Orthogonal Nanoparticle Size, Polydispersity, and Stability

Article

pubs.acs.org/journal/apchd5

Orthogonal Nanoparticle Size, Polydispersity, and Stability Characterization with Near-Field Optical Trapping and Light Scattering Perry Schein,†,§ Dakota O’Dell,‡,§ and David Erickson*,†

† ‡ Sibley School of Mechanical and Aerospace Engineering and School of Applied and Engineering Physics, Cornell University, Ithaca, New York 14853, United States

*S Supporting Information

ABSTRACT: Here we present and demonstrate a new technique for simultaneously characterizing the size, polydispersity, and colloidal stability of nanoparticle suspensions. This method relies on tracking each nanoparticle’s motion in three spatial dimensions as it interacts with the evanescent field of an optical waveguide. The motion along the optical propagation axis of the waveguide provides insight into the polydispersity of a nanoparticle suspension. Horizontal motion perpendicular to the propagation axis gives the diffusion coefficient and particle size. In the direction normal to the surface, statistical analysis of the scattered light intensity distribution gives a map of the interaction energy landscape and insight into the suspension stability. These three orthogonal measurements are made simultaneously on each particle, building up population level insights from a single-particle rather than ensemble-averaged basis. We experimentally demonstrate the technique using polystyrene spheres obtaining results consistent with the manufacturer’s specifications for these suspensions. For NIST-traceable polystyrene size standard spheres, we measure a variability in the hydrodynamic radius of ±5 nm, compared with the manufacturer’s certified measurement of ±9 nm in the geometric diameter made using transmission electron microscopy. KEYWORDS: nanoparticle analysis, optical trapping, near-field photonics, force measurement, size measurement, colloidal stability

s nanoparticles become increasingly important for internal reflection microscopy (TIRM) offer highly sensitive A applications including biosensing,1 drug delivery,2 catal- measurements of particle−surface interaction forces that are ysis,3 and enhanced oil recovery,4 quality control and indicative of system stability, but do not provide size verification of expected behavior remain important concerns.5 information.15 Colloidal probe atomic force microscopy 6−9 Three key quantities for quality assurance are particle size, (AFM) also allows for measurements of surface-interaction 10,11 12 polydispersity, and interaction strength, because these forces16,17 but requires extensive sample preparation and suffers metrics can give an estimate of the suspension’s stability and from very low throughput, making it largely impractical for performance. large-scale quality control.18 Because of these drawbacks, it is Currently there are several existing techniques for character- often necessary to perform multiple measurements on a given − izing subsets of these nanoparticle properties. Size and sample in order to gain a complete picture.18 20 polydispersity characterization can be accomplished by making ff In this work we address this problem through an optical measurements of nanoparticle di usion through methods such waveguide trapping technique that allows us to make as dynamic light scattering and nanoparticle tracking analysis, orthogonal and simultaneous measurements of particle size, which give a hydrodynamic size, by measuring size-dependent − polydispersity, and colloidal stability. Using the optical forces to optical or electrical properties, as in UV vis spectroscopy or transport nanoparticles, we track the optically confined motion with the Coulter principle, or by directly imaging the size using in three dimensions by imaging the light that each particle electron microscopy on a dried and prepared sample. 13 scatters as it interacts with the evanescent field. Particles are Nanoparticle tracking analysis (NTA) is one such sizing technique that can make single-particle size measurements in measured successively in a high-throughput, conveyer-belt-like the native suspension environment. In NTA, particle rapid interrogation, building population level metrics from suspensions in a channel pass through a light sheet and scatter single-particle data. This extends our previous experimental and light. Particle trajectories are tracked by capturing video of the theoretical work with tracking the nanoparticle motion in the y- scattered light pattern, and the mean-square displacement is and z-directions and adds a new simultaneous characterization computed. This is linked to the diffusion coefficient and ultimately the particle size through the Stokes−Einstein Received: August 23, 2016 relation.13,14 Other techniques such as those that use total Published: December 16, 2016

© 2016 American Chemical Society 106 DOI: 10.1021/acsphotonics.6b00628 ACS Photonics 2017, 4, 106−113 ACS Photonics Article of the transport velocity in the x-direction to the picture of the surface of the waveguide, and optical scattering and (coordinate system shown in Figure 1), bringing in a new absorption forces that act along the direction of propagation. The forces that can be applied in these near-field optical traps cover the pico-Newton range and are tunable through the input optical power, allowing for force spectroscopy in a range of interest for many physical systems.29 These forces are also strongly dependent on particle size,30 giving significant sensitivity in the transport behavior to variations in particle radius. In addition to the optical forces, the nanoparticle transport is influenced by hydrodynamic effects as well, which themselves are affected by the presence of the nearby surface.31,32 Three-Dimensional Scattered Light Nanoparticle Tracking. An additional effect of the particle’s interaction with the evanescent field is that the particle scatters light. This Figure 1. Orthogonal nanoparticle characterization scheme. (a) A scattering depends on the size and refractive index of the particle is transported along an optical waveguide, scattering light as it particle, but for a given particle the amount of light that it interacts with the evanescent field. This scattered light is captured and scatters is proportional to the local optical intensity in the recorded using a CMOS camera (example frame shown). The particle evanescent field. Given that the evanescent wave decays position is localized in each frame (red circle).The centroid position of exponentially, it is possible to use this intensity as a measure the particle is tracked with subpixel resolution, and the total intensity of the distance between the particle and the top of the of light scattered by the particle is integrated in each frame. (b) In the fl x-direction (coordinate system shown in the upper-right corner of this waveguide. As we demonstrate herein, this uctuation in figure) the particle translates at a terminal velocity, and the distribution intensity, coupled with the ability to track the centroid of the in terminal velocities over the particle population gives a measurement scattered light in the x−y plane, allows for a particle’s motion to of sample polydispersity. (c) In the y-direction, the particle undergoes be tracked in all three spatial dimensions. confined and hindered diffusion in a harmonic potential well near the Figure 1 outlines the orthogonal characterization procedure. surface, which can ultimately be related to the particle size. (d) In the From a captured image of the scattered light as the nanoparticle z-direction, the particle scatters more light when it is close to the interacts with the waveguide, the particle position is localized in waveguide and less when it is far away, so the scattered light intensity each frame, as illustrated by the red circle in Figure 1a. Based is used to track the z-position. Over many samples, the statistical fi distribution of scattered light intensity gives the probability on 2D Gaussian tting the x- and y-position of the particle distribution of finding the particle at a given energetic state, centroid are localized with subpixel resolution as shown in corresponding to a height in the potential energy well. Using the Figure 1b and c, respectively.33 The intensity of the measured Boltzmann distribution, these probabilities give a map of the potential light signal is integrated around this centroid point, giving a energy landscape, which is related to the energy barrier preventing the value for the total intensity scattered by the particle as shown in particle from sticking to the surface and therefore indicative of the Figure 1d, corresponding to the position in the z-direction. suspension stability. These values are captured in every frame from a tracked particle, giving the particle’s velocity, which is related to the ff ffi dimension where the physics are much more sensitive to the polydispersity, the y-direction di usion coe cient, which is particle size. In addition to the analytic advances, we present related to the particle size, and the z-direction interaction demonstration experiments on real nanoparticle suspensions. energy landscape, which indicates the relative strength of We show how measuring these three axes yields insights into repulsive surface interactions. The details of how this the suspension properties of polystyrene nanoparticles with information is extracted are provided in the following three radii of 260 and 400 nm that are missed using bulk techniques. sections. A video showing this frame-by-frame 3D tracking is While the initial demonstrations presented here do not included as Supporting Information. y fi completely address all of the drawbacks of the existing Particle-Size Information from -Direction Con ned techniques, we believe that making simultaneous measurements Brownian Motion. In the y-direction, the particle sees a in three dimensions is a promising approach for high- potential energy well due to the optical intensity gradient of the throughput nanoparticle analysis. mode profile of the waveguide. For single-mode operation, this will be strongest above the center of the waveguide and ■ RESULTS AND DISCUSSION decreasing toward the edges. This results in an optical gradient Waveguide-Based Optical Trapping. The primary force restoring the particle to the central intensity maxima. For element of our experimental system is a single-mode silicon small displacements from the center of the waveguide, these nitride waveguide. Similar waveguides have been explored as forces can be approximated as being linear in the y- tools for capturing and characterizing nanoparticles due to their displacement, and the particle experiences a harmonic potential 34 optical confinement on the same length scale as the well. This is a useful approximation because a Brownian − nanoparticles of interest.21 27 In the present experiment fluid particle in a harmonic potential well is a canonical problem in containing nanoparticles is delivered to the waveguide via a the statistical mechanical literature, and many developments microfluidic channel (see our previous work28 and the Methods have been made by previous researchers in measuring physical section herein for details). When a nanoparticle interacts with particle parameters from this motion.35 We have previously the evanescent field of the waveguide, it exerts a net force on developed a theoretical method for applying this harmonic the particle, which is commonly decomposed as an optical model for particle sizing along the y-direction,36 of which we gradient force acting downward and inward toward the center will give an abbreviated summary here.

107 DOI: 10.1021/acsphotonics.6b00628 ACS Photonics 2017, 4, 106−113 ACS Photonics Article

For a particle conﬁned within a harmonic potential, the time evolution of its position can be described by the Smoluchowski equation:

⎛ 2 ⎞ ∂ ∂ ktrap ∂ Py(, ty|= , t ) D⎜ + yPy⎟ (, ty| , t ) 0 0 ⎝ 2 ⎠ 0 0 ∂t ∂y kTB ∂ y (1) | fi where P(y, t y0, t0) is the probability density function of nding a particle at position y at time t given initial position y0 at time ’ ff ffi t0, D is the particle sdiusion coe cient, ktrap is the spring ff ’ constant of the e ective harmonic potential, kB is Boltzmann s constant, and T is the absolute temperature. In the limit of very short time lags, Δt, between observations, the solution to this equation is a Gaussian function whose variance, σ, grows linearly with time: 2 σ ()Δ≈tDt 2 Δ (2) By applying a linear fit to the variance over time in this Figure 2. Analysis of y-direction motion. (a) Variance in y-position as ff ff ffi a function of lag time for example R = 260 nm (red curve) and R = regime, an e ective di usion coe cient can be extracted. For 400 nm (blue curve) nominal sized particles (only short lag times more details about this approximation, please see the shown). In the limit of short lag times, the particle does not yet have Supporting Information (Section S1). Near the surface of the time to respond to the restoring forces of the optical trap. In this waveguide, however, this diffusion coefficient is not the same as diffusion-dominated regime, the variance in position is linear in lag its bulk value; rather, it is hydrodynamically hindered by a time, and the particle undergoes normal diffusion. Linear fits are factor, here denoted as β∥(z, R), which depends in general on shown with dashed lines. The slope of these lines corresponds to the both the height above the surface and the particle size: diffusion coefficient, as indicated in eq 2. (b) Population level measurements of diffusion coefficient. The smaller diameter particles ff Dz()= β (, zRD ) bulk (3) di use faster, allowing for the two particle populations to be distinguished. where D∥ is the hindered diffusion coefficient in the x−y plane ff ffi and Dbulk is the free-space di usion coe cient. Detailed theoretical calculations of β∥(z, R) are well established in the the slope and the measured diffusion coefficient. For more literature.32 In our previous work, we demonstrated that for details on the variance at longer lag times and on the noise in very small heights above the surface this converges to roughly these experiments, please see the Supporting Information 1/3 the bulk diffusion for all values of R. Refactoring this (Figure S1). Figure 2b shows a boxplot with aggregated equation, we can then relate the measured diffusion coefficient effective diffusion coefficients from all particles measured. N =8 directly to the hydrodynamic particle radius: particles are plotted for the 260 nm set, and N = 25 for the 400 ⎛ ⎞ nm set. This plot shows the distribution of the measured 1 kT diffusion coefficient for the particles in the measured R ≈ ⎜ B ⎟ population. 36⎝ πηDz (= 0)⎠ (4) If we compare the mean value of the diffusion coefficient for where η is the fluid viscosity and D∥(z =0)isthe the two data sets, the 260 nm beads are indeed distinguishable experimentally measured diffusion coefficient assuming a from the 400 nm beads by their effective diffusion coefficient. If negligible particle surface separation distance. To demonstrate we take the approximation that the ability to distinguish differently sized nanoparticle DD≈ 1/3 (5) populations using this analysis method, we performed two bulk experiments: one using R = 260 nm polystyrene beads and the however, we find a measured radius of 149 and 238 nm, other with R = 400 nm polystyrene beads. The results of these respectively: 60% of the nominal radius for both particles. This experiments are shown in Figure 2.InFigure 2a, the first three overestimate of the diffusion coefficient might be attributable to data points of the short time data are plotted for one particle of the equilibrium height being above the surface. We hypothesize each size. We focus on the short time data because this is the that this might be the case with these particles whose size is regime where eq 2 is the most accurate. The data points here comparable to the width of the waveguide, as part of the represent the variance in the displacement of a single particle in particle may “overhang” the waveguide, experiencing hydro- the y-direction. Each point is computed by looking at how far dynamic hindering from the substrate further below rather than the particle is displaced after a time of Δt from each frame in its the waveguide itself. This would lead to less hindering than trajectory and taking the variance of these displacements. As predicted by the model, consistent with our experimental expected, the variance in the 260 nm particle motion increases observation. This is not likely attributable to undersampling the more rapidly than the 400 nm one, consistent with a higher particle motion in the presence of the force field, as this would diffusion constant (and therefore a smaller particle). The slope result in an underestimate of the diffusion coefficient. of a linear fit to this short time data is taken, and it is used to Additional experiments must be conducted to determine the compute the measured diffusion coefficient using eq 2. The origin, but even with this bias, the populations of particles are nonzero intercept, not included in eq 2, is the result of still separable. Testing this hypothesis could be accomplished Gaussian sources of noise in the experiments such as those due through experiments on smaller particles, which would require to localization errors in the particle tracking.37 As long as these a higher sampling rate than is currently available in our sources of noise are frequency independent, they will not alter experiments. The primary limitation to the sampling rate is the

108 DOI: 10.1021/acsphotonics.6b00628 ACS Photonics 2017, 4, 106−113 ACS Photonics Article

Figure 3. Analysis of x-direction motion. Top: x-position traces for (a) R = 260 nm and (b) R = 400 nm particles. The particles reach terminal velocity far faster than the time scale of these measurements. As the velocity depends on R5, the spread in the terminal velocity (spread in the slopes) is related to the sample polydispersity. (c) Spread in particle radii (ΔR) for 260 and 400 nm samples. The coefficient of variation calculated with our methodology is consistent with the values certified by the manufacturer as determined through TEM. data transfer rate over the USB 3.0 interface of full-waveguide light in a vacuum, and λ is the optical wavelength. The accuracy images. As data transfer standards have greatly improved in of this approximation decreases for larger sized particles; please recent years, we expect that these experiments will become see the discussion below and the Supporting Information possible with low-cost CMOS cameras in the coming years, (Section S3) for more details regarding when use of this allowing for further validation and extension of these approximate model is justified. This optical propulsion is techniques to smaller size ranges. counterbalanced by the hydrodynamic drag force, Fdrag, which Sample Polydispersity Information from x-Direction for these submicrometer particles can be modeled using Stokes’ Transport Velocity. The y-direction analysis is valuable equation: because it yields a hydrodynamic estimate of particle size, FRU= 6πη which is independent of the particle’s optical properties or the drag 0 (7) optical power used. However, this is a stochastic estimator, and η fl where is the uid viscosity, R is the particle radius, and U0 is there is a lower bound on the variance in size estimate. As such, the velocity in the x-direction. For a lossless dielectric particle, it can be useful for distinguishing, for example, 300 nm particles the optical absorption forces are negligible, and by equating from 600 nm particles, but cannot resolve small deviations, for Fdrag from eq 7 and Fscat from eq 6, we derive an expression for example, 300 nm particles from 305 nm. These small this terminal velocity: differences in size can, however, be very significant for 2 determining the reliability of the particle’s size-dependent 4 ⎛ εε− ⎞ 64πεI m ⎜ pm⎟ 5 functionality. To determine this spread in the particle size U0 = ⎜ ⎟ R λη4 ⎝ εε+ 2 ⎠ distribution, we add an additional orthogonal measurement 9c pm (8) from the x-direction motion. This velocity is very strongly dependent (R5) on the particle In the x-direction, the particle is propelled along the size, so small differences in the particle size can yield easily waveguide in the direction of optical propagation by its ff fi 21 measurable di erences in the measured velocity. The prefactor interaction with the evanescent eld. This motion arises from in eq 8 is in general unknown, so the radius cannot be found the optical scattering and absorption forces. These are balanced directly from the velocity and may be further complicated due by the hydrodynamic drag on the particle. This results in fl to the increased hydrodynamic drag near a surface. If a transport at a terminal velocity with some uctuations due to suspension of multiple nanoparticles is measured under the changes in the optical forces resulting from the coupled same experimental conditions, e.g., on the same waveguide and motions in the other directions, as well as due to Brownian at the same optical power, however, the velocity of two particles motion in the x-direction itself. For a particle in the Rayleigh can be directly compared to find the difference in radius: regime (whose size is small compared to the optical ⎡ 1/5 ⎤ wavelength), the optical scattering force, Fscat, can be expressed ⎛ U ⎞ 23 ⎢⎜ 0,(RR+Δ ) ⎟ ⎥ as ΔRR=−⎢⎜ ⎟ 1⎥ ⎣⎝ U0,mean ⎠ ⎦ 2 (9) 5 ⎛ εε− ⎞ 128πεI m ⎜ pm⎟ 6 F = ⎜ ⎟ R Here, U0,mean is the mean measured particle velocity, R refers to scat 3cλ4 ⎝ εε+ 2 ⎠ pm (6) the nominal sample radius, and U0,(R+ΔR) is the velocity of an individual measured particle. If a statistically significant number where I is the locally available optical intensity in the of particles are processed, this gives a highly sensitive fi ϵ evanescent eld, m is the relative permittivity of the medium, measurement of the variance in the particle size within the ϵ p is the relative permittivity of the particle, c is the speed of sample. Combined with the mean radius determined from the

109 DOI: 10.1021/acsphotonics.6b00628 ACS Photonics 2017, 4, 106−113 ACS Photonics Article y-direction motion, it is also possible to calculate the coefficient contaminants or heterogeneous subpopulations that might be of variation of the nanoparticle distribution, a useful quality missed just by looking at the ensemble-averaged size. control metric to quantify polydispersity within the distribution. We demonstrate this dimension by looking at the interaction In Figure 3 we plot the results of this experimentally for potential energy landscapes between 260 and 400 nm radius nominally monodisperse R = 260 nm and R = 400 nm nanoparticles with the silicon nitride waveguide surfaces. Here nanoparticle suspensions (the same particles as shown in Figure we look at the same particles depicted in Figures 2 and 3, but 2). In Figure 3a and b we show the nanoparticle displacement we now obtain information about the z-direction based on the in the x-direction as a function of time for particles in each scattered light intensity. The results of this analysis are shown suspension. The linearity of the data indicate that each particle in Figure 4. For more details, please see the Supporting travels at a relatively constant velocity, subject only to very Information (Section S2). small fluctuations. These can be attributed to small variations in I due to input power fluctuations or the nanoparticle motion in the other spatial dimensions. From particle to particle, within each set there is some spread in the observed slope, corresponding to U0. The velocity is steady over the length of the observation window, allowing for much less error in the measurement compared with the stochastic y-direction motion. By comparing the velocity of each trajectory to the average velocity for the full data set, we can apply eq 9 to find differences in the particle size to single nanometer precision. We can use these variations to compute the standard deviation in particle radius, which when divided by the nominal sample radius supplied by the manufacturer gives us the coefficient of variation (CV). In Figure 3c, we plot the spread in the radius for each particle using a box-and-whiskers plot (top and bottom bars indicate largest and smallest particles, box indicates 25th and 75th percentiles, line indicates median). The computed coefficient of variation is shown in the figure. For the nominal R = 400 nm particles, the spread in particle hydrodynamic radii is found to be ±5 nm, yielding a coefficient of variation of 0.5%. This corresponds favorably to the CV of 0.6% and geometric diameter of ±9 nm specified on the Certificate of Analysis from the manufacturer, as measured by transmission electron microscopy (TEM). Figure 4. Analysis of z-direction motion. (a, b) Potential energy Sample Stability Information from z-Direction Poten- landscapes for (a) R = 260 nm and (b) R = 400 nm particles. The tial Energy Landscape. In addition to the motion in the x−y black curves with solid circles indicate the raw potential energy landscapes as computed from the Boltzmann distribution. The blue plane, the nanoparticles also experience forces and resulting fi − curves indicate the ts of the optical energy model to the optically motion normal to the surface in the z-direction. Unlike the x y dominated regime data. The red curves with solid squares are the measurements that track the centroid position of the particle, surface interaction energy components that remain after the optical the z-direction motion is tracked by spatially integrating the component is subtracted. total intensity scattered by the particle at a given time; when fi the particle is near the surface, the evanescent eld intensity is As the figure shows, the potential well (black curves in Figure stronger so the particle scatters more light and a brighter signal 4a and b) data are consistent for nominally monodisperse is observed. This approach is similar to the TIRM 15,38,39 particles. An interesting aspect of the data is that the optical technique, and we have previously demonstrated its component of the potential well (blue curves) varies somewhat application to optically trapping structures40 and specifically to 28 among these particle populations, but the surface components single-mode waveguides. Concisely, this technique relies on retain similar shapes. This makes sense due to the strong (R3) mapping the statistical distribution of total scattered light by the size dependence of the optical force. In this situation we expect particle onto the Boltzmann distribution and using this to the primary surface interaction force to be electrostatic in ff measure the potential energy di erence as a function of nature, and this is typically modeled as depending on R. The − particle surface separation distance. This technique relies on height of the repulsive energy barrier in both cases is indicative the long-term probability distribution of the particle’s position of the stability of these suspensions. as it undergoes Brownian motion and samples different states in Discussion. Currently, our estimates of size from the y- the z-direction potential energy well. While the dynamics of the direction diffusion suffer from relatively large uncertainties, particle’s short time scale motion between these states will be which make it difficult to discern small differences in the size. influenced by the hydrodynamic presence of the wall, here we Because confined Brownian motion is a stochastic process, rely on the long time scale equilibrium statistical mechanics. there will always be a degree of variance in the measured Here, we focus on what this information adds to the diffusion coefficient. The lower bound on this uncertainty will characterization picture when combined with orthogonal improve with more frames, however, as will any systematic measurements of the x−y nanoparticle motion. These measure- biases in the measured size due to undersampling the diffusive ments can show different physical mechanisms influencing motion. Other similar measurements of near-wall diffusion in particles of the same size, informing about the presence of the presence of force fields have reported similar measurement

110 DOI: 10.1021/acsphotonics.6b00628 ACS Photonics 2017, 4, 106−113 ACS Photonics Article biases of diffusion in the direction of the force field.41,42 As a ⎛ ⎞2 RU Iε εεpm− result, the accuracy of this technique can be improved 0 5 m ⎜ ⎟ 7 Pe||,0z = =≈128π 4 ⎜ ⎟ R significantly by observing the motion with a faster camera. D λ c ⎝ εεpm+ 2 ⎠ (10) Given the rapid progress in camera quality and data transfer ́ ff rates in recent years, we predict that it will soon be possible to The notation Pe∥,z=0 indicates the Peclet number for di usion greatly improve the uncertainties of the sizing technique with parallel to the surface at a height of z = 0, i.e., right on the low-cost equipment. surface (note that this is for illustrative purposes only; this The x-direction analysis gives results that are physically model is a limiting case of the optical and hydrodynamic effects sensible and consistent with the manufacturer’s specification for that does not account for additional surface interactions). It is these particles. However, the analysis technique is highly interesting to note that this expression is very strongly dependent on the specific balance of forces in this physical dependent on the particle radius (R7). As the particle size system and is therefore limited to only a narrow regime of decreases, the relative effect of the diffusion on the x-direction particles. The upper bound on the size is determined by transport will become much more significant, undergoing a transitions to a regime of different optical physics, while the rapid transition from the regime studied here to a regime where lower bound on size is determined by a transition to a regime diffusion along the x-direction is prominent. This sets an where the particle motion is no longer defined by bulk effective lower bound on the size of particles that can be ϵ transport at constant velocity. measured, which will also be a function of particle material ( p) ́ The upper bound on the particle size for the x-direction and applied power (I). In an intermediate Peclet number ≈ measurements is determined by the optical physics of the Mie regime (Pe 1), it may be possible to determine an average regime. In deriving eq 6, the Rayleigh approximation was used. transport velocity and use this for one analysis as well as fl While the particles studied here are not strictly within the looking at uctuations from that average to perform a typically considered bounds of the Rayleigh regime (2πR/λ ≪ decoupled analysis of what should be the hydrodynamically ff 1), the simplified expressions derived using this approximation hindered di usion in the absence of a potential well (as there is are still illustrative of their behavior, as they are not large no optical gradient in the x-direction). This measurement is enough to experience morphology-dependent resonances and potentially interesting, as in this regime a much lower sampling other Mie regime complications.43,44 There is also recent frequency could yield accurate results. Measurements made in 45 this way should in principle be similar to those made using experimental evidence observing Rayleigh regime physics on ́ polystyrene spheres with 2πR/λ ≈ 1, similar to the borderline NTA. However, due to the very sharp transition in Peclet number with size, the range of sizes this will work for is very cases discussed here. However, as we extend further into the ́ ff Mie regime, the size dependences of the forces change, and in narrow. For low Peclet number particles, the free di usion in fact the horizontal optical forces are no longer even completely the x-direction may yield more accurate sizing than the y- direction approach used in this paper; however the sensitive monotonic in size. This is illustrated qualitatively in the polydispersity information will be lost. Supporting Information (Figure S3). As a result, we do not Effectively, based on this physics, we expect this technique to envision this technique being applicable to particles with be useful for dielectric particles roughly in the size range from diameters larger than about 1 μm. That being said, sub-1-μm 250 to 1000 nm in diameter. While there are many applications particles are of interest in many application areas, and we that rely on nanoparticles with smaller diameters, this envision the future use of this technique in characterizing measurement does fill an important niche. Specifically, this smaller particles than the ones studied here, where the size range matches very well with the so-called “subvisible inaccuracies caused by using the Rayleigh approximation will measurement gap” noted by researchers investigating the sizes be smaller. There has also been some analytic progress in of aggregate particles in suspensions of protein therapeutics.48 computing the full Mie solutions for the light scattered by 46,47 We therefore envision a possible application of this technique particles under evanescent excitation. More detailed to simultaneously measuring the sizes, polydispersity, and analysis based on this theory is a potential area for future surface interactions of these types of particles for quality investigation. assurance purposes. A key physical limitation on the x-direction mechanics is that In the z-direction, the data show relatively high potential it relies on the net transport of the nanoparticles. As this energy barriers, preventing surface sticking, and remarkably ff technique is applied to smaller particles, the di usive motion in consistent surface interaction energy profiles among particles of the x-direction can begin to become important. The analysis the same population. This provides a key piece of insight presented in Figure 3 depends on the particle having a well- missing from many particle size characterization techniques, as fi ’ de ned terminal velocity. This will happen when the particle s a very different interaction profile for a particle of the same size transport velocity is much greater than its diffusion, in other would indicate the presence of a secondary particle population, words, when the particle’sPeclet́ number is much greater than possibly an impurity or contaminant within the sample. As 1. Where we have a large (≫1) Peclet́ number, the motion is these measurements are brought up from an individual particle characterized by bulk transport at a terminal velocity, and the basis, the interaction energy curve of any single particle is analysis presented here makes sense. For low Peclet́ numbers, available in addition to the diffusive and convective transport the diffusion becomes significant and the particle’s velocity will data for that same particle. This can help in figuring out what is fluctuate. Near to the wall, however, the diffusion is hindered happening with any possible outliers in a sample. We envision and the bulk expression for the Peclet́ number is also altered. If further implementations of this technique playing a role in 1 we consider the limiting case where D approaches /3Dbulk (i.e., quality assurance applications. a particle very near the surface, see eq 5), we can define a Peclet́ Here, we have demonstrated the principle of making number for transport along the surface of the waveguide using orthogonal measurements to gain enhanced information the terminal velocity from eq 8: about nanoparticle suspensions by tracking the motion of the

111 DOI: 10.1021/acsphotonics.6b00628 ACS Photonics 2017, 4, 106−113 ACS Photonics Article nanoparticle in three spatial dimensions. We have performed ■ ASSOCIATED CONTENT proof of concept experiments on model nanoparticle *S Supporting Information suspensions and obtained results that are physically consistent The Supporting Information is available free of charge on the and in line with expectations. Our measurements in the x- ACS Publications website at DOI: 10.1021/acsphoto- direction based on the variation in the optical transport velocity nics.6b00628. between different members of a population give results consist with the manufacturer’s specifications, although this technique Additional details illustrating the longer time evolution of is unfortunately limited to particles where the optical velocity the y-position variance and characterizing the noise in the dominates the Brownian motion in the x-direction. Measuring experimental system, uncertainties in the z-direction the y-direction hydrodynamically hindered diffusion shows that measurements, and more details about the optical model particles of different sizes can be distinguished, although used here (PDF) absolute size determination remains inaccurate. Simultaneous Video animation of Figure 1 (ZIP) tothesemeasurementswehavealsomappedoutthe interaction energy landscapes for these particles. The pilot ■ AUTHOR INFORMATION scale demonstrations reported here pave the way for future Corresponding Author studies to extend these techniques to a wider size range of *E-mail (D. Erickson): [email protected]. particles and further validate these techniques on larger sample ORCID sizes with polydisperse inputs. This technique can be used both Perry Schein: 0000-0001-8768-4000 to gain quantitative information about nanoparticle populations Author Contributions and to identify outlying particles in terms of size or chemical § ’ composition and identify the role that these play in suspension P. Schein and D. O Dell contributed equally to this work. stability. Notes The authors declare the following competing financial ■ METHODS interest(s): DE declares an equity interest in Optofluidics, Inc., manufacturer of the NanoTweezer apparatus used in the Nanoparticle Suspensions. The particles used in the experiments here. experiments were Fluoro-Max (Thermo Scientific R500, lot no. 42116) with a nominal diameter of 520 nm and NIST traceable ■ ACKNOWLEDGMENTS certified mean diameter polystyrene spheres (Thermo Scientific 3800-05, lot no. 44639) with a diameter of 799 ± 9 nm with a This work was supported by the United States National coefficient of variation of 0.6% certified by TEM measurement. Institutes of Health through grant 1R01GM106420-01. Experi- Particle concentrations of 0.002% and 0.0015% solid fraction, ments were performed in the Nanobiotechnology Center respectively, were used. Particles were suspended in a solution shared research facilities at Cornell. λ of 0.237 mM KCl to create a Debye screening length, D =20 nm. ■ REFERENCES Optical and Fluidic Measurement System. These (1) Saha, K.; Agasti, S. S.; Kim, C.; Li, X.; Rotello, V. M. Gold Nanoparticles in Chemical and Biological Sensing. Chem. Rev. 2012, experiments used the NanoTweezer system and chips − (Optofluidics Inc., Philadelphia, PA, USA). Light was coupled 112, 2739 2779. into the chips from the system’s integrated 1064 nm laser. The (2) Ghosh, P.; Han, G.; De, M.; Kim, C. K.; Rotello, V. M. Gold nanoparticles in delivery applications. Adv. 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113 DOI: 10.1021/acsphotonics.6b00628 ACS Photonics 2017, 4, 106−113