1

The use of cylindrical micro-wire electrodes for nano-impact experiments; facilitating the sub-picomolar

detection of single nanoparticles

Joanna Ellisona, Christopher Batchelor-McAuley

a, Kristina Tschulik

a and Richard G. Compton

a*

Department of Chemistry, Physical & Theoretical Chemistry Laboratory, Oxford University, South Parks

Road, Oxford, OX1 3QZ, UK.

Abstract

Electrochemical impact experiments can be used to detect and size single nanoparticles in suspension and at

low concentrations. This is generally performed using a micro-disc working electrode; however, for the first

time we report the use of cylindrical micro-wire electrodes for nanoparticle impact experiments. These

electrodes provide much enhanced detection limits; specifically decreasing the concentration of nanoparticles

measurable by over two orders of magnitude. In addition, the use of micro-wire electrodes reduces the

shielding effect due to absorption of particles to the insulating sheath that surrounds a micro-disc electrode.

Micro-wire electrodes are fabricated and their electrochemical response analysed via cyclic voltammetry

experiments using molecular species. This provides a theoretical framework which is used to calculate the

reduced concentration of nanoparticles required for an impact experiment at a micro-cylinder electrode in

comparison to the micro-disc. Experimentally, it is demonstrated that impact experiments on the micro-

cylinder electrodes can indeed be used for accurate characterisation of ultra-low concentrations ( ≈ 0.1pM) of

silver nanoparticles.

Keywords: Micro-electrode; Micro-cylinder electrode; Nanoparticle voltammetry; Detection limit; Silver

nanoparticles

*Corresponding author. Fax: +44(0) 1865 275957

Email address: richard.compton@chem.ox.ac.uk (Richard. G. Compton)

2

Vitae

Joanna Ellison

Joanna Ellison undertook her MChem at the University of Oxford and is now working with Prof. Compton as a

first year D.Phil student, funded via the ERC to investigate the electrochemistry of nanoparticles.

Christopher Batchelor-McAuley

Christopher Batchelor-McAuley undertook his MChem and D.Phil at the University of Oxford under the

guidance of Prof. Compton. He is a co-author of the textbook ‘Understanding Voltammetry: Problems and

Solutions’ and is currently funded as a post-doc via the ERC to investigate the electrochemistry of

nanoparticles.

Kristina Tschulik

Kristina Tschulik received her doctoral degree from the Dresden University of Technology and joined Prof.

Compton's group as a post-doctoral researcher in November 2012. She holds a “Diplom” (German equivalent

to a Master's degree) in Chemistry and was granted a prestigious Marie Curie IEF Fellowship to continue

collaboration with the Oxford Group.

Richard G. Compton

Richard G. Compton is a professor of chemistry and Aldrichian Praelector at Oxford University (UK) and CAS

Visiting Professor at the Institute of Physical Sciences, Hefei (PR China). He has published in excess of 1200

papers, numerous patents and 7 books. He is the Editor-in-Chief and the Founding Editor of the journal

Electrochemistry Communications (Elsevier). His H-index is 74.

3

1. Introduction

The use of nanoparticles has rapidly expanded over recent years, leading to an increased need for their

quantitative detection and characterisation in solution. This may be for environmental monitoring[1]

or

fundamental analysis. The properties of nanoparticles are both size and shape dependent[2]

, and these physical

parameters can be tuned by changing the synthesis methodology[3-5]

. Therefore, the need for reliable

characterisation is imperative; specifically for fundamental studies, the need for detection of individual

nanoparticles. Nanoparticles in a suspension often feature a diverse size distribution which may be due to the

synthesis methodology and/or agglomeration effects[6-8]

. Measurements based on the entire ensemble do not

allow differentiation between discrete nanoparticle sizes, and hence do not provide crucial size information on

the nanoparticle sample. However, single nanoparticle detection allows these variations to be analysed. There

are several methods for identifying individual nanoparticles [9-12]

, though many of these involve the use of

microscopy techniques which require the nanoparticles to be studied ex-situ. Ex-situ methods are impractical

for many nanoparticle research areas; for example investigations into aggregation effects, and the study of

nanoparticles in environmental samples. In both these cases it is important to account for the effects of the

solution media on the nanoparticles. Recently, significant work has gone towards the development of new in

situ analytical methods for individual nanoparticle detection. Examples include both microscopy[13]

and

electrochemical methods. The latter of which encompasses both anodic particle coulometry[14]

and resistive

pulse sensing[15]

.

The focus of this paper will be nanoparticle impact experiments, specifically anodic particle coulometry. Here,

single nanoparticles impact a microelectrode, which is held at a suitably oxidising or reducing potential, thus

leading to the oxidation/reduction of impacting nanoparticles. This can be observed by an increase, ‘spike’, in

the current-time response. Analysis of these individual current ‘spikes’ allows the characterisation of single

nanoparticles in the solution, with the charge passed in the ‘spike’ related to the number of atoms in the

nanoparticle. This method has been successfully demonstrated using silver[14]

, gold[16]

and nickel[17, 18]

metal

nanoparticles, as well as metal oxides[19]

and organic nanoparticles[20]

, allowing their detection, sizing and

determination of their agglomeration state[6]

. Furthermore, impact experiments can be used for the study of

mediated electrochemical reactions. Here, on contact with the working electrode surface, the nanoparticle

itself can act as an electrode on which the electrochemical reaction can take place. If the electrochemical

4

process under study occurs preferentially on the nanoparticle surface over that of the electrode, single

nanoparticle collisions can be observed by the electrocatalytic amplification[21-29]

. Throughout these impact

experiments a micro-electrode is almost involuntarily employed, providing benefits such as increased mass

transport, low electrical noise and reduced capacitance[30, 31]

. Nevertheless, micro-disc electrodes do

experience a shielding effect, which can cause perturbations in current due to absorption of particles to the

surrounding insulating sheath, as discussed later.

Due to their comparatively large size, nanoparticles have fairly low diffusion coefficients. The diffusion

coefficients can be estimated from the Stokes-Einstein equation[32]

(assuming the nanoparticle radius is greater

than 5 nm)[33]

, to give values of the order of magnitude 1.5 x 10-11

m2s

-1 for a 30 nm nanoparticle, where, the

radius is taken to be the hydrodynamic radius of the particle. A large number of total spikes are needed to

allow statistically relevant analysis and thus this slow rate of diffusion experimentally results in relatively high

concentrations of nanoparticles being required to ensure enough impacts with the electrode occur over the

experimental time frame. For a micro-disc electrode of radius 5 µm a concentration of 15 pM of 30 nm

diameter NPs would be required to detect a reasonable amount of impacts (20)[17]

during a five second

chronoamperogram. Therefore, there is a desire to reduce the concentration of nanoparticles required for

detection. This decrease is critical for the detection of nanoparticles in the environment where typically very

low concentrations would be present[34, 35]

. Moreover, from an analytical perspective, generally having large

amounts of nanoparticles in a solution will lead to an increase in aggregation and agglomeration (aggregation

is defined as the irreversible adhesion of particles, and agglomeration their reversible sticking to each other[6]

).

This can be minimised by careful choice of the solution medium[36]

, or by decreasing the nanoparticle

concentration.

To date nanoparticle impact experiments have been performed using a micro-disc electrode, consisting of a

thin (several microns in diameter) conducting wire surrounded by a much larger insulating glass sheath, onto

which nanoparticles can adsorb throughout the experiment. However, it has recently been shown theoretically

that this adsorption can significantly influence the magnitude of the observed current and decrease the

number of impact ‘spikes’ seen[37]

. One option for decreasing the concentration of nanoparticles required for

impact experiments would be by the use of an array of microelectrodes. This would allow many electrode sites

for nanoparticle impacts, thus allowing less nanoparticles to be present to achieve the same number of total

5

recorded impact ‘spikes’ However, this would likely encounter some of the shielding problems described

above. A second option for enhanced nanoparticle detection would be the use of a cylindrical micro-wire

electrode. Here, by virtue of the cylindrical electrode shape, there is a much enhanced surface area over which

nanoparticle impacts can occur. In addition because the electrode will only be encapsulated at one end of the

wire, any shielding effects are significantly reduced. The development and use of wire electrodes for

nanoparticle impact experiments will be explored throughout this paper.

When using a wire electrode it is important to consider the wire material. In order for the micro-metre thin

wire to retain its straight cylindrical shape in the solution and not bow over, it must be fairly rigid and thus

have a high Young’s Modulus, where Young’s Modulus is given by the normal stress divided by the linear strain

of the material[38]

. This value is 78 GPa for gold and 168 GPa for platinum[39]

and significantly higher (230

GPa[40]

) for a carbon fiber making it suitable for use as an electrode. Furthermore, carbon fiber is a less

expensive and fairly electrochemically inert material and thus would be suitable for future indirect impact

experiments, where the electrochemical process is required to occur preferentially on the nanoparticle over

the electrode.

Herein, we report the fabrication and characterisation of carbon fiber wire electrodes and for the first time

demonstrate their use for nanoparticle impact experiments. First, the fabricated micro-cylinder electrodes are

analysed by considering their responses during cyclic voltammetry experiments and it shown that the results

are in good agreement with those predicted theoretically[41]

. Second, electrochemical impact experiments are

then performed as proof-of-concept for the detection of low concentrations of nanoparticles in solution using

silver nanoparticles (AgNPs). Specifically, chronoamperograms are run, and the resulting impact spikes

analysed to give a size distribution of the nanoparticles. Third, this is then shown to be in good agreement with

the SEM sizing of the nanoparticles; thus, demonstrating, that even at ultra-low concentrations (≈ 0.1 pM) it is

possible to accurately identify and size single nanoparticles using electrochemical impact experiments.

2. Experimental

2.1 Fabrication of Electrodes

Cylindrical micro electrodes of approximately 1 mm in length were desired for impact experiments. First, 7.0

μm diameter carbon fiber (Goodfellow Cambridge Ltd) was connected to a conducting metal wire using silver

6

epoxy (RS Components Ltd) conductive adhesive. The adhesive was set by heat treatment in an oven for 15

minutes at approximately 60 °C. The wire was then threaded through a plastic pipette tip so that only the

carbon fiber extended out of the end. The interstice between the carbon fiber/metal wire and the plastic tip

was sealed using cyanoacrylate adhesive, thus preventing electrical leakage. Finally, the carbon fiber tip was

cut down so that a length of approximately 1 mm protruded past the sealed pipette end.

2.2 Nanoparticle synthesis

Citrate-capped AgNPs were synthesised according to a method developed by Wan et al[5]

utilising a stepwise

seeded growth method. Initially, AgNPs of nominally 4 nm diameter were synthesised as starter seeds by

adding an aqueous solution of AgNO3 (silver nitrate) and NaBH4 (sodium borohydride) to a citrate solution at

70 °C. This temperature was maintained for one hour before the solution was cooled to room temperature.

The size of the NPs was confirmed to be 4 nm by transmission electron spectroscopy (TEM). These ‘seed’

particles were then added to a boiling citrate solution, and further amounts of AgNO3 were added. This

solution was then refluxed for 1 hour, prior to cooling to room temperature. This process was repeated a total

of three times. The exact size and shape of the NP was confirmed by SEM (Leo Gemini 1530, Zeiss). Here, the

nanoparticles were drop cast onto a TEM grid in order to reduce the amount of AgNP agglomeration which is

common on conventional SEM holders. Analysis of the SEM data showed spherical AgNPs with a radius with a

mean and standard deviation of 13.6 ± 3.7 nm[36]

.

During the synthesis a total concentration of 3.1 mM Ag was used, providing a nanoparticle stock suspension

with a concentration of 5 nM AgNPs (assuming a AgNP radius of 13.6 nm as derived from the SEM analysis).

This stock suspension was diluted by a factor of one thousand and the diluted nanoparticle suspension added

to the electrolyte to give a total AgNP concentration of 0.09 pM.

2.3 Reagents and equipment

All chemicals were purchased from Sigma Aldrich unless otherwise stated and used in their analytical grade. All

solutions were made using ultrapure water (Millipore, resistivity not less than 18.2 MΩ cm at 25 °C).

Characterisation of the electrodes was performed in 0.10 M KCl and 1 mM Hexamine Ruthenium (III) chloride

and thermostated to 25 ± 0.2 °C. Electrochemical impact experiments were performed in 0.10 M tri-sodium

citrate (BDH chemicals).

7

Electrochemical experiments were performed using a μAutolab II potentiostat (Metrohm-Autolab BV, Utrecht,

Netherlands). The μAutolab II has a low pass filter, and the rise time was measured experimentally to be

roughly 6ms, providing a value for the measurement bandwidth of approximately 60 Hz. A standard three

electrode setup was used for experiments and in all cases the working electrode consisted of a fabricated

cylindrical micro-electrode. For electrode characterisation experiments a graphite rod (3 mm diameter) was

used as a counter electrode and a saturated calomel electrode (SCE, potential E = 0.244 V versus standard

hydrogen electrode) as a reference electrode. For NP impact experiments a silver wire was used as a pseudo

reference and a platinum mesh as a counter electrode. Chronoamperograms were run for a length of 5

seconds, with a sample time of 0.5 ms allowing the maximum number of data points (10,000) to be collected.

In order to prevent the effect of a reduced concentration of nanoparticles in the vicinity of the electrode

following a chronoamperogram, a time of at least 30 seconds was waited between successive scans.

In order to prevent nanoparticle contamination all equipment was prepared as follows prior to impact

experiments: The electrochemical cell was cleaned in aqua regia (3:1 hydrochloric acid: nitric acid) for 30

minutes and then sonicated in ultrapure water for 15 minutes. The platinum mesh counter electrode was

soaked in 1M HNO3 for a minimum of 30 minutes, rinsed in H2O and then held in a flame, and the silver wire

reference was cleaned mechanically with sand paper.

Analysis of the impact spikes was performed using the software SignalCounter[6]

developed by Dario Omanovic,

(Centre for Marine and Environmental Research, Ruder Boskovic Institute, Croatia). This allowed for baseline

correction, peak identification and the determination of peak areas. Spikes were identified based on an

algorithm utilising a derivative transformation of the signal. For this a minimum height (approximately double

the height of the noise) and duration (4ms) were selected as parameters for automatic spike recognition. The

area of the identified spikes was then determined by the trapezoid rule. All other data was analysed and fitted

in OriginPro 8.5.1 (Origin Lab Corporation).

3. Results and discussions

First the fabricated micro-electrodes were characterised to allow their electrochemical response to be

analysed. Second, this was used to establish a theoretical estimate for the nanoparticle concentration required

for the impact experiments. Third, experimental tests at this concentration of silver nanoparticles

8

demonstrated the successful use of micro-cylindrical electrodes for the detection of reduced nanoparticle

concentrations.

3.1 Electrochemical Characterisation of electrodes

In order to electrochemically characterise the fabricated micro-wire electrodes, cyclic voltammetry

experiments were performed and the voltammetric response analysed based on the following theoretical

considerations presented below.

Due to the angular isotropy of the cylinder, diffusion towards a micro-cylinder is a one dimensional problem.

Solving the diffusion equation provides an equation for the expected current, and an approximation is given by

Szabo et al[42]

:

� = (2�����) (�) (1)

with

(�) =���√��/��

√��+

�

��[(�� �)�."#��" $⁄ ]� = 4�(/)

�

where, n is the number of electrons transferred, F is Faraday’s constant (96485 C mol-1

), D0 is the diffusion

coefficient (m2

s-1

), C0 is the bulk concentration of electroactive species, l is the electrode length (m), r0 the

electrode radius (m), and t the time in seconds. The value γ = 0.5772156… and is a constant derived from the

limits of the Bessel functions in the full formula for (�). The approximate equation shown above is valid with

a 1.3% error over all times[42]

.

At short times the above equation reduces to the Cottrell equation. However, at long times the � term

becomes large and hence the logarithmic � term dominates, reducing the equation to[43]

:

�*++ =,�-./�012

��(�)(2)

Thus, at long times the current remains dependent on time and a quasi-steady state current (iqss) is predicted.

The quasi steady state behaviour is observed for a micro-electrode due to the relative size of the diffusion

length relative the electrode dimensions, leading to an increase in mass transport.

The diffusional behaviour during a cyclic voltammogram should now be considered. Here, quasi-steady state

behaviour would be observed in the voltammograms by the presence of a characteristic diffusion peak, with

9

the peak height dependent on scan rate i.e. the length of time the diffusion layer has to grow. Theoretical peak

current (Ip) values can be calculated based on the work of Aoki et al[41]

, and these values will later be compared

with those determined experimentally for the fabricated electrodes. To derive the predicted peak currents,

within a 2% error range, for varying scan rates Aoki derived the following equation:

34

��-.0�/�2= 0.4467 + 0.3357.�:,<�(ℎ7 = (��)

�>/?@�).: (3)

where v is the scan rate (V s-1

).

Here, the first term in the equation corresponds to the linear diffusion towards the electrode and the second

accounts for deviations from this due to cylindrical curvature effects, i.e. radial diffusion. The dependence of

current on the square root of scan rate is demonstrated by a plot of the dimensionless peak current as a

function of scan rate, and will be given later both for theoretical and experimental peak currents.

In order to characterise the fabricated electrodes by comparison with the above theory, experiments were run

in 1mM hexamine ruthenium (III) chloride with 0.1M KCl as supporting electrolyte. The solution was

thoroughly degassed by purging with nitrogen for 15 minutes prior to the experiments, and thermostated to a

constant 25°C. Cyclic voltammograms were then run from a potential of 0.25 V to -0.5 V (vs SCE) and back;

corresponding to the reduction of the [Ru(NH3)6]3+

to [Ru(NH3)6]2+

and subsequent re-oxidation. This was

performed at varying scan rates from 10 mV s-1

to 2000 mV s-1

and can be seen in figure (2).

For each scan rate the peak current was measured and a plot of 34

��-.0�/�2 vs p (as described in equation 3) was

then derived. The diffusion coefficient of [Ru(NH3)6]3+

in this electrolyte has previously been measured to be

8.43 x 10-10

m2

s-1

.[44]

Consequently, the length of the electrode, is the only unknown parameter in the

equation, and as such was used as a fitting parameter. Specifically, a theoretical line was plotted from

equation (3) above, and the experimental data fitted to this by varying the electrochemical length of the

electrode. Figure (3) shows the theoretical and fitted experimental data with an electrode length of 1.25 mm.

At higher scan rates it can be seen that the theoretical and experimental points are in good agreement. In this

region there is a quasi-steady state current and mass transport to the electrode is dominated by linear and

radial diffusion. The quasi-steady state current is exemplified in figure (2) by the peak-like shape of the

voltammograms.

10

At very low scan rates the experimental data begins to deviate from that calculated theoretically, showing

higher than predicted peak currents. This effect can be attributed to natural convection[45]

. Until now we have

assumed that mass transport of the electro-active species to the electrode is dominated by diffusion;

specifically from the Nernst diffusion layer surrounding the electrode. However, as the diffusion layer expands,

density gradients are established and convection additionally comes into play. In this region there will be

enhanced mass transport of the electro-active species, leading to an increased current. As a result, at low scan

rates, where the diffusion layer has more time to expand due to the longer experimental time frame, steady

state behaviour as opposed to quasi-steady state behaviour is observed. This is exemplified by the sigmoidal

wave-shape at low scan rates in the voltammogram, which is apparent in figure (2) at 10 mV s-1

.

It has therefore been demonstrated that the fabricated wire electrodes exhibit the quasi-steady state

diffusional behaviour predicted for a cylindrical electrode of these dimensions. At very low scan rates, i.e. at

times when the diffusion layer is significantly expanded, the effects of convection are seen. Therefore, for the

impact experiments it can be assumed that the Szabo equation for the current to a micro-cylinder electrode

will apply. In the following experimental section, chronoamperograms will be run for a 5 second period where

the effects of convection should be minimal. Moreover, due to their large size (as compared to molecules),

nanoparticles have low diffusion coefficients, and so the build-up of the diffusion layer will be slow.

3.2 AgNP impact experiments:

To demonstrate the use of cylindrical wire electrodes for ultra-low nanoparticle detection, nanoparticle impact

experiments were performed. First it is useful to consider the theoretical concentration of nanoparticles

required for these experiments both at a conventional micro-disc electrode and a micro-cylinder.

At a micro-disc electrode the expected current during a potential step chronoamperogram derived from the

diffusion equations is given by:

A = 4��)� (�) (4)

where the function f(t) can be approximated, within an accuracy of 0.6%, by the Shoup-Szabo expression[43]

:

(�) = 0.7854 + 0.8862�D.: + 0.2146FD.GH�I���."

<�(ℎ� = 4�(/)J� (5)

11

Multiplication of this by the Avogadro constant, NA, converts the equation to a form referring to the number of

particles. To determine the number of particle impacts expected within a given time, the Shoup-Szabo

equation needs to be integrated and this has previously been performed by series expansion[17]

. From this it is

possible to calculate the concentration of nanoparticles required for a total number of 22 impacts to be

observed over the experimental time (i.e. a 5 second duration chronoamperogram). Taking an electrode radius

the same size as that of the cylindrical electrode (3.5 µm), and a nanoparticle diffusion coefficient derived from

the Stoke’s Einstein equation, we get that a total of 23 pM of nanoparticles would be required. Here, it has

been assumed that the nanoparticles have a radius equal to that given by the SEM data (13.6 nm).

Comparatively, for a micro-cylinder electrode the current per mole is given by the Szabo equation (equation 1),

and is similarly converted to current per particle by multiplication by the Avogadro constant. As above, the

integrated version of this equation is required and can be calculated numerically. Doing this for an electrode of

length 1 mm yields a required concentration of 0.09 pM AgNPs for a total of 22 impact spikes.

It can be seen from these calculations that the concentration required for AgNP detection during impact

experiments is significantly reduced by use of a micro-cylindrical electrode. On account of the relatively long

length and thus increased surface area, the total concentration of nanoparticles required for detection can be

decreased by over two orders of magnitude.

To test if impacts at this theoretical concentration can be observed experimentally, impact experiments were

run using the synthesised AgNP. A solution of 0.1M tri-sodium citrate was used; a medium which has

previously been shown to minimise AgNP agglomeration[36]

. Pre-dispersed AgNPs were added to give a total

nanoparticle concentration of 0.09pM and chronoamperograms were recorded for a period of 5 seconds each.

Here, a potential of +0.6 V vs Ag wire was chosen as a suitable potential for NP oxidation[36]

. It is assumed that

the nanoparticles are completely oxidised on impact with the electrode, and indeed it has been shown

theoretically that after impacting the nanoparticle is likely to remain in the vicinity of the electrode and that

complete oxidation will occur[46]

.

The chronoamperograms show positive current spikes (figure 4), due to the faradaic oxidation of the impacting

nanoparticles. As expected, no spikes were observed in scans run in the absence of AgNPs. A total of 20 scans

were recorded in the presence of nanoparticles, yielding 190 impact spikes. Analysis of the area of each spike

12

yielded the charge per nanoparticle impact, and application of Faraday’s law converted this into the number of

moles of Ag per nanoparticle. Converting this into radius provided a size distribution for the single impacting

nanoparticles[14]

.

A histogram of the nanoparticle sizes was plotted, with a bin size of 1 nm and is shown in figure (5). From this

a mean and standard deviation of 14.7 ± 2.0 nm AgNP radius are obtained. This value is in very good

agreement to those taken from SEM analysis, where the AgNP radius was given as 13.6 ± 3.7 nm. Therefore, it

can be seen that impact experiments using the micro-wire electrodes have given an accurate nanoparticle

sizing.

It should be commented that the average number of spikes obtained per scan was 10, which is lower than the

value predicted theoretically, (22 impacts). These deviations can be attributed to variations in the true

concentration of nanoparticles in the solution. Specifically, the overall concentration of nanoparticles in the

solution may decrease throughout the experiment due to the absorption of nanoparticles to the cell

components. Nevertheless, despite this slight reduction in experimentally observed impacts, the observed

number is still significantly higher than that expected for a micro-disc electrode, which at this low a

concentration would observe effectively no nanoparticle impacts. As a result, we have shown that the use of a

cylindrical wire electrode has allowed enhanced detection of nanoparticles by electrochemical impact

methods, and thus this provided an improved method for low concentration detection and characterisation of

nanoparticles.

4. Conclusions

In this work we have shown that cylindrical micro-electrodes can be fabricated and successfully used for the

detection of ultra-low concentrations of nanoparticles. Characterisation of the electrodes demonstrates that

they give current responses as predicted by the Szabo equation; leading to quasi steady state diffusional

behaviour. Deviations at low scan rates, i.e. long experimental times, highlighted the importance of convection

for an electrode of these dimensions.

Application of the Szabo equation to the impact experiments demonstrated that the concentration of

nanoparticles required for detection can be reduced by over two orders of magnitude by use of a cylindrical

micro-electrode (of length ≈ 1 mm) rather than a micro-disc electrode. This concept was demonstrated

13

experimentally, providing an accurate nanoparticle size distribution at an ultra-low concentration (0.09 pM) of

silver nanoparticles. Therefore, we have established a method for allowing precise detection and

characterisation of low concentrations of nanoparticles in solution. The increased detection limit will be of

significant benefit for the detection of nanoparticles in environmental systems, where typically very low

concentrations need to be analysed. Furthermore, it will be advantageous in systems where agglomeration

needs to be minimised by a reduction in the overall nanoparticle concentration.

Acknowledgements:

We acknowledge funding from the ERC Grant Agreement. K.T. was supported by a Marie Curie Intra European

Fellowship. J.E, C.B.M. and R.G.C. acknowledge funding from the European Union's Seventh Framework

Programme (FP/2007-2013)/ERC Grant Agreement no. [320403].

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Figure Captions:

Figure 1: Schematic diagram showing the fabricated wire and the nanoparticle impact principle; an impacting

nanoparticle and its subsequent oxidation

16

Figure 2: Cyclic voltammograms of 1mM hexamine ruthenium (III) chloride in 0.1M KCl supporting electrolyte

run at varying scan rates on a fabricated micro wire electrode

Figure 3: Variations in the dimensionless peak current with p, both theoretically (solid line) and experimentally

(dotted line)

17

Figure 4: An example chronoamperogram (E=0.6V vs Ag wire) showing a blank scan in the absence of AgNP

(red line) and a scan in the presence of AgNP showing oxidative current spikes (black line)

Figure 5: A histogram showing the size distribution of AgNPs as determined by nanoparticle impact

experiments