Np-Dimer Lab Report

Second, we further studied the continuous rotation dynamics of NP-dimers with increasing asymmetries, and observed a full transition picture from the conventional diffusive to superdiffusive rotation, and further to ballistic rotation. Because a better statistic is needed for revealing this transition picture, we performed the following experiments in the continuous e-beam imaging mode where each experiment could contain hundreds to thousands of data points. Presented in Fig. 4A are the typical snapshots of a NP-dimer (D1), with two NPs in similar diameters of 60 and 67 nm (with ratio 1:1.1), respectively, at different fs-laser illumination times (repetition rate 1kHz; fluence 2.4 mJ/cm2) (see the trajectory in Fig. S6 and Movie S2). Notably, at this low fluence, the continuous motion is induced by the accumulation of the repeated pulse heating, as the heating from one single pulse is insufficient. Before illumination, the NP-dimer is stabilized in the liquid cell by the weak substrate attraction (first image of Fig. 4A). Evidently, upon excitation, the NP-dimer shows distinct orientations and positions at different times, as indicated by the red-blue arrow pairs; while the rotation direction reverses at certain times, as indicated by the pink arc arrows. Therefore, the dimer rotates and translates in the manner of “random walk” under the repeated laser pulse excitation. To further analyze the statistical properties of the rotation angle , we extract an ensemble of the dimer trajectories at different starting times and ending times t later, thus the angular displacements of these trajectories are . For simplifying, we define the counter-clockwise as the positive direction whereas the clockwise as the negative direction. The angular displacement of D1 dimer nearly follows to thea Gaussian distribution yet with a slight bias toward the negative side (first column of Fig. 4B). This behavior indicates the nearly equal probability to rotate in clockwise or counter-clockwise, which interprets the random rotation directions observed in our single-shot measurements. Moreover, the mean square angular displacement (MSAD) is linearly fitted with a slope of ~1.11, over two decades of time in the log-log plot (black annulus in Fig. 4C), which is ~10% larger than the unity value predicted by Einstein’s theory of rotational Brownian motion (the deviations at t >10 s are the result of low statistics at these lag times). According to Einstein’s model, the MSAD is for the traditional diffusive rotation in two-dimensions, where is the rotational diffusion coefficient, as plotted in Fig. 4B by the cyan dashed line for comparison (the slope is 1 in log-log plot). The slight discrepancy of the slope is due to the tiny bias of the angular displacement distribution, which is probably caused by the imperfect symmetry of the NP-dimer. These results demonstrate that the D1 dimer, with the two NPs in similar size, behaves almost in a normal diffusive rotation, where both the direction and magnitude of the impulsive torques are random. The extracted rotational diffusion coefficient = 4.68 rad2/s, which is two to four orders of the magnitude of those of the colloidal nanorods without laser excitation (28, 29). The rise of such high rotational diffusion coefficient is a result of large random impulsive torques induced by the rapid vaporization of water near the particle surface and the rapid generation and collapse of NBs. In addition, its translational mean square displacement (MSD) also shows a normal diffusion (see Fig. S7), with a translational diffusion coefficient of ~ nm2/s, which is four orders of magnitude greater than that of the gold NPs diffusion in water without laser excitation (21). By increasing …show more content…
S8 and also Movie S3 and S4), typical anomalous rotation dynamics begin to emerge (Fig. 4B and C). The diameters of the two NPs for D2 and D3 dimers are 60 and 80 nm (with ratio 1:1.3), and 60 and 90 nm (with ratio 1:1.5), respectively, as shown by the inset images in Fig. 4C. It is interesting to find that the angular displacement distribution of D2 dimer strongly biases to the negative side (second column of Fig. 4B), indicating a much higher probability of clockwise rotation than that of counter-clockwise rotation. In sharp contrast, the angular displacement of D3 dimer totally distributes at the positive side (third column of Fig. 4B), representing a unidirectional counter-clockwise rotation with random step length, where the photoinduced impulsive torques are unidirectional but random in