Nanofiber-Based Total Internal Reflection Microscopy for

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C: Physical Processes in Nanomaterials and Nanostructures

Nanofiber-Based Total Internal Reflection Microscopy for Characterizing Colloidal Systems at the Microscale Joshua Villanueva, Qian Huang, Nicholas O Fischer, Gaurav Arya, and Donald J Sirbuly J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b03167 • Publication Date (Web): 04 Sep 2018 Downloaded from http://pubs.acs.org on September 5, 2018

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The Journal of Physical Chemistry

Nanofiber-Based Total Internal Reflection Microscopy for Characterizing Colloidal Systems at the Microscale Joshua T. Villanuevaa, Qian Huanga, Nicholas O. Fischerb, Gaurav Aryaa1, and Donald J. Sirbuly*ac2 a

Department of NanoEngineering, University of California, San Diego, La Jolla, California 92093, USA

b

Physical and Life Sciences Directorate, Lawrence Livermore National Laboratory, Livermore, California 94550, USA c

Materials Science and Engineering, University of California, San Diego, La Jolla, California 92093, USA

1

Current address: Department of Mechanical Engineering & Materials Science, Duke University, 144 Hudson Hall, Box 90300, Durham, North Carolina 27708 2 Corresponding author: [email protected], (858) 822-4143

ACS Paragon Plus Environment

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ABSTRACT

Bulk colloidal interactions are dictated by the physical properties of individual particles dispersed in solution. However, for many applications it remains challenging to predict systemlevel colloidal behavior. Comprehensive characterization typically requires disparate techniques that can observe correlations between microscale particle-surface interactions and physical particle properties. In this work we present a unique tin dioxide (SnO2) nanofiber-based total internal reflection microscopy (TIRM) method to efficiently characterize colloidal behavior as a function of particle-level properties in complex fluidic conditions. We develop and model the device physics to understand the physical underpinnings of the raw device data, and then use these models to design proof-of-concept experiments to verify device function. Statistical trends in the data collected from a nominal system of 80 nm gold nanoparticles correspond to theoretical predictions as we vary key design parameters such as particle size, surface charge, and solution ionic strength. Lastly we consider the practical limitations of the technique gleaned from our studies and offer suggestions for utilizing the platform to quantitatively analyze nonideal colloidal systems with distributed or heterogeneous system parameters.


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INTRODUCTION A number of different industries leverage colloidal nanoparticle systems for various applications.1,2 The broad utility of nanoparticles is a result of their capacity to be chemically and physically tuned, which makes these systems amenable to bottom-up functional design. Particles can be designed with respect to properties such as size and surface charge, which influence how particles interact with each other and with their environment.3–5 Such particle interactions underlie bulk colloidal behavior and ultimately determine system-level functions. However, despite the versatility of these systems, the inherent challenges of synthesizing particles with specific properties (e.g., narrow size distributions, uniform surface charge densities, etc.), and non-ideal solvents, results in colloidal systems with complex behavior that is difficult to characterize and predict.6-11 Therefore, the development of accurate and versatile nanoparticle characterization methods is crucial for manufacturing robust and reproducible nanoparticle-based products. Several techniques have been developed to characterize nanoparticle properties and interactions. Three common methods are dynamic light scattering (DLS), atomic force microscopy (AFM), and optical traps. DLS quantifies average particle size by optically measuring the diffusion coefficient of the particles in the sample.12,13 In the same setup, the zeta potential can be obtained by applying an electric field across the sample and measuring the electrophoretic mobility of the particles.14 AFM and optical traps can characterize particlesurface and particle-particle interactions by mapping out the force profiles as a function of separation distance.15–19 AFM leverages the mechanical response of a flexible cantilever, whereas optical traps use the stiffness of the trapping potential in a highly focused laser beam as force feedback. While each technique has its distinct advantages, none are without limitations.


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For example, while DLS setups are relatively simple and can analyze entire samples, accurate characterization requires careful sample preparation. Data interpretation can also be confounded by nanoparticle aggregation, multiple scattering effects, and scattering from the enviornment.20,21 AFM and optical traps offer high resolution measurements on individual particles, but they are traditionally low-throughput techniques, which makes accurate sample-level (i.e., large statistical data sets) characterization difficult and inefficient.22,23 Because of these technique limitations, new approaches to nanoparticle characterization continue to be explored to meet the demands of nanoparticle-based industries. Total internal reflection microscopy (TIRM) is a promising alternative method being developed that combines the high-throughput, multi-particle analytical capabilities of DLS with the ability to probe individual particle-surface interactions like AFM and optical traps.24,25 TIRM characterizes the solution-average interaction between a sample and a surface by accumulating individual particle-surface distance measurements to map out the probability density function (PDF) of the system. This measured PDF can be converted to a system-averaged potential energy profile and used to get the average particle size and surface charge by model fitting.26 Traditional TIRM setups use a flat, planar substrate with an evanescent field that extends into the bottom of a sample volume.27 The evanescent field occurs as a result of the total internal reflection (TIR) of a laser beam directed at the interface between the high refractive index substrate and the low refractive index sample solution. As particles diffuse near the substrate, they scatter evanescent light with intensity related to their proximity to the surface. A calibrated distance-scattering relation facilitates subwavelength particle-surface distance measurements.28– 30

In this traditional TIRM setup, particles typically sample the space above the substrate

according to the balance of gravitational and electrostatic forces acting on them.26 To further


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explore the versatility of the TIRM method, we investigate the use of an optical nanofiber geometry to support a more compact and portable evanescent field that can be placed anywhere in the sample volume. A nanofiber-based TIRM would lend itself to higher sampling densities (i.e., larger sensing surface area) in confined environments that are difficult to access with planar TIRM optics. EXPERIMENTAL AND THEORETICAL METHODS Using a nanofiber’s evanescent field to measure sub-micron distances via optical scattering is fundamentally similar to the planar TIRM case. However, since the evanescent field decays normal to the index-mismatched interface, a nanofiber allows for all-around sensing where particle scattering occurs anywhere in the sample volume surrounding the fiber (typically within 200 nm of the fiber surface). As such, the nanofiber TIRM geometry probes potential profiles whose shape depends on a particle’s location around the fiber. This subtle difference changes how the intensity data must be interpreted and related to distances. It will be shown that the usual form of the intensity-distance relationship used in planar TIRM data analysis has limited applicability for the nanofiber case and another intensity-distance relation must be used. Consequently, in the new relation the exposure time will prove to be an important experimental parameter. To examine the feasibility of using a nanofiber TIRM system for nanoparticle characterization, we first establish a simple device model to aid in data interpretation. Next the model is validated by comparing experimental data to theoretical trends predicted for sweeps of various system parameters. We then use the model to form a mechanistic understanding of why the nanofiber TIRM data differs from planar TIRM data. Lastly, we consider the practical limitations of the nanofiber-based approach and discuss potential future improvements.


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System Description The active element in our fiber-based TIRM platform is a single-crystalline tin dioxide (SnO2) nanofiber optical waveguide, which is suspended across an etched channel in a silicon oxide (SiOx) substrate (Figure 1). Typical fiber dimensions are around 200 x 400 nm in cross section and 200-300 μm in length. The fibers are chemically robust and highly flexible, exhibiting excellent waveguiding properties in water with a core refractive index of 2.1.31 An evanescent field is generated around the nanofiber because waveguiding relies on TIR.32 Light is coupled into the optical cavity via free-space excitation of the SnO2 material by focusing a 325 nm line of a continuous-wave helium-cadmium (HeCd) laser (10 mW power at the focusing lens) to a roughly 20 μm spot over the nanofiber end facet. The laser excites the SnO2 above its band gap (3.6 eV) and subsequent sub-bandgap defect (oxygen vacancies) emission in the SnO2 crystal generates broad-spectrum light in the visible range, which is guided down the nanofiber.33


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Figure 1. The nanofiber-based total internal reflection microscopy platform. The experimental setup shown at different scales. The assembled device under the microscope objective (left), the suspended fiber geometry (middle), and the TIRM mechanism relating scattering intensity, IS, with distance, d (right).

Signal Generation Model The relevant system physics considered here are highlighted in Figure 2. For our proof-ofconcept studies we focus on freely diffusing charged particle systems in well-controlled buffer environments. Here we assume the particle-surface interactions are dominated by repulsive, electrostatic interactions, which simplifies our model development. Estimates for the strength of van der Waals (vdW) forces between the nanoparticles and waveguide indicate that the vdW interactions are weak compared to electrostatic interactions (see Figure S5, Supplemental Information). As nanoparticles diffuse near the nanofiber surface, they are repelled by the electrostatic interaction of their charged surfaces, which is mediated by an electric double layer (EDL). In this work, we utilized the interacting EDL model formulated by Ståhlberg34 where the linearized Poisson-Boltzmann equation was solved for the potential distribution 𝛹(𝑑) between


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two charged, flat surfaces in an electrolyte solution. The interaction potential energy 𝑈

was

calculated from 𝛹(𝑑), and applying the Derjaguin approximation yielded an expression for 𝑈 between a sphere and an infinite flat wall: 𝑈

=−

(𝜎

+𝜎

) 𝑙𝑛(1 − 𝑒

) + (𝜎

−𝜎

) 𝑙𝑛(1 + 𝑒

)

(1)

where 𝑅 is the sphere radius, 𝜺 is the relative permittivity of the surrounding medium (here we used the value for water), 𝜀 is the permittivity of free space, 𝜅 is the inverse of the Debye length, 𝜎

and 𝜎

are the surface charge densities of the sphere and flat wall, respectively, and

𝑑 is the surface-to-surface distance between the sphere and wall. Given that our particle sizes are on the order of 80 nm and the fiber widths are on the order of 200 to 400 nm, our use of eq. 1 derived for a sphere interacting with an infinite plane is a reasonable assumption.

Figure 2. Relevant physics associated with the nanofiber-TIRM platform. Waveguide and scattering theory explain the TIRM mechanism. Electrostatic interactions between Brownian particles and the SnO2 nanofiber relate measured distances to particle and solution properties. Collection dynamics describe how the raw data is generated.

As mentioned previously, in the planar TIRM case the total particle potential energy includes a gravity component towards the TIR substrate. The gravitational force opposes the electrostatic


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repulsion of the particles away from the planar TIR substrate. This results in an energeticallyfavored equilibrium height above the substrate corresponding to a minimum in the total potential energy profile. The position dependence of the potential energy profile for the nanofiber comes from the fact that the gravitational force must be projected onto the surface-normal direction. However, since the scattering from many particles is accumulated during an experimental run, the mapped out PDF arises from a potential profile averaged over all particle locations around the fiber. In our case, differences in the potential profiles due to gravity are negligible and furthermore cancel out, assuming a symmetric fiber cross-section and a uniform electrostatic potential around the fiber. It is then reasonable to describe the average particle-surface interaction using the purely electrostatic potential energy in eq 1. Distance PDFs can then be predicted as a function of system variables by using eq 1 in the expression for the Boltzmann distribution, 𝑃 ∝ exp(−𝑈

⁄𝑘 𝑇).

TIRM data are related to these interaction models by converting the measured scattering intensities to distances. In traditional planar TIRM, scattering intensity converts to nanoparticlesubstrate distance using a calibrated intensity-distance relationship typically described by a decaying exponential35 𝐼 = 𝐼 exp

(2)

where 𝐼 is the collected particle scattering intensity at a distance 𝑑 from the nanofiber, 𝐼 is the scattering intensity at contact, and 𝜏 is the decay constant. While the determining 𝐼 and 𝜏 is nontrivial,28–30 once obtained the intensity is readily converted to distance via a simple one-to-one correspondence. However, using eq 2 for the nanofiber data results in experimental PDFs that do not agree with those predicted from theory. We suspect that this is because the form of eq 2 is not appropriate for the nanofiber system because it is a static equation whereas the particles


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freely diffuse around the fiber. Due to the finite exposure times used to collect the scattering data, we cannot assume a one-to-one intensity-distance correspondence as implied by eq 2. Instead we must develop a new model to understand the dynamics of the signal generation process as scattered light is accumulated on the electron-multiplying CCD (EMCCD) detector. As particles diffuse near the fiber they scatter light proportional to an exponential decay, but the distance to the fiber at any given time is stochastic due to Brownian motion. The instantaneous scattering of the particle is thus also stochastic, and it is this signal that is accumulated on the EMCCD to form a single scattering image. Therefore, measured scattering intensities actually represent particle trajectories rather than particle positions. Figure 3 schematically depicts this idea. Mathematically, the signal generation can be expressed as an integral over a stochastic variable: 𝐼 =

𝐴 𝑒𝑥𝑝

( )

𝑑𝑡

where 𝐼 is now the total intensity integrated over the exposure time 𝑡

(3) , 𝐴 is the instantaneous

scattering intensity at contact, 𝑑(𝑡) is the instantaneous distance for a stochastic particle trajectory, and 𝜏 is the same decay constant as in eq 2. The similarity between eqs 2 and 3 should be noted. In fact, eq 2 can be derived from eq 3 when the particle-fiber distance is constant, in which case the integral can be evaluated and 𝐼 = 𝐴𝑡

.


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Figure 3. Varying instantaneous scattering of a diffusing Brownian nanoparticle during a 5 ms exposure time. A single quantified scattering event imaged by an EMCCD in the far-field is obtained by integrating the intensities plotted by the black line over the exposure time, here 5 ms. The intensities change as the particle randomly diffuses near the nanofiber surface according to eq 2 and shown here as the exponentially decaying surface. This intensity represents the nanoparticle’s trajectory, rather than a single position. The color of the slope indicates intensity, with low intensities more red and high intensities more yellow.

In order to relate experimental TIRM data to the EDL models, the measured intensities still need to be converted to distances, but this is not possible with eq 3 because the stochastic integral cannot be reduced to a simple analytical form. Therefore, we simulate the random particle motion around the waveguide to obtain theoretical predictions for the distribution of scattering intensities, rather than using the distance PDF. The motion of the particles is expected to be largely independent of each other based on their dilute concentration in the solution (mean particle separation is much larger than particle size) and mutually repulsive electrostatic interactions (particles rarely come into close proximity). Such motion was modeled using


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Brownian dynamics (BD) simulations, which calculates in an iterative manner the random path taken by a colloidal particle using the overdamped Langevin equation36 𝒓(𝑡 + 𝛥𝑡) = 𝒓(𝑡) +

∆𝑡 + 𝜁(𝑡),

(4)

where the particle position 𝒓(𝑡 + 𝛥𝑡) at time 𝑡 + 𝛥𝑡 (where 𝛥𝑡 is the simulation time step) is predicted from the particle’s current positon 𝒓(𝑡), its displacement −𝛻𝑈

⁄𝛾 ∆𝑡 due to the

electrostatic force, and its stochastic displacement 𝜁(𝑡) due to thermal fluctuations. We neglected hydrodynamic interactions in eq. 4 based on the rationale that the particles rarely come into close proximity with the surface as a result of their strong electrostatic repulsion (see Figures S6-S8, Supplemental Information). The electrostatic displacement is calculated from the drag velocity obtained as the negative spatial gradient of the potential energy 𝑈

in eq 1 normalized by the

viscous drag 𝛾 equal to 6𝜋𝜇𝑅 for spherical particles, where 𝜇 is the solution viscosity and 𝑅 is the radius. The stochastic motion of the particle, 𝜁(𝑡), is modeled as Gaussian white noise, uncorrelated in time, with zero mean and standard deviation equal to the mean squared displacement (MSD) of a spherical particle expected during the simulation time step 𝛥𝑡 (𝑀𝑆𝐷 = √2𝐷𝛥𝑡 where the diffusivity 𝐷 equals 𝑘 𝑇/γ, and 𝑘 𝑇 is the system thermal energy; 𝑘 is the Boltzmann constant and 𝑇 is the system temperature). Equation 4 allows us to simulate the onedimensional stochastic trajectories of individual non-interacting particles moving in the electrostatic potential field described by eq 1. Substituting these trajectories into eq 3 then allows us to obtain individual scattering intensities observed over each exposure time 𝑡

as well as

distributions in scattering intensity measured experimentally using the nanofiber-TIRM method. See the next section for simulation details. Experiment and Simulation Description


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For device fabrication, the single-crystalline SnO2 nanofibers were synthesized in-house via a chemical vapor transport process using a standard benchtop tube furnace.31,37 To assemble the devices, synthesized fibers were positioned across microchannels etched into a SiOx substrate using a 3-axis micromanipulator equipped with a tungsten dissecting probe. Channels were approximately 50 μm wide and 20 μm deep and were fabricated using standard cleanroom processes. Fibers were secured in place with polydimethylsiloxane (PDMS), and after full assembly the device was cleaned in a three-part process using diluted piranha, aqua regia, and oxygen plasma. Sample preparation involved an exchange of the commercial nanoparticle buffer with deionized water (via centrifugation) before suspension of particles in PBS buffer. The prepared sample was contained in a volume over the fiber using a PDMS spacer with a cutout. To collect scattering data, the spacer holding the sample was covered with a thin glass coverslip. Far-field imaging was done using an upright, dark field microscope equipped with a 50x 0.55 N.A. air objective and EMCCD camera. This assembly was precisely positioned and focused under the microscope while concurrently focusing the laser beam on the fiber end facet to maximize the waveguide output intensity. The EMCCD was aligned with the fiber axis perpendicular to the pixel shift direction to operate in frame transfer mode. Video data was typically recorded with 5 or 10 ms exposure times with a gain of 200 at a frame rate of 190 Hz for a total of 160,000 frames unless otherwise stated. This corresponds to approximately 20 mins of data collection. Between runs, the device was disassembled, cleaned using the same three-part process described above, loaded with a new prepared sample, and realigned under the microscope objective, which took another 20-25 minutes. Videos were processed in MATLAB in three parts: signal detection, intensity quantification, and data filtering. Scattering event were detected using a one-dimensional peak finding


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algorithm with a dynamic threshold to localize scattering events in both space (pixel location) and time (video frame). Intensities were quantified as the raw pixel count value of the localized signals and normalized to the waveguide output signal in the corresponding frame. Normalization reduced signal variation due to fluctuations in waveguide coupling and differences in experimental setup between runs. Quantified intensities from the experiment were plotted in histograms with a bin size of 0.01 (arbitrary units of output-normalized intensity). A Gaussian cluster analysis was used to partition true detected signals from background noise and reduce Type 1 error in the final histograms. The evolution of various system parameters over time were also monitored to identify experimental instabilities (i.e. stage drift, flocculation, aggregation), which were accounted for in the data processing to prevent data skewing. The experimental results were compared to the results from 1D simulations of the experiment utilizing eqs 3 and 4 as described in the previous section. We simulated 500 independent particle trajectories for each experimental condition, assuming that the nanoparticle concentration is sufficiently low that the particles do not interact with each other. Each simulation is started from a random position of the particle (according to a uniform probability distribution) within 1 μm distance from the fiber surface; the fiber surface was placed at the coordinate x = 0 μm and a reflecting boundary condition was implemented at x = 1 μm. The simulation time step was taken to be 105 times smaller than the simulated exposure time (50 ns for the usual 5 ms exposure time) and each simulation was performed for a total of 5x106 time steps, resulting in 49 calculated scattering events per particle, or 24,500 scattering events comprising each simulated scatteringintensity histogram. Unless otherwise stated, particle sizes were uniform in the simulation and matched the nominal size in the experiments. The viscosity of the dispersion medium was assumed to be that of water (8.9x10-4 Pa∙s) and the system temperature was set to room


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temperature, 298 K. The scattering intensity of the particle was calculated for every time step of eq 4 using eq 2. We used the experimentally obtained value for 𝜏 determined using an AFM calibration method29 (34 nm) to calculate each scattering intensity. To evaluate eq 3, a Riemann sum was used to approximate the integral over the stochastic intensity signal for a given exposure time. All simulated intensities were normalized to the scattering of an 80 nm particle at contact to eliminate the need to define a value for 𝐴. While the normalization method for the experiment and simulation is different, it does not preclude examination of qualitative trends in the intensity distribution trends as a function of physical system parameters. Further explanations of the experimental procedure, data processing, and simulations can be found in the Supplemental Information. RESULTS AND DISCUSSION In the following proof-of-concept studies we performed single-variable parameter sweeps to characterize various gold nanoparticle systems. We examined particles of different sizes and different surface coatings in solutions of different ionic strength. The effect of exposure time on the TIRM signal was also investigated. Ionic Strength We studied intensity trends under different ionic solutions to validate eq 1 for approximating the interaction trends in our particle-fiber system. A nominal solution of commercially-available 80 nm citrate-coated (non-functionalized) gold nanoparticles was prepared and suspended in various dilutions of 1x PBS (162 mM ionic strength). We examined solutions ranging from 0.005x PBS to 0.1x PBS, which correspond to Debye lengths (𝜅

) from 10 nm to 2 nm and

ionic concentrations of 0.8 mM to 16 mM. The pH of the final solutions was approximately 7.4 (the pH of the PBS stock) for all experiments. The full list of corresponding Debye lengths and


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ionic strengths are shown in the Supplemental Information. For the citrate-coated 80 nm particles (collected at 𝑡

= 10 ms ) the effect of changing the ionic strength is shown in Figure 4a with

the simulated trends in Figure 4b.

Figure 4. (a) Experimental and (b) simulated intensity distribution trends for a batch-prepared 80 nm citrate-coated gold nanoparticle sample dispersed in solutions of varying PBS concentration and imaged with a 10 ms exposure time. Increasing the ionic concentration of the dispersing medium (here shown as a higher concentration of PBS) screens particle surface charges, resulting in an increase in the high-intensity edge of the distributions. The same general trend is reflected in the both experimental and simulated data. Differences in distribution shape and intensity value are due to the detection sensitivity of the experiment and the different normalization method used for the experimental and simulated datasets.

As expected, the distribution intensities (horizontal axes) are different due to the different intensity normalization factors; however, here we focus on the qualitative differences in the shape of the distribution. At high intensities the experimental and simulated distributions exhibit


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the same general trend as a function of 𝜅. The high intensity distribution edges for both plots are indicative of the salt-mediated EDL interactions. Higher salt concentrations screen the surface charges more effectively, allowing particles to get closer to the nanofiber on average. As a result, the distributions shift towards higher intensities as the solution ion concentration increases. At low intensities, the experimental and simulated distributions are different. Experimental distributions show a count drop off while simulations effectively go to infinity (not shown) as the intensity goes to zero. This difference is due to the detection sensitivity of the TIRM technique, which is not accounted for in the simulations. In the simulations all particle scattering is quantified regardless of distance because intensities are simply calculated from eq 3. Experimentally, however, particles far from the fiber cannot be detected, as they do not scatter enough light to be distinguished from the background noise in the processing algorithm. This sensitivity cutoff is present for all experimental data shown. The shape and position of the low intensity edge in the experimental distributions is determined by the factors that influence the scattering signal and its detection including waveguide coupling efficiency, background noise, focusing, and data filtering parameters. This means the location of the experimental distribution peak has no physical meaning, contrasting with traditional TIRM data where the histogram peaks indicate energy minima because the particles diffusing above the planar substrate typically stay within the limits of detection. The range of PBS concentrations examined here represents the limits of operation for this particular nanofiber and nanoparticle system. For ionic concentration lower than 0.005x PBS the nanoparticles are too far from the fiber to be detected. Between 0.005x PBS and 0.1x PBS, there is a low probability of particle attachment during the typical 20-minute experiment time, which allows for proper data collection. Since we are only concerned with behavior of freely diffusing


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particles, the scattering from any attached particles is ignored in the data processing unless otherwise stated. At PBS concentrations higher than 0.1x PBS the electrostatic repulsion is sufficiently screened such that particles have a high probability of attaching to the nanofiber surface during the 20 min data collection window, which obscures the scattering from other particles in solution. Surface Charge Density Surface functionalization represents a major design aspect in colloidal systems.38–40 Therefore we also tested our platform’s ability to distinguish between nanoparticles with different surface coatings. We compared the dataset for citrate-coated nanoparticles in 0.05x PBS from the previous study with new data for similarly-sized DNA-coated particles also in 0.05x PBS. The distribution for the citrate-coated particles from Figure 4a is replotted in Figure 5a along with the distribution from the DNA-coated particles (𝑡

= 10 ms ). Simulations corresponding to

these experiments are shown in Figure 5b where we used 0.012 Cm-2, 0.019 Cm-2, and 0.05 Cm-2 for 𝜎

, 𝜎

, and 𝜎

respectively (see Supplemental Information for details on

determining these values). Details of the DNA coating including particle synthesis and characterization were described previously.37


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Figure 5. (a) Experimental and (b) simulated intensity distribution trends for citrate- and DNA-coated 80 nm gold nanoparticles with different surface charge densities in 0.05x PBS and imaged with a 10 ms exposure time. The 0.05x PBS distribution from Figure 4a is replotted in black in (a) for comparison to a similarly sized, DNA-coated nanoparticle sample in 0.05x PBS. The addition of the DNA coating increases the average electrostatic interaction between the sample particles and the nanofiber surface. The DNA also presents a physical barrier that prevents the gold scattering center from getting as close to the nanofiber as the citrate-coated particles. Both effects may contribute to shifting the DNA-coated particle distribution to lower intensities. The difference in distribution shape for the experimental data is due to different particle concentrations between the two samples.

With DNA’s negative backbone and the strands’ covalent linkage to the gold particles, the DNA-coated nanoparticles are expected to have a more negative surface charge density and larger electrostatic potential than the (adsorbed) citrate coated particles.41,42 The higher potential pushes particles further away from the nanofiber resulting in a high intensity distribution edge shifted to smaller intensities. This is reflected in the experimental comparison. The large


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difference in peak heights in the experimental data is due to a difference in detection rate between the two systems. The DNA-coated particles were prepared as a separate sample with a particle concentration higher than the citrate-coated particle batch. Since the high intensity edge of the DNA-NP sample is lower than the citrate-NP distribution, rescaling would still show the DNA distribution shifted to smaller intensities than the citrate-NP distribution. The simulations isolated the electrostatic differences between the citrate and DNA-coated particles and show only a subtle shift in the distributions. This discrepancy from the experiments could be due to errors in the estimates of the surface charge, or there may be other unaccounted phenomena that are influencing the intensity distributions. Optical differences between the two particles should be negligible because the additional layer is expected to have an effective refractive index similar to the solution. Thus, the scattering cross section would not change significantly. Moreover, any refractive index change would likely result in a larger scattering cross section and a shift in the DNA particle distribution towards higher intensities, which is contradicted by the experiments. Other than electrostatic and optical system differences, it is also possible that the finite thickness of the DNA coating versus the citrate coating around the nominal 80 nm particles may provide a physical barrier (steric repulsion) preventing the particles from getting as close to the fiber as the citrate-coated particles. The gold scattering center of the DNA-coated particle could be surrounded by as much as an 8.5 nm thickness (25 base pairs, 3.4 Å per base pair), which would also result in a lower intensity distribution. A combination of both steric and electrostatic effects could be contributing to the distribution differences. Regardless it is clear that the nanofiber TIRM method is able to distinguish between similarly-size particles with different coatings in the same dispersing medium.


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Particle Size In addition to different particle coatings, particle size is also an important design parameter of colloidal nanoparticle systems.4,43,44 Varying nanoparticle size is expected to alter the electrostatic interactions of the system, the particle diffusivity, as well as the scattering crosssection. To accurately interpret the scattering signal from the experiments and properly simulate size-dependence of the measured signals, we need to first quantify the size dependence of the scattering rate 𝐴 from eq 3. To do this we examine the limiting case where a particle is stuck in contact with the nanofiber surface. This particle trajectory, 𝑑(𝑡), is equal to zero for all time and the integral simplifies to the linear expression: 𝐼 = 𝐴𝑡

+𝐵

(5)

where 𝐴 is the same scattering rate as in eq 3. We have added the offset 𝐵 to account for any background signal. Using eq 5, we can get an experimental value for the scattering rate by collecting the scattering intensity of attached particles as a function of varying exposure time and performing a linear regression. This exposure time analysis can then be used to obtain the value of 𝐴 for different particle sizes. In these experiments we perform an exposure time analysis of 4 different particle sizes (80 nm, 100 nm, 150 nm, and 200 nm citrate-coated nanoparticles in 0.1x PBS), which are shown in Figure 6. Solutions were left unperturbed in the experimental setup (>40 mins) until nanoparticles attached to the fiber by chance. After a few particles attached, 5000 video frames were collected at different exposure times without adjusting the experimental setup.


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Figure 6. Exposure time analysis of particles in contact with fiber surface as a function of particle size. Top Row: Blue data points show mean scattering from individual attached particles at various exposure times; all scattering data from a single particle are fit to linear trends shown in blue. Red data points represent the mean scattering of all particles collected at a given exposure time with the slope of red line equal to the estimated scattering rate, 𝐴, of the particles of a given nominal size. All data for each nanoparticle size was collected from a single experimental run. Bottom Row: The particle-averaged scattering rate, 𝐴, for each nanoparticle size on a log-log plot. Trends shown in blue correspond to different attached nanoparticles. Each data point represents the mean scattering intensity of a particle over the 5000 frames collected at a given


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exposure time with error bars indicating the standard deviation. Linear regressions were performed on scattering data from the same particle. The high linearity of the data (especially for the 80 nm particles) validates eq 5, but we see that the slopes also vary for different particles of the same nominal size. This variation can come from a number of different sources including size polydispersity and particle shape. This means several particles must be analyzed to get acceptable average values for 𝐴 and 𝐵. However, minimizing error due to particle heterogeneity requires many experimental runs to collect large datasets, but these multiple runs also introduce error from variations in the experimental setup. To avoid experimental setup error, we analyze only a single experimental run on a few attached particles to get a rough estimate of the sizedependence of the particle scattering for our proof-of-concept study. The mean scattering from all particles at given exposure time is plotted as the red data points with the error bars the standard deviation of the scattering from the different particles. The slope of the red line fit to the red data points is 𝐴, the instantaneous scattering rate of the particle at contact. 𝐴 is plotted as a function of particle size in the bottom plot in Figure 6 with the black error bars equal to the minimum and maximum slopes fit to the red data points including the corresponding red error bars. A general expression (assuming the same 34 nm scattering intensity decay for 𝜏) for the scattering rate as a function of particle size can be obtained by fitting a linear model to the loglog data in Figure 6: 𝐴 = 0.39(particle diameter)

.

(6)

This faster-than-linear trend makes sense compared to the experimentally derived relation for dielectric particles presented by Prieve and Walz.35 The scattering here is from the plasmonic particles, thus the size dependence of the scattering cross section should be stronger as compared to dielectric particles.


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With eq 6, we were able to account for the size-dependent scattering intensity of 80 nm, 100 nm, and 150 nm citrate-coated gold nanoparticle systems in the simulations for a more accurate comparison to experimental datasets. Since all simulated data is normalized to the scattering of an 80 nm particle at contact, each calculated intensity was simply scaled according to the trend in eq 6 relative to 𝐴(80 nm). We assumed the same surface charge density for all nanoparticles as they were all commercially purchased and stabilized in a citrate buffer. The results of the size experiments and the corresponding simulations (particles suspended in 0.1x PBS; 𝑡

=

5 ms ) are shown in Figure 7. As the particle size increases, the scattering intensity also increases, and there is good agreement between the experimental and simulated distributions when we account for the differences in scattering cross-section. If we only considered the electrostatic model described by eq 1 without regard for the size-dependent scattering, we would have expected the distributions to shift to lower intensities as a function of increasing particle size (that increases the particle-fiber electrostatic repulsion). It is evident from the data that understanding the optical properties of the examined nanoparticles is critically important for interpretation of the TIRM data. Only a select range of nanoparticle sizes were analyzed since there are size limitations for the nanofiber-TIRM setup. For example, gold particles larger than 150 nm begin to show a gravitational potential that creates faster flocculation. Additionally, the larger particles diffuse slower. These two phenomena result in a change in the detection rate statistics, which makes it much more difficult to collect large datasets. On the other hand, particles smaller than ~50 nm will scatter less evanescent light and also move much faster. These two effects lead to a lower signal-to-noise ratio for a given exposure time and therefore longer exposure times are needed to


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Figure 7. (a) Experimental and (a) simulated intensity distribution trends of citrate-coated gold nanoparticle samples with varying nominal particle size in 0.1x PBS and imaged with a 5 ms exposure time. Increasing particle size slightly increases the electrostatic interaction between particles and the nanofiber surface, which would imply decreasing intensity with particle size if particle scattering was consistent for all particle sizes. However, experimental trends show an increase in scattering intensity with particle size, indicating that scattering differences must be accounted for in the data. Simulated data shown here was corrected to account for differences in scattering cross-section for the different sized particles, which results in a trend that matches the experimental distributions. properly image the scattering events. The effect of altering the exposure time will be examined in the next section. Exposure Time From our understanding of the far-field imaging dynamics, individual scattering events represent random particle trajectories as modeled by eq 3. In general, longer exposure times mean larger trajectories are associated with the resulting scattering signal. Thus, the longer the


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exposure time, the larger the error is of mapping a measured scattering signal to a single nanoparticle position using eq 2. This mapping error will influence the accuracy of parameters estimated from distance distributions derived from the experimentally measured intensity distributions. To quantify this error, we investigated the effect of varying the exposure time during data collection for a solution of 80 nm citrate-coated gold nanoparticles in a 0.1x PBS solution. Without adjusting the physical setup between runs, we changed the camera settings to vary 𝑡

from 1.2 ms to 50 ms similar to the scattering rate experiments. Although, here were

are concerned with the transient scattering from freely diffusing particles instead of the scattering from attached particles. The resulting experimental distributions are shown in Figure 8a. Based on eq 3 we expect that the imaged scattering signal from a particle will generally increase with increasing 𝑡

because

more photons are being collected on the EMCCD sensor. However, the normalized intensity shows the intensity distributions shifting towards lower intensities as 𝑡

increases. This trend is

reasonable because the scattering signal from a freely-diffusing particle integrated on the EMCCD increases at a slower rate with 𝑡

than the integrated signal from a constant intensity

source (here the waveguide output). The experimental trend qualitatively matches the simulations shown in Figure 8b where the intensities were also normalized to a constant intensity source (a nanoparticle at contact). Since we know exactly the calibrated form of eq 2 that was used to generate the scattering intensities in Figure 8b (inset), we can use this to convert the simulated intensities back to a distance distribution according to standard TIRM data analysis methods. Figure 8c shows the theoretical distance distributions calculated from the data in Figure 8b using eq 2 with 𝐼 = 1 and 𝜏 = 34 nm. The converted distance distributions show a trend as a function of 𝑡

where the distribution is shifted to further distances as exposure time


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increases, and an accumulated population of particles begins to form and get larger. This is an interesting result because in the simulation (and experimentally) we did not change the physical properties of the system between exposure times, so there is no reason why the distance PDF should change as 𝑡

changes. This confirms the inherent error in mapping the trajectory-

generated scattering intensity to a single distance, and shows that this error increases with increasing 𝑡

(i.e. as the length of Brownian trajectory increases). As 𝑡

decreases, the

converted distance distributions approach the theoretically predicted distance distribution for the simulated system, shown as the dotted line in Figure 8c, which was calculated using the Boltzmann distribution and scaled to align with the other distributions at large distances. To examine the intensity-distance mapping error further, we can use the known trajectories calculated in the BD simulations to get a better idea of what particle positions are actually represented by the measured scattering signals. In Figure 9 we plot the trajectory means (colored data points) and standard deviations (grey lines span ±1 standard deviation) at the corresponding scattering intensity calculated from that trajectory. Equation 2 is shown as the black line for comparison. It can be seen that as the exposure time increases the trajectory means shift to distances further from the nominal curve and the standard deviation (gray lines) of the trajectory positions increases. This is consistent with diffusion-convection statistics described by the Fokker-Planck equation,45,46 and supports the idea that only at very short time scales is eq 2 appropriate for analyzing TIRM data. Thus, to minimize the mapping error, the exposure time must be as small as possible. However, reducing the exposure time poses challenges in practice because a finite exposure time is always necessary in any far-field imaging method. Enough photons must be collected by the sensor to generate a signal that can be distinguished from the background.


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Figure 8. Effect of exposure time on experimental and simulated distributions. (a) Experimentally measured and quantified scattering from 80 nm citrate-coated gold nanoparticles in 0.1x PBS collected at varying exposure times, normalized to the waveguide output. (b) BD simulation of the experiment, normalized to the scattering of stationary particle at contact. The inset shows the intensity-distance calibration curve described in eq 1 with a decay constant of 34 nm and contact scattering of 1. (c) Theoretical distance PDFs obtained from calculating the distance values from the simulated intensities in (b) using the calibration curve shown in the inset. The theoretical distance distribution for the system is shown as the dotted line (corresponding to intensity data collected with 0 ms exposure time) scaled so the flat portion of the theoretical PDF coincides with the flat portion of the simulated PDFs.


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Figure 9. Intensity-trajectory relationship obtained from BD simulations. Simulated particle trajectories plotted at calculated intensities for different exposure times. Colored data points are the mean position of each trajectory; gray lines span the position standard deviation in each trajectory. Equation 3 is plotted for comparison (𝐼 = 1 and 𝜏 = 34 nm).


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Considerations for Practical Implementation The main limiting factor for collecting TIRM data of freely-diffusing systems is maintaining a state where the sample particles diffuse near the nanofiber surface without attaching to its surface or falling out of solution. To achieve this, a balance must be struck between particle size, particle and fiber surface charges, and solution ionic strength. These considerations suggest that the parametric sweep analysis similar to the one presented here is an integral component of the characterization process using the nanofiber TIRM approach. The possibility of using the nanofiber-TIRM platform for backing out real, quantitative parameters of a colloidal system requires optimizing the exposure time for each set of experiments. A small exposure time is desired to minimize the mapping error, but it must also be long enough to maintain an appropriate signal-to-noise ratio in the imaged scattering events. If this can be achieved, the measured intensities can be more accurately related to single distances, and the distance PDFs generated from the scattering data may be sufficient to estimate the colloidal model parameters. Alternatively, the dynamics of the system could be slowed down by increasing the viscosity of the dispersing medium, although such changes will require reevaluation of the new system within the context of the final application of the nanoparticles. Future efforts will also focus on deriving an analytical form of eq 3 that accounts for the particle dynamics in the intensity to distance mapping. In exploring these errors associated with the nanofiber TIRM method, we also question why these considerations have not been considered previously in traditional TIRM measurements. This distance mapping error is specifically related to the fact we are taking non-equilibrium measurements of multiple particles using the nanofiber architecture as opposed to the equilibrium measurement of a single particle collected using planar TIRM methods. The main


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difference between the two types of measurements is in the form of the stochastic nanoparticle trajectories. In traditional TIRM with the additional gravitational term that opposes the electrostatic repulsion between particles and a surface, the particles are trapped in a potential well above the planar substrate. The stochastic trajectory then samples a space about an equilibrium height above the substrate. However, in the nanofiber case, the repulsive particlewaveguide system does not offer a concave energy landscape that can trap the particles (bound system), but rather the landscape exhibits no minima, leading to an open system. This is a subtle difference between these two different types of TIRM. Particle diffusion in traditional TIRM can be described as a mean-reverting random walk (or Ornstein-Uhlenbeck process) whereas for the nanofiber TIRM, particle diffusion is better described by a biased random walk (or Wiener process).46 In the former case, the energy minimum anchors the nanoparticle trajectories, thus changes in 𝑡

primarily contribute to mapping errors associated with the stationary particle

diffusion about a defined equilibrium position. With enough distance measurements, the true PDF (with its peak corresponding to the location of the energy minimum) should still be obtained using eq 2. However, in the nanofiber case, no such energy minimum exists and therefore the changes in 𝑡

result in mapping errors from both diffusion and drift due to the

electrostatic interaction. The drift mapping error cannot be easily corrected or accounted for without knowing the electrostatic properties of the system a priori, which motivates further work on developing an analytical form of the intensity-distance relationship that can account for the particle dynamics. In order to push the capabilities of the nanofiber TIRM approach, the particle-fiber interaction models may also need further improvement. Beyond the intensity-distance conversion, there are errors associated with the accuracy of eq 1. For example, for our proof-of-concept we modeled


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the interaction between a charged sphere and a charged, infinite flat wall. We expect that this model overestimates the interaction potential because it does not consider the finite dimensions of the nanofiber. Additionally, in this work the nanoparticles were modeled as hard spheres with uniform surface coatings. While we assumed that the large datasets collected in these experiments averaged out particle asymmetries and heterogeneity in the sample, analysis of more complex nanoparticle samples could require revising aspects of the simple physical model presented here. We also do not consider the possible spatial dependence of the diffusion coefficient as these particles diffuse near the nanofiber, which may affect the imaging dynamics. The accuracy of any quantitative measurements obtained from this technique will have to discuss the implications of all these approximations to truly present a complete characterization of a novel colloidal system. However, despite the approximations used in this current work, we have highlighted the most important physical aspects of the nanofiber TIRM system. Using simple models we were able to form a mechanistic understanding of how changes in the properties of the nanoscale systems under investigation will manifest themselves in the optical signals obtained from this novel approach. With this foundation, we were able to showcase the qualitative trends expected when using this platform to characterize a diverse set of colloidal samples. CONCLUSIONS Here we present a novel nanofiber-based TIRM platform for characterizing colloidal systems. The limitations of our nanofiber-TIRM approach are outweighed by the added capabilities of the nanofiber platform over previously established techniques. The TIRM approach combines the benefits of both single-particle and solution-level characterization methods. These include: 1) the ability to make high-throughput measurements of particle-surface interactions (e.g., > 2000


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measurements in about 20 minutes) without having to change the experimental setup, and 2) the ability to accumulate colloidal interactions with a surface, and characterize solution-average properties of the system, without susceptibility to distribution skewing from small populations of more strongly scattering contaminants in the solution. Additionally, using a nanofiber probe expands the versatility of the traditional planar TIRM substrate, allowing for localized measurements anywhere in a sample volume. The analysis presented here leverages both a theoretical and experimental treatment of the characterization problem in an iterative manner which we believe is the ideal way of studying these types of nanoscale systems. Future work will focus on developing more detailed physical models that will allow quantitative characterization and prediction of a wide variety of colloidal systems. ASSOCIATED CONTENT Supporting Information. Detailed descriptions of the experimental methods, data processing, and calculations for simulations. (PDF) ACKNOWLEDGMENT The authors would like to acknowledge financial support from the National Science Foundation (ECCS 1150952) and the University of California, Office of the President (UC-LFRP 12-LR238415).


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