ARTICLE pubs.acs.org/ac
Quantitative Sizing of Nano/Microparticles with a Tunable Elastomeric Pore Sensor Robert Vogel,*,† Geoff Willmott,‡ Darby Kozak,§ G. Seth Roberts,§ Will Anderson,§ Linda Groenewegen,|| Ben Glossop,|| Anne Barnett,|| Ali Turner,^ and Matt Trau§ †
School of Mathematics and Physics, The University of Queensland, St. Lucia QLD 4072, Australia The MacDiarmid Institute of Advanced Materials and Nanotechnology, Industrial Research Limited, Lower Hutt 5040, New Zealand § Biomarker Research and Development Centre, Australian Institute for Bioengineering and Nanotechnology, The University of Queensland, St. Lucia QLD 4072, Australia Izon Science Ltd., Bishopdale, Christchurch, 8543, New Zealand ^ Jenner Institute, Oxford University, Headington, Oxford, OX3 7DQ, United Kingdom
)
‡
bS Supporting Information ABSTRACT:
The use of a “size-tunable” polyurethane resistive pulse sensor for quantitative sizing of nano- and microparticles is presented. A linear relationship, as first suggested by Maxwell, between particle volume and change in electric resistance across the pore was observed. Particle sizes were quantified for a given size-tunable membrane, by first creating a linear calibration curve to a series of monodisperse carboxylated polystyrene particles of various diameters and then applying this curve to calculate the size of “unknown” nanoparticles. The diameters of a selection of synthetic and biological particles, being PMMA and nonfunctionalized polystyrene particles, along with biological nanoparticles (adenovirus) were calculated using this methodology. Calculated particle diameters and coefficients of variation were shown to be in good agreement with both transmission electron microscopy and dynamic light scattering results.
Q
uantitative size measurements of nanoparticles are essential for studies of colloidal and macromolecular solutions. Standard methods for sizing are electron microscopy (SEM and TEM), static and dynamic light scattering (SLS and DLS),1 ultracentrifugation,2 disk centrifugation,3 capillary hydrodynamic fractionation,4 asymmetric field flow fractionation,5 nanoparticle tracking analysis,6 chromatography,7 and gel electrophoresis.8 Quantitative resistive pulse sensing of nanoparticles using Coulter-type counters has been shown to hold promise as a fast and accurate alternative to established sizing methods.9 Resistive pulse sensors allow for high-throughput single particle measurements as colloids and/or biomolecular analytes are driven through pores, one at a time.9b,10 Particles traversing the pore are detected as a transient change in the ionic current, which is denoted as a blockade event with its amplitude denoted as the blockade magnitude. r 2011 American Chemical Society
Recent advances in nanofabrication techniques have given rise to a plethora of pore-based sensors, using materials including carbon nanotubes (CNTs),9b,11 glass,12 silicon,13 polycarbonate,14 PET,15 and PDMS.16 The size and shape of these pores can be controlled through the fabrication technique and characterized by methods such as electron microscopy. These nanopores have been used to calculate the size of synthetic9b,11a,12a and biological nanoparticles,17 and applied in the detection of colloidal based immunoassays.10b,18 In one detailed account of synthetic particle size measurement using a cylindrical nanopore, Ito et al.9b made a direct comparison with DLS and TEM using a multiwall CNT.9b
Received: January 23, 2011 Accepted: March 24, 2011 Published: March 24, 2011 3499
dx.doi.org/10.1021/ac200195n | Anal. Chem. 2011, 83, 3499–3506
Analytical Chemistry Like in larger aperture Coulter counters the fixed pore size of nanopores enables sensitive size measurements, but also limits their analysis size range, which has implications for the measurable sample polydispersity.19 This limitation is overcome by using size-tunable pores that allow for the optimization of the resistance pulse magnitude relative to the background current by matching the pore-size closely to the particle-size. We recently reported on the fabrication and use of resizable elastomeric thermoplastic polyurethane (TPU) nanopores.20 Tuning the size of the nanopore to the particulate system at hand10c was shown to improve the detection and discrimination between particle size populations in a polydisperse suspension. Furthermore, changing the pore size also enabled the detection of nanoparticles with and without a DNA surface coating.10c We also have shown that changes in electrophoretic mobility and concentration of particles in colloidal dispersions can be detected with tunable nanopores.20c These nanopores are relatively economical to fabricate,20a and the tuning is easily achieved in real time by mechanical actuation of the membrane on macroscopic scales.20a,b Herein we demonstrate the quantitative sizing capability of a stretchable polyurethane nanopore membrane, using polystyrene calibration particles. First, we investigate the stability of blockade data reproduction during stretch-cycling of individual nanopore specimens. Then, multiple particle sets are used to show that the relationship between blockade magnitude and particle volume is consistent with Maxwell’s theory,21 enabling a simple linear fit to be used to quantify particle size, regardless of the stretched pore size. Resistance pulse measurements are also made at different stretch settings to investigate both the optimization of resistance pulse size relative to the background current, and the limit at which particle size becomes comparable with the smallest dimension of the pore. Finally we show the applicability of this methodology for sizing biological nanoparticles, in particular adenovirus.
’ MATERIALS AND METHODS Polystyrene and PMMA Particles. Carboxylated polystyrene particle standards with nominal diameters of 200, 400, and 780 nm were purchased from Thermo Fisher Scientific (XPR 1961 series). Carboxylated polystyrene microspheres with a nominal diameter of 2 μm (Polybead series) and unmodified polystyrene particles (NIST traceable size standards) with nominal diameters of 125, 300, and 500 nm were purchased from Polysciences. The particles are denoted as Th200, Th400, Th780, Poly2, NT125, NT300, and NT500, respectively. Monodisperse PMMA particles were prepared by the method of Schroden et al.22 and Waterhouse et al.23 Electrolytes and Buffers. Electrolyte, consisting of 0.1 M KCl, 15 mM Tris buffer, 0.01% v/v Triton X-100, 3 mM EDTA, and HCl to adjust to pH 8, was used in all experiments. Nanoparticles were immersed in electrolyte at concentrations of approximately 1091010 /mL. The resistivity of the buffered electrolyte was measured to be 0.69 Ωm at 22 C. Adenovirus. Recombinant adenovirus serotype H5 encoding green fluorescent protein (GFP) was constructed and grown using a system based on the ViraPower adenoviral expression system (Invitrogen). The adenovirus serotype H5-GFP virus was produced in HEK293 cells followed by cell lysis to release the virus particles. The viral particles were purified from the cell culture lysate using sequential discontinuous and isopycnic CsCl
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Figure 1. Confocal cross sectional image (a) and SEM-images of the large (b) and small (c) pore openings of a typical membrane at a stretch of 3 mm.
gradients and finally exchanged into buffer containing 10 mM Tris, 7.5% w/v sucrose (pH 7.8). For resistive pulse sensing analysis, the virus was diluted in phosphate buffered saline containing CaCl2 and MgCl2. A typical virion is spherical and about 7095 nm in diameter. Dynamic Light Scattering (DLS). Average intensity-weighted particle diameters were measured on a Malvern Zetasizer 3000HSA. Diameters of PMMA nanoparticles were measured, using refractive indices of 1.33 and 1.49 for water and PMMA, respectively. Transmission Electron Microscopy (TEM). Transmission electron microscopy images of nano/microparticles on carbon grids were collected on a JEOL 1010. The electron microscope was calibrated using a catalyze crystal (lattice spacings of 8.75 and 6.85 nm)24 at high magnification and a carbon replica grating (grid spacing or 463 nm) at low magnification. All particles were imaged using the same instrument at similar magnifications. Particle size distributions were analyzed using Image-Pro software using a minimum of 300 particles per sample. Scanning Electron Microscopy (SEM). Scanning electron microscopy images of TPU membranes and pores were collected on a JEOL 6700 field emission system. Membranes were coated with 5 nm of gold/palladium prior to imaging. Both small and large sides of the pores were imaged at different membrane stretches (0, 3 mm). Confocal Microscopy. As described in Roberts et al.,10c fluorescent rhodamine 6G solution (104 M) was used to dye the walls of the nanopore. The membrane was imaged using a confocal microscope (Zeiss LSM 710, with LD Plan-Neouar 20x/0.4 Korr M27 objective) with laser excitation of wavelength 514 nm. Z-stack images were reconstructed into cross-sectional images using Zeiss ZEN 2008 software. Images of the pores were taken at two different stretches of the respective membranes (3, 8 mm). q-Nano and Membranes. Tunable nanopores were fabricated in TPU membranes (Elastollan1160D, BASF), as detailed in Sowerby et al.20a and Willmott et al.20b Membranes were mounted on q-Nano (IZON Science) and stretched open until the desired pore size was reached.20c Electrolyte was placed in both fluid cells which contain one electrode each, below and above the membrane. Please note that a range of TPU membranes was used for the experiments related to Figures 25. Current pulse signals were collected using IZON proprietary software. The analog digital converter operates at 1 MHz, which is reduced to a sampling rate of 50 kHz through electronic filtering. The peak of the current pulse and the stable steady state current are denoted as blockade magnitude and background current, respectively. Blockade counts pertinent for these studies typically ranged between 150 and 2000 events. Please note that the terms “current pulse” and “resistive pulse” are used interchangeably throughout this document. 3500
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Table 1. Pore Dimensions as Determined by Confocal Microscopy and SEMa confocal stretch [mm]
DS [μm]
SEM
DL [μm]
L [μm]
DS [μm]
DL [μm]
1.22
20.2
3
1.1 ( 0.2
20 ( 2
113 ( 11
8
1.4 ( 0.3
30 ( 3
89 ( 9
5
1.2 ( 0.2
24 ( 3
103 ( 10
a
Confocal pore dimensions at 5 mm stretch are interpolated using confocal dimensions determined at 3 and 8 mm stretch.
Theoretical Basis. A review of relevant theoretical approaches is given in the Supporting Information. To summarize, a cone model was used to calculate blockade magnitudes ΔR in the present work. For a pore of length L, symmetric around the z-axis of a cylindrical polar coordinate system with the origin located at one end of the pore, the resistance change is Z L dz R ΔR ¼ F 0 AðzÞ
Here electrolyte resistivity F is assumed to be homogeneous throughout the pore, A(z) is the unobstructed cross-sectional area of the pore, and R is the pore resistance when no blockage is present. This approach closely follows Heins et al.’s25 calculation of resistance change for truncated cone geometry, although we have also accounted for access resistance and bulging field lines in the small sphere limit.26 We contrast this calculation with two models developed for cylindrical pores. Maxwell21 and Lord Raleigh27 developed a simple expression for small particles, in which ΔR is a linear function of the particle volume (eq S1 in Supporting Information). Deblois and co-workers summarized this and other approaches for cylindrical pores, finding that the relationship between ΔR and particle volume becomes increasingly nonlinear with increasing particle diameter (eq S2).10a,26
’ RESULTS AND DISCUSSION Elastomeric Pore Characteristics. Confocal microscopy and SEM images of a typical thermoplastic polyurethane pore are shown in Figure 1. Pores made using different tungsten needles can vary in geometry due to variations in the needle shape and the puncturing process.20a Confocal and SEM images were taken at 3 mm membrane stretch, a third of the typical maximum stretch (910 mm). SEM images show that large (b) and small (c) pore openings are noncircular in shape. Interestingly, the cross sectional confocal images (a) indicate that the pore has a slightly trumpet-like shape. However, for modeling of blockade magnitudes we assume a conical pore shape. Pore dimensions, including small (DS) and large (DL) pore diameters and membrane thickness (L) have been extracted from confocal and electron microscopy images (Figure1), and are listed in Table 1. DS and DL are the effective diameters of the small/large pore openings, such that the area of circles of diameters DS/L is the same as the actual area of the openings. Confocal microscopy and SEM results at 3 mm stretch are shown to be in good agreement. Confocal images at 3 and 8 mm stretch demonstrated that the pore openings DS and DL increase and the membrane thickness decreases with increasing stretch. Please note that resistive pulse measurements were carried out at a 5
Figure 2. Average relative blockade magnitudes for Th200 were measured at different stretches (17 mm), while cycling between them. The dotted line indicates the order in which stretches were cycled.
mm stretch of the membrane. Pore dimensions at 5 mm stretch were estimated by interpolating the experimental confocal pore dimensions at 3 mm and 8 mm stretch. Elastomeric materials such as TPU undergo stress-softening when initially stretched (the Mullins effect28). The stretch strain relationship becomes repeatable after approximately 610 cycles, provided that the specimen is not stretched above the maximum extension during cycling.20b,29 Blockade magnitudes for a given monodisperse particle set (in this case Th200) were measured when membrane stretch was cycled, to investigate if measured blockade magnitudes became repeatable after several stretch cycles. Figure 2 shows typical average relative blockade magnitudes ΔI/I, with ΔI and I being magnitude and baseline current, respectively. The dashed line shows the stretch cycling pattern used. Initially the membrane was stretched between 1 and 3 mm, followed by stretches between 1, 3, and 5 mm, going to higher extensions until a maximum stretch of 7 mm was reached. At each point during the continuous cycling process the average relative blockade magnitude of Th200 was measured. For each stretch setting, an initial decrease in relative blockade magnitude over the stretch cycle is apparent, before the data become more reproducible. This result is in agreement with the Mullins effect for elastomeric materials and suggests that after initial prestretching of the membrane, average relative blockade magnitudes are expected to be reasonably consistent at any specific stretch. Relationship of Particle Size and Blockade Magnitude. Figure 3 shows a typical current trace (a), a blockade magnitude distribution (b), and a TEM image (inset in b) for a highly monodisperse Th400 (right) sample, which is representative of the standards used in this study. Blockade magnitude distributions were used to calculate mean and mode blockade magnitudes and coefficients of variation which are a measure of polydispersity. While modal (peak) analysis is advantageous when using multimodal particle sets and analyzing signals just above the noise level, mean analysis does not require very high count rates. Please note that the difference between the mode and the mean for a typical monodisperse sample is within 3%. 3501
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Figure 3. Representative current trace (a) and blockade magnitude distribution (b) for Th400. Inset of part b shows a TEM image for the same particle set.
The mean blockade magnitudes for several particle types with nominal diameters between 125 and 780 nm were measured using three different membranes (Figure 4a,c,d). In all cases the mean blockade magnitudes scale linearly with mean particle volumes, with R2 values ranging between 0.995 and 0.998. Linear fits (solid lines) were error weighted and forced through (0, 0). Error estimates in measured blockade magnitudes include systematic and random components due to uncertainty in signal and data processing and a blockade magnitude shift due to off-axis transfer of particles.18b,30,31 The finite sampling frequency used possibly also adds to the errors by underestimating blockade magnitude and increasing its variance, which is discussed in more detail later. A cone model (see Theoretical Basis subsection) was used to calculate a theoretical fit to the experimental data in Figure 4a, which was acquired using the same membrane as characterized in Figure 1 and Table 1. The membrane thickness L was fixed by the value obtained using confocal microscopy (Table 1). The smaller opening size DS was then optimized so that the modeled gradient over the range covered by the experimental data agreed with the gradient of the error-weighted linear fit, to within 0.01%. During optimization, the larger pore opening DL was varied so that the calculated pore resistance remained constant (eqs S4 and S5), and consistent with the experimental baseline current. This constraint in baseline current makes the modeling effectively a one variable approach. The fitted plot (labeled Heins,25 see Supporting Information) is largely linear over the range displayed in Figure 4a and in perfect agreement with the error-weighted linear fit. It is clear that ΔI is close to a linear function of particle volume over a wide range of particle sizes when the pore geometry is approximated by a cone. Therefore, the linearity of the experimental plots has been reproduced using a realistic theoretical model. The linear trend further suggests that the experimental range lies within the small sphere limit, justifying the correction factor for bulging field lines used in the theoretical approach. Further exploration of this trend is seen in Figure 4b, where the modeled cone result is extrapolated to larger particle sizes. Comparison is made with models where the pore geometry is modeled as a cylinder of the same radius as the fitted small pore radius from Figure 4a, with pore length varied to obtain the same baseline current. The plot for the conical model is more linear
than the approach established by Deblois et al.26 (eq S2), which is most appropriate for a cylindrical pore.10a Both cylindrical results predict a higher value of ΔI than the conical result at small particle sizes, because in these cases the pore constriction extends over the whole z-axis length containing the particle. Maxwell’s approach21 (eq S1) is by definition linear with respect to blockade resistance, but slightly deviates from a linear relation with blockade current when the particle diameter d approaches DS, due to the effect described by eq S6. The values obtained for the geometric parameters using this fitting procedure were DS = 1.7 μm and DL = 33.8 μm. The difference compared with experimental results (Table 1) is thought to be due to image scaling uncertainty, the imperfectly conical pore shape, with real pores appearing to be trumpetlike (Figure 1), and uncertainty in the conductivity of the electrolyte. This discrepancy further suggests the need for calibration of the pores. Tuning of the pore size, by macroscopically relaxing an elastomeric TPU pore membrane from 4.6 to 2.9 mm, was used to improve particle size measurement sensitivity, as shown in Figure 5. The average relative blockade magnitudes (ΔI/I) for Th200 and Th400 particles were found to increase as the pore diameter decreased. This is due to increased relative blockade size when narrowing the pore restriction size. At larger pore sizes (pore stretches greater than 3.6 mm) ΔI/I follows a linear relationship with particle volume. Linear fits were error weighted, but error bars were omitted for clarity. Reducing the pore stretch by 1 mm increased the measurement sensitivity by 60%, as calculated from the increase in slope from 1.16 to 1.85 for a change in pore stretch from 4.6 to 3.6 mm. Within this 1 mm stretch range the linear relationship between blockade magnitude and particle volume was maintained. Decreasing the pore size below 3.6 mm of stretch was shown to impart a more nonlinear relationship between ΔI/I and the particle volume, as indicated by the higher than weighted linear fits for the Th400 magnitudes. This nonlinear behavior is to be expected when the particle size is approaching the size of the pore restriction (see Supporting Information), and cannot be explained with the simple linear expression developed by Maxwell21 and Lord Raleigh.27 For stretches smaller than 2.9 mm, the 400 nm Th400 sphere blockade events were not observed and the baseline current 3502
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Figure 4. Plots of mean blockade magnitude versus mean particle volume using various pores (a, c, d) and particle types. Cone (Heins) and error weighted linear fits are in perfect agreement in the range of particle volumes depicted in part a. Part b shows the cone fit plotted against other theoretical results for a wider range of particle volumes; the range covered by part a is indicated by the boxed area in the lower left corner.
Figure 5. Relationship of relative blockade magnitude and particle volume (Th200, Th400) at different membrane stretches. Error weighted fits are displayed. A SEM image of the pore is shown in the inset.
became erratic. Th400 stopped traversing the pore and started to cause blockages. This observation serves to estimate the size of the pore restriction to be approximately 400 nm at 2.9 mm stretch. The SEM image in the inset of Figure 5 shows the small side of the pore membrane at no stretch, much below the 2.9 mm of stretch used in this study, with a 400 nm sphere to illustrate the scale and noncircular shape of the pore opening.
Figure 6. Dependence of relative blockade magnitude with background current for Th200 and Th400 at different membrane stretches. The relative blockade magnitude values of Th200 were multiplied by 7 to allow a direct comparison with respective values of Th400.
For all the applied stretches the deviation from the linear relation was below 11%, which is believed to be within error for most particle sizing applications, considering that an 11% change in blockade magnitude translates to less than 4% in particle radius. 3503
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Table 2. Particle Diameters and CVs of Calibration Particles as Determined with TEM Compared with Nominal Values Supplied by Vendors sample
diameterTEM [nm](CV)
nominal diameter [nm] (CV)
Th100
89 (7.4%)
100 (
