The Mechanisms for Nanoparticle Surface Diffusion and Chain Self

Article pubs.acs.org/JPCC

The Mechanisms for Nanoparticle Surface Diffusion and Chain SelfAssembly Determined from Real-Time Nanoscale Kinetics in Liquid Taylor J. Woehl* and Tanya Prozorov Ames Laboratory, U.S. Department of Energy, Ames, Iowa 50011, United States

Downloaded by UNIV OF CALIFORNIA SANTA BARBARA on August 31, 2015 | http://pubs.acs.org Publication Date (Web): August 27, 2015 | doi: 10.1021/acs.jpcc.5b07164

S Supporting Information *

ABSTRACT: The mechanisms for nanoparticle self-assembly are often inferred from the morphology of the final nanostructures in terms of attractive and repulsive interparticle interactions. Understanding how nanoparticle building blocks are pieced together during self-assembly is a key missing component needed to unlock new strategies and mechanistic understanding of this process. Here we use real-time nanoscale kinetics derived from liquid cell transmission electron microscopy investigation of nanoparticle self-assembly to show that nanoparticle mobility dictates the pathway for self-assembly and final nanostructure morphology. We describe a new method for modulating nanoparticle diffusion in a liquid cell, which we employ to systematically investigate the effect of mobility on self-assembly of nanoparticles. We interpret the observed diffusion in terms of electrostatically induced surface diffusion resulting from nanoparticle hopping on the liquid cell window surface. Slow-moving nanoparticles self-assemble predominantly into linear 1D chains by sequential attachment of nanoparticles to existing chains, while highly mobile nanoparticles self-assemble into chains and branched structures by chain−chain attachments. Self-assembly kinetics are consistent with a diffusion-driven mechanism; we attribute the change in self-assembly pathway to the increased self-assembly rate of highly mobile nanoparticles. These results indicate that nanoparticle mobility can dictate the self-assembly mechanism and final nanostructure morphology in a manner similar to interparticle interactions.

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resolution TEM imaging.27 The kinetics of the nanoparticle self-assembly process have been likened to multistep chemical reactions,29 such as polymerization,30 where interparticle interactions are thought to determine the rate constants for assembly of differently sized and shaped nanostructures.31,32 In general, interparticle interactions are conventionally believed to dictate self-assembly mechanisms, with the kinetics of the process thought to be a result of these interactions. However, in many cases there is not a clear relation established between the self-assembly kinetics and the interparticle interactions thought to dictate the rate constants. A number of directed and self-assembly strategies employ techniques in which the assembly occurs in a confined nearly 2D liquid layer, such as liquid−liquid interfacial self-assembly,33 Langmuir−Blodgett self-assembly,34,35 and capillary and evaporation induced self-assembly.3,22,36 In each of these techniques, nanoparticles self-assemble in a liquid film with a thickness on the order of the nanoparticle size. Liquid cell TEM and scanning TEM (STEM) have been established as techniques uniquely capable of observing real-time nanoscale dynamics in confined thin liquid layers, particularly for observing “nonclassical” nanoparticle growth involving aggre-

INTRODUCTION Various types of colloidal nanoparticles are known to selfassemble into nano- and mesostructured materials.1−6 These materials display hierarchical ordering at length scales ranging from atomic to microscopic, which imparts them with highly tunable properties with applications in catalysis,7 functional materials,8 battery electrode materials,9−11 water treatment,12,13 and biomimetic systems.14−16 Nano- and mesostructures are typically formed in solution via self-assembly of nanoparticle building blocks.17 Self-assembled one-dimensional (1D) chains of nanoparticles are of particular interest for plasmonic6,18 and sensing19 applications. Self-assembly of nanostructures is often explained in terms of an intricate balance between attractive interparticle forces, such as induced dipolar20,21 and capillary drying forces,22 and repulsive forces, like electrostatic and steric repulsion.23−27 For example, anisotropic electrostatic interactions between nanoparticles can be tuned with the buffer ionic strength to rationally design 1D linear chains.25 While there are numerous reports employing interparticle interactions as design parameters to tailor self-assembly, equilibrium models for these interactions cannot completely describe these highly dynamic systems. In particular, current models and characterization techniques cannot explain how nanoparticle building blocks are assembled to form the final nanostructure. Selfassembly kinetics have been probed via low spatial resolution X-ray spectroscopy,23,28 optical microscopy,3 and low temporal © XXXX American Chemical Society

Received: July 23, 2015 Revised: August 19, 2015

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DOI: 10.1021/acs.jpcc.5b07164 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

m−3. For the diffusion coefficient experiments (Figure 1), the nanoparticle suspension was diluted 10 times with the acetate

gation, coalescence, and oriented attachment.21,37−40 Several researchers have demonstrated liquid cell (S)TEM visualization of nanoparticle self-assembly and aggregation38,41 and interpreted the results based on equilibrium interparticle interactions, such as electrostatic,40,42 dipolar,21,43 and stereohindrance effects.43 While liquid cell (S)TEM is the only technique capable of real-time observations of nanoscale dynamics in liquid, the imaging electron beam44−47 and confinement effects48,49 have been shown to affect the chemistry and physics of liquid cell experiments. For instance, electron-beam-induced nanoparticle nucleation and growth mechanisms in the liquid cell are influenced by the beam current44 as well as the imaging mode used (e.g., TEM vs STEM).50 Confinement effects drastically reduce the mobility of nanoparticles, leading to self-diffusion coefficients several orders of magnitude lower than theoretical predictions.38,48,49,51−53 On the other hand, electron beam charging of the liquid cell imaging windows affects nanoparticle motion, in some cases even quickly expelling nanoparticles from the imaging area.45,47 These electron beam and confinement effects are typically deemed experimental artifacts; however, once they are understood and quantified,50 they can be exploited to systematically study real nanoscale systems. For example, the electron beam current was used as a surrogate reducing agent to determine the nucleation and growth mechanisms for in situ platinum,37 silver,44 and gold nanocrystal54 growth and to simulate electrochemical breakdown of commercial lithium battery electrolytes.55 In this article, we use nanoscale kinetic measurements derived from real-time liquid cell STEM observations to show that the rate and pathway for gold nanoparticle self-assembly are dictated by the nanoparticle mobility. We employ a newly discovered proportionality between the nanoparticle mobility and imaging electron beam current to systematically investigate the effect of mobility on self-assembly. Real-time nanoscale kinetics revealed that nanoparticles with a relatively low mobility self-assembled predominantly by sequential attachment of single nanoparticles to existing chains, while highly mobile nanoparticles quickly aggregated and self-assembled by attachment of chains with each other. Highly mobile nanoparticles tended to form branched structures while nanoparticles with low mobility formed linear 1D chains. This suggests that mobility can play a role in self-assembly similar to interparticle interactions, in this case modulating the final nanostructure morphology. Here the nanoparticles were confined to a ∼200 nm thick liquid layer, but we expect this methodology to open up avenues for directly observing the selfassembly kinetics of 3D nano- and mesostructures in thicker liquid layers.

Figure 1. Electron beam current modulated nanoparticle mobility in the liquid cell. (a, b) ADF-STEM images showing example trajectories of several nanoparticles over 150 s at beam currents of 122 pA (a) and 634 pA (b). The scale bar in (a) is 200 nm. Nanoparticle trajectories are drawn in red; nanoparticles are marked with blue dots for clarity. (c) Box plots of the nanoparticle diffusion coefficients as a function of beam current. (d) Median diffusion coefficient as a function of beam current; the black line is a least-squares fit with a Pearson’s correlation coefficient of P = 0.985.

buffer. The nanoparticles had a zeta potential of ξ = −12 ± 0.7 mV, determined by dynamic light scattering (Malvern Zetasizer Nano ZS). Liquid Cell Sample Preparation and STEM Imaging. A commercial liquid cell holder platform (Hummingbird Scientific, Lacey, WA) was utilized for the nanoparticle selfassembly experiments. A thin liquid layer (typically 100−300 nm thick) was formed by sandwiching two SiN-coated silicon chips with a 50 × 200 μm opening etched from the center. The 50 nm thick SiN is electron transparent and spans the etch pit in the chip center, creating an imaging window. The liquid layer and silicon chips were hermetically sealed to prevent evaporation of the liquid. One SiN window had a 100 nm SU-8 spacer, while the other had no spacer. To get the majority of the nanoparticles to adhere to the top SiN window, we dropcast 2 μL of the nanoparticle solution on the top SiN window for 5 min, covered it to avoid evaporation, and then sandwiched with the other chip to form the liquid layer. In situ imaging of gold nanoparticle mobility and selfassembly was performed with a 200 kV FEI Tecnai G2 F20 TEM operating in annular dark field (ADF) STEM mode. The STEM was operated at a magnification of M = 56000×, pixel dwell time of 2 μs, and image area of 512 × 512 pixels, resulting in a single frame scan time of 0.5 s. The electron beam currents used were between 107 and 634 pA, obtained by changing the size of the second condenser lens aperture and the spot size of the microscope (i.e., strength of the second condenser lens). The beam current at each spot size and aperture setting was measured prior to the in situ experiments through a hole in a carbon grid on the TEM phosphorescent screen following a

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EXPERIMENTAL METHODS Nanoparticle Preparation. Gold nanoparticles functionalized with carboxylic acid via a monolayer poly(ethylene glycol) (PEG) linker were obtained from Ocean NanoTech (San Diego, CA). The nanoparticles had a nominal diameter of 30 nm with ∼15% polydispersity; the PEG monolayer added approximately 3−4 nm to the hydrodynamic radius of the nanoparticles. For the self-assembly experiments (Figure 3), 30 μL of nanoparticles was washed by centrifugation and the pellet resuspended in 20 μL of an acetate buffer containing 27 mM sodium acetate and 2 mM magnesium acetate, with the pH adjusted to 4.5 with glacial acetic acid. The concentration of nanoparticles in the stock solution was approximately 2 × 1011 B


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The Journal of Physical Chemistry C previous method.44 Continuous capture movies were recorded at each beam current for approximately 3 min using a freeware screen grabber, AutoScreenRecorder (Wisdom Software), that recorded images at a rate of 8 frames/s. Kinetic data and diffusion coefficients were extracted from the ADF-STEM movies with custom particle tracking algorithms in MATLAB. See the Supporting Information for further details on the second-order aggregation kinetics used to quantify the selfassembly rate and the method for measuring the diffusion coefficient of the nanoparticles.

We did not observe any dependence of the diffusion coefficient on the position of the nanoparticles within the imaging area. The diffusion coefficient distribution shifted to higher values as beam current was increased. Figure 1d shows that despite the broad distributions, the median diffusion coefficient clearly increased with beam current, indicating an overall increase in nanoparticle mobility. Interestingly, the experimentally measured nanoparticle diffusion coefficients ranged from Dexp = 0.1−7 nm2/s, which are 7−8 orders of magnitude smaller than the Stokes−Einstein value of the molecular self-diffusion coefficient, Dth = (kBT/ 6πμa) = 1.63 × 107 nm2/s, where kB is Boltzmann’s constant, T is temperature, μ is the solution viscosity, and a is the particle radius.56 Hindered nanoparticle diffusion in liquid cells has been observed by several research groups,38,48,51,57 but the mechanism causing the decreased nanoparticle mobility remains unclear. Current hypotheses include increased viscous drag near the window surface,38,48 surface roughness,48 highly viscous ordered liquid layers,48,53 and strong nanoparticle− window interactions.48,51,53 The increased viscous drag force on a particle near a solid wall only accounts for a decrease in the diffusion coefficient of less than an order of magnitude.53,58 Alternatively, the hindered nanoparticle mobility is likely brought about by the strong interaction of nanoparticles with the SiN window surface. These interactions likely include dipolar, electrostatic, and possibly depletion interactions. Verch and co-workers investigated the diffusion of gold nanoparticles in an 80% glycerin solution using liquid cell STEM imaging and proposed that nanoparticle movement occurred by electrostatic ejection of nanoparticles from the SiN window, followed by strongly hindered Brownian motion in an ordered high viscosity layer of liquid near the surface.53 In contrast with our findings of a beam current-dependent diffusion coefficient (Figure 1c,d), they observed that the electron beam current had no significant effect on the overall diffusion coefficient of the nanoparticles. We expect the difference in behavior is a result of different suspending liquids, as Liu et al. also found that nanoparticle motion was exaggerated at higher beam currents in pure water.40 The model proposed by Verch et al. does not account for the beam current dependence or sticking behavior we observed during nanoparticle motion. On the basis of our observations, we propose that nanoparticle motion in this case was due to continuous hopping of nanoparticles on the SiN window surface (Figure 2). The hopping-mediated mechanism proceeds as follows. The electron beam charged the SiN window positively (Figure 2i), and through contact electrification positive charge was transferred to the gold nanoparticles.59 The nanoparticles acquired the same charge as the window surface and were ejected into the bulk fluid by Coulombic repulsion (ii). While in the fluid, the nanoparticles were electrostatically stabilized and freely diffused by Brownian motion (iii). After a time, the nanoparticles lost their positive charge to the buffer (iv), allowing van der Waals and image charge forces to “pull” the nanoparticles back to the SiN window (v). While the nanoparticles were continuously imaged, this charge−discharge hopping process repeated, giving the appearance of nanoparticle motion with intermittent sticking. Particle migration described by the model above is reminiscent of surface dif f usion and bears little resemblance to Brownian motion resulting from molecular diffusion. Classical surface diffusion is typically interpreted in terms of thermal forces inducing hopping of


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RESULTS AND DISCUSSION We imaged 30 nm gold nanoparticles suspended in a ∼200 nm thick layer of buffer in the liquid cell using continuous ADFSTEM. The concentration in the field of view during liquid cell imaging (cf. Figure 1a) was ∼1019 m−3, considerably higher than the stock solution likely due to preferred adsorption of the weakly charged nanoparticles onto the SiN windows during specimen loading (see Experimental Methods). Prior to imaging, the gold nanoparticles were randomly dispersed on the SiN window surface (cf. Figure 1a, t = 1 s). The nanoparticle suspension was stable ex situ before imaging in the liquid cell; however, all nanoparticles appeared to adhere to the SiN surface at the beginning of the imaging experiment. The nanoparticles became mobile within seconds of imaging and moved parallel to the SiN surface (Figure 1a,b; Supporting Information Movie 1 and Movie 2). Mobilization of the nanoparticles only occurred directly in the area irradiated by the electron beam. Previous reports have indicated that electron-beam-induced nanoparticle motion in the liquid cell is a result of electron beam charging of the SiN windows.45,47,53 The nanoparticles’ trajectories (red lines, Figure 1a,b) appeared to be a superposition of a drift velocity over time and diffusive movement. The nanoparticle motion was not continuous, as particles were observed to intermittently stick to the SiN window. The steady drift was due to electron beam charging of the SiN windows in the irradiated area, which was associated with movement of the imaging electron beam, not the nanoparticles. The diffusive movement was reminiscent of Brownian motion; however, the intermittent sticking behavior is typically not associated with Brownian motion. Qualitatively, we observed the nanoparticle mobility to depend on the imaging electron beam current, i.e., the flux of electrons through the liquid cell. At low beam currents, drift was predominant in the nanoparticle trajectories, and diffusive movement was only a minor component of the trajectories (red lines, Figure 1a; cf. Movie 1). At higher beam currents, drift behavior similar to the lower beam current was observed in a small fraction of the imaged nanoparticles (e.g., bottom right corner, Figure 1b), but most nanoparticles were highly mobile and displayed rapid diffusion, moving several hundreds of nanometers from their origin over 2−3 min (cf. Movie 2). We determined the effective diffusion coefficient, Dexp, of several nanoparticles as a function of the imaging beam current by measuring their mean-squared displacements (see Supporting Information and Figure S1 for details).34,43,50 Figure 1c shows box plots of the diffusion coefficients of 8−12 nanoparticles at each beam current. There was a broad distribution of diffusion coefficients at each beam current, typically spanning nearly an order of magnitude. This is consistent with our qualitative observations that while some nanoparticles were highly mobile at high beam currents, a few did not move far from the initial position (Figure 1b, Movie 2). C


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nanoparticles more time to migrate by molecular diffusion and increases their hopping distance and observed diffusion coefficient (Figure 2, dashed lines). These simple comparisons of charging time scales do not take into account more complex interactions, such as the amount of electron-beam-induced charge and dipolar forces. Nevertheless, our model qualitatively agrees with several experimental observations, including the observed intermittent nanoparticle sticking and the magnitude of the measured diffusion coefficient. This newly proposed electrostatically induced surface diffusion mechanism sheds light on several previously unexplained observations of nanoparticle diffusion in the liquid cell that were attributed to hindered or confined Brownian motion.38,48,49,51−53,57 Additional work must be performed to develop a more complete surface diffusion model to quantitatively describe nanoparticle motion in the liquid cell. While most self-assembly studies have investigated the effect of tuning various attractive and repulsive interparticle interactions, our goal here is to examine the role of nanoparticle mobility on self-assembly kinetics and final nanostructure morphology. We systematically varied the nanoparticle mobility using the electron beam current and performed in situ electronbeam-induced self-assembly experiments with higher concentration nanoparticle suspensions. Conveniently, the median diffusion coefficient increased approximately linearly with the imaging beam current (cf. Figure 1d). Continuous STEM imaging of higher concentration suspensions of gold nanoparticles induced self-assembly of the nanoparticles into 1D chains and branched structures over several minutes. In these experiments, the stock solution had an order of magnitude higher concentration of nanoparticles than in the mobility experiments. (cf. Figure 3a). Figure 3 shows typical time-lapsed

Figure 2. Schematic representation of electrostatically induced surface diffusion of a nanoparticle in the liquid cell. Solid lines indicate ejection, diffusion, and impingement of the nanoparticle at low beam currents, while the dashed lines indicate the same processes at high beam currents.

adatoms between surface sites with the hopping rate, Γ, described using a Boltzmann function, Γ = ν exp(−EA/kT), where v is the attempt frequency, EA is the potential energy barrier to hopping, and kT is the thermal energy.60 Here surface diffusion is a result of electron-beam-induced electrostatic forces, so we term this mechanism “electrostatically-induced surface diffusion”. In the context of the hopping rate equation above, the potential energy barrier to nanoparticle hopping in this case is due to attractive van der Waals forces, while the exponential term should be scaled to the electrostatic forces instead of thermal forces. Simple scaling arguments for the contact electrification and discharge times emerge from the proposed surface diffusion model. The characteristic charge relaxation time derived from Maxwell’s equations is τ = εε0/σ, where εε0 and σ are the relative permittivity and electrical conductivity of the dielectric medium transferring charge, respectively.61 The time scale for charging of the nanoparticle when it is in contact with the highly insulating SiN window (σ = 10−12 S/m, ε = 7) is τc ≈ 10 s, while the time scale for discharge in the conducting buffer solution (σ = 0.228 S/m, ε = 80) is τd ≈ 10 ns. If we assume the simplest case of nanoparticle charging on the SiN window for τc ≈ 10 s followed by ejection and diffusion for τd ≈ 10 ns, the time scales indicate that the nanoparticle spends most of its time on the SiN window, only migrating by molecular diffusion for nanoseconds at intermittent times. These time scales show that nanoparticle hopping, not molecular diffusion, is the ratelimiting process that controls mobility. The hopping rate and surface diffusion coefficient are related by Dsurface = Γa2/4, where a is the particle radius.60 Assuming that the hopping rate is equal to the inverse of the charging time (Γ = 1/τc = 0.1 s−1), the predicted surface diffusion coefficient from our model is Dsurface ≈ 5 nm2/s, which is within an order of magnitude of our experimental measurements. Changing the electron beam current does not affect the charging time scale as it is inherent to the dielectric properties of the SiN window,61 so this is a simple estimate of surface diffusion that does not account for the electron beam current dependence. The beam current could affect the surface diffusion in several ways. Increasing the beam current will increase the rate of electron beam charging, which would increase the hopping rate and observed diffusion coefficient. Another possibility is that the increased magnitude of charge occurring at higher beam currents ejects the nanoparticles farther from the window, which allows the

Figure 3. Nanoparticle mobility-dependent self-assembly. Time-lapsed ADF-STEM images of self-assembly of gold nanoparticle chains over 150 s. The nanoparticles were imaged at beam currents that yielded median diffusion coefficients of D̃ exp = 1.75 nm2/s in (a) and D̃ exp = 1.75 nm2/s in (b). The scale bar in the final panel of (b) is 200 nm.

ADF-STEM image series of self-assembly of nanoparticles with low (Figure 3a) and high (Figure 3b) mobilities. Similar to the lower nanoparticle concentration mobility experiments, the gold nanoparticles were initially randomly deposited on the SiN window surface (cf. Figure 3a, t = 1 s). Nanoparticles imaged at a beam current that yielded a relatively low measured nanoparticle mobility (D̃ exp = 0.1 nm2/s) became mobile within seconds of imaging and collided with neighboring nanoparticles to form dimers (Figure 3a, t = 50 s) and eventually 1D chains (t = 150 s) (see Movie 3). Nanoparticles D


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with their total number decreasing monotonically with their size. The number of monomers decreased more rapidly than that for the lower mobility nanoparticles. The population of dimers decreased monotonically over the entire assembly process, while the number of trimers peaked at ∼15 s and decreased over the rest of the observation period as well. The number of tetramers and pentamers increased until 50 and 90 s, respectively, and then decreased monotonically until 165 s. The rapid decrease in the number of monomers, which led to a near absence of single nanoparticles after 75 s, and the formation of branched structures (e.g., red arrows, Figure 3b) suggest that chain−chain attachments were predominant during selfassembly of highly mobile nanoparticles. Branched nanostructures formed almost exclusively by attachment of chains with each other, not by attachment of single nanoparticles to the sides of chains. On the basis of these kinetic data, we identified two selfassembly pathways in the liquid cell: slow sequential growth of linear chains by monomer−chain attachment for nanoparticles with low mobility (Figure 4a) and fast simultaneous growth of different-sized chains and branched nanostructures by chain− chain attachment for highly mobile nanoparticles (Figure 4b). Self-assembly at intermediate nanoparticle mobilities occurred by a combination of these two pathways (cf. Figure S2). The formation of branched nanostructures from highly mobile nanoparticles further supports the chain−chain attachment pathway, as two nanoparticle chains have been shown to have a lower probability of end-to-end assembly than a chain and a particle.27 To further quantify the self-assembly kinetics in the liquid cell and understand the role of nanoparticle mobility, we measured the rate of nanoparticle self-assembly with secondorder aggregation kinetics.32,63−65 We tracked the number of single nanoparticles, i.e. monomers (n1), as a function of time using custom image analysis algorithms. We determined the effective self-assembly rate, i.e. the rate of depletion of monomers (kM), from the slope of the inverse number of monomers as a function of time (Figure 5a, see Supporting Information for details). The slope of the inverse number of monomers clearly increased with nanoparticle mobility, indicating more rapid self-assembly for more mobile nanoparticles (Figure 5). Importantly, since kM measures how fast monomers were depleted from the system, it quantitatively corroborates our previously suggested mechanism for the change in self-assembly pathway with nanoparticle mobility. For low nanoparticle mobilities, depletion of monomers was relatively slow and monomers persisted throughout the selfassembly process, driving further self-assembly by sequential monomer-chain attachments (cf. Figures 3a and 4a). For highly mobile nanoparticles, monomers were depleted quickly, causing the self-assembly to occur predominantly by chain−chain attachments (cf. Figures 3b and 4b). We previously indicated that beam current modulates the nanoparticle mobility (cf. Figure 1); however, the electron beam also has been shown to affect liquid cell self-assembly experiments in other ways. An increase in nanoparticle mobility is often associated with increased thermal energy. Several previous liquid cell studies have shown that temperature increases in the liquid cell are typically only on the order of single Kelvin, so electron beam heating does not likely have a significant contribution to nanoparticle mobility or selfassembly.45,57,66 Liu et al. proposed that self-assembly of functionalized nanoparticles in the liquid cell was due to


imaged at a beam current that yielded an order of magnitude increase in mobility (D̃ exp = 1.75 nm2/s) detached from the SiN window immediately upon exposure to the imaging electron beam, diffused rapidly, and assembled into trimers and tetramers within the first seconds of imaging (Figure 3b, t = 1 s, see Movie 4). Self-assembly proceeded between neighboring nanoparticles to form higher-order chains (t = 50 s) and branched structures (e.g., red arrows in Figure 3b, t = 150 s). Previous reports suggested that formation of 1D nanoparticle chains, as opposed to 2D or 3D structures, was a result of dipolar20,40 and anisotropic electrostatic interactions.25,42 Self-assembly kinetics were extracted from in situ liquid cell STEM movies by counting the number of nanoparticle chains with lengths ranging from one to five nanoparticles (Figure 4).

Figure 4. Number of nanoparticle chains with sizes ranging from 1 to 5 nanoparticles as a function of time, for the self-assembly examples in (a) Figure 3a and (b) Figure 3b.

In agreement with our qualitative observations in Figure 3a, the first ∼15 s of self-assembly of the nanoparticles with low mobility led primarily to dimer formation (Figure 4a). The number of dimers increased to a maximum at ∼25 s, accompanied by a monotonic decrease in the number of monomers and the appearance of trimers at ∼20 s. Tetramers appeared at ∼50 s and increased in number monotonically until 75 s. Comparing the kinetic data with direct observations of self-assembly (Figure 3a and Movie 3) revealed that tetramer formation proceeded primarily by monomer−trimer attachment. At 75 s, the numbers of dimers and trimers began to decrease, tetramer numbers continued to increase, and pentamers began to form. The majority of the nanostructures formed during the observation period were linear 1D chains. Overall, the appearance of each nanoparticle chain length in the kinetic data was well separated in time, suggesting that selfassembly of nanoparticles with low mobility occurred by sequential addition of single nanoparticles to existing chains. In stark contrast to the low mobility case, the self-assembly pathway for highly mobile nanoparticles was marked by simultaneous formation of mixed chain lengths and eventual formation of branched nanostructures (Figure 4b). After ∼0.5 s of imaging, all chain lengths measured had already appeared, E


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a function of the median diffusion coefficient shows a clear linear dependence and demonstrates that the increase in selfassembly rate with mobility is consistent with a diffusionlimited aggregation mechanism (Figure 5b). Considering the highly confined environment of the liquid cell and the previously discussed electron beam effects, it is not intuitive that this simple scaling analysis would explain the driving force for self-assembly in this case. Importantly, the agreement of our self-assembly kinetics with classical diffusion-limited aggregation demonstrates that if all electron beam effects are accounted for, the phenomenon observed in the liquid cell can provide important insights for conventional benchtop experiments, in this case identifying nanoparticle mobility as an important alternative kinetic design parameter for tailoring self-assembly. Because the self-assembly occurred in a near 2D confined liquid layer, our results may be applicable to methods where the nanoparticle self-assembly occurs in a 2D environment, such as Langmuir−Blodgett techniques, self-assembly at liquid−liquid or liquid−air interfaces, or evaporation-induced self-assembly. Specifically, the strong interaction of the nanoparticles with the SiN window during self-assembly will make our results important to consider for 2D self-assembly techniques where there is a strong interaction between the nanoparticles and interface.69,70 These in situ experiments using electrons to induce self-assembly must still be compared to lab scale experiments to determine to what extent these results can inform design of new self-assembly strategies. Taken together, the aggregation kinetics and diffusionlimited aggregation mechanism revealed that the rate of selfassembly and pathway were ultimately controlled by the nanoparticle mobility (Figure 6). We propose the following

Figure 5. Diffusion-driven nanoparticle self-assembly. (a) Inverse number of monomers normalized to the original number of monomers, n01, as a function of time for three measured nanoparticle mobilities indicated in the plot. The black lines are least-squares fits to the first 20 s of self-assembly. (b) Self-assembly rate, kM, as a function of the median diffusion coefficient, D̃ exp. The solid black line is a leastsquares fit to the data; the Pearson’s correlation coefficient is P = 0.98. Error bars are equal to two standard deviations of the mean of three measurements.

degradation of the surface functional groups by radicals, which decreased the nanoparticle surface charge and allowed van der Waals interactions to induce aggregation.40 Alternatively, several researchers have suggested that creation of radiolytic species in the liquid could lead to an increase in the ionic strength of the solution,42,67 compressing the electrical double layer and facilitating nanoparticle aggregation. However, radiolysis simulations indicated that radiolytic ionic species were produced at concentrations less than a millimolar,67 which would lead to negligible compression of the electrical double layer in this case, as the ionic strength of our buffer was 33 mM (Debye length of λD = 1.7 nm). Radiolysis modeling also showed that reduction of the solution pH due to radiolytic production of hydronium ions only occurs at near neutral pH or higher.67 The acetate buffer used in these experiments was pH = 4.5; therefore, aggregation due to a pH-induced decrease in nanoparticle surface charge is unlikely to occur as well.67 The nanoparticles in this study were stabilized by a PEG monolayer and carboxylate groups that were likely degraded by the electron beam, which destabilized the nanoparticles and allowed van der Waals forces to induce aggregation. A nanoparticle mobility-dependent self-assembly rate is consistent with classical diffusion-limited aggregation,68 so we hypothesize that the increased nanoparticle mobility caused the increase in self-assembly rate. To test our hypothesis for diffusion-driven self-assembly, we consider the classical Smoluchowski kinetic treatment of diffusion-limited aggregation in which the flux, J, of surrounding particles toward a central “test” particle is formulated as J = 2πDr(∂c/∂r), where c is the particle concentration and r is the distance from the test particle surface.68 It follows from the argument that the rate of aggregation of single particles into dimers, i.e. kM, is proportional to the particle flux and is therefore linearly dependent on the particle diffusion coefficient.68 A plot of kM as

Figure 6. Schematic representation of the mechanism for gold nanoparticle chain self-assembly.

mechanism for the gold nanoparticle self-assembly in the liquid cell. The electron beam charged the SiN window, which caused the gold nanoparticles to become mobile (cf. Figures 1 and 2). Simultaneously, radicals created by ionization of the water molecules in the buffer degraded the PEG monolayer and charged carboxyl groups on the nanoparticle surfaces, reducing their overall stability. Even though the nanoparticles were destabilized, they remained mobile due to the electron beam charging of the SiN window. Once mobile, the nanoparticles self-assembled via diffusion-limited aggregation. Nanoparticles with a lower average mobility were less likely to collide with neighboring nanoparticles than highly mobile nanoparticles, and formed linear chains due to anisotropic electrostatic interactions. Consequently, single nanoparticles persisted throughout self-assembly, driving further chain growth via monomer−chain attachment. Highly mobile nanoparticles quickly collided with neighboring particles, causing rapid depletion of single nanoparticles, and further self-assembly proceeded via chain−chain attachment. As a result, branched F


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nanostructures, mesostructures, and mesocrystals.72 Advanced STEM and TEM imaging techniques such as 3D optical sectioning,73,74 electron tomography,75 and iterative reconstruction methods76 could be applied to visualize these more complicated 3D structures in liquid.

nanostructures formed during self-assembly of highly mobile nanoparticles. Using a similar in situ liquid cell technique, Grogan et al. observed 5 nm gold nanoparticles contained in a 200 nm thick water layer to aggregate into large 3D fractal aggregates.41 Their key observation was that highly confined 3D fractal aggregates retained characteristics of 3D diffusion-limited aggregation because the aggregates were not confined at the early stages of aggregation. Likewise, we expect that the early time selfassembly will most closely mimic 3D solution phase selfassembly, while self-assembly at later times or with longer chains will be subject to confinement effects. No anisotropic growth of aggregates was noted by Grogan and co-workers,41 likely because they observed later stages of aggregation compared to the early stages that we observe in the current study. The difference in aggregate morphology was also likely due to differences in nanoparticle size, as 5 nm nanoparticles have a relatively larger thermal energy (compared to drag forces), allowing them to more easily overcome anisotropic energy barriers. Here we expect nanoparticles self-assembled into chains instead of fractal aggregates due to the greatly reduced mobility coupled with anisotropic electrostatic interactions between nanoparticles and chains.25,26,42 While in this case the beam current was used to modify the nanoparticle mobility and self-assembly process, we expect the results of this study to readily translate to other parameters that control the mobility (e.g., as determined by the Stokes−Einstein equation for the self-diffusion coefficient, Dth = kBT/6πμa), such as solution viscosity, μ, temperature, T, and particle size, a.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.5b07164. Diffusion of a dilute suspension of gold nanoparticles at 122 pA beam current (AVI) Diffusion of a dilute suspension of gold nanoparticles at 634 pA beam current (AVI) Self-assembly of gold nanoparticles with a median diffusion coefficient of 0.1 nm2/s (107 pA beam current) (AVI) Self-assembly of gold nanoparticles with a median diffusion coefficient of 1.75 nm2/s (634 pA beam current) (AVI) Kinetics at all nanoparticle mobility conditions and methods for measuring diffusion coefficient and selfassembly rate (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected] (T.J.W.). Present Address

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T.J.W.: Material Measurement Lab, National Institute of Standards and Technology, Boulder, CO 80305.

CONCLUSIONS In conclusion, we directly observed the kinetics of nanoparticle chain self-assembly using liquid cell STEM imaging. The combination of real-time nanoscale observations and kinetic measurements allowed insight into the self-assembly mechanism. We discovered that the mobility of nanoparticles was modulated by the imaging electron beam current, and this effect was exploited to explore the role of mobility on selfassembly. We interpreted the observed diffusion in terms of electrostatically induced surface diffusion driven by nanoparticle hopping on the liquid cell window surface. By systematical varying the nanoparticle mobility, we observed the self-assembly pathway to change from sequential monomer−chain attachments for nanoparticles with a relatively low mobility to chain−chain attachments for highly mobile nanoparticles. Second-order aggregation kinetics revealed that the self-assembly rate increased approximately linearly with the nanoparticle diffusion coefficient, consistent with a diffusiondriven self-assembly mechanism. Some limitations exist for our technique as the self-assembly is induced by the imaging electron beam and occurs in a thin liquid layer. The selfassembly may not be representative of a fully 3D system due to confinement effects but should translate to methods that utilize 2D liquid layers such as evaporation induced self-assembly and Langmuir−Blodgett techniques. We do not have independent control over the imaging conditions (i.e., scan speed, magnification, and beam current) and self-assembly conditions, but use of a pump−probe technique such as dynamic TEM (DTEM) could allow for independent control of these two variables.71 Nevertheless, we expect our results on mobilitymediated self-assembly to translate to other self-assembly stimuli, like capillary drying forces or electric or magnetic fields, as well as self-assembly of other types of 2D and 3D

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Cari Dutch and William Ristenpart for assistance in developing the image analysis algorithms for single particle tracking and diffusivity measurements. T.P. acknowledges support from the Department of Energy Office of Science Early Career Research Award, Biomolecular Materials Program. This work was supported by the U.S. Department of Energy, Office of Basic Energy Science, Division of Materials Sciences and Engineering. The research was performed at the Ames Laboratory, which is operated for the U.S. Department of Energy by Iowa State University under Contract DE-AC0207CH11358.

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The Mechanisms for Nanoparticle Surface Diffusion and Chain Self

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