Supplementary Materials for

Transcription

1 Supplementary Materials for Tracking Nanoparticle Diffusion and Interaction during Self- Assembly in a Liquid Cell Alexander S. Powers, Hong-Gang Liao, Shilpa N. Raja,, Noah D. Bronstein, A. Paul Alivisatos,,, Haimei Zheng,,* Department of Chemistry, Department of Materials Science and Engineering, University of California, Berkeley, CA 94720, United States Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA. Kavli Energy NanoScience Institute, Berkeley, CA 94720, United States * To whom correspondence should be addressed. hmzheng@lbl.gov This Supporting file includes: Supporting Text Image Analysis Algorithm Size Distribution Analysis Morphological Analysis Particle Conformation Analysis Calculation of Nanoparticle Forces from Trajectories Supporting Movie captions Supporting Figures S1 to S14 References 1

2 Supporting Text Image Analysis Algorithm Intensity in a TEM image is a result of the scattering of electrons off the sample, which is affected by the local thickness of the scattering medium. Consequently, a perfectly spherical particle should show an approximately Gaussian intensity being thickest at the center and progressively thinner toward the edge. Gaussian intensity blobs in the image are identified by convolving the image with a Laplacian of the Gaussian filter (LoG), which produces strong signal at the center of a blob matching the size of the filter. This is fast, which is critical for the large size of the images across the hundreds of frames of the movie as seen in Figure S1. The algorithm developed for this study utilizes a scale space approach, which applies successively larger filters to identify different blobs at different scales. The noisy lower resolution videos used filters from 7x7 to 19x19 pixels and the higher resolution used filters from 19x19 to 37x37 pixels. The size of the filter corresponds to 2*ceil(3*sigma)+1 where the radius of a blob is approximated at 1.5*sigma. At each scale the local maximums of the filtered image were selected and a threshold applied to obtain particle centers, though the threshold applied differed depending on the scale. Because the particles are likely identified at multiple similar scales as in Figure S2, particles with some percent of their area overlapping are filtered by keeping only the particle that gave the largest intensity response to the LoG filter. Accuracy of the detection method was defined as 1 - (number of particles missed + incorrectly identified noise)/(total number of particles). An example of identification in a difficult image can be seen in Figure S3. Size Distribution Analysis We used our automated algorithm to measure the particle diameters and polydispersity over the course of the videos. Some degree of variance in particle sizes was beneficial for assessing the effect of size on properties; however, too much variance would interfere substantially with the assembly process such as limiting close packing. The particles between both videos are, on average, < 5 nm in diameter with standard deviations ranging from 12-16%. Toward the end of video S1, Ostwald ripening effects and particle fusion events lead to significant broadening of distribution well after the culmination of the assembly process (Figure S7). More extreme sized particles where often not part of the main assembly process. Thus the local distribution was often significantly lower at ~10% (Figure S8). The automated measurement of the size is complicated by a difficulty in measuring the particle size at low resolution particularly in Movie S1. When compared against a hand measured diameter, the automated sizing method gave a random error of ~5% likely due to a dependence of the method on the nanoparticle intensity profile, not just the edge. This error inherently broadened the effective distribution 2

3 Morphological Analysis We characterized the nanoparticle roundness, circularity, area, and Feret diameter using hand outlined particles (Figure S9). This analysis supported the qualitative observation that the particles 2-D projections are spherical to slightly elliptical with a few exceptions, specifically large elliptical particles formed due to fusion of smaller particles. On average, there was a 12% difference between the particle diameter calculated from the 2D projected area assuming a sphere and the Feret diameter (the longest distance across the particle). This difference indicated the majority of the particles were slightly elliptical. We analyzed the 3D particle morphology by tracking the 2-D projections of several particles over time (Figure S10). This indicated the particle shape was consistent over time and likely spherically symmetric. The distribution in areas of each particle over time was roughly Gaussian and likely mainly due to intensity and contrast fluctuations in the image itself. If the particles had a more anisotropic 3-D morphology we would have expected to see different projected shapes over time (such as circles and ellipses for a rotating nanorod). Indeed, there was no correlation between the projected area and any shape descriptions such as circularity. Particle conformational analysis Particles were classified purely based on relative position into packed, chains, and random configurations. An example of classification can be seen in Figure S4 using mock particle center points. First, particles with more than 4 neighbors less than 1.5 times the average particle diameter were classified as packed along with these neighbors. Next, chains were identified from the remaining particles based on two parameters, the distance between particles as well as the angle formed by drawing line segments to connect the centers of any three particles. By stepping along particles that met the criteria, chains were identified particle by particle (though different possible chains can be identified based on the order of the center points). Figure S5 shows an example using mock center points of the effect of changing these two parameters, allowing the selection of chains that are straighter or have particles that are closer together. A typical angle limit was 100 degrees and a typical length limit 7 nm. Two examples of chain identification can be seen in Figure S6. A second method was then applied that connects together chains or adds particles that may have been missed the first time through. Finally, the remaining particles are classified as random. 3

4 Calculation of Nanoparticle Forces from Trajectories We use the following equation to represent the potential between two nanoparticles of radius R, magnetic moment m, and center separation l:,, = 3( )( ) + When the particles aligned dipoles, this equation simplifies to: ( )= ( +2 ) ( ) + ( ) The derivative of this potential gives an expression of the force that particles exert on each other: (, )= 6 ( +2 ) ( ) ( ) = 0 4 We measure the relative velocity of nanoparticle movements (v) when a spherical nanoparticle approaches another nanoparticle. The velocity is expressed as v = 0.5(dL/dt) where the distance between nanoparticles (L) is defined as the nearest distance between the inorganic surfaces of two nanoparticles and t is time. From the Fluctuation Dissipation Theorem, velocity can be related to the applied force by the drag coefficient. 10 r r F =ξ v The Einstein relation then relates the drag coefficient to the diffusion coefficient of the nanoparticle. 10 ξ frictional = The diffusion coefficient (D) of a nanoparticle is estimated by tracking the movements of an individual, isolated nanoparticle of the same size in the same growth solution and within the same field of view. The 2-D diffusion coefficient (D) is calculated by plotting the mean squared displacement vs. time (Figure S11). The plots are fit to the equation = +4. This procedure yielded an average value from 4 trajectories of D=0.11 ± 0.08 nm 2 /s in Movie S1 and D=0.19 ± 0.1 nm 2 /s in Movie S2. The selected nanoparticles are relatively far from other nanoparticles, thus the movements can be considered as not being biased by interparticle attraction. From an estimation of the electron beam effects, including local heating, momentum transfer, and electron charges, we believe the electron beam effects on the particle motion can be neglected at the current imaging condition. k B T D diff 4

5 Therefore, the interaction force in newtons can be calculated from the relative velocity as: F = k B Tv/D Determination of Electric and Magnetic Dipole Magnitudes from experimental data The force vs. distance data in Figure S12 was fitted to the general force model. The fitting parameters allowed a determination of the dipole moment. Because the electric and magnetic dipoles both have the same functional form, decaying as 1/r^3, we wanted to distinguish between the two. We compared the values obtained for magnetic and electric dipole moments of individual nanoparticles obtained from liquid cell TEM videos of assembly to values in the literature for semiconductor and metal nanoparticles. Semiconductor nanoparticles have innate permanent electric dipole moments ~100 D due to differences in stoichiometries of facets and surface and ligand effects 1-3 while metal nanoparticles are less likely to have intrinsic dipole moments and to date there are no studies showing intrinsic dipole moments in metal nanoparticles to the best of our knowledge. 1 Below, we calculated and have found that the value for the magnetic dipole moments of individual FePt 3 nanoparticles matches very closely the magnetic dipole moment value obtained in this work based on experimentally measured values of the magnetic dipole moment in the literature. We found a value of ~65 D for the electric dipole moment, this is very high given the literature consensus that metal nanoparticles have no dipole moment 1 and also, previous work has shown that metal atoms (which are far more polarizable than large metallic clusters) 4,5 have an induced dipole moment of ~0.5 D when brought into the proximity of polar molecules. 6 Therefore, we considered and conducted calculations of the electric dipole induced onto the nanoparticles by the electric field of the TEM electron gun high voltage source and also the electron beam at the sample to see if the electron beam or source could be inducing an electric dipole. These calculations, explained in more depth below, indicate far better agreement for magnetic dipole moments than electric dipole moments, suggesting that the driving force for assembly is more likely to be a magnetic interaction between nanoparticles than electrostatic interaction. Calculations of Magnetic Dipole Moment: Previous work on similarly synthesized nanoparticles with a similar degree of chemical disorder has shown magnetic dipole moments ~0.5-1[µB] per FePt 3 formula unit for FePt 3 nanoparticles. 7 Using this value, a weighted average density for FePt 3 of ~18 g/cm 3 and the known atomic and formula weights for Pt, Fe, and FePt 3, we found an overall magnetic dipole moment per nanoparticle (sizes of 5-8 nm) of 1.24e-20 A*m 2 to 5.1e-20 A*m 2. This compares reasonably with the experimentally obtained value of 1.877e-20 A*m 2. Calculations of Electric Dipole Moment: As previous work indicates no electric dipole in metallic nanoparticles, 1 we computed it via two techniques. In the first method, we 5

6 assumed a ~250 kv high voltage electron source with an anode-cathode separation of ~3 cm, resulting in an electric field of 8500 kv/m. With a typical electron beam column length of 1-2 m (assumed 1.5 m) this results in an electric field at the sample surface of ~213 V/m. Using textbook equation for the polarizability of metallic spheres (since the polarizability of metallic nanospheres with thousands of atoms should be very similar to the bulk polarizability 4,8 ) we obtain a polarizability of 3.055e-35 F*m 2. Using the abovementioned value for the electric field this corresponds to an induced polarization per nanoparticle of ~2e-03 D, orders of magnitude smaller than the experimentally observed one (~65 D). Therefore, it is unlikely that the field due to the electron beam source in the TEM is inducing the electric dipole. We also considered the electron beam as a disk of static charge density in which the sample is contained at the center. 9 For a properly focused and aligned microscope the illumination area should be in the center of the beam or the disk of charge; the electric field at the center of a uniformly charged disk is zero, 9 meaning that it is unlikely that the electron beam incident on the sample is inducing the dipoles. Supporting Movie captions Movie S1. Rapid growth and assembly of PtFe nanoparticles at a resolution of 0.9 nm/pixel covering a cropped area from a total imaging area of 500 nm x 500 nm with a capture speed of 5 frames per second. Particles are present in both packed and chain configurations. Movie plays at 4x original speed. Movie S2. Rapid growth and assembly of PtFe nanoparticles at a resolution of 0.2 nm/pixel covering an imaging area of 100 nm x 100 nm with a capture speed of 5 frames per second. Movie plays at 4x speed. Movie S3. Pure platinum nanoparticles were grown and imaged under identical conditions to the previous movies. Movie plays at 4 times original speed. 6

7 Figure S1. Raw TEM image from Movie S1 illustrates the full 500 nm x 500 nm imaging areas. The imaging region contains both regions of close packing (lower left) as well as chains (center). Figure S2. Example of particle analysis from Movie S1 shows particle identification at multiple length scales prior to filtering overlapping particles. 7

8 Figure S3. Particles identified by the algorithm are marked with a red dot at their center. This image from Movie S1 illustrates identification at multiple length scales, with poor contrast, and low resolution. Figure S4. Particle classified into 3 different configurations using mock center points to validate the classification algorithm. The 3 configurations and corresponding colors are random (black), chains (blue with red connecting line), and close-packed (yellow). Figure S5. Chain identification using mock particle centers showing the effect of varying two parameters, the angle between any three particles and the distance between nearby 8

9 particles. A smaller threshold for the angle and distance results in more linear, shorter chains (lower right example). Figure S6. Numbered, colored lines label algorithmically identified chains from actual particle centers in two images from Movie S1. Chains wrapped into loops as well as intersecting chains are successfully identified. Figure S7. Distribution of nanoparticle diameters from Movie S1 at time 4.2 seconds followed a normal distribution with SD of 12.7%. Over time the SD ranged from 12-20% although assembly was largely complete at 30 seconds before the SD rose above 16%. 9

10 Figure S8. The distribution of nanoparticles in a local cluster from Movie S2 had a SD of only 11% but still followed a roughly normal distribution. Figure S9. The circularity vs. roundness of over 100 hand outlined particles is plotted on left. A perfect sphere has the maximum circularity and roundness values of 1. The color of each data point corresponds to the particle diameter. On right, the distribution of particle sizes was calculated using two methods. In blue, the effective particle diameter was calculated from the area assuming a sphere. In orange, the Feret diameter is the longest distance across the particle. 10

11 Figure S10. (a) The 2D projections of three particles were tracked and plotted over time from left to right (not based on actual spatial location). Each adjacent time point is separated by 0.2 seconds. (b) The area of the projections from (a) are tracked over time with corresponding colors. (c) A histogram of the areas measured in (b) for each of the three particles. Figure S11. The mean squared displacements vs. time of particles from different ranges of sizes. The diffusion coefficients were measured by fitting these curves to the formula = +4 which corrects for camera drift in the measurement. 11

12 (A) (B) (C) (D) Figure S12. (a) Colored lines indicate the tracked paths of two nearby nanoparticles. The estimated relative particle velocity is used to color-code the paths. The starting position of the particles is indicated by black circles as well as the position at an intermediate time-point upon contact. (b) The relative velocity was measured for pairs of similarly sized particles. This relative velocity is plotted vs. the surface-to-surface distance of the pair. As particle near each other within 10 nm, they are strongly attracted. (c) The velocity was translated into a force using the Einstein relation and the known diffusivity of the corresponding particle size. The zero velocity at close distances indicates the point at which ligand repulsion becomes significant. (d) The force vs. distance from c is fitted to a potential with combines a magnetic dipole term and Lennard-Jones term. 12

13 Figure S13. The net dipole magnetic moment was estimated based on fitting interaction potentials to particle force trajectories. The magnetic moment increased with increasing particle size as seen on left. On the right, the magnetic moment per volume was calculated by dividing the net moment by the particle volume. The measurements on the left deviated from the mean of 0.08E(-20) A*m 2 /nm 3 (red line) by at most 30% and on average 16% suggesting fairly high precision between measurements and a reasonable trend. The expected moment per volume was approximately 0.05E(-20) A*m 2 /nm 3 as calculated in Reference 7. Figure S14. An example of a validation test of the method to determine the orientation of dipoles that gives minimum total energy. This test uses a hexagonal array of 36 point dipoles at the locations shown. The dipoles orientations are solved for using a gradient descent minimization algorithm with the angle as variables. 13

14 Figure S15. Validation test 2 of the method to determine the orientation of dipoles that gives minimum total energy using a 4x4 grid of point dipoles. Figure S16. Demonstration of the alignment of dipoles giving minimum total energy for particles aligned in chains. The directionality of the dipoles indicates that dipoles in chains are well aligned at the energy minimum. Figure S17. Demonstration of the alignment of dipoles giving minimum total energy for particles aligned in chains and packed. 14

15 Figure S18. Distribution of spacing between packed nanoparticles to estimate ligand shell thickness. The particles on average approach to a distance of 1 nm indicating that the ligand shells interpenetrate to some extent. References 1. Shim, M.; Guyot-Sionnest, P. Permanent Dipole Moment and Charges in Colloidal Semiconductor Quantum Dots. J. of Chem. Phys. 1999, 111, Zhang, X.; Zhang, Z.; Glotzer, S. C. Simulation Study of Dipole-Induced Self- Assembly of Nanocubes. J. Phys. Chem. C. 2007, 111, Talapin, D. V.; Shevchenko, E. V.; Murray, C. B.; Titov, A. V.; Král, P. Dipole Dipole Interactions in Nanoparticle Superlattices. Nano Lett. 2007, 7, Griffiths, D. J. Introduction to Electrodynamics; Pearson Higher Ed: Harlow, Coker, H. Empirical Free-Ion Polarizabilities of the Alkali Metal, Alkaline Earth Metal, and Halide Ions. J. Phys. Chem. 1976, 80, Luo, Y. R.; Benson, S. W. Dipole-Dipole Induced Forces in the Reaction of Alkali Metal Atoms with Polar Molecules. J. Phys. Chem. 1988, 92, Margeat, O.; Tran, M.; Spasova, M.; Farle, M. Magnetism and Structure of Chemically Disordered FePt3nanocubes. Phys. Rev. B 2007, 75, Kresin, V. Static Electric Polarizabilities and Collective Resonance Frequencies of Small Metal Clusters. Phys. Rev. B 1989, 39, Holbrow, C. H.; Lloyd, J. N.; Amato, J. C.; Galvez, E.; Parks, M. E. Modern Introductory Physics; Springer Science & Business Media, Dill, K. A. Molecular Driving Forces: Statistical Thermodynamics in Chemistry and Biology; Garland Science: New York,