Pulse Size Distributions in Tunable Resistive Pulse Sensing

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Pulse Size Distributions in Tunable Resistive Pulse Sensing Eva Weatherall, Peter Hauer, Robert Vogel, and Geoff R. Willmott Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.6b01818 • Publication Date (Web): 29 Jul 2016 Downloaded from http://pubs.acs.org on July 29, 2016

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Analytical Chemistry

Pulse Size Distributions in Tunable Resistive Pulse Sensing Eva Weatherall,ab Peter Hauer,ab Robert Vogel,cd and Geoff R. Willmott∗ae a b c

The MacDiarmid Institute for Advanced Materials and Nanotechnology

School of Chemical and Physical Sciences, Victoria University of Wellington, New Zealand

Izon Science Limited, 8C Homersham Place, PO Box 39168, Burnside, Christchurch 8053, New Zealand d

School of Mathematics and Physics, The University of Queensland, Brisbane 4072, Australia e

The Departments of Physics and Chemistry, The University of Auckland, New Zealand ∗ Corresponding

author

Email: [email protected] Phone: (64) (0)9 3737599 Fax: (64) (0)9 3737445

1

ACS Paragon Plus Environment


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Abstract The use of resistive pulse sensors for submicron particle size measurements relies on clear understanding of pulse size distributions. Here, broadening of such distributions has been studied and explained using conical pores and nominally monodisperse polystyrene particles 200 - 800 nm in diameter. The use of tunable resistive pulse sensing (TRPS) enabled continuous in situ control of the pore size during experiments. Pulse size distributions became broader when the pore size was increased, and featured two distinctive peaks. Similar distributions were generated using finite element simulations, which suggested that relatively large pulses are produced by particles with trajectories passing near to the edge of the pore. Other experiments determined that pulse size distributions are independent of applied voltage, but broaden with increasing pressure applied across the membrane. The applied pressure could also be reversed in response to a pulse, which enabled repeated measurement of individual particles moving back and forth through the pore. Hydrodynamic and electrophoretic focussing each appear to affect particle trajectories under certain conditions.

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Introduction Resistive pulse sensors are pore-based technologies used to analyse submicron colloidal particles. 1 They measure the transient change in resistance (a ‘pulse’), which goes in hand with a change in current (∆I), when a particle displaces conductive electrolyte as it passes through a pore - a methodology also known as the Coulter principle. Tunable resistive pulse sensing (TRPS) is distinctive from other resistive pulse sensors because the elastomeric membrane containing a tunable pore can be actuated to change the size of a pore. Methods have been developed for using TRPS to measure the size, 2 concentration, 3 and charge 4 of nanoparticle populations. TRPS technology is currently best suited for particle sizes ranging from tens of nanometers upwards, bridging the important gap between single molecules and cells, 5 which is also relevant for other resistive pulse sensing systems 6–8 and techniques such as centrifugal sedimentation. The range of particles studied using TRPS has recently been reviewed, 1 and includes drug delivery vehicles, 9,10 viruses 2,11 and bacteria, 12 particles functionalized as sensors or diagnostics, 13–15 and (increasingly) extracellular vesicles, 16–19 among other types. In comparison with other techniques, 1,9,11,16,20,21 TRPS is flexible to operate, and provides particle-by-particle data (similarly to particle tracking analysis), with high throughput. Particle size measurements have been reported for multi-modal distributions, 20,22,23 and for very disperse particle sets. 16,24 In TRPS, a potential (V0 ) is applied across a thermoplastic polyurethane membrane, generating a ‘baseline’ ionic current (I0 ) through a pore in the membrane. When a particle passes through the pore, a resistive pulse occurs and a brief reduction in current is observed (Figure 1(a)). The TRPS sizing method established in experiments 2,20,21 can be summarized using the simple relation that ∆I is proportional to particle volume, 25 and so calibration particles of known diameter are typically used in size

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measurements. Alternatively, particle size can be determined using the explicit geometry of a conical pore, 2 but the calibration method is usually more precise due to geometrical uncertainty. It is assumed that each pulse accurately measures the size of a single particle, so that particle size histograms can be constructed. However, Figure 1(b) demonstrates that the breadths of TRPS size distributions are not determined solely by particle dispersity, in this case varying with the stretch applied to a membrane. Moreover, direct comparisons often report that nanoparticle size distributions vary between different measurement techniques. 11,19–21,26 Addressing, understanding, and reducing uncertainty represents important progress for such measurements. In this paper, we study the breadth of TRPS pulse size distributions generated by nominally monodisperse particle size standards. Factors that are known to affect pulse size distributions include insufficient sampling frequency, 27,28 detection thresholds, 17,29 and reduction of pulse heights for charged particles in low molarity electrolytes. 30 Here, the initial hypothesis is that off-axis transport is responsible for the distribution broadening. Particle trajectory has not been thoroughly studied using TRPS, and it has previously been shown that resistive pulses increase in size with the distance of the particle from the central axis of cylindrical pores, using theory and simulations 31–33 as well as experimental systems. 33–37 In early cell-counting work, it was shown that the electric field is relatively large near the edge of a pore, 38 consistent with observations of relatively large pulses for cell trajectories near the pore edge. 34,35 Later, Berge et al. 36 studied resistive pulses generated by 15 µm spheres, which suggested that differences in pulse magnitude (< 10%) were overestimated in initial analytical work. 31 Saleh and Sohn 37 studied ∼500 nm latex colloids, and suggested a correction to Berge et al.’s empirical correlation to account for particle trajectory. Qin et al. 32 used finite element modelling (FEM) to propose a new correlation between resistance change and off-axis trajectories. Most recently, Tsutsui et al. 33 used FEM alongside experiments to study 510-900 nm particles travelling through SiN pores 4


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with low aspect ratios of membrane thickness to pore width (≤ 1). In Figure 1(b), two discrete peaks can be observed in the distribution obtained with the highly stretched membrane, similar to the bimodal pulse distributions studied by Shank et al. 35 There is not an obvious explanation for the two peaks, as there is a continuum of possible particle trajectories. For this reason, we first present a FEM numerical investigation of particle trajectories through a pore, and their influence on the resistive pulses generated. Advancing on previous simulations, 32,33 a distribution of calculated trajectories is used to predict the distribution of pulses generated by monodisperse particles. In particular, the emergence of two peaks is addressed. The simulations include inertia, which can influence the distribution of trajectories by causing particles to move across stream lines in pressure-driven flow. This effect, called hydrodynamic focussing, has been widely studied for microfluidic applications. 39,40 Subsequently, detailed experimental results are presented, firstly for particle populations, then for individual particles. Aside from the specific technology and materials used, these experiments advance upon previous works because we are able to systematically step through changes in the pore size using TRPS. The double peaks in size distributions are measured and explained. As in some previous work, 36,37 the most important transport mechanism in our experiments is pressure-driven flow. We study the effect of varying the applied pressure, and we include data obtained from ‘pressure reversal’ experiments, in which the same particle is repeatedly passed back and forth through the pore by changing the direction of the applied pressure. This pressure reversal technique, which has been used elsewhere, 36,41 is advantageous because the generated pulse size distribution is independent of particle dispersity. The conical geometry of tunable pores (Figure 1(c)) is also distinctive. Although some pores used for resistive pulse sensing are similarly conical 42–46 and produce asymmetric pulses, 47 cylindrical pores are more commonly used. In conical pores, the resistive pulse is generated when the particle 5



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is near the small pore opening, similarly to high resolution pores in thin membranes, 33 although end effects are less important than for such pores. 32

Experimental Table 1: Polystyrene particle sets used, including coefficients of variation (CVs) in the diameter.

label

nominal diameter

supplier

CV

nm

CV (DLS)

A

220

Bangs Labs

1.9%a 25.3%

B

350

Polysciences

2.5%a 24.4%

C

220

Thermo-Fisher

1000 pulses at each stretch. Figure 3(c) plots average baseline durations for pulses in each histogram bin, for size histograms at two stretches from (a). Durations are normalised by the average for all data, and error bars indicate the standard deviation (not shown for single events).

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under an electron beam, and statistics limited by the time required for sample preparation and image analysis. DLS data for both particle sets A and B are much more broadly distributed than for either SEM or TRPS (Table 1). Light scattering data is dominated by relatively large particles, 26,29 which can produce high uncertainties for linear size measurements of smaller particles. 9 At high stretches, the shape of the distribution changes in addition to the width, and a second peak becomes apparent. When the same distributions were fitted with two Gaussian peaks (using OriginPro 8 software), the distance between these peaks approximately doubled over the stretch range used (in normalised diameter units, see ESI). In Figure 3(a), separate measurements using the two peaks would produce size differences of up to ∼ 11% at 52 mm stretch. Our simulations suggest that the peak at smaller ∆I is produced by a large range of trajectories near the pore axis which produce similar pulses, and the peak at larger ∆I is caused by raised concentration of particles at the edge of the pore. If only one of the two peaks was to be consistently used for sizing, the peak at lower ∆I is more appropriate, because the electric field is more uniform near the pore centre, and there is an averaging effect when particles are relatively large compared to spatial changes in the field. 34 The observations in Figure 3(a) suggest that the difference between extreme ∆I / I0 values increases with pore size. To investigate this trend, the geometric parameters of pore 1 were estimated using measurements of R0 and the relation

i ρ h π R0 = d + (a + b) , πab 4

(3)

which assumes that the pore is conical, current flow is axial, and electrolyte resistivity is homogeneous (ρ = 0.86 Ω m for 0.1 M KCl at 293 K 51 ). End effects are included. 47 The membrane thickness can be scaled according to a hyperelastic material model, 52 assuming a resting value of 210 µm at 41.5 mm stretch. 53 The larger pore radius b is determined by the equivalent radius from SEM imaging at 45 mm 15



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stretch (11.6 µm, see ESI), and a and b are assumed to scale proportionally to each other. Using this approach, values of a = 500 and 790 nm were obtained for stretches of 45 and 52 mm respectively - a 58% increase. Using previous models for cylindrical pores, these values of a can be used as the pore radius in order to estimate the effect of changing pore size. Eq. 2 produces a very slight decrease in the range of normalised pulse sizes between 45 mm and 52 mm stretch (0.05%, opposite to our experimental trend). Using Eq. 1 with a constant value of α = 4.2, the normalized pulse size range also decreases from 2.1% to 0.7%, although the empirical values of α obtained by Berge et al. increased with pore size. In contrast, Smythe et al.’s tabulated values 31 predict greater ∆I for a particle at a constant distance from the pore wall when the particle to pore size ratio increases. Comparisons with recent simulations 33 are inconclusive; a smaller pore gave a larger change in ∆I for any given value of the absolute particle position (equal to ra), but the possible range of particle positions increases with pore size, and also the changes in pore width and length were not studied independently. Pore measurements are restricted to a finite range of particle sizes, based on the pore diameter. The upper size limit is determined by whether or not particles can pass through the pore unhindered. As the stretch is increased, larger particles are able to pass through the pore, possibly causing size distribution broadening. This explanation for broadening is inconsistent with two observations here. Firstly, TRPS CVs exceed the independently measured CVs, suggesting that broadening occurs regardless of the actual size distribution. Secondly, inclusion of larger particles does not explain the presence of two peaks in the distribution. The smallest pulses are clearly above the electronic noise threshold of the instrument, so the lower size detection threshold is not important. Figure 3(c) provides further evidence for the correlation between off-axis transport and large pulses, showing that larger events also had longer pulse durations. Particles travelling near the pore edge in 16


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pressure-driven flow will travel more slowly than those in the centre of the flow (see ESI and elsewhere 36,37 ). The same trend was observed by Tsutsui et al., 33 in that case explained by electro-osmotic effects. Note that error bars in Figure 3(c) may be large when there are few events in a bin.

Pressure Variation Figure 4(a) shows the measured pulse size distributions for particle set A at different applied pressures. The size distribution CVs for Figure 4(a) (particle set A, pore 1) increased approximately linearly with pressure from 6.1% to 11.0%, exceeding the value obtained using SEM (Table 1). For a similar pressure sweep (particle set A, pore 2), CVs increased from 7.5% to 11.0%. When the particle size distributions were fitted with two peaks, the distance between the peaks also increased with pressure. Separate measurements using the two peaks would produce size differences of up to ∼ 11% at 8 cm H2 0 for the data in Figure 4(a) (see ESI for CV and peak separation data). The decrease in mean pulse height with increasing pressure (Figure 4(a) inset) is likely to be caused by undersampling of the peaks, because the experiments at relatively high applied pressures could have FWHM durations shorter than 0.1 ms (the usual standard for other data). Undersampling is also consistent with broadening of the size distribution. However, this does not explain the appearance of two peaks in the data, which is again attributable to particle trajectory variation. In Figure 4(a), it is apparent that the peak at larger values of ∆I becomes smaller at increased P relative to the other peak. This trend was not observed for changing stretch, and is not explained by undersampling. Large ∆I pulses are produced by particles near the pore edge which travel slowly, and the data therefore suggest that these become less frequent as the pressure is increased. However, the volumetric flow rate for laminar pressure-driven pipe flow (πc4 P 0 / 8 for radius c) is linear with respect to the pressure gradient P 0 . Therefore the observed trend is not explained by pipe flow, because the 17



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FIGURE 4: TRPS pulse size distributions as a function of pressure. Figure 4(a) plots distributions as a function of applied pressure for particle set A and pore 1 at 48 mm stretch, normalised by the mean blockade magnitude of the > 1000 pulses at each pressure (inset), with bin size 0.025. Figure 4(b) plots data obtained from pore 4 and particle set C, with 0.28 V < V0 < 1.02 V and ≥ 180 pulses per data point. Lines are linear fits to all data from the three runs at each pressure setting.

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proportion of fluid passing through an annulus at any particular distance from the centre of the pore is independent of P 0 . Hydrodynamic focussing, which causes particles to move across stream lines, forms part of the Discussion. Further data (Figure 4(b)), obtained using a different pore and particle set, independently verify the dependence of resistive pulse distributions on pressure and stretch, including over repeated measurements (runs). For these experiments, V0 was varied with stretch so that I0 and ∆I were approximately constant between different stretch settings - in the previous experiments, V0 was held constant and current measurements were varied with stretch. Both stretch and pressure have positive correlations with respect to distribution breadth.

Single Particles with Pressure Reversal Pulse size distributions were also obtained for single particles moving back and forth through tunable pores (Figure 5). These experiments were carried out by alternating the direction of the pressure-driven flow applied to the fluid cell, with each reversal triggered by observation of a resistive pulse. When the pressure was reversed, the magnitude of the baseline current undulated due to changes in the ionic distribution. 30,41 These variations were removed using Clampfit software, and the pulse magnitudes were measured relative to the local baseline current for individual 400 nm (set D) and 800 nm (set E) particles. These data were obtained using pore 5 at the same stretch and voltage conditions. There was less variation in blockade magnitude for larger particles relative to I0 , as the pulse distribution CVs for particles from sets D and E were 4.4% and 1.0% respectively. As in a similar previous experiment, 41 CVs are lower than those recorded in ensemble measurements because data for individual particles remove the effects of particle dispersity.

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FIGURE 5: TRPS measurements for single particles moving back and forth through a pore due to applied pressure alternating between ±6 cm H2 0. Pore 5 was used at 45.8 mm stretch, and V0 = 0.32 V. The main figure compares pulse histograms for 79 pulses from 400 nm particles (set D, upper right) and 60 pulses from 800 nm particles (set E, lower right).

Discussion Double peak distributions arise from variations in particle trajectory, as explained by the model used to obtain Figure 2(c). However, several points of comparison between the modelling and the experiments deserve further discussion. Inclusion of inertia and therefore hydrodynamic focussing in FEM simulations is computationally expensive, so it was appropriate to study this effect using a 2D conservative-case comparison (Figure 2). Two characteristics of the calculated trajectories are especially noteworthy. Firstly, hydrodynamic focussing is minor in the experiments presented. The particle centre of mass simply follows stream lines (as in the point particle simulations) at low values of the channel Reynolds number,

Re =

ρU D . η

20


(4)

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Here ρ and η are the fluid density and viscosity (respectively 998 kg m−3 and 1.00 x 10−3 Pa s at 293 K 51 ), U is the fluid flow velocity and D is the channel diameter. For pressure-driven flow through a conical pore, the volumetric flow rate is conserved, so U ∼ D−2 . Therefore Re ∼ D−1 , and inertial effects are maximised at the small pore opening where D = 2a. The estimated maximum (high pressure) value from simulations is Re ≈ 0.10. Experimental pores were smaller, so Re values are smaller for the same applied pressure. In comparison, Berge et al.’s observations 36 of hydrodynamically focussed particles have associated Reynolds numbers between 0.7 and 2.4. Secondly, the effect is usually associated with focussing of the particles at an off-axis equilibrium position 36,40 when Re is in the approximate range from 1 to 100. 39 In contrast, Figure 2(b) suggests that all particles are pushed towards the pore centre as they approach the pore, then in the opposite direction as they move further into the diverging channel. This interesting effect arises from the sharp constriction of the flow between the pore and the adjacent half-space, the details of which are left to further work. Here, the important result is that trajectories may be slightly shifted towards the central axis within the pore constriction, consistent with the experimental result that the relative size of the peak at higher ∆I decreased with increasing P . For individual particles in pressure reversal experiments (Figure 5), distribution broadening is relatively small, because a particle’s trajectory is correlated from one pulse to the next. For 400 nm particles, pulses prior to 50 s (∼ 13 reversals) after the start of an experiment are relatively large compared to those that occur afterwards. This is consistent with an initial period of focussing in which a particle moves sideways ∼ 0.1 µm during each traversal (see Figure 2(b)). For comparison Berge et al., 36 using 2 Hz pressure reversals with long (aspect ratio ∼10) cylindrical pores and 15 µm particles, found that the particles came to an (off-axis) equilibrium position after 20-80 reversals. The non-monotonic variation in pulse heights in Figure 5 suggests that Brownian motion has con21



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siderable influence on the particle position over the timescale of the pressure reversals. Assuming one-dimensional diffusion at 293 K, a sphere in water has a root mean square displacement of 1.3 µm after 3.8 s, which is the average time per pulse for 400 nm particles in Figure 5; the equivalent calculation for 800 nm particles gives a root mean square displacement of 1.0 µm after 3.3 s. The smaller pore opening does not exceed a few microns in width (see ESI), confirming that Brownian motion should be responsible for the fluctuations in the pulse magnitude. The distribution CV for 800 nm particles is considerably smaller than for the 400 nm particles, even though the same pore was used at the same stretch setting. Aside from differences in Brownian motion, this result is also consistent with the trend of increased size distribution broadening at increasing stretch (Figure 3), i.e. with decreasing particle to pore size ratio. In Tsutsui at al.’s recent simulations, 33 electrokinetic transport was dominant, and Brownian motion competed with electrokinetic focussing towards the pore centre, due to the electrostatic force between the membrane surface and a similarly charged particle. A key piece of experimental evidence for this focussing was that resistive pulse profiles (and hence trajectories) varied prior to the pulse peak, but were mostly uniform thereafter. We have observed similar evidence, in that the experimental pulse profiles suggest some differences prior to the pulse peak (see ESI). There is no evidence for large differences following the pulse peak, despite the results of simulations based on hydrodynamics alone. Electrokinetic focussing is also consistent with experimentally observed trends. With increasing stretch or higher pressure, electrokinetic transport becomes relatively weak, so distribution broadening would be expected. During repeated measurements, particles can be focussed on-axis, producing a more uniform pulse size distribution. Other forms of electrokinetic transport have thus far been neglected, and this is primarily justified by the independence of the size distribution and the applied voltage (see ESI). The assumption is that 22


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pressure-driven flow is dominant. The relative significance of transport mechanisms can be estimated for TRPS using a semi-analytic model. 54 Calculations (see ESI) estimate that for the geometry used in the model, axial pressure-driven flow typically dominates all electrokinetic mechanisms by at least a factor of 400. For the experimental geometry, pressure-driven transport is approximately equivalent to electrophoretic or electro-osmotic contributions (which act in opposing directions) when only the inherent pressure head is applied. If electrokinetics (other than focussing) were significant, it is expected that the relative flow rates between the centre and the edge of the pore would vary with voltage due to the plug flow profile characteristic of electro-osmosis. 55 Also, the electrolyte resistivity is assumed homogeneous in our simulations due to the thin electrical double layer (∼1 nm), but it is possible for size distributions to be affected by voltage-dependent electrolyte concentration distributions, albeit typically at electrolyte concentrations below ∼50 mM. 30 These effects did not produce any experimental size distribution variations as a function of voltage.

Conclusion The important practical outcome of this work is improved understanding of how pulse size distributions are generated in resistive pulse techniques, particularly TRPS. Under certain experimental conditions, distribution broadening and double peaks can generate significant size measurement uncertainties. Broadening (and hence the uncertainty) can be reduced by working with relatively small pores, or limiting analyses to those data within the peak at lower ∆I. A measured resistive pulse distribution can be interpreted as the convolution of the particle size distribution with a broadening distribution, and examples of the latter are approximately represented by the data obtained for single particles.

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This process could be reversed via a deconvolution to obtain data more closely reflecting a particle size distribution, similarly to a previous empirical approach. 37 This study also highlights the care that must be taken when interpreting experimental resistive pulse size distributions. A distribution mode calculated using a histogram with clearly defined bin size is often the best single indicator of size, especially for monodisperse particles. Other central statistics (mean, median) are affected by outlying aggregates, distribution asymmetry, 26 and thresholding, 29 regardless of any broadening during measurement. Similar considerations also apply to resistive pulse measurements of particle charge, shape, or for reliable discrimination between particle types (as in a recognition assay). In terms of further work, the ideal physical model would include electrokinetic transport, ionic concentration variation, and Brownian motion, all implemented in 3D. However, close definition of the experimental material properties (including surface charge) and pore geometry probably represent the greatest immediate opportunity for increased measurement precision with any resistive pulse sensing system.

Supporting Information The Supporting Information includes further details of the finite element modelling, as well as supplementary experimental data: SEM images of particles and a pore, and pulse size distributions as a function of stretch, pressure, pore orientation, and voltage. There are also comparisons of experimental and modelled pre- and post-peak pulse shapes, and calculations of the relative importance of transport mechanisms. Conflict of Interest Disclosure: Robert Vogel is an employee of Izon Science. Eva Weatherall was employed by Izon Science for nine months in 2012-2013.

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Acknowledgements This work was supported by a Royal Society of New Zealand Rutherford Discovery Fellowship.

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References (1) Weatherall, E.; Willmott, G. R. Analyst 2015, 140, 3318–3334. (2) Vogel, R.; Willmott, G. R.; Kozak, D.; Roberts, G. S.; Anderson, W.; Groenewegen, L.; Glossop, B.; Barnett, A.; Turner, A.; Trau, M. Anal. Chem. 2011, 83, 3499–3506. (3) Willmott, G. R.; Vogel, R.; Yu, S. S. C.; Groenewegen, L. G.; Roberts, G. S.; Kozak, D.; Anderson, W.; Trau, M. J. Phys.: Condens. Matter 2010, 22, 454116. (4) Vogel, R.; Anderson, W.; Eldridge, J.; Glossop, B.; Willmott, G. R. Anal. Chem. 2012, 84, 3125–3132. (5) Kozak, D.; Anderson, W.; Vogel, R.; Trau, M. Nano Today 2011, 6, 531–545. (6) Luo, L.; German, S. R.; Lan, W.-J.; Holden, D. A.; Mega, T. L.; White, H. S. Annu. Rev. Anal. Chem. 2014, 7, 16.116.23. (7) Holden, D. A.; Watkins, J. J.; White, H. S. Langmuir 2012, 28, 7572–7577. (8) Pevarnik, M.; Schiel, M.; Yoshimatsu, K.; Vlassiouk, I. V.; Kwon, J. S.; Shea, K. J.; Siwy, Z. S. ACS Nano 2013, 7, 3720–3728. (9) Eldridge, J.; Colby, A.; Willmott, G. R.; Yu, S.; Grinstaff, M. In Selected Topics in Nanomedicine; Chang, T. M. S., Ed.; World Science: Singapore, 2013; Chapter 10: Use of Tunable Pores for Accurate Characterization of Micro- and Nanoparticle Systems in Nanomedicine, pp 219–255. (10) Kozak, D.; Broom, M.; Vogel, R. Curr. Drug Delivery 2015, 12, 115–120. (11) Heider, S.; Metzner, C. Virology 2014, 462-463, 199–206. 26


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(12) Allen, C. S.; Loo, J. F. C.; Yu, S.; Kong, S. K.; Chan, T.-F. Appl. Microbiol. Biotechnol. 2014, 98, 855–862. (13) Alsager, O. A.; Kumar, S.; Willmott, G. R.; McNatty, K. P.; Hodgkiss, J. M. Biosens. Bioelectron. 2014, 57, 262–268. (14) Platt, M.; Willmott, G. R.; Lee, G. U. Small 2012, 8, 2436–2444. (15) K¨ uhnemund, M.; Nilsson, M. Biosens. Bioelectron. 2015, 15, 11–17. (16) van der Pol, E.; Coumans, F.; Varga, Z.; Krumrey, M.; Nieuwland, R. J. Thromb. Haemostasis 2013, 11, 36–45. (17) Anderson, W.; Lane, R.; Korbie, D.; Trau, M. Langmuir 2015, 31, 6577–6587. (18) de Vrij, J.; Maas, S. L. N.; van Nispen, M.; Sena-Esteves, M.; Limpens, R. W. A.; Koster, A. J.; Leenstra, S.; Lamfers, M. L.; Broekman, M. L. D. Nanomedicine 2013, 8, 1443–1458. (19) van der Pol, E.; Coumans, F. A. W.; Grootemaat, A. E.; Gardiner, C.; Sargent, I. L.; Harrison, P.; Sturk, A.; van Leeuwen, T. G.; Nieuwland, R. J. Thromb. Haemostasis 2014, 12, 1–11. (20) Anderson, W.; Kozak, D.; Coleman, V. A.; J¨amting, ˚ A K.; Trau, M. J. Coll. Interf. Sci. 2013, 405, 322–330. (21) Bell, N. C.; Minelli, C.; Tompkins, J.; Stevens, M. M.; Shard, A. G. Langmuir 2012, 28, 10860– 10872. (22) de Vrij, J.; Maas, S. L. N.; van Nispen, M.; Sena-Esteves, M.; Limpens, R. W. A.; Koster, A. J.; Leenstra, S.; Lamfers, M. L.; Broekman, M. L. D. Nanomedicine 2013, 8, 1443–1458. 27



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 28 of 31

(23) Roberts, G. S.; Kozak, D.; Anderson, W.; Broom, M. F.; Vogel, R.; Trau, M. Small 2010, 6, 2653–2658. (24) Kozak, D.; Anderson, W.; Grevett, M.; Trau, M. J. Phys. Chem. C 2012, 116, 8554–8561. (25) DeBlois, R. W.; Bean, C. P. Rev. Sci. Instrum. 1970, 41, 909–916. (26) Somerville, J. A.; Willmott, G. R.; Eldridge, J.; Griffiths, M.; McGrath, K. M. J. Coll. Interf. Sci. 2013, 394, 243–251. (27) Willmott, G. R.; Broom, M. F.; Jansen, M. L.; Young, R. M.; Arnold, W. M. In Molecular- and Nano-Tubes; Hayden, O., Nielsch, K., Eds.; Springer: Berlin, 2011; pp 209–262. (28) Garza-Licudine, E.; Deo, D.; Yu, S.; Uz-Zaman, A.; Dunbar, W. B. Portable nanoparticle quantization using a resizable nanopore instrument - The IZON qNano. 32nd Annual International Conference of the IEEE EMBS. pp 5736–5739. (29) Bogomolny, E.; Willmott, G. R.; Beal, J. H. L.; Arnold, W. M. Int. J. Nanotechnology (in press). (30) Weatherall, E.; Willmott, G. R. J. Phys. Chem. B 2015, 119, 5328–5335. (31) Smythe, W. R. Rev. Sci. Instrum. 1972, 43, 817–818. (32) Qin, Z.; Zhe, J.; Wang, G. X. Meas. Sci. Technol. 2011, 22, 045804. (33) Tsutsui, M.; He, Y.; Yokota, K.; Arima, A.; Hongo, S.; Taniguchi, M.; Washio, T.; Kawai, T. ACS Nano 2015, 10, 803–809. (34) Adams, R. B.; Gregg, E. C. Phys. Med. Biol. 1972, 17, 830–842. (35) Shank, B. B.; Adams, R. B.; Steidley, K. D.; Murphy, J. R. J. Lab. Clin. Med. 1969, 74, 630–641. 28


Page 29 of 31

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(36) Berge, L. I.; Jossang, T.; Feder, J. Meas. Sci. Technol. 1990, 1, 471–474. (37) Saleh, O. A.; Sohn, L. L. Rev. Sci. Instrum. 2002, 73, 4396–4398. (38) Grover, N. B.; Naaman, J.; Ben-Sasson, S.; Doljanski, F. Biophys. J. 1969, 9, 1398–1414. (39) Di Carlo, D. Lab. Chip 2009, 9, 3038–3046. (40) Martel, J. M.; Toner, M. Annu. Rev. Biomed. Eng. 2014, 16, 371–396. (41) German, S. R.; Hurd, T. S.; White, H. S.; Mega, T. L. ACS Nano 2015, 9, 7186–7194. (42) Stober, G.; Steinbock, L. J.; Keyser, U. F. J. Appl. Phys. 2009, 105, 084702. (43) Heins, E. A.; Siwy, Z. S.; Baker, L. A.; Martin, C. R. Nano Letters 2005, 5, 1824–1829. (44) Lan, W. J.; Holden, D. A.; Zhang, B.; White, H. S. Anal. Chem. 2011, 83, 3840–3847. (45) Wu, S.; Park, S. R.; Ling, X. S. Nano Lett. 2006, 6, 2571–2576. (46) An, R.; Uram, J. D.; Yusko, E. C.; Ke, K.; Mayer, M.; Hunt, A. J. Opt. Lett. 2008, 33, 1153–1155. (47) Willmott, G. R.; Smith, B. G. ANZIAM J. 2014, 55, 197–213. (48) Blundell, E. L. C. J.; Mayne, L. J.; Billinge, E. R.; Platt, M. Anal. Methods 2015, 7, 7055–7066. (49) Rasband, W. S. ImageJ. 1997-2016. (50) DeBlois, R. W.; Bean, C. P.; Wesley, R. K. A. J. Colloid. Interf. Sci. 1977, 61, 323–335. (51) Haynes, W. M. CRC Handbook of Chemistry and Physics; CRC Press: Boca Raton, 2015.

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Page 30 of 31

(52) Willmott, G. R.; Chaturvedi, R.; Cummins, S. J. W.; Groenewegen, L. G. Exp. Mech. 2014, 54, 153–163. (53) Eldridge, J. A. Nanoparticle Charge and Shape Measurements using Tuneable Resistive Pulse Sensing. Ph.D. thesis, 2016. (54) Willmott, G. R.; Fisk, M. G.; Eldridge, J. Biomicrofluidics 2013, 7, 064106. (55) Innes, L. M.; Chen, C. H.; Schiel, M.; Pevarnik, M.; Haurais, F.; Toimil-Molares, M. E.; Vlassiouk, I.; Theogarajan, J. L.; Siwy, Z. S. Anal. Chem. 2014, 86, 10445–10453.

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For ToC Only par t i cl e count

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Pulse Size Distributions in Tunable Resistive Pulse Sensing

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