# Nano- to submicron particle analysis in microfluidics: Unveiling the potential of light extinction spectroscopy in flow

Paul Bresson, Tamar Kurdadze, Sophie Charton, Sylvain David, Isaac Rodríguez-Ruiz, Fabrice Lamadie

► To cite this version:

Paul Bresson, Tamar Kurdadze, Sophie Charton, Sylvain David, Isaac Rodríguez-Ruiz, et al. Nano-to submicron particle analysis in microfluidics: Unveiling the potential of light extinction spectroscopy in flow. Talanta, 2026, pp.129526. 10.1016/j.talanta.2026.129526. hal-05511573

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# Nano- to submicron particle Analysis in Microfluidics: Unveiling the Potential of Light Extinction Spectroscopy in Flow

Paul Bresson<sup>a</sup>, Tamar Kurdadze<sup>a</sup>, Sophie Charton<sup>a</sup>, Sylvain David<sup>b</sup>, Isaac Rodriguez-Ruiz<sup>b**</sup>, Fabrice Lamadie<sup>a*</sup>

<sup>a</sup>CEA, DES, ISEC, DMRC, Univ Montpellier, 30207 Bagnols-sur-Ceze, Marcoule, France

<sup>b</sup>Laboratoire de Génie Chimique, CNRS, UMR 5503, 4 Allée Emile Monso, 31432 Toulouse

## Abstract

The light extinction spectroscopy (LES) technique is emerging as a versatile analytical tool for multiphasic systems comprising nano- to submicron particles suspensions. Coupling LES at the microfluidic scale offers new avenues for characterization of particle suspensions in this range, enabling precise control of fluid dynamics and reduced sample volumes. This study explores the applicability of LES at the microfluidic scale, focusing on its use for characterizing dielectric and metallic nano- to submicron particles of various sizes and morphologies. Different modelling methodologies employed to calculate particles extinction cross-sections are discussed, emphasizing the impact of their nature and morphology on optical resonances. For metallic nanoparticles, the study highlights the significant role of plasmonic resonances in extinction spectra and evaluates the impact of size distribution and shape anisotropy. Comparative experiments performed in two different microfluidic configurations (continuous flow, and segmented – i.e., droplets - flow) validated the modelling approaches for both latex and silica submicron particles. Experimental data on gold and silver nanoparticles exhibited excellent agreement with theoretical models, even on synthesis, demonstrating the capability of LES for accurately determining particle size and morphology distributions. These results are moreover consistent with TEM analysis.

## 1. Introduction

Nanoparticle characterization is pivotal across various fields, including biomedical diagnostics [1,2], drug delivery [3,4], environmental monitoring [5,6], and material science [7,8]. A critical challenge in these different applications is the need for precise, real-time monitoring, particularly in complex environments or during dynamic processes. In situ characterization enables monitoring of nanoparticles under their actual working or formation conditions, helping in understanding their dynamics, interactions and behaviours. Microfluidics with its ability to handle small volumes of fluids in controlled and reproducible environments, enables superior analytical performance when coupled with different characterizations, compared to bulk analytical setups, including in dynamic environment.

In this regard, the integration of advanced optical techniques with microfluidics allows for the development of reliable analytical tools capable of delivering high-resolution data on nano- (and submicron) particle properties such as size, shape, and optical behaviour [9–11]. In particular, Light

Extinction Spectroscopy (LES) has emerged as a robust and versatile technique, particularly well-suited for integration with microfluidic systems, though scarcely implemented on chip up to date [11–13]. LES measures the attenuation of light as it passes through a suspension of particles. It differs from UV-Vis absorbance spectroscopy by its ability to capture both absorption and scattering phenomena. When a beam of light passes through a medium containing particles, part of the light is absorbed or scattered, reducing the transmitted intensity. Measuring this reduction allows for the characterization of the optical properties of these materials. By quantifying this interaction, LES provides valuable information on their size distribution, concentration, and optical properties.

The importance of this technique lies in its ability to probe both dielectric materials (such as silica, SiO₂) and metallic materials (such as silver or gold), which exhibit vastly different optical properties. Nanoparticles, in particular, are of great interest due to their unique properties, non-exhibited at larger scale, as e.g., surface plasmon resonances in metallic nanoparticles and specific absorption behaviours in dielectric particles. In this regard, nanomaterials have numerous applications in optics, ranging from the design of ultra-sensitive sensors to the development of optoelectronic devices
and energy-related materials. Specifically, the plasmonic resonances exhibited by noble metallic nanoparticles like gold or silver (where conduction electrons at the particle's surface interact strongly with light, resulting in characteristic absorption peaks) are highly dependent on the size, shape, and purity of the particles, making extinction spectroscopy particularly well-suited for their study. Overall, this makes LES a potential tool for characterizing polydisperse systems, non-spherical particles, and samples in turbid media conditions under which traditional UV-Vis spectroscopy faces well-known limitations due to the superposition of absorption and scattering contributions, the loss of accuracy at high optical densities, and the difficulty of interpreting spectra from heterogeneous particle ensembles [14–16].

When compared to dynamic light scattering (DLS), LES also demonstrates superior performance in flow-based measurements. While DLS relies on analyzing fluctuations in scattered light intensity caused by Brownian motion, these measurements are easily distorted under flow conditions, making it less reliable or more difficult to analyze/interpret in dynamic microfluidic setups, and requiring very specific configurations and operational conditions [17,18]. LES, in contrast, relies on transmitted light intensity, making it inherently robust in flowing systems, and particularly suited for Photonic Lab on a Chip architectures [10]. It remains unaffected by velocity gradients, providing accurate, real-time data without artifacts, as it has recently been demonstrated at the microfluidic scale, using a flow device with a multiple optical path configuration [11]. Indeed, the simplicity and adaptability of LES further enhance its suitability for microfluidic applications from an implementation point of view. Unlike DLS, which requires precise laser alignment and can be challenging to integrate into compact setups, LES requires only a light source and detector aligned with the flow path (see figure 1a). This streamlined configuration works effectively with the small sample volumes typical of microfluidic systems, enabling seamless integration and continuous-flow analysis. Moreover, LES can be used to effectively analyse a wide range of particle sizes, from tens of nanometres to micrometres, and is particularly convenient at handling polydisperse and aggregated samples. This is a key advantage over DLS, which assumes uniform diffusion coefficients and struggles with systems containing a mixture of particle sizes. Another distinguishing feature of LES is its sensitivity to particle morphology. Extinction spectra recorded by LES are directly influenced by shape, refractive index, and aggregation state. Detailed morphological information about nanoparticle and submicron particle systems can be extracted by coupling extinction spectra with computational modelling. In contrast, DLS provides only an effective hydrodynamic diameter, assuming an equivalent spherical size for the particles, and offers little insight into anisotropic or irregular shapes distribution.

This work proposes a first comprehensive systematic study of LES relevance for nano- to submicron particles characterization in micro/milli-fluidic applications. By employing computational approaches such as the Discrete Dipole Approximation (DDA) and T-Matrix methods, a special emphasis was placed on modelling and analysing the influence of most common sources of experimental error on the sensitivity and accuracy of the measurements. The focus is

on assessing the technique's performance on different particle types, including dielectric and metallic particles. The integration of experimental data obtained using two different microfluidic setups with knowledge from modelling, provides a detailed understanding of the uncertainties and limitations inherent in this approach. Through this combined experimental and computational framework, this work aims to demonstrate the potential of LES-microfluidic analytical systems for accurate and efficient nano and submicrometric particle characterization, offering a versatile tool for applications ranging from materials development to biomedical research.

## 2. Materials and Methods

### 2.1. *Microfluidic systems and experimental setup*

To explore the robustness of the on-chip LES implementation, two microfluidic formats with inherently different optical environments and application domains were tested. A chip designed for single-phase continuous flow was employed to provide stable and well-defined conditions for benchmarking, as these conditions are considered well suited for quantitative assays, calibration procedures, and analytical method development. In addition, LES was implemented in a plug-flow microdevice representative of high-throughput screening, kinetic studies, and droplet-based synthesis, where the effective optical path is rendered less controlled by droplet curvature, refractive-index mismatch, the continuous-phase lubrication film, and dynamic interfaces that introduce scattering and shape variability. Demonstrating LES performance in both regimes shows that it is not limited to idealized optical paths and remains reliable across architectures with very different operational constraints and application scopes.

To this end, for single-phase flow characterization and benchmarking, a custom-designed glass chip was manufactured by FEMTOPRINT, following our specifications. The chip includes a microfluidic channel conforming three optical paths of varying lengths (1.5 mm, 3.5 mm, and 15 mm). This design enables the adjustment of the effective optical path length and thereby measurements over a wide range of concentrations [19–22]. The glass chip features six self-aligning channels designed for coupling/decoupling light to the system by means of pig-tailed optical fibers insertion, along with six pairs of monolithically integrated 2D microlenses. These microlenses, optimized using a ray-tracing method described in prior research [10], have an effective focal length of 925 µm, enabling efficient beam collimation. Each channel is 650 µm wide and 250 µm deep, minimizing the volume of suspension needed for the analyses. At both ends of each optical channel the chip features parallel windows with optical-grade finishes for optimal light transmittance. For extinction measurements, a reference solution was firstly injected in the chip and measured, and subsequently a sample was injected into the device. In this configuration, sample and reference are measured alternately, with a time offset of several minutes.
<figure><img src="image_3.png" /><figcaption>Figure 1: a - Design of the microfluidic device for plug flow comprising three inlet channels for oil, sample, and reference solutions injection and one interrogation area, b- view of the alternating plug flow (sample, reference) through the interrogation area.</figcaption></figure>

As discussed above, a second chip was designed to provide a multiphasic plug-flow with the particularity of allowing the generation of droplets of 2 different aqueous solutions in alternance (sample and reference). Solutions were dispersed in a continuous Krytox GLP 100 oil (DUPONT) with 0.5 % w/w of 008-fluorosurfactant (RAN biotechnologies). This configuration allows for a more precise and repeated measurement of reference samples along time, accounting for any possible evolution of references in time (related to possible physic-chemical changes or cell fouling/dirtying), and hence minimizing experimental error. Due to the specificity of the multiphasic flow, alternating reference, sample and continuous phase spectrophotometric measurements, a special algorithm for automated data treatment was developed (see "spectra acquisition in plug flows" and figure S1 & S2 in supporting information for further details).

The device is depicted in figure 1a and b, and consists of 3 inlets for reagents injection and an optical interrogation region, analogous to the one previously described for the glass chip

(optical path of 600 µm corresponding to channel's width). The chip, made of polydimethylsiloxane (PDMS, SYLGARD™ 184 Silicone Elastomer, from Dow) plasma-bonded to a glass substrate, and with a channel depth of 250 µm, was fabricated using a low-cost procedure based on soft lithography techniques previously reported [23].

For fluids operation, a Nemesys (Cetoni) syringe pump system was used for solutions injection at controlled flowrates. The spectrophotometric measurements were carried out by coupling one balanced broad-spectrum halogen-deuterium light source (AvaLight-DH-S-BAL, Avantes), and one UV-Vis-NIR spectrometer (AvaSpec-ULS2048CL-EVO, Avantes) to the microfluidic systems by means of solarization resistant fiber optics, (200 µm core, NA=0.22, Thorlabs).

## 2.2. Particle Solutions Preparation

**Standard Nanoparticles:** Two families of particles, dielectric (SiO₂, Latex) and metallic (Ag, Au), were studied. Each particle type was procured in a range of sizes to assess the technique's resolution across different scales.

Silica submicron particles with nominal diameters of 889 nm, 696 nm, 507 nm, 415 nm, 212 nm, and 119 nm were purchased from Microparticles GmbH. Additionally, 550 nm silica particles were sourced from Dr. Lerche KG (SediTest™ product line), and 400 nm silica particles were acquired from Bangs Laboratories Inc. Latex sphere standards with diameters of 400 nm, 200 nm, 150 nm, 70 nm, 50 nm, 40 nm, 30 nm, and 20 nm were purchased from Thermo Fisher Scientific (USA), and 300 nm latex spheres were obtained from Masphere Inc. (Pasadena, CA, USA). The standard solutions were diluted to various concentrations using milli-Q water (obtained from Fisher Scientific Accu100). The dilutions, summarized in table 1, were prepared to ensure that the measured transmission remained within the optimal range for LES analysis (10–100%), as a function of the different explored optical paths on chip. Moreover, for dielectric particles, nominal size and polydispersity were verified by measuring the hydrodynamic diameter using Dynamic Light Scattering (DLS) before any measurement.

Gold nanoparticles were supplied in solution by Nanopartz Inc. (Loveland, CO, USA) in different morphologies (e.g., triangular, rod-shaped), and in limited quantities (refer to Table 2). All the concentrations indicated by the supplier were validated by transmission measurement and from the corresponding molar absorption coefficients of gold. The features of two samples of cylindrical particles were also confirmed by SAXS measurement.

All the nanoparticle initial and sample solutions were sonicated for 30 minutes to minimize aggregation prior to samples preparation and measurement.
<table><caption>Table 1: Summary of the main features of the dielectric particle solutions</caption><thead><tr><th>Particle Type</th><th>Particle sizes (nm)</th><th>DLS measurements, Hydrodynamic diameter (nm)</th><th>Particle concentrations (ppm)</th></tr></thead><tbody><tr><td rowspan="7">SiO2</td><td>889±20</td><td>950.65 (0.07)</td><td>20-5120</td></tr><tr><td>696±20</td><td>736.01 (0.09)</td><td>20-5120</td></tr><tr><td>550(±not provided)</td><td>520.02 (0.1)</td><td>20-5120</td></tr><tr><td>507±20</td><td>508.79 (0.12)</td><td>20-5120</td></tr><tr><td>415±9</td><td>475.69 (0.02)</td><td>20-5120</td></tr><tr><td>400±40</td><td>457.75 (0.07)</td><td>10-10000</td></tr><tr><td>212±6</td><td>227.15 (0.08)</td><td>20-5120</td></tr><tr><td>119±4</td><td>129.29 (0.05)</td><td>20-10240</td></tr><tr><td rowspan="10">Latex</td><td>400±9</td><td>424.24 (0.04)</td><td>1-1000</td></tr><tr><td>300±15</td><td>318.52 (0.04)</td><td>10-400</td></tr><tr><td>200±5</td><td>225.38 (0.04)</td><td>10-480</td></tr><tr><td>150±5</td><td>172.85 (0.07)</td><td>10-500</td></tr><tr><td>70±3</td><td>88.17 (0.12)</td><td>630-10000</td></tr><tr><td>50±3</td><td>59.09 (0.05)</td><td>630-10000</td></tr><tr><td>40±4</td><td>42.19 (0.06)</td><td>1-8000</td></tr><tr><td>30±3</td><td>31.99 (0.16)</td><td>160-1250</td></tr><tr><td>20±2</td><td>25.51 (0.24)</td><td>630-10000</td></tr></tbody></table>

<table><caption>Table 2: Summary of the main features of the gold nanoparticle solutions (H: length, e: edge length, D: Diameter).</caption><thead><tr><th rowspan="2">Particle Type</th><th colspan="2">Particle dimensions (nm)</th><th rowspan="2">Particle concentrations (ppm)</th></tr><tr><th>H</th><th>D</th></tr></thead><tbody><tr><td rowspan="3">Rods Gold</td><td>50</td><td>10</td><td>15.9</td></tr><tr><td>29</td><td>10</td><td>5.8</td></tr><tr><td>19</td><td>10</td><td>13.3</td></tr><tr><td rowspan="2">Cube Gold</td><td>e</td><td></td><td></td></tr><tr><td>70</td><td></td><td>47.8</td></tr><tr><td rowspan="2">Triangle Gold</td><td>H</td><td>e</td><td></td></tr><tr><td>50</td><td>30</td><td>32.4</td></tr><tr><td rowspan="2">Bi-cone Gold</td><td>H</td><td>D</td><td></td></tr><tr><td>70</td><td>20</td><td>1.0</td></tr></tbody></table>

**Benchmark synthesized silver nanoparticles:** silver nanoparticles were synthesized as a representative “real-world” case study. The synthesis procedure was adapted from previously reported protocols [24,25]. Briefly, a 1.8 mM solution of silver nitrate (99,999%, Sigma-Aldrich) was freshly prepared on the day of the experiment using milli-Q water (obtained from Fisher Scientific Accu100). This solution included polyvinylpyrrolidone (PVP, MW = 44,000 g·mol⁻¹, Sigma-Aldrich) and ascorbic acid (BioXtra >99,0%, Sigma-Aldrich). Additionally, a 1.256 M aqueous solution of acetic acid was prepared from glacial acetic acid (ReagentPlus >99%, Sigma-Aldrich) and equilibrated to room temperature prior to use. A stock 4.5 M solution of sodium borohydride (ReagentPlus, 99%, Sigma-Aldrich), diluted in 50% NaOH (Sigma-Aldrich), was also prepared. From this stock, a 0.036 mM sodium borohydride solution was prepared and adjusted to pH 12. The reagents were added sequentially into a 3 mL glass vial as follows: silver nitrate, PVP, and acetic acid were first combined and thoroughly mixed using a vortex mixer. While continuously mixing, sodium borohydride was added, prompting the appearance of a pale-yellow color. A few

seconds later, ascorbic acid was added, causing a rapid color change in the solution. The mixture was then left undisturbed for 3 minutes before the addition of 40 µL of a thiol quencher solution. To prepare the thiol quencher solution, 1-dodecanethiol (≥98%, Sigma Aldrich, 8 mg, 0.040 mmol, 1 equiv.) and Octaethylene glycol monohexadecyl ether (C16E8, BioXtra, ≥98.0%, Sigma Aldrich, 23.78 mg, 0.040, 1 equiv.) were mixed by the addition of 1 mL of milliQ water, 100 µL at a time, under vigorous stirring [26]. The resulting transparent solution was diluted 10 times prior use. Table S1 in the supporting information summarizes the range of reagent concentrations explored, which yielded nanoparticle solutions with visible colors and absorption maxima between 443 and 641 nm.

<figure><img src="image_4.png" /><figcaption>Figure 2: a- TEM images of the synthesized silver nanoparticles (B7), b- Results of detection by image processing: small spheres are shown in red, discs in blue, and triangles in yellow, c- Relative frequency by particle count for each of the three categories.</figcaption></figure>
The synthesized nanoparticles were characterized by transmission electron microscopy (TEM) using a JEOL JEM 1400 operated at 120 kV. For analysis, a 10 µL aliquot was deposited onto a carbon-coated copper TEM grid (400 mesh) and left to dry at room temperature for 24 hours. The remaining nanoparticle solution was stored at room temperature in the dark until further on-chip injection and LES analysis. Figure 2 presents two examples of synthesized nanoparticle samples.

Due to the synthesis and quenching steps, the resulting nanoparticles consist of two predominant interrelated morphologies (triangular and disk-like shapes) along with a smaller-size population of spherical nanoparticles. These spherical particles are likely byproducts of a rapid silver reduction that occurred in the residual solution following quenching. To quantify the size and distribution of each population, TEM images were analyzed using a custom Python script based on watershed segmentation [27], as illustrated in figure 2. This automated analysis extracted size distributions and Ferret diameters. The results, which are compared to extinction measurements in the following sections, are summarized in Table 3.

<table><caption>Table 3: Summary of the main features of the 7 silver particles syntheses - % displayed correspond to the proportion of each particle family.</caption><thead><tr><th rowspan="2"></th><th rowspan="2">λ<sub>max</sub><br>(nm)</th><th colspan="2">Spheres</th><th colspan="2">Triangles</th><th colspan="2">Disks</th></tr><tr><th>⟨Feret<sub>max</sub>⟩<br>(nm)</th><th>%</th><th>⟨Feret<sub>max</sub>⟩<br>(nm)</th><th>%</th><th>⟨Feret<sub>max</sub>⟩<br>(nm)</th><th>%</th></tr></thead><tbody><tr><td>B12</td><td>443</td><td>2</td><td>70</td><td>8</td><td>2</td><td>8</td><td>28</td></tr><tr><td>B2</td><td>503</td><td>2</td><td>66</td><td>12</td><td>6</td><td>12</td><td>28</td></tr><tr><td>B6</td><td>530</td><td>2</td><td>59</td><td>14</td><td>5</td><td>14</td><td>36</td></tr><tr><td>B7</td><td>545</td><td>2</td><td>75</td><td>22</td><td>11</td><td>22</td><td>14</td></tr><tr><td>B8</td><td>555</td><td>2</td><td>65</td><td>19</td><td>13</td><td>18</td><td>22</td></tr><tr><td>B4</td><td>589</td><td>2</td><td>92</td><td>22</td><td>3</td><td>23</td><td>5</td></tr><tr><td>B10</td><td>641</td><td>2</td><td>62</td><td>28</td><td>21</td><td>30</td><td>17</td></tr></tbody></table>

### 3. Light Extinction Spectroscopy principles and modelling considerations

LES measures the total attenuation of light (resulting from both absorption and scattering) caused by particles suspended in a medium. In short, the technique involves a simple recording of a broadband collimated light beam after its passage through the medium. To interpret the experimental data, the obtained spectra are compared to those predicted by light scattering and absorption models of particle extinction via classical (least-squares) minimization processes. In this work 3 theoretical models, Lorenz Mie theory (LMT) for spherical particles [14,28], and T-Matrix [29,30] and discrete dipole approximation (DDA) [31–33] methods for non-spherical particles were employed. Optical cross sections of spherical particles are calculated using Lorentz–Mie theory [14], which provides an exact analytical solution to Maxwell’s equations for light–matter interactions with homogeneous spheres. The method is based on a multipolar expansion in spherical harmonics and enables accurate evaluation of scattering, absorption, and extinction. For cylindrical particles, calculations are performed using the T-matrix method implemented in the SMUTHI Python package [34], which relies on the Null-Field Method [35]. This rigorous boundary approach enforces Maxwell’s equations by imposing the vanishing of the total electromagnetic field within a fictitious

surface surrounding the particle. Expansion of the incident and scattered fields into vector spherical or cylindrical wave functions yields a transition (T-) matrix that links the corresponding expansion coefficients, allowing accurate modelling of non-spherical geometries while accounting for particle size, shape, and optical properties. Particles with more complex geometries (e.g., triangular, cubic, or conical) are treated using a multipole dipole decomposition implemented in the DDSCAT code [36], based on the Discrete Dipole Approximation. In this framework, the particle is represented as an array of coupled polarizable dipoles, and the response is obtained by solving the dipole–dipole interactions. Although highly versatile, this approach entails increased computational cost, particularly at high spatial resolution. Theoretical spectra were computed over the whole experimental wavelength range (200–1100 nm) for comparison with measured data.

The extinction of a light wave is the sum of contributions from scattering and absorption by each particle. For dielectric particles, absorption is generally weak, making scattering the dominant mechanism. The optical properties of particles—such as size, shape, and refractive index—determine their efficiency in scattering light. These properties directly influence the extinction cross-section, a key parameter that characterizes the total amount of light attenuated by the particles.

Dielectric particles, which are non-conducting materials, are primarily characterized by their optical properties, and most notably, their refractive index. This parameter plays a critical role in determining how the particles interact with light, particularly through scattering and refraction. The contrast between the refractive index of a particle and that of the surrounding medium directly influences the intensity of the scattered light. Particles with a significantly different refractive index from their environment strongly scatter light, while those with similar refractive indices appear nearly transparent. The refractive index of dielectric media is typically real in the visible spectrum (k≈0, see figure 3), indicating that scattering is the sole contributor to extinction, with absorption being absent or negligible.

Unlike dielectric particles, noble metallic particles absorb light, leading to plasmonic resonances where absorption is particularly effective. Noble metallic nanoparticles, being conductive, are characterized by a complex refractive index. The real part of this index measures the speed at which light propagates through the material relative to that in a vacuum, while the imaginary part describes light absorption.

For transparent dielectric materials, the refractive index generally decreases monotonically as the wavelength increases, as illustrated in figure 3a and b. That means that for any optical characterization of dielectric nanomaterials in suspension, the more we approach to the UV wavelength, the higher the contrast with respect to the bulk phase. The evolution of the refractive index for metallic materials (as illustrated in figures 3 c and d) is in contrast generally less monotonic than for dielectrics: the imaginary part (i.e., the absorption) increasing with wavelength.

Once taken into account the refractive index considerations, and in order to evaluate the sensitivity of LES technique, the next parameter to account for particles characterization is their extinction cross-section, which is both size and wavelength dependent. Figure 4 a and b illustrate this dependence for
dielectric SiO₂ and Latex spheres surface-normalized extinction cross-sections, calculated by applying the LMT. Several phenomena can be observed. First, the extinction cross-section of particles is generally of the same order of magnitude as their projected surface area. For a fixed diameter, the evolution considering the wavelength is rather monotonic and does not exhibit any peak. Additionally, smaller particles transmit light much more efficiently than the larger ones. It is also noticeable that larger particles absorb less light at wavelengths in the blue range (380-450 nm), and as the particle size increases, extinction becomes more effective over a broader range of wavelengths. Finally, in the case of latex, a local minimum can be observed at the shortest wavelengths in the UV range, which is consistent with the wavelength-dependent evolution of the refractive index. Analogously, using LMT, the extinction cross-section of a sphere of noble metal, such as silver or gold, can be calculated (see figure 4 c and d). From this map, it can be observed that for each diameter, certain wavelengths maximize the extinction cross-section due to the plasmonic resonances of the metal. Unlike dielectric particles, the small metallic particles are more effective at extinction than the larger ones. Once the extinction

cross-section of particles calculated for given size and wavelength, the calculation of the transmission spectrum becomes relatively straightforward:

$$T = \frac{I}{I_0} = e^{-NC_{ext}L} \qquad \text{Eq. 1}$$

Where N is the particle concentration, L is the path length of the light, and C<sub>ext</sub> is the extinction cross-section.

Considering an arbitrary, but small optical path approaching the ones considered in our microfluidic devices (1mm) for illustration purposes, we can observe that the transmission spectra of dielectric particles exhibit a relatively monotonic behaviour, with broader transmission spectra as particles diameters increase, as illustrated in figures 5 a and b. These transmission spectra were plotted for different diameters, selecting for each diameter a particle concentration such that the minimum transmission was 0.1. For metallic nanoparticles in analogous conditions, several resonance peaks can be observed in both the cross-section map (figures 4 c and d) and the transmission spectra (figures 5 c and d), with their amplitude decreasing as the particle size increases, while the number of resonances grows.

<figure><img src="image_5.png" /><figcaption>Figure 3: Evolution of refractive index of a) Silica (SiO2) b) Latex, c) Silver and d) Gold as a function of wavelength. Blue color represents the real part and red color the imaginary part. Data obtained from the Refractiveindex.info database of optical constants [37].</figcaption></figure>
<figure><img src="image_6.png" /><figcaption>Figure 4: Surface-normalized extinction cross-section for a disc-shaped (i.e., a sphere) particle as a function of the wavelength for dielectric particles suspended in water: a) Silica (SiO2), b) Latex; and for metallic particles suspended in water: c) Silver and d) Gold.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>Figure 5: Transmission spectra of a) SiO₂ b) latex c) silver and d) gold nano- to submicron particles with diameters ranging from 20 nm to 1000 nm.</figcaption></figure>
As a detailed example, the first plasmon resonance for gold appears at ≈ 520 nm for spherical particles of 10 nm in diameter and red-shifts to 660 nm for particles about 165 nm in diameter, at which size a second resonance also emerges near 520 nm. For silver, the first resonance occurs around 385 nm for 10 nm spheres and shifts to 488 nm for particles of roughly 100 nm in diameter. In both cases, the resonance wavelength shift with the particle diameter follows a second-order polynomial trend, more pronounced for gold than for silver, implying higher measurement sensitivity for larger particles than for smaller ones (cf. Figure 6). Even small changes in the geometry can lead to pronounced shifts in the plasmon resonance, due to the strong dependence of localized surface plasmon modes on size, shape, and aspect ratio. This is clearly illustrated in Figure 6b, where the geometry of a gold nanoparticle is varied from a perfect cube to a sphere by gradually increasing the edge curvature. As the corners become more rounded, the plasmon resonance progressively shifts toward shorter wavelengths, while the extinction efficiency decreases as a result of the reduction in the effective particle cross-section, and the weaker field enhancement at the edges.

<figure><img src="image_8.png" /><figcaption>Figure 6: a) Illustration of the resonance wavelength shift versus particle diameter for gold and silver nanospheres. b) Extinction spectra of gold nanoparticles evolving from a cube to a sphere by gradual edge rounding, showing a blue shift and reduced efficiency. The color code corresponds to the nominal wavelength of the resonance.</figcaption></figure>

Such sensitivity suggests that LES has the potential to provide informative spectral signatures related to particle-shape evolution, as encountered in precipitation, crystal growth, dissolution or attrition processes, thereby offering a basis for future studies on nanoscale structure-property relationships.

By knowing the extinction cross-section and considering the same optical path length of 1 mm, it is also possible to establish a range of sensitivity by determining the range of concentrations for which the transmission varies significantly (approximately 30%) within the visible spectrum, and therefore a reliable concentration range for measurements. Figure 7 illustrates this range of concentrations for both dielectric (Figure 7a) and metallic nano-to submicron particles (Figure 7b). It can be observed that, for the case of dielectric particles, for each particle diameter, there is a range of concentrations spanning two orders of magnitude where measuring the transmission spectrum can potentially yield relevant results. In the case of metallic particles, for the smallest sizes, there is a wide range of concentrations, spanning several orders of magnitude, where transmission measurements can be relevant, whereas this range narrows for larger particles due to the relatively flat nature of their transmission spectra. It is worth noting that modifying the optical path length is a way to linearly shift these limits, as it will be discussed hereafter.

<figure><img src="image_9.png" /><figcaption>Figure 7: Range of concentrations where the transmission varies by at least 30% within the visible spectrum.</figcaption></figure>

In practical applications, the transmission T is measured using a spectrometer on a full range of wavelengths using a broadband light beam passing through the particle cloud [38]. The spectral transmittance T, at all the wavelengths, is then:

$$T = \frac{I_T - I_b}{I_o - I_b} = e^{-NL\bar{C}_{\text{ext}}} \qquad \text{Eq. 2}$$

where $I_o$ and $I_T$ are the spectral intensities of the illuminating and transmitted beams, respectively, and $I_b$ accounts for noise (electronic dark noise, background optical noise).
Equation 2 can be reformulated as:

$$ \ln(T) = -N \cdot L \cdot M_{\text{Cext}} \cdot D_d \qquad \text{Eq. 3} $$

where:

* T is the vector containing the measured transmission values at different wavelengths.

* D_d is the vector of the normalized discrete size distribution, representing the proportion of each size class in the distribution.

* M_{Cext} is the matrix containing the extinction cross-sections for each size-shape class at the considered wavelengths.

* N is the particle concentration (in particles/m³)

* L is the optical path length. in m)

The particle size distribution can be retrieved from transmission measurements using a non-parametric approach, in which no assumption is made regarding the distribution shape. This leads to the formal direct inversion:

$$ D_d = -\frac{1}{N \cdot L} \cdot (M_{\text{Cext}}^t M_{\text{Cext}})^{-1} \cdot M_{\text{Cext}}^t \cdot \ln(T) \qquad \text{Eq. 4} $$

Although Eq. 4 provides the formal solution of Eq. 3, the inversion is generally ill-conditioned. Consequently, small

numerical errors or experimental perturbations (e.g., spectrometer noise, contamination, or light-source fluctuations) may result in large reconstruction errors. In practice, only limited information—such as low-order moments or regularized non-parametric estimates—can be reliably obtained, at the expense of resolution and robustness to noise [39].

Alternatively, a parametric approach may be adopted by prescribing the functional form of the size distribution (e.g., Gaussian, log-normal, or monodisperse). This formulation renders the inverse problem well posed and substantially reduces its sensitivity to experimental noise. The inverse problem then reduces to a least-squares optimization over a limited number of parameters (e.g., mean size and standard deviation), rather than the full distribution:

$$ \chi^2 = \sum_{i=1}^{N} \frac{(\ln(T_i) + N \cdot L \cdot (M_{\text{Cext}} \cdot D_d)_i)^2}{\sigma_{w,t}(T_i)} \qquad \text{Eq. 5} $$

where w_i is a weight assigned to each data point.

In this work, the parametric approach is employed, with physically motivated constraints imposed through the assumed form of the particle size distribution (e.g., a Dirac delta function for monodisperse systems or parametric Gaussian mixtures for polydisperse samples).

<figure><img src="image_10.png" /><figcaption>Figure 8: Logarithm of $\chi^2$ representing the discrepancy between the simulated transmission of a particle of 500 nm, and the transmission of particles with different diameters and concentrations.</figcaption></figure>
To verify the uniqueness of the diameter-concentration
pairs in the simulated spectra, and for illustration purpose, this
indicator was calculated by comparing a simulated spectrum at
a given diameter and concentration with simulated spectra
over a wide range of diameters and concentrations (see Figure
8). In this case, D<sub>d</sub> is a vector containing only one non-zero
value, as the distribution used is a Dirac distribution.

A single minimum can be observed on this map, verifying
the uniqueness of the pair, diameter - concentration in the
simulated spectra. Additionally, a valley is noticeable where
the discrepancy with the initial spectrum is lower. Similarly,
the maps show a single minimum for silver particles,
corresponding to the diameter and concentration of the
reference simulation. As with dielectric particles, a valley of
minimal deviation is observed; however, for metals, this valley
is oriented differently.

4. Results and discussion.

4.1. Exploring the experimental limit of applicability of LES
on-chip measurements

As outlined in the Materials and Methods section, two
distinct microfluidic setups were investigated to study two
different flow regimes: continuous flow, using a multi-optical-
path microfluidic chip [20–22], and segmented flow, using the
device shown in Figure 1. The results obtained in both
configurations are presented and compared below, considering
both dielectric and metallic particles in suspension and based
on the prior discussion on simulated extinction spectra.

4.1.1. *Dielectric materials:*

Figure 9 shows the transmission spectra for 696 nm silica
particles at different concentrations, measured continuously
flowing the suspension across the three microfluidic optical
path lengths: 1.5 mm (a), 3.5 mm (b), 15 mm (c). Each graph
compares experimental (solid lines) and simulated (dashed
lines) transmission data calculated using the LMT and for
given particle size, shape, and concentration. As expected,
transmission decreases as the particle concentration increases,
across all the optical path lengths. The shorter wavelengths
(200 - 400 nm) exhibit stronger attenuation, while transmission
gradually increases at longer wavelengths (> 400 nm). The
impact of the optical path length at equivalent concentrations
is evident, as the transmission is highest for the shortest path
length and progressively decreases for 3.5 mm and 15 mm.

However, for transmissions below 10% high deviations are
observed between the experimental and simulated spectra, that
can be attributed to the multiple scattering effects occurring for
very high concentrations, and not taken into account by the
LES model. From these observations, the optimal transmission
range for in-line analysis purpose is between 10% and 100%,
with a wavelength range between 250 nm and 1100 nm. Using
these parameters, all measured spectra can then be processed
to achieve a chosen level of precision in determining the
particles' diameter and concentration.

<figure><img src="image_11.png" /><figcaption>Figure 9: Experimental (straight line) and simulated (dashed line) transmission spectra of silica 696 nm spheres over a wide range of concentrations (20 ppm to 5120 ppm) across (a) 1.5 mm, (b) 3.5 mm and (c) 15 mm optical path lengths.</figcaption></figure>

The log plot presented in Figure 10 compares the measured
particle diameters with their nominal values, for both the silica
and latex standard particles. The solid black line represents the
first bisector, meaning perfect agreement. The dashed lines
indicate ± 20 % deviation range. The results show that for
particles larger than 100 nm, LES provides a correct size
estimation with deviations which mainly fall within ~ 20 %.

These results demonstrate that reliable measurements of
nano- to submicron particles properties can be achieved on a
microfluidic chip, in agreement with theoretical expectations.
In particular, latex particles, owing to their relatively large
extinction cross-sections, yield more precise measurements
than silica particles of analogous diameters (see Figure 10).
Conversely, as anticipated, the accuracy of measurements
decreases for particles with smaller sizes. This is due to their
inherently low extinction cross-sections, which produce
weaker optical signals and make the measurements more
sensitive to noise, possible lamp power fluctuations,
instrument precision limits, and to any potential sample
contamination.
<figure><img src="image_12.png" /></figure>

Figure 10: Experimental performance of LES on the optofluidic chip for particle size determination. For each nominal particle size, multiple measurements were performed across the available concentration and optical-path-length settings. The red symbols represent the mean measured diameter obtained from all measurements for a given particle size, with circles for latex and triangles for SiO₂. Error bars indicate the standard deviation of these measurements around the mean. Different colors correspond to different optical path lengths (O.P.). The solid bisector denotes perfect agreement between nominal and measured diameters, while the dashed lines indicate a ±20% deviation from this ideal trend.

In addition, it should be noted that the dispersion observed when averaging the results obtained for different optical paths mainly reflects the fact that the optimal optical path depends logically on the investigated system. In practical terms, larger optical paths are better suited for samples with low optical density (small particle size, low concentration, or weakly absorbing materials), whereas smaller optical paths are preferable for systems with high optical density (large particles, high concentrations, or strongly absorbing materials). This provides a simple guideline for selecting the appropriate optical path in real applications, beyond the blind-test approach adopted in this study.

Concentration measurements, shown on a logarithmic scale in Figure 11, also demonstrate good accuracy and do not appear to depend exclusively on particle size. However increased variability is consistently observed for smaller particles (below 40 nm), as indicated by the grey arrows in Figure 11. The increasing underestimation of particle concentration observed at high concentrations, as well as the larger deviations for particles above 40 nm, can be attributed to the onset of multiple-scattering effects. As discussed in Section 4.1.1, only data points corresponding to transmission values between 10% and 100% are considered, since lower transmissions are known to be strongly affected by multiple scattering. It is worth emphasizing that multiple scattering scales with the product of optical path length and particle concentration, which explains why the use of the shortest optical path is essential at high concentrations. The variable optical-path chip architecture therefore enables concentration measurements to remain reliable over a wider dynamic range. Finally, the generally higher accuracy obtained for latex particles compared with silica arises from their larger scattering cross-sections at the measurement wavelength (see

Figure 4), which enhances detectability, particularly for particle sizes below 200 nm.

<figure><img src="image_13.png" /></figure>

Figure 11: Scatter plot of nominal weight concentrations versus measured weight concentration of latex (orange disk) and silica (blue disk) particles, for on-chip measurements performed in continuous flow configuration. The disk size indicates only the nominal size class used to label each dataset and does *not* represent the actual particle diameter measured in these experiments.

Analogously, same experiments were reproduced using the segmented-flow microfluidic device. It must be reminded that the optical path length is fixed by the size of the plugs, hence limiting the range of concentrations achievable. As an illustrative example, Figure 12 depicts the extinction spectra for a series of concentrations of latex spheres of 151 nm diameter, obtained considering plugs (and therefore an optical path) of 0.6mm.

<figure><img src="image_14.png" /></figure>

Figure 12: Experimental (straight line) and simulated (dashed line) transmission spectra of latex 151 nm spheres over a wide range of concentrations (10 ppm to 1000 ppm) across 0.6 mm optical path length.

The precision of the diameter measurements is remarkable regardless of the particles size and chemical nature (Figure 13). However, the precision on concentration measurements appears to be weaker (Figure 14). The transmittance remains monotonic across the measured range, without distinct peaks, but exhibits different slopes depending on the material. In particular, the steeper slope observed for latex particles (spectra in Figure 12 compared to those of SiO₂ in Figure 9) enhances the ability to distinguish between materials based on their optical response.

Overall, a precision of approximately 20% is generally achieved for both diameter and concentration measurements, with the notable exception of smaller particles, for which the precision declines. This decrease is again attributed to their lower extinction cross-sections, which yield weaker optical signals and thus greater susceptibility to noise and measurement variability.
<figure><img src="image_15.png" /><figcaption>Figure 13: Performance of LES on the segmented flow optofluidic chip for measuring particle diameter comparing experimental results to nominal values. The red color represents the average measured diameters for latex (circles) and SiO2 particles (triangles). The straight bisector corresponds to the perfect fit between predicted and nominal diameters, and dashed lines to the 20% deviation from the fit.</figcaption></figure>

<figure><img src="image_16.png" /><figcaption>Figure 14: Scatter plot of nominal weight concentrations versus measured weight concentration of latex (orange disk) and silica (blue disk) particles, for on-chip measurements performed in plug-flow multiphasic configuration. The disk size indicates only the nominal size class used to label each dataset and does not represent the actual particle diameter measured in these experiments. The specific concentration ranges accessed reflect the limitations of the single optical path chip with respect to the measurement using three optical path lengths.</figcaption></figure>

Analogously to the continuous flow observations, measurements involving SiO₂ particles also show reduced precision, primary due to its the lower extinction cross-section compared to other materials. Despite these limitations, the results demonstrate that dielectric nano- to sub-micron particles such as latex and SiO₂ can be effectively characterized in segmented-flow using this method. Nevertheless, the reliability of the measurements is highly dependent on the optical properties of the particles.

### 4.1.2. Noble metallic materials

A similar analytical approach was applied to two metallic plasmonic nanoparticles, namely gold and silver. Standard gold nanoparticles were first analyzed with the continuous chip. It is important to note that segmented-flow experiments were not conducted with the gold standards due to the very limited amount of sample available and their high cost, which

required recovery of the material after each measurement. Subsequently, as a more comprehensive case study, complex “real world” silver nanoparticles solutions, synthesized as described in Sec. 2.2., were characterized in both flow configurations, allowing for a direct comparison between the two implementation.

### 4.1.3. Gold nanoparticle standards

The concentrations and resonances derived from the in chip LES measurements for the six gold nanoparticle standards are given in Table 5. Good agreement is observed with the supplier’s data (indicated in parentheses). A detailed analysis of the spectra (see supporting information) reveals, for all samples, a strong polydispersity in both size and shape, resulting in a shift between the simulated spectra for ideal particles and the experimental acquisitions (see Figure 15).

It should be noted that this polydispersity is consistent with the supplier’s data, which indicate variations of ±10% in each dimension. Similarly, transmission electron microscopy images [40] show that the particle edges are not perfectly sharp but rather rounded (see figures S3 to S6 in supporting information), which also has a significant impact on the position of the resonances (see Figure 6b).

<table><caption>Table 4: Comparison of the expected vs measured concentrations and main resonance peak for the nanogold standard particles.</caption><thead><tr><th>Particle Type</th><th>Particle concentrations (ppm)</th><th>Main resonance peak (nm)</th></tr></thead><tbody><tr><td rowspan="3">Rods Gold</td><td>13.2 (15.9)</td><td>904 (900)</td></tr><tr><td>6.9 (5.8)</td><td>694 (700)</td></tr><tr><td>14.3 (13.3)</td><td>605 (600)</td></tr><tr><td>Cube Gold</td><td>47.9 (47.8)</td><td>543 (542)</td></tr><tr><td>Triangle Gold</td><td>21.5 (32.4)</td><td>576 (575)</td></tr><tr><td>Bi-cone Gold</td><td>6.0 (1.0)</td><td>718 (725)</td></tr></tbody></table>

These results confirm the feasibility of measuring the size and concentration of metallic nanoparticles on a microfluidic chip with a precision of a few percent. Note that, the available nanoparticle volumes did not allow the same experiments to be carried out on the segmented-flow optical chip. Figure 15 presents a comparison between experimental measurements and numerical simulations performed for populations of geometrically ideal and strictly monodisperse nanoparticles across the three types of rods. To this end, the T-MATRIX model was used assuming ideal cylinder geometries. The vertical lines denote the theoretical wavelengths corresponding to the transverse and longitudinal resonance peaks. The results are in good agreement, yet the experimental measurements confirm the presence of polydispersity, manifested by a reduced intensity, as well as geometric imperfections of the nanorods, which result in a blue-shift of the resonance wavelength. The same observation holds for the different standards employed in this study, namely cubes, triangles, and bi-cones (see figures S7 to S9 in supporting information).
<figure><img src="image_17.png" /><figcaption>Figure 15: Experimental (straight line) and simulated (dot-dashed line) transmission spectra of 3 different gold nanorods (yellow, 19 nm; red, 29 nm; and purple, 50 nm), across an optical path of 15 mm. The vertical lines denote the theoretical wavelengths corresponding to the transverse and longitudinal resonance peaks.</figcaption></figure>

## 4.2. Case-study: synthetized silver nanoparticles

As briefly introduced above, the seven different silver nanoparticle syntheses were characterized using the two microfluidic devices, the chip with three optical paths, (more specifically using the 1.5 mm optical path) and the chip designed for segmented flows characterization. In this case, the size and shape distributions of the nanoparticles are polydisperse and complex, and the interpretation of the spectra must be based on several assumptions. Figure 16 shows the different transmittance spectra obtained on the three optical paths chip.

<figure><img src="image_18.png" /><figcaption>Figure 16: Transmittance spectra measured on-chip for the different silver nanoparticles syntheses, across an optical path of 1.5 mm on a static single-phase flow.</figcaption></figure>

The variations in wavelength and absorption intensity are typical of the diversity of syntheses achieved. The spectra acquired using the two measurement configurations are in close agreement (see Figure S10 in the supporting information), demonstrating that, for the present case,

measurements performed across plugs in segmented-flow and in static channels are equivalent within experimental uncertainty. The spectral analyses and interpretations discussed hereafter are based on experimental acquisitions performed in the continuous flow configuration; however, the results obtained in segmented-flow are quantitatively comparable.

The optical response of the different particle geometries found in each synthesis was modeled using distinct computational approaches: LMT for spheres, the T-matrix method for cylinders, and DDSCAT for triangles. Here, the model considers perfect geometric shapes because it is impossible to account for all the local variations in curvature. The free parameters in the fitting procedure included the relative proportions of spheres, cylinders, and triangles; the thickness of the cylinders and triangles; and the relative abundance of each size within the size distributions of spheres, cylinders, and triangles (one free parameter per size, with a resolution of 1 nm). To preserve the overall shape of the experimentally measured distributions, the proportion of each size was constrained by first smoothing the experimental distribution and then allowing each size fraction to vary within a factor of two. For a Gaussian distribution, this corresponds to shifting the peak within the full width at half maximum (FWHM). The initial parameter values were set to those obtained from the experimentally measured distribution by image processing. The goodness-of-fit metric was defined as the least-squares difference between the experimental and simulated spectra. Figure 17 illustrates the fit between the model and the experimental data for three representative syntheses (B4, B6, and B12).

<figure><img src="image_19.png" /><figcaption>Figure 17: Experimental (straight line) and simulated (dashed line) transmission spectra of 3 different silver nanoparticles syntheses (yellow, sample B4; green, sample B6; and blue, sample B12), across an optical path of 1.5 mm.</figcaption></figure>

Table 5 presents a comparison between the results obtained by LES and those derived from the analysis of TEM images for all the syntheses. For the sake of clarity and readability, the particle size distributions for each particle morphology considered are not included here; however, as an example, Figure S11 to S17 in the supporting information compares the particle size distributions measured by LES with the ones obtained by TEM image analysis. It can be observed that the orders of magnitude are consistent between the two
approaches. However, sampling for TEM imaging as well as the subsequent image segmentation tend to overrepresent the larger particles, while a significant fraction of the smaller ones remains undetected. As a result, it is reasonable to argue that the distribution measured by LES is likely closer to the actual physical reality of the sample. Regarding the particle thickness, the spectral fitting suggests nanoparticles with a thickness between 3.3 and 4.5 nanometers, which is also fully consistent with the TEM observations.

<table><caption>Table 5: Comparison between the volume proportions measured for the three categories of nanoparticles (spheres, triangles, and disks) by image processing and by LES.</caption><thead><tr><th rowspan="2">Sample</th><th colspan="2">Spheres</th><th colspan="2">Triangles</th><th colspan="2">Disks</th></tr><tr><th>Image processing</th><th>LES</th><th>Image processing</th><th>LES</th><th>Image processing</th><th>LES</th></tr></thead><tbody><tr><td>B12</td><td>9%</td><td>19%</td><td>4%</td><td>3%</td><td>87%</td><td>78%</td></tr><tr><td>B2</td><td>4%</td><td>14%</td><td>14%</td><td>16%</td><td>82%</td><td>70%</td></tr><tr><td>B6</td><td>4%</td><td>13%</td><td>9%</td><td>16%</td><td>87%</td><td>71%</td></tr><tr><td>B7</td><td>4%</td><td>14%</td><td>33%</td><td>28%</td><td>63%</td><td>59%</td></tr><tr><td>B8</td><td>4%</td><td>16%</td><td>28%</td><td>26%</td><td>68%</td><td>58%</td></tr><tr><td>B4</td><td>12%</td><td>11%</td><td>32%</td><td>31%</td><td>56%</td><td>58%</td></tr><tr><td>B10</td><td>2%</td><td>3%</td><td>39%</td><td>36%</td><td>59%</td><td>61%</td></tr></tbody></table>

As shown in Figure 18, the comparison between the concentrations estimated from LES modeling and the nominal values derived from the initial silver salt content indicates good agreement for most syntheses. In most of the syntheses, the calculated concentrations reach about 80% of the expected values. While this level of agreement supports the reliability of the approach, the systematic underestimation may partly reflect alterations during storage, transport, or the delay between synthesis and measurement, which could promote partial sedimentation of the suspensions. This explanation is further supported by the results of syntheses B6 and B7, where markedly lower concentrations were obtained and visible particle deposits were observed in the storage vials (see inset in Figure 18), confirming the effect of sedimentation on the measured values.

<figure><img src="image_20.png" /><figcaption>Figure 18: Comparison between nanoparticle concentrations estimated by LES modeling and nominal concentrations from silver salt content for the 7 different silver nanoparticle syntheses. Inset: photographs of storage vials showing particle sedimentation in syntheses B6 and B7.</figcaption></figure>

These results confirm that LES can be effectively applied to real nanoparticle syntheses, such as silver colloids, providing size and concentration estimates that are consistent with TEM analyses. Beyond reproducing reference measurements, LES also proves advantageous for handling complex mixtures of morphologies and for detecting deviations related to sample handling or stability, which highlights its potential as a practical and complementary tool for nanoparticle characterization.

### 4.3. Discussion on methodological limitations

Overall, the combination of LES and microfluidic systems provides a robust and versatile platform for nano- to submicron particle characterization, offering reliable analysis across a wide range of particle types and applications. Nevertheless, some of the limitations of this approach have been highlighted, especially related to the intrinsic nature and possible evolutions of the studied systems, and therefore must be considered when interpreting the results. Specifically for dielectric particles, any possible aggregation phenomena could present additional challenges for a reliable interpretation and measurement at the microfluidic scale, potentially biasing results. Additionally, while computational models provide insights into these effects, their complexity increases for non-spherical geometries, requiring significant computational resources. Real-time monitoring or improved sample dispersion methods could help addressing these issues. Moreover, extending the spectral range into the UV region using more powerful spectrometers and light sources may enhance sensitivity, provided that contamination and noise are adequately controlled. For metallic nanoparticles, the need for advanced computational models, such as DDA and T-Matrix, highlights the importance of continued development in theoretical methodologies. These models, while accurate, are computationally intensive, necessitating efforts to improve their efficiency for practical applications.

## 5. Conclusions

This work demonstrates the applicability of light extinction spectroscopy (LES) integrated with microfluidic systems for the characterization of nano- to submicron particles across a wide variety of materials, sizes, and morphologies. By combining multipath continuous and segmented flow configurations, different optical path lengths and flow regimes, and considering either metallic or dielectric particles of various size and/or shape, a comprehensive evaluation of the performance of LES was performed, showing that reliable measurements of particle size and concentration can be achieved within an accuracy of approximately 20% for most cases.

For dielectric particles such as silica and latex, the method provided consistent results, with improved accuracy for larger sizes and for materials with higher extinction cross-sections. For smaller particles, increased variability was observed, reflecting the inherent limitations imposed by weaker optical signals and noise sensitivity. Metallic nanoparticles, including
gold standards and complex silver colloids, were also successfully analyzed. In particular, for silver nanoparticle syntheses, LES provided results coherent with TEM analyses while offering additional advantages, such as improved representation of polydisperse distributions and the ability to detect alterations arising from sample storage or handling.

Overall, these results establish LES on-chip as a relevant, easy to implement and complementary tool for particle characterization. Its strengths lie in the capacity to handle complex mixtures and to provide quantitative information on both size and concentration in real-time microfluidic environments. At the same time, the method's limitations are closely tied to the intrinsic properties of the studied systems—particle size, morphology, and optical response—as well as to experimental conditions. Continued advances in computational modeling and microfluidic design are expected to further enhance the accuracy, efficiency, and range of applicability of the method. Moreover, the combination of LES and microfluidics holds significant potential for *in situ* and *in operando* characterizations [41], enabling real-time studies of colloidal stability, aggregation dynamics, and optical properties, paving the way to direct in line particle characterization during their synthesis in microfluidics [42] and to automated optimization of synthesis parameters.

## Acknowledgments

This work is funded by ANR project 22-PEXD-0007 (2FAST). The authors thank Drs. P.-B. Flandrin and F. Malloggi, as well as Ms. E. Couderne, for providing the nanogold standards and for fruitful discussions.

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