On-the-Fly Calibrated Measure and Remote Control of Temperature and Viscosity at Nanoscale.

A novel on-the-fly calibration method of optical tweezers is presented, which enables in situ control and measure of absolute temperature and viscosity at nanoscale dimensions. Such noncontact measurement and control at the nanoscale are challenging as the present techniques only provide off-line measurements that do not provide absolute values. Additionally, some of the present methods have a low spatial resolution. We simultaneously apply the high temporal sensitivity of position autocorrelation and equipartition theorem to precisely measure and control in situ temperature and the corresponding microrheological property around the focal volume of the trap at high spatial resolution. The femtosecond optical tweezers (FOTs) use a single-beam high repetition rate laser for optical trapping to result in finer temperature gradients in comparison to the continuous-wave laser tweezers. Such finer temperature gradients are due to the additional nonlinear optical (NLO) phenomena occurring only at the nanoscale focal plane of the FOTs. Because NLO processes are laser peak power-dependent, they promote an effective study of physical properties occurring only at the focal plane. Using FOTs at optically benign near-infrared wavelengths, we demonstrate microrheological control and measurement in water by adding a highly absorbing yet low fluorescent dye (IR780).

Introduction

Optical tweezers[1] have been developed extensively to pursue the study of natural processes ranging from micron to molecular dimensions.[2−4] Optical tweezers with higher spatiotemporal resolution can overcome the challenges to access the measurement of nanometer displacements and piconewton forces on millisecond timescales. In doing so, instrumentation, techniques, and theoretical developments have been improved simultaneously to solve practical challenges which are relevant to mankind.[5−8] Still, reliable and accurate temperature sensing at the nanoscale dimension in a contactless fashion is highly challenging because of the nonavailability of absolute calibration of optical tweezers at high spatial resolution. Some available techniques[9,10] use magnetic probe particles to measure temperature in a contactless fashion remotely but only work at submillimeter spatial resolution. Thus, contactless temperature measurement with absolute calibration process with spatial resolution from micro- to nanodimension is indeed needed as, for example, temperature sensing in water at nanodimension is of fundamental interest and practical significance. We have developed a new method for absolute on-the-fly calibration of femtosecond optical tweezers (FOTs) using the combination of position autocorrelation[11] and equipartition theorem[12] presented as normalized position autocorrelation function (NPAF). Our on-the-fly NPAF calibration method signifies that the user can experimentally achieve in situ absolute values at a high spatiotemporal resolution with easy processing of time-domain data without Fourier transforms. The method presented here is simple to use and requires a very low-level instrumentation compared to other methods which use auxiliary lasers[13,14] or acousto-optic deflectors.[15] Additionally, the NPAF[16,17] approach has the major advantage over frequency-domain measurements, especially for probing fast biophysical processes. This is because the resolution of the commonly used approach of the power spectral density (PSD) method depends on the “measurement time” of the trapping data, whereas in the “time-domain” measurement, the resolution does not get restricted by the “measurement time”, rather it depends on the “sampling rate”. Furthermore, in our NPAF approach, we only use a single wavelength for all the three purposes: for trapping, for heating, and for probing. The versatility of this approach promises to open its applicability to numerous fields of research. For example, optical tweezers will now offer to probe the behavior of biomolecules’ flexibility[18] during heating or the way in which enzymes control the metabolic activities of microbes at different physiological temperatures.[19,20]

For temperature rise demonstration purposes, we have successfully applied our theoretical method which experimentally utilizes the aqueous solution of the IR780 dye (see S1, Figure S1) for precise control and measurement of temperature (T) and viscosity (η) around the trapping zone. There is a continuous effort to measure the temperature rise occurring at small volumes because of optical tweezers at different continuous laser wavelengths,[21−24] which has remained a subject of interest. For example, a temperature rise occurs at 1064 nm because of absorption arising from the vibrational combination band (2ν1 + ν3)[25,26] of water, which has been of active interest.[27−30] However, because water has very low absorption[31,32] at a wavelength of 780 nm because of vibrational combination band 3ν1 + ν3,[25,26] trapping at 780 nm does not produce an appreciable temperature rise around the focal volume. The solution of the IR780 dye in water has a wide near-infrared (NIR) absorption band. The temperature rise occurs as the IR780 dye absorbs some of the 780 nm trapping laser and undergoes a strong nonradiative relaxation via thermal emission from its excited state.[33] Our technique offers an extremely high gradient of temperature at very low diffraction-limited spot size[34] as femtosecond high repetition rate laser pulses are used. The IR780 dye shows peak power-dependent nonlinear optical (NLO) phenomenon, also known as saturable absorption (see S2, Figure S2). Thus, the number of molecules to be excited is controlled by the peak power of the femtosecond laser used. We have interpreted the characteristic Brownian motion[35] of a 550 nm radius (r) trapped polystyrene bead to determine the surrounding temperature and viscosity. Additionally, we have demonstrated this approach as a function of wavelength to prove that it could be used as a new tool for microrheological measurement and control in liquids with tunable lasers. In future, multiphoton absorbing nonfluorescent molecules can increase the spatial resolution of the control of temperature through the higher-order NLO process[36,37] possible to be measured through FOTs.

Experimental Methods and Materials

Optical Tweezers Setup and Material

In our FOT setup (Figure ), mode-locked Ti:sapphire laser (MIRA-900F pumped by Verdi V5, Coherent Inc.) was used, which generates femtosecond laser pulses centered at 780 nm wavelength with a repetition rate of 76 MHz. For the trapping experiments reported here, a laser pulse width of 150 fs was used. The wavelength can be tuned from 730 to 900 nm with higher pump power. The sample chamber was placed on a piezoelectric stage (NSP3, Newport Co. USA), which was operated with a piezo controller (NSP3, Newport Co., USA) connected to a personal computer via a NI data acquisition (DAQ) card 6212 (National Instruments USA). This DAQ was used to provide the known sine function to the piezoelectric stage for voltage calibration using LabVIEW program. For achieving tight focusing, an oil immersion objective (UPlanSApo, 100×, 1.4 NA, Olympus Inc. Japan) was used, and the forward scattered light was collected and focused with another oil immersion objective (60×, PlanApo N, 1.42 NA, Olympus Inc. Japan) onto a quadrant photodiode (QPD) (2901, Newport Co. USA) that had a rise time of 5 μs. The QPD output was connected to a digital oscilloscope (Waverunner 64Xi, LeCroy USA) interfaced with a personal computer through a GPIB card (National Instruments, USA). The LabVIEW program was used for DAQ. The commercially available fluorophore-coated polystyrene bead of radius 550 nm (Figure a) with a concentration of 2.7 × 1010 particles/mL suspended in water was purchased from Life Technology, USA (F8820, lot number 30724W, currently Thermo Fisher, USA). The stock solution was diluted at a subnanomolar concentration for the trapping experiment and well sonicated for immediate use. We used 24 × 50 mm no. 0 cover glass sample chamber that was assembled by placing a coverslip 22 × 22 mm no. 1 separated by spacers of a double-sided sticky tape. A CCD camera (350 K pixel, E-Mark Inc. USA) was used for monitoring the video of the trapping event. A red filter was used before CCD to follow a single trapped particle event. We used a white light source for bright-field illumination. The IR780 dye was purchased from Sigma-Aldrich and used without further purification. The dye was dissolved in 4–5 drops of spectroscopic grade methanol, and then the 25 mL volumetric flask was filled with distilled water. The absorption spectrum of IR780 (Figure b) was collected by the absorption spectrometer (Lambda 900, PerkinElmer USA) at a concentration of ∼3.33 × 10–5 (M).

Figure 1

FOT setup. WP: half-wave plate; PBS: polarizing beam splitter; L1: concave lens (f: 10 cm); L2: collimating convex lens (f: 20 cm); DM(1,2): dichroic mirror; O: objective lens; PZS: piezoelectric sample stage; PZC: piezoelectric controller; DAQ: data acquisition card; C: condenser lens; GF: green filter; L3: focusing lens (f: 5 cm); QPD: quadrant photodiode; SM: silver mirror; RF: red filter; CCD: camera (charge-coupled device); PC: personal computer.

Figure 2

(a) Measured differential light scattering through our buffered fluorophore-coated polystyrene bead sample solution showing the average particle distribution size to be 550 nm. (b) Absorption spectrum of the IR780 dyes.

Dynamic Light Scattering (DLS) Measurements

For DLS measurements, we used the Malvern Nano ZS instrument that had a 4 mW He–Ne laser (λ = 632.8 nm) and was also equipped with a thermostat coupled sample chamber. In this instrument, the detector angle was fixed at 173°.

Results and Discussion

Theoretical Section

Our theoretical development is based on Einstein’s theory of Brownian motion. This theory explains that the Brownian motion of a particle will change because of continuous energy transfer between the particle and the surrounding solvent in the form of the thermal energy of solvent into the kinetic energy of the particle. The equation of motion of a particle in a viscous Newtonian fluid, undergoing Brownian motion within a harmonic potential well, can be expressed by the Langevin equation as follows[11,38,39]where m denotes the mass of the particle, x signifies time-dependent position, γ (=6πηr) is the viscous drag coefficient as per Stokes’ law of particle having radius r moving in a solution having a viscosity of η, κTS is the trap stiffness, and F(t) is the time-dependent random thermal force. We have saved position fluctuation data of a 550 nm radius trapped particle using QPD with a sampling rate of 100 kHz. We have ignored the inertial effects as the characteristic inertial time scale (m/γ ≈ 10–9 s) is beyond our detection method. Thus, the motion of particles takes place at a small Reynolds number where viscous drag dominates over inertial forces. The NAPF for this particle when time-averaged over all the initial times t0 is[16,40]where λ (=κ/γ) is the characteristic relaxation rate of the compound system. We intend to use the piezoelectric stage coupled to a sample chamber to probe the experimental signal from our initial known signal. We have moved the sample stage sinusoidally with an amplitude of Ad = 178 nm at a drive frequency of fd = 50 Hz such that it does not overcome the particle’s natural Brownian motion. Such a typical experimental technique using a trapped Brownian particle closely follows the theoretical expectations as the technique involves providing an additional known sinusoidal motion to the tweezers, which enables absolute calibration in the time domain for the experiment. Thus, the oscillation in the autocorrelation curve comes from the provided drive signal, and our only region of interest is the decay before the oscillatory behavior, that is, on fast time scales. Here, the position of the stage varies as a function of time when the drive motion is on as follows:

As a result of this, the corresponding response function can be obtained as[41]

The time shift appears because of the phase difference, which can be ignored while taking position autocorrelation for a long time as compared to the diffusion time scale of the particles. Then the equation of motion of the spherical bead in the trap is

The amplitude calibration also needs to be done to minimize the effect of ground voltage and electrical impedance. We have performed amplitude calibration in water at room temperature. The NPAF is thus represented as

The coefficient b in the above equations is useful for the absolute on-the-fly calibration at a specific sampling rate of DAQ. This calibration leads to the voltage to position conversion factor (Cf) through the following equation:where ⟨x2⟩ is the variance in the position of the oscillating trapped particle. The motion of trapped particles in harmonic potential[42,43] with characteristic corner frequency fC will have a trap stiffness κ = 2πγfC. For sufficiently long measurement time (t ≫ fC – 1), we can calculate the trap stiffness by applying the equipartition theorem as follows[13]

For absolute calibration, we have calculated calibration factor from eq and have numerically solved and measured the temperature rise as per the following equation

Here, the dynamic viscosity, η(T), of the fluid depends on the temperature of the fluid and kB is the Boltzmann constant. A general formula for the dynamic temperature-dependent viscosity of water is given by[44]

This phenomenological expression can be used to track the effective friction coefficient as a function of temperature.

We have utilized this method to measure the local temperature around the optically trapped bead and the femto-newton/nanometer spring constant with high accuracy. In this method, the interfacial temperature is calculated from the viscosity of the surroundings of a trapped spherical bead. There is no specific restriction on the tweezers for the application of this approach. Last but not the least, this calibration technique also does not require an additional correction term for interacting with the surface[45] as the near-interface viscosity always has a higher value because of friction with the surface of the cover glass. However, this absolute calibration technique can measure that effect.

Experimental Section

We have used FOTs to trap and manipulate 550 nm radius fluorophore-coated polystyrene beads. Our trapping experiments are performed with 10–30 mW average power and at 740–820 nm trapping wavelengths in the aqueous solution of IR780. The femtosecond pulse produces a huge instantaneous gradient force at small average powers.[46,47] Such technological developments in optical tweezers have resulted in exploring the three-dimensional world of micro- to nanoscale.[48,49] Here, for temperature sensing studies, we have used an IR780 dye solution that has high absorption at our trapping wavelength.

The IR dye shows a peak power-dependent NLO, such as saturable absorption and reverse saturable absorption that occurs only at the focal plane (resulting in 340 nm in our FOT system).[50,51] The mechanism of heating in an aqueous solution of the IR780 dye occurs because of nonradiative relaxation of the photoexcited molecule that increases the local temperature. As the amount of heat deposited in the system depends on the amount of radiationless relaxation, the number of photoexcited molecules dictates the local temperature. We have probed the Brownian motion of a trapped spherical polystyrene bead. The Brownian motion has changed because of a continuous energy transfer between the trapped bead and the solvent, resulting in the transformation of the thermal energy of the solvent into the kinetic energy of the trapped bead.[15] We have measured the corner frequency and variance from the Brownian motion of the trapped particle to correlate with the local temperature.

Pulsed tweezers have several advantages[52−54] over conventional continuous-wave laser tweezers because of the availability of high peak powers at low average powers. Specifically, in absorbing media, the available average power to the trapped bead is very small, which may not generate dominant gradient force to trap the bead. Additionally, for lower sized particles to probe nanodimensional local temperature, it is even impossible to monitor the Brownian motion at low power as it will not be able to trap the particle. Besides, at high average powers, convection flow will destabilize the trap. The power-dependent studies (10–30 mW) of our optical tweezers (Figure ) have been performed at the central laser wavelength of 780 nm (Table and see S3, Table S1) with the laser pulse width of ∼150 fs at an IR780 dye concentration of 1.25 × 10–5 and 3.33 × 10–5 (M).

Figure 3

NPAF of the 550 nm radius trapped particle in linear-log plot with a delay time (τ) (a) at different trapping laser powers within (a) 1.25 × 10–5 (M) concentration of the IR780 dye in water and (b) 3.33 × 10–5 (M) concentration of the IR780 dye in water.

Table 1

Fittings and Observed Physical Parameters in 1.25 × 10–5 (M) IR Dye

power (mW)	fitting parameter (a)	fitting parameter (b)	corner frequency λ (Hz)	drag coefficient γ (nN·s/m)	viscosity η (cP)	calibration factor Cf (nm/mV)2	temperature rise ΔT (K)
10	0.720	0.229	179	8.29	0.799	0.285	5.1 (±0.4)
12.5	0.774	0.228	189	7.52	0.725	0.263	9.7 (±0.7)
17.5	0.638	0.226	295	7.11	0.685	0.352	12.5 (±1.1)
22.5	0.685	0.222	341	6.20	0.598	0.328	19.8 (±1.6)
25	0.657	0.224	414	5.99	0.577	0.382	21.7 (±1.7)
30	0.679	0.211	495	5.21	0.502	0.380	29.9 (±2.3)

For the wavelength-dependent (740–820 nm) study (Table and see S4, Table S2) through optical tweezers (Figure ), we have used a constant average power of 25 mW at ∼150 fs pulse width.

Table 2

Fittings and Resulting Physical Parameters in 1.25 × 10–5 (M) IR Dye

wavelength (nm)	fitting parameter (a)	fitting parameter (b)	corner frequency λ (Hz)	drag coefficient γ (nN·s/m)	viscosity η (cP)	calibration factor Cf (nm/mV)2	temperature rise ÄT (K)
740	0.714	0.270	317	7.29	0.703	0.262	11.3 (±0.7)
750	0.687	0.301	570	6.68	0.644	0.247	15.7 (±1.0)
760	0.734	0.263	378	6.47	0.624	0.334	17.5 (±1.5)
780	0.729	0.258	414	5.81	0.560	0.283	23.4 (±1.6)
790	0.731	0.260	470	5.94	0.572	0.270	22.2 (±1.3)
800	0.721	0.263	424	6.29	0.606	0.261	19.0 (±1.1)
810	0.692	0.274	352	7.25	0.699	0.255	11.6 (±0.7)
820	0.676	0.291	310	8.22	0.793	0.338	5.5 (±0.3)

Figure 4

NPAF of the 550 nm radius trapped particle in linear-log plot with delay time (τ) at different trapping wavelengths and within (a) 1.25 × 10–5 (M) concentration of the IR780 dye in water and (b) 3.33 × 10–5 (M) concentration of the IR780 dye in water.

We have acquired the position of the particle at 100 kHz using a quad detector and analyzed only the first 0.5 s data. Such DAQ has allowed us to measure the temperature and viscosity in all cases by probing the thermal fluctuation of the 550 nm radius fluorophore-coated polystyrene bead position with a LabVIEW controlled piezoelectric stage. Such a demonstration of power and wavelength tunability of our FOTs also indicates the general applicability of this method. At higher dye concentrations, a strong convection flow[55,56] directed to the focal region occurs, resulting in a velocity gradient toward the beam focus. As long as the gradient force predominates over the convection flow at the beam focus, it is easier to trap. With time, the flow rate expeditiously increases even at constant power and concentration, as the IR780 molecules accumulate near the focal volume (see media file). We have measured the temperature change to indicate that thermal flow exists, and the bead displacement due to this flow is coupled with that of a regular confined Brownian motion. We only correlate the measure of the displacement of the confined Brownian motion as long as it is not very large to our temperature change model. Also, we have only analyzed initial 0.5 s of trapping data to keep the convection flow mostly decoupled with the Brownian motion, thus throughout our measurement we have ignored the convention effect. Furthermore, we have used a 100 kHz mechanical shutter controlled via the LabVIEW program (SR475), which can have an opening time that is shorter than or comparable to the thermal relaxation time. The thermal relaxation time is defined as the average time required in achieving the maximum temperature at the surface of the bead.[57] This method can be further modified to measure the temperature in the presence of higher convection flow using traditionally modeled Boussinesq approximation.[58] Our study indicates that for the IR780 dye in water, at concentrations of 3.33 × 10–5 and 1.25 × 10–5 (M) a temperature rise of 1.64 K/1.0 mW and 1.13 K/1.0 mW, respectively, is observed (Figure a). Also, the wavelength-dependent temperature rise is shown in Figure b.

Figure 5

(a) Temperature around trapped bead vs trapping laser power (at 780 nm) experimental data (red circle) and its linear fit (blue line) at an IR780 dye concentration of 3.33 × 10–5 (M) and experimental data (green circle) and its linear fit (orange line) at an IR780 dye concentration of 1.25 × 10–5 (M). (b) Temperature around trapped bead vs trapping wavelength (at 25 mW power) experimental data (red circle) and corresponding Lorentzian fit (red line) at an IR780 dye concentration of 3.33 × 10–5 (M) and experimental data (green circle) and its Lorentzian fit (green line) at an IR780 dye concentration of 1.25 × 10–5 (M).

Advantages of Temperature Control with FOTs

We have developed an in situ method at a micro-to-nanoscale dimension to measure and control the absolute temperature and hence the corresponding microrheological property of viscosity in the condensed phase. We have also measured nano- to femto-newton force constant (κ = 2πγfC) (see S5, Figure S3) for an optical trap in absorbing conditions. Our approach of FOTs has several advantages as compared to the other available techniques as discussed below:

The FOT approach results in the on-the-fly calibration, which utilizes the high temporal sensitivity of position autocorrelation and equipartition theorem (for detailed derivation, see S6). This method provides a very high spatial resolution as compared to the other existing contactless methods.[10,59] For example, the spatial resolution is 1 mm in fiber-optic infrared radiometer, whereas our method can go down to a few nanometers, only by probing the trapped single nanoparticle.[52,60] Probing temperature at nanoscale volume requires a fast diffusing nanoparticle, and hence, small trapping data are sufficient. In our time-domain measurement, the resolution is not restricted by the measurement time, whereas in the existing PSD approach, the resolution inversely depends on the measurement time.

We used the high repetition rate femtosecond laser for optical trapping, which enables finer temperature gradients as compared to other techniques. This is possible because of the additional NLO effect occurring at the focus of the FOTs with a low average power that least perturbs the trapping medium.

In our FOTs, we also observed that at high dye concentrations, the trapped bead accelerates toward the beam focus because of the strong convection flow directed toward the focal region. Trapping is easily possible at the beam focus as long as the gradient force predominates over the convection flow. By changing the laser fluence, wavelength, dye concentration, and beam waist at the focal volume, we can also control the convection current flow. This phenomenon would be very useful for directional drug delivery with FOTs.

The PSD analysis has also been used earlier for on-the-fly calibration in the frequency-domain measurements of optical tweezers.[39] However, the PSD analysis uses the formalism of Fourier transforms to study the Brownian fluctuations of the bead in the frequency domain. The PSD analysis is thus computationally intensive requiring a heavy-duty field-programmable gate array or digital signal processor integrated circuit to do this calculation on-the-fly. The resolution of PSD depends on the inverse of the measurement time. Consequently, for a trapping event over a very short timescale (e.g., trapping of a quantum dot or a highly diffusing nanoparticle), it is difficult to estimate the absolute measurement. For our time-domain-based approach, however, the resolution is not restricted by the length of the measurement, it is, in fact, dependent on the sampling rate. Thus, our method presented here is computationally simple and even works for small duration trapping in both Newtonian and nonNewtonian fluids.[61]

Furthermore, in our NPAF approach, only single wavelength is used for all the three purposes: for trapping, for heating, and for probing, which minimizes the instrumentation level and cost of the auxiliary laser.

There are also a few other indirect techniques of optical tweezers that require additional coupled measurements, such as fluorescence correlation spectroscopy, fluorescence intensity, and additional thermocouple to compare their efficiency in measuring the temperature around the trapped bead. Such indirect methods highly increase the complexity of the optical tweezers’ arrangement and cater only to fluorescence active particles without offering any measurement advantage. On the other hand, our direct FOT technique is straightforward and also works for nonfluorescent particles because we only analyze the scattering data.

Conclusions

We have demonstrated a novel on the fly calibration method of optical tweezers. Such a technique also provides an in situ control and a measure of the absolute temperature and viscosity at nanoscale dimensions. The experiments involved a polystyrene bead trapped with a noninvasive NIR pulsed laser, which responded spontaneously to a known sinusoidal modulation provided by the user to result in the self-calibrated optical tweezers. Such in situ measurement and control of absolute temperature and viscosity at nanoscale dimensions are big challenges. Present techniques provide off-line measurements that do not provide absolute values in real time. In our technique, the oscillation in the autocorrelation curve comes from the provided drive signal, and we are only interested in the decay before the oscillatory behavior region, that is, on fast time scales. This method is even very useful to achieve high spatial resolution as the time-domain measurement is not restricted by the measurement time.