FIB-Milled Quartz Nanopores in a Sealed Nanopipette

Abstract

We report the use of laser-pulled quartz nanopipettes as a new platform for microfabricated nanopores. A quartz nanopipette is prepared on a laser puller and sealed closed prior to focused-ion beam (FIB) milling. A quartz nanopore can then be FIB-milled into the side walls of the sealed pipette and used to analyze single nanoparticles. This method is fast, reproducible and creates nearly cylindrical nanopores in ultrathin quartz walls with controllable diameter down to 66 nm. Both pore size and wall thickness can be readily controlled in the FIB milling process by adjusting milling parameters and milling at different locations along the pipette walls. FIB-milled quartz nanopores combine the advantages of the pipette pores and silicon chip-based membrane pores into one device while avoiding many of the challenges of two popular nanopore devices. First, they can be used as a handheld probe device like a quartz pipette. Second, the use of an ultrathin quartz membrane gives them superior electric property enabling low noise recording at a higher bandwidth and a highly focused sensing zone located at a farther distance away from the highly restricted tip region. The inner and outer diameters of the resulting pore can be precisely measured using scanning electron microscopy (SEM). As an application, FIB-milled side nanopores are used to study translocation of polystyrene nanoparticles. In addition to studying the dependence of translocation time on the pore length, we demonstrate detection of nanoparticles in parallel nanopores of different lengths and use finite-element simulation to confirm the identity of the two resulting populations. Our results show that FIB-milled side nanopores are a useful platform for future analytical applications like studying nanoparticle translocation dynamics.

1. Introduction

A nanopore is often referred as a nanometer-scale aperture formed inside either an ultrathin solid-state membrane (an artificial nanopore) or a biological protein molecule such as an ion-channel protein. Nanopore-based sensors have attracted enormous interests in analytical chemistry due to their high sensitivity and easy of use.¹ For example, depending on the pore size and the analyte of interest, one can detect various species ranging from single-stranded DNA,^2–5 RNA,⁶ small molecules,^7,8 proteins,⁹ viruses,^10,11 and larger nanoparticles.^12,13 Nanopore sensors normally operate on a resistive-pulse mechanism, also known as the Coulter counter method.¹⁴ In resistive-pulse measurements, one normally holds a constant voltage across the nanopore membrane while measuring the ionic current passing through the pore over time. A transient change in the ionic current is detected when an analyte particle translocates through the nanopore providing useful information about the analyte particle, such as shape and electrophoretic mobility,¹⁵ charge,¹⁶ and size.¹⁷,¹⁸ A current decrease is often observed due to a particle partially blocking the flow of the ions. The detection frequency can be used to analyze particle concentration. Based on the shape and duration of the current pulse, one can also obtain information about the pore geometry.¹⁹

Protein pores can give reproducible pore size and somewhat tunable chemistry of the inner pore walls. However, their analytical use is often limited by the short lifetime of the lipid membrane the pores are inserted in and their narrow size range. Artificial pores, on the other hand, can be made in a variety of materials including glass,^20,21 silicon nitride,²² polycarbonate and polyethylene terephthalate (PET),²³ metals,²⁴ carbon nanotubes,²⁵ and single or few layer graphene.²⁶ Popular fabrication methods include glass/quartz pipette pulling,²⁷ milling of a thin membrane using a focused beam of electrons²⁸ or ions,²⁹ electric breakdown,³⁰ and track etching of a polymer membrane.³¹ Depending on the fabrication technique, one can make cylindrical or conical nanopores from as small as a few angstroms³² to hundreds of nm enabling detection of analyte species of various sizes. The methods for nanopore fabrication in some of the above materials have been well reviewed.^1,33,34

Pipette pulling is an easy and fast method to prepare size-tunable conical glass/quartz nanopores with benchtop equipment.^35,36 Pipette nanopores are low cost, disposable, and can be quickly filled with an electrolyte solution for leak-free electric measurements. Furthermore, they can be used as useful scanning probes for high-resolution imaging in liquids.³⁷ However, pipette pores are normally made with a long taper which lowers their analytical sensitivity due to the added solution resistance. Focused ion-beam (FIB) or electron-beam milled silicon nitride or oxide membrane pores can have tunable size and shape and high sensitivity due to ultrathin pore thickness and a highly-focused sensing zone. However, a key challenge has been the high electric noise due to the large membrane size and the use of conductive silicon support.^38,39

Here we describe a fabrication method which creates quartz nanopores that combine the easy use of handheld pipette pores, the superior electric property of quartz, and the versatility of FIB milling in one analytical device. Figure 1a is a cartoon showing a comparison of particle translocation through a pipette end pore and an FIB-milled side pore. The regular pipette pore is located at the far end of the tip and has a long highly restricted zone. On the other hand, a side pore is created in the side walls of a sealed quartz pipette and is far from the pipette tip. This allows one to tune pore length over a large range from <50 nm to >4 μm by selectively milling at different distances from the pipette tip. The nanopore’s sensing zone can be highly focused by largely avoiding the ionic resistance in the long pipette taper. Figures 1b and 1c are scanning electron microscopy (SEM) images of a 66-nm-diameter and a 156-nm-diameter side pore milled in two separate pipette substrates.

Figure 1.

(a) A cartoon showing nanoparticle translocation through a laser-pulled pipette pore and an FIB-milled side pore. (b) and (c) are SEM images of a 66 nm (b) and a 156 nm (c) diameter side pores milled in two separate quartz pipettes.

We show that these side pores have smooth, conical geometries with the smaller diameter orifice on the inside, and exhibit low current rectification under the conditions used. We characterize the pores using SEM and cyclic voltammetry (CVs) and use them to study nanoparticle translocation. We observe the translocation of a single population of polystyrene nanoparticles and then successfully discriminate between two differently sized populations of polystyrene beads. Finally, we demonstrate the versatility of the system by comparing the dynamic forces acting on particle translocation through two parallel pores of different length in the same membrane. Our results indicate that this system can be used as a model to explore particle transport in single nanopores as well as multi-pore membranes. Their future applications may include low noise recording of particle translocation events and combined electrical and optical detections of fluorescently labeled biomolecules and nanoparticles.

2. Experimental Section

2.1. Materials.

Potassium chloride (KCl) was from Fisher. Potassium phosphate monobasic and dibasic was from J. T. Baker. Triton X-100 was from Aldrich. Polystyrene nanoparticles with diameters of 57 nm and 112 nm were from Polysciences. Ag/AgCl quasi-reference electrodes (QRE) were prepared by immersing 0.5 mm diameter silver wire from Alfa-Aesar into Tough Guy brand ultra-bleach until the wire turned a noticeable shade of purple-grey. Quartz capillaries with a filament were from Sutter (I. D. 0.7 mm, O. D. 1.0 mm).

2.2. FIB-Based Nanopore Fabrication.

Quartz capillaries were pulled into nanopipettes with a Sutter P-2000 laser-based micropipette puller using the standard thin-walled quartz recipe (Heat=700, Filament=4, Velocity=60, Delay=150, Pull=175). The nanopipettes were then sealed at the tip by carefully heating the tip on a Narishige MF-83 microforge. Sealed pipettes were electrically tested in 100 mM KCl to ensure a fully sealed tip. The sealed pipettes were sputter coated with an amorphous carbon film (SPI Supplies) to provide a conductive surface for SEM imaging and FIB milling. Nanopores were milled in the coated pipette wall using a dual beam FEI XL830 FIB. Beam current and exposure time were varied according to the depth of the nanopore being drilled. After FIB milling, the carbon film was removed from the pipettes with O₂ plasma in a Diener Femto plasma cleaner for 10 minutes.

2.3. Nanopore Measurements.

The conductance of FIB-milled nanopores was initially tested in 100 mM KCl by scanning between −1 and +1 V (all potentials hereafter were applied to the electrode inside to the electrode outside of the pipette). As an example, Figure S1 shows a typical current-voltage response of a 263 nm diameter quartz side nanopore. The potential was controlled by an EG&G PAR Model 175 function generator and a Dagan Chem-Clamp potentiostat. The Dagan was interfaced to a PC through a National Instruments 6251 DAQ card and a National Instruments BNC-2120 breakout box. Following conductance measurements, the solution in the pipettes was replaced with a solution of 100 mM KCl, 10 mM phosphate, and 0.1% Triton X-100 that was buffered to pH 7.4. An Axopatch 200B (Molecular Devices) was used for all nanoparticle translocation recordings. The signal was digitized using a Digidata 1440A (Molecular Devices) that was interfaced with the computer using USB. Two Ag/AgCl QRE were used as the driving electrodes. All solutions used were filtered through a 200 nm PTFE syringe filter prior to use.

The tip of the pipette was submerged in the 100 mM KCl, 10 mM phosphate, 0.1% Triton X-100 solution as a control to observe baseline current in the absence of nanoparticles. Following this the outer solution was exchanged with the same solution with 112 nm or 57 nm polystyrene particles added at a concentration of 5 × 10¹⁰ particles/mL. Translocation experiments were performed by initially applying a series of positive potentials versus the outer electrode as a control to rule out particle translocations at this polarity. The voltage was then switched to negative and measured at −100, −200, −300, and −400 mV for at least two minutes so one can collect tens to hundreds of particle translocation events. Pore clogging was noted as an increase in root mean square (RMS) noise and was accompanied with a decrease in conductivity. We attempted to revive pores by applying a +1.4 V pulse through the application of the Axopatch’s zap function. In the event of an unclogging we observed a decrease in RMS noise and an increase in conductance to the original level along with the return of translocation events as shown in Figure S2. Typically, the current was filtered at 10 kHz by a low-pass filter and digitally sampled at 100 kHz. For longer pores at low voltages where the translocation events were sufficiently long the current was filtered at 5 kHz to increase the signal-to-noise ratio.

2.4. Finite Element Simulations.

Nanopore conductance simulations with and without the presence of an insulating nanoparticle in the sensing zone was performed using COMSOL Multiphysics 5.2a.

3. Results and Discussion

3.1. Nanopore Fabrication.

In this study we used thin-walled quartz capillaries with an I. D. of 0.7 mm and an O. D. of 1.0 mm. The use of thin-walled quartz gave the greatest range of pore lengths to choose from during FIB milling. Quartz is also an ideal choice for low noise nanoparticle studies because of its superior electrical property⁴⁰ and a lower surface charge density than borosilicate.⁴¹ The lower charge density reduces the electroosmotic force therefore increasing nanoparticle translocation time, assuming electroosmosis is the dominant force acting on the particle. It also reduces electrostatic repulsion between the negatively charged quartz nanopore walls and the negatively charged polystyrene particles, although this interaction was already significantly diminished by the high salt concentration in these experiments.

The thickness of the quartz wall of the pulled pipette increases away from the tip. We use the FIB to mill a pore in the taper of the pulled capillary at a specific distance from the tip. We have previously demonstrated that the I. D./O. D. ratio of the quartz capillary is kept during the laser pulling process.^42,43 Figure S3 shows that the measured ratio of the quartz pipette follows the initial ratio prior to laser pulling. By examining the diameter of the sealed pipette at the milled location one can calculate the pore length (or, pipette wall thickness) based on the dimension of the original glass capillary. To demonstrate this unique capacity, we have created multiple nanopores in the same pipette (Figure 2). Four nanopores were milled with nominal lengths from 500 nm to 4 μm. SEM images show that these side pores are circular in shape ranging from ~250 to 350 nm in diameter. For all pores used in the following study, the inner pore diameter was controlled in the range of 150 to 250 nm and the outer pore diameter was between 250 to 350 nm.

Figure 2.

SEM image of locations on the sealed quartz capillary taper for FIB milling to create pores that are nominally 500 nm, 1 μm, 2 μm, and 4 μm long. The scale bars for the inset nanopores are 200 nm.

To eliminate sample drift and vibration during FIB milling it is beneficial to use a relatively large beam current for fast milling. This is especially important for thicker pore walls. The outer pore diameter is almost always greater than its inner pore diameter and a conical nanopore geometry is assumed with a half-cone angle between 2° to 10°. The application of xenon difluoride (XeF₂) during ion milling has been proven to reduce this angle. In this study the application of XeF₂ creates a nearly-cylindrical pore with measured cone angles below 7°.⁴⁴ Cone angles were calculated based on the inner and outer diameters and the pore length, as illustrated in Figure S4. Even with the most conservative SEM measurements half-cone angles were always less than 7° with this angle decreasing sharply with pore length to one or two degrees in pores over a micrometer long.

In the case of “good” pores we observe smooth walls inside the pore as shown in Figure S5. Nanoparticle translocations were hardly observed in pores with rough edges even though the apparent pore diameter as determined with SEM and resistance measurements was twice as large as the particle diameter. This is likely caused by possible redepositing of the milled material inside the pore, occluding particle translocation. The application of XeF₂ during milling increased our success rate from ~10% to nearly 100%. This was especially helpful in milling longer pores for which the XeF₂ not only reduced redeposition but also increased the milling rate reducing the drifting effect.

A critical aspect of nanopore recording is the signal to noise ratio (S/N). Chip-based solid-state nanopores fabricated in silicon-supported thin-films of silicon nitride (SiN_x) or silicon oxide (SiO_x) typically exhibit significantly higher noise than quartz nanopores.³⁸ There have been several efforts to reduce the noise of these silicon based nanopores including the use of an additional oxide insulating layer between the silicon and the nanopore membrane.⁴⁵ Their small chip size also makes it quite challenging to mount them without possible leaks.

We measured the noise at 10 kHz bandwidth of laser-pulled pipette nanopores (referred hereafter as end pores) and FIB-milled side pores with an ionic current of 0 nA and −8 nA, a current representative of our −100 mV recordings. End pores had RMS noise of 3.65 pA and 5.28 pA at 0 nA and −8 nA, respectively. At 0 nA and −8 nA, the 1.3 μm long side pore had an RMS noise of 4.64 pA and 4.70 pA and the 2 μm long pore had 6.03 pA and 6.65 pA respectively. The increase in low-frequency noise is expected with longer pore length and comes from the larger availability of charge states within the nanopore.^46,47 For comparison, the RMS noise of silicon-based nanopores has been reported as being as high as 38 pA at 0 nA, and noise over 100 pA with an ionic current being passed through the pore.³⁸ Although these silicon pores are smaller than our side pores, it is worth noting that larger pores usually have higher electric noise. All told we observed a negligible difference in noise between laser-pulled end pores and FIB-milled side pores and measurements of tens of picoamperes was easily performed with all pores. This is particularly evident in our double pore experiment, in which current blockades of ~20 pA are measured on top of an ~8000 pA baseline.

3.2. Nanopore Conductance.

The nanopore conductance was measured in 100 mM KCl. As shown in the representative i-V response in Figure S1, all side pores had linear i-V responses between −1 V and +1 V. The diameter was determined from the i-V curve using the equation for the ionic resistance of a cylindrical nanopore:⁴⁸

$$R=\frac{4L+\pi D}{\pi \kappa D^{{}_{{}^2}}}$$ (1)

Where L is the length of the pore as determined from SEM, D is the pore’s diameter, and κ is the conductivity of the electrolyte solution. Discrepancies between the measured SEM diameter and the electrically measured diameter arose for the shortest of our pores. We ascribe this to an increased resistance due to the taper of the pipette as it constricts toward its point, as discussed later.

3.3. Electroosmosis-Driven Nanoparticle Translocation.

The translocation of polystyrene nanoparticles through the nanopore manifests as resistive-pulses in a current-time trace. Figure S2 displays a typical current-time response showing nanoparticle detection through a 263 nm FIB-milled side nanopore with a length of 1259 nm. At a pH of 7.4 and a salt concentration of 100 mM the 57 nm and 112 nm polystyrene nanoparticles have a slight negative zeta potential of −6 mV and −5 mV respectively as measured with dynamic light scattering.

In previous studies on nanoparticle translocation through nanopores there have been three controllable forces in play: pressure, electroosmosis, and electrophoresis.⁴⁹ In this study we do not apply a differential pressure and instead rely on electroosmosis and electrophoresis. These forces depend on the electric field within the pore. Electroosmosis pulls the cations within the double layer of the pore sidewalls into the pore when a negative potential is applied within the pore relative to the outside, which in turn pulls solution into the pore through viscous forces. Electrophoresis pulls the negatively charged nanoparticles into the pore when a positive potential is applied relative to the outside. Electroosmosis and electrophoresis will always work against each other because both the side walls of the pore and the surface of the particles are negatively charged. The dominant force can be determined by observing the polarity of the potential under which particles translocate. Only when a negative potential applied inside the pore relative to outside did we observe translocations. We thus concluded that the electroosmotic force was the dominant force for the nanoparticle translocation.

Figure 3a displays the change in the translocation time with pore length. The half-width of translocation events changes exponentially with pore length. All pores had an inner diameter of 150–250 nm and an outer diameter of 250–350 nm with pore lengths ranging from 495 to 3688 nm. Half-widths were all measured at −100 mV. The dashed line is an exponential fit to the data. Despite a variation in the pore size, the translocation time does show an interesting exponential increase with pore length, which can be qualitatively understood from two factors, the increased sensing zone length and the decreased electroosmotic force as pore length gets greater. The increase in length creates a larger distance which the particle must travel. If this were the only factor, one would expect the translocation time to increase linearly with pore length. The electroosmotic force weakens because the same potential is now falling across a larger distance, lowering the magnitude of the electric field within the pore assuming the same potential is applied. The effect of changes in geometry on the electric field is shown in more detail in the supplemental information in Figures S13-S15.

Figure 3.

(a) The half-width of translocation events changes exponentially with pore length. Half-widths were all measured at –100 mV. The dashed line is an exponential fit to the data. Error bars are one standard deviation. (b) Representative resistive current pulses for the 495 nm, 1259 nm, 1987 nm, and 3688 nm long nanopores. All pores had an inner diameter between 150 to 250 nm and an outer diameter between 250 to 350 nm. Additional example traces can be found in Figure S8.

Figure 3b compares the translocation current blockades of the 495 nm and 1259 nm long nanopores. The pore diameters are 210 nm for the 495 nm long pore and 265 nm for the 1259 nm pore. Here, we observe an unexpected higher current blockade in the 1259 nm long nanopore. This was originally puzzling because it has been suggested that the magnitude of the current blockade is related to the volume ratio of nanoparticle itself and the nanopore. For a cylindrical nanopore,²⁵

$$\frac{\mathrm{\Delta }{i}_c}{i_c}=S(d_s,d_c)\frac{d_s^3}{l_c\text{'}{d}_c^2}$$ (2)

where i_c is the baseline current, Δi_c is the amplitude of the current pulse, d_s is the diameter of the particle, d_c is the diameter of the nanopore, and l_c’ is the “end effect” corrected length given by: l_c’=l_c + 0.785d_c. The correction factor S(d_s,d_c) is dependent on the ratio of d_s to d_c,

$$S(d_s,d_c)=\frac{1}{1-0.8{\left(\frac{d_s}{d_c}\right)}^3}$$ (3)

However it has been suggested that this is not the sole contributor to the current blockade and observations of this nature have also been reported by others using FIB-milled nanopores.⁴⁸ We hypothesize that in our system the overall current ratio Δi_c/i_c is controlled by both the volume of the nanopore and the additional volume of the pipette’s taper as the position of the nanopore is moved toward the tip. The 495 nm long pore is only ~20 μm from the tip while the 1259 nm long pore is ~50 μm from the tip. The constriction of the pipette between these pores adds additional resistance to the 495 nm long pore which is evident in its lower ionic conductance and the lower current blockades of translocating nanoparticles of the same diameter. Later we perform experiments and simulations to affirm this hypothesis in a double-pore setup. When pore length further increases, the overall current ratio starts to be dominated by the pore resistance. This is shown in the case of the 1987 and 3688 nm pores where both pores have current decreases less than 1% of their baseline.

To demonstrate the ability of our pores to analyze nanoparticles of different sizes, which is an important characteristic of any Coulter counter, we detected two different populations of polystyrene beads. Figure 4a is an 8-second-long detection trace in a buffer solution containing both 57 nm and 112 nm polystyrene nanoparticles using a 210 nm diameter, 495 nm long nanopore at −400 mV. Figure 4b is a histogram of detected current blockades containing the two particle populations. The larger 112 nm particles gave a larger current blockade of ~500 pA while the smaller 57 nm particles gave a ~70 pA blockade. The predicted current ratio of the two nanoparticle populations based on equation 2 is 0.13 (57³/112³) which is in excellent agreement with the measured current ratio (70/500 = 0.14). Figure S7 shows traces of nanoparticle translocations of each individual population as well as the voltage dependence on the percent current blockade. Although only two particle sizes are studied here, this result indicates that FIB-milled side pores can be a useful platform for sizing nanoparticles.

Figure 4.

(a) An 8-second current-time trace collected at –400 mV showing particle size discrimination between 57 nm and 112 nm polystyrene nanoparticles using a 495 nm long nanopore. (b) Histogram of current blockades showing the two populations of nanoparticles. N = 386.

3.4. Double Pore Translocations.

It has previously been demonstrated that multiple protein nanopores can be used in the same membrane to detect single molecules.⁵⁰ The ability to create multiple nanopores can significantly increase detection frequency. To further demonstrate the ability of FIB milling to create multiple nanopores in the same pipette substrate, we milled two pores in a same pipette substrate and used them to study particle translocation. These pores had different lengths with the shorter pore being 376 nm long with an inner diameter of 186 nm and outer diameter of 269 nm and the longer pore being 1007 nm long with an inner diameter of 180 nm and outer diameter of 277 nm. We observed the translocations of 112 nm particles through each of these pores simultaneously as shown in Figure 5a, with one population having roughly three times the amplitude of the other. Populations at each voltage measured are shown in Figure S9.

Figure 5.

(a) An 8-second current-time trace collected at –400 mV using a sealed pipette containing two pores of different lengths showing detection of 112 nm polystyrene particles. The 376-nm-long pore has an inner diameter of 186 nm and the 1007-nm-long pore has an inner diameter of 180 nm. (b) A scatter plot of individual detection events showing their half-widths and current blockades from results in (a). (c) Histogram of current blockades for the 376 nm and 1007 nm long nanopores. Overlaid are Gaussians fit to each of the peaks. N = 321 for –400 mV, N = 453 for – 100 mV.

Further analysis revealed that the larger amplitude blockades had longer half-widths and therefore belonged to the particles translocating the 1007 nm long pore as shown in Figures 5b and 5c. The relationship of half-width and current blockade follows that of the single pore experiments (Figure 3) where we see the 1259 nm long pore having larger current blockades of 2.96% versus the 1.59% blockades of the 495 nm pore.

The trend of increasing current blockade from the shorter nanopores to the ~1000 nm long nanopores is shown in Figure 6. All percent current blockades were observed in translocation experiments at −100 mV. The double pores follow the same trend of the single pores due to the added electrical resistance leading up to the shorter pores. Resistive-pulse amplitude depends upon volume excluded by the pore, and in this case the overall pore volume is that of the two pores combined. The blockades decrease dramatically from their single pore values to 0.82% and 0.27% in the double pore experiment for the longer and shorter pore, respectively. While the double pore geometries are not the same as their single pore comparisons, the trend they exhibit is similar.

Figure 6.

Percent current blockades observed in nanoparticle translocation experiments at –100 mV. The double pores follow the same trend of the single pores due to the added electrical resistance leading up to the shorter pores.

The electric field, which electrophoresis and electroosmosis depend upon, should not change as the potential difference across each pore remains the same. We do observe an increase in the average halfwidth of particle translocations, from 0.309 ms in the 495 nm long single pore to 0.478 ms in the 376 nm long pore and from 0.744 ms in the 1259 nm long single pore to 0.969 ms in the 1007 nm long pore. We hypothesize that these could be caused by the intermixing of the electroosmotic flows coming through both pores and down the length of the pipette taper. However, there is not as large of a difference between single and double pore experiments with respect to translocation time as there is with the current blockade.

3.5. Finite Element Simulations.

To further understand particle translocation in a double-pore pipette, we performed a finite-element simulation of the translocation experiment using COMSOL Multiphysics 5.2a. The geometries of the two pores in the double pore experiment were simulated using SEM measurements to construct the pores. An electric potential of −100 mV is applied across the nanopore from the inside of the pipette to 0 mV outside the pipette. An electric potential map and electric field is generated, the magnitude of which is used to determine the flux of ions through each pore as shown in Figure 7. A more detailed summary of the numerical simulation process is found in the supporting information. We use a method for simulating the ionic current blockade that is outlined elsewhere using the Nernst-Planck equation for an ionic species i while ignoring convection:¹⁶

$$J_i=-D_i\left(\mathrm{\Delta }{C}_i-\frac{z_{i}F}{RT}{C}_i\nabla \varphi \right)$$ (4)

with J_i being the flux, D_i the diffusion coefficient, C_i the concentration, and z_i the charge of ionic species. F, R, and T, are the Faraday’s constant, universal gas constant, and temperature. The quantity ϕ is the electric field as determined from our simulation. The ionic flux is calculated at each pore orifice and summed.

Figure 7.

(Top) Simulated potential surface profile for the double pores of lengths 376 nm and 1007 nm. The cumulative in-series resistance of the pipette taper and the shorter 376 nm pore is greater than that of the 1007 nm pore. Only the extent of the pipette tip including the two pores is shown. (Bottom) Table comparing observed current blockades with those simulated.

The double layer on the nanoparticle and the sidewalls of the pore was ignored for this simulation because of the large difference between the Debye length and pore diameter at the salt concentration used. Our simulation was only of the change in conductivity of the pore with and without an insulating particle displacing electrolyte solution and not of forces acting on the particle. In our simulation, we assume the conductance of the electrolyte solution within the pore to be the same at every location and the same as the bulk solution conductivity. This is not entirely accurate as there is a double layer along the sidewalls of the nanopore which perturbs the concentration of ions and alters the conductivity. However, under the salt conditions used (100 mM), this double layer has a Debye length of ~1 nm which is small when compared with a 100 nm radius pore.⁵¹ When solution within the pore is displaced by a particle it will likely have the bulk solution conductivity that is unperturbed by the ion concentration gradients within a few nm of the sidewalls. This assumption was not made only because of convenience, but because of experimental evidence showing that the double layer, and therefore electroosmosis, was not noticeably affecting the conductivity of the pore. In cases where the size of the double layer approaches the size of the pore a phenomenon known as ionic current rectification³⁶ is seen where the concentration of cations within the double layer near the pore orifice alters the conductivity of the nanopore and gives the nanopore a rectified i-V response. All side pores tested showed a linear Ohmic response in 100 mM KCl at negative and positive potentials.

The simulations show a decreasing potential along the length of the taper of the pulled pipette. This is from an additional resistance between the 376 nm long pore and the 1007 nm long pore which is farther up the taper. This additional resistance results in a smaller current blockade from translocating nanoparticles in the shorter pore. These simulations support both our single and double pore experiments with respect to observed current blockades.

To simulate a maximum blockade a 112 nm diameter sphere was placed within the same plane as the inner pore, which has the smaller diameter. This was done separately for each pore in the double pore experiment and the current reduction in each case was compared with the current when there was no particle present. The shorter 376 nm long pore had about half of the conductance of the larger 1007 nm pore and because of this had a smaller blockade when a particle was present in its sensing zone.

4. Conclusions

In summary, we have demonstrated the use of sealed quartz nanopipettes as a new platform for FIB-milled nanopores. An FIB milling process is used on the side walls of a sealed quartz pipette enabling fast and reproducible fabrication of low noise, conical shape quartz nanopores down to ~70 nm in diameter with tunable pore size and length. Pores of smaller dimensions can be prepared using more advanced FIB systems, such as an FEI Helios NanoLab DualBeam or a Zeiss Auriga 60. Nanopore size, length, and cone-angle, can be fully characterized using SEM. A side pore avoids the highly restricted volume in the tip region and its associated mass-transfer and ionic resistance. Nanoparticle translocation has been demonstrated using both single pores and double pores. The use of double pores further underscores the differing particle dynamics of pores of different lengths. This unique system will prove useful for further studies on particle translocation dynamics and development of nanopore-based sensors.

Research highlights:

Laser-pulled quartz nanopipettes were used as a new platform for microfabricated nanopores

Focused-Ion Beam milling allows precise control of nanopore size and length

Nanoparticles translocating through two nanopores in the same substrate create different current responses

Numerical simulation can be used to understand nanopore translocation through different nanopores