Letter pubs.acs.org/NanoLett
Nanoparticle Dynamics in a Nanodroplet Jingyu Lu,†,‡,§,∥ Zainul Aabdin,†,‡,§,∥ N. Duane Loh,†,∥ Dipanjan Bhattacharya,†,⊥ and Utkur Mirsaidov*,†,‡,§ †
Center for Bioimaging Sciences and Department of Biological Sciences, National University of Singapore, 14 Science Drive 4, Singapore 117543 ‡ Graphene Research Center and Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore, 117551 § NUSNNI-Nanocore, National University of Singapore, 5A Engineering Drive 1, Singapore 117411 ⊥ Singapore-MIT Alliance for Research and Technology, 1 CREATE Way, Singapore, 138602 S Supporting Information *
ABSTRACT: We describe the dynamics of 3−10 nm gold nanoparticles encapsulated by ∼30 nm liquid nanodroplets on a flat solid substrate and find that the diffusive motion of these nanoparticles is damped due to strong interactions with the substrate. Such damped dynamics enabled us to obtain time-resolved observations of encapsulated nanoparticles coalescing into larger particles. Techniques described here serve as a platform to study chemical and physical dynamics under highly confined conditions. KEYWORDS: in situ TEM, nanodroplet, interfacial liquids, diffusion one acquires images at rates higher than ∼109 Hz. As this paper will show, when particles are confined to length scales comparable to its diameter, bulk diffusion properties become irrelevant and much slower imaging rates of dynamics are permitted. Recent development of in situ TEM enabled direct imaging of physical and chemical processes in gases10 and liquids,11−17 as well as biological molecules18−22 in physiologically relevant environments.18,23 In these studies, a thin layer of nanoscale specimens is sandwiched between two electron translucent membranes of a liquid cell that isolates liquid samples from the high vacuum of a TEM column. The dynamics of ultrathin liquid layers24,25 and nanodroplets,1 which form when the former dewets, have been studied in this manner. Here, we use these liquid cells to study the dynamics of nanoparticles enclosed in zeptoliter-scale nanodroplets. We loaded approximately 400 nL of 1 mM HAuCl4 aqueous precursor solution into a liquid cell,1,12 which is comprised of two ultrathin (∼14 nm) electron translucent SiNx membranes separated by ∼200 nm with spacers. Prior to solution loading, these liquid cells were oxygen plasma treated to make their SiNx membrane surfaces hydrophilic.1 Each liquid cell, sealed with a copper gasket, is inserted into the TEM using a specimen holder. We used a JEOL 2010FEG TEM operated at 200 kV for in situ imaging with electron doses ranging from 2000 to 5000 e/(Å2·s). We imaged at a rate of 10−25 frames per second with ORIUS SC200 (Gatan, Inc.) CCD camera. This allows us observation windows of more than 300 frames for most of the
D
ifferent physical effects dominate when macroscopic systems are scaled down to the nanometer range. For example, physical properties of nanometer-size water droplets have been shown to deviate from that of bulk water.1 New engineering possibilities emerge when these effects are manipulated, including the use of surface tension in nanodroplets to form nanoscale architectures out of two-dimensional materials such as graphene,2,3 or serve as a vessel for chemical and physical processes confined to small volumes.4,5 Probing chemical reactions in nanoscale systems also permits direct comparison with in silico theoretical models that are currently limited in complexity by computational capabilities.6−8 In this paper, we see how a departure in the nanoscale fluid-particle dynamics from bulk, macroscopic behavior can lead to a unique opportunity to study particle−particle interactions. In bulk fluids, diffusive movement of particles is generally governed by the fluid’s viscosity. The classical Einstein−Stoke’s equation predicts the bulk diffusion coefficient for water at temperature T = 300 K for a spherical nanoparticle of radius R = 2 nm in water of viscosity η = 9 × 10−4 Pa·s to be9 Dt =
kBT ≈ 1 × 10−10 m 2·s−1 (6πηR )
(1)
where kB is Boltzmann’s constant. Similarly, the rotational diffusion coefficient of such particles should obey9 Dr =
kBT (8πηR3)
≈ 2 × 107 rad2 ·s−1
(2)
By these equations, images of 2 nm radius particles will be severely blurred by rotational and translational averaging unless © 2014 American Chemical Society
Received: January 24, 2014 Published: March 18, 2014 2111
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trajectories were memoryless, radius-tagged diffusion coefficients, DMSD(R), from all the 68 nanoparticles independent of observation time or particle label were found to depend inversely on nanoparticle radius (see Figure 1D), as predicted by eq 1. A total of 27 130 (Figure 1E) of these experimentally measured D(R)s were fitted to eq 1, which would suggest that the corresponding effective viscosity was ∼2.6 × 106 Pa·s (assuming temperature T = 300 K). This is a remarkable 9 orders of magnitude higher than that of bulk water, which strongly suggests that there is another dominant interaction that dampens the movement of the nanoparticles other than the viscous drag of bulk water. These diffusion coefficients are consistent with Figure 1F, where the distribution of average diffusion coefficients for 68 gold nanoparticles trajectories averages to DMSD ≈ 4.8 × 10−20 m2·s−1, which compares well with similar thin-film studies24,28 but poorly against the prediction in eq 1. Having accounted for variations owing to particle radius in Figure 1D, the large error bars in diffusion coefficients are likely due to other factors such as interactions between a particle and the liquid cell’s membrane, the boundary layer of fluid on the membrane. We investigate the last effect later in this paper. Strongly damped dynamics also occurs when nanoparticles are confined to nanoscale droplets. Figure 2A shows eight such
particles that we tracked, which is sufficient for estimating their diffusive movement to less than 10% error (Supporting Information). When illuminated by TEM electrons the ∼100 nm thick water layer in the liquid cell retracts leaving behind an ultrathin water film (>10 nm thick) on the surface of SiNx membrane.26,27 This precursor solution of Au ions is rapidly reduced by TEM electrons to Au0, which then forms gold nanoparticles as described previously.12,17 Prolonged imaging dewets the water film into nanodroplets that occasionally encapsulate previously formed gold nanoparticles, which allows one to image the dynamics of these confined nanoparticles. To begin, we observed the movement of nanoparticles, whose diameters are less than 10 nm, in a large liquid ultrathin film24,25,28 and are far from the film boundaries (Figure 1A,B).
Figure 1. Gold nanoparticles diffusing in an ultrathin water film. (A) TEM snapshots of gold nanoparticles enclosed in water film. (B) Path traces for seven selected particles shown in (A). (C) Mean square displacement of nanoparticles versus time (curve colors correspond to circle colors enclosing nanoparticles as shown in (A) at t = 0 s). (D) Diffusion coefficients computed from individual particles’ meansquare-displacement are associated with their instantaneous particle radii, DMSD(R). These are averaged (black disks with blue error bars) by radius categories regardless of particle label and observation time. The full set of DMSD(R) and not just their averaged ones are fitted (red line) to Einstein−Stokes’s equation where DMSD ∼ R−1. (E) Histogram of the number of observation counts in each radius category in (E). (F) Histogram of the average diffusion coefficient for each of the 68 particles that we tracked in (A). Inset: we superimposed these 68 particle traces with each particle’s starting point brought to common origin (red disk).
Figure 2. Gold nanoparticles diffusing in a nanodroplet. (A) Time series images of eight gold nanoparticles enclosed in a nanodroplet imaged with TEM. The image at t = 0 s shows path traces of each individual nanoparticle during 50 s. (B) Instantaneous velocities for particle 6 (bright blue), 4 (red), 8 (bright green), and 5 (black) as labeled in (A). (C) Instantaneous velocity distribution in x (left column) and y (right column) directions for the same four particles (solid curves are Gaussian fits). (D) Mean square displacement of eight particles (curve colors correspond to label colors in (A) at t = 0 s).
The diffusion coefficient DMSD of individual particles can be estimated from the slopes of their mean squared displacement (MSD) plots as a function of time t (Figure 1C): DMSD = MSD/(4t). Further, the slopes of the MSD plots, and hence the diffusion coefficients, vary between different nanoparticles and over time as well for individual particles. A possible cause of variation, as suggested in eq 1, is due to changes in nanoparticle radius. To investigate this, we also quantified each nanoparticle’s equivalent disk radius during its trajectory. From the MSDs between consecutive frames for each of the 68 nanoparticles we computed the effective diffusion coefficients DMSD, which were then tagged with each nanoparticle’s instantaneous radii. Assuming that these random nanoparticle
gold nanoparticles (Supporting Information Video 1), whose trajectories are random and erratic as seen from their uncorrelated instantaneous speeds, v = (v2x + v2y )1/2, plotted in Figure 2B. Here vx = Δx/Δt and vy = Δy/Δt are instantaneous horizontal and vertical in-plane velocities of the particles’ center of mass respectively, as determined from consecutive images separated by time interval Δt. The observed distribution of particle velocities fit Gaussian profiles (Figure 2C) centered about zero, as expected of diffusion in the absence of persistent drift currents. The computed time-dependent MSD of 2112
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Figure 3. Measuring gold nanoparticles’ rotational diffusion. (A) Particles near a three-phase contact line, marked by a dashed line only for the t = 1.0 s image. (B) Fourier intensities from the indicated regions show 2.4 Å reflections associated with the gold nanocrystal’s lattice spacing in the (111) direction. These reflections change direction indicating that particles undergo rotational movement inside the nanodroplet. (C) Plots of mean squared angular displacement for the two particles in (A), colored according to the particles’ bounding boxes in (A). The straight lines are the linear fits for respective curves.
particles studied here, could dominate the viscous drag of particles close to membrane. Within this ultrathin film, the few monolayers of liquid molecules closest to the bottom membrane of the liquid cell will have properties that are different from those of bulk liquid.30−32 The quantification of this effect is the subject of further investigation. Damping due to direct interaction between particles and the solid substrate is unlikely since nanoparticles in the absence of liquid do not show noticeable diffusion. The peak-to-trough roughness of SiNx membrane is ∼1.5 nm (see Supporting Information Figure S5), which is comparable to the radius of many of nanoparticles we observed (see Figure 1E). This roughness is encountered by a diffusing nanoparticle and may be related to the broad distribution of diffusion coefficients in Figure 1D. Although potential specimen heating from TEM electrons is negligible,24,33 its inclusion will only widen the difference between eqs 1 or 2 against our observations in Figures 1, 2, and 3. The strongly damped dynamics seen here provides extended contact time between neighboring particles. For example, a diffusion time that is protracted by 109 times will increase opportunities for interparticle interactions and intraparticle reconfiguration by the same order of magnitude. These nanodroplets serve conveniently as vessels for observing chemical and physical processes that occur in highly confined environment (Figure 4A,B). For example, the coalescence of nanoparticles seen in ultrathin liquid films is thought to be a key mechanism for nanoparticle growth in solution.12−15 As the trajectories of these nanoparticles in nanodroplet overlap they fuse into a larger nanoparticle (Figure 4B,C). Particle crystallinity is not completely destroyed during this fusion, as evident from the (111) reflection in the coalescing particles’ Fourier Transform (t = 33.31 s in Figure 4B). When observed in fortuitously oriented particles, these Fourier reflections persist only for a few seconds due to the nanoparticle’s out-ofplane rotational diffusion. Figure 4D shows growth in particle size after coalescence. Using the imaging methods described above, we were able to observe complex many-particle interactions within a nanodroplet (Figure 5A). Lateral confinement by the droplet’s boundary limits the particles’ range of translational diffusion, thereby increasing interaction opportunities between particles. The persistence of crystallinity and rotational diffusion during coalescence seen in Figure 4 are also evident in Figure 5A,B and Supporting Information Figure S1. The chemical composition
individual nanoparticles (Figure 2D) indicate an average diffusion coefficient of DMSD ≈ 5 × 10−20 m2·s−1, which is comparable to the damped dynamics shown in Figure 1. This suggests that in-plane particle confinement by the lateral boundary of the nanodroplet, dominant only in Figure 2 but absent in Figure 1, is insignificant from the observed deviation from bulk diffusion Dt. Measurements of rotational diffusion in our systems can be decoupled from translational diffusion in the Fourier intensities of the obtained images (see Supporting Information). Leveraging the fact that crystalline planes of gold nanoparticles only appear at specific angular intervals (see Supporting Information), similarly, the appearance and disappearance of their associated Bragg reflections will delimit these intervals. Figure 3A shows high-resolution images of crystalline gold nanoparticles confined in the liquid phase near a gas−solid− liquid triple phase boundary of a thin liquid film (Supporting Information Video 2). These gold nanoparticles remain on a liquid side of three phase contact line during small agitations of contact line, consistent with observations of Zheng et al.24 This suggests that particles are hydrophilic29 and hence should occur within the liquid. The rotations of these crystals are evident both in the TEM images and the Bragg reflections present in the images’ Fourier transforms. Figure 3B shows the (111) Bragg reflection of a gold nanocrystal. Similar reflections for comparable particles are continuously detectable for typically 1−5 s before disappearing. In a typical instance, the angular width of the (111) reflection of the randomly rotating, 3 nm radius gold nanocrystal, θ⊥ ∼ 0.3 d111/R ≈ 0.02 rad (Supporting Information), persists for ∼2 s. In this case, the particle’s rotational diffusion coefficient Dθ can be estimated from the persistent time t of this reflection across its angular width via the relation9 ⟨θ⊥2 ⟩ = 2Dθ⟨t⟩. This results in a diffusion coefficient of Dθ ≈ 10−4 rad2/s. Alternatively, applying this diffusion relation to the mean squared in-plane rotation (Figure 3C) of a R = 3 nm and R = 4 nm nanoparticle in Figure 3A for a time interval when the reflection was continuously present, we obtain diffusion coefficients of approximately 7 × 10−3 and 1 × 10−3 rad2/s respectively. These estimates are 9−10 orders of magnitude smaller than the rotational diffusion coefficient predicted in eq 2. The strongly damped translational and rotational diffusion we report here likely arises from dominant surface effects in ultrathin films. This ultrathin layer is typically 10−20 nm (Supporting Information), which is comparable to the radii of 2113
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In summary, we find the following: (1) the motion of nanoparticles on ultrathin films is measurably damped by strong particle-surface interactions mediated by the few atomic layers of liquid in between them; (2) nanodroplets of a few zeptolitters (10−21 L) can be formed by electron-induced dewetting of thin films, which effectively encapsulate nanoparticles and confine their interactions; and (3) the combination of the previous two findings enhance the coalescence of nanoparticles, which can be imaged effectively by time-resolved in situ TEM. Insights from observing the dynamics of surface-interaction dominated nanoparticles in very small fluid volumes can drive novel experimental design and/or engineering applications. With further chemical modifications to these fluid vessels, one could envision studying reaction-limited and diffusion-limited interactions to nearatomic resolution.
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ASSOCIATED CONTENT
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AUTHOR INFORMATION
S Supporting Information *
Figure 4. Coalescence of two gold nanoparticles in a nanodroplet. (A) Schematic of nanodroplet-confined particle−particle coalescence. (B) Time series TEM images of two gold nanoparticles coalescing in a nanodroplet. The image at t = 33.31 s shows the Fourier intensities from fused gold nanoparticles with the 2.4 Å reflection (red circle), which corresponds to lattice plane spacing of gold crystal in the (111) direction. (C) Path traces of individual gold nanoparticles. (D) Mean square displacement of two particles before (red and blue curves) and after (green curve) coalescence as labeled in (A). (E) Projected area of gold nanoparticles before and after coalescence.
Additional information, calculations, and figures. This material is available free of charge via the Internet at http://pubs.acs.org. Corresponding Author
*E-mail:
[email protected]. Author Contributions ∥
J.L., Z.A., and N.D.L. are equal contributors.
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the Singapore National Research Foundation’s Competitive research program funding (NRFCRP9-2011-04). N.D.L. thanks the support of Lee Kuan Yew endowment fund.
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REFERENCES
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NOTE ADDED AFTER ASAP PUBLICATION This paper was published on the Web on March 24, 2014. Changes were made to author footnote for D.B., equation 2, and units in the fourth paragraph. The corrected version was reposted on March 26, 2014.
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