Construction and Operation of a Light-driven Gold Nanorod Rotary Motor System

1. Circularly Polarized Optical Tweezers for Nanoparticle Rotation

1. Construct the setup around a suitable inverted microscope and use a visible red-wavelength laser (660 nm). A schematic of the experimental setup is presented in Figure 2. Make sure to choose a laser with a stable output power up to 500 mW (producing a power at the sample plane of around 50 mW). Also ensure that the rest of the components perform well at the trapping laser wavelength.
2. Use a dry objective with a numerical aperture (NA) of 0.95 and 40X magnification.
3. Always wear safety goggles and maintain good laser security (especially if using non-visible lasers). Perform alignment on the minimum laser power. Encapsulate the whole laser path for both safety and to avoid thermal drift and dust in the light path.
   NOTE: Depending on the polarization state of the output from the laser, the optical tweezers could benefit from placing a linear polarizer as the initial optical component. If the polarization of the laser is already linear, this component can be omitted.
4. Use a pair of positive lenses in a Keplerian telescope configuration (lenses at bottom of Figure 2) to expand the laser beam such that the beam diameter is slightly larger than the back aperture of the trapping objective.
   NOTE: This enables use of the entire NA of the objective and will produce a diffraction limited focus of the trap¹¹, resulting in optimal trapping stiffness.
5. Make sure that the trapping laser is properly collimated after the beam expander. This can be done by making sure the beam size is close to unchanged when propagating to the objective (or by using a shearing interferometer).
6. Use two mirrors (M1 and M2 in Figure 2), mounted on kinematic mirror mounts (and if needed, a translation stage), to direct the laser beam into the microscope setup.
   Note 1: Keep enough space between laser mirrors and microscope to be able to add additional optical elements such as waveplates and beamsplitters.
   Note 2: Make sure that the laser is always filtered away from the ocular or any other accessible light exiting the microscope.
7. Use a beamsplitter (50/50 partial transmission/reflection is used here, but a dichroic could also work well) inside the microscope to couple laser light into the objective, without losing imaging and measurement capability in the microscope setup.
8. Include a camera (see Figure 2) in the setup for subsequent experimental observation and for data recording. If a system without an ocular is used, this is vital for any alignment.
9. Focus the laser on a glass slide or a mirror. If the laser is aligned and enters the objective at a correct angle, the laser intensity pattern is radially symmetric when changing the focus above and below the focal point.
10. Fine-tune the angles of the laser mirrors (M1 and M2 in Figure 2) to obtain optimal laser alignment (as described in 1.9).
11. Circularly polarize the laser light.
    1. On the light path to the objective, pass the laser through a quarter-wave plate (QWP; λ/4 in Figure 2) oriented with its fast axis at 45° to the linear polarization of the laser light to convert the linearly polarized light into circularly polarized light at the sample plane.
    2. Set up a 360°-rotatable linear polarizer and a power meter in front of the objective.
    3. Check polarization by rotating the linear polarizer and noting the maximum and minimum power, corresponding to the major and minor axis or the polarization ellipse.
       NOTE: The ratio should be higher than 0.9 for optimal rotation performance. If this is not reached, see step 4.2 for a solution.
12. Measure the laser power at the sample plane.
    1. Use an optical power meter to probe the laser power at the sample plane. Take care to collect all the light passed through the objective for a correct gauging of trapping power.
    2. Perform a linear sweep of output laser powers and record the corresponding powers at the sample plane for subsequent conversion to power density in the trap.
13. Set up a dark field (DF) system in Köhler illumination using an oil immersed DF condenser to enable visualization of particles and trapping events. This will allow for both imaging and spectroscopic measurements of the trapped nanoparticles.

2. Instrumentation for Measurements of Rotation, Rotational Brownian Dynamics, and Spectroscopic Properties

1. Photon correlation spectroscopy using a single-pixel detector.
   1. Insert a beamsplitter (30R/70T) into the optical path in order to extract backscattered light from the nanoparticle.
   2. Connect a fast single-pixel Si photodiode to a data acquisition card to enable recording of signals.
      NOTE: It is important to have a photodiode/DAQ that is capable of measuring the rotational frequencies expected (several tens of kHz).
   3. Focus light onto a collection fiber fixed in a xy-translation mount. Insert a linear polarizer before the collection fiber.
   4. For collection fiber alignment, couple visible light to the exit end of the fiber to illuminate the substrate. This allows visualization and analysis of the collection region of the fiber.
   5. Adjust the position of the fiber using the xy-translation mount, so that its collection region coincides with the position of the optical trap. Connect the exit end of the fiber to the Si-detector and fine tune the position of the fiber to maximize the collected back scattered signal.
2. Dark field spectroscopy setup.
   1. Bear in mind that care needs to be taken in choosing all optical components in the path between the sample and spectrometer, in order not to block light within the spectral range of interest.
   2. Take caution as direct scattered and/or reflected laser light might damage the spectrometer sensor. Block the laser light using appropriate filters and/or dichroic beamsplitters. Always perform alignment of the setup on the minimum laser power.
   3. Insert a beamsplitter/mirror in the optical path to redirect light to the spectrometer (in this protocol, a free-space coupled spectrometer is used). One of the microscopes output ports could also be used, if suitable.
   4. Use notch filters to remove the intense trapping laser light (filters of total OD12 at the laser wavelength were needed for sufficient blockage in our case), which in other case will obscure the spectral response of the nanoparticle of interest.
   5. Adjust the position of the optical tweezers by the guiding mirrors (M1 and M2 in Figure 2) so it coincides with the position of the spectrometer slit.
      Note 1: Changes in position of the optical trap will require realignment of the photon correlation measurement system (instructions 2.1.4-2.1.5).
      Note 2: At the new position of the optical tweezers, instructions 1.9-1.10 need to be repeated to reach a well aligned optical trap.

3. Experimental Procedure

1. Preparation of particles for experiments.
   1. Dilute the particles in DI-water. An appropriate concentration of nanorods should be in a range between 0.1-0.01 pM. Sonicate the diluted solution in an ultrasonic cleaner bath for 2 min to break apart possible aggregates and homogenize solution.
   2. Tune the concentration of nanorods in the dilution in order to avoid trapping of multiple particles. The longer the experiment that will be performed, the lower the concentration required to reduce the risk of trapping multiple particles or contaminations.
2. Preparation of sample cell.
   1. Wash a microscope slide and a cover glass (No. 1.5) in acetone and subsequently isopropanol under sonication for five minutes, respectively.
      NOTE: Make sure that the surface charge of the glass slide during experiment has the same polarity as the colloidal nanoparticles. Nanoparticles stabilized by the surfactant hexadecyltrimethylammonium bromide (CTAB) are positively charged.
   2. Place a 100 µm spacer tape well on the glass slide.
   3. Disperse 2 µL of the diluted nanoparticle solution on the microscope slide within the well and 2 µL on the cover glass. Solution on both surfaces allows for a more controllable assembly of the sample cell.
   4. Connect the two parts of the sample cell together while avoiding forming any air bubbles inside the chamber.
   5. Place the cell on the microscope stage and place a drop of index-matched (immersion) oil on top of the sample and one drop on the condenser. Drops on each side avoid bubbles in the oil that scatters light and reduces the contrast of the DF illumination.
3. Performing an experiment.
   1. Locate a particle through observation in the DF imaging system. A single nanorod can usually be identified through observation of its Brownian motion (more erratic than aggregates) and color (corresponding to the strongest LSPR resonance).
   2. Start/unblock the trapping laser.
   3. Through a series of stage movement and focus corrections, push the chosen particle via radiation pressure in the laser's propagation direction towards the water-glass interface. At the interface, the z-movement is constrained by a balance between radiation pressure and Coulomb repulsion between CTAB molecules on the nanoparticle surface and the positively charged surface. The xy-fluctuations are confined by gradient forces in the optical tweezers.
   4. Through small focus corrections, maximize trapping stability or rotation speed, gauged from the autocorrelation data (as described below in instruction 3.4).
   5. At this point, record both rotational dynamics and spectroscopic properties of the trapped nanorod. See instructions 3.4 and 3.5 below on how to probe these. This can be done over extended periods of time, up to several hours if needed.
4. Rotational dynamics measurements.
   1. Make sure to have a collection region from the fiber that is large enough to always enclose the image of the particle during its translational motion.
   2. Collect intensity oscillation signal with the Si photodetector at an appropriate probing frequency and collection time. Choose 65536 Hz and 1 s acquisition time to start with and adjust if needed.
      NOTE: Probing frequency should be at least two (and optimally ten) times larger than the rotation frequency multiplied by the degree of detectable rotational symmetry (N, see below). Collection time should be long enough to be able to obtain frequencies significantly lower than the rotation frequency.
   3. After having collected a set of intensity fluctuation data from a rotating nanoparticle, calculate the autocorrelation of the intensity fluctuation. This is done by calculating the correlation of the signal with a time-delayed copy of itself for each delay time τ (i.e.,C(τ) = {I(τ)·I(0)}).
   4. Perform a fit to the theoretical autocorrelation function
      
      where I₀ is the average intensity, I₁ is the amplitude of the intensity fluctuation and N is the degree of detectable rotational symmetry (for rod-like particles N=2)^2,3.
   5. From the fit, extract the rotation frequency f_rot and decay time of the autocorrelation signal τ₀ (related to rotational Brownian motion dynamics).
5. Spectroscopic measurements.
   1. Record a white light spectrum (I_white(λ)) by collecting illumination light. This can be done by densely dispersing uniformly scattering polystyrene beads on a surface and collecting their scattering response.
   2. Record a background spectrum (I_bkg(λ)) by collecting the stray light in the trapping spot when a particle is not trapped.
      Note 1: This should be done for each individual measurement, since background properties can vary significantly between different sample cells and even locations within a sample.
      Note 2: Recording background spectra should be done for the same laser power as used for optical trapping. This allows one to remove any possible auto-fluorescence from the glass slide, excited by the high laser intensities in the focus.
   3. Record a dark spectrum (I_dark(λ)), when blocking all the light coming to the detector. Then, record a raw spectrum of a trapped nanoparticle (I_raw(λ)).
   4. Access the actual nanoparticle scattering spectrum by calculating
      
   5. To extract information about the LSPR peak positions, fit the DF scattering spectrum in energy scale with a bi-Lorentzian fitting function including a linear correction term for interband transitions in gold. The model function reads:
      
      where E is the energy, I_B is a baseline intensity, k the slope of the linear correction, I_i are intensity maxima, Γ_i the full width at half maxima (FWHM) and E_0,i the peak positions of the two Lorentzian peaks.

4. Troubleshooting and solution to common problems

1. Problems related to gold nanorod properties.
   1. Poor trapping stability.
      1. Make sure that the main resonance (usually longitudinal resonance in case of nanorods) is on the blue wavelength side of the trapping laser wavelength. If not, the gradient force will become repulsive instead of attractive³⁷.
      2. As a nanorod's size decreases, the motion from Brownian fluctuations increases, and at the same time the stabilizing force from Stokes drag decreases. Assure the nanorods are large enough for the xy-gradient force to overcome these destabilizing forces.
   2. Overlapping or broad spectral features.
      1. Rods need to have a large enough aspect ratio for LSPR peaks to be sufficiently separated to be individually resolved (see Figure 1b).
         NOTE: The laser wavelength puts an upper limit for the shape anisotropy, since the longitudinal LSPR redshifts for longer rods.
      2. The nanoparticles should preferably be small enough to not support higher order LSPR modes in the visible regime, since this complicates the analysis. Nanoparticle selection is a balance between this consideration and the trapping stability issue in instruction 4.1.1.2.
2. Inadequate circular polarization of trapping laser.
   NOTE: To obtain the optimal performance of rotation of the trapped nanoparticle, the laser light reaching the specimen plane should be circularly polarized. Beamsplitters and other optical components can be polarization dependent, which might make it impossible to obtain perfect circular polarization using only a QWP.
   1. Insert a half-wave plate (HWP; λ/2 in Figure 2) after the QWP in the path, to compensate for beamsplitter birefringence.
   2. Set up the linear polarizer and power meter configuration and perform an analysis of the laser's polarization state (as in instructions 1.11.2-1.11.3).
   3. For each position in increments of five degrees of the QWP, rotate the HWP through its entire angular range (90°) in steps of five degrees and measure the power ratio for each position. Strive to find the angles of QWP and HWP that maximize the ratio between maximum and minimum power.
      NOTE: In our experience, the maximum ratio between the maximum and minimum powers was 0.75 without and 0.98 with the HWP correction.
3. Particles sticking to interface at laser power inadequate to confine particles in the xy-plane.
   1. Tune the concentration of stabilizing surfactant, through a particle washing procedure and subsequent re-dispersion of the nanorods in a controlled concentration of CTAB.
      1. Centrifuge the stock solution of nanoparticles until particles sediment (~5 min at 600g).
      2. Remove the suspension liquid.
      3. Re-disperse in water. This dilutes the CTAB content of the stock solution.
      4. Repeat steps 4.3.1.1. and 4.3.1.2. once more.
         NOTE: Since CTAB acts as the colloid stabilizing agent, avoid excessive centrifugation time and speed in succeeding washing steps since the risk of aggregation increases as the CTAB is washed away.
      5. Most of the CTAB surfactants in the original colloidal solution is now removed and a new, well controlled, concentration of CTAB can be introduced to the colloid. From our experience, dispersing the stock solution in water with 20 µM of CTAB and subsequent DI-water dilution to the experimental solution concentration results in a surface coverage that produces sufficient Coulomb repulsion.
      6. Possible fine tuning of the CTAB concentration might be needed to create appropriate particle/surface repulsion for the particular batch of nanoparticles used. Iterate the above procedure and slightly alter the CTAB concentration to find a proper one.
   2. Glass surface washing to negatively charge surface.
      NOTE: This washing procedure produces a negatively charged surface that will be coated with free CTAB molecules in the experimental solution, making it positive and electrostatically repulsive for the particle during 2D trapping.
      1. Take a microscope slide and clean it in a mixture of water and 2 wt% of basic detergent heated to 80 °C for about 10 minutes until the surface is visibly hydrophilic.
         NOTE: Avoid washing glass slides too long or harshly, since this can make the glass surface porous and produce a multitude of contamination particles.
4. Problems with photon autocorrelation spectroscopy.
   1. Low amplitude of the intensity oscillations or noisy signal.
      1. Insert a bandpass filter (BP filter in Figure 2) before the collection fiber, which passes the laser light and blocks dark-field illumination light.
         NOTE: In principle, the measurement works when collecting all light as well. However, unpolarized white light DF illumination efficiently excites out of plane modes, and since a nanorod rotates about its short axis in a plane normal to the optical axis, this is the out of plane transverse LSPR. This mode does not carry any shape anisotropy during rotation and collecting light from it only reduces the signal to noise ratio of the measurement.
   2. Additional decay in autocorrelation function.
      1. Make sure the core size of the collection fiber is large enough to contain the image of the nanoparticle during all of its excursions due to translational Brownian motion.
      2. If a fiber with a too small core size is used, replace it with a larger one.
      3. Check alignment of the new fiber, as in instructions 2.1.4-2.1.5.