1. Introduction

Optical traps are widely known and applied tools for the investigation and manipulation of atoms [1,2], molecules, such as DNA or molecular motors [3,4], vesicles [5,6], and whole cells [7–10]. Their working principle is based upon a stable potential well that is created by the non-uniform field of one or more laser beams for dielectric particles displaying a higher refractive index than their surrounding medium [11]. Optical tweezers are most prevalently used in this field [12,13]. However, over the last few years another kind of optical trap has regained importance: The dual-beam laser trap, invented by Ashkin [11] even earlier than optical tweezers, consists of two opposing, divergent laser beams. Because the beams in this configuration are not focused, fiber lasers can be used directly as light sources, which renders the trapping optics independent from the microscope optics used to characterize the trapped object [14,15]. Dual-beam laser traps are also easily combined with spectroscopic techniques [16] and integrated in microfluidic systems for the rapid serial analysis of many objects in suspension [17,18].

This is relevant because microfabrication and microfluidics are fast growing research branches with a steadily increasing demand for small-scale experimental environments. Studies in life sciences are a prominent example, with often only limited amounts of sample volume available and the objects to be investigated on the micrometer or nanometer scale. The latest approach in this area is to create a “lab on a chip”, where a complete assay can be done on cells, organelles, or molecules in micrometer-sized structures combined on one single chip [19–21]. Such assays can include optical inspection or manipulation, targeted (bio)chemical reactions, and eventually also sorting of the objects examined. The complexity of such miniature labs sets high standards not only for the fabrication of the chips, but also for the measurement techniques to characterize experimental conditions such as temperature, pH-value, flow velocities, etc. Using conventional sensors, these parameters cannot be measured directly at the reaction site without disturbing the flow characteristics of the setup. Additionally, it is hard to obtain spatially resolved profiles of the parameters as macroscopic measurements can only deliver averaged results.

In this paper we present a method to measure absolute temperatures and their distributions with submicron resolution in microfluidic setups by employing laser induced fluorescence (LIF) of two dyes as a temperature indicator. This is exemplified by the characterization of the thermal effects in a microfluidic dual-beam laser trap.

Some fluorescence dyes, including Rhodamine B, have a well characterized temperature dependent LIF [22,23]. Using one such dye alone for the temperature measurements can result in problems due to local fluctuations in excitation light intensity and dye concentration, which makes the calibration of the LIF-dependence on temperature very difficult if not impossible. These problems can be avoided by using a second fluorescent dye with temperature independent fluorescence, such as Rhodamine 110, as a reference [24]. In combination with imaging on a laser scanning confocal microscope, temperature distribution profiles of a fluid in a microfluidic channel can be obtained with high resolution.

2. Materials and methods

As the temperature indicator we chose the xanthene dye Rhodamine B (83689, Fluka, Steinheim, Germany), since it has high temperature sensitivity (2.3% K^-1). Rhodamine 110 (83695, Fluka, Steinheim, Germany), also from the xanthene group, was used as the reference dye, as demonstrated by Sakakibara [24]. The difference between the two emission peaks (575 nm vs. 520 nm) is large enough to distinguish both fluorescence signals. A dye solution was prepared from Rhodamine B (0.1 mM) and Rhodamine 110 (0.1 mM) in carbonate buffer (20 mM).

A dual-beam laser trap was integrated with a microfluidic environment as previously described by Lincoln et al [17]. Briefly, two 1064 nm fiber lasers (YLM–2–1064, IPG Photonics, Germany) were used as light sources for the optical trap. The two single-mode optical fibers were axially aligned opposing each other at a distance of 540 μm (cf. Fig. 1). A square glass capillary of 80 μm inner diameter and with 40 μm thick walls (ST8508, VitroCom, USA) was placed perpendicularly between the fibers. All components were submersed in index matching gel to avoid reflection and diffraction effects at the surfaces. The dye solution was pumped through the capillary using a simple syringe pump and was stopped completely during the measurements.

 

Fig. 1. Microfluidic setup of the dual-beam laser trap. The two opposing laser beams diverge from the fiber cores in the optical fibers through the index matching gel into the glass capillary where they form an optical trap. The fluorescence of the aqueous dye solution within the capillary is imaged from below within the marked area.

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The fluorescence images were taken with a laser scanning confocal microscope (TCS SP2, Leica, Germany). For fluorescence excitation, the available 488 nm and 514 nm laser lines of the microscope were used. Two-dimensional images were taken at the center plane of the trap. The region of interest was scanned at a resolution of 512 × 256 pixels with a 10× objective (HC PL FLUOTAR, 0.3 NA, Leica, Germany). The pixel size in each image was less than 0.4 × 0.4 μm. The final fluorescence images represent an average of 40 successive scans, except for the time resolution measurement, where no averaging was done to achieve sufficient time resolution. All measurements were done at an ambient temperature of 21 °C.

The dependence of the fluorescence on temperature was calibrated in the same glass capillary as used for the trap setup. The capillary was surrounded by a temperature controlled water flow to keep the dye in the capillary at constant temperature. A PT100 temperature sensor (Conrad Elektronik, Germany) was used to determine the temperature at the capillary. Fluorescence intensities of both dyes were measured in the temperature range of 22 – 46 °C.

The thermal behavior of the microfluidic device was also evaluated numerically. The partial differential equation governing the relationship between the temperature distribution and heat conduction for a convection-free medium is the nonhomogeneous heat equation [25]

where T is the temperature distribution, k is the thermal conductivity, S is the thermal source distribution, c_p is the heat capacity (at constant pressure), ρ is the density, and t is time. The source distribution S is given by S = αI. The optical irradiance distribution, I, is approximated to be unmodified by absorption over the dimension of the device. This simplification allows for the irradiance in the trap to be represented simply in terms of a superposition of two Gaussian beams counter-propagating along the azimuthal axis.

An upper limit on the time-constant of the system is estimated from equation (1) using dimensional considerations as τ_equ = L ² c_P ρk ^-1 < 5 ms for a characteristic length L taken as the capillary internal dimension. This is shorter than the time resolution of the current measurement instrumentation. Thus, equation (1) can be evaluated at equilibrium to become Poisson’s equation

which was solved using the finite volume technique [26]. The geometry used for the simulation was chosen to represent the experimental setup shown in Fig. 1. Dirichlet boundaries were used at the edges of the simulation region, and the overall size of the region is selected to minimize the effect of these boundary conditions.

3. Results

Figure 2 shows the temperature dependence of the fluorescence intensity ratio of Rhodamine B and Rhodamine 110. The measurement curves were reproducible without further normalization. This implies that absolute temperatures can be measured with this method. The resolution of the temperature measurement is better than 2 °C, with a spatial resolution of less than 0.5 μm.

 

Fig. 2. Calibration function; the fluorescence ratio of Rhodamine B and Rhodamine 110 as a function of temperature. The error bars are the standard error of mean (SEM; N = 5).

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A color-coded representation of the temperature distribution measured at the horizontal plane through the center of the trap is shown in Fig. 3(a). The graph of the temperature distribution along the azimuthal axis displays a temperature rise of 25 °C over a background temperature of 21 °C for a total power of 2 W (1 W per beam) in the trap (Fig. 3(b)). All measured temperature profiles exhibit characteristic convex slopes of the graph and agree well with the theoretical model (Fig. 4), which predicts a temperature rise of 25 °C.

 

Fig. 3. (a) Color-coded temperature distribution in the imaging plane through the center of the trap within the capillary. The ratio of the fluorescence profiles was measured and scaled with the calibration function shown in Fig. 2. The power in each of the two laser beams was 1 W and the wavelength was 1064 nm. (b) Line profile of the temperature distribution along the microfluidic channel indicated by the dashed line in (a). The slight asymmetry is caused by residual flow. For comparison with Fig. 4, please note that the temperature values shown are room temperature (21 °C) plus the temperature increase caused by the laser heating.

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Fig. 4. Theoretical simulation of the distribution of the temperature increase in and around the capillary. The position of the two laser beams (1064 nm; 1 W each) is indicated by the white dashed lines, the position of the capillary by the black squares. Please note that the color scale differs between Fig. 3 and Fig. 4.

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Temperature measurements at different laser powers ranging between 1 and 2.5 W (0.5 to 1.25 W per beam) reveal a linear temperature dependence on laser power as expected, with a temperature rise of (13 ± 2) °C/W in the center of the dual-beam laser trap (Fig. 5).

 

Fig. 5. Dependence of the maximum temperature reached in the center of the trap on total incident laser power (1 W = 0.5 W in each beam). Shown are measurements (N = 4) with SEM and the 95% confidence interval.

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Figure 6 shows the temporal development of the heating process. The temperature distribution is established within fractions of a second, consistent with the theoretical estimate. After the laser is turned on, the temperature rises almost instantaneously to the final temperature.

 

Fig. 6. Temporal development of the heating process. The lasers are turned on at t = 2 s (indicated by the dashed line).

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4. Discussion

We have demonstrated that measuring the LIF-ratio of the two xanthene dyes Rhodamine B and Rhodamine 110 is a powerful method to determine absolute temperatures in microfluidic devices without any sensor disturbing the flow characteristics of the setup. In the range from 20 – 50 °C a temperature resolution of about 2 °C is achieved. The use of a confocal laser scanning microscope permits submicron spatial resolution, which is appropriate for the study of microfluidic devices, and also facilitates 3D measurements. The temporal resolution of fractions of seconds allows the tracking of moderately fast thermal processes in such environments.

The quality of the results is comparable to the fluorescence lifetime temperature method [27], but less technical equipment is required for the method presented, which makes it more readily applicable for general microfluidic and optics labs.

Sakakibara had argued for the use of Rhodamine 110 as a reference dye for the normalization of the temperature dependence of Rhodamine B because of the spectral similarity of both dyes and the very low temperature dependence of Rhodamine 110 [24]. An additional argument is the chemical similarity of both dye molecules in size and charge, which makes it unlikely that the method is susceptible to thermophoresis effects [28]. Also, distortions of the temperature profile due to convective flow could be ruled out, because the Rayleigh number for the fluid in the capillary was sufficiently small (Ra ≈ 1 ≪ 1000, onset of free convection [29]), which were also not observed experimentally.

It is also worth pointing out that the experimental results agree well with the theoretical calculation. This substantiates the quality of the temperature measurement method. At the same time it suggests the use of analogous numerical simulation for cases where thermal measurement itself may be infeasible, the thermal design is to be optimized, or predictions of the heating effects for other trapping-laser wavelengths and beam parameters are desired. Since the heating correlates linearly with the absorption coefficient of light in water, the choice of the trapping-source wavelength has a great influence on the maximum temperatures in the trap. We calculated maximum temperatures in the same trap geometry of about 1.7 °C/W and 200 °C/W with an 800 nm and a 1340 nm source, respectively. The applied trapping wavelength is thus an important parameter for the reduction of thermal effects, but also for the intentional heating of samples in an optical trap or for thermophoretic trapping [30].

Although this is, to our knowledge, the first temperature measurement in a dual-beam laser trap, it can be compared to measurements and calculations for optical tweezers. Peterman [31] measured temperature increases of about 8 °C/W at 1064 nm, while a theoretically predicted value was 2 °C/W for 850 nm lasers [32]. Thus, the order of magnitude of the heating in the various optical traps is comparable. While one might expect larger heating effects in focused beams due to the higher light intensity and greater local heat deposition, it needs to be considered that the temperature gradient and, thus, the heat transport away from the source is greater than in non-focused, divergent beams.

In conclusion, we have demonstrated that this method of remotely and non-intrusively measuring temperature distributions in microfluidic systems with submicron resolution can be used for the study of thermal effects, which are important in practical applications of optical traps.