Charged Particles Modulate Local Ionic Concentrations and Cause

Jan 9, 2014 - The importance of the findings for resistive-pulse analysis is discussed. .... benefits and challenges in applications and data analysis...
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Charged Particles Modulate Local Ionic Concentrations and Cause Formation of Positive Peaks in Resistive-Pulse-Based Detection Justin Menestrina,†,‡ Crystal Yang,§,‡ Matthew Schiel,∥ Ivan Vlassiouk,⊥ and Zuzanna S. Siwy*,†,§,∥ †

Department of Physics and Astronomy, §Department of Chemistry, and ∥Department of Biomedical Engineering, University of California, 210G Rowland Hall, Irvine, California 92697, United States ⊥ Oak Ridge National Laboratory, Bethel Valley Road, Oak Ridge, Tennessee, 37831, United States S Supporting Information *

ABSTRACT: We study the effect of electrolyte concentration on the shape of ion current pulses in resistive-pulse sensing. We show that electrokinetic passage of several hundred nanometers in diameter charged polystyrene particles through a micropore leads to formation of current increase when the particles exit the pore. The particle entrance, as reported before, causes formation of the current decrease, which is a measure of the particle size. Formation of the double peak, i.e., current decrease followed by a current increase, is especially pronounced if the resistive-pulse experiments are carried out in KCl concentrations below 200 mM. In order to explain the pulse shape, experiments were designed in which the particles passed through the pore only by either electroosmosis or electrophoresis. The presented experiments and modeling indicate that while both electroosmosis and electrophoresis affect the ion current pulse, formation of the positive peak is mainly determined by the latter effect and the charged state of the particle. The importance of the findings for resistive-pulse analysis is discussed.

I. INTRODUCTION Passage of single molecules and particles through pores is the basis of resistive-pulse sensing.1−12 When an electric potential or a pressure difference is applied across a single-pore membrane, the translocation of single particles is observed as a change of the transmembrane current (typically a decrease) called a resistive pulse.6−8 The relative amplitude of the resistive pulse, expressed as a percentage change of the baseline current, carries information on the particle size. In order to obtain a high signal-to-noise ratio, experiments are often performed at high ionic strengths of the background electrolyte solution. In cases when particle agglomeration becomes a problem, solutions with low salt content (e.g., 10 mM KCl) must be used to enhance electrostatic repulsion. Passage of hydrogels through glass pipettes and polymer pores was successfully reported only when performed in solutions of concentration between 10 and 100 mM KCl.13−15 Detection of DNA in low ionic strength solutions led to observation of concentrationdependent magnitudes and even relative sign of the resistive pulses. The presence of DNA in the pore causes either a current decrease or a current increase depending on whether the number of ions excluded by the molecule is higher or lower than the number of DNA counterions brought into the pore to fulfill electroneutrality.16,17 Experiments of DNA sensing in low aspect ratio solid state pores also led to a surprising find that for certain pore diameters higher signal-to-noise ratios for DNA translocation can be obtained in experiments performed in low salt concentrations.18 © 2014 American Chemical Society

In this article, we studied the effects of ionic strength on the detection of negatively charged polystyrene particles in single pores. We show the shape of the resistive pulses is influenced by the background electrolyte concentration. In all studied solutions, the particle entrance caused a current decrease, which was used to calculate the effective size of the particles. In salt concentrations below ∼200 mM, the current decrease was followed by a current increase whose amplitude decreased with increasing KCl concentration. The current increase occurred at the end of the translocation event, and its magnitude in some cases exceeded the amplitude of the current blockage. The existence of the positive peak indicates there are additional ions passing through the pore compared to ionic transport in an empty pore. The presence of the positive current spike at the end of a resistive pulse was reported before in experiments of DNA molecules passing through sub-2-nm in diameter SiN pores.19,20 We show the effect is also present in the detection of large, several hundred nanometer in diameter spheres passing through micropores. Ion current increase in the resistive pulse is largest when both the particles and the pore walls are charged but is also present when the pore walls are neutral. We provide experimental and theoretical evidence that the positive peak results from transient modifications of the electrolyte concentration caused by the charged particle. Received: December 11, 2013 Revised: January 9, 2014 Published: January 9, 2014 2391

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Figure 1. Example shapes of resistive pulses obtained when (a) 470 nm carboxylated particles and (b) 410 nm carboxylated particles translocated a 1400 nm pore. KCl concentration and voltage for each pulse are indicated in the figure. Events are vertically offset to facilitate comparison.

The pores used in the experiments were prepared in 12 μm thick films of polyethylene terephthalate by the track-etching technique.21−23 Track-etched pores in this material are characterized by an undulating pore diameter reflected in the shape of resistive pulses.23 During its translocation, a spherically shaped particle blocks a pore to a larger extent when passing through a section with a narrower constriction zone compared to when translocating a wider region. The amplitude of subpeaks in a resistive pulse is considered a measure of the local pore diameter. We find that for bulk electrolyte concentrations below 200 mM the relative amplitude of ion current changes within a pulse is also a function of the electrolyte concentration. The presented results are very important for interpretation of resistive pulses and relating the current change with the size of the translocating particle and pore diameter.

purchased from Bangs Laboratories. Sulfonated polystyrene particles were obtained from Life Technologies. Sizes of the purchased particles were measured by the Zetasizer Nano ZS (Malvern Instruments, Westborough, MA). All purchased particles had ∼15% variation in their diameter. Surface charge of the carboxylated particles was between −0.16 and −0.22 C/ m2 (or −1.0 and −1.4 e/nm2). Sulfonated particles were less charged with −0.06 C/m2 (−0.31 e/nm2). Ion Current Recordings. Measurements of ion current in time were performed using the Axopatch 200B and 1322A Digidata system (Molecular Devices, Inc.). Membranes were placed in a custom-made conductivity cell, and two homemade Ag/AgCl electrodes were placed on both sides of the membrane. Data analysis was performed with Clampfit 9.2 and Origin 9.0. Detection of particles was performed from KCl solutions between 10 and 400 mM. Concentration of particles was ∼108 per mL. Solutions of carboxylated particles contained 0.01% of Tween 80; sulfonated particles were detected from solutions containing 0.015% of Tween 80. Comsol Modeling. Coupled Poisson−Nernst−Planck and Navier−Stokes equations were solved using the Comsol Multiphysics 4.3 package.15,27 Cylindrical pores that were 2 μm long were connected with 20 μm long cylindrical reservoirs. A very fine triangular mesh of 0.1 nm was used close to the charged walls. Surface charge density of the channel wall was either 0 or −0.25 e/nm2, while surface charge of particles was either 0 or ±0.75 e/nm2. In the remaining parts of the modeled structures, the mesh was reduced to the point when no change in the observed concentration profiles and currents was observed upon further mesh decrease. The dielectric constant of the solution ε = 80, particle ε = 4, and diffusion coefficients 2 × 10−9 m2/s were used for both potassium and chloride ions. In all calculations, a potential difference of 0.1 V was applied to the right reservoir while the left reservoir was grounded.

II. EXPERIMENTAL SECTION Preparation of Pores. Single pores in 12 μm thick films of polyethylene terephthalate (PET) were prepared by the tracketching technique as described before.21−23 Briefly, films were irradiated with single energetic heavy ions (e.g., 11.4 MeV/u Au and U ions) at the UNILAC linear accelerator of the GSI Helmholtzzentrum für Schwerionenforschung in Darmstadt, Germany. Wet chemical etching of the films in 0.5 M NaOH, 70 °C and 2 M NaOH, 60 °C leads to preparation of pores with undulating pore diameter along the pore axis.23,24 Both conditions were used to fabricate pores presented in this manuscript. The mean pore diameter was estimated from the current−voltage measurements performed in 1 M KCl and relating the pore diameter with its conductance.25,26 Experiments presented here were performed with pores with an opening diameter between 500 and 1500 nm. The walls of track-etched PET pores contain carboxyl groups and are negatively charged at pH values above 3.8.25 Particles. All carboxylated polystyrene particles and uncharged poly(methyl methacrylate) (PMMA) particles were 2392

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Figure 2. Average ratios of maximum current decrease and maximum current increase as a function of voltage, recorded for two pores with average opening diameters of (a) 1400 and (b) 980 nm. Ratio was calculated for different particles and KCl concentrations as indicated in the figure.

III. RESULTS AND DISCUSSION Polystyrene particles with diameters of 180, 200, 280, 410, and 470 nm were detected during their voltage-induced passage through single pores in a polyethylene terephthalate (PET) film. The 180 nm particles were modified with sulfonate groups, which assured they were negatively charged in a wide spectrum of pH values down to pH ≈ 1.0.28 The remaining particles were modified with carboxyl groups. Since pores in polyethylene terephthalate films used in the experiments also contain carboxyl groups on the walls, all studied particles and the pore walls were negatively charged at pH values above ∼4. As a result, particles transport occurred by a combination of electrophoresis and electroosmosis. Particles were moving toward a positively biased electrode, indicating the effect of electrophoresis dominated the particle passage. All solutions of particles for the resistive-pulse experiments were prepared in KCl as the background electrolyte. KCl concentration was varied between 10 and 400 mM. Additional experiments were performed with 400 nm in diameter uncharged poly(methylmethacrylate) (PMMA) particles in 100 mM KCl. Example recordings of polystyrene particles passing through a pore with an average opening diameter of 1400 nm are shown in Figure 1. Experiments were performed at pH 10 to maximize the surface charge on the pore walls and particles. As observed by us and other groups before, entrance of the particles into a pore causes a current decrease whose modulation reflects the shape of the pore.7,15,23,29−33 The roughness of pores in PET occurs due to the laminar structure of the foils and overetching of the strata at elevated temperatures.34 Larger modulations of the current indicate larger modulations of the pore diameter. Reproducibility of the current shapes when different particles pass through the same pore was reported by us before,15,23 and more examples of resistive pulses are shown in the Supporting Information. Recordings presented in Figure 1 reveal resistive pulses of polystyrene particles recorded in KCl concentrations below ∼300 mM have a double-peak character, i.e., an initial current decrease is followed by a current increase above the baseline level. Experiments in different KCl concentrations had to be performed in different voltages, which will be discussed below. In the case of the 1400 nm pore and 470 nm particles in 10 mM KCl, the amplitude of the current increase accompanying a particle exit exceeded the amplitude of the current decrease. The positive peak at the end of resistive pulses recorded with 470 nm particles was not present at 400 mM and higher KCl concentrations; passage of 410 nm particles through the same pore did not cause a current increase at KCl concentrations

equal to and higher than 300 mM. The small amplitude and absence of the positive peak coincide with the convergence of the shape of the resistive pulses so that the pulse shape becomes KCl concentration independent. Experiments in Figure 1 suggest that in order to image the pore topography using the resistive-pulse technique experiments have to be performed in at least 200 mM KCl. More concentrated solutions also increase the signal-to-noise ratio, facilitating the ability to distinguish finer topography changes. Resistive-pulse experiments with polystyrene particles at low KCl concentrations revealed that particle transport was observed at significantly higher voltages compared to the recordings at higher ionic strengths. Thus, when comparing the resistive-pulse shapes, one has to take into account a possible dependence of the pulse shape on the applied voltage. Figure 2 shows the ratio of a maximum current decrease and the maximum current increase observed when the particles were exiting the pore recorded for different voltages and particle diameters for two pores with opening diameters of 1400 and 980 nm, respectively. Each point represents an average of at least 200 pulses. The graph suggests the ratio is fairly voltage independent for the 1400 nm pore but increases with increasing bulk electrolyte concentration and the diameter of the translocating spheres (Figure 2a). A weak voltage dependence of the current decrease and current increase ratio was found for pores with diameters below 1 μm; however, the voltage effect was less significant compared to the influence of KCl concentration and particle diameter (Figure 2b). In order to explain the presence of the positive peak, we first found its area as a function of voltage and bulk KCl concentration. The peak area is equal to the number of ions that pass through the pore in addition to the ionic transport that constitutes the baseline current in an empty pore. For almost all examined pores and particles sizes, the integrated area under the peak is at least a few times larger than the number of ions that were displaced by a single sphere (Table 1). Thus, the positive peak cannot be explained by only the influx of ions into the pore when the particle exits. A similar shape of resistive pulses with a current blockage followed by a current increase was observed with DNA molecules passing through a subnanometer SiN pore.19,20 Experiments were subsequently modeled approximating a DNA molecule as a charged cylinder whose transport through the pore was described by the coupled Poisson−Nernst−Planck (PNP) and Navier−Stokes (NS) equations.35 The positive peak was predicted to occur in cases when the electrical doublelayer thickness was comparable to the pore dimensions. The authors concluded that the positive peak was observed in 2393

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with carboxylated particles (Figure 3). Although passage of 410 nm in diameter carboxylated polystyrene particles created a clear current increase at the pore exit, resistive pulses of PMMA particles of similar diameter had only a current decrease. Elimination of electroosmosis was more challenging since carboxylated polystyrene particles have similar surface chemistry to the chemical characteristics of the pore walls. The isoelectric point of the track-etched PET surface is 3.8.25 At this pH, carboxylated polystyrene particles would also be uncharged. Therefore, experiments were performed with particles whose surfaces were modified with sulfonate groups which only lose their charge at pH ≈ 1. Figure 4 compares resistive pulses obtained with sulfonated particles at pH 3.5 and 5.5 as well as carboxylated particles of a similar diameter at pH 10 (Figure 4). Although the exit of the particles at pH 5.5 and 10 caused a clear current increase, the positive peak was absent in the pulses of single sulfonated particles recorded at pH 3.5 (Figure 4a). However, we noticed the recordings at pH 3.5 often had events with double amplitude, suggesting that two particles translocated the pore together. Particle agglomeration also caused frequent blocking of the pores and probably originates from the low surface charge density of the particles (maximum of −0.06 C/m2). Since the diameter of the pore was below 600 nm and the particles were 180 nm, our system did not detect translocation of triple particles. However, the double events did show a nonzero current increase with a smaller amplitude than events recorded at higher pH (Figure 4b and 4c). The presence of the current increase with double particles is in agreement with our earlier results (Figure 1), indicating the current increase is more pronounced with larger particles. The small amplitude of the current increase most probably results from partial protonation of the sulfonate groups at pH 3.5. It is also important to mention that due to the low surface charge density of sulfonated particles, their electrophoretic transport was only observed at pH values below 6 when the carboxyl groups on the pore walls are partially protonated. We were successful in recording passage of the particles at pH 8.0, but transport occurred by electroosmosis since the surface charge density on the walls was higher at these conditions than that on the particles. Experiments with PMMA and sulfonated particles suggest the current increase only occurs in experiments when the

Table 1. Number of Ions Obtained after Integration of a Positive Peak in Resistive Pulses Recorded when 470 nm Particles Were Exiting a 1400 nm in Diameter Pore (Npositive_peak)a

KCl concentration

no. of ions displaced by a volume of a single particle (Nvolume)

no. of ions obtained from integrating positive peaks of resistive pulses at different voltages (Npositive_peak)

10 mM

3.26 × 105

100 mM

3.26 × 106

2 V: (1.28 ± 0.20) × 107 3 V: (1.30 ± 0.21) × 107 4 V: (3.11 ± 0.65) × 107 0.6 V: (8.28 ± 1.77) × 106 1 V: (1.14 ± 0.15) × 107 1.3 V: (9.81 ± 1.78) × 106

Npositive_peak/ Nvolume 39 40 95 2.5 3.5 3.0

± ± ± ± ± ±

6 7 20 0.6 0.5 0.6

a

These ions pass through the pore in addition to the ions constituting the baseline current. Values from recordings in 10 and 100 mM KCl at different voltages are given. Number of ions displaced by a volume of a single particle is shown as well.

simulated experiments only when the PNP and NS equations were solved simultaneously, in other words, when both effects of electrophoresis and electroosmosis were taken into account. Although electrophoresis dominated, since, e.g., negatively charged particles moved toward a positively biased electrode, this effect alone could not lead to formation of a current increase at the end of the resistive pulse. Dimensions of our system are significantly larger than the size of DNA molecules and solid state nanopores considered in the simulations;35 thus, the model cannot be directly applied to explain our results. We decided however to test experimentally which phenomenon, electrophoresis or electroosmosis, dominates formation of the positive peak in our experimental system. The effect of electrophoresis was eliminated in the transport of 400 nm in diameter uncharged PMMA particles. Experiments were performed at pH 10 to maximize the charge on the pore walls and enable electroosmotic passage of the uncharged particles. The concentration of KCl solution used in these experiments was 100 mM KCl. Recordings in 10 mM KCl were too noisy and did not allow for reliable detection of the pulses. As expected, the PMMA particles passed through the pore at voltages of opposite polarity compared to previous experiments

Figure 3. Ion current pulses obtained when 410 nm carboxylated particles (1.5 V) and 400 nm uncharged PMMA particles (−1.5 V) passed through a pore with an opening diameter of 980 nm. Recordings were performed in 100 mM KCl, pH 10. 2394

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Figure 4. (a) Example of resistive pulses obtained with single 180 nm in diameter sulfonated particles passing through a 510 nm in diameter pore at pH 3.5, 2.2 V. (b) Resistive pulse of two sulfonated particles translocating the 510 nm pore together at 2 V. (c) Sulfonated particle passing through a different pore with an opening of a 540 nm pore at pH 5.5, 4 V. (d) As a comparison, a pulse of a 220 nm carboxylated particle at pH 10, 2.2 V in the 510 nm pore is shown as well. Dashed line facilitates observation of the positive peak at the end of the pulses. Bulk KCl concentration was 50 mM.

Figure 5. (Left) Results of numerical modeling of ionic concentrations along an axis of a 510 nm in diameter pore and at pore entrances with (a,b) and without (c) a 220 nm charged particle placed at two pore entrances (a,b). Length of the modeled pore was 2 μm. Concentrations along the pore axis are shown; thus, the discontinuity in a and b is due to the presence of the particle. Bulk KCl concentration was 10 mM. (Right) Schematic representation of ionic distributions and direction of potassium and chloride ions movement (red and blue arrows, respectively) for all cases shown in the left column.

translocating particles carry surface charge. Formation of the positive spike accompanying the particle’s exit does not require charges on the pore walls. In order to unravel the physical basis for the shape of resistive pulses in low KCl concentrations, we performed numerical modeling of ionic concentrations and ionic current through a single pore with and without a particle placed at different locations along the pore axis (Figures 5 and 6). Modeling involved solving coupled PNP and NS equations, which is computationally very expensive.15,27 Therefore, modeling was performed with a 2 μm long pore (vs ∼11 μm experimentally studied structures) and at a lower voltage of 0.1 V. The surface charge density of the pore walls and the particle was set −0.25 and −0.75 e/nm2, respectively. For simplicity, a cylindrical geometry was considered. The opening diameter of the modeled pore was 510 nm, thus equal to the diameter of the structure experimentally examined in Figure 4a, 4b, and 4d. Figure 5c shows the profile of KCl concentration along the axis of an empty pore and electrolyte reservoirs placed on both sides of the membrane. On the side of the membrane with a

positively biased electrode, the salt concentration was depleted by ∼1% compared to the bulk concentration (10 mM KCl), while on the opposite side the concentration was enhanced. Due to the large opening diameter of the pore, the difference in concentration of potassium and chloride was negligible along the pore center. We concluded the slight modulations of KCl concentration at the pore openings originate from concentration polarization caused by an enhanced sourcing of potassium ions through a negatively charged pore. Concentration polarization is typically associated with nanopores and ionic selectivity, and indeed, depletion/enhancement of ions at pore entrances is small in micrometer size pores.36 Figure 5a and 5b shows how the distribution of ionic concentrations along the pore axis changes when a 220 nm in diameter negatively charged particle is placed at one of the two pore entrances. When approaching the pore, the particle depletes the region adjacent to the pore entrance with co-ions, chloride in the case of negatively charged particles considered here (Figure 5a). Since co-ions are moving in the same direction as the particle, the current carried by chloride 2395

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Figure 6. Relative current change, χ, when a 220 nm particle is passing through a 510 nm diameter pore. (a−d) Results of numerical modeling based on coupled PNP−NS equations; 0.1 V is applied across the membrane, with the right-hand side being at the positive potential. (a) Both the particle and the pore walls carry negative surface charge, and the particle moves from left to right. (b) Particle is uncharged; thus, it passes electroosmotically from right to left. (c) Particle and channel have opposite charges positive and negative, respectively. Particle travels from right to left, and the peak positions are swapped. (d) Negative particle passes electrophoretically through a neutral pore (left to right). (e) Same as in a but modeled by PNP only (no solvent movement, particle travels left to right). All simulations were performed in 10 mM KCl as the background electrolyte.

In addition, we considered a positively charged particle translocating a negatively charged pore, a situation which would be difficult to test experimentally due to electrostatic attraction and possible adsorption of the particles on the walls. A positively charged particle would move in the opposite direction compared to the transport of a negative particle (Figure 6c). Changing directions corresponds to swapping of the position of the blockage and enhancement peak. As a result, an exit of a positively charged particle is still accompanied by current increase. The modeling suggests the charge state of the translocating particles is critical for the shape of resistive pulses. In order to further corroborate the finding that the positive peak in resistive pulses is present independently of the charged state of the pore (as long as the particles are charged), we modeled the ion current pulse of a charged particle in a neutral channel (Figure 6d). Similar to what was obtained in the experiments (Figure 4b), the modeled pulse contained both negative and positive parts. Finally, we “turned off” any possible solvent movement including electroosmosis by solving only PNP (Figure 6e) and not the full set of PNP−NS. The current increase was still present in the predicted pulse, although the amplitude of the current change was smaller than in the case when PNP and NS were solved together. This result points to a finite influence of the concentration polarization on the shape of resistive pulses. The modeling presented in the manuscript was performed for a pore whose shape is cylindrical. However, the pores used in the experiments are characterized by an undulating diameter. Thus, one can expect modulation of ionic concentrations at the boundaries between segments of different opening diameter. We wanted to check whether the possible modulations could

diminishes. The potassium current decreases as well, since these ions are sourced from the entrance where the concentration is lowered by the concentration polarization. When the particle exits the pore (Figure 5b), the pore end from which potassium is sourced contains a higher concentration of K+ brought about by the particle. Chloride is sourced from the opposite entrance that is in contact with enhanced KCl concentration due to the concentration polarization effect. As a result, the particle exit leads to an increase of the recorded ion current. Modulation of ionic concentrations induced by the charged particle is larger than the modulation caused by the concentration polarization; thus, the current increase is observed even with micrometer size pores (Figure 1). One can calculate the corresponding ion current through the pore/particle system when the particle is placed at different locations along the pore axis. This current vs position relation is equivalent to the signal of current vs time measured in experiments. It is convenient to measure the ionic current blockage/ enhancement degree as a percentage of the baseline current, I: χ = ΔI/I (Figure 6), where ΔI is the difference of currents measured without and with a particle.35 The ion current pulses predicted by the modeling are in qualitative agreement with our experiments. In Figure 6a, a negatively charged particle moves electrophoretically toward a positively biased electrode; the current increase in the modeled pulse indeed occurs when the particle leaves the pore. We also modeled electroosmotic transport of a neutral particle through a charged pore, and as expected, the predicted resistive pulse consists only of the current decrease (Figure 6b). 2396

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IV. CONCLUSIONS In this article we report a series of experiments which were aimed at understanding how the concentration of the background electrolyte influences the shape of resistive pulses obtained with polystyrene particles. We identified conditions when the exit of an electrophoretic passage of particles through a pore is accompanied by a current increase above the baseline level. In low concentrations and large ratios of the particle and pore diameters, the amplitude of the current increase exceeded the amplitude of the current decrease. Resistive pulses observed at low concentrations of KCl affect the ability to measure size of the particles correctly if the particles are charged. The article presents rather surprising results thata surface charge of several hundred nanometer hard sphere particles can modulate ionic concentrations at the pore entrance. This effect was observed before at the nanoscale in conditions at which the size of the system was comparable to the thickness of the electrical double layer.19,20,35 Here we show the importance of the electrostatics in micrometer size pores. The article also reports resistive-pulse experiments performed in conditions when only electroosmosis or electrophoresis influenced particle transport. Our results indicate that in order to understand passage of particles through pores the ability to separate different modes of transport might be very important.

affect the particle sizing using the formula describing the resistive-pulse depth7,10,37 R particle − R empty =

4ρd3 ⎛ d ⎞ S⎜ ⎟ π D4 ⎝ D ⎠

(1)

where Rparticle and Rempty are resistances of a pore with a particle and an empty pore, respectively, and S is a factor that depends on the ratio of particle diameter, d, to pore diameter, D, which can be approximated by7,10,37 −1 ⎛d⎞ ⎡ ⎛ d ⎞3 ⎤ S⎜ ⎟ = ⎢1 − 0.8⎜ ⎟ ⎥ ⎝D⎠ ⎣ ⎝D⎠ ⎦

(2)

Using the maximum current decrease to determine Rparticle, eq 1 relates the minimum pore diameter with the particle size. Equation 1 was used before to analyze particle passage through pores characterized by undulating opening diameter.7 For each pore, the diameter of the narrowest constriction zone was determined from the maximum current decrease measured with 280 nm particles at 400 mM KCl; at these conditions the modulation of ionic concentrations in the pore and at the pore entrances is expected to be the weakest. Using this constriction size, we calculated the effective particle diameter based on recordings at various KCl concentrations. A summary of experiments performed with 4 different pores is shown in Figure 7. Collected data indicate the size of the

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ASSOCIATED CONTENT

S Supporting Information *

Reproducibility of resistive pulses recorded in two different concentrations. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Phone: 949-824-8290. E-mail: [email protected]. Author Contributions ‡

These authors contributed equally

Author Contributions

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

Figure 7. Effective size of translocating particles as a function of bulk electrolyte concentration used in resistive-pulse experiments. Data from different pores are marked with different colors and types of symbol. Pores had the following average opening diameter: pore 1, 1330 nm; pore 2, 890 nm; pore 3, 1400 nm; pore 4, 980 nm. Dashed horizontal lines indicate particle size as determined by light-scattering approach.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Irradiation with swift heavy ions was performed at the GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany. This research was supported by the National Science Foundation (CHE-1306058) and UC National Lab Fee Program 12-LF- 236772.

particles can be reliably determined when the resistive-pulse experiments are performed in KCl concentrations of 100 mM and higher. The largest discrepancy in the effective particle diameter, as determined by the resistive-pulse approach and dynamic light scattering, was recorded for the lowest examined KCl concentration of 10 mM for 410 and 470 nm particles. Particles 410 nm in diameter appear smaller in lower concentrations since the additional ions they bring to the pore partly offset the pore occlusion. Surprisingly, the 470 nm particles have a larger effective size in 10 mM KCl compared to the resistive-pulse recordings in higher ionic strengths. We do not have an explanation for that yet.

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REFERENCES

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The Journal of Physical Chemistry C

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dx.doi.org/10.1021/jp412135v | J. Phys. Chem. C 2014, 118, 2391−2398