In-Situ Measurement of the Size Distribution and Concentration of

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In-Situ Measurement of the Size Distribution and Concentration of Insulating Particles by Electrochemical Collision on Hemispherical Ultramicroelectrodes Zejun Deng, Ridha Elattar, Fouad Maroun, and Christophe Jacques Renault Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.8b03550 • Publication Date (Web): 04 Oct 2018 Downloaded from http://pubs.acs.org on October 7, 2018

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Analytical Chemistry

In-Situ Measurement of the Size Distribution and Concentration of Insulating Particles by Electrochemical Collision on Hemispherical Ultramicroelectrodes Zejun Deng, Ridha Elattar†, Fouad Maroun, Christophe Renault*

Physique de la Matière Condensée, CNRS, Ecole Polytechnique, 91128 Palaiseau, France ABSTRACT: One of the greatest limitations in electrochemical collision/nano-impact methods is the inability to quantify the size of colliding species due to the uneven current distribution on a disk ultramicroelectrode UME (so-called edge effect). This phenomenon arises since radial diffusion is greater at the edge than the center of the active electrode surface. One method of solving this problem is fabrication of a hemispherical UME. We describe the fabrication of a hemispherical Hg UME on a disk UME by a solution-based electrochemical method, chronocoulometry. The use of hemispherical Hg UME to detect collisions of individual aminefunctionalized polystyrene beads removes the "edge effect" and enables simultaneously measurements of the concentration and the size distribution of colloids in suspension. Using finite element simulations, we deduce a quantitative relation between the distribution of current step size and the size distribution of the bead. The frequency of collision measured for a given size of bead is then converted into a concentration (in mol/L) by a quantification of the relative contributions of migration and diffusion for each size of bead. Under our experimental conditions (low concentration of supporting electrolyte), migration dominates the flux of bead. The average size of polystyrene beads of 0.5 and 1 µm radius obtained by electrochemistry and scanning electron microscopy (SEM) differs by only -8% and -9%, respectively. The total concentration of polystyrene beads of 0.5 and 1 µm radius obtained by electrochemistry is found in close agreement (< 10% of error) with their nominal concentrations (25 fM and 100 fM).

according to nature, charge, size and shape of the particle as well as its interaction with the surface and the electrolyte composition. Insulating particles are typically detected by electrochemical “blocking”. In this experiment, a redox reporter in solution is being oxidized/reduced at a UME to produce a steady state current. When an insulating particle adsorbs on the UME and blocks its surface, a step-like decrease of the amplitude of the current is recorded. Blocking was used to detect the presence of proteins, virus, quantum dots, silica nanoparticles, vesicles, bacteria, and polystyrene particles.10-17 Several attempts were made to determine the concentration and size of particles from the analysis of the current steps. For example, the concentration of particle can be obtained through the analysis of the frequency of steps.11 The analysis of the magnitude of the current step was used to estimate the size of the insulating particles.18 However, Crooks and coworkers reported that, on a disk-shaped UME, the size of the current step is not solely a function of the bead size.19 They observed by fluorescence microscopy the position of polystyrene microbeads landing on disk UMEs and correlated this position to the magnitude of the current step. Hence, they showed that a bead located on the perimeter of the disk is producing current steps about four to seven times larger than a bead (of similar dimension) located at the center of the disk. This “edge effect” results from the inhomogeneous flux of redox reporter at the surface of a diskshaped UME. Consequently, it is difficult to measure accurately the size distribution of insulating beads by electrochemical blocking on disk-shaped UMEs. The determination of the bead concentration is also subject to some uncertainties. When there is not enough supporting electrolyte to carry all the current, the beads undergo significant migration. Thus, the probability for a bead to land at certain position on a disk-shaped UME is not equal everywhere but depends on the local flux of redox reporter, the charges at the

INTRODUCTION We report an analytical method to characterize the size distribution and concentration of electrically insulating particles in suspension. The method is based on single particle detection by electrochemical blocking, where a single particle’s collision with the electrode surface is characterized by adsorption and blocking of the active electrode area. The novelty of this work resides in the use of hemispherical ultra-microelectrodes (UMEs) instead of diskshaped UMEs. The hemispherical geometry of our UMEs enables the measurement of both the size distribution of the particles and their concentration. These two parameters are obtained through a detailed analysis of the diffusion and migration of the particles as well as numerical simulations. We used polystyrene microbeads as a benchmark to validate our approach. The analytical performances of our method are validated with a gold standard technique, SEM. Common techniques used to measure the size of particles in solution are DLS and ultrasound.1,2 Their resolution ranges from few nanometers to several micrometers. While the size of the particle can be easily obtained it is generally more complex to obtained their concentration.3,4 Among the rare analytical tools able to measure accurately both size and concentration of particles one can find single nanoparticle tracking analysis (NTA). The NTA instrument tracks the scattering signal of individual particles to reconstruct trajectories and count them in a rapid and accurate manner.5 However, the cost, size and fragility of this equipment are restricting its usage to large facilities. Single entity electrochemistry is emerging as an inexpensive and sensitive method to observe individual micro- and nanoparticles in solution.6-9 This method relies on the detection of discrete variations of current (or potential) caused when a single particle, initially floating in solution, collides with the surface of a microelectrode.10 The shape and intensity of the signal will differ 1

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surface of the beads and their size. Consequently, it not possible under migration to estimate precisely the concentration of bead for an unknown size distribution.

of bead is then converted into a concentration (in mol/L) by a careful quantification of the relative contributions of migration and diffusion for each size of bead. Based on our quantitative analysis, the analytical limits of the electrochemical blocking are discussed. We finally compare the size distribution obtained by electrochemistry with the size distribution measured by SEM.

EXPERIMENTAL SECTION Chemicals and Instruments. Amine-functionalized polystyrene beads of 0.5 and 1 µm radius (product numbers: L1030 and L9529, respectively), sodium nitrate (NaNO3), mercury nitrate (Hg(NO3)2), hexaammineruthenium(III) chloride ([Ru(NH3)6]Cl3), acetate acid (CH3COOH) and sodium acetate (C2H3NaO2) were purchased from Sigma-Aldrich (Saint Louis, USA). Acetate buffer (pH = 5) was prepared by mixing 59 ml of 0.1 M acetic acid and 141 ml of 0.1 M sodium acetate. The 10 μm disk platinum UMEs are fabricated by heat-sealing a 5 µm radius Pt wire (hard tempered, Goodfellow) inside the borosilicate glass capillary (2 mm outer diameter, 1.16 mm inner diameter, Sutter Instrument, Novato USA). The Pt disk is polished with abrasive disks (600, 800, 1200 grit) and alumina slurry (1, 0.3 and 0.05 µm, Buehler, Lake Bluff, USA) until a mirror-like surface is observed under an optical microscope. The connection between a platinum wire and a tungsten wire (0.25 µm diameter, ChemPure, Karlsruhe, Germany) was made with a conductive silver paste (RS Components, Northants, UK). Milli-Q water with the resistance of 18.2 MΩ.cm1 was used throughout the experiment. The zeta potential of the 0.5 and 1 µm radius amine-functionalized polystyrene beads was measured in a solution containing 1 mM acetate buffer (pH = 5) and 3 mM [Ru(NH3)6]Cl3 using a Zetasizer Nano ZS (Malvern Instrument). The size distribution of polystyrene beads was obtained by scanning electron microscopy (Hitachi S-4800, see Supporting Information).

Figure 1. (A) Simulated concentration profiles of a redox molecule being oxidized/reduced at mass transfer-limit on a disk and a hemispherical UME. The grey and light blue colors represent the electrode and the glass sheath, respectively. The concentration of redox reporter above the electrode is indicated by the colormap. (B) The black and red traces correspond to the dimensionless flux simulated at a disk and a hemispherical UME, respectively. The radial position is normalized by the radius a of the UME. The letters Φ, D and C correspond to the flux, the diffusion coefficient and the concentration of the redox reporter, respectively.

Fabrication of the hemispherical Hg UMEs. The hemispherical Hg UMEs were made by depositing Hg on 5 µm radius Pt disk UMEs by chronocoulometry at a potential of -0.1 V in a solution of 10 mM of Hg(NO3)2 in 100 mM NaNO3. The solution is continuously bubbled with Ar to remove O2. A typical chronocoulogram is shown in Supporting Information. A theoretical charge of 3.415 µC corresponds to the reduction of Hg2+ required to form a hemisphere of 5 µm radius. In practice we observed that a charge of 5.997 ± 0.257 µC is necessary to produce a hemisphere. The faradaic yield is thus 57%. The final size of the Hg hemisphere is measured by cyclic voltammetry of [Ru(NH3)6]Cl3. When the steady-state current increases by a factor 1.58 ± 0.16 (theoretical difference in steady state current for a hemispherical and disk-shaped UME) we stop the electrodeposition.

Interestingly the flux on a hemispherical UME is different from the flux on a disk-shaped UME. This difference is shown in Figure 1. The simulated concentration profiles of a redox molecule being oxidized/reduced at mass transfer limit on a disk and hemispherical UME are shown Figure 1A. While the symmetry of the hemispherical UME is radial and thus all the positions on the hemisphere are equivalent it is not the same situation on the diskshaped UME. The edge of the disk has access to a larger volume of solution than the center of the disk. This results in a flux of redox molecule larger at the perimeter than the edge of the disk. Fluxes of redox molecule simulated at the surface of a disk-shaped and hemispherical UME of radius a are shown Figure 1B. The flux at the edge of a disk is about seven times larger than at its center, in agreement with previously reported observations.19 On the other hand, the flux at the surface of a hemisphere is constant. Hence, current steps produced by a bead located at the top of the hemisphere or its edge are expected to be identical (this point was confirmed by numerical simulation provided in Supporting Information). Note also that, the average flux is 1.58 times larger on a hemisphere than on a disk of same radii. We report the blocking of ruthenium hexamine reduction by the adsorption of individual amine-functionalized polystyrene beads of 0.5 and 1 µm radius at the surface of a 5 µm radius Hg hemispherical UME. Ruthenium hexamine was chosen as the analyte of interest such that the Hg surface would be cathodically protected during the electrochemical experiment, as Hg can oxidize at mild potentials and in the presence of mild oxidants, such as ruthenium hexamine and oxygen. We use numerical simulations to deduce a quantitative relation between the current steps and the size of the bead. The frequency of collision measured for a given size

Electrochemical measurements. All electrochemical measurements were performed using a homemade two-electrode setup placed in a Faraday cage. Briefly, a current amplifier (DDPCA-300, Femto GmbH, Berlin, Germany) is used to record the current applied between the UME and the reference electrode. The reading of the amplifier and the application of the desired potential between the two electrodes are performed with an acquisition card (USB 6212, National Instruments, Austin, USA) controlled with a PC and a home-made Labview (v2013) program. Details about the setup are provide in Supporting Information. A 2 mm diameter leakless miniature Ag/AgCl 3 M KCl reference electrode (ref: ET072, EDAQ, Warsaw, Poland) was used as the reference/counter electrode. Prior to use, stock solutions of beads were centrifuged and re-dispersed in Milli-Q water three times. The cell is kept under an Ar blanket at all-time. The cell was stirred by bubbling Ar in solution for approximately 10 s right before running 2


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Analytical Chemistry chronoamperometry measurements in order to ensure a homogeneous concentration. The Ar inlet was then raised above the surface of the liquid right before the measurement to minimize convection. Chronoamperograms are recorded for 120 s for each run. Before addition of beads in solution, chronoamperograms are recorded over 120 s to ensure that no steps are observed.

Numerical simulations. Numerical simulations were performed with a finite-element simulation package, COMSOL Multiphysics 4.4. The current step size was estimated by simulating the steadystate current produced by the reduction at mass transfer limit of Ru(NH3)63+ on a Hg hemispherical UME in absence and in presence of an insulating bead. Details about the model and a full COMSOL report are provided in Supporting Information.

RESULTS AND DISCUSSION Collision on hemispherical UMEs. A scheme of the experimental setup is shown in Figure 2A. Blocking experiments are carried out with hemispherical (relec = 5.7 ± 0.3 µm) UMEs made by electrodeposition of a Hg hemisphere onto a disk-shaped Pt UME. The protocol of electrodeposition is described in the experimental section. The final Hg UME is biased at -0.4 V vs Ag/AgCl (3 M KCl) and dipped in a solution containing 3 mM of Ru(NH3)63+ and 1 mM acetate buffer pH 5. The solution is degassed with Ar. At 0.4 V vs Ag/AgCl 3 M KCl, the Ru(NH3)63+ is reduced at mass transfer limit (E° Ru(III)/ Ru(II) = 0.1 V) and a steady state current of 7.5 - 7.8 nA is measured at the UME. Figure 2B shows typical chronoamperograms obtained in the absence (red trace) and in the presence (black trace) of 1 µm radius amine-functionalized polystyrene beads. The red trace evidences sharp discrete current steps that are not observed in absence of bead. Each current step on the black trace is associated with the irreversible adsorption of a single polystyrene bead at the Hg surface. This observation is consistent with previous reports of adsorption of polystyrene bead on Au disk UMEs.10 An optical micrograph of the UME at the end of a collision experiment is shown in Supporting Information. Polystyrene beads are visible on the surface of the Hg hemisphere. Several chronoamperograms were recorded in order to observe a statistically relevant number of steps (c.a. 200). Each chronoamperogram corresponds to either a freshly prepared Hg UME or a Hg UME that was cleaned to remove the beads (see Supporting Information for details about the cleaning procedure). A maximum of 11 collisions is recorded per chronoamperogram. This corresponds to a bead coverage of less than 50 %. The probability to have a collision between a particle already adsorbed on the surface and a particle coming from the solution is thus at most 50%. Under these conditions we can consider that particles on the surface are rather independent. The size distribution of the current steps is plotted in red in Figure 3. The current steps (Δi) are normalized by the steady state current (iss) right before the step and then plotted in ‰. Typical steps are on the order of few pA while the steady state current is close from 7-8 nA. For the sake of comparison, we also plotted (in black Figure 3) the size distribution of current steps obtained with a disk-shaped UME of radius similar to the hemispherical UME (5.35 µm). The step size distribution obtained with the hemispherical UME ranges between 2‰ and 8‰ while it spans over c.a. 2-3 times larger range (3‰ and 22‰) for a disk UME. Both distributions have an asymmetrical shape with a tailing toward large step size. This tailing is much more pronounced for the disk-shaped UME than the hemispherical UME. Here we want to emphasize that the two distributions shown in Figure 3 are measured with the same beads but nonetheless they are different. This observation clearly proves that the step size distribution is not directly proportional to the bead size distribution although it may be seducing to assume it.13

Figure 2. (A) Scheme of the experimental setup. When an insulating polystyrene bead sticks to the surface of the UME then the flux of Ru(NH3)63+ toward the electrode (white arrows) is hindered and a discrete decrease of current is recorded. The concentration of Ru(NH3)63+ in the cell is indicated by the colormap. (B) Chronoamperograms recorded in absence (black trace) and in presence of 100 fM (6.022 x 107 particle/mL) of 1 µm radius amine functionalized polystyrene beads. The solution contains 3 mM of Ru and 1 mM of acetate buffer (pH = 5). The UME is biased at -0.4 V vs Ag/AgCl. As explained in the introduction, a disk-shaped UME is expected to create a broadening of the distribution with the apparition of “large steps”. These large steps are caused by beads landing on the edge of the disk UME where the flux is the largest. On hemispherical UMEs these large steps are not observed. Hence, we conclude that hemispherical UMEs can effectively reduce the edge effect. The reduction the edge effect does not allow a direct comparison of step size distribution and bead radius distribution. Indeed, we will see in the next section that both the step size and frequency of collision are functions of the radius of the bead and not always linear functions. Determination of the radius and concentration of beads. In order to convert the current steps into a bead radius we proceeded as follows. First we used finite element simulations to determine the current step produced by a bead of a given radius. Details about the simulations are provided in the Supporting Information. Note that these simulations are valid for spherical objects and cannot be used if the particle present a high aspect-ratio. Several simulations were performed with beads of various radii in order to generate the calibration curve shown in Figure 4A. To generalize this calibration curve to any system featuring a spherical particle on a hemispherical UME, the bead radius is normalized by the electrode radius and plotted in % while the step size is normalized by the steady-state current and plotted in ‰. The red curve corresponds to 3


Analytical Chemistry a least square fitting of a second order polynomial: Ax2+Bx. The coefficients A and B equal 0.0187 and -0.1012, respectively (R2 = 0.999). This equation holds for any ratio of bead/electrode (e.g. 0.05 µm radius particles/0.5 µm radius bead) shown in Figure 4A. In the above polynomial function, the quadratic component dominates. In other words, the current step size depends mainly on the projected area of the bead. Note that the quadratic dependence of the step size with bead radius implies that a symmetrical distribution of bead size should lead to an asymmetric distribution of step size. A quadratic behavior was also obtained when simulating a disk-shaped UMEs.18

30

20 Counts

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

10

0

6

12

18

i/i ini(‰)

Figure 3. Distribution of the amplitude of the current steps corresponding to the collision of 1 µm radius amine functionalized polystyrene beads on a 5 µm radius Hg hemispherical UME (red bars, 170 counts) and a 5 µm radius disk Pt UME (black bars, 194 counts). The steps are counted over c.a. 15 chronoamperograms of 120 s each.

Figure 4. (A) Simulated calibration curve of the step size vs bead size. Details about the simulation are provided in Supporting Information. The red line corresponds to a least square fitting of a second order polynomial: Ax2+Bx. The coefficients A and B equal 0.0187 and -0.101, respectively (R2 = 0.999). (B) Normalized collision frequencies as a function of the radius of the bead. The black and red lines correspond to the diffusion and migration components, respectively. These frequencies are calculated using Eqs 1, 2, 3 and the experimental parameters: relec = 5.3 µm, 𝐷[𝑅𝑢(𝑁𝐻3)6]3 + = 8.4 x 10-6 cm2.s-1, [Ru(NH3)63+] = 3 mM, [acetate buffer] = 1 mM, [Cl-] = 9 mM, [Na+] = 1 mM, 𝜇Ru3 + = 9.82 x 10-8 m2.V-1.s-1, 𝜇acetate buffer= 4.24 x 10-8 m2.V-1.s-1, 𝜇Cl ― = 7.92 x 10-8 m2.V-1.s-1, 𝜇Na + = 5.19 x 10-8 m2.V-1.s-1, 𝜎bead = 36 µC.m-2, η = 8.9 x 10-5 Pa.s, T = 293 K.

The calibration curve Figure 4A indicates that a relative step size of 0.5 ‰, the minimum step that could be distinguished experimentally, corresponds to a bead with a radius of 8.3% of the radius of the UME. The range of radius that can be detected by a UME of a given size spans typically between ≈ 8% to 30% of the radius of the UME. For 5 µm radius UMEs, beads between 0.4 and 1.5 µm radius could be detected. This range is imposed by the signal-to-noise ratio (S/N) of the experiment and a minimum number of collision that can be recorded with one UME before completely covering its surface. It is indeed preferable to avoid multilayers as the analysis becomes more complex.11 In some specific conditions particles with a size down to 0.05% of the size of the UME can also be detected by blocking. For example, single proteins of few nm in radius were detected using 75 nm radius nanoelectrode and extremely high concentrations of redox reporter (300 mM). Thanks to this large concentration of redox reporter, a large steady state current was obtained and thus the S/N ratio of the experiment increased enough to detect extremely small particles. However, high concentrations of charged redox molecules can easily destabilize colloidal suspensions and thus is not compatible with most of the particles (such as polystyrene beads). The precision on the bead size depends on the precision on the current step, the numerical simulation and the relative size of the bead/electrode. The precision is comprised between 100 nm and 50 nm for the smallest and the biggest beads, respectively. A discussion of the precision is given in Supporting Information.

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Analytical Chemistry Once the radius of the bead is known it is then possible to convert the frequency of steps into a concentration of bead in mol/L. The frequency of steps, f(rbead), (defined as the average time interval between current steps) for beads of radius rbead, is the sum of two contributions: a frequency of diffusion, fdif, and a frequency of migration, fmig, (Eq. 1 left and right terms in brackets, respectively). If we consider a 100% sticking probability, the frequency of collision is related to the concentration of bead, their size and other experimental parameters by the relation (see Supporting Information):

(

𝑓(𝑟𝑏𝑒𝑎𝑑) = 𝑓𝑑𝑖𝑓 + 𝑓𝑚𝑖𝑔 = 2𝜋𝑁𝑎𝑟𝑒𝑙𝑒𝑐𝐶𝑏𝑒𝑎𝑑

𝛼

𝑟𝑏𝑒𝑎𝑑

)

+ 𝛽𝑟𝑏𝑒𝑎𝑑 Eq 1.

The quantities Na, relec and Cbead are the Avogadro’s constant, the radius of the electrode and the concentration of bead, respectively. The coefficients α and β are defined as follows: 𝑘𝑇

Eq 2.

𝛼 = 6𝜋𝜂 𝛽 = 𝐷𝑟𝑒𝑑𝑜𝑥𝐶𝑟𝑒𝑑𝑜𝑥

2𝜎𝑏𝑒𝑎𝑑 3𝜂

1

∑𝜇 𝐶

𝑖 𝑖

Eq 3.

where k, T, η, Dredox, Credox, σbead, μi and Ci are the Boltzmann constant, the temperature, the dynamic viscosity of the medium, the diffusion coefficient of the redox reporter, the concentration of the redox reporter, the surface charge density of the bead, the mobility of the ions “i” in solution and their concentration, respectively. These two coefficients are weighting the respective contribution of diffusion (α) and migration (β) on the frequency of collision. They depend solely on known experimental parameters and the surface charge density of the beads measured independently (see Supporting Information). The respective contribution of diffusion and migration to the collision frequency is plotted in Figure 4B as a function of the size of the bead. These two frequencies are normalized by the concentration of bead and the radius of the electrode. Note that these frequency values are specific to the condition used here. Figure 4B highlights that, under our experimental conditions (low concentration of supporting electrolyte), the flux of bead is dominated by migration. The flux by migration is about 100 times larger than the flux by diffusion on the whole range of bead size used in this work (0.5 - 1 µm radius). This is the reason why we choose a reduction reaction to attract our positively charges amine-functionalized polystyrene beads (ζ-V ≈ 44 mV). The detection of negatively charged particles (for example carboxylated beads) would require an oxidation reaction such as ferrocenemethanol oxidation. Another important point about mass transport. Eq 1 reveals that diffusion and migration have opposite trends with respect to the size of the beads. The smaller is a bead and the faster it diffuses. On the other hand, the bigger is a bead and the faster it migrates. It is thus necessary to calculate the migration and diffusion flux for a given set of experimental condition and size of bead.

Figure 5. Bead size distribution measured by electrochemistry (red) and SEM (black) for 1 µm radius (A) and 0.5 µm radius (B) aminefunctionalized polystyrene microbeads. The straight lines are least square fitting of Gaussian functions of the histograms. For the 1 µm radius beads the average radius ± standard deviation and R2 of the electrochemical and SEM data are 0.91 ± 0.09 µm, 0.908 and 0.97 ± 0.03 µm, 0.988, respectively. For the 0.5 µm radius beads the center ± standard deviation and R2 of the electrochemical and SEM data are 0.47 ± 0.06 µm, 0.997 and 0.51 ± 0.04 µm, 0.995, respectively. Using the calibration curve in Figure 4A and the Eq. 1 we converted the current steps and collision frequency of each bin of the histogram shown in Figure 3 into bead radius and concentration, respectively. The histogram of the bead radius is shown in Figure 5A in red. In order to test the sensitivity of our approach we also recorded collisions of 0.5 µm radius amine functionalized polystyrene beads (10% of the electrode size) and, following the same exact procedure as for the 1 µm radius bead, converted the step size distribution into a bead size distribution. The data corresponding to the 0.5 µm radius beads are shown in Figure 5 B. Typical chronoamperograms and the step size distribution corresponding to the 0.5 µm radius beads are provided in Supporting Information. The size distributions measured by electrochemistry is compared to the size distributions measured by SEM (black histograms Figure 5). The straight lines correspond to least square fit of Gaussian functions on the experimental data. The average radius ± standard deviation found by collision and SEM are reported in Table 1. The average size of the beads found by electrochemistry and SEM differs by -8% to -9% while the width of the distributions differs by a factor 1.5 to 3 for the 0.5 and 1 µm radius bead, respectively.

5



that, beside the edge effect, there is another phenomenon that biases the size distribution in electrochemical blocking. This bias introduces current steps smaller than expected for a given size of bead. The smallest currents steps recorded with the 1 µm radius beads are 1.56 times smaller than the current step predicted from the smallest size of bead found by SEM and our calibration curve Figure 3A. Several hypotheses to explain this bias may be pointed out. The variability on the radius of the Hg hemisphere is at most 10% for all experiments and cannot explain a broadening by a factor of three. Also, uncertainties on the values of α and β can affect the symmetry of the distribution but not its width. Eventual numerical errors on the relation between step size and bead size should decrease as the size of the bead gets closer to the size of the UME and thus we do not expect the large deviation on the 1 µm radius beads. Finally, interactions between beads can produce smaller steps (for example formation of multilayers). However, we keep the probability to observe two beads colliding one on the other very low by limiting the number of collision on a UME. We plotted the magnitude of the step size as a function of the number of beads on the UME for all the chronoamperograms (see Supporting Information) and could not evidence any trend (decrease or increase).

We compared in Table 1 (bottom rows) the total amount of bead (i.e. all sizes together) initially added in solution and the total amount of bead detected by collision. The sum of the concentration for each bin of the red histogram Figure 5 gives a total concentration of 98 fM (5.902 x 107 particle/mL) and 23 fM (1.385 x 107 particle/mL) for the 1 µm and 0.5 µm radius beads, respectively. This value is in excellent agreement with the total concentration of bead initially added in solution, 100 fM (6.022 x 107 particle/mL) and 25 fM (1.506 x 107 particle/mL) for the 1 µm and 0.5 µm radius beads, respectively. Table 1. Comparison of the size and concentration found by electrochemistry and SEM. Nominal radius (µm) Methods Mean radius ± SD (µm) Difference in radius (%) Cbead (fM)* Difference in Cbead (%)

0.5 Echem 0.47 ± 0.06

1

Standard* 0.51 ± 0.04

Echem 0.88 ± 0.10

-8 23

-9 25

-8

Standard* 0.97 ± 0.03

98

100 -2

*The average radius was measured by SEM. The concentration was determined by using the concentration of the stock solution given by the provider.

CONCLUSIONS We report the use of hemispherical UMEs to detect the collision of individual polystyrene beads by electrochemical blocking. We evidenced that the shape of the UME has a considerable importance on the size distribution of the current steps. Importantly, the effect of the geometry of the UME on the step size was fully analyzed by numerical simulations and we showed that edge effect encountered on disk shaped UMEs is drastically reduced on hemispherical electrodes. We evidenced the existence of a second bias. This bias tends to overestimate the small current steps. The origin of the bias is not identified yet. In conclusion, we determine within less than 10% of error the average diameter of polystyrene bead of 0.5 and 1 µm radius. The size distribution of the 0.5 µm radius bead was also correctly determined while a large deviation is observed for the 1 µm radius beads. The total concentration of bead is found within less than 10% of error for both the 0.5 and 1 µm radius beads. We believe that the quantitative analytical method presented in this work can offer a useful alternative to optical techniques incompatible with opaque samples, for example. The next challenges to be addressed would be the replacement of Hg by another metal, less toxic and more stable at anodic potentials, as well as the multiplexing of several UMEs of different sizes in order to widen the dynamic range of bead size detectable with one device. We are also investigating the origin of the bias observed for the size distribution of the 1 µm radius beads.

One major advantage of migration over diffusion is the possibility to detect extremely low concentrations of particle (for example tens of fM, ≈ 106 particle/mL, in our case) in a reasonable amount of time (< 1h). Indeed, the limit of sensitivity of the single particle blocking technique is not fixed by the capacity to detect a particle but the time necessary to record a statistically meaningful number of collision. Because the flux of particle is stationary the limit of sensitivity is directly proportional to the time of the measurement. For example, under our experimental conditions it takes about 30 min to detect ≈ 200 collisions of 1 µm radius microbeads at 100 fM (6 x 107 particle/mL). In principle we could detect 10 fM (6 x 106 particle/mL) of the same beads in 5 h. In absence of migration (i.e. with only diffusion) the same measurement would take about 14 days. In order to speed up the collision rate it is possible to increase the size of the electrode (both α and β are proportional to relec). This strategy has been employed to detect the electro-dissolution of individual Ag nanoparticles on cylindrical carbon fiber UMEs.20 Concentrations of few tens of fM (≈ 106 particle/mL) were readily detected within few min. However, as we saw previously for a detection scheme based on blocking, the size of the electrode has to scale with the size of the beads to keep a reasonable S/N ratio. When the flux of bead is dominated by migration (like in the present work), the precision on the concentration depends directly on the precision of the surface charge density of the beads (see Eqs. 1 and 3). In order to determine the surface charge density of the beads we carried out in an independent measurement of their mobility (by Zetasizer) and then calculated a surface charge density. Details about the measurement and calculations are provided in Supporting Information. Importantly, the surface charge density is kept constant by addition of an acetate buffer with a pH of 5, largely below the pKa of the amines decorating the beads (the apparent pKa is around 8, see Supporting Information). The relative difference in average radius found by electrochemistry and SEM is negative and similar for the two sizes of bead. For the 0.5 µm radius beads the width of the distribution found by electrochemistry is close to the width found by SEM. On the other hand, the difference between the width of the distributions found by electrochemistry and SEM is quite large for the 1 µm radius beads. For both sizes of beads, the width of the size distribution is larger in electrochemistry than in SEM. We conclude

ASSOCIATED CONTENT Supporting Information The following elements can be found in Supporting Information: derivation of Eqs. 1, 2 and 3, details about the numerical simulations, chronoamperograms and size distributions obtained with 0.5 µm radius beads, magnitude of the step size as a function of the number of beads on the UME, optical micrographs of the UME, SEM characterization of the beads, discussion on the precision of the bead diameter, details about the measurement of the pKa of the amine functionalized beads, calculation of the surface charge density of the beads, experimental details on the electrodeposition of the Hg hemisphere, details about the analysis of the current steps and the electrochemical setup. The Supporting Information is available free of charge on the ACS Publications website. 6


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Analytical Chemistry (9) Michael V. Mirkin, S. A. Nanoelectrochemistry, CRC Press, 2017. (10) Quinn, B. M.; van't Hof, P. G.; Lemay, S. G. Timeresolved electrochemical detection of discrete adsorption events. J. Am. Chem. Soc. 2004, 126, 8360-8361. (11) Boika, A.; Thorgaard, S. N.; Bard, A. J. Monitoring the electrophoretic migration and adsorption of single insulating nanoparticles at ultramicroeletrodes. J. Phys. Chem. B 2013, 117, 4371-4380. (12) Dick, J. E.; Hilterbrand, A. T.; Boika, A.; Upton, J. W.; Bard, A. J. Electrochemical detection of a single cytomegalovirus at an ultramicroelectrode and its antibody anchoring. Proc. Natl. Acad. Sci. U. S. A. 2015, 112, 53035308. (13) Kim, B.-K.; Boika, A.; Kim, J.; Dick, J. E.; Bard, A. J. Characterizing emulsions by observation of single droplet collisons-attoliter electrochemical reactors. J. Am. Chem. Soc. 2014, 136, 4849-4852. (14) Dick, J. E.; Renault, C.; Bard, A. J. Observation of single-protein and DNA macromolecule collisions on ultramicroelectrodes. J. Am. Chem. Soc. 2015, 137, 8376-8379. (15) Dick, J. E.; Renault, C.; Kim, B.-K.; Bard, A. J. Simultaneous detection of single attolitter droplet collisions by electrochemical and electrogenerated chemiluminescent responses. Angew. Chem. Int. Ed. 2014, 53, 11859-11862. (16) Lebègue, E.; Anderson, C. M.; Dick, J. E.; Webb, L. J.; Bard, A. J. Electrochemical detection of single phospholipid vesicle collisions at a Pt ultramicroelectrode. Langmuir 2015, 31, 11734-11739. (17) Lee, J. Y.; Kim, B.-K.; Kang, M.; Park, J. H. Label-free detection of single living bacteria via electrochemical collision event. Sci. Rep. 2016, 6, 30022. (18) Bonezzi, J.; Boika, A. Deciphering the magnitude of current steps in electrochemical blocking collision experiments and its implications. Electrochim. Acta 2017, 236, 252-259. (19) Fosdick, S. E.; Anderson, M. J.; Nettleton, E. G.; Crooks, R. M. Correlated electrochemical and optical tracking of discrete collision events. J. Am. Chem. Soc. 2013, 135, 59945997. (20) Ellison, J.; Batchelor-McAuley, C.; Tschulik, K.; Compton, R. G. The use of cylindrical micro-wire electrodes for nano-impact experiments; facilitating the sub-picomolar detection of single nanoparticles. Sensor. Actuat. B-Chem. 2014, 200, 47-52.

AUTHOR INFORMATION Corresponding Author * Email: [email protected]

Present Addresses †[email protected]

Author Contributions The manuscript was written through contributions of all authors. / All authors have given approval to the final version of the manuscript.

ACKNOWLEDGMENT This work is support by the CNRS, the Agence Nationale de la Recherche (ANR-17-CE09-0034-01, “SEE”) and the China Scholarship Council (201706370055).

REFERENCES (1) Hipp, A. K.; Storti, G.; Morbidelli, M. Particle sizing in colloidal dispersions by ultrasound model calibration and sensitivity analysis. Langmuir 1999, 15, 2338-2345. (2) Glatter, O. In Scattering Methods and their Application in Colloid and Interface Science; 1st Ed., Elsevier: 2018, 223. (3) Tomaszewska, E.; Soliwoda, K.; Kadziola, K.; TkaczSzczesna, B.; Celichowski, G.; Cichomski, M.; Szmaja, W.; Grobelny, J. Detection limits of DLS and UV-Vis spectroscopy in characterization of polydisperse nanoparticles colloids. J. Nanomater. 2013, 1-10. (4) Poon, W. C. K.; Weeks, E. R.; Royall, C. P. On measuring colloidal volume fractions. Soft Matter 2012, 8, 2130. (5) Gallego-Urrea, J. A.; Tuoriniemi, J.; Hassellöv, M. Applications of particle-tracking analysis to the determination of size distributions and concentrations of nanoparticles in environmental, biological and food samples. TrAC-Trend. Anal. Chem. 2011, 30, 473-483. (6) Peng, Y.-Y.; Qian, R.-C.; Hafez Mahmoud, E.; Long, Y.T. Stochastic collision nanoelectrochemistry: A review of recent developments. ChemElectroChem 2017, 4, 977-985. (7) Wang, Y.; Shan, X.; Tao, N. Emerging tools for studying single entity electrochemistry. Faraday Discuss. 2016, 193, 939. (8) Stevenson, K. J.; Tschulik, K. A material driven approach for understanding single entity nano impact electrochemistry. Current Opinion in Electrochemistry 2017, 6, 38-45.

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