Force-detected nanoscale absorption spectroscopy in water at room temperature using an optical trap

The ability to study a chemical reaction by simply watching the change in the absorption spectrum of a single molecule may become possible with several recent advances in single-molecule detection and spectroscopy.^1–6 Here, we report an instrument developed to measure photoinduced forces between a surface-immobilized sample and an optically trapped probe over the 400-800 nm range. These force spectra are measured for CdSe/ZnS nanocrystals and organic dye model chromophores in water at room temperature [Fig. 1(a)]. The force spectra are comparable to linear absorption spectra obtained using other methods. It is found that optically trapped gold nanoshells can serve as a near-field force probe, which responds to the photoexcited molecules by a mechanical displacement that enables the readout of absorption. The measurement volume is estimated to contain ∼10² quantum dots. This proof-of-concept measurement sets up a new paradigm for performing absorption spectroscopy in solution and paves the way toward realizing single molecule absorption spectroscopy.

By which mechanism does a photoexcited molecule exert a force on a gold nanoshell? Analogous force-encoded spectroscopies detected by atomic force microscopy (AFM) have been explained using electrostatic, dipole-induced dipole coupling or photothermal expansion.^7–9 AFM-based infrared spectroscopy (AFM-IR) is a nanoscale spectroscopy that uses the AFM probe to detect the thermal photoexpansion in a sample resulting from infrared absorption.^3,10–12 Photoinduced force microscopy (PiFM) has demonstrated single molecule sensitivity in absorption, Raman, and pump-probe spectroscopies and derives contrast not from measuring photoexpansion, but rather from the photoinduced electromagnetic forces exerted onto the metal-coated cantilever.^5,13,14 Due to the radically different thermal transport and electrostatic screening properties in solution, force-detected spectroscopies in solution may derive contrast from other mechanisms.

Optical tweezers (OTs) provide a compelling force-detection technique for force-detected absorption spectroscopy in water at room temperature. The high Q factor of AFM cantilevers in air is critical to the success of AFM-IR,^3,11,12 PiFM,^5,13,14 and MRFM^15,16 spectroscopies. As an order of magnitude estimate for an electrostatic dipole-induced dipole contrast mechanism, the force exerted between a dipole of μ = 1 D and its image in a conductor separated by 1 nm will be on the order of ∼μ²/4πϵ₀r⁴ = 0.1 pN. In this regime, direct comparisons have found OT to be more sensitive than AFM.^17,18 The sensitivity of AFM has been estimated to be 200 fN,⁹ whereas fN-scale forces have been measured with OT to characterize the electrostatic potential between colloids,^19,20 the Casimir force,²¹ and forces due to direct light scattering.^22,23 In our method, the exquisite force sensitivity of OT is exploited to measure molecular absorption spectra at the nanoscale. The experiments presented here provide proof of principle for a new method that adds to a growing body of nanoscale non-fluorescence-based spectroscopies, including surface-enhanced and tip-enhanced Raman,^1,4,24 SEIRA,²⁵ IR s-SNOM,^26,27 single particle spatial modulation spectroscopy,²⁸ and photothermal absorption spectroscopies.^2,6

For force-detected spectroscopy, the signal arises from displacement of a microscopic probe, which is here monitored using laser interferometry. Relative to low-light detection schemes, the optical dark noise and detector background noise are negligible.²⁹ To optimize the sensitivity of a mechanical-oscillator probe to external forces, we will show that it is desirable to minimize the force constant or stiffness, κ. Photoexcitation of the sample ultimately exerts a force on the probe ΔF, which gives rise to an observable deflection, Δx = ΔF/κ. Therefore, the signal increases as the stiffness is reduced; however, reduced stiffness also increases the noise. In solution, the noise is dominated by the thermal fluctuations of the particle, which is described by the equipartition relation, $12κx2=12kBT.$ Therefore, the signal to noise ratio can be estimated as

Equation (1) indicates that the signal to noise scales as κ^−0.5, where κ = 5–10 fN/nm in our work. To measure the photoinduced force difference, the excitation laser pulse train is modulated at frequency f_mod and the force difference between on and off periods is averaged to generate the force spectrum, $ΔF(λ)=FYOn(t;λ)−FYOff(t)$⁠. To provide requisite contrast, f_mod must be slow enough to allow the probe to respond. The mechanical relaxation time of the probe is characterized by the corner frequency, f_C, where the modulated laser appears continuous for f_C ≫ f_mod.³⁰ In our measurements, f_C ≈ 100 Hz and f_mod = 3 Hz, which allows the probe to adequately sample an equilibrium distribution during the laser-on and laser-off periods.

The instrument for measuring optically induced forces is shown in Fig. 1(b). A focused 1064 nm CW Yb fiber laser (IPG Photonics) forms the optical trap. The free-space output passes through a λ/2 waveplate and polarizing beamsplitter for intensity control followed by an acousto-optic deflector, which can be used to steer the optical trap but was not utilized in these measurements. The beam is expanded by a telescope (L2:L1 = 6.7) to overfill the back aperture of the objective before being coupled into the microscope body. The objective (Plan-APO 40×/1.4 Oil, Carl Zeiss) and sample holder (Nano-LP300 and MicroStage, Mad City Labs) are mounted in a modified stand (Axio Observer A1, Carl Zeiss). This high NA objective has 65% transmission at 1064 nm and outstanding apochromatic color correction from the UV to the IR. A condenser lens collects the transmitted and scattered 1064 nm light for interferometric back-focal-plane detection^31,32 on a quadrant photodiode (QPD, QP154-Q-HVSD, First Sensor). Data are acquired, low-pass filtered to 25 kHz, and saved to hard disk using a field-programmable gate array (National Instruments).

Brightfield Köhler illumination is provided by an 850 nm LED, which is aligned to counter-propagate along the 1064 nm beam path by using a beamsplitter (DM2, ZT1064rdc-sp, Chroma Technology). This beamsplitter also rejects visible excitation light from the QPD, which is further suppressed by means of a notch filter (F1, FL1064-10, ThorLabs).

The excitation light is generated by a supercontinuum source (WhiteLase SC400-4, Fianium) operating at 40 MHz. The output passes through a home-made grating monochromator producing ∼1 mW across the 400-800 nm region (excitation spectra are shown in Fig. 4). This approach was found to be superior to the use of a high-speed acousto-optic tunable filter for wavelength selection and maintained the high mode quality from the fiber output.³³ The 40 MHz excitation pulse train is chopped mechanically to allow differential force detection. The excitation light underfills the back aperture of the objective and is overlapped spatially with the optical trap but focused to 10 μm diameter to minimize generation of additional optical gradient forces. The excitation laser is linearly polarized [$E→∝ŷ$⁠, as defined in Fig. 1(a)].

The optical excitation is combined with the 1064 nm trapping laser using a dichroic mirror (DM1, ZT1064rdc-sp, Chroma Technology) housed in the filter-cube assembly of the microscope stand. Epifluorescence, backscattered excitation light, and the brightfield illumination are split off from the excitation path using a broadband 50/50 beamsplitter (BS) and imaged onto a CMOS camera. Removable filters allow for visualization of the scattered 1064 nm trapping laser, scattered visible excitation, fluorescence, or the brightfield image (F2, NF1064-44, Thorlabs; and/or ET570lp, T565lpxr, Chroma Technology). A description of the sample chamber construction and functionalization with semiconductor nanocrystals or organic dye appears in the supplementary material.

Figure 2 shows the results of calibrations performed to convert the QPD outputs into physical displacements of the probe and the attendant forces. Following the procedure outlined by Tolić-Nørrelykke et al.,³⁴ a nanoshell bead was trapped d = 5 μm away from the coverslip surface, with the nanostage being driven by a sine wave (amplitude = 180 nm and f_drive = 25 Hz). The QPD outputs, designated as S₁, S₂, S₃, and S₄, were acquired at 25 kHz and digitized in the following combinations:

These hybrid signals were Fourier transformed to obtain corresponding power spectral densities, as exemplified by

where T is the measurement time.³⁴ Typically ten calibrations that were acquired over 10 s durations were averaged. The power spectral densities were fit to a Lorentzian spectrum to obtain the trap stiffness (κ in fN/nm) and the response at the driving frequency was fit to obtain the sensitivity (β in nm/V). Figure 2(a) shows the power dependence of the trap stiffness. Linearity over this power regime demonstrates that optically trapping the gold nanoshells does not cause significant heating.³⁵ We choose a relatively weak trap that maintains stable optical trapping to maximize the signal to noise [Eq. (1)]. Figure 2(b) shows selected $PSYf$ profiles at specific incident powers to demonstrate how the corner frequency scales with laser intensity. These calibrations were used for all trapping distances, without correction for the altered diffusion near the coverslip surface, and result in a 15% error in the reported forces.

A gold nanoshell bead is translated into the optical trap by moving the microstage, after which it is brought into contact with the bottom coverslip surface coated with the sample, the excitation light is turned on, and the signal is collected for 30 s per wavelength. The displacement of the probe from the center of the trap, y(t), is obtained from the QPD output using the sensitivity, β, y(t; λ) = βS_Y(t; λ). The force on the probe is obtained from the displacement using the trap stiffness, κ, F_Y (t; λ) = κy(t; λ) = βκS_Y (t; λ).

Figure 3(a) shows the QPD output, calibrated to indicate the displacement, y(t; λ), and the force, F_Y (t; λ), for 5 s of data acquisition overlaid with the chopper output signal. No displacement of the probe is visible by simple inspection of the excitation on/off periods, but a histogram analysis reveals a 13 nm shift in the average position of the probe particle [Fig. 3(b)]. The wavelength is stepped in 5 nm or 10 nm increments from 400 to 700 nm with 30 s of data acquisition per point to acquire a set of F_Y(t; λ) profiles. The force trajectories are converted to force spectra, ΔF(λ), by averaging the difference between on and off periods, $ΔF(λ)=FYOn(t;λ)−FYOff(t).$

To assemble a force spectrum, the analysis presented in the section titled Light-induced forces is repeated for each wavelength. The data shown in Fig. 3 corresponds to the 510 nm data point of Qdot525 [cf. gray dashed circle in Fig. 4(a)]. Figures 4(a)–4(e) shows how the force spectra change for different samples and as the probe is moved away from the surface. Three sizes of semiconductor nanocrystals were chosen to study the correlation between the absorption spectrum and the force spectrum; an organic dye, Alexa555, was studied to test if the signal arises from a nanocrystal-specific effect. Distance-dependent spectra are acquired by translating the cover slip toward the optically trapped probe in Δd = 50 nm or 100 nm increments with d = 0 defined as the point of surface-to-surface contact. At the current level of data analysis, finer spatial resolution is not justified; while the center of the optical trap can be controlled accurately, the probe particle undergoes restricted diffusion within the optical trapping potential. This causes the probe to sample a distribution of positions with respect to the surface [illustrated in Fig. 4(f)] and the spectra shown in Figs. 4(a)–4(e) represent an averaged force exerted on the particle when the trap is at the distance specified. Finer spatial resolution may be extracted at the expense of signal to noise by further analysis of data such as that shown in Fig. 3(a) in post-processing.

The force spectra in Figs. 4(a)–4(d) appear to probe the same energy levels observed in the conventional absorption spectra. For each sample, a peak is seen only at the closest approach (gray arrows) and moving the center of the trap 50 nm away from the surface greatly diminishes the signal. No signal is seen in the control experiment with an uncoated glass slide [Fig. 4(e)]. This control demonstrates that direct scattering of the excitation light off the probe particle and heating of the probe particle may contribute to noise but do not yield peaks in the force spectra. Despite the fact that all of the model systems are bright fluorophores, the observed peaks correlate with the bulk absorption spectrum rather than the Stokes-shifted fluorescence. However, it is evident that the bulk absorption spectra are not faithfully reproduced in the nanoscale force spectra. The major differences in the nanoscale force spectra are that the bands appear narrower and some transitions are absent relative to the bulk absorption. While the signal to noise precludes lineshape analysis, narrowed bands have been observed in hole-burning³⁶ and single particle photon-correlation spectroscopies³⁷ of CdSe clusters and ascribed to incomplete ensemble averaging. For the nanocrystal samples, transitions that are higher in energy than the lowest exciton (1S ← 2S_1/2) are absent. This may arise if the force spectra are sensitive to the lifetime of the populated state; it has been observed that electronic relaxation into the lowest energy exciton occurs on a rapid, 30 fs time scale.³⁸ The presence of signal for Alexa555 demonstrates that the signal does not arise from a feature specific to the nanocrystals, such as static charging.

At this point, it is not clear what is the most relevant bulk measurement for comparison. The data shown in Fig. 4 do not allow for the photoinduced forces to be decomposed into contributions from electostatic, photothermal, and plasmonic contributions. We have chosen to present minimally processed data, $ΔFλ$⁠, rather than normalizing for the excitation source, $ΔFλIλ$⁠. Therefore, the bulk comparisons shown in Figs. 4(a)–4(d) are the molar absorptivity scaled by the excitation spectrum, $Iλϵλ$⁠. Further understanding of the underlying signal generation mechanism will allow for a better choice of a bulk comparison, as well as suppressing sources of noise and background. The baseline in the force spectra may be influenced by mechanical vibrations of the sample chamber relative to the position of the optical trap, which peak when the probe is in contact with the sample chamber at d = 0 nm. Currently, it is believed that the non-uniformity of the gold coating on the nanoshell particles is a major contributor to the noise (see Figs. S5 and S6 of the supplementary material).

In this work, we have presented the first evidence that optically trapped gold nanoshells may be used to measure a fN-scale photoinduced force that reports on the absorption spectrum of chromophores located in the near-field of the probe in water at room temperature. However, the experiments herein raise many questions about the underlying physical mechanism. The photoinduced forces characterized by PiFM are on the 10 pN scale,⁸ which is two orders of magnitude larger than the effect observed here. Thermal and electrostatic contributions have been considered as contrast mechanisms for AFM photoinduced microscopies,^9,13 and the same controls may be used to study the mechanism of optical tweezers force-detected spectroscopy. Electrostatic contributions have been shown to result in dispersive line shapes sensitive to the real component of the first-order response and to show a steep, d⁻⁴ distance dependence.^5,8,13 By varying the thermal conductivity and heat capacities of the solvent, one may quantify the magnitude of a photothermal contrast.³⁹ Solvent-dependent force spectra may be measured using the recently developed technology to stably trap core/shell microspheres in organic solvents.⁴⁰ A study on the effects of metal-coating thickness will reveal the importance of electrostatic contributions to force-detected spectra and the possible role of a plasmon enhancement to the excitation.

The mechanistic studies listed above will also be critical to understanding the information content of force spectra for its application to molecular spectroscopy. The finite excitation bandwidth and potentially the spectrum of the nanoshell plasmon resonance must be factored out in order to observe intrinsic molecular properties. For the gold nanoshell beads used here, the model of Averitt et al. predicts that the plasmon resonance peaks near 4500 nm,⁴¹ and, thus, is not expected to play a significant role. However, TEM images of the nanoshell particles demonstrate that the gold coating is neither uniform nor contiguous, and thus the plasmon resonance may vary on a particle-to-particle basis (see Figs. S5 and S6 of the supplementary material). Additional signal weighting may be caused by the lifetime of the electronic state populated, as suggested by the absence of spectral features from higher-energy excitons in the quantum dots. Expanding the samples measured to include excited states of different symmetries, extinction coefficients, fluorescence quantum yields, and relaxation times will allow for a better understanding of how force spectra encode molar absorptivity.

The signal to noise ratio of the data presented here may be improved by utilizing advances in optical trapping technology. Optical sources of noise may include localized heating of the gold nanoshell beads induced by the excitation and scattering. The latter is a trivial photoinduced force signal caused by direct scattering of the excitation off the probe always accompanies the excitation and is oriented in the +z direction. As the force spectrum is detected in an orthogonal direction (y), this background may couple if the optical trapping laser and excitation laser are not perfectly collinear and parallel to the surface normal vector. The Mie scattering that describes optical scattering and gradient forces is known to have a complicated wavelength dependence.⁴² 

As the ultimate goal of signal to noise improvements is to reach single molecule sensitivity, it is worth estimating the number of molecules in the observation volume. As a conservative estimate, if the microscope coverslip was covered in a monolayer of nanocrystals (15 nm diameter/particle after passivation and coating⁴³) and the probe particle is in contact with the surface, then 40 qdots will be within 3 nm of the probe particle. For a longer range force, (i.e., 10 nm range), then 140 qdots will be within proximity of the probe particle. The distance dependence of the force responsible for generating contrast is a key parameter in determining the current sensitivity and how much of an improvement is necessary to reach the single molecule limit. While the particle displacements measured here are on the order of 10 nm, displacements as small as 0.1 nm may be measured with differential back-focal-plane detection⁴⁴ while maintaining stability over the course of hours.⁴⁵ The advantages of this sensitive detection technology, coupled with its applicability to measure nanoscale force spectra in water at room temperature, make it a compelling path forward toward broadly applicable single molecule absorption spectroscopy.

See supplementary material for synthetic methods and TEM images of the gold nanoshells.

This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE1122492 to J.W.B. A.P. acknowledges support from an NIH Biophysical Training Grant No. T32GM008283. We would also like to acknowledge the anonymous reviewer who suggested the Alexa555 experiments.