Rapid structural analysis of nanomaterials in aqueous solutions

Rapid structural analysis of nanoscale matter in a liquid environment represents innovative technologies that reveal the identities and functions of biologically important molecules. However, there is currently no method with high spatio-temporal resolution that can scan individual particles in solutions to gain structural information. Here we report the development of a nanopore platform realizing quantitative structural analysis for suspended nanomaterials in solutions with a high z-axis and xy-plane spatial resolution of 35.8 ± 1.1 and 12 nm, respectively. We used a low thickness-to-diameter aspect ratio pore architecture for achieving cross sectional areas of analyte (i.e. tomograms). Combining this with multiphysics simulation methods to translate ionic current data into tomograms, we demonstrated rapid structural analysis of single polystyrene (Pst) beads and single dumbbell-like Pst beads in aqueous solutions.

Thereby, the size of materials passing through a nanopore can often be obtained quantitatively by using a series resistance model consisting of a pore resistance and access resistances in series. Nanopore structures thus realize label-free sensing, allowing us to estimate the size of materials passing through a nanopore from pulsed ionic current blockades with high throughput [18]. During recent years these pulse sensors have been developed not only for size but also for concentration, surface charge density and shape of analyte [19]. Here, the zaxis spatial resolution can be enhanced by decreasing the depth of the nanopores, while the diameter should be large enough to allow their translocation [20][21][22][23][24][25][26]. Accordingly, a smaller aspect ratio defined as the ratio of the depth to the diameter provides greater spatial resolution, i.e. tomograms of a material passing through a nanopore ( figure 1(b)). Structures of individual particles and molecules can thus be deduced by combining low-aspect-ratio nanopores with simulation methods to translate ionic resistive pulse data into tomograms. However, the low-aspect-ratio structures cause difficulties for numerical analyses of the resistive pulses because a change in the access resistance due to analyte translocations becomes non-negligible when compared with high-aspect-ratio structures. Mathematically, this is demonstrated by noticing that the access resistance is no longer invariant in low-aspect-ratio pores. Recently, since much effort has been made to understand the origin of the change inaccess resistance for lowaspect-ratio nanopores, the finite element method (FEM) and numerical simulations have found that the size, shape and surface charge density of the analyte play a key role in determining the value of the resistance [27][28][29]. We herein report quantitative structural analyses of negatively charged polystyrene (Pst) beads suspended in aqueous solutions using low-aspect-ratio nanopores (see online supplementary figure S1, available at stacks.iop.org/NANO/28/155501/mmedia) with multiphysical modeling and simulations taking account of the size, shape and surface charge density of the analyte [30,31]. The ionic current I ion under an applied DC voltage (V b ) was measured using a high-speed amplifier because the z-axis spatial resolution in the present structural analysis can be further improved by employing a high-speed current detection system to track the fast electrophoretic motions of materials in a nanopore [32][33][34]. The performance and reliability of the amplifier are discussed in the supplementary information (see online supplementary figure S2).

Fabrication of low-aspect-ratio nanopores
We fabricated nanopores in a thin Si 3 N 4 membrane having thickness-to-diameter aspect ratios of 0.035 as follows (see online supplementary figure S1). A 0.3 mm square region of the unpolished side of a Si 3 N 4 (35 nm)/Si (0.5 mm)/Si 3 N 4 (35 nm) wafer was exposed to reactive ion etching (CF 4 , 100 W) to partially remove the Si 3 N 4 layer. We then wetetched the exposed 0.5 mm thick Si layer in a KOH solution (40 wt%) at 125°C. In order to prevent the increment in the wt% due to the evaporation of water we used a clock glass for the etching. As a result, we obtained a 35 nm thick Si 3 N 4 membrane. After that, we patterned a circle of diameter d=1000 nm in a resist layer (ZEP520A) coated on the substrate using an electron beam lithography process. Subsequently, a pore was sculpted by exposing the substrate to reactive ion etching (CF 4 , 100 W). Finally, the residual resist layer was removed by immersing the sample in N,N-dimethylformamide for 15 min at 90°C followed by oxygen plasma cleaning. This yielded Si 3 N 4 nanopores with an aspect ratio of 0.035.

Preparations of Pst bead solutions
Single Pst beads (780 nm diameter) dissolved in H 2 O were purchased from Thermo Scientific. The solution was mixed with TE buffer (10 mM Tris-HCl, 1 mM EDTA, pH 8.0) at a ratio of 1:10 for the present experiments (not KCl solution). The double-Pst bead solution was prepared by storing the single-Pst bead solution at room temperature because the surface of negatively charged Pst beads in a solution including positively charged buffer molecules (Tris) is neutralized, causing aggregation and absorption.

Nanopore device sealing
In our experiments, we stuck polydimethylsiloxane (PDMS) blocks, onto which a microchannel was patterned, on both sides of the pore device. We specifically prepared an SU-8 mold on a Si/SiO 2 wafer using a photolithographic method. PDMS (Sylgard 184) was cured on the mold at 80°C for 1 h. Three holes were pierced in each PDMS block: one for placement of an Ag/AgCl electrode and two for inlet and outlet of the particle solution. The PDMS channel and the sample substrate were treated with oxygen plasma for surface activation and attached together to obtain permanent bonding between PDMS and Si 3 N 4 . We introduced dispersed Pst beads in solution in the cis chamber and buffer solution in the trans chamber via the PDMS channel.

Measurement system to detect ionic currents
For nanomaterial detection, an electrophoretic field V b was applied to the pore utilizing two Ag/AgCl electrodes at both PDMS blocks, and the ionic current I ion was monitored (at a sampling rate of 10 MHz) using an amplifier backed by a digitizer (National Instruments NI-5922) and stored in a RAID hard drive (National Instruments HDD-8265) under LabVIEW control (see online supplementary figures S2 and S3). The 10 MHz ionic current-time data were compressed to 1 MHz by averaging 10 data points for the quantitative analysis of the current data. Thus, the time resolution of the present current measurement system was 1 MHz. Ionic current-time (I ion -t) traces were measured at V b =0.1 V between the electrodes in an electrolyte buffer solution containing negatively charged Pst beads. The flow of Pst beads from the cis to the trans chamber was induced through the pores by electrophoretic forces originating from the electric field.

Multiphysics model calculation
To estimate the open-pore ionic current and blockage of the current due to nanomaterial penetration, we established a multiphysical model by coupling (1) the Navier-Stokes equation for liquid flow throughout the nanopore, (2) the Poisson equation for the electrical potential distribution, (3) the Nernst-Planck equation, and (4) ionic currents passing through nanopores I p for ionic transport in the nanopore system (see online supplementary figure S4): In these expressions, ρ is the density of water, u  is the velocity of the liquid, p is the hydrodynamic pressure, η is the viscosity of the solution, E  is the electrical field within the solution, ε is the permittivity of the fluid, ρ e is the net charge density caused by the difference between local cation and anion concentrations, e is the elementary charge, n i is the concentration of the ith species of ion in the solution, D i and μ i are the diffusion coefficient and electrical mobility, respectively, of the ith species of ion, and z i is the valency of ion i. The variables R and a show the radius of the pore and particle, respectively, v a indicates the ionic advection velocity along the z-direction, and E z corresponds to the applied electric field. Open boundary conditions were used at the ends of the cis and trans chambers for the Navier-Stokes equation, while a salt concentration C Tris =10 mM was imposed at the ends for the Nernst-Planck equation. Electrically, the end of the cis chamber was kept at a voltage U=0 V, and that of the trans chamber was kept at the applied voltage U. In the calculation, COMSOL ® was employed to solve these coupled equations. The physical parameters used in the calculation are ε = 7.08 × 10 −10 F m -1 , η=8.91×10 −4 Pa s, μ Cl = 7.909× 10 −8 m 2 s -1 V -1 , and μ Tris+ =3.092×10 −8 m 2 s -1 V -1 . The surface charge densities of the pore σ pore and Pst beads σ pst were 0 and −6.05×10 −3 C m -2 because σ pore was negligible in this study (see online supplementary figure S4). The present σ pst used matches with the data sheet for Pst beads (from Thermo Scientific). In addition, the σ pst are comparable to estimated values from zeta potentials [35].

Results and discussion
I ion -t profiles for Pst beads with a diameter (D) of 780 nm were measured using low-aspect-ratio nanopores with an aspect ratio of 0.035 (L=35 nm, d=1000 nm), as shown in figure 2(a). We observed resistive pulses denoting Pst bead translocations (figure 2(b)) with a capture rate of about 10 Hz, which was comparable to our previous report on detection ofPst beads using a low-aspect-ratio nanopore [28]. The electrical signals were characterized by the peak current (I p ) and the peak duration (t d ) (inset figure 2(b)). The baseline current (I b ) corresponding to open-pore conductance agreed with the value estimated by considering the drift mobility of ions. In an effort to analyze I ion -t profiles ( figure 2(b)), histograms of peak current I p and duration time t d were constructed from 454 resistive pulses (figures 2(c), (d) and S5). Since I p depends on the volume of a material inside a nanopore, the I p histogram essentially denotes the size (diameter) distribution of the Pst beads [19]. This histogram was theoretically studied by a method based on a standard model consisting of a pore resistance and access resistances in series, which has been found to be valid for single beads passing through a low-aspect-ratio nanopore (see online supplementary figure S6) [28]. This analytical study provides minimum and maximum I p s of 476 pA and 771 pA,respectively, since the nominal uniformity of the size of the Pst beads used in this study is <5% (D=741-819 nm). Because the estimated I p range of 476-771 pA is comparable to the I p distribution shown in figure 2(c), the distribution of I p is attributed to the size distribution of the Pst beads. Gaussian fitting to the present histogram shows a symmetrical monomodal distribution centered at approximately 610 pA (figure 2(c)), indicating that the resistive pulse at about 610 pA is due to the translocation of 780 nm diameter Pst beads. However, the I p histogram slightly depends on the axes of Pst bead translocations in the nanopore because the off-axis translocations cause deviations of the intensity and shape of the resistive pulses [36,37]. The change in the spike height of the resistive pulses by the off-axis effect shouldthus be discussed carefully. According to a theoretical calculation regarding the offaxis effect [36,37], the present I p histogram shown in figure 2(c) was found to be affected by off-axis translocations. Calculation considering only the central axis translocations of the Pst beads indicates an I p distribution centered at 599 pA, which is slightly smaller than the experimental distribution (612 pA) (see online supplementary figure S7). Because the off-axis translocations cause a larger pulse intensity than the central axis translocations [36,37], the present distribution difference between the experiment and calculation could be due to off-axis translocations. Brownian motion of the beads in the xy-plane is also considered to affect I p even if the axis translocates. Although Brownian motion induces the off-axis translocations [38], displacements due to the motion during bead translocations in a nanopore are theoretically found to be almost negligible compared with I p in this study (see online supplementary figure S8). Here, we recall that the length scale of the transverse displacement strongly depends on sizes of the pore and the target materials, and the translocation time of the targets, and therefore the influence of transverse Brownian motion on I p , should be discussed for every individual case. On the other hand, two peak duration times were observed at 1.55 ms and 3.05 ms in the t d histogram ( figure 2(d)). Here, the duration of single nanoparticles is naturally anticipated to be 1.55 ms, whereas the fact that the longer duration time of 3.05 ms is about double the shorter one suggests the translocation time of a two-particle system has a dumbbell-form.
To investigate the structures of both beads showing shorter and longer peak durations, resistive pulses (shorter, 400 signals; longer, 10 signals) were collected for scalar maps ( figure 3(a)). The map of signals with shorter t d consists of single resistive pulses as shown in figure 3(a), indicating the translocation of a single Pst bead. However, some of peaks show asymmetric flared current blockades resulting from bead translocations in the entrance of a pore. These resistive pulses have recently been found to be due to off-axis translocations [38]. Because Pst beads entering a nanopore on an off-axis pass close to the pore wall, they would tend to experience relatively strong drag due to electro-osmotic flows (EOF) [39], resulting in wide resistive pulses. These results indicating off-axis translocations are reasonable for the present I p distribution discussed above. On the other hand, double-resistive pluses were confirmed in the scalar map of peaks with longer t d . In brief, the double peaks are considered to denote a two-particle system in a dumbbell-form. The resistive pulse intensities I p of the double peaks were found to be comparable to those of the single peaks, although the longer structure seemed to cause a larger ionic current blockade, meaning a larger change in the access resistance.
In order to translate these I ion data into tomograms and understand the present signals, we employed multiphysics simulations that we used to study fluid dynamics of single DNA molecules within nanopores [30,31]. The method uses hydromechanics, electromagnetism and ionic transport theory, and can treat ionic currents with consideration for configurations of a nanopore and nanomaterials on the central axis of a pore in a steady state. In the simulation for single pulses we first used a translocation velocity of 5.26×10 −4 m s −1 =(780 nm+35 nm)/1.55 ms as derived from the t d histogram ( figure 2(d)). On the other hand, multiphysics calculations indicated that the ionic current tends to change before the Pst beads enter the nanopores ( figure 3(b)). Here, the central position of a nanopore is defined as z=0.
The actual speed has thus been underestimated because the translocation duration would be shorter (1.01 ms according to our calculations). Assuming that Pst beads pass through nanopores at a constant velocity of 8.06×10 −4 m s −1 , estimated from the translocation time of 1.01 ms, multiphysical simulations for single Pst beads with a diameter of 780 nm quantitatively reproduced the typical experimental I ion -t profiles, as shown in figure 3(c). However, we should note that this assumes an ideal situation where a particle passes through the central axis of the pore with a uniform motion. In real cases, Brownian motion in the z-axis deteriorates the sensing capability by imposing three-dimensional random displacements of the particle during translocation that have a non-negligible influence on the ionic current spike patterns (shapes); for the present experimental conditions this may blur the particle shape by several tens of nanometers (see online supplementary figure S8). Moreover, it is remarkable to note that the theoretical simulation could reproduce the typical double-peak signals with t d~3 .05 ms as well as yielding a Pst structure having a neck diameter of about 380 nm ( figure 3(d)). This dumbbell-like Pst bead structure was confirmed to exist in the solution by scanning electron microscopy (SEM) observations ( figure 3(d)). Although the simulation reproduces one of the dumbbell-like Pst beads quantitatively from the double peaks, the experimental double-peak signals show more variability of the pulse shape than single pulses, as shown in figure 3(a). This variability could be attributed to variation in the shape of the dumbbell-like Pst beads. Since the present Pst beads have the size distribution discussed above, the differences in I p between the first and second peaks in the double pulse denote the size difference of the beads. However, most of the ionic current blockade due to the neck region of the dumbbell-like Pst beads (position II in figure 3(d)) shows nearly the same values, suggesting a small variation in the neck diameter of the dumbbell-like Pst beads. In fact, many of the dumbbell-like Pst beads were found to have a neck diameter of 380 nm in SEM observations (see figure S9). Therefore, the present resistive pulse sensing enables us to discuss the quantitative structure of the analyte and discriminate nanomaterials comprising a minority of 2.2% (0.022=10/454), which cannot be identified in the I p -t d scatter plots (figure 3(e)), by the structural analysis. Figure 4 shows electric potential maps for single (a) and dumbbell-like (b) Pst bead translocations. The maps enable us to qualitatively understand the change in the access resistance. Since the potential drop was found to be localized not only in the nanopore but also in the orifice of the pore, a Pst bead in the vicinity of the pore entrance (z=407.5 nm) could also cause ionic current blockade. It is interesting to note that the potential drop when the dumbbell-like Pst bead is positioned at z=340 nm (figure 4(b) center) is almost same as that of a single beads at z=0 nm (figure 4(a) right). This means that the contribution of the top bead of the dumbbell-like Pst bead to the ionic current blockade is quite small. In addition, since the range of the potential drop (a magnified map is shown in figure 4(c) left) was found to be about 320 nm, the effective tomogram causing the ionic current blockade seems to correspond approximately to the volume of a bead inside a nanopore (i.e. π(D/2) 2 L). This is the reason why the I p due to dumbbell-like Pst beads is comparable to that of single beads, although the dumbbell-like beads occupy a larger area in the orifice of a pore than the single beads, and the series resistance model is available for single beads passing through a low-aspect-ratio nanopore [28]. On the other hand, the potential drop region when the dumbbell-like Pst beads were at z=0 nm was slightly broadened to about 420 nm, compared with the case of a single bead (320 nm) at z=0 nm (a magnified map is shown in figure 4(c) right). This fact indicates that the effective tomogram of the neck region is not equivalent to the volume of the neck region inside a nanopore. These broadened potential drops are thus considered to represent an increment in the access resistance. Furthermore, the potential drop region was found to depend on the surface charge density of the beads σ pst ( figure 4 (d)). The larger σ pst results in broader potential drop regions, indicating an increment in the access resistance. This relation between the surface charge density and the access resistance is in qualitative agreement with the numerical study reported by Wang et al [29].
We finally discuss the spatial resolution of the present structural analysis. A Pst bead at positions I (z=407.5 nm) and III (z=−407.5 nm) in figure 5(a) results in ionic current blockade while the inside of the nanopore is completely unoccupied, as discussed above. Here, the baseline current corresponds to currents at t=0 and 1.55 ms. Because the translocation time was 1.01 ms and the total migration length was 815 nm, the migration length during 1 μs (because the time resolution of the present measurement system is 1 MHz) was determined to be 0.807 nm. In addition, the displacement in the z-direction due to Brownian motion was found to be 1.1 nm in 1 μs, as shown in online supplementary figure S8. Thus, the z-axis spatial resolution is estimated to be 35.8±1.1 nm (the sum of the 35 nm pore thickness, the 0.807 nm migration length, and±1.1 nm displacement). Here, the cross sections of the tomograms are tentatively defined as the summation of the pore thickness and the migration length of Pst beads for 1.0 μs. The standard deviation of 0.35 nm is evaluated by the distribution of average translocation speed of each particle that can be estimated from I p and t d histograms (figures 2(c) and (d)). On the other hand, xy-plane resolution depends on the noise level of the current measurement system. Because the peak-to-peak noise in the measurements of Pst bead detections was 38 pA, as shown in figure S2, the present system can recognize signals of at least 40 pA. Such a precision corresponds to discrimination between 780 nm and 768 nm beads in the present resistive pulse sensing setup. Therefore, the xy-plane resolution is estimated to be 12 nm.