Tunable Resistive Pulse Sensing: Better Size and Charge

Perspective pubs.acs.org/ac

Cite This: Anal. Chem. XXXX, XXX, XXX−XXX

Tunable Resistive Pulse Sensing: Better Size and Charge Measurements for Submicrometer Colloids Geoff R. Willmott*,†,‡ †

The MacDiarmid Institute for Advanced Materials and Nanotechnology, Wellington 6140, New Zealand The Departments of Physics and Chemistry, The University of Auckland, Auckland 1142, New Zealand

‡

ABSTRACT: Tunable resistive pulse sensing (TRPS) uses the Coulter principle to detect, measure, and analyze particles at length scales ranging from tens of nanometers through to micrometers. The technology and its associated methods have advanced so that TRPS is regularly used as a characterization technique in peer-reviewed studies. This Perspective is concerned with opportunities to further develop TRPS, with a specific focus on improved measurement of size and charge for submicrometer particles. There is currently broad demand for increased rigor in such measurements. Particular points of interest include consistent use of statistics, development of accurate physical models, and realistic assessment of uncertainties associated with the usual measurement protocols. Highlights from recent studies involving TRPS are also reviewed. The technique is particularly popular in the burgeoning research field relating to extracellular vesicles, and the range of biologically relevant applications also includes liposomes, viruses, and on-bead assays.

T

unable resistive pulse sensing (TRPS) is a measurement technique that is used to analyze colloidal particles suspended in aqueous solutions. The method is based on the Coulter principle: when a particle passes through a single pore in a thin membrane, the ionic current passing through that pore is blocked for a short time, producing a “resistive pulse” (Figure 1). This electronic signal can be analyzed, and particle populations can be characterized on a particle-by-particle basis by recording many resistive pulses. TRPS, which first appeared around a decade ago,1 uses a mechanically “tunable” polyurethane membrane so that the size of the pore can be altered. General methods have gradually emerged for using TRPS to determine the concentration,2,3 size,4 and charge5,6 of particles. Operation of TRPS and its applications have been thoroughly reviewed,7 and there are other useful general tutorials8−10 and operational tips11,12 available. TRPS is one method within the broader field of resistive pulse sensing. Much literature has been devoted to resistive pulse sensing for single-molecule genomics and proteomics.13−15 Molecular-scale pores can be challenging to use; pores which are relatively easy to make and use are more suited to sensing larger particles, and there are various resistive pulse sensors which operate at scales from ∼10 nm up to ∼10 μm (cellular scale).7,16,17 TRPS operates over these length scales and is being used at an increasing rate in published research for a number of reasons. Aside from actual sensing and measurement capabilities, the flexibility of the experimental procedure is of interest to researchers, because the pore can be tuned during the measurement setup. TRPS is also reasonably © XXXX American Chemical Society

Figure 1. An experimental resistive pulse, with a schematic cross section of the sensing process inset. A tunable elastomeric pore is filled with aqueous electrolyte, with electrodes in the half space on either side of the membrane measuring the ionic current (I0). When a single submicrometer polystyrene sphere passes through the pore, the pulse magnitude is ΔI. In TRPS, pores are roughly conical, and pore size can be actuated by stretching the membrane. Main figure reprinted with permission from ref 59. Copyright 2014 Cambridge University Press. Inset reprinted with permission from ref 51. Copyright 2013 Elsevier.

accessible due to availability of the qNano apparatus (Izon Science) and pore samples which are disposable consumables. Received: December 7, 2017 Accepted: February 14, 2018 Published: February 14, 2018 A

DOI: 10.1021/acs.analchem.7b05106 Anal. Chem. XXXX, XXX, XXX−XXX

Analytical Chemistry

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Perspective

SIZE MEASUREMENTS Improving the accuracy of submicrometer colloidal particle size measurements is a difficult, yet important task. A recent editorial40 provides a reminder of the importance of rigor in such analytical methods, identifying that “the nanomaterials community has been much slower [than organic chemistry] to standardize characterization procedures and requirements.” The range of experimental parameters presents a key difficulty for standardized measurement of colloidal particles, especially as materials of biological origin become more widely studied. Such parameters include the solution (including salt concentration and pH), possible agglomerates, the particle concentration, and the range of particle sizes. The measurement standards community has been addressing this issue. Kestens et al.44 recently studied a mixture of silica nanospheres (nominally ∼20 nm and ∼80 nm diameter) suspended in water. Several measurement methods were used (DLS, EM, NTA, centrifugal liquid sedimentation, atomic force microscopy, and asymmetrical-flow field-flow fractionation) in 30 independent laboratories. The particles studied are candidates for measurement standards, and there was reasonable agreement between measurement techniques for such a chemically simple mixture. However, the study noted issues that are more widely applicable, such as the need for all laboratories use a precisely defined statistic for the diameter, given that populations of particles were being characterized. Also, the study ultimately presented values for particle diameter that were specific to the measurement method, reflecting the physical differences between methods. These issues are raised in other work on colloidal size measurement standards and policy,45,46 and they are relevant for our consideration of TRPS measurements here. Statistics and Sampling. Data from multiple experimental techniques should be compared in order to understand and improve the quality of colloidal particle size measurements. This comparison is only useful if the measurements are clearly defined, and data are compared in a consistent format. In the literature, particle populations are often described by a single central tendency value, usually the average particle diameter, without clear definition of the averaging process.47 Usually the value is provided by an analysis algorithm, such as the Z-average generated by DLS or the number-average diameter used by TRPS analysis software. It is questionable whether a mean value is the best indicator of central particle size, given that means are affected by the skew of a particle size distribution (PSD) and by outlying data far from the center of a PSD. Both the mean and the median may become unrepresentative of a population when limits on the size measurement range are considered (see below). In many cases, a mode may be the most appropriate single measure to describe a population. The peak in a PSD does not depend on outliers and should be consistent between measurement techniques as long as equivalent data are used. The bin size in PSD histograms is important when calculating the mode, and indeed generally for presentation of TRPS data. Figure 2 demonstrates how the uncertainty in a mode should be at least equal to half a bin width due to dependence on the position of bin boundaries. There is a trade-off between reducing bin size in order to reduce this uncertainty and using bins that are large enough to reduce statistical variations which can lead to misidentification of a mode. In general, there is no clear optimal method for calculating histogram bin sizes.48

A broad range of studies making use of TRPS was summarized in 2015.7 In that review, the major application categories for TRPS included diagnostics and genomics, extracellular vesicles (EVs), nanomedicine, phages, viruses, and bacteria. These studies span approximately two orders of length scale magnitude, a range containing many interesting biological particles.18 At the time of writing, more than 100 further studies have appeared which are concerned with TRPS.19 In particular, TRPS is now regularly used as a size and concentration measurement tool for EVs, exosomes, microparticles, and similar particles.12,20−28 Other recent studies notable for their use of TRPS have studied aptamer binding processes,11,29 viruses,30,31 protein adsorption on to silica beads,32 microgels,33,34 particles engineered for medical imaging,35,36 and noble metal−titania core−shell nanostructures.37 The performance of TRPS has been tested in many studies which compare size and concentration measurements between different methods. In addition to those listed previously,7 there have been useful recent comparisons with nanoparticle tracking analysis (NTA), 2 3 − 2 6 , 3 8 dynamic light scattering (DLS),20,24,33−35,38 versions of flow cytometry (FC),20,24,26 and electron microscopy (EM),26,30 among others. Varenne et al.’s study39 should be highlighted for their comparison of nine methods for evaluating multimodal nanoparticle size distributions, including a classification of measurement types. Boriachek et al.’s27 summary of concentration detection limits covers more than ten assay techniques relevant to exosomes. Comparative studies often show that TRPS and other methods are best used in conjunction with each other, rather than for independent measurements. TRPS often performs well when a simple comparison between particle populations (rather than absolute measurement) is required, where particle-by-particle measurements are an advantage, and where the test solution properties (e.g., particle size and concentration, and electrolyte) are most compatible with the technique. Ongoing use of TRPS in research suggests that the degree of measurement accuracy and precision is considered adequate by many researchers, but shortcomings are also obvious in presented data. This Perspective discusses opportunities to improve TRPS measurement performance. Improvements would extend the range of applications, encourage measurements which are absolute rather than comparative, and improve the consistency of data presentation and analysis. There is general demand for improved quality of analytical measurements for nanomaterials,40 but there are considerable difficulties associated with such improvements, many of the which present fundamental scientific and technological challenges. The focus here is on measurement of particle size, as well as the charge inferred from electrophoretic mobility. Particle size is the most common measurement reported in the TRPS literature, and there is a well-established analysis protocol. Sources of uncertainty associated with this method, and its limitations under certain conditions, are covered here. Use of TRPS for particle charge measurement has been established,5,6 but only a handful of studies have recently been using this technique,21,31,32,36,41,42 including Vogel et al.’s wide-ranging study of biological nanoparticles.43 Here, the steps linking a particle’s surface chemistry to a measured ζ-potential value are recounted, with consideration of uncertainties. Other aspects of TPRS development will also be discussed, including concentration and shape measurements. B


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Figure 2. Schematic demonstrating the importance of bin size in PSDs. Upper, a Gaussian particle size distribution (PSD) has a mean indicated (in all plots) by the black dashed line, and standard deviation σ indicated by the dashed red lines. Middle, with a bin size of 0.25σ the particular bin locations shown produce a mode (yellow dashed line) which is 0.1σ less than the mean. Variations within ±0.125σ are possible. Lower, with a bin size of 0.5σ the particular bin locations shown produce a mode which is 0.2σ greater than the mean. Variations within ±0.25σ are possible.

Figure 3. Reconciliation of TRPS and DLS particle size distributions for an oil emulsion stabilized by β-lactoglobulin in 50 mM aqueous phosphate buffer (pH 6.9), measured at various time intervals after manufacture. Reprinted with permission from ref 51. Copyright 2013 Elsevier. (a) Size distributions by volume, and (b) the same data plotted by particle number. Each data point indicates the population fraction in a bin centered at that droplet size. Bins are evenly spaced on the log scale.

Care should also be taken when quantifying the breadth of a PSD. The International Union of Pure and Applied Chemistry (IUPAC) defines particle diameter “dispersity” (D) as the ratio of the mass-average colloidal diameter to the number-average colloidal diameter, that is,

D=

4 3 ∑ Nd i i / ∑ Nd i i ∑ Nd i i / ∑ Ni

data are obtained as population fractions by particle volume, distributed within bins that are evenly spaced on a log scale (Figure 3a). Therefore, the PSDs by particle volume have relatively smooth fits. The DLS distribution within each bin is unknown, so the TRPS data have been allocated to the same bins. To move from a volume distribution to a number distribution (Figure 3b), the same data are scaled by the cube of the droplet size. For TRPS data, this emerges directly from particle-by-particle data. The DLS data are scaled using the central value of the relevant histogram bin. Note that to identify the mode of these distributions with logarithmic bins, the proportion found in each bin should be divided by the bin width. In this study51 one conclusion was that data obtained using different techniques may be inconsistent due to the uncertainties associated with the light scattering PSDs, which are largely unquantified. Use of number distributions from DLS is not recommended; in Figure 3b, less than 0.1% of the recorded light intensity data contribute to the presented data for droplets smaller than 500 nm. Beyond understanding statistics following a measurement, the sampling and measurement process for particle-by-particle methods should be consistent for each particle in order to build up a representative PSD. For example, researchers using EM images must be careful that the imaging method does not involve systematic size-selection and that the analysis does not exclude particles that are small or otherwise difficult to measure. For TRPS, there are inherent higher and lower limits on the

(1)

where Ni denotes the number of particles of diameter di.47 The IUPAC has addressed definitions of dispersity to avoid ambiguity and cautions against use of the term “polydispersity”.49 The latter term is widely used in the literature, along with the “polydispersity index” usually associated with DLS data. It is possible (and often advisable) to present a range of statistics when describing a PSD. For example, box-and-whisker plots can provide a good practical way to summarize both breadth and central tendency and to compare these between different measurements. However, when choosing which statistics to use, any limitations of the measurement data should be considered. For example, some “ensemble” measurement methods such as DLS directly find statistics for the entire population. Such methods are efficient, but uncertainties can be introduced, such as the well-known disadvantage of DLS that a small number of large particles can dominate the result for solutions with some size dispersity.50 Particle-by-particle approaches are used in TRPS and methods such as NTA, FC, and EM. In these cases, the PSD is determined by measuring many individual particlesthe more, the better for statistical significance. Particle-by-particle approaches can be advantageous because distribution statistics may be calculated directly from discrete raw data. Statistics can be manipulated to enable consistent, direct comparisons. A case study demonstrating a consistent comparison of PSDs obtained using TRPS and DLS is shown in Figure 3.51 DLS C


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Analytical Chemistry particle size. At the larger limit, particles will simply not fit through the pore. A lower limit on the resistive pulse size (therefore, particle size) is used in analysis algorithms, because small resistive pulses cannot be discriminated from the electronic noise. These cutoffs are intuitive; they have been directly discussed,12,22 and in some cases researchers have combined data obtained using pores of different sizes to cover a broad range of sizes.7,52 If particles between these upper and lower limits are equally likely to be sampled, and sampling events are independent, the sampling function can be represented by a top hat function, as described schematically in Figure 4a. The measured distribution

populations (e.g., exosomes derived from different cell lines) within the isolated range. Analytical Model. In size measurements using resistive pulse sensing techniques, it is almost universally assumed that the resistive pulse magnitude is proportional to particle volume. DeBlois and co-workers,54,55 who are often credited with developing this model, actually concluded that the resistance change is best described by an empirical relation which does not scale linearly with the particle volume,

ΔR ≈

2ρa3 ⎛ a ⎞ S⎜ ⎟ πa04 ⎝ a0 ⎠

(2)

where ⎛a⎞ S⎜ ⎟ = ⎝ a0 ⎠

1 3

()

1 − 0.8

a a0

(3)

Here a and a0 are the particle and pore radii (respectively), and ρ is the particle resistivity. Note that ΔR/R0 ≈ ΔI/I0 when ΔR ≪ R, and that ΔR and ΔI refer to the pulse magnitude (Figure 1). When a ≪ a0, then S ≈ 1 and volumetric relation is retrieved. However, when a is a significant fraction of the pore width, S deviates significantly from 1. Equation 2 was able to reproduce a numerical solution56 to within 1% when a/a0 < 0.8. A different, widely used approach is to find the resistive pulse size by integrating resistivity along the cylindrical (z) axis of the pore, using

Figure 4. Schematic demonstration of how sampling functions can affect PSDs. The left vertical axis represents the number of particles in the actual population (blue) and the measurement (green). The right vertical axis represents the sampling probability functions (red). The two plotted sampling functions have the same upper and lower size limits, and between these the sampling probability is either (a) constant or (b) size-dependent.

R≈ρ

∫

dz A (z )

(4)

Here A(z) is the conducting area of the pore in the plane normal to the z-axis (Figure 5a). Gregg and Steidley57 used this approach to obtain good agreement with experiments involving relatively large particles, but resistance was significantly underestimated when a ≪ a0. An empirical correction factor of 3/2 is required to reproduce the volumetric result for small spheres.54 This underestimate is due to nonuniformity of the electric field across the pore width. Nevertheless, eq 4 is useful for analytically studying particular pore and particle geometries58,59 with the empirical factor of 3/2 retained. Figure 5b demonstrates that there are deviations between the different models as the relative particle size increases. In this case, the relation between ΔI and particle volume was close to linear for experimental measurements within the box. This box actually represented particle sets with nominal diameters covering a large range, from 200 to 780 nm. The overall result is typicalthe volumetric assumption usually gives satisfactory results in experimental studies but is not fail-safe. For TRPS size measurements, use of calibration particles is usually best practice. Absolute measurements using models such as eqs 2 and 4 are possible but require precise knowledge of the pore geometry. Characterizations and modeling carried out for TRPS7 have shown how the pore becomes larger and can change shape during stretching, while remaining roughly in the shape of a truncated circular cone. Determining this geometry is not straightforward for any submicrometer pore, and this is especially the case when the pore width varies along its length. Commercially available calibration particles typically have a well-defined nominal diameter and are in some cases traceable to standardized EM measurements. Size measurements are then simply calibrated using the mean value and

will be missing information about particles falling outside of the limits, but will otherwise preserve the shape of the distribution. The mode of the distribution can be identified if it falls between the limits. However, PSDs obtained using TRPS are probably further affected by size-dependent sampling. For example, particles slightly below the larger size limit may be relatively less likely to pass through a pore due to steric interactions with the membrane. Sampling may also depend on size due to variations in particle transport, for example via inertial focusing53 or electrophoretic transport, if particle mobility has size dependence (see “Charge Measurements” below). Figure 4b demonstrates how a size-dependent sampling function can distort the measured distribution, in this case by reducing the distribution width and shifting the mode. Size-dependent sampling effects are most important when the actual population of particles has high size dispersity. Difficulties with broad PSDs are common in colloidal particle sizing. Therefore, precise data describing actual populations (blue lines in Figure 4) are not generally available, so that it is difficult to determine sampling functions (red lines in Figure 4). Future studies investigating sampling functions would therefore be useful. For difficult specimens, it is possible to prepare samples for measurement using an isolation or purification technique.31 Such preparation steps effectively apply a sampling function prior to measurement,12 but they also provide practical benefits and enable direct comparisons between different D


Perspective


to their fabrication method. In the case of conical pores (as used for TRPS), the maximum deviation from baseline current occurs when the particle is at or near the smaller pore entrance. Semianalytical models based on eq 4 and accounting for access resistance at pore entrances have been developed for nonstandard geometries and have had some success predicting the size and asymmetry of resistive pulses,61,62 despite the need for simplifying assumptions relating to fields near the pore entrance. The models described above contain the assumption that the spatial distribution of ionic charge within the electrolyte is homogeneous. However, membrane materials such as the polyurethane used for TRPS inherently carry surface charge. In aqueous electrolyte, an electrical double layer (EDL) is set up close to the pore wall, screening this surface charge. The EDL has a characteristic thickness (the Debye length) which decreases with increasing salt concentration.63 Significantly for sizing measurements, the membrane charge also results in concentration polarization across the ends of the pore. As a result, resistive pulses which are biphasic (containing both resistive and conducting elements) have been reported using TRPS and for similar pores,64−67 with the form of pulses depending on the direction of particle motion and the polarity of applied voltage. Related asymmetric effects such as ion current rectification (ICR) had previously been established for molecular scale68 and glass69 pores. However, evidence for charge-asymmetry effects with larger pores was somewhat unexpected, because in such cases the EDL does not extend significantly across the pore width. The explanation for biphasic pulses established by TRPS experiments66 is that the conductive part of the pulse is generated by ions screening the surface charge on the particle. When the particle enters a region in which the ionic concentration is relatively low, the extra ions around the particle increase the overall pore conductance. The importance of particle charge in this process has been confirmed in other studies.64,65,70 The limiting conditions for which concentration polarization significantly affects TRPS pulse shapes have been investigated, and notably pulses which are strongly biphasic only appear at salt concentrations well below physiological levels.66 TRPS was recently used to study how PSDs can broaden depending on the pore size,71 a phenomenon which obviously presents an issue for precision of size measurements. In that study and others using similar resistive pulse sensors,72,73 it was shown that particles passing near the edge of a pore create relatively large resistive pulses, because the electric field is concentrated at the pore edge. It is possible to deconvolute a measured PSD from the broadening function in order to remove this effect from the data. However, the broadening function must first be known, and the probability distribution of particle trajectories is required for a calculation.71 To summarize opportunities with regard to size measurement, more research is required to understand and quantify the limitations of the volumetric resistive pulse model. This model has found widespread use due to its simplicity, so the challenge is to find the conditions of particle size, electrolyte, or surface charge (for example) which require the model to be significantly adjusted. Experimental studies can be supported by finite element modeling (FEM, see also “Conclusion”), which can simultaneously address complications due to pore geometry, surface charges, and off-axis trajectories. TRPS studies are also yet to rigorously address the issue of highly

Figure 5. (a) Typical geometry used for semianalytic modeling of TRPS. Cylindrical polar coordinates are z and r. R(z) is the radius and A(z) is the area of a conical pore with length d and opening radii a and b. A potential V0 is applied, and an artificial cone at angle θ to the membrane can be used to calculate access resistance. Reprinted with permission from ref 59. Copyright 2014 Cambridge University Press. (b) Resistive pulse magnitude models proposed by Heins et al.58 (based on eq 4), Maxwell54 (ΔI∝ volume), and DeBlois et al.54 (based on eq 2) plotted as a function of particle volume. Within the indicated box, experimental TRPS size measurements using standard polystyrene particles sets of nominal diameter 200−700 nm gave a linear relation between ΔI and volume, with R2 = 0.996. Reprinted with permission from ref 4. Copyright 2011 American Chemical Society.

assuming that ΔI is proportional to particle volume. Care must be taken over the particular statistics and distributions used for the calibration and the test solution, but calibration uncertainty is reduced by the relatively low PSD dispersity of standard particle sets. Ideally, measurement conditions for calibration particles should be identical to those for the test solution. Some recent studies in biological media have taken this to an extreme by “spiking” the test solution with calibration particles.60 Models such as those described by eqs 2 and 4 were initially developed for infinitely long cylindrical pores. Variation of pore width was not included, nor was the necessarily abrupt interface between bulk solution and a pore. In pores with geometry that approaches a long cylinder, the maximum deviation from baseline current occurs when the particle is well within the pore, in which case these models are appropriate for calculating ΔI. However, many pores used for RPS have variable width due E


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Analytical Chemistry conductive particles, with most models assuming that the particle is an insulating sphere. Development of further experimental and analysis techniques for dealing with solutions with high PSD dispersity would also be of high practical benefit, especially for the increasing number of TRPS studies of biomaterials.

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CHARGE MEASUREMENTS There is high demand for improved charge measurements for colloidal particles. Charge is important for determining the stability of colloids in solutionthat is, their propensity to remain dispersed rather than coalesce or form aggregates. Particle charge can also give an important indication of surface chemistry, which is relevant in sensing applications. For example, the charge may change when a chemical target binds to an aptamer or antibody on the surface of a bead, or the charge may allow a researcher to distinguish between different types of bioparticle which are similar in size. Charge measurement using TRPS is less widely used than methods for concentration or size measurement, and DLS (an ensemble method) is used for most studies of colloidal charge in the literature. TRPS provides many of the same benefits for charge measurements as it does for size measurements. The technique is relatively flexible to use and can provide particleby-particle data, although (as with sizing) accurate particle-byparticle results require measurements to be consistent for each particle. Therefore, there is ample opportunity to trial and develop improvements to TRPS charge measurements. TRPS derives particle charge from measurement of a particle’s electrophoretic mobility (μ). This mobility plays a role in physical models for transport through the pore. Raw data can be analyzed using such a model in order to calculate the mobility. The three steps in this process, shown schematically in Figure 6, will be discussed here in turn. First (Figure 6a), it is important to be clear about the quantity measured. Colloidal particle charge measurements are often presented as a zeta potential (ζ), which is the electric potential at the hydrodynamic slip plane when an EDL forms around the charged particle. The theoretical details of EDL structure, which link ζ to actual surface charge, have been established.63,74 For the types of particles typically measured using TRPS, Smoluchowski’s approximation applies because the EDL adjacent to the particle is very thin in comparison with the particle radius. In this case63 |v| ϵζ =μ= |E| η

Figure 6. Usual steps for charge measurements using TRPS. (a) A particle’s velocity and an applied electric field are measured in order to calculate mobility, which is related to electronic charge screened by an EDL, as described by ζ using Smoluchowski’s approximation. (b) A model of transport through the pore is required to derive μ from raw data. Here, the model of a conical pore with surface charges has potential difference V0 and pressure ΔP = P1 − P0 applied across the membrane. Arrows indicate the directions of electro-osmotic flow (EOF), electrophoresis (EPH), and pressure-driven flow (PDF) when V0 and ΔP are positive and ζ and ζpore are negative. (c) Raw data are used to find either values of V0 and ΔP at which J is minimized (top, Reprinted with permission from ref 5. Copyright 2012 American Chemical Society.) or the duration of pulses at particular fractions of ΔI (bottom, Reprinted with permission from ref 41. Copyright 2016 American Chemical Society.).

(5)

where v is a particle’s velocity when it is placed in an electric field E, and ϵ and η are respectively the solution permittivity and viscosity. Based on eq 5, models can be constructed which allow calculation of μ and therefore ζ (Figure 6b). Published TRPS charge measurements tend to use essentially the same analytical approach, which accounts for the most relevant transport mechanisms (namely pressure-driven flow, electrophoresis, and electro-osmosis),5 (ζ − ζpore) J Q =ϵ E+ C η A

sectional pore area. The left-hand side of this equation is usually measured in experiments, and fluid properties η and ϵ are well known, so the uncertainty in the model usually lies in measurement and calculation of ζpore, E, and Q/A. If the pore geometry is known, it is possible to build semianalytic models for the electric field, because the potential difference across the membrane (V0) is known. Similarly, the pressure driven flow can be modeled if the pressure head across the membrane (ΔP = P1 − P0) is measured. However, pore geometry is difficult and inconvenient to measure. As with size measurements, calibration particles have been used to reduce measurement uncertainty by removing the need for knowledge of pore geometry, thereby reducing the

(6)

Here J is the particle flux, C is the particle concentration, ζpore is the zeta potential at the pore wall which drives electro-osmosis, Q is the volumetric pressure-driven flow rate, and A is the crossF


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Individual pulse durations can be analyzed in different ways. Recent studies have used a protocol in which the pulse width is analyzed at several different points and compared with pulses for calibration particles.41−43 Measurements are taken over a range of V0 and ΔP values so that the pore geometry is not required to be known. However, large uncertainties can emerge if the linearities E ∝ V0 and Q/A ∝ ΔP are not verified, or if lines are extrapolated from a small number of data points to find an intercept. In other studies, the methodology used to measure charge has been unclear,21,32 or else a simplified version of a full charge measurement method has been used.31,36 TRPS charge measurements have been most effective when particle sets have been directly compared. Figure 7 shows an

number of unknowns in eq 6, especially drawing on expectations that E ∝ V0 and Q/A ∝ ΔP; both V0 and ΔP can be controlled in measurable steps. However, charge calibration approaches have two major drawbacks at present. First, whereas size standards can be calibrated using EM, colloidal charge is not traceable to a gold-standard measurement technique. DLS is typically used to determine the charge of calibration particles. Second, the particles’ EDL structure and therefore ζ can be expected to depend on solution pH and salt concentration, so that calibration particles must be standardized under the same conditions as the test sample. Calibration measurements on TRPS should also be carried out under the same conditions. Use of calibration does not remove perhaps the most significant uncertainty, attributable to ζpore. Pore wall charge can be measured using streaming potential measurements, both on flat surfaces of the elastomeric membrane material5,75 and in situ.76 However, ζ and ζpore are usually of comparable magnitude: ζpore will depend on the solution properties, and the term ζ − ζpore appears in eq 6, so it is difficult to avoid a large contribution to uncertainty in absolute measurements of ζ. Chemical modification of pore surfaces can be used to manipulate and potentially passivate pore surface charge. For example, a polymeric layer-by-layer dip coating method has recently been used to functionalize tunable pore surfaces with layers of opposite net charge, resulting in observable changes in ICR, especially for relatively large pore sizes and low molarity (5−50 mM).77 Calculations using eq 6 usually involve significant simplifying assumptions. Although several variables are written as vectors, these transport quantities are usually assumed to act parallel to the axis, equivalent to an assumption that the particle travels through a long cylinder. The space filled with electrolyte is assumed to be homogeneous, in terms of both ionic charge distribution and the electric field. Individual particles are often assumed to move at a single pressure-driven flow rate, equivalent to an assumption that all particles move along the central axis. Therefore, while the model is useful, care should be taken when interpreting calculations. Figure 6c shows two major ways in which raw data have been analyzed. In the first, the point at which J = 0 is identified by considering data for many resistive pulses and finding the applied pressure at which pulse rate or particle speed is minimized. This can be achieved with good precision.5,75 Using the pore geometry, the value of ζ can then be calculated using eq 6. This is effectively an ensemble measurement, because many particles are sampled. It is also possible to calculate ζ for individual resistive pulses, noting that the particle velocity is given by J/C in eq 6. Using the duration of resistive pulses as a proxy for (inverse) particle velocity, an experimental pulse can be used to calculate ζ using either the pore geometry6,78 or calibration particles.79 The particle-by-particle approach follows the work of Arjmandi et al.,80 who (working with different pores and neglecting electroosmosis) assumed that each pore had a constant “sensing zone” length, so that velocity could be averaged over that distance. This type of approach includes an assumption that all particles are at the same position when the corresponding resistive pulse reaches a certain fraction of ΔI (Figure 6c), introducing some uncertainty if particles are different in size. A more complete analysis is possible by combining the particle velocity from eq 6 with the model for current change as a function of particle position based on eq 4.

Figure 7. TRPS results from a study of fractions of lentiviral particles. The vertical axis indicates the duration between the pulse maximum and half the pulse height, while particle size is plotted on the horizontal axis. Reprinted with permission from ref 31 under the terms of the Creative Commons Attribution 4.0 International License. Copyright 2017 Heider et al.

example in which the size and pulse duration of different fractions of lentiviral particles are compared.31 The duration is not further analyzed, removing the need for a model to find ζ, yet the data clearly indicate that one of the fractions has different charge from the others. Overall, more work is required to improve absolute measurements of ζ, especially improving the characterization of calibration particles and ζpore. Researchers presenting particle-by-particle data should consider issues relating to understanding distribution statistics, as discussed above for size measurements. In some studies, surfactant has been added to solution to aid ease of measurement, in which case the effect of surfactant on the charge measurement should be assessed. Finally, studies of biphasic pulses present an opportunity for a different charge measurement technique, because the conductive pulse size is approximately linearly related to the nominal particle charge.66

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FURTHER OPPORTUNITIES AND CONCLUSION Beyond size and charge, the most common use of TRPS is for concentration measurements. Many of the recent studies which have used TRPS to study exosomes have included concentration measurements, and the reader is referred to Vogel et al.’s work on this topic.81 In pressure-driven flow, the rate of resistive pulses is predicted to be proportional to the flow rate, and therefore to the concentration. This proportionality is often confirmed in reported data, and calibration beads of known concentration can be measured under identical conditions to obtain results with good accuracy. There are relatively minor G


Perspective

Analytical Chemistry Notes

questions relating to dependence of pulse rate on particle size and homogeneous distribution of particles. Throughout this Perspective, particles have been considered to be spherical. Clear exceptions are evident in TRPS research to date, with recent additions including dimer and trimer aggregates32,38 and even core−shell nanostructures.37 Nonspherical particles were studied earlier in the development of resistive pulse sensors,82 and resistive pulses for aggregates have been explicitly simulated using the same approach as eq 4, qualitatively reproducing experiments.61 These studies demonstrate that extracting shape information from resistive pulses would be useful. So far, the models used to interpret data have included the assumption that the electrolyte is homogeneous. As with size measurements, it is unnecessary to know the exact pore geometry if spherical particles are used for calibration or comparison. However, rigorous absolute measurement of particle shape has not been demonstrated. Aside from simplifications in the models used, assumptions or inferences must be used when analyzing a resistive pulse in order to decouple variability in particle trajectories, geometries, and possibly charge from the unknown orientation of a particle. There is clearly an opportunity for development of TRPS in this area. For colloidal particles, tunable pores present opportunities relating to particle squeezing,34,83 trapping, and gating that remain largely unrealized. Recently, fluorescence microscopy has been coordinated with TRPS to provide particle-by-particle information on optical properties.84 More generally, sizetunable submicrometer pores in polymeric membranes can be thought of as a basic geometric tool that could be applied in any number of micro- and nanotechnologies. Measurement of submicrometer colloidal particles will remain the core use of TRPS. For the size and charge measurements discussed above, improved understanding and reporting of measurement protocols and statistics would increase the value of literature reports. Careful experimental design is also helpful and will increasingly extend to sample preparation techniques, methods for handling particles with high size dispersity, and control of pore surface chemistry. Investigations which are comparative (or robustly calibrationbased) are a particular strength of the TRPS technique. Some of the drawbacks of present measurement protocols can be attributed to oversimplification of the physical model used. One obvious research direction is to extend FEM simulations, focusing on aspects of the analysis techniques that are currently problematic. Studies akin to recent work with TRPS,71 similar pores,64−67,73,85 and even conical nanopipets,86 can account for the interplay between ion concentrations, pore and particle surface charge, and pressure-driven hydrodynamics. There is a challenge to clearly describe even simple experimental observations with reasonable accuracy using FEM, because characterization of geometry and material properties is required. Improved fabrication control and more efficient characterization of pore geometry and actuation87 would be generally beneficial for the use of tunable pores.

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The author declares no competing financial interest.

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

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Corresponding Author

*E-mail: [email protected]. Phone: (64) (0)9 3737599. Fax: (64) (0)9 3737445. ORCID

Geoff R. Willmott: 0000-0001-5079-2622 H


Perspective

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Tunable Resistive Pulse Sensing: Better Size and Charge

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