Toward Continuous Nano-Plastic Monitoring in Water by High Frequency Impedance Measurement With Nano-Electrode Arrays

We explore the potentiality of high frequency impedance measurements with CMOS nano-electrode (NE) arrays for nano-plastic pollutant particles monitoring in water. This technology offers benefits as nano-scale resolution, high parallelization, scalability, label-free single particle detection, and automatic measurements without operator intervention. Simple models are proposed for size and concentration estimation. The former integrates measurements of adjacent electrodes and shows uncertainty comparable to the nominal one with mean prediction error lower than 45% down to 50 nm radius. The latter accounts for noise in the definition of the sensing volume. We report a worst case concentration error lower than a factor 1.7 under stationary and continuous flow, which demonstrates the potential of this technology for automated measurements.

The ionic strength of water varies widely depending on the source and the location on earth, depth, ground composition, temperature, and nearby human activity [12]. The average salinity of water can vary from essentially zero in pure water to 0.05% for tap water and freshwater (≈10 mM), 0.05% to 3% for brackish water, up to 3.5% for seawater (≈500 mM) [12]. In spite of increasing research efforts and the World Health Organization (WHO) calling for more attention to microand nano-plastic pollution in water [13], neither well-defined standards on sampling, detection and measurement techniques have yet been defined [4], [10], [14], [15], nor consensus has been reached for plastic pollutant nomenclature based on size [16], [17].
In this context, current analytical technologies for monitoring pollutants in water are mainly based on optical microscopy and vibrational spectroscopy, which are bulky, expensive, time-consuming, and require complex sampling procedures carried out by skilled operators [4], [15]. In particular, Fourier transform infrared spectroscopy (FT-IR) and Raman spectroscopy have limitations in detecting particles smaller than 1 µm diameter [10], [15], thus preventing their use for nano-plastics monitoring [4], [10], [11], [15]. A shortlist of techniques recently proposed to overcome these limitations is given in Table I [23], [24], [25], radio frequency resonators [26], [27], and electrochemical impedance spectroscopy (EIS) [28] (sometimes integrating computer vision technology [29], [30]), have been published as well. EIS was also proposed for real-time monitoring of pollutants in graphene filters [31], and capacitive measurement for particle detection in lubricating oil [32]. High frequency impedance spectroscopy (HFIS) with nano-electrodes (NEs) array [33], [34], [35], [36] is a still largely unexplored (bio)sensing technology, with demonstrated capability to directly detect by purely electrical means single nano-particle (NP) as small as 40 nm diameter on top of bovine serum albumin immobilization layer [33]. HFIS offers numerous interesting features, such as the mitigation of the salinity-dependent sensitivity limits imposed by the decay of the electrical potential due to ions accumulating at the electrode-electrolyte interface (Debye screening), and the inspection of frequency-dependent electrical properties of analytes for fingerprinting. Moreover, the compatibility with CMOS technology enables a high degree of miniaturization, parallel operation at multiple sensing sites and possibly mass production at low costs. Dimensional scaling of the array along the progress of Moore's law points toward label-free single-particle detection and imaging with better-than-optical nanoscale resolution [33], [34]. Despite a few recent reports of impedance measuring systems with electrode arrays [37], [38], [39], [40], [41], [42], [43], [44], the platform employed in this work remains one of the best in terms of array and electrode size, spatial and capacitance resolution, maximum frequency [33], [45].
This work investigates the potential and challenges of HFIS with CMOS-based NE arrays for detection of nano-pollutants in aqueous solutions. In particular, we examine, by experimental analysis assisted by numerical simulations, the detection of polystyrene (PS) NPs, which is a common water pollutant [4], [7], [15], with sub nanoelectrode pitch dimensions dispersed in phosphate buffer saline (PBS), as well as their size and concentration estimation. The chosen medium has a physiological salt concentration (≈160 mM) matching biological samples, and comparable to seawater, brackish water, and some types of freshwater.
In the following, we denote polymeric spheres with diameter smaller than 1 µm as "nano-plastic" and debris within the same size limits as NPs in general, in agreement with recent published reviews [7], [10], [15], [16], [17], [46]. In addition, although some publications denote "real-time measurements" the ones that operators perform on site of sampling, we prefer to name "continuous flow" those measurements without an operator that could be implemented online at non-zero flow rate, for instance, along a bypass pipe.
This article proceeds as follows. Section II describes the experimental setup, the measurements procedure, and the numerical simulation methods used to assist data interpretation. Section III reports the results of size and concentration estimation; Section IV discusses their significance.

A. Experimental Setup
In this work, we use the HFIS NE array sensor chip (see Fig. 1) extensively described in [33], [34], [35], [36], and [47]. For the sake of a self-contained paper, we summarize in the following its key features. The chip integrates 256 × 256 individually addressable NEs (radius 90 nm, pitch p x × p y = 600 × 720 nm) fabricated with 90 nm low-power CMOS technology. The calibrated chip provides frequency resolved 256 × 256 pixels images of the capacitance measured at each electrode in the 1-70 MHz range [33], [36], with potential extension up to 500 MHz [45]. The sensing information is derived as the capacitance change caused by the perturbation of the ac electric field induced by the analyte(s) C = C mean,w/analyte − C mean,wo/analyte (1) where C mean refers to the mean value of 100 samples of the measured capacitance (as described in [33]). Fig. 2 reports an example of capacitance signal with the NP detection event and the resulting C map. In our nomenclature, the term mean refers to the temporal mean, while average or ave and std refer to the mean and standard deviation over sample space, respectively (e.g., the ensamble of NPs or NEs in the array). The C of each NE is mainly related to the analyte's conductivity and dielectric permittivity, dimensions, and position with respect to the electrodes [33], [48], [49].
The HFIS NE array chip is integrated in an experimental setup (Fig. 1) that includes: 1) the chip's initialization and interrogation electronics [field programmable gate array (FPGA) board by Intel and custom dual layer printed circuit board (PCB)]; 2) the temperature control system (Peltier cell model ET-127-10-13-RS by adaptive, proportional-integralderivative (PID) temperature controller model PR-59 by Laird Technologies); 3) the microfluidic chamber confinement around the NE array (socket by ARIES electronics and a novel dogbone shaped polydimethylsiloxane (PDMS) ring, optimized to enhance the probability of analytes passing above the sensing array); and 4) the microfluidic system (polyetherether-ketone (PEEK) tubes by Upchurch Scientific, step-motor syringe pump model NE-300 by KF-Technology, 10 mL Luer Lock disposable syringe by Cole Parmer, 1.5 mL safe-lock tubes by Eppendorf). More information about each sub-system are given in [33].

B. Numerical Simulation Setup
Numerical simulations of the sensor response to the measured analytes are based on ENBIOS [50], which selfconsistently solves the Poisson-Boltzmann equation and the coupled Poisson-Drift-Diffusion equations in steady state and in the time-harmonic, linear small signal regime (AC), respectively, for all ion species in the electrolyte [50]. The capacitance response in the switching regime adopted by the hardware ( C (s) ) is derived from the AC simulations as described in [33]. The effectiveness of this procedure in accurately reproducing, predicting and supporting interpretation of the sensor acquisitions has been proven in numerous previous studies [33], [34], [35], [48], [49], [50], [51]. Fig. 2 defines the main geometrical and physical parameters used in this work. The simulation grid is created with Netgen [52] and extends over a 5 × 5 array of NEs with the same radius and pitch as the chip, Section II-A. The NP is implemented as a sphere with radius R and position (d x , d y , d z + R) with respect the center of the central electrode of the 5 × 5 array [hereafter denoted as pixel (0, 0), which is, by definition, the one which gives the higher C (see Fig. 2)]. The NP permittivity (ε r,NP ) and conductivity (σ NP ), as well as the dielectric permittivity and the ion concentrations in the electrolyte, are assigned consistently with experiments, as reported in Table II.
3) The diluted NPs-PBS sample was filtered with 3 µm pores syringe filter membrane (Fluoropore, 47 mm, PTFE, by Millipore) and sonicated (Cole Parmer CPX-750 Ultrasonic Homogenizer) before and after the filtering. The NPs size was also measured with dynamic light scattering (DLS), a common NP size estimation method [53]. We obtained measured DLS radii 53.8 ± 6, 278.3 ± 28, and 500.4 ± 30 nm, essentially confirming the reported nominal values. Therefore, the nominal values will be taken as reference below.
Once the sample was prepared, the following measurement procedure was carried out.
1) The chip's platform and the temperature control system were turned on, the chosen measurement conditions were set (see Table II) and the system was allowed to reach the thermal steady state. 2) The microfluidic system was flushed with ≈3 mL isopropyl alcohol (IPA, purchased by Sigma-Aldrich), filtered with 0.2 µm pores syringe filter, with a flow rate of 100 µL/min. This procedure cleans the tubes and the NE array, eliminates air bubbles, and allows us to eliminate upfront possible fluid leakages. 3) The system was briefly flushed with ≈1 mL of PBS, to minimize undesired mixing of the NPs sample with IPA. 4) The NPs-PBS sample is introduced into the microfluidics. 5) Once the data were collected, the system was flushed with ≈3 mL of deionized H 2 O (Sigma-Aldrich, Germany), filtered with 0.2 µm pores syringe filter, and ≈3 mL of IPA with a flow rate of 200 µL/min for cleaning.
The ambient temperature was ≈22 • C, equal to the temperature controller setpoint; therefore the fluid temperature does not affect the measurement.
Three experiments were performed for radius and concentration estimation, one for each NP. Overall, more than 100 objects were analyzed for each radius. Additionally, five tests were run with 500 nm radius NPs to estimate concentration at different dilutions. In particular, starting from nominal concentration n P = 1.27 · 10 9 #NP/mL, dilutions of 1:2, 1:5, 1:10, and 1:20 were considered. Experiments were repeated with the latter samples according to the above procedure. In order to investigate static and continuous flow conditions, the flow rate φ n was initially set to zero, and then to 10, 100, 10, and again 10 µL/min, each for a time interval T n ≈ 75 s for total examined volume V sample = n φ n · T n = 158 µL, equal for each concentration value.
Finally, the data were elaborated according to [33] and a 5 × 5 C(i, j) matrix centered on the electrode (0,0) with maximum response C(0, 0) was calculated with (1) after the object detection procedure. Given the large amount of raw data generated by the experiments (≈246 MB/min), and the upfront lack of a robust object detection algorithm, the NPs detection was only partially automated during the first experiments. In particular, we applied the MATLAB function findchangepts on the capacitance signal of each NE to extract the instants when the measured capacitance significantly changes its mean value (detection event). Then, we calculated C mean,w/analyte and C mean,wo/analyte from values respectively following and preceding the particle arrival event. Last, the NPs in the first experiments (Section III-A) were identified manually to form a dataset of ≈300 objects (≈100 for each NP size). Once the radius estimation model was derived, for the concentration estimation, a simple automated object detection algorithm for monodisperse solutions (described in Section II-D2) was used to identify the right objects in the image, count them and then estimate the NPs concentration, n P,est . In this way the NPs concentration estimation is not operator-dependent, and the radius estimation model was also validated on new, automatically detected sets of particles with respect to the previously manually selected 300 NPs.

D. Methods for Size and Concentration Estimation
1) Sub-Pitch Radius Estimation: Size estimation for NPs with dimensions smaller than the pitch of the imaging array (50-500 nm NP radius and pitch p x = 600 nm, p y = 720 nm), poses new challenges with respect to existing water-pollutants monitoring systems [15] and to previous works on this same platform but with larger microparticles [33], [35], [48]. Three aspects can be interdependently taken into consideration: 1) at high enough frequency, the AC electric field propagated in the electrolyte by one electrode spreads laterally beyond one pitch distance [33]; 2) the C magnitude is proportional to the particle volume (thus, to the cube of its radius) [49]; and 3) possible displacement of the NP in the 2-D plane can result in a significant response of adjacent electrodes. Since sub-pitch sizes are considered, only a 3 × 3 matrix is examined, to avoid adding data from electrodes with very small and noisy response to the NP.
Based on these considerations, we first estimated the particle offset in xand y-directions (d x and d y , see Fig. 2) with respect to the electrode featuring the highest response as follows: where (i, j) ∈ [(−1, +1), (−1, +1)], with p x = 600 nm and p y = 720 nm. Then we calculated which represents the 3 × 3 matrix of distances of each first neighbor pixel from the pixel with largest response (i.e., the coordinates origin) shifted according to the NP position (d x,est , d y,est ) estimated using (2) and (3). Exploiting symmetry reasons, we constructed a four elements vector γ (e) by averaging [ C(i, j)d 2 (i, j)]/C 0 over symmetric pixel locations: e = 1 for (i, j) = (0, 0), e = 2 for (i, j) = (±1, 0), e = 3 for (i, j) = (0, ±1), and e = 4 for (i, j) = (±1, ±1). Here C 0 is the ensemble average capacitance measured by the chip NEs in dry air at 50 MHz and T = 22 • C. Eventually, we expressed the estimated particle radius as follows: where p(e) is a vector of calibration coefficients, actually taken all equal in this work. This reduces the model parameters to only one scalar value p. From a single experiment with NPs of nominal radius R nom detecting N data objects, the mean value R, the uncertainty u R , and the prediction error ϵ R were calculated according to 2) Noise-Based Sensing Volume Definition for Concentration Estimation: The accurate determination of NPs concentration (n P ) requires to quantify the volume inspected by the measurement system, hereafter called sensing volume, V sens . This is a challenging task for sensors based on impedance measurement, due to the rapid decay of the electric field magnitude induced by Debye screening, and the hypersensitivity of low frequency measurements to surface phenomena. In fact, Debye screening is largely dependent on measurement frequency and ionic concentration [34]. Since, at first order, the NE capacitance response C is proportional to the squared unperturbed AC electric field at the particle center location (i.e., the one in the absence of a particle, denoted E 2 ) [49], we can define the sensing volume as the region above the array surface where the squared unperturbed AC electric field is larger than the threshold value (E 2 thr ) that corresponds to C thr = 3·σ noise,ave , where σ noise,ave is the ensemble experimental standard deviation of the electrode capacitance measured in the absence of analytes. The dominant noise generation mechanism is electronic, as discussed in [33].
In practice, the following procedure was used to calculate V sens for each NP radius. First, a statistical analysis of the capacitance noise from experiments without NPs was performed. In particular, we verified that: 1) in the chosen conditions (see Table II), the C noise of each electrode was Gaussian with zero mean and 2) the measured σ noise (i, j), i.e., the empirical standard deviation of the C, was homogeneously distributed over the entire array ((i, j) ∈ [ (1, 256), (1, 256)]), i.e., σ noise,std ≪ σ noise,ave , where σ noise,ave and σ noise,std are the empirical average and standard deviation of σ noise of the ensemble of all 256 × 256 electrodes. If these were verified, we assumed that all electrodes behave the same and the maximum sensing distance was essentially constant above all electrodes, regardless of i and j. Second, exploiting the available accurate simulation setup, we determined the threshold distance d z,thr , such that the simulated C (s) (dz > d z,thr ) < C thr , and the corresponding E 2 thr = E 2 (0, 0, d z,thr + R nom ). The electrolyte region where z sens (x, y) = d z,thr + R nom such that for z < z sens (x, y) : E 2 (x, y, z) > E 2 thr defines a surface in the 3-D space over a single electrode. Thus, exploiting the generalization verified in the first step, V sens is where is the portion of the array corresponding to a single electrode Note that, for the calculation of V sens the knowledge of the salinity of the sample is necessary, for instance by advanced techniques as those reported in [54] and [55]. Once V sens was calculated, the NP concentration (n P ) was estimated according to n P,est = λ · ζ · N P V chamber + n φ n · T n (10) where N P is the cumulative number of NPs detected in a given experiment, V chamber is the volume of the measuring chamber (A array · z max ≃ 7.1 nL). φ n is the flow rate set for time T n (as described in Section II-C, for experiments evaluating continuous measurements n φ n · T n = 158 µL). ζ = V chamber /V sens is the coefficient that takes into account the reduction of the volume inspected by the NE array with respect the total V chamber . Finally, the correction factor λ (derived experimentally) reflects the observation that in continuous flow measurement (i.e., non-zero flow rate) N P did not scale proportionally to the flowing sample volume. Thus, λ is taken equal to 1 in case of static measurements, whilst λ ̸ = 1 in continuous flux conditions. N P was computed with the following procedure: the MATLAB function findchangepts was used to detect significant variations of mean capacitance for each electrode, as described before. Afterward, the radius estimation model described in Section II-D1 was used to filter non-NP events (noise, local drifts, bubble, impurities, etc. . .) defined as R est < 0.5 · R nom and R est > 1.2 µm (consistently with the choice to consider a 3 × 3 array with approximate size 1.2 × 1.44 µm), R nom being the nominal radius of the monodisperse NPs. Finally, the concentration estimation error was calculated as follows: ϵ n P % = n P,est − n P,nom n P,nom · 100.

A. Sub-Pitch Size Estimation
As described in Section II-D1, the unit-less coefficient of the radius estimation model was calibrated on measurements (300 objects) obtaining p = −434.4, while the average capacitance in air at 50 MHz and T = 22 • C is C 0 ≃ 0.40 fF. Fig. 3 shows the predicted nominal radius, whereas Table III reports model prediction results (R ± u R ) and errors (ϵ R %) according to (6)- (8). Further validation of the radius estimation model is reported in Section III-B, where the model was used to automate the NPs detection for n P estimation. Fig. 4 (left) shows the probability density function (PDF) of the σ noise measured for each electrode in four experiments without analytes, at zero flow rate and conditions reported in Table II. Each σ noise was calculated from 200 capacitance measurements per electrode, and the mean value of the noise is zero. The figure also shows σ noise,ave (red dashed line).  Table III.  The resulting value of σ noise,ave is 2.9 aF, with a standard deviation σ noise,std of 0.7 aF. Fig. 4 (right) shows σ noise,ave ± σ noise,std for varying flow rates at T = 22 • C (top) and for zero flow rate and varying temperatures (bottom), showing stable values regardless of the considered environmental conditions.

B. Concentration Estimation
Following the method described in Section II-D2, d z,thr and E 2 thr were calculated from numerical simulations to determine V sens . Fig. 5 (top) shows the simulated C (s) as a function of d z for particles centered on the electrode, as discussed in Section II-D2. The intersections of the curves with the 3 · σ noise,ave threshold yields d z,thr . Fig. 5 (bottom) shows the corresponding V sens in log-scale for different radii. Fig. 6 (bottom) shows the concentration error under stationary conditions (φ = 0, λ = 1) according to (11) versus the nominal radius. The estimated n P is the average over four V sens calculations at φ = 0 µL/min and four different instants. Fig. 6 (top) shows the corresponding radius estimation error in boxcharts; as discussed in Section II-D2, the radius estimation was part of the automated procedure for NPs detection.  In agreement with results reported in Section III-A, we observe that the model overestimates the expected value for 50 nm NPs, and also has larger spread. Fig. 7 shows the results of experiments where dilution was varied, and where continuous measurements (with flux) were investigated. The unit-less correction factor λ is 1 at zero flow and 1740 otherwise. The top graph shows the estimated concentration in this case versus the nominal concentration. The middle graph reports the estimated radius for each concentration value, showing predictions independent of concentration, as it should be. The bottom graph shows the concentration estimation error under both steady (φ = 0) and continuous flow (φ ̸ = 0) conditions. While V sens calculation enables concentration estimation, further optimization of the measurement chamber may be necessary to improve the accuracy and efficiency of the measurement. In fact, since the NPs outside V sens are not detectable by the NE array, the height of the measuring chamber can be optimized guiding the sample flow in this region, or the measurement frequency increased to further reduce Debye screening.

IV. DISCUSSION AND CONCLUSION
As anticipated in the introduction, current water pollutant monitoring systems suffer several limitations, particularly so in detecting particles in the nanoscale. This study investigated the potential of a new monitoring paradigm based on high-frequency impedance measurement with CMOS NE arrays for continuous monitoring of nanoparticles in water. An analytical model for size estimation of NPs with (subpitch) radii smaller than the theoretical resolution of the array (pitch 600 × 720 nm) has been developed. Compared to nominal values, the model slightly underestimates larger NP dimensions (275, 500 nm), while overestimating those with smaller radii (50 nm). Nevertheless, the worst case mean error is always lower than 45%. The spread of the estimated radii (Table III, Fig. 3) is only slightly larger than the nominal one, and essentially in line with DLS sizing experiments, which confirmed very low deviations (<7%) from the nominal NP radii. Possibly, the slightly larger variability in the measured capacitance may reflect that of the unknown vertical position of the particle.
We also addressed the challenging goal of estimating the concentration of PS-NPs in stationary and continuous flow conditions, as a model system for more general nano-plastic monitoring in water. Our approach defines the sensing volume and accounts for it considering the noise associated with the capacitance measurement of the nanoelectrodes. Promising results are obtained for all NP concentrations (Figs. 6 and 7) and for different radii. They demonstrate a worst case estimation error of a factor 1.7.
Notice that all experiments were run in high ionic strength solutions (PBS ∼160 mM) compared, for instance, to common tap water. Although Debye screening limitations are mitigated at the chosen 50 MHz operating frequency, the sensing distance remains much smaller than the microfluidic chamber height; therefore, our evaluations may be overpessimistic with respect to tap water conditions of large interest. We also point out that the simple analytical models proposed to extract R est and n P rely on only two calibration parameters, easily estimated from two dedicated experiments which is a valuable feature in view of low-power Internet of Things (IoT) applications.
Several aspects deserve more extensive future investigations. First, the estimation of the nano-plastics surface charge density, which recent papers suggest to play an important role in NPs cytotoxicity [10], [56], is definitely in the potential of the HFIS CMOS NE array, thanks to its spectrally resolved operating mode and large bandwidth. Second, since capacitance spectroscopy is sensitive to the dielectric permittivitly and conductivity of the analyte, a potential for NP material classification of pollutants exists. Common plastic pollutants (e.g., polystirene, PVC, and PET) have similar ε r (in the 2-4 range); discrimination among their responses appears challenging given the electronic noise floor of current chip implementations and the variability of the response induced by the unknown position above the array surface. On the contrary, discrimination between dielectric and metallic NPs (and likely materials in between) is possible via inspection of the measured C, whose sign depends on the conductive versus dielectric nature of the analyte, and is likely improved by fingerprinting of the capacitance spectra as shown in [35] and [34]. The explored concentrations interval is on the high side for common micro and nano pollutants' concentration in water. Furthermore, aggregates have been avoided via sonication, but should be part of more extensive studies beyond the scope of this work. Notwithstanding all the above considerations, to the best of our knowledge, this is the only CMOS electronic sensing technology reporting single nanoparticle detection and size/concentration estimation in continuous flow with NP radii down to 50 nm to date.