Microscopic Movement of Slow-Diffusing Nanoparticles in Cylindrical

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Microscopic Movement of Slow Diffusing Nanoparticles in Cylindrical Nanopores Studied with Three-Dimension Tracking Luyang Zhao, Yaning Zhong, Yanli Wei, Nathalia Ortiz, Fang Chen, and Gufeng Wang Anal. Chem., Just Accepted Manuscript • DOI: 10.1021/acs.analchem.5b04944 • Publication Date (Web): 12 Apr 2016 Downloaded from http://pubs.acs.org on April 20, 2016

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Analytical Chemistry

Microscopic Movement of Slow Diffusing Nanoparticles in Cylindrical Nanopores Studied with Three-Dimension Tracking Submitted to Anal. Chem. for publication Luyang Zhao, Yaning Zhong, Yanli Wei, Nathalia Ortiz, Fang Chen, and Gufeng Wang* Chemistry Department, North Carolina State University, Raleigh, NC 27695 *Corresponding Author: Gufeng Wang, email: [email protected] Chemistry Department, North Carolina State University, Raleigh, NC 27695

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ABSTRACT: To study the slow mass transport in confined environments, we developed threedimension (3D) single particle localization technique to track their microscopic movements in cylindrical nanopores. Under two model conditions: (1) increased solvent viscosity, which slows down the particle throughout the whole pore, and (2) increased pore wall affinity, which slows down the particle only at the wall, particles are retained much longer inside the pores. In viscous solvents, the particle steps decrease proportionally to the increment of the viscosity, leading to the macroscopically slow diffusion. As a contrast, the particles in sticky pores are microscopically active by showing limited reduction of the step sizes. A restricted diffusion mode, possibly caused by the heterogeneous environment in sticky pores, is the main reason for the macroscopically slow diffusion. This study shows that it is possible to differentiate slow diffusion in confined environments caused by different mechanisms. Keywords: 3D particle tracking, confined diffusion, cylindrical nanopores, correlation coefficient mapping, liquid/solid interfaces


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Understanding mass transport in confined environments such as nanopores, planar micro- to nanochannels, and cytoplasm is an important step for many advanced applications such as separations,1-5 micro- to nanofabricated tools,1,6 controlled drug releases,6,7 enzymatic reactions,8,9 and other biological processes. We are particularly interested in objects with a size of tens to hundreds of nanometers, which covers the size range of biomolecules, viral particles, small bacteria, and some cell organs. Mass transport of these nano-objects in a confined space with similar sizes in one or more dimensions can be significantly different from those in the bulk solution. A reduction of diffusion coefficient (D) is usually reported in the literature but the extent of the observed slowing down varies hugely. Different mechanisms have been proposed to explain the slow mass transport. For example, Durand et al. found that the effective diffusion coefficient of a protein (38 kDa) in 50 nm high nanochannels were four orders of magnitude smaller than that in bulk solutions.10 This was explained by dynamic adsorption and desorption of molecules on glass channel surface. Similarly, Pappaert et al. measured the diffusion coefficient of DNA molecules in one dimensional micro- and nanochannels; more than 30% decrease of the D was observed when the channel size dropped to 260 nm.11 Ma et al. studied protein molecules in unmodified and polyethylene glycol (PEG)-passivated anodisc alumina oxide (AAO) membrane filters with cylindrical pores and found orders of magnitude slowing down of the protein molecules.12,13 They concluded that in addition to adsorption, there must be other factors, e.g., anomalously large viscosity of the solvent near the pore wall, contributing to the slowing down. Han et al. studied the electromigration and diffusion of polystyrene nanoparticles in AAO membranes.14 They found that both the electromigration and passive diffusion of the particles slowed down by ~20 times and ascribed them to the microenvironment difference in nanopores. Kaji et al. observed a three-time slowing down of 50 nm carboxylated polystyrene beads diffusing in 400 nm-height channels, which was ascribed to the unusual viscosity due to the confinement.15 Eichmann et al. studied the diffusion of 50 nm gold nanoparticles in 350 nm-height channels. Observed lateral diffusion coefficient was 50% smaller than the predicted value, which was explained by hydrodynamic interactions and electroviscous effect due to the overlap between the electrostatic double layers around the particle and the wall surfaces.16 The observed discrepancies may be caused by many factors: the size of the confinement, the materials of the pores and the particles/molecules, the solvent being used, and the detection techniques, etc. Note that some of the proposed mechanisms, e.g., increased viscosity of solvents in a pore large than several nanometers, has been under debate for a long time. Some argue that the unusually large viscosity can only extend to ~1 nm scale into the solution,17,18 while others suggest that long-range interfacial effect has been observed and the microenvironment in pores as large as tens to hundreds of nanometers can be significantly different than the bulk solution.19-23 To differentiate the mechanisms for the slow mass transport, one key is to know how the diffusing entities move microscopically in the confined 3D space. For example, an increased microviscosity will impact on the diffusion entity in the whole pore volume, while increased adsorption/desorption will only slow down the particle at the pore wall. So far, the dominant methods in studying mass transport in confined spaces are based on ensemble measurements. In this study, we developed an astigmatism-based 3D single particle tracking technique that has an axial working distance as large as ~10 µm to monitor microscopic diffusional motion of nanoparticles in AAO cylindrical nanopores. Astigmatic imaging with a spheroidal point spread function (PSF),24,25 as well as other 3D localization techniques such as double helix PSF,26 wedged prism,27 bifocal plane imaging,28,29 etc., has been used to locate the axial position of 3 ACS Paragon Plus Environment


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particles and molecules. Here, we introduced a weak cylindrical lens into the optical path so that the horizontal and vertical rays are focused on different planes that are 5 µm apart. The astigmatic image of a point object is well expanded to diamond-like patterns depending on its axial position. The difference between patterns that have a 200 nm axial gap can be visually differentiated in a total range over 10 µm (i.e., working distance) given sufficient signal strength. For 100 nm particles, their axial positions can be precisely located (~15 nm at 30 frames per second) within a range of ~5 µm in AAO membranes. EXPERIMENTAL Chemicals and sample preparation. Dye-doped, carboxylated polystyrene nanoparticles with different sizes were purchased from Life Technology or Thermo Fisher Scientific. Porous alumina membrane filters with nominal pore diameter of 200 nm and a thickness of 60 µm were from Whatman International (Maidstone, U.K.). C18/PEG modification of pore wall. The alumina membrane filters were first boiled in 30% hydrogen peroxide for 15 min to introduce -OH groups on the surface for further modification. The filters were then boiled in deionized water for 15 min to clean up the surface. They were dried gently with purified air flow and modified immediately after drying. First, hydroxy(polyethyleneoxy)propyltriethoxysilane (PEG) (Gelest; MW:350-750, or 8-12 repeating CH2CH2O units; fully extended length 3~5 nm) was dissolved in 20 mL of anhydrous toluene to make a 1% (v/v) PEG solution. Chloro(dimethyl)octadecylsilane (C18) (Sigma-Aldrich, MW:347.09) was dissolved in 20 mL of anhydrous toluene to make a 5% (w/w) C18 solution. By mixing the above two solutions with proper ratios, we obtained the modification solutions with desired mole fraction of C18 in total silanes (C18+PEG). The membrane filters were incubated in the modification solution for 1 h, followed by rinsing with toluene, acetone and DI water.30,31 All membrane filters were conditioned in relevant buffer before use. Epi-fluorescence Microscopy and CCD Camera. An upright Nikon Eclipse 80i microscope was used in single particle 3D tracking experiments. To obtain the axial position of the particle, a cylindrical lens (f = 1.0 m) was placed between the microscope objective and the tube lens (7.5 cm from the tube lens) to induce astigmatism in the imaging. The signal was collected by a 100× Apo TIRF/1.49 oil immersion objective. A P-725 PIFOC long-travel objective scanner from Physik Instrument (model no. P725.2CD) was used to control the axial distance from the sample to the objective. The images and movies were acquired by an Andor iXon 897 camera (512×512 imaging array, 16 µm pixel size). 30 ms integration time was used in all dynamic tracking unless specified. To track the particle movement both in pores and in solution, we parked one of the focal planes near the membrane surface so that we can precisely locate the particles ~ 5 µm into the pores. MATLAB and NIH ImageJ were used to analyze and process the collected images and videos. The 3D images were rendered in Visage Imaging Amira (Berlin, Germany). RESULTS AND DISCUSSION Three-dimensional tracking and its localization precision. By inserting a cylindrical lens with a focal length of 1.0 m between the microscope objective and the tube lens in an epi-fluorescence microscope, we obtained unique diamond-like image patterns, depending on the sample position in the z-direction. A model-based, correlation coefficient mapping method32 was developed to recognize the image pattern and recover the particle position in the 3D space (detailed 4 ACS Paragon Plus Environment

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description of the methodology with figures are in Supporting Information 2.1 and 2.2). Compared to other 3D localization techniques, e.g. spheroidal PSF,25 bifocal plane imaging, 28,29 double-helix PSF,26 wedged prism,24,27 etc., this method allowed us to track individual fluorescent nanoparticles in arbitrarily shaped systems with a z-distance as large as ~10 µm. The tracking precision varied with the particle size and the integration time. In this study, we used 100 nm fluorescent, carboxylated polystyrene particles with an integration time of 30 ms. The tracking precision was 8 nm, 12 nm, and 15 nm for x, y, z-axis, respectively, within a distance of ~5 µm between the two focal planes for the horizontal and vertical rays. 3D trajectories of particles diffusing in nanopores. To find out how particles were slowed down, we tracked the microscopic movement of 100 nm fluorescent nanoparticles in AAO filters bearing cylindrical pores with a nominal diameter of 200 nm under different model conditions: (1) in unmodified and PEG-coated pores in regular buffer: 25 mM CHES buffer at pH 10.0; (2) in pores filled with viscous buffer: 50% (volume) glycerol:50% regular buffer; and (3) in pores with increased particle-wall interaction: the pore wall was coated with C18/PEG at different C18 fractions from 0%-20%. Note that the percentage of C18 refers to that in the modification solution rather than on the pore wall. In all these conditions, we were able to track the 3D trajectories of particles diffusing in and out of the AAO membrane filters. For example, Figure 1 and Movie 1a show a particle diffusing in an unmodified membrane filter in viscous buffer. The particle diffuses in one pore for ~11 s, moves out of the pore, diffuses in the bulk solution briefly, and enters another pore, and diffuses there for ~21 s. The particle movement was tracked and displayed in Movie 1b. The top and side views of the 3D trajectory are shown in Figures 1b and 1c, respectively. Such particle diffusing in-and-out of the pores was commonly observed at all experimental conditions (for another example, see Movie 2 and Figure S5). We also observed particles moving from one pore to its neighboring pore inside the membrane filter, indicating that the pores were interconnected by defects (Figures S6-7 and Movies 3-4. Discussion in Supporting Information 2.3). The recovered 3D trajectory in part reflects the nanopore cylindrical geometry. Interestingly, we found that the pores are not perfectly cylindrical: they show slight distortion and twisting, which is consistent with the SEM images (Figure S8). From the SEM images, the measured pore diameter ~3 µm below the filter surface is 300 ± 50 nm. In our recovered 3D trajectories, their projections have a mean of 330 ± 50 nm measured from both the x and y directions for 20 trajectories. It is slightly bigger than the actual area the particle can move in theory, which is ~200 nm in diameter considering 100 nm particles in 300 nm pores. The possible reasons for the slight expansion include: (1) the localization errors expand the spot by ~ 50 nm; (2) the pores are skewed and have irregular shapes along the z-direction so their projection on xy-plane is expanded; and (3) the particles are in larger pores. Through carefully studying the 3D trajectories, we conclude that the irregular pore shapes is the dominant reason. For example, Figure 1d displays the projection of the 3D particle distribution within a thin z-slice (500 nm), which shows that most of the particle positions can be enclosed in a 200 nm-circle. Thus, we can exclude the possibility that our measurement is biased by selecting large pores. Axial diffusion coefficient of particles in nanopores. From the 3D trajectories, we were able to estimate the particle axial diffusion coefficient using the conventional mean squared displacement (MSD) method:

< L2 >= 2nD∆t

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where L is the particle step size in each observation time interval ∆t; is the mean squared displacement; n is the number of dimensions; D is the diffusion coefficient. Generally, we calculated the MSDs in the axial direction using movie clips that were longer than 6 seconds (~200 steps). The MSD up to 15% of the total collection time was calculated. When the MSD curve deviated from a straight line, the initial linear portion was fitted to obtain a diffusion coefficient. Figure 2a shows the representative MSD curves of particles diffusing in the zdirection under different conditions. For unmodified pores and the regular buffer, the median axial diffusion coefficient of 33 particles calculated from the linear portion of the MSD curves is 1.4 ± 0.5 × 10-12 m2/s (median ± standard deviation, Supporting Information 2.4 and Table 1). The median values are generally used in this study to minimize the impact of outliers in the diffusion coefficient measurements. More importantly, using the 3D tracking trajectory, the diffusion coefficient can be estimated from the individual steps of the particles. Brownian diffusion of nanoparticles can be modeled as random walks, where the particle step size L after each observation time interval ∆t is normally distributed with a standard deviation σL:

σL2 = 2nD∆t

(2) Figure 2b shows one representative histogram of individual axial step sizes of a particle in an unmodified pore. By using non-linear least squares (NLLS) fitting, the axial diffusion coefficient can be extracted from the standard deviation of the Gaussian distribution. The diffusion coefficient obtained this way more reflects the particle diffusion in a shorter time scale (30 ms), or in a microscopic length scale (~300 nm). As a comparison, the MSD method gives a D value that more reflects the particle diffusion in a longer time scale (~seconds), or in a larger length scale (several µm for the observation volume). The histogram of the 33 D’s obtained using individual steps is plotted in Figure 2e. The median axial diffusion coefficient of the 33 particles is 1.3 ± 0.6 × 10-12 m2/s, which is consistent with the D’s estimated using the MSD method. This shows that the particle axial diffusion in unmodified pores follows the random diffusion model both microscopically (at a scale of ~300 nm representing the particle individual steps) and in a relatively larger length scale (~5 µm representing the observation volume). Above data were acquired in unmodified pores in CHES buffer at pH 10.0, at which both the particle and the pore wall were negatively charged. To completely passivate the pore wall, we also coated the pore wall with 100% PEG. The median axial diffusion coefficients for 22 particles measured in PEG pores are 1.4 ± 0.7 × 10-12 m2/s using the MSD method and 1.0 ± 0.4 × 10-12 using the individual steps, respectively (Figure S9). This shows that there is minimal adsorption for both PEG-modified and unmodified pores. The measured diffusion coefficient is ~3 times smaller than that predicted by EinsteinStokes equation for 100 nm particles (4.4 × 10-12 m2/s) in the bulk. To exclude the possibility that the discrepancy is caused by systematic errors, we also measured the D of the particles in the bulk (a solution chamber sandwiched between two pieces of glass slides with a gap of ~ 10 µm). The diffusion coefficient in the axial direction was 3.9 × 10-12 m2/s from multiple measurements using the individual step sizes (for an example, see Figure S10), which is consistent with the theoretical value. The 3 times difference between the Ds in the pore and in the bulk solution can be explained by the increased hydrodynamic friction in the pores (see detailed discussions in Supporting Information 2.5 and 2.6).33 Residence times of the particles in nanopores. Next, we studied the 3D trajectories and individual steps when the particles were forced to slow down by using viscous buffer or “sticky” 6 ACS Paragon Plus Environment

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pore wall. When we compared the particle diffusing under the different conditions, the first feature we noticed was that the particles stayed in the pores for much longer times in viscous buffer or C18/PEG modified nanopores. Movie 5 shows the unmodified nanopores and regular buffer, in which we can see the 100 nm particles diffuse in and out of the pores quickly. As a contrast, in viscous buffer (Movies 1 and 2) or 1% C18/PEG modified pores (Movies 3, 4, and 6), the particles stay in the pores for much longer time. To quantitatively compare the apparent slowing down, we counted the total residence times of particles staying in the nanopores under these conditions (for counting criteria, see Supporting Information 2.7). The median residence times are 2.6 s, 22.5 s, and 7.2 s, for unmodified pores, viscous buffer, and 1%C18 modified pores, respectively (Figure 3). Thus, both viscous buffer and increased particle-surface interaction augment the particle’s residence time significantly. Since the particles’ residence times are related to conventional ensemble measurements of particle diffusion coefficients, the direct conclusion is that the particle movement in the presence of viscous solvent or increased particle-surface interaction will slow down the particle diffusion macroscopically. Effect of increased solvent viscosity on particle diffusion in nanopores. We further studied how the particle axial diffusion was affected by viscous solvent or increased particle-wall interaction. In the viscous buffer where the viscosity increased by a factor of ~7,34 the particles were moving much slower in the z-direction, indicated by the slow changing pattern of the particle image (e.g., Movies 1 and 2). Similarly, we can estimate the D from the MSD plot and individual axial steps. Figure 2c shows a representative histogram of the step sizes of a particle in unmodified pores with viscous buffer. The median diffusion coefficient through Gaussian fitting of the step size distributions from 29 particles is 0.21 ± 0.10× 10-12 m2/s (Figure 2f and Table 1), which is consistent with the D’s calculated using the MSD method (0.30 ± 0.12 × 10-12 m2/s). Notably, when the viscosity of the buffer becomes ~7 times larger, the MSD slope and the mean squared step sizes decrease by a factor of 5~7. This shows that the increased viscosity is the main reason for the particle slowing down: it slows down the microscopic particle movement proportionally, leading to the slowing down of the particles macroscopically. Effect of increased particle-surface interaction on particle diffusion in nanopores. However, in C18/PEG modified pores, a quick glance of the movies (e.g., 1% C18, Movies 3, 4, and 6) allowed us to find that the particles were moving fast in the axial direction in the cylindrical pores. A statistical analysis of the individual axial steps of particles in 1% C18 modified nanopores shows that the step sizes are comparable to those in unmodified pores with regular buffer (Figure 2d). Analysis of 43 particles gives the median axial D calculated from individual steps of ~ 1.1 ± 0.5 ×10-12 m2/s (Figure 2g and Table 1), which is consistent with the D’s calculated using the MSD method (1.2 ± 0.4 × 10-12 m2/s). Note most of the MSDs for 1% C18 pores leveled off within 1 s (e.g., Figure 2a). Only the linear portion was used to calculate the D. The mean step size drops only by ~15% in 1% C18 modified pores as opposed to that in unmodified pores. Compared to the 200% increase of the residence time macroscopically, our 3D trakcing data gives a picutre that the movement of particles in the C18 modified pores are microscopically active. First, why the step size of the particles decreased by 15% in 1% C18 pores? The decreased step size should be a result of the increased particle-wall interactions. With the modification of C18, the pore wall becomes more hydrophobic, resulting in a stronger van der Waals interaction between the particle and the pore wall. To confirm this, we varied the surface 7 ACS Paragon Plus Environment


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C18 concentration by changing the C18-to-PEG ratio in the modification solution. Table 2 and Figure 4a show the apparent axial diffusion coefficients at different C18 fractions calculated from the individual steps of ~ 20 actively diffusing particles each, respectively. Note that firmly adsorbed particles were observed for all C18 fractions. Most of them were permanently adsorbed and they were excluded from the estimation of the D. When the percentage of C18 is increased from 1% to 20%, the apparent axial diffusion coefficient decreases from 1.1 to 0.55 ×10-12 m2/s. Over 20% C18, the pore wall property has a sharp transition and becomes adsorptive: most of the particles adsorb permantly onto the surface immediately upon contact. The whole changing trend clearly shows that the C18-modified pores do have an increased attractive interaction for the particles. To find out how C18-modified pores slow down the particle individual steps, we carefully scrutinized the trajectories of the active particles. We can conclude that long time adsorption, which is defined as the immobilization of the particle for a few frames, or ≥100 ms, is very rare and not a main factor that slows down the particle diffusing. Even in 20% C18 modified pores where the particle D drops by a factor of 50%, there is still no obervable long time adsorption event for the active particles. However, we cannot exclude the possibility of short time adsorption, i.e., the particle is frequently immobilized on the surface at the µs time scale and diffuses through the adjacent solvent phase between the adsorption events,35 or temporary retention in the potential energy surface (PES) well near the pore wall (within a distance of ~5 nm) because of van der Waals interaction. We are unable to distinguish the two processes but generally describe the retention as “particle being withheld by the pore wall”. Such withholding time tw is short so that these events are not readily detected due to the limited temporal resolution of current imaging techniques. Considering the above discussion, we have the model that the particle step size decreases because of many transient withholding events by the pore wall. Since Brownian motion is cumulative, the mean squared particle step size is proportional to the total diffusing time within the observation interval tf. Thus, the fractional time of the particle being withheld by the pore wall can be estimated (Supporting Information 2.8): tw D − D' (3) = 0 tw + td D0 where tw is the average time a particle being withheld by the pore wall; td is the average time a particle diffusing in the pore before it is withheld by the pore wall; D0 is the diffusion coefficient in an unmodified pore; D’ is the apparent diffusion coefficient in C18 modified nanopores. Using Equation 3, we can estimate that the total withholding time is ~15% for particles in 1%C18 modified pores. Further, the Gibbs free energy change ∆G for the withholding of the particles on the pore wall can be estimated (Supporting Information 2.8):

∆G = −RT ln(

D0 − 1) D'

(4)

where R is the gas constant; T is the temperature. As C18 fraction increases, D’ and ∆G decreases as expected (Table 2). Note D’ is always smaller than D0 in the presence of particlewall attraction in Equation 4. When D’ approaches D0, ∆G becomes a large positive value, indicating the particle-wall interaction is very unfavorable. ∆G here only reflects the free energy change of the transient withholding of the particle by the pore wall. The firm adsorption possibly involves further surface changes on the particle and/or the pore wall. Its free energy change is 8 ACS Paragon Plus Environment

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not considered here. If we take a further assumption that the activation energy Ew for withholding is a constant (Figure 4c), i.e. the energy barrier for the particle to go over and be withheld by the surface is independent of C18 fraction; and the activation energy for de-retention Ed is linearly proportional to the fraction of C18 on the surface, i.e., the more C18, the more energy the particle needs to depart from the surface, we can obtain a linear relationship (Supporting Information 2.8):

RT ln(

D0 −1) = Ed0 × fC18 − Ew D'

(5)

where Ed0 is a constant; f18 is the fraction of the C18. Interestingly, Figure 4b shows that the experimental data can be satisfactorily fitted with the linear relationship. From the linear fitting, we obtain Ed0 = 26 kJ/mol, Ew = 4.4 kJ/mol, and Ed’s for different C18 percentages are listed in Table 2. The Ew and Ed at low C18 concentrations are similar to the thermal energy (1.5 kBT = 3.7 kJ/mol), which means that the withholding and de-retention happen quickly. The fact that our experimental data matches Equation 5 is an indication that our assumption about the reduced particle step size and the transient withholding events are self-consistent.

Restricted diffusion in viscous nanopores. Second, in all C18 modified pores, the particles are microscopically active by showing very limited reduction in step sizes: e.g., 15% reduction for 1% C18 coated pores. The total withholding time (e.g., ~15% of the frame time for 1% C18 modified pore) does not sufficiently account for the increased residence time (200% increment for the samely modified pores). According to Einstein equation (Equation 1), the residence time of the particle in the pore should be inversely proportional to the particle’s diffusion coefficient. If the D estimated from the individual steps is adopted, it predicts that the particle residence time will only increase by 18% rather than 200% measured experimentally. Why the particles were retained in the pores for much longer time? To answer this question, we further analyzed the MSD ~ t plots of the particles in all three conditions. We found that in unmodified pores, the majority (~80%) of the particles show linear MSD ~ t curves within an observation time of ~1 s. The rest of the curves show different extents of leveling off within the 1 s window. In viscous buffer, the number of linear MSD curves drops to slightly larger than 50%. However, in C18 modified nanopores, the majority of the particles (~80%) show MSD curves leveling off within 0.1 ~ 0.5 s, which corresponds to a diffusion distance of ~500-1000 nm. Figure 2a shows a representative MSD ~ t plot for particle diffusion in C18/PEG modified nanopores (blue curve). The leveling off of the MSD curve is an indication of non-Brownian motion and restricted diffusion in the axial direction during the observation period. Because of the confinement, the mean squared displacement over a long time does not increase, leading to a small macroscopic diffusion coefficient although its microscopic step is still large. In this study, the confinement possibly reflects the heterogeneous environment inside the pore so that the particles tend to be restricted, or “trapped”, within certain segments of the pore. This can be better seen in particles’ z-trajectories (for typical examples, see Figure 5). In PEG modified pores (Figure 5a), the particle moves drastically in the axial direction, giving a lot of sharp spikes in the trajectory. As a contrast, in 1% C18 modified pores (Figure 5b), relatively “flat” regions of the trajectory are observed. These “flat” regions show the particle’s z-value fluctuating within 500 nm~1 µm, which means that the particle prefers to stay within the 500 nm~1 µm segment of the pore during the period of time. This restricted diffusion shall explain why the particles show non-linear MSD ~ t plots in C18 modified pores. The length scale of the axial confinement is 9 ACS Paragon Plus Environment


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estimated to be 500 nm ~ 1 µm from Figure 5b, which is consistent with the MSD plot that shows the leveling off starting from 0.1 ~ 0.5 s. When the restricted diffusion happens in the pores, the total residence time increases as the particle needs more time to diffuse out of the confined region, or from one confined region to the other. To be noted, although the whole trajectory in Figure 5b appears less fluctuating for the C18 modified pore, its individual step size does not decrease drastically. The mean squared step size of the particle in Figure 5b is ~ 85% of that in Figure 5a. Finally, as a contrast, in viscous solvent (Figure 5c), the individual steps decrease drastically, giving a much smoother trajectory. What causes this restricted diffusion and non-Brownian motion in sticky pores? An easy answer is that the microenvironment in the pore is heterogeneous from segment to segment because C18 may be coated on the wall inhomogeneously. Some part of the pore wall is more “sticky”, which will retain the particles in that region of the pore for longer time. This reflects static inhomogeneity in the pore. Or, in a different scenario, even the coating is uniform, the increased number of the particle-wall interactions may also lead the whole system to be far away from the equilibrium so that the diffusion becomes non-Brownian. In the first case, one would observe high probability of particle presence in one or more fixed regions in the nanopore while in the latter case, there is no such region showing higher affinity to the particles. Due to the limited lengths of the trajectories one can capture within a single pore, we are unable to determine which factor, the static or dynamic heterogeneity, contributes more to the observed non-Brownian diffusion inside nanopores (for an example of the particle z-distribution in the nanopore, please see Figure S11). The restricted diffusion model discloses two points: (1) whether the observed diffusion is slow or not is relevant to the scale of our observation volume. That is, depending on the detection technique, different researchers may obtain completely different conclusions. The particles in C18 modified pores show a typical example where their microscopic and macroscopic behaviors are opposite. Caution should be exercised when we compare D values obtained from different experiments. (2) It also has new insights in mass transport in confined environments and in separations. For example, in adsorption and partition chromatography, the adjusted retention time is defined as the total retention time minus the void time, which can be viewed as the total time that the solute is being retained by the stationary phase. However, our experiments suggests that the time that the solute (particles) being directly “withheld” by the C18-modified pore wall only explains a small portion of the adjusted retention time when the solute (particles) is similar in size to the pores. The particles tend to be “trapped” inside the pores for prolonged time as a result of the particle-surface interaction (Figure S12).

CONCLUSIONS To summarize, we developed a 3D single particle tracking method to monitor microscopic motion of nanoparticles in cylindrical alumina nanopores with a z-span as large as several micrometers. We show that increasing the buffer viscosity uniformly in the pores will slow down the particle microscopically thus leading to a macroscopically slow diffusion. As a contrast, increasing the pore wall affinity slows down the particle’s microscopic motion little. Non-Brownian motion is possibly responsible for the macroscopically slow diffusion and explains the contradictory diffusion behaviors observed at different length scales. These observations show that it is possible to differentiate slowing down in confined environments caused by different mechanisms using 3D tracking techniques.


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Acknowledgment. This work was supported by the North Carolina State University start-up funds and a FRPD award to G.W. Y.W. is supported by a funding from NSF of China (NO 21507076). N.O. acknowledges a GAAN Fellowship. F.C. acknowledges a Graduate Fellowship by Chem. Dept., NCSU. We acknowledge Analytical Instrumentation Facility (AIF) center, North Carolina State University for providing SEM measurements. Supporting Information Available: 8 movies, Materials and methods, Supplementary results and discussion, and 12 supporting figures. This material is available free of charge via the Internet at http://pubs.acs.org.



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Table 1. Measured axial diffusion coefficient of 100 nm carboxylated polystyrene nanoparticles in 300 nm pores (median ± standard deviation).

Theoretical D in bulk Unmodified pores Glycerol/Buffer C18/PEG pore

D (10-12 m2/s) MSD ~ t slope in linear region 4.4 1.4 ± 0.5 0.30 ± 0.12 1.2 ± 0.4

Table 2. D, ∆G and Ed for C18 modified nanopores. C18 fraction in D (10-12 m2/s) C18/PEG Indiviudal steps 1% 1.1 ± 0.5 5% 1.0 ± 0.4 10% 0.86 ± 0.4 20% 0.55 ± 0.2

∆G (kJ / mol ) 4.23 2.98 1.66 -0.77


D (10-12 m2/s) Indiviudal steps 1.3 ± 0.6 0.21 ± 0.10 1.1 ± 0.5

Ed (kJ / mol ) 0.26 1.3 2.6 5.2


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FIGURES AND CAPTIONS

Figure 1. Three dimensional particle distribution when diffusing in two cylindrical pores sequentially. (a) 3D view. (b) Top view. (c) Side view. (d) The top view of the particle distribution in a thin slice in the z-direction.


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Figure 2. Axial diffusion coefficients for particles in 3 different types of pores. The fitting results show that the diffusion coefficients are 1.5 (bare pore), 0.25 (viscous buffer), and 1.2 (C18/PEG pore) × 10-12 m2/s, respectively. (a) Representative MSDs as a function of time for particles diffusing in different types of pores. (b) (c) and (d) Histograms of particle individual steps in the z-direction under different conditions. (e) (f) and (g) Histograms of particle axial diffusion coefficients obtained from individual steps under different conditions. (b) and (e) Unmodified pores. (c) and (f) Unmodified pores with viscous buffer. (d) and (g) C18/PEG modified pores.



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Figure 3. Histograms of residence times of partilces in cylindrical pores. (a) Unmodified pores. (b) Unmodified pores with viscous buffer. (c) C18/PEG modified pores. There were numerous events that particles stayed transiently on the membrane surface or went into the pore for a very short distance. Only particles went ~500 nm below the membrane filter surface were counted.


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Figure 4. Particle-pore wall interaction at different surface C18 fractions. (a) D as a function of C18 fraction. Note C18 fraction referes to the volume fraction in the modification solutions. (b) D RT ln( 0 − 1) vs. f C18 . (c) Energy diagram. Ew: activation energy for withholding; Ed: activation D' energy for leaving the withholding status.



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Figure 5. Typical z-trajectories of particle diffusing under different conditions. (a) A particle diffusing in a PEG-coated pore in regular buffer. (b) A particle diffusing in a 1% C18 modified pore in regular buffer. (c) A particle diffusing in viscous buffer in unmodified pores.


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For TOC only

Three-dimensional single particle tracking shows the microscopic movements of particles respond to increased solvent viscosity and increased particle-wall interaction differently.


Microscopic Movement of Slow-Diffusing Nanoparticles in Cylindrical

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