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Characterization of Individual Magnetic Nanoparticles in Solution by Double Nanohole Optical Tweezers Haitian Xu, Steven Jones, Byoung-Chul Choi, and Reuven Gordon Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.6b00288 • Publication Date (Web): 15 Mar 2016 Downloaded from http://pubs.acs.org on March 16, 2016

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Characterization of Individual Magnetic Nanoparticles in Solution by Double Nanohole Optical Tweezers Haitian Xu†, Steven Jones‡, Byoung-Chul Choi† and Reuven Gordon‡,* †

Department of Physics and Astronomy, University of Victoria, Victoria V8P 5C2, Canada

‡

Department of Electrical and Computer Engineering, University of Victoria, Victoria V8P 5C2,

Canada KEYWORDS: optical trapping, double nanohole, magnetic nanoparticles, nanoplasmonics

TABLE OF CONTENTS GRAPHIC

ABSTRACT: We study individual superparamagnetic Fe3O4 (magnetite) nanoparticles in solution using a double nanohole optical tweezer with magnetic force setup. By analysis of the trapping optical transmission signal (step size, autocorrelation, the root mean square signal and

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the distribution with applied magnetic field), we are able to measure the refractive index, magnetic susceptibility, remanence and size of each trapped nanoparticle. The size distribution is found to agree well with scanning electron microscopy measurements, and the permeability, magnetic susceptibility and remanence values are all in agreement with published results. Our approach demonstrates the versatility of the optical tweezer with magnetic field setup to characterize nanoparticles in fluidic mixtures, with potential for isolation of desired particles and pick-and-place functionality.

First demonstrated by Ashkin and Dziedzic in 1986,1 laser-based optical tweezers have emerged as powerful tools with a wide range of applications in biomedicine and biophysics,2–4 including the isolation, manipulation and characterization of dielectric and metal nanoparticles,5– 12

semiconductor nanowires,13–15 carbon nanotubes16 and graphene nanoflakes.17 Tethering of

biomolecules to plasmon nanoparticles18 or super-paramagnetic beads extends manipulation and analysis capabilities of optical tweezers to biological systems.19–23 Example applications include detection, selective separation and non-invasive manipulation of biomolecules inside microfluidic channels,24–26 trapping and transport of microorganisms,27 sorting of magneticallyloaded molecules using local magnetic field gradient,28 and mechanical force manipulation and characterization of DNA molecules.29–31 The increase in laser power requirement in conventional optical tweezers with the decrease in particle size32 can be overcome with planar waveguides33 and plasmonic nano-apertures in metallic films.34,35 These nanostructures localize and enhance the optical field to subwavelength dimensions,36,37 enabling accurate, high-speed, non-tethered trapping, manipulation and characterization of subwavelength nanoparticles at moderate laser powers.38–41 For example,


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double nanohole (DNH) structures in metallic thin films have a well-defined trapping site in the gap region between the nanoholes, and have been shown to be capable of trapping nanometersized dielectric particles as well as single proteins.42 In this work, we employ an Optical Tweezer with Magnetic Field (OTMF) arrangement with DNH aperture geometry for the quantitative analysis of complex refractive index, magnetic susceptibility, remanence and size distribution of superparamagnetic Fe3O4 (magnetite) nanoparticles in solution. For each trapped nanoparticle, we calculate its refractive index by comparing the increase in transmission signal to that of a reference polystyrene nanoparticle using the Clausius-Mossotti factor. By analyzing the autocorrelation decay and changes in the root mean square (RMS) transmission intensity distribution, we calculate the force of the applied magnetic field on the nanoparticle. Using the field-dependence of this magnetic force, we find its magnetic susceptibility and remanence, which in turn, enable us to obtain a size distribution of the nanoparticles in solution by performing the analysis over multiple trapping events. Figure 1 shows the schematic of the DNH aperture OTMF setup based on a modified Thorlabs Optical tweezers kit (Thorlabs OTKB). A fiber-coupled 855 nm distributed feedback diode laser (Eagleyard DFB-0855) was focused onto the DNH through a 100× oil-immersion microscope objective (numerical aperture (N.A.) = 1.25, spot size ~1.1 µm) with a power of 0 – 15 mW at the trapping site. A half-wave plate was used to align the polarization of the laser such that the electric field is perpendicular to the axis of the DNH cusp (Figure 1, lower right inset) to give maximum local field enhancement, and hence trapping stiffness.34 Light transmitted through the DNH was collected via a 10× condenser objective (N.A. = 0.25) and the intensity measured by an avalanche photodetector (APD, Thorlabs APD110A) at a sampling rate of 20 kHz. A current-controlled non-saturating magnetic field was applied in the vicinity of the trapping site


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using a small electromagnet. The APD voltage signal was recorded for trapping events under various applied fields, H. The upper left and lower right insets in Figure 1 show SEM images of the magnetite nanoparticles and DNH aperture used in our experiment respectively, obtained using a Hitachi S-4800. The DNH was fabricated with a focused-ion beam (FIB, Hitachi FB2100) on a commercial 100 nm gold film with 2 nm titanium adhesion layer on a glass substrate (EMF Corp.) The diameter d of the nanoholes was 200 nm and the tip separation was 35 nm. For the superparamagnetic particle, commercial Fe3O4 (magnetite) nanoparticles with d = (30 ± 2) nm (diluted to 10-3 % weight per volume, 747408 Sigma-Aldrich) was used. Prior to all trapping experiments, the magnetite solution was first sonicated for ~ 1 hour to minimize particle aggregation, after which 10 µL was dropped and sealed in a microfluidic chamber at the gold surface containing the DNH aperture, using a 150 µm glass coverslip (Figure 1, upper right inset).

Figure 1. DNH aperture OTMF setup. Insets: (upper left) SEM image of 30 nm Fe3O4 nanoparticles; (upper right) detailed arrangement of the highlighted region showing: 1. glass cover slip, 2. microfluidic chamber, 3. 100 nm gold film, 4. glass substrate, 5. electromagnet, applying an external field H away from the DNH; (lower right) SEM image of DNH aperture in


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100 nm gold with electric field (E) polarization direction. Abbreviations: LED: light emitting diode; APD: avalanche photodiode; ODF: optical density filter; DI: dichroic reflector, L: lens; MO: microscope objective; PES: piezoelectric stage; BS: beam splitter; M: mirror; BE: beam expander; HWP: half-wave plate; OF: optical fiber. Figure 2 shows a typical transition from the vacant to the trapped state, as well as a transition from zero to non-zero applied magnetic field in the trapped state, represented by the temporal trace of the APD voltage signal. We operated with the laser wavelength red-detuned with respect to the DNH plasmon resonance, indicating positive back-action effect.43 The presence of the magnetite nanoparticle slightly red-shifts the resonance towards the laser wavelength, giving rise to increased transmission and local field intensity (see Supporting Information, Figure S1, S2 for more information), which is measured as a step in the ADP voltage.

Figure 2. Typical APD signal vs. time for a transition from vacant to trapped state, as well as transition effect of the applied field H in the trapped state. Solid line is the moving average (2000 points). Inset: typical autocorrelation curve of the APD signal in the trapped state. We can determine the refractive index n and extinction coefficient k of the trapped nanoparticle by calibrating the percentage increase in transmission (trapping step size) and trap


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stiffness κ against a reference nanoparticle with identical size and known refractive index. The step size and stiffness measure the trapping efficiency, which correlates with the real part (Re{}) of the Clausius-Mossotti factor K,38 where: =

− . + 2

(1)

Here εp and εm are the relative permittivities of the trapped nanoparticle and the surrounding medium, respectively. At 855 nm, εm (water) = 1.77,2 and εp = (n + ik)2 where n = 1.93 and k = 1.02 for magnetite (see Supporting Information, Figure S3).44 Polystyrene nanospheres (εp = 2.46,2 Thermo Scientific 3030A) with the same diameter (d = 30 ± 3 nm) and concentration (10-3 % weight per volume) was chosen as reference. Figure 3 shows typical step transition measurements from the vacant to the trapped state, for both polystyrene (red), with an average increases of (5.1 ± 1.4) % in transmission; and magnetite (blue), with an average increase of (11.2 ± 3.2) % in transmission. The average increase in transmission from polystyrene to magnetite is (218 ± 22) %. Numerical simulations (Lumerical Solutions, Inc., see Supporting Information, Figure S2) show that for our setup, the increase in transmission is determined by refractive index n, and k plays a negligible role at the experimental wavelength, therefore to first order, the step size scales linearly with K(n) = (n2 – 1.77)/(n2 + 3.54),42 which gives a magnetite refractive index of n = (1.89 ± 0.07) at 855 nm, in reasonable agreement with material data (see Supporting Information, Section 2). The stiffness κ, which scales linearly with Re{K}, can then be used to determine the extinction coefficient, k. For magnetite and polystyrene, κ = 1.02 fN/nm-1 and 0.38 fN/nm-1 respectively (calculated using equations (4) and (5) in the following sections), which gives a ratio of 270 % in Re{K}, and a magnetite extinction coefficient (0.73 ± 0.05) at 855 nm (see Supporting Information, Section 4), 28% lower compared to the reference


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data, which can be explained by the polystyrene nanoparticles being slightly larger than specification: (31 ± 2) nm, according to Wheaton et al.45

Figure 3. Transition from vacant to trapped state for 30 nm magnetite (blue) and polystyrene (red) nanoparticles using the same DNH aperture at identical laser power. The greater increase in transmission for the magnetite nanoparticle is a result of its higher refractive index at 855 nm. Lines are moving averages (2000 points). Due to Brownian motion, the probability of the magnetite nanoparticle displacement from the trapping center follows Boltzmann’s distribution2 ,

(2)

+ + + ⋯ . 2

(3)

∝ exp −

where kBT is the thermal energy and U(x) is the potential energy of the trap, given by = +

For dielectric spheres in a trap, the RMS transmission intensity is linearly proportional to the potential energy.38 The coefficients of U(x) can therefore be solved by fitting a polynomial function to the probability distribution of the RMS APD voltage signal. Typically, U(x) is


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approximated as a harmonic potential (a = b = c = 0 in equation (3)), giving rise to a Gaussian probability distribution46 parametrized by the trap stiffness κ. The presence of the applied magnetic field H exerts a constant force on the nanoparticle, (linear a term in equation (3)) giving rise to a field-dependent modification of the trapping potential U(x), which can be investigated by measuring the changes in the probability distribution of the RMS APD signal, and hence changes in the coefficients of U(x), under various applied fields, as shown in Figure 4. For optimal fitting results, non-zero coefficients up to the 4th power were included in U(x) (a, b, c ≠ 0 in equation (3)), in order to accommodate the increase skewness with increasing applied field (Figure 4 (f)). Note that, in our OTMF configuration (Figure 1), H acts to pull the nanoparticle away from the trap (i.e., a < 0).

Figure 4. (a) – (e) RMS APD signal distribution histograms within a single trapping event under various applied fields. Total count = 150 per plot. (f) Normalized fitting curves for H = 0 Oe (dotted line) and H = 303.6 Oe (solid line). Note the increase in skewness towards higher RMS signal values with increasing applied fields. The force exerted on the trapped magnetite nanoparticle by the field gradient can be estimated using the linear coefficient of the fitting curve for U(x) in equation (3), FM = κa. The trap


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stiffness κ was calculated from autocorrelation analysis of the APD signal (Figure 2 inset) without applied magnetic field, using the method described in a previous work.35 The relationship between κ, the characteristic time of the autocorrelation of the APD signal τa, and the Stokes drag coefficient of the fluid medium γ, is given by47 # !" = ,

(4)

where τa can be obtained from a single exponential fit of the autocorrelation function. For a trapped nanosphere with radius r, in a liquid with dynamic viscosity η, the Stokes drag coefficient can be approximated using Faxén's law as48 #=

6&'( . 9 ( 1 ( 45 ( 1 ( 2 )1 − 16 , . + 8 , . − , . − 16 , . 3 ℎ ℎ 256 ℎ ℎ

(5)

Here terms involving h, the effective distance between the center of the nanoparticle and the trap wall, represent additional drag from the walls of the DNH structure. In the case of ~ 30 nm magnetite particles in a 35 nm trap, h is taken as 20 nm, assuming 5 nm average wall-particle separations. For a laser power of 8.25 mW at the trapping plane, κ was found to be equal to 1.02 fN/nm (see Supporting Information, Section 3). FM for each experimentally applied field can then be calculated by substituting the value of κ back into equation (3). Calculated FM for seven H values within a single trapping event are shown in Figure 5 (blue circles). Uncertainties in the fitting coefficients are taken into account by the error bars.


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Figure 5. Plot of magnetic force FM on the trapped nanoparticle vs. applied field B for a single trapping event. Blue circles: experimental results from autocorrelation and RMS APD signal distribution analysis; red line: calculated quadratic best fit curve based on equation (8). The force exerted on a trapped nanoparticle by the applied field can be calculated directly from the magnitude and gradient of the applied field H, and the magnetic properties of the nanoparticle. The force acting on a magnetic particle by a magnetic field is given by27 45 =

67 : ⋅ < : + =6<>9 ⋅ : , 89

(6)

where V is volume of the magnetic particle in m3, µ0 = 4π × 10-7 (T·mA-1) is the vacuum permeability, B = µ0H is the applied field in Tesla, M0 is the initial magnetization (remanence) of the magnetite particle, ρ = 5180 kg/m-3 is the density of nanoparticle, and χ is its susceptibility. In one dimension, equation (6) simplifies into 45 =

67 d: d: : + =6>9 , 89 d@ d@

(7)

where field gradient dB/dz along the axis of the electromagnet (z-direction) is measured experimentally at the trapping site using a Gaussmeter (Alpha Lab model GM-2). Since the field


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gradient at the trapping site scales linearly with B: C0B = dB/dz, equation (7) can be reduced into a quadratic function in B, 45 =

A9 67 : + =6>9 A9 : = AB : + A :. 89

(8)

By fitting equation (8) to the set of FM values in Figure 5 (red curve), constants C1 and C2, and hence M0 and χ can be calculated. Using d = 30 nm, the calculated remanence and susceptibility for the trapped nanoparticle are M0 = (13.1 ± 1.7) emu/g and χ = 7.8 ± 0.5 respectively. These results are in reasonable agreement with magnetization curve data for magnetite nanoparticles measured using vibrating-sample magnetometry (VSM) in existing publications.50–52 Note that χ relates to the initial slope of the magnetization curve, dM/dH via the following conversion emu Am d>[ 4& kg 4& d> g , kg ] 7 = =[ ] = , 10 m dK[Oe] 1000 OK M→9

(9)

where dM/dH is in units of [emu/g]/[Oe].

Similar analysis was performed for twelve separate trapping events under a constant laser power of 8.25 mW and applied fields between 107.2 Oe and 334 Oe. For each trapping event, a value of FM was calculated from the aforementioned autocorrelation and RMS APD signal distribution analysis. Substituting FM into equation (8) and using the previously calculated values of M0 and χ, we can now solve for the only unknown in equation (8), namely the volume of the nanoparticle, V, and hence its diameter d: B

645 O=P Q A9 7 4& 8 : + =>9 A9 :

(10)

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To improve accuracy, N (~7) different fields were used per trapping event to obtain an average value in d, with uncertainty estimated as σ/√N, where σ is the standard deviation in the


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average. (see Supporting Information, Tables S1, S2). The size distribution (d) for the 12 trapped nanoparticles is shown in Figure 6 (a). The average diameter based on the twelve trapped nanoparticles is calculated as (30.8 ± 1.9) nm, close to the supplier specification of (30 ± 2) nm. To verify these results experimentally, the nanoparticle solution was spin-coated at 1500 rpm onto a silicon wafer, and a diameter distribution was obtained by imaging and manually measuring individual nanoparticles using an SEM (Hitachi S-4800, Figure 6 (b) inset). The resulting distribution for 55 measured nanoparticles is shown in Figure 6 (b). The diameter of each imaged nanoparticle was obtained through image analysis. The uncertainty in d is given by the resolution of the SEM images, estimated to be ± 0.5 nm. The average diameter based on SEM measurements is calculated as (30.5 ± 2.9) nm, which contains a slightly larger spread than the distribution obtained from the smaller sample of twelve trapped nanoparticles, the results are nevertheless in reasonable agreement. During both trapping experiments and SEM imaging, aggregate nanoparticles (d >> 30 nm) were occasionally observed and omitted in our analysis (see Table S2, Figure S4 in Supporting Information).

Figure 6. Magnetite nanoparticle size distributions obtained using: (a) trapping analysis (12 nanoparticles, blue); (b) SEM measurements (55 nanoparticles, red). Best-fit lines are added as guides for the eye. Inset: a selection of SEM images of spin-coated magnetite nanoparticles on silicon wafer used for size distribution calculation.


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In conclusion, we used a DNH aperture OTMF platform to characterize refractive index, magnetic susceptibility, remanence and size of trapped superparamagnetic Fe3O4 nanoparticles. The values we obtained for complex refractive index, susceptibility and remanence were found to be consistent with previously published data, and the size distribution we obtained for trapped particles was found to be consistent with both supplier specifications and direct SEM measurements of the nanoparticles. This work is of interest to the selective study of nanoparticles in a disperse population containing different magnetic materials. It is also interesting to consider the possibility of isolating specific magnetic particles with the desired characteristics using this platform. The ability to translate nanoparticles using the DNH on the end of fiber probe may allow for pickand-place assembly of magnetic nanoparticles in future devices.

ASSOCIATED CONTENT Supporting Information. Numerical simulations of nanoparticle effect on transmission spectrum and local field profile, refractive index and trap stiffness calculations, sample nanoparticle size measurements, SEM image of aggregate nanoparticles. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Author *Email: [email protected]. Notes


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The authors declare no competing financial interest. ACKNOWLEDGMENT The authors acknowledge useful discussions with Abhay Kotnala. We acknowledge funding from the NSERC (Canada) Discovery Grants program. REFERENCES (1)

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