## Ultrafast studies using liquid cells

Advances in microscopy techniques aim to make it possible to study materials under more realistic conditions, such as in liquid cells, or to use fast probes to capture dynamics. Fu *et al.* combined liquid cell transmission electron microscopy with ultrafast pump-probe spectroscopy to perform time-resolved studies of nanoscale objects (see the Perspective by Baum). They successfully captured the change in rotational dynamics of coupled gold nanoparticles and also observed the dynamics as two particles fused together in a liquid environment.

## Abstract

In real time and space, four-dimensional electron microscopy (4D EM) has enabled observation of transient structures and morphologies of inorganic and organic materials. We have extended 4D EM to include liquid cells without the time resolution being limited by the response of the detector. Our approach permits the imaging of the motion and morphological dynamics of a single, same particle on nanometer and ultrashort time scales. As a first application, we studied the rotational dynamics of gold nanoparticles in aqueous solution. A full transition from the conventional diffusive rotation to superdiffusive rotation and further to a ballistic rotation was observed with increasing asymmetry of the nanoparticle morphology. We explored the underlying physics both experimentally and theoretically according to the morphological asymmetry of the nanoparticles.

Liquid cell electron microscopy provides one approach for studying liquid-phase processes in real space by means of a direct visualization technique (*1*–*3*). Applications of this technique have been demonstrated in broad areas of research, including nanocrystal growth (*4*–*7*), electrochemical reactions (*8*, *9*), imaging of labeled structures within living biological cells (*10*–*12*), and the reconstruction of the three-dimensional structure of individual particles (*13*).

However, in previous work, the images were either static or taken at long time intervals, the limitation being the millisecond response of the detector in conventional microscopes. To visualize fast intrinsic dynamics, a time scale on the order of nanoseconds or picoseconds is required, and our method of choice is four-dimensional electron microscopy (4D EM) (*14*–*19*).

We studied the rotational dynamics of gold nanoparticles (NPs) by using liquid cell 4D EM to investigate the relation between these dynamics and the NPs’ morphological asymmetry. The gold NPs (60 to 90 nm in diameter) were capped by citrate ligands for stabilization and dispersed in aqueous solution sealed in a liquid cell (*20*). An ultrafast laser pulse triggered the rotation of the gold NPs, and another ultrafast electron pulse probed the subsequent dynamics. Different temporal resolutions, from picoseconds to nanoseconds and longer times (fig. S1), were obtained by using two laser systems (Fig. 1A). Single-shot imaging shows that after an incoming laser pulse, the initially weakly bound gold NPs on the liquid cell substrate begin to levitate in 10 to 20 ns and subsequently rotate by specific angles at different delay times, as observed in real time and space. Combined model simulations and experimental results indicate that the rotational dynamics are actuated by an impulsive torque (peak value of 4.6 × 10^{3} nN**·**nm, duration of ~14 ns) stemming from the photoinduced generation, expansion, and collapse of steam nanobubbles (NBs).

Experiments were performed with our upgraded ultrafast EM instrument (UEM-1) (*18*) with the integration of a liquid cell, as schematically depicted in Fig. 1. The structure of the liquid cell is shown in Fig. 1B. It contained a thin layer of solution (gold NPs in water) sandwiched between two electron-transparent, 20-nm-thick silicon nitride membranes (*20*) (fig. S2). The solution was ~300 nm thick, as determined by focusing the electron beam (e-beam) on the NPs absorbed near the bottom and top membranes (fig. S3). The precisely timed laser pulse (in green) and electron pulse (in blue) arrived at the NPs in the liquid cell through the silicon nitride membrane window (Fig. 1C). Single-shot images, which were acquired by one electron pulse, were then recorded at specific delays on the same particle to trace its dynamics in aqueous solution.

We studied the rotational dynamics of isolated gold NP dimers induced by impulsive laser excitation. First, we traced the transient rotational morphologies of a gold NP dimer (which consisted of two NPs with respective diameters of 57 and 66 nm) induced by a single femtosecond laser pulse with a fluence of 10 mJ/cm^{2} (Fig. 2). Images in the first, second, and third columns of Fig. 2 show the morphologies of the NP dimer before the process, at specific delays (single-shot images), and at the end of the process, respectively. In the absence of a laser pulse, the images in the first (before) and third (end) columns were acquired by accumulating more than 15 electron pulses to enhance the contrast. The red-blue arrow pairs in the first and third columns indicate the initial and final orientations of the NP dimer.

At different delays, the NP dimer orientation changes by specific angles with respect to the initial state. For easy comparison, the orientations of the NP dimer before the process (black dashed lines), at specific delays (solid blue lines), and after the process ended (solid pink lines) are presented in the fourth column of Fig. 2. The relative rotation angle increases with the delay time (single-shot images at additional time points are shown in fig. S4). The rotation angles are 0°, 2°, 12°, 17°, 22°, and 29° at time delays of 10, 20, 26, 42, 90, and 150 ns, respectively. The rotation angles are absolute values because the rotation direction is random (clockwise or counterclockwise) in each single-shot experiment, as indicated by the pink arc arrows (Fig. 2). Considering that the Brownian dynamics of the NPs are ballistic at this nanosecond time scale (*21*), the evolution of the dimer rotation angle with the delay time was plotted in Fig. 3A (blue dots). The rotation angle only increases to 2° from 10 to 20 ns, whereas it increases rapidly to 17° at 42 ns, followed by a very slow increase. The rotation angle at the delay of 150 ns (29°) is nearly 90% of the observed total rotation angle (33°) after the excitation pulse. From the work of the Alivisatos group (*22*, *23*), it is known that NPs inside a thin layer of solution sandwiched in a liquid cell are weakly bound near the substrate surface by the weak electrostatic interaction. Upon the femtosecond laser pulse excitation, the particle acquires an angular momentum in ~20 ns; the hindered rotation is damped in hundreds of nanoseconds as a result of the surrounding drag, with the translation occurring on similar to longer times. There are several processes that may actuate the particle dynamics, including those involving the direct interaction between the electromagnetic field of the laser pulse and the NPs (*24*, *25*). However, such processes (e.g., the Kerr effect) are complete in the duration (~350 fs) of the laser pulse.

Because of the strong optical absorption of gold NPs at 520 nm by localized surface plasmon enhancement, the laser pulse heats up the NPs in hundreds of picoseconds upon excitation (*14*). This results in a nonequilibrium temperature of ~900 K for the NPs at the fluence of 10 mJ/cm^{2}, which is below the melting point of gold (*26*). If the laser fluence is above the threshold of melting for the gold NPs, the NP dimer fuses into a bigger NP in a few tens of nanoseconds (fig. S5), which has also been demonstrated by El-Sayed, Link, and others (*26*). The thermal energy in the pair subsequently dissipates to the surroundings, including the liquid and the low-frequency van der Waals modes between the particle and the substrate. The high nonequilibrium temperature of the NP, which is far above the boiling point of water (~400 K), is sufficient to overcome the latent heat of water and to convert the adjacent water molecules into steam NBs (*27*). Because of the nonuniform heating caused by the imperfect symmetry of the NP dimer, rapid nucleation, expansion, and collapse of steam NBs near the NP surface could induce an impulsive force and torque on the dimer to trigger the dynamics, as schematically shown in Fig. 3B. This mechanism was experimentally confirmed by continuous e-beam imaging of the gold NP dimer rotation induced by a train of femtosecond laser pulses (Fig. 3, C and D, and movie S1) and of a gold NP cluster rotation induced by a single femtosecond laser pulse (fig. S6 and movie S2). The high image contrast of the continuous e-beam imaging mode allows the NB to be visible near the initial position of the dimer (an example is shown in Fig. 3D, where the NB is indicated by a circle), and the dimer is actuated to rotate and translate by the impulsive force stemming from the NB.

We set up a simple model to explore the underlying physics of the rotational dynamics, in which the dynamical equation is given by(1)where θ(*t*) is the rotation angle, *I*_{0} = 4.4 × 10^{–12}_{}g**·**nm^{2} is the moment of inertia of the gold NP dimer, γ is the damping rate constant due to the surrounding drag, and *f*(*t*) is the impulsive torque. In our data analysis, a Poisson function was considered for the impulsive torque because of its simple analytic form, which allows an easier nonlinear curve fit (a Gaussian shape pulse also works)(2)where *A* is a constant related to the peak value of the impulsive torque, and *n*** × **τ_{c} is the delay time of the peak value. In the fit of the experimental data, we chose 4 for the parameter *n* (a change of its value from 2 to 6 does not affect the fit meaningfully).

The fit is shown by the violet curve in Fig. 3A, and the retrieved impulsive torque is depicted by the red dashed curve. As shown in the inset, the impulsive torque has a full width at half-maximum (FWHM) of ~14 ns, and it reaches the peak value of 4.6 × 10^{3} nN**·**nm at ~11 ns. The duration of the impulsive torque agrees well with the lifetime of the femtosecond pulse–induced steam NBs around the gold NPs in water, as measured by the optical scattering method (*27*, *28*), which further verifies our hypothesis. The magnitude of the effective damping effect, which is due to the surrounding drag involving both the friction from the liquid and the interaction from the substrate, was also extracted from the fit as a damping constant γ of 0.03 ns^{−1}.

We further studied the continuous rotational dynamics of NP dimers by increasing their morphological asymmetry, and we observed a full transition from conventional diffusive rotation to superdiffusive rotation and further to a ballistic rotation. This experiment was conducted in the continuous e-beam imaging mode in order to obtain better statistics for revealing this transition. As presented in Fig. 4A, the typical snapshots of a NP dimer (D1)—with its two NPs with similar diameters of 60 and 67 nm (a ratio of 1:1.1)—were recorded at different femtosecond laser illumination times (fluence of 2.4 mJ/cm^{2}; see the trajectory in fig. S7 and movie S3). Before illumination, the NP dimer is stabilized in the liquid cell by the weak substrate attraction (first image of Fig. 4A). Upon laser excitation, the NP dimer shows distinct orientations and positions at different times, as indicated by the red-blue arrow pairs. At this low fluence, the continuous motion is induced by the accumulation of the repeated pulse heating, because the heating from one single pulse is insufficient. The rotation direction reverses at certain times (pink arc arrows). Therefore, the dimer rotates and translates in the manner of “random walk” under the repeated laser pulse excitation.

To analyze the statistical properties of the rotation angle θ(*t*), we extracted an ensemble of the dimer trajectories at different starting times τ_{0} and ending times *t*. The angular displacements of these trajectories are given by Δθ(*t*) = θ(*t +* τ_{0}) – θ(τ_{0}). For simplification, we define counterclockwise as the positive direction. The angular displacement of the D1 dimer nearly follows a Gaussian distribution, with a slight bias toward the negative side (first column of Fig. 4B). This behavior indicates the almost equal probability to rotate either clockwise or counterclockwise. By increasing the NP dimer shape asymmetry [D2 and D3 dimers, with the two NPs having diameters of 60 and 80 nm (a ratio of 1:1.3) and 60 and 90 nm (a ratio of 1:1.5), respectively], the angular displacement distribution becomes biased to one side (negative or positive), as shown in the second and third columns of Fig. 4B (see their snapshots and trajectories in fig. S8 and movies S4 and S5). The angular displacement of the D3 dimer is completely biased toward the positive side (third column of Fig. 4B), representing a unidirectional counterclockwise rotation with random step length.

The mean square angular displacements (MSADs) (*20*) of the three NP dimers show linear increases in the log-log scale plot, but with distinct slopes (Fig. 4C). The MSADs follow a power law of _{}, where the exponent α increases with the bias of the angular displacement distribution. The retrieved value of α increases from 1.11 for the D1 dimer, to 1.51 for the D2 dimer, and further to 1.95 for the D3 dimer. According to Einstein’s theory (*21*) and the description of the Langevin equation (*29*) for two-dimensional rotational Brownian motion, _{} represents a diffusive rotation, where *D*_{r}* *is the rotational diffusion coefficient, whereas _{} represents a ballistic rotation, where ω_{rms} is the root mean square (RMS) angular velocity. Both of them are plotted in Fig. 4B. For the D1 dimer, with the two NPs of similar size, both its MSAD (α ≈ 1) and the translational mean square displacement (MSD; fig. S9) show the conventional diffusive behavior. Because of the large random impulsive torques induced by the photoinduced steam NBs, the rotational diffusion coefficient (4.68 rad^{2}/s) of D1 is nearly four orders of magnitude larger than those of the colloidal nanorods without laser excitation (*30*, *31*). The D2 dimer (1 < α < 2) displays a superdiffusive rotation, where the random impulsive torques have a much higher probability in one direction than in the opposite one. The highly asymmetric D3 dimer (α ≈ 2) exhibits a ballistic rotation, where the impulsive torques are unidirectional but random in magnitude. The ballistic rotation of the highly asymmetric D3 dimer indicates that the photoinduced NBs occur at an almost identical position on the dimer and result in the unidirectional (counterclockwise) random impulsive torques.

The effect of laser fluence on the MSADs of the NPs was also investigated. As shown in Fig. 4D, the highly asymmetric D3 dimer maintains ballistic rotation (α = 1.97 for the MSAD) under a higher laser fluence of 3.2 mJ/cm^{2} (see the trajectory in fig. S10), which is also evidenced by its angular displacement distribution (last column of Fig. 4B). Therefore, for a given NP, its rotational dynamics are insensitive to the laser fluence used in this work but are dominated by its morphological asymmetry (Fig. 4C). Moreover, the RMS angular velocities ω_{rms} of D3 at the fluences of 2.4 and 3.2 mJ/cm^{2} are 0.94 and 1.72 rad/s, respectively—that is, ω_{rms} almost doubles when the laser fluence increases only by 30%. Such an increase is much higher than the estimation assuming equipartition of the kinetic energy with the temperature, where ω_{rms} ∝ √*T*—further verifying that the random impulsive torques on the asymmetric gold NPs are dominated by the photoinduced steam NBs, rather than collisions from the thermal motion of the liquid molecules.

We performed numerical simulations of the MSADs of random rotation with different biased angular displacement distributions to unravel our experimental observations (*20*) (fig. S11). In line with the theoretical analysis for the translational diffusion (*32*), we assumed a scheme of one-dimensional random walk for our rotational dynamics and considered that the exponent α depends on the bias of the angular displacement distribution, which is dominated by the dimer asymmetry (Fig. 4). Specifically, the rotation direction was controlled by a random number between 0 and 1, and the step length of the rotation was a random number with a Gaussian weight (*20*). As shown in fig. S11, all the MSADs closely follow the power law of _{}, and their exponent α increases from 1 to 2 as the bias of their angular displacement distributions increases from 0 (no bias, conventional diffusive rotation) to 1 (total bias to one direction, ballistic rotation), which is in good agreement with the experimental results. Therefore, both our experimental results and simulations support that the full transition of the rotation dynamics is dominated by the shape asymmetry of the NP dimer.

We used liquid cell 4D EM to study the rotational dynamics of gold NPs in real time and space. We demonstrated the ability for the visualization and temporal control of the particle orientation at the nanometer scale and elucidated a range of anomalous behavior, thus revealing the mechanism in different processes. The demonstrated liquid cell 4D EM with ultrafast time resolution will allow measurement of the instantaneous velocity of an individual Brownian particle to study its nonequilibrium dynamical behavior with a connection to the particle structure, as well as the hydrodynamics of its surrounding fluids (*33*). This advance also opens up the possibility for time-resolved three-dimensional structure reconstruction of individual nanocrystals and biomolecules for the same particle and in their native environments.

## Supplementary Materials

www.sciencemag.org/content/355/6324/494/suppl/DC1

Materials and Methods

Supplementary Text

Figs. S1 to S11

Movies S1 to S5

## References and Notes

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**Acknowledgments:**This work was supported by the Air Force Office of Scientific Research, grant FA9550-11-1-0055S, for research conducted at The Gordon and Betty Moore Center for Physical Biology at the California Institute of Technology. We thank J. S. Baskin for very helpful discussion and for his help setting up the new femtosecond laser system. We appreciate J. K. Barton, R. A. Marcus, and J. F. Brady for helpful discussion and suggestions. We also thank J. Hu and H. Li for fruitful discussion.