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Ultrafast spinning of gold nanoparticles in water using circularly polarized light Anni Lehmuskero, Robin Ogier, Tina Gschneidtner, Peter Johansson, and Mikael Käll Nano Lett., Just Accepted Manuscript • DOI: 10.1021/nl4010817 • Publication Date (Web): 18 Jun 2013 Downloaded from http://pubs.acs.org on June 22, 2013

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Ultrafast spinning of gold nanoparticles in water using circularly polarized light Anni Lehmuskero1*, Robin Ogier1, Tina Gschneidtner2, Peter Johansson1,3, and Mikael Käll1* 1

Department of Applied Physics, Chalmers University of Technology, S-412 96 Göteborg,

SWEDEN 2

Department of Chemical and Biological Engineering, Chalmers University of Technology, S-

412 96 Göteborg, SWEDEN 3

School of Science and Technology, Örebro University, S-701 82 Örebro, SWEDEN

ABSTRACT Controlling the position and movement of small objects with light is an appealing way to manipulate delicate samples, such as living cells or nanoparticles. It is well-known that optical gradient and radiation pressure forces caused by a focused laser beam enables trapping and manipulation of objects with strength that is dependent on the particle’s optical properties. However, by utilizing transfer of photon spin angular momentum, it is also possible set objects into rotational motion simply by targeting them with a beam of circularly polarized light. Here we show that this effect can set ~200 nm radii gold particles trapped in water in 2D by a laser tweezers into rotation at frequencies that reach several kilohertz, much higher than any previously reported light driven rotation of a microscopic object. We derive a theory for the fluctuations in light scattering from a rotating particle and we argue that the high rotation frequencies observed experimentally is the combined result of favorable optical particle

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properties and a low local viscosity due to substantial heating of the particles surface layer. The high rotation speed suggests possible applications in nanofluidics, optical sensing and microtooling of soft matter.

KEYWORDS Optical tweezers, spin angular momentum, optical torque, photothermal effects, hydrodynamics TEXT Spin angular momentum (SAM) is an inherent property of circularly polarized light having a value of ± per photon, where is the reduced Planck’s constant and the sign indicates the polarization handedness 1. When an absorbing particle is illuminated by circularly polarized light, the SAM of the absorbed photons is transferred to the particle, resulting in a light induced torque. The optical torque is counteracted by resistive torques, in particular due to the drag force in the case of viscous media, causing the particle to spin with a constant frequency around some particular preferred axis of rotation. This phenomenon was first observed for microscopic CuO particles 2 and later demonstrated for plasmonic silver nanowires 3, both of which rotated by a few turns per second. Other optical rotation techniques rely on the shape asymmetry of the trapped object

4, 5, 6

, on birefringence 7, or on transfer of orbital angular momentum carried by a

laser beam with a particular phase structure 2 , 8, 9, 10, 11. Particles can even be made to spin using linearly polarized light, but this typically requires mechanical rotation of optical components. The highest optical rotation frequency reported to date, ~360 Hz, was obtained for a 1 µm thick birefringent calcite crystal trapped three-dimensionally in a 300 mW focused laser beam 7. Sub-wavelength sized particles have optical properties that can be dramatically different from what might be expected from their macroscopic counterparts. Noble metal nanoparticles are particularly interesting in this respect because they support surface plasmon resonances that have


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profound influence on their interaction with light, including optical force interactions 16

12, 13, 14, 15,

. We chose to work with colloidal gold particles with an average radius R = 200 nm (citrate

stabilized colloidal gold nanoparticles from Sigma Aldrich) and a Ti:Saph trapping laser (Spectra-Physics 3900S) operated at a wavelength of 830 nm, which is within the window of low absorption of water. The gold particles have a round shape and their size is well matched to the diameter of a focused near-infrared laser beam. Together with the relatively high particle absorption cross-section, this ensures an efficient transfer of SAM. The gold nanoparticles were rotated in an optical tweezers setup constructed around an inverted microscope (Nikon TE300) equipped with white-light dark-field-illumination for the detection of the particles (Figure 1a). The particles were diluted with purified water (Milli-Q) to low enough concentration to avoid simultaneous trapping of several particles. Samples consisted of ~3 µl droplets of diluted colloid suspension placed between two glass cover slides separated by a 100 µm spacer. The relatively large metal particles considered here cannot be trapped in 3D using a single focused laser beam because the radiation pressure caused by absorption and reflection overcomes the optical gradient force in the light propagation direction. We therefore utilize a 2D trapping scheme in which particle movement along the optical axis is restricted by the upper cover glass in the sample cell (Figure 1b). Circularly polarized laser light is focused onto the sample by an air microscope objective (60X, NA = 0.7) and the light scattered from a trapped particle is collected with a fiber-coupled avalanche photo diode (APD) and analyzed with an autocorrelator (ALV–500).


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Figure 1. Measuring rotation frequency of gold nanoparticle. (a) Schematic of the setup. The near-infrared trapping laser beam ( 830 nm) is expanded to fill the back aperture of the objective and circularly polarized using appropriate optical components. The sample is also illuminated with white light through a dark field (DF) condenser. The light scattered from the trapped particle is recorded by an avalanche photo diode (APD) and analyzed by an autocorrelator. (b) The gold particle is optically trapped between two cover glass slides and pushed against the upper cover glass by the radiation pressure. The particle starts to rotate by absorbing spin angular momentum from the circularly polarized laser beam. (c) Transmission electron microscope image of the gold particles. The particles are round, with average radius of 200 nm, but with irregular deviations that results in a light scattering intensity that fluctuates with the periodicity of the optical rotation. (d) Intensity autocorrelation functions for a particle


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subject to circular (blue squares) and linearly polarized laser light (red triangles). The solid lines represent fits to the data using Equation (9) (blue) or a simple exponential decay (red).

Because the particles are irregular in shape (Figure 1c and Supporting Information Figure S1d), the amount of scattered light collected by the detection system depends on the particle orientation. Consequently, when the particle rotates at constant angular velocity, the light intensity oscillates periodically around some average value. In reality, however, there is also rotational Brownian motion, i.e. the angular velocity of the particle fluctuates. This means that the scattered intensity from the particle shows short-time oscillatory correlations, but eventually, for a sufficiently large lag time τ (temporal separation of two intensity data points), the correlations vanish. Experimental results for the intensity autocorrelation function for a particle trapped with circularly and linearly polarized light, respectively, are shown in Figure 1d. As is clearly seen, only circular polarization produces an oscillating autocorrelation function, corresponding to rotating motion, whereas linearly polarized light only produces an exponentially decaying correlation. It should be noted that although the particle’s translational Brownian motion has an effect on the autocorrelation function, the periodic oscillation that we observe here cannot originate from it. We have discussed this topic in the Supporting Information. The rotation frequency of the particle can be read off as the inverse of the time elapsed between two peaks in the autocorrelation function. The precise analytical expression for the intensity autocorrelation function can be derived from the Fokker-Planck equation

17, 18

. To start with, let


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us assume that the particle only rotates around the z-axis and that the scattering intensity varies with the rotation angle as

cos , (1) where N is an integer describing the dominating deviation from spherical symmetry of the particle (degree of detectable rotational symmetry). In practice, N=1 and N=2 are the only cases that we judge as relevant here. The intensity correlation function for a lag time can then, assuming without loss of generality that 0 0, be written

0

cos . (2)

The rotation around a single axis, driven by an external torque Me from the incident light, is governed by an equation of motion that can be written

!" !# !$ , (3) where J=2mR2/5 is the moment of inertia of a sphere with mass m and radius R, ω is the instantaneous angular velocity of rotation, Mf is a friction torque proportional to ω and Ms finally, is a stochastic torque. For a light intensity I, photon energy % and a particle absorption cross section &abs , the external torque due to SAM transfer is !" &abs /%

19

. This optical

torque is counteracted by a viscous frictional torque, which for laminar flow (low Reynolds number) and a spherical particle of radius R in a liquid with dynamical viscosity η is given by Stokes equation, !# *8+,- . %

20

. When ω equals the average angular velocity Ω, the optical

and frictional torques exactly balance each other, i.e. !" !# 0, which yields an average rotational frequency


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/

0

1

2345

61 78 9 : .

.

(4)

It is also likely that friction against the coverglass resist the rotational motion. Although difficult to quantify, such a friction term would in a first approximation be proportional to the radiation pressure and therefore reduce the rotation frequency by a constant factor. To calculate f from Equation (4), we have approximated the shape of the trapped particles by a sphere with radius R = 200 nm and the laser field is locally approximated by a plane wave. The particle absorption cross-section can then be obtained from Mie theory (Supporting information Figure S1), which yields &1 when there are no correlations left between the angular positions and velocities, something that is already satisfied for τ~10 µs here.

Equation (8) describes a

Gaussian distribution that at each instant is centered around Ωτ and that gradually spreads out as τ increases. The width of the distribution grows as √ , characteristic for a random walk, while a large friction β reduces the rate with which the distribution of angular positions broadens. Knowing the distribution function W we can calculate the correlation function in Equation (2), and arrive at

exp G*

2 WB C `

Q cosΩ . (9)

Thus for N=1, the correlation function oscillates with the average rotational frequency f=Ω/2π, while the oscillation amplitude decays with a characteristic time constant

` 8+,- .s rW C Wq C. (10) q

As can be seen from the fit of the experimental data in Figure 1d, Equation (9) gives an excellent description of the measured correlation function29. We measured the rotation frequency f and the correlation time for 14 different particles by fitting their autocorrelation functions to (the oscillating part of ) Equation (9) with N = 1 because of the low-symmetry particle shapes seen in the TEM image (Figures 1c and S1d). Figure 2 shows the results for two representative particles as a function of laser power. As shown, the


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frequency of the signal increases for increased laser power P indicating faster rotation due to increased angular momentum transfer. Also the correlation time changes as a function of the power, as an increased power leads to a higher particle temperature. This is predicted by Equation (10) according to which an increase of the particle temperature and the consequent decrease of the water viscosity reduces the correlation time.

Figure 2. Representative autocorrelation functions. (a,b) Evolution of the measured autocorrelation functions for two different particles as the power in the sample plane increases


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from 11.3 to 39.3 mW. The rotation frequency, f, and the correlation time, , were obtained by fitting the experimental data to Equation (9).

Figure 3 gives a power dependent scatter plot of f and for all measured particles together with the theoretical predictions obtained from Equations (4) and (5) for f and Equation (10) for . The observed rotation frequencies in Figure 3a are of the order 0.1–3 kHz for laser powers between about P = 10 mW and 50 mW (measured in the sample plane) while the highest oscillation frequency is f = 3.6 kHz, i.e. an order of magnitude higher than the previously reported maximum rotation frequency value7. Keeping the aforementioned uncertainty concerning the actual particle surface temperature and our neglect of cover glass friction in mind, the theory is in surprisingly good quantitative agreement with the experiments for both the correlation time and the rotation frequency power dependencies, albeit with a considerable spread in the experimental values. We assign this variation between different particles mainly to differences in particle shape and size (the size polydispersity is approximately 12%), which will affect the optical forces as such, as well as the friction. We expect that more irregular particles have higher friction and thereby increased correlation time and reduced rotation speed. Indeed, particle b in Figure 2 (the gray data points in Figure 3) displays both longer correlation times and smaller rotation frequencies than particle a (the orange data points in Figure 3), which is consistent with the larger friction.


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Figure 3. Power dependence of the rotation frequency and the correlation time. (a) Scatter plot of the power-dependent measured rotation frequencies and their 95 % confidence limits for 14 different nanoparticles together with a theoretical estimate of the rotation frequency (dashed black line) obtained from Equations (4) and (5). (b) Measured correlation times for the same 14 particles as in (a), together with their 95 % confidence limits. Theoretical correlation times (dashed black line) are obtained from Equation (10). Each nanoparticle has been coded with a single unique color.

In conclusion, we have demonstrated that transfer of spin angular momentum from circularly polarized light to absorbing gold nanoparticles can cause the particles to rotate at frequencies of several kHz, much faster than previously reported results of optical spinning. The experimental observations are altogether well described by classical electromagnetic and hydrodynamic


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theory. Possible application areas include microtooling of soft matter membranes, rapid mixing in nanofluidics

31

30

, for example cell

, and to use the rotation parameters as probes of

nanoscale viscosity 32, 33, 34 and/or temperature. It was concluded that the heating of the particles at high laser powers facilitates optical spinning because it lowers the viscosity and friction of the embedding water, but the exact extent of this effect is uncertain at present. Laser heating at the nanoscale is interesting in its own right and subject to considerable research efforts in biophysics and nanomedicine 35. One might here note that recent results on laser induced heating of gold nanoparticles indicate that water vapor can form close to the particle surface at illumination conditions similar to what has been used here28. Although we did not observe actual vapor bubble formation, very high rotation frequencies are indeed expected if particles can be made to rotate freely in a gas or vacuum environment 36.

ASSOCIATED CONTENT Supporting Information. The supporting information includes the scattering, absorption and extinction cross-sections calculated by Mie-theory together with the measured spectra. In addition, a high resolution TEM image demonstrating the irregular shape of the particles is provided. We also show that free, linear oscillations of the particle in the trapping potential cannot lead to the intensity fluctuations we have observed. This material is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author * E-mails: [email protected], [email protected]


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Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Funding Sources Göran Gustafsson Foundation, the Swedish Research Council, and Chalmers Nanoscience Area of Advance. ACKNOWLEDGMENT This work was supported by the Göran Gustafsson Foundation, the Swedish Research Council and Chalmers Nanoscience Area of Advance. We thank Mokhtar Mapar, Dr. Liaming Tong, and Gülis Zengin for valuable experimental assistance ABBREVIATIONS SAM, spin angular momentum; APD, avalanche photo diode; DF, dark field. REFERENCES 1. Poynting, J. H. The wave motion of a revolving shaft, and a suggestion as to the angular momentum in a beam of circularly polarised light. Proc. R. Soc. Lond. A 1909, 82, 560–567. 2. Friese, M. E. J.; Enger, J.; Rubinsztein-Dunlop, H.; Heckenberg, N. R. Optical angularmomentum transfer to trapped absorbing particles. Physical Review A 1996, 54, 1593-1596. 3. Tong, L.; Miljković, V. D.; Käll, M. Alignment, Rotation, and Spinning of Single Plasmonic Nanoparticles and Nanowires Using Polarization Dependent Optical Forces. Nano Letters 2010, 10, 268–273. 4. Messina, E.; Cavallaro, E.; Cacciola, A.; Saija, R.; Borghese, F.; Dent, P.; Fazio, B.; D’Andrea, C.; Gucciardi, P. G.; Iati, M. A.; Meneghetti, M.; Compagnin, G.; Amendola, V.; Marago, O. M. Manipulation and Raman Spectroscopy with Optically Trapped Metal Nanoparticles Obtained by Pulsed Laser Ablation in Liquids. The Journal of Physical Chemistry C 2011, 115, 5115–5122. 5. Jones, P. H.; Palmisano, F.; Bonaccorso, F.; Gucciardi, P. G.; Calogero, G.; Ferrari, A. C.; Maragó, O. M. Rotation Detection in Light-Driven Nanorotors. ACS Nano 2009, 3, 3077–


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3084. 6. Liu, M.; Zentgraf, T.; Liu, Y.; Bartal, G.; Zhang, X. Light-driven nanoscale plasmonic motors. Nature Nanotechnology 2010, 5, 570–573. 7. Friese, M. E. J.; Nieminen, T. A.; Heckenberg, N. R.; Rubinsztein-Dunlop, H. Optical alignment and spinning of laser-trapped microscopic particles. Nature 1998, 394, 348–350. 8. Dienerowitz, M.; Mazilu, M.; Reece, P. J.; Krauss, T. F.; Dholakia, K. Optical vortex trap for resonant confinement of metal nanoparticles. Optics Express 2008, 16, 4991–4999. 9. Simpson, N. B.; Dholakia, K.; Allen, L.; Padgett, M. J. Mechanical equivalence of spin and orbital angular momentum of light: an optical spanner. Optics Letters 1997, 22, 52-54. 10. Allen, L.; Beijersberger, M. W.; Spreeuw, M. R. J. C.; Woerdman, J. P. Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes. Physical Review A 1992, 45, 8185-8189. 11. He, H.; Friese, M. E. J.; Heckenberg, N. R.; Rubinsztein-Dunlop, H. Direct observation of transfer of angular momentum to absorptive particles from a laser-beam with a phase singularity. Physical Review Letters 1995, 75, 826-829. 12. Dienerowitz, M.; Mazilu, M.; Dholakia, K. Optical manipulation of nanoparticles: a review. Journal of Nanophotonics 2008, 2, 1–32. 13. Juan, M. L.; Righini, M.; Quidant, R. Plasmon nano-optical tweezers. Nature Photonics 2011, 5, 349–356. 14. Arias-González, J. R.; Nieto-Vesperinas, M. Optical forces on small particles: attractive and repulsive nature and plasmon-resonance conditions. Journal of the Optical Society of America A 2003, 20, 1201-1209. 15. Agayan, R. R.; Gittes, F.; Kopelman, R.; Schmidt, C. F. Optical trapping near resonance absorption. Applied Optics 2002, 41, 2318-2327. 16. Miljković, V. D.; Pakizeh, T.; Sepulveda, B.; Johansson, P.; Käll, M. Optical Forces in Plasmonic Nanoparticle Dimers. The Journal of Physical Chemistry C 2010, 114, 7472– 7479. 17. Chandrasekhar, S. Stochastic Problems in Physics and Astronomy. Rev. Mod. Phys. 1943, 15, 1–89. 18. Risken, H. The Fokker-Planck Equation; Springer: Berlin, 1996. 19. Marston, P. L.; Crichton, J. H. Radiation torque on a sphere caused by a circularly-polarized electromagnetic wave. Physical Review A 1984, 30, 2508-2516.


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20. Landau, L. D.; Lifshitz, E. M. Fluid Mechanics, 1st ed.; Pergamon Press Ltd.: Oxford, 1959. 21. Ruijgrok, P. V.; Verhart, N. R.; Zijlstra, P.; Tchebotareva, A. L.; Orrit, M. Brownian Fluctuations and Heating of an Optically Aligned Gold Nanorod. Physical Review Letters 2011, 107, 037401. 22. Fogel’son, R. L.; Likhachev, E. R. Temperature dependence of viscosity. Tech. Phys. 2001, 46, 1056–1059. 23. Govorov, A. O.; Richardson, H. H. Generating heat with metal nanoparticles. Nano Today 2007, 2, 30–38. 24. Bendix, P. M.; Reihani, S. N. S.; Oddershede, L. B. Direct Measurements of Heating by Electromagnetically Trapped Gold Nanoparticles on Supported Lipid Bilayers. ACS Nano 2010, 4, 2256–2262. 25. Kyrsting, A.; Bendix, P. M.; Stamou, D. G.; Oddershede, L. B. Heat Profiling of ThreeDimensionally Optically Trapped Gold Nanoparticles using Vesicle Cargo Release. Nano Letters 2011, 11, 888–892. 26. Setoura, K.; Werner, D.; Hashimoto, S. Optical scattering spectral thermometry and refractometry of a single gold nanoparticle under CW laser excitation. Phys. Chem. C 2012, 116, 15458–15466. 27. Neumann, J.; Brinkmann, R. Boiling nucleation on melanosomes and microbeads transiently heated by nanosecond and microsecond laser pulses. J. Biomed. Opt. 2005, 10, 024001. 28. Fang, Z.; Zhen, Y.-R.; Neumann, O.; Polman, A.; Abajo, F. J. G. d.; Nordlander, P.; Halas, N. J. Evolution of Light-Induced Vapor Generation at a Liquid-Immersed Metallic Nanoparticle. Nano Lett. 2013, 13, 1736–1742. 29. In case that particle can rotate around two axes (and is symmetric around a third axis) we may assume that the scattered intensity varies with two angles θ and φ (defining the position of one point on the particle surface) as I(τ)=I0+I2 sinθ cosφ which yields a correlation time that is shorter by a factor of 2 compared with the result found above for the one-axis case. 30. Urban, A. S.; Fedoruk, M.; Horton, M. R.; Ra dler, J. O.; Stefan, F. D.; Feldmann, J. Controlled nanometric phase transitions of phospholipid membranes by plasmonic heating of single gold nanoparticles. Nano Lett. 2009, 9, 2903–2908. 31. Terray, A.; Oakey, J.; Marr, D. W. M. Microfluidic control using colloidal devices. Science 2002, 296, 1841–1844. 32. Bishop, A. I.; Nieminen, T. A.; Heckenberg, N. R.; Rubinsztein-Dunlop, H. Optical microrheology using rotating laser-trapped particles. Phys. Rev. Lett. 2004, 92, 198104.


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33. Pralle, A.; Florin, E.-L.; Stelzer, E.; Hörber, J. Local viscosity probed by photonic force microscopy. Appl. Phys. A 1998, 66, S71–S73. 34. Pesce, G.; Sasso, A.; Fusco, S. Viscosity measurements on micron-size scale using optical tweezers. Rev. Sci. Instrum. 2005, 76, 115105. 35. Cole, J. R.; Mirin, N. A.; Knight, M. W.; Goodrich, G. P.; Halas, N. J. Photothermal Efficiencies of Nanoshells and Nanorods for Clinical Therapeutic Applications. J. Phys. Chem. C 2009, 113, 12090–12094. 36. Manjavacas, A.; García de Abajo, F. J. Vacuum Friction in Rotating Particles. Phys. Rev. Lett. 2010, 105, 113601.


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Halogen lamp + DF condenser

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Mirror

IR Laser

⃗ E

Laser-line filter 60X 0.7 NA Objective

250 nm Mirror Beam expander

Dichroic beamsplitter Hot mirror

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Linear polarizer

Quarter waveplate

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f≈0.5 kHz τ0≈3.6 ms

f≈0.1 kHz τ0≈38.9 ms

f≈1.6 kHz τ0≈1.5 ms

f≈0.3 kHz τ0≈15.1 ms

f≈2.4 kHz τ0≈1.4 ms

f≈0.5 kHz τ0≈8.5 ms

f≈3.0 kHz

f≈0.8 kHz τ0≈6.1 ms

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Au 1 2 3 4 5 6

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T = 1/f

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Au 1 2 3 4 5 6

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T = 1/f

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