Wavelength selection is a critical but flexible aspect of the quantification of particle mixtures in suspension. While it is important to choose different wavelengths for the determination of each particle, it is not essential to choose a specific wavelength or to follow a particular protocol for wavelength selection. Unlike molecular absorption spectra, the dispersion of radiation by suspended particles does not necessarily have a maximum whose wavelength can preferably be selected. This is corroborated by Figure 2, where the single-particle spectra did not display maximum absorption bands at any wavelength. As described above (Equation (1)), the total R corresponds to the contribution by each particle present in the mixture due to the absorption and dispersion of radiation, as illustrated in Figure 2 by the spectra of Fh, Fe₂O₃, and combinations.

As presented in Figure 2, each particle under study displays a different spectrum. Since these particles do not react with each other or with other suspension components, the sum of the independent spectra agrees well with the spectrum obtained from a suspension made with a binary mixture, maintaining a pH near 2.2 ± 0.2. For example, the sum () of the spectra made with Fe₂O₃ and Fh agrees well with the spectrum obtained from a suspension made with both particles (◯) at same concentration. This behavior is consistent at each wavelength and is independent of the particle or medium composition if there is no reaction between either of the components. Another way to demonstrate the absence of interaction between the particles is to compare the DLS size distribution of the single particles to the distribution obtained for the mix (Figure S2). In the case of an interaction between the Fh and Fe₂O₃ particles, one should expect a strong size distribution shift from the single-particle to the mixed-particle system. This is not the case, since after combination the intense distribution located at 81 and 83 nm for the single-particle Fh and Fe₂O₃ DLS size distributions, respectively, (Figure 1) grew into a more intense distribution present for the mix at 85 nm (Figure S2). The secondary, less important distribution for Fh was not detected for the mix with Fe₂O₃, probably due to a dilution effect.

For any binary system, solving the concentration of mixed-particle suspensions requires that particles should not interact with each other or with other suspension components, a low level of background interference from the matrix (total R, absorption + dispersion measurement should not surpass 2.0 reading values), and maintaining stability in the suspension during the measurements, avoiding coagulation and sedimentation processes as much as possible.

All in all, any binary systems need to have their R measured at two different wavelengths. For instance, the binary mixtures of Fh, Fe₂O₃, and NA were quantified by measuring R at 450, 500, and 550 nm, as displayed in Figure 3.

The experimental points for calibration curve construction are presented for each particle. Concentration was determined after gravimetry measurements using reference material prepared from stable suspensions of each particle, displaying high precision with low standard deviation (horizontal error bars) at each point. Then, each reference material was measured, obtaining R_λ at three different wavelengths (450, 500, and 550 nm). Linear regression was selected as the statistical model [54] to explain the relationship between concentration (independent variable) and the reading, R (dependent variable). The model’s limitations required us to consider different concentrations and reading values for each binary system, as would be proven going forward. As can be observed, there is a linear relationship between the magnitude of R, and concentration, C_P, for each particle at the different wavelengths. Linear regression analysis was performed after this, and slope values were calculated. Thus, these systems can be used to construct a data matrix with the calculated slopes at different wavelengths, K_λ, for each particle, as presented in

Table 1. Values of K_λ calculated from calibration curves in Figure 3.

	K450	K500	K550
	(mL mg−1)
Fh	-	1.062 ± 0.001	0.411 ± 0.001
Fe2O3	2.681 ± 0.109	1.497 ± 0.016	0.345 ± 0.016
NA	0.380 ± 0.002	0.277 ± 0.002	0.204 ± 0.000

.

Theoretically, with this information it is possible to formulate an equation system considering at least two different particles measured at two different wavelengths. Solving this system of equations yields the concentration for each particle in the mixed solution. For example, to solve a binary mixture between Fh and Fe₂O₃, an equation system can be established using the measurements at 500 and 550 nm wavelengths values.

$${\mathrm{R}}_{500}=1.497 \times {\mathrm{C}}_{{\mathrm{Fe}}_2{\mathrm{O}}_3}+1.062 \times {\mathrm{C}}_{\mathrm{Fh}}$$

(8)

$${\mathrm{R}}_{550}=0.345 \times {\mathrm{C}}_{{\mathrm{Fe}}_2{\mathrm{O}}_3}+0.411 \times {\mathrm{C}}_{\mathrm{Fh}}$$

(9)

Then, the measurements at 500 and 550 nm replace the values for R₅₀₀ and R₅₅₀ in the equation system. For instance, a mixture of Fe₂O₃ and Fh with the respective theoretical concentration of 0.2 and 1.0 mg mL⁻¹ was prepared. R₅₀₀ and R₅₅₀ were measured, resulting in 1.388 and 0.491, respectively. Solving the equation system with these data provides experimental concentrations of 0.20 and 1.03 mg mL⁻¹ of Fe₂O₃ and Fh, respectively, corresponding to a high accuracy with a percentual error less than +3%. Similar equation systems may be developed for other particle pairs if R_λ measurements are made considering at least two different wavelengths for each.

Table 2. Theoretical and experimental concentrations of particles in binary mixtures after measurements at different wavelengths, and corresponding R_λ values. All binary particle mixtures maintained pH values around 2.0–2.9.

Mix	Theoretical Concentration (mg mL−1)		Rλ		Experimental Concentration ± Standard Deviation (%error) (mg mL−1)
	Fe2O3	Fh	500 nm	550 nm	Fe2O3	Fh
M1	0.2	1.0	1.388	0.491	0.20 ± 0.00 (0.0)	1.03 ± 0.06 (+3.0)
M2	0.6	0.6	1.575	0.465	0.61 ± 0.03 (+1.7)	0.61 ± 0.02 (+1.7)
M3	1.0	0.2	1.748	0.434	1.03 ± 0.08 (+3.0)	0.19 ± 0.02 (−5.0)
	Fe2O3	NA	500 nm	550 nm	Fe2O3	NA
M4	0.2	1.0	0.606	0.281	0.21 ± 0.00 (+5.0)	0.99 ± 0.07 (−1.0)
M5	0.6	0.6	1.126	0.353	0.60 ± 0.04 (0.0)	0.61 ± 0.02 (+1.7)
M6	1.0	0.2	1.676	0.433	1.03 ± 0.06 (+3.0)	0.23 ± 0.05 (+15.0)
	Fe2O3	NA	450 nm	550 nm	Fe2O3	NA
M7	0.2	1.0	0.974	0.281	0.23 ± 0.00 (+15.0)	0.96 ± 0.05 (−4.0)
M8	0.6	0.6	1.905	0.353	0.63 ± 0.01 (+5.0)	0.58 ± 0.01 (−3.3)
M9	1.0	0.2	2.501	0.433	0.83 ± 0.03 (−17.0)	0.72 ± 0.02 (+260.0)

provides the complete set of paired-particle mixtures prepared at different theoretical concentrations and their effective experimental concentrations after light scattering measurement, using K_λ from Table 1 for calculations.

As illustrated in Table 2, the determined experimental concentrations were in close agreement for most theoretical values, except for M9. Notably, the M9 mixture surpasses the method’s limit in terms of the maximum concentration of Fe₂O₃ that maintains a linear response with R₄₅₀. As can be observed in Figure 3, at 450 nm Fe₂O₃ displays a linear response until reaching 0.8 mg mL⁻¹. This observation indicates that the procedure requires that the particle mixture measurements are made under single-particle concentrations less than or equal to those used for the construction calibration curves. The R₄₅₀ values for M9 were as high as 2.5, meaning that the sample practically transmitted less than 1% of the incident light. This clearly surpasses the method’s limits, since concentrated samples do not obey Beer’s law. This is also observed for M10, M11, and M12, presented in the Supplementary Information (Table S1), where the high R₄₅₀ values generate low accuracy. Theoretically speaking, measurements can be made at any two different wavelengths, but in the case of Fe₂O₃, measurements at 450 nm have the highest standard deviation (Table 1). This example demonstrates how high-absorption/scattering samples are not adequate and will provoke erroneous concentration calculus, lowering the accuracy of the method. Taken together, these data demonstrate that the present method allows for the resolution of particle mixtures stably suspended using a simple and straightforward method, irrespective of particle origin, composition, or size. Nevertheless, method design needs to consider wavelength selection, avoiding high absorption/scattering datapoints that will surely lower the method’s accuracy.

The limit of detection (LOD) and limit of quantification (LOQ) are key parameters to evaluate the sensitivity of a method.

Table 3. Quality analytical parameters for Fh, Fe₂O_3, and NA at three wavelengths.

	LOD (mg L−1)			LOQ (mg L−1)
Wavelengths (nm)	450	500	550	450	500	550
Fh	-	1.5	3.0	-	5.1	9.8
Fe2O3	0.2	1.1	3.5	0.8	3.6	11.7
NA	1.6	5.9	6.0	5.3	19.5	19.8

provides these analytical parameters for the particles in this study at different wavelengths.

Both LOD and LOQ were highest at 550 nm, coinciding with the lowest values of K, indicating decreased sensitivity at higher wavelengths. The LOD and LOQ of Fe₂O₃ at 450 nm were 0.2 and 0.8 mg L⁻¹, respectively, corresponding to the highest sensitivity observed during the study. These values are acceptable considering the simplicity of the methodology. Zhou et al. (2016) [30] developed a method employing a Size Exclusion Chromatography–Inductively Coupled Plasma Mass Spectrometry (SEC-ICP-MS) technique for the determination of mixtures between metal oxide particles (MOs) and free-metal (Mⁿ⁺), and obtained an LOD of 0.390 μg L⁻¹ for MOs. This represents an LOD 500 times lower than present UV-vis spectroscopy techniques. SEC-ICP-MS offers superior sensitivity, selectivity, and size characterization, making it ideal for precise quantification and differentiation of nanomaterials, especially in complex matrices. However, it is costly and requires sophisticated instrumentation. In contrast, UV-Vis spectroscopy provides a simple and cost-effective alternative for rapid screening but suffers from lower specificity and sensitivity, particularly for polydisperse or complex samples.

The method developed herein to resolve particle mixtures in liquid suspensions represents an accessible, cost-effective approach with adequate sensitivity. Binary particle mixtures were resolved; however, ternary or more complex combinations (particles and dissolved solutes) are possible systems that would require us to escalate present methods. For instance, this straightforward method could be adapted to the real-time monitoring of nano-/microparticles discharge from industrial effluents into water bodies or to follow up with particle-related parameters (concentration, size-shifts, etc.) in controlled industrial processes.

Finally, the stability of the standards through time is analyzed.

3.3. Aging of Reference Material

The stability of the reference materials proves the usefulness of the proposed methods to characterize samples using standards stored for a long time. Calibration curves were re-measured and constructed after one week of reference material preparation, as displayed in Figure 4.

Figure 4 shows three different calibration curves for Fe₂O₃ suspensions measured at 500 nm. The freshly prepared and stored standards yielded almost the same calibration curve. For instance, the evaluation of the Fe₂O₃ suspension with K₅₀₀ equal to 0.888 with curves (1), (2), and (3) yields concentrations of 0.582, 0.576, and 0.580 mg mL⁻¹, respectively. There is a maximum of 1% difference in the resulting Fe₂O₃ concentration if fresh or stored standards are employed for the construction of the calibration curve, indicating that the method is stable across at least this period.

From the reference material measured in Figure 4, K_λ determination was compared between freshly prepared standards and the standards that had been stored for one week, as shown in

Table 4. Slope variation through time for Fh and Fe₂O₃ calibration curves.

		Fh		Fe2O3
		Fresh	One-Week Old	Fresh	One-Week Old
K500	(mL mg−1)	1.062	1.069	1.497	1.525
K550		0.411	0.416	0.345	0.346

.

As presented in Table 4, there is a good stability of the reference material within one week of preparation, with less than +2% variation observed between the fresh and stored standards. The stability of a calibration curve over time depends on the stability of the suspension and the size of the nanoparticle over time. In this case, the commercial Fe₂O₃ particle suspension possesses a stabilizer agent to guarantee suspension stability over time. In general terms, the effect of calibration curve aging must be treated on a case-by-case basis, as similarly sized nanoparticles can vary in their stability.

4. Conclusions

The results demonstrate that this method, based on the measurement of the reduction in light intensity (transmitted radiation), effectively resolves mixtures of commercial, natural, and synthesized nano- and sub-micrometric particles with adequate sensitivity. Our outcomes showed that, for stable particle suspensions, the calibration curves maintain their quality through time for at least one week after being prepared. The sensitivity of the method varied with wavelength and particle type, yielding LOD values at tested wavelengths as low as 1.5, 0.2, and 1.6 mg L⁻¹ for ferrihydrite (500 nm), Fe₂O₃ (450 nm), and natural allophane (450 nm), respectively. The limitations of the method are that particles should not interact with each other or with other suspension components, no other species which absorb or disperse radiation at the same wavelength should be present, and combined light absorption/scattering values should not surpass reading values of 2.0. This method represents an economic, straightforward approach to characterizing the composition of particle mixtures, something that is important when monitoring particle synthesis protocols and the environmental impact of particle-based remediation strategies, among others. Further application to real-life applications or consideration of ternary mixture quantifications are possible, but require a case-by-case evaluation of the system, as presented in this research.