Measuring the Electric Charge and Zeta Potential of Nanometer-Sized

Aug 17, 2012 - Here, we present a simple, widely applicable, robust, and precise method to measure the zeta-potential of different nano-objects using ...
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Measuring the Electric Charge and Zeta Potential of NanometerSized Objects Using Pyramidal-Shaped Nanopores Nima Arjmandi,*,†,‡ Willem Van Roy,† Liesbet Lagae,†,‡ and Gustaaf Borghs†,‡ †

IMEC, Kapeldreef 75, 3001 Leuven, Belgium Department of Physics and Astronomy, Katholieke Universiteit Leuven, Celestijnenlaan 200 D, 3001 Leuven, Belgium

‡

S Supporting Information *

ABSTRACT: Nanometer-scale pores are capable of detecting the size and concentration of nanometer-sized analytes at low concentrations upon analyzing their translocation through the pore, in small volumes and over a short time without labeling. Here, we present a simple, widely applicable, robust, and precise method to measure the zeta-potential of different nanoobjects using nanopores. Zeta-potential i.e., a quantity that represents electrical charge in nanocolloids, is an important property in manufacturing of pharmaceuticals, inks, foams, cosmetics, and food. Its use is also imperative in understanding basic properties of complex dispersions including blood, living organisms, and their interaction with the environment. The characterization methods for zeta-potential are limited. Using the nanopore technique, the zeta-potential and the charge of nanoparticles can be measured independently of other parameters, such as particle size. This simple method is based on measuring the duration of the translocation of analytes through a nanopore as a function of applied voltage. A simple analytical model has been developed to extract the zeta-potential. This method is able to detect and differentiate nanometer-sized objects of similar size; it also enables the direct and precise quantitative measurement of their zeta-potential. We have applied this method to a wide range of different nanometer-sized particles and compared the results with values measured by commercially available tools. Furthermore, potential capability of this method in detection and characterization of virions is shown by measuring the low zeta-potential of HIV and EBV viruses.

N

few microliters without any labeling or major sample preparation.18−23 The ability of the nanopore technique to differentiate between various nanoparticles has traditionally been based on the discrimination of particles according to their size. Robertson et al. in a pioneering work on nanopore mass spectroscopy have shown discrimination of polymers with even a single monomer size difference using biological nanopores.19 However, different particles composed of different materials with different properties can have similar sizes, and in complex samples, such as biological samples, many such particles exist.23 Thus, we cannot rely only on the size of the particles to differentiate and detect particles. In addition, particle size is usually determined by measuring the amplitude of the ionic current’s change during particle translocation through a nanopore, and as it has formulated by Reiner and his colleagues for a specific polymer chain translocating through a relatively small biological nanopore; this amplitude is a function of other parameters, including the ionic concentration of the solution, particle material, and the applied voltage, in addition to the size of the analyte.25 Other experiments have confirmed these dependencies of the spike amplitude in different conditions as well.24,26 Reiner’s model also shows dependence of translocation duration on size and other parameters for a polymer chain that is translocating through a small biological nano-

anometer-sized objects in liquids are important materials in many respects. These include biological macromolecules,1−3 organelles, viruses, synthetic polymers,4 and nanoparticle colloids in biosensors,5 photovoltaics,6 cosmetics,7 and nanomedicine.8 Despite the numerous applications and the importance of these nanometer-sized floating objects, their detection and the techniques used to characterize them are relatively limited. For instance, DNA sequencing is usually too time-consuming and expensive.9 Detection and characterization of viruses, especially in the early stages of infection, is expensive and time-consuming. Transmission electron microscopy (TEM) and different mass spectroscopy techniques cannot characterize particles in their liquid environment. Dynamic light scattering (DLS)10 requires a relatively large volume and cannot function with optically active analytes and at high or low concentrations in addition to other limitations similar to centrifugation,11 field flow fractionation,12 hydrodynamic fractionation,13 chromatography,14 and gel electrophoresis.15 Electroacoustic methods16 and microelectrophoresis combined with nanoparticle tracking analysis can only work with particles that are large enough to be visible using optical microscopy, and problems such as electrode polarization and the introduction of gas bubbles may be encountered.17 Nanometer-sized pores in a membrane (Figure 1) have previously been introduced as a promising tool for the detection of nanometer-sized objects dispersed in a liquid at concentrations perhaps lower than 105 particles per milliliter, with times as short as a few seconds and volumes as small as a © 2012 American Chemical Society

Received: March 12, 2012 Accepted: August 17, 2012 Published: August 17, 2012 8490

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Figure 1. The nanopore device. a) Three-dimensional schematic representation of the nanopore device. A silicon membrane separates two microfluidic chambers composed of poly(methyl methacrylate) (PMMA) and sealed by poly dimethyl siloxane (PDMS). A pyramidal nanopore in the membrane connects the two chambers. Nanometer-sized objects are electrophoretically driven from the front chamber, through the nanopore and into the back chamber. The white blades represent the Ag/AgCl electrodes that are used to apply the voltage to the liquid. b) Transmission electron microscopy (TEM) cross section image of a 40 nm nanopore (for TEM sample preparation purposes the nanopore is filled with silicon dioxide). The scale bar is 10 nm. c) Scanning electron microscopy (SEM) image of a 120 × 120 nm nanopore. The nanopore is the white square at the center of the image where it is the end of the pyramidal etch pit that has resulted from KOH wet etching. The scale bar is 200 nm.

pore.25 Therefore, we advocate use of the derivative of translocation duration due to the applied voltage for measuring the zeta-potential. Nevertheless, measuring the zeta-potential of colloids45,62,63 is required in many applications, such as protein purification,3 production of paint and minerals, clay and drilling fluids, ceramics, pharmaceuticals, and paper as well as in ore processing, water and wastewater coagulation, and biosensors.27 The zeta-potential is usually defined as the electrical potential between the inner Helmholtz layer near a particle’s surface and the bulk liquid in which the particle is suspended. It is a parameter that represents the charge of a particle. Detection of electrophoretic mobility (which is a parameter related to the zeta-potential) by nanopores was predicted,18 and translocation duration of polystyrene particles through a 3 μm long and 132 nm wide channel made of a multiwall hollow carbon nanotube was related to their mobility at a specific salt concentration and voltage.28−30 Solid-state nanopores are the subject of intense research as promising analytical tools.31 Hereby, we present a simple, reliable, accurate, and generally applicable method that can be used to measure the zetapotential and, consequently, the charge of nanometer-sized objects. This method uses pyramidal shaped solid-state

nanopores to extract the zeta-potential of the analytes from their electrophoretic motion. To achieve this, some classical issues have been solved: unlike classical electrophoresis, in nanopore experiments the velocity-voltage curve is shifted and it is not passing through the origin.33 This offset is partially originated from asymmetries between the two sides of the nanopore that can produce different electrochemical potentials and different capillary pressures on the two sides of the nanopore. Another origin of this offset is a certain voltage that is needed to give enough energy to the analytes to overcome the entropic and energy barrier of the nanopore and make the translocation probable.34−36,60,61 Introduction of a derivative form of electrophoretic mobility that we have called translocation mobility has eliminated the effects of these offsets in the velocity-voltage curve. Furthermore, symmetrical and closed microfluidics on the two sides of the nanopore are employed to eliminate this effect. Moreover, using a sharp edged pyramidal nanopore we have minimized the electroosmotic effects and probability of pore-particle interaction that introduce deviation from electrophoretic models in long and rough pores.32,33 This is further verified by the simulations (see the Supporting Information). Application of these sharp edged pores has also increased the signal-to-noise ratio and field 8491

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Figure 2. Translocation spikes. a) A typical current recording of a nanopore and translocation spikes that are caused by translocation of 80 nm big citrated gold nanoparticles with about 109 particles per milliliter concentration. All of these experiments are performed in 30 mM KCl with a 100 nm pyramidal nanopore by applying 100 mV across the membrane. b) A close-up view of translocation spikes of three different particles. The solid arrows indicate the translocation durations; the empty arrow indicates the amplitude of the highest spike. The baseline currents of the recordings were removed. The baseline currents were about 2 nA.

confinement.37−39 Using a new definition of translocation duration that is least affected by noise and is physically meaningful and using appropriate data analysis algorithms, translocation duration has been measured accurately, precisely, and independently of the amplitude of the translocation spikes and the size of the analytes.43 Operating the pore in the horizontal direction (the membrane is vertical and analytes are translocating horizontally) has removed gravitational effects.44 Using this approach, several different nanometer sized objects ranging from 20 to 200 nm in size, 3 mV to 65 mV in zeta-potential and made of different materials, have been analyzed with different nanopores in different electrolytes and measurement conditions, and the results were compared with commercial methods. Furthermore, we have used this method to measure zeta-potential of the human immunodeficiency virus (HIV) and the epstein-barr virus (EBV). Due to the low zetapotential of these viruses, accurate measurement of their zetapotential by DLS is not available, while the proposed nanopore method has resulted in precise measurement of their zetapotential. This method not only provides a fast and precise measurement of zeta-potential of any nanoparticle mixture even in conditions of low concentrations, low zeta-potentials, small volumes, and different salt concentrations, particle sizes, and particle materials, with better than ±2 mV precision (see the Supporting Information). It also provides perspectives for reliable detection and differentiation between various particles including biological particles of similar size based on voltage dependence of translocation duration, using a nanopore. Such an application is of signicant importance in detection and characterization of viruses, their activity, and epidemics.52−55

nanoparticle in the nanopore changes the electrical resistance of the nanopore that can be detected as a temporal change in the ionic current between the two chambers.38 Earlier theoretical investigations based on the calculation of electrophoretic, electro-osmotic, and drag forces have shown the electrophoretic force to be the dominant force in these conditions.40,41 In addition to the calculation of these forces based on the measured dimensions, electrical properties, and surface charges of our devices,42,43 we have also determined the electrothermal,44 Brownian, and gravitational forces using a continuum model (see the Supporting Information). Our theoretical studies confirm the dominance of the electrophoretic force when the largest dimension of the nanoparticle is sufficiently smaller than the pore size with a sharp pyramidal nanopore and thin electric double layer (EDL) compared to the pore size. Thus, the electrophoretic and drag forces determine the translocation kinetics, and we can adopt the concept of electrophoretic mobility. According to the classical theory of electrophoresis the electrophoretic mobility is μ=

v (x ) ∂v(x) = E (x ) ∂E(x)

(1)

where v(x) and E(x) are position dependent velocity and electric field,59 and x is the position of the analyte. However, as described in the Introduction, in the nanopore the velocityvoltage curve is shifted and has an offset of tens of millivolts. Thus, eq 1 is not generally valid. So, we have to use the derivative form of the electrophoretic mobility. In addition to elimination of voltage offset, as we will show in the next section, high precision can be achieved simply by measuring the voltage dependence of translocation duration. Furthermore, in theory it may be possible to extract v(x) and E(x) from the translocation spikes to calculate the mobility and obtain zeta-potential from it. However, in practice it would be a rather difficult and inaccurate numerical calculation. On the other hand, we can easily measure the average values of the velocity and electric field. One can mathematically show the following: if we define the translocation mobility (μTr) as follows, it will be proportional to the electrophoretic mobility of the particles in the bulk, and the proportionality factor will be

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OPERATION PRINCIPLES Nanopore devices are composed of two microfluidic chambers separated by a membrane with a nanopore that connects the two chambers (Figure 1). A liquid fills the two chambers, one of which contains the nanometer-sized analytes. By applying a voltage between the chambers, an ionic current flows from one chamber, through the nanopore, and into the other chamber. Furthermore, an electric field is created and acts on the particles near and inside the nanopore. This field can drive the nanoparticles from one chamber, through the nanopore, and into the other chamber. The temporary presence of a 8492

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the ratio of the two distances over which we average the speed and electric field

μTr =

∂v ̅ ∂E ̅

( ) = A ∂( ) 1

∂ t ηl 2 Tr ζ= εr ε0 ∂V

where v ̅ = ls/tTr and E̅ = V/le are the average velocity and electric field in the nanopore, tTr is the measured translocation duration, V is the applied voltage, ls is the length of the device’s sensing zone, and le is the distance at which the applied voltage drops. Considering the fact that voltage drop out of the nanopore is negligible and most of the voltage drops where the sensing happens (see the Supporting Information), usually we can write l = ls = le. In the proposed method of zeta-potential measurement by nanopore, l is a fitting parameter that is included in a calibration constant that will be described later on. One may also calculate l for a specific nanopore device through numerical simulations (see the Supporting Information). We have defined the time that the center of nanoparticle enters the sensing zone as the start of the spike and the time that its center leaves the sensing zone as the ending point. A simple analytical calculation shows that these are the times at which the second derivation of the signal reaches its maximum and minimum43 (Figure 2). According to Henry’s solution for electrophoretic motion45 μTr

σ=

σ=

(3)

2 1 − 3 2(1 + 0.072(ka)1.13 )

(5)

( ),

∂ μTr = l

2

1 tTr

∂V

tTr =

εr ε0ζ εr ε0kBT qzn∞

(9)

ZETA-POTENTIAL MEASUREMENTS We applied the zeta-potential measurement method to tens of different nanometer-sized objects with different sizes and zetapotentials that were composed of biological or synthetic materials. We used gold, polystyrene, and silica nanoparticles with diameters ranging from 20 to 120 nm. To have a wider range of particles with different properties and zeta-potentials, the nanoparticles were capped with citrate (C3H5O(COO)33‑), carboxyl (COOH), amine (NH2), 1-mercapto-11-undecyl-tri (ethylene glycol) (SH(CH2)11(OCH2CH2)3OH), its carboxyl derivative (SH(CH2)11(OCH2CH2)6COOH), and deoxyribonucleic acid (DNA) linked with 5′-mercaptohexanol. Low zetapotential of human immunodeficiency virus (HIV) and epsteinbarr virus (EBV) have been measured as well. Measurements were performed using different nanopore devices measuring from 20 to 500 nm in width and about 720 nm in length in 20 × 20 μm membranes. Nanoparticle investigations and measurements were performed in 1 mM to 3 M aqueous solutions of potassium chloride (KCl). Virions have investigated in their growth medium after 10-fold dilution in aqueous KCl solutions. Some of the particles that were stable at higher ionic concentrations (see the Supporting Information) were investigated and measured at such concentrations as well. In all of the experiments, the translocation duration was reduced and the amplitude of the translocation spikes was increased by increasing the applied voltage (Figure 3). A typical relationship between the translocation duration and the applied voltage is shown in Figure 4a. According to the aforementioned theory, the translocation duration is inversely proportional to the applied voltage. To evaluate this relationship, the average velocity, which is the inverse of the translocation duration multiplied by the nanopore effective length, was calculated as a

Using eq 5 and the aforementioned parameters, the following relation between the average translocation velocity, applied voltage, translocation mobility, zeta-potential, and the measured translocation duration can be obtained ⎛1 ⎞ v ̅ = l⎜ ⎟, ⎝ tTr ⎠

(8)

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(4)

εr ε0ζ η

⎛ zqζ ⎞ 8n∞εr ε0KBT sinh⎜ ⎟ ⎝ 2kBT ⎠

Accordingly, by measuring the zeta-potential, we can measure the surface charge density of nanometer-sized objects using a nanopore.

where k = ((2q2z2n∞)/(εkBT))1/2, q is the elementary charge, z is the valence of the EDL’s ions, n∞ is the bulk ionic concentration, kB is the Boltzmann constant, and T is the absolute temperature. For zeta-potentials of approximately 100 mV or higher, we can apply O’Brien’s correction factor,46 and for jelly or porous particles, which are highly conductive, we can apply Dukhin’s correction factor.47 Although these correction factors can improve measurement accuracy, in most practical cases and applications, reasonably accurate results can be obtained without them. Because ka ≫ 1 in our nanopore devices, we can use Smoluchowski’s approximation48 and simply write μTr =

(7)

In most of the cases in which the zeta-potential is smaller than 100 mV, eq 7 can be approximated by the following linear equation

where εrε0 and η are solution permittivity and viscosity inside the nanopore that are generally different from permittivity and viscosity in bulk,56−58, and ζ is the zeta-potential of the particle. f(ka) is a correction factor that depends on Debye length, 1/k, and particle’s diameter, a, and can be curve fitted by the following equation f (ka) =

∂V

where C is an integration constant that is the voltage offset −i.e. a generally unknown parameter that can vary in each experiment. In addition to C, it is not easily possible to know the exact values of l, η, and εrε0; while (∂(1/tTr))/(∂V) can be simply measured. Thus, by extracting A = (ηl2)/(εrε0) from a calibration experiment with a particle of known zeta-potential, zeta-potential of other particles can be simply calculated using eq 7. Knowing the zeta-potential and assuming all of the particle’s electric charge to be on its surface, we can use Graham’s equation to calculate the surface charge density of the particles:45,46

(2)

2ε ε ζ = r 0 f (ka) 3η

1 tTr

ηl 2 (V + C)ζεr ε0 (6) 8493

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Figure 3. Scatter plots of translocation events obtained at different voltages. On the bottom and on the left axis, the Gaussian fits to the histograms of the distributions are depicted. The sample that was used is a colloid of citrated gold nanoparticles with a diameter of 20 nm and ζ = −49 mV; the diameter and zeta-potential of the particles are normally distributed with standard deviations of approximately 10% of their means. Measurements were performed using a 120 nm nanopore; the nanoparticle concentration was 7 × 1010 particles/mL, and the solution was 30 mM KCl.

Figure 5. Zeta-potential of the nanoparticles, HIV and EBV viruses measured by the nanopore device versus their zeta-potential measured by a commercial DLS system. Error bars show the distribution in the population; the measurement precision is better than ±2 mV for the nanopore method (see the Supporting Information) and ±5 mV for DLS. The blue line shows the translocation mobility as predicted by the theory, and dotted lines show the approximated dispersion due to the dispersion in zeta-potential of different particles.

function of voltage. As shown in Figure 4b average translocation velocity linearly changes with the cross membrane voltage as predicted by the theory. As mentioned previously, the velocity-voltage curves have a shift that can change from one device to another or from one sample to another; however, the slopes of these curves are not affected by these shifts. Thus, the slope represents a more precise and reliable parameter for the measurements. Translocation mobility can be calculated by multiplying the slope of the velocity-voltage curve by a constant number, as described by eq 6. A linear relationship between the translocation mobility and the zeta-potential measured by DLS has been found (see Figure S-6) which is in agreement with the theory. As predicted by theory, the translocation mobility is independent of nanoparticle size (see Figure S-5). Finally, eq 7 was used to extract the zeta-potential of the nanoparticles by multiplying the slope of 1/tTr versus voltage curve by A = (ηl2)/(εrε0) ≈ 21.6 × 10−6 V2 s that is extracted from calibration experiments as mentioned earlier. The results are compared with the zeta-potential of the same particles measured under similar conditions by DLS (Figure 5). As shown in this figure, the nanopore technique provides a simple

and advantageous method of measuring the zeta-potential of nanometer-sized objects. According to eqs 7 and 8, knowing the zeta-potential of a nanoparticle gives the particle’s surface charge.

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CONCLUSION We have introduced a novel method for measuring the zetapotential and, consequently, the surface charge of nanometersized objects suspended in a liquid. Because this method is based on a nanopore technique, it does not require labeling and functions with optically active and inactive as well as opaque and transparent samples. It requires only very small sample volumes and concentrations, works in ionic concentrations ranging from 1 mM to 3 M, and can measure zeta-potentials lower than 3 mV with better than 2 mV precision provided that the largest dimension of the analyte is much smaller than the length of the nanopore, smaller than the diameter of the nanopore’s orifice, and its translocation produces a spike more than 5 times the noise level.

Figure 4. Voltage dependence of the translocation kinetics. a) Translocation duration as a function of the applied voltage for SH(CH2)11(OCH2CH2)6COOH coated gold nanoparticles with 50 nm diameter and ζ = −38 mV; the diameters and zeta-potentials of the particles are normally distributed with standard deviations of approximately 10% of their mean values. Measurements were performed using a 120 nm nanopore; the nanoparticle concentration was 7 × 1010 particles/mL, and the solution was 30 mM KCl. The error bars show the standard errors of the population of the recorded translocation spikes. b) The average translocation velocity as a function of the applied voltage calculated by dividing the nanopore effective length by the translocation duration and removing the voltage offsets (see the Supporting Information). 8494

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local maxima and minima of the second derivative of the signal to find the starting and ending point of each spike and reports all the parameters related to each spike in a tab-delimited file.

This simple method not only enables the precise and accurate measurement of the zeta-potential of nanometer-sized analytes using a nanopore technique, it also allows for the detection of and differentiation between analytes based on their surface charge. Measuring the voltage dependence of the translocation spikes also enhances the precision, reliability, and repeatability of size measurements and reduces the need for calibration according to size. This nanopore technique has therefore been improved to provide an inexpensive charge and size spectroscopy technique capable of characterizing analytes in their natural liquid environments in small amounts and over a short period of time.

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ASSOCIATED CONTENT

S Supporting Information *

Size measurement, stability study of the nanoparticles, calculating the forces acting in a nanopore, simulating the current spikes, accuracy of the proposed method, mobility-size and mobility-zeta potential relations. This material is available free of charge via the Internet at http://pubs.acs.org.

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MATERIALS AND METHODS Device Fabrication. We have previously described the fabrication process of similar pores.49 Briefly, a pit was etched through the back side of silicon on an insulator wafer (SOI, 720 nm Si on 1 μm buried SiO2 on 700 μm Si) by potassium hydroxide (KOH) wet etching to produce a 20 × 20 μm membrane on the front side of the wafer that consists of 720 nm Si on 1 μm SiO2. A nanopore patterned by an electron beam lithography (EBL) process50 was etched away through the 720 nm thickness of the front side’s silicon by anisotropic KOH wet etching, followed by buffered hydrofluoric acid (BHF) wet etching to remove the 1 μm buried oxide and open the nanopore. Nanopore devices of various sizes between 20 and 500 nm have been fabricated with better than 10 nm precision. The devices were packaged between two closed and identical microfluidic flow cells, which provided inlets and outlets for fluids, visual access, and Ag/AgCl electrodes for electrical contacts. Measurement Setups. We have used an Axopatch 200B (Axon Instruments) patch clamp amplifier to apply the desired voltage and measure the current. A MiniDigi (Molecular Devices) was used for digitization, and a pCLAMP 10 (Molecular Devices) was used for data acquisition. All measurements were performed in a Faraday cage on an antivibration table in a dark room. Sample Preparation. Commercially obtained citrated, carboxyl-capped, and amine-capped gold nanoparticles (Ted Pella), silica nanoparticles (Keiser Biotech), and polystyrene nanoparticles (Interfacial Dynamics) with concentrations ranging from 5 × 109 particles/mL to 7 × 1011 particles/mL were diluted 5 to 200 times in the desired KCl aqueous solutions. The thiol- and DNA-capping processes and the investigation of the stability of these functionalized particles are described elsewhere.51 We used various aqueous KCl solutions of concentrations ranging from 1 mM to 30 mM for less stable particles and up to 3 M for highly stable particles. Inactivated HIV virions (Advanced Biotechnologies, Inc.) were investigated in 0.1 mM glycine, 0.1 mM EDTA, 0.005% Triton x-100, and 18 mM KCl. Inactivated EBV viruses (Advanced Biotechnologies, Inc.) were investigated in 0.1 mM glycine, 0.01% Triton x-100, and 36 mM KCl. Signal Processing. All signals were low-pass filtered by a 10 kHz 4-pole Bessel analog built-in filter in the amplifier. We developed software specifically for nanopore signal processing.43 This software first reduces the noise in the signal by a 5 kHz 8-pole Gaussian low-pass filter and uses a Bior3.9 wavelet for wavelet denoising. It then removes the baseline by fitting a two component exponential. It detects any fluctuation which is more than six times larger than rms noise and uses a selection algorithm to find the translocation signals. Finally, it uses the

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Gert Matthijs for useful discussions and suggestions on biological materials; Hilde and Karolien Jans for discussions and in preparation of the used colloids, investigation of their stability and DLS measurements; and Don Dautovich for editing.

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dx.doi.org/10.1021/ac300705z | Anal. Chem. 2012, 84, 8490−8496