2.1 Single Particle Polarized Spectroscopy

Birefringent upconverting NaYF₄ microparticles doped with Er³⁺ and Yb⁺³ ions were synthesized by a hydrothermal method, as described elsewhere.^[25] These particles present a hexagonal disk-shaped morphology (see Figure 1a) with average thickness and diameter of 1.4 ± 0.2 µm and 4.4 ± 0.3 µm, respectively (see Figure 1b and data included in Synthesis section of Experimental Section). The hexagonal β-phase crystal structure of the UCPs was confirmed by X-ray diffraction analysis (see Section S1 and Figure S1, Supporting Information) A single-beam optical tweezers setup is used for the isolation of a single UCP. Optical trapping is achieved by focusing an 808 nm laser beam into the chamber containing an aqueous UCP suspension. The optical torque orientates the UCP within the trap with its hexagonal face parallel to the wavevector of the 808 nm radiation. If the 808 nm laser radiation is linearly polarized, then the UCP reaches a fixed position with its hexagonal face parallel to the laser polarization (Figure 1c). On the other hand, when the 808 nm laser radiation is circularly polarized, the transfer of angular momentum results in a continuous rotation of the UCP (Figure 1d).^[26] The polar plots of the 808 nm trapping radiation when it is linearly and circularly polarized are included in Figure S2 (Supporting Information).

The presence of both Er³⁺ and Yb³⁺ ions within the UCP allows optical excitation of visible emission under either 808 or 980 nm illumination. Due to the water absorption band at 980 nm and to avoid undesirable laser heating, in this work experiments were performed under 808 nm excitation.^[27] Under direct Er³⁺ excitation at 808 nm, the Er³⁺ ions in the NaYF₄ crystal are directly excited up to high energy levels via sequential absorption of pump photons (Figure 1e), thus resulting in a visible emission from Er³⁺ ions. This visible emission is constituted by three bands, centered at 530, 550, and 660 nm, corresponding to the ²H_11/2,⁴S_3/2 → ⁴I_15/2 (green bands) and to the ⁴F_9/2 → ⁴I_15/2 (red band) transitions, respectively.^[28-30] Because of the anisotropic crystal field of NaYF₄ UCPs, both the green and red bands are polarized, and the shape of the emission spectra depends on the relative orientation between the electric field of the emitted radiation ($$\overrightarrow {{{E}_{em}}} $$) and the optical axis of the NaYF₄ UCP ($$\vec{c}$$ axis, that aligns perpendicularly to the hexagonal face of the UCP).^[22] To assess the polarized emission of an individual UCP in water, a single UCP was optically trapped with a linearly polarized 808 nm laser beam that resulted in its fixed orientation within the trap. The polarization properties of the visible emission were recorded using a rotating linear polarizer located in the emission pathway. Figure 1f,g show the green and red emission spectra from a single, optically trapped, NaYF₄ UCP as obtained when $$\overrightarrow {{{E}_{em}}} \bot \vec{c}$$ (α configuration) and when $$\overrightarrow {{{E}_{em}}} \parallel \vec{c}$$ (π configuration). The dashed lines in Figure 1f,g indicate the specific wavelengths where the polarization dependence of luminescence becomes more evident. The obtained polar diagrams of the ratio between these intensities (Figure 1h) reveal that both green and red bands are polarized, although the red band exhibits a significantly larger degree of polarization dependence. Indeed, the degree of polarization calculated for the I₅₄₃/I₅₅₀ (green) and I₆₆₇/I₆₆₃ (red) intensity ratios were determined to be 0.28 and 0.44, respectively.

2.2 Single Particle Polarized Luminescence Thermometry

2.3 Luminescence-Based Velocimetry for Viscosity Sensing

It is important to remark here that the measured viscosity corresponds to the viscosity of the medium in physical contact with the rotating UCP, i.e., at the local temperature T_l that is here assumed to be equal to the temperature of the UCP. We have also explored the possible temperature dependence of R_r (see Section S5 and Figure S4, Supporting Information) concluding that it is, within experimental error, a temperature-independent intensity ratio. This was, indeed, expected as this red band is not generated by thermally coupled states. Thus, we conclude how a proper analysis of the shape fluctuations of the red band provides us with a reliable reading of the rotation speed.

2.4 Real-Time, Decoupled Temperature and Viscosity Sensing

Sections 2.2 and 2.3 revealed how multiband ratiometric analysis of the luminescence generated by a rotating UCP opens the possibility of decoupled readout of temperature and viscosity. To demonstrate this, we conducted a proof-of-concept experiment in which the rotating UCP is used for simultaneous sensing of viscosity and temperature during fluid mixing (Figure 4a). A single UCP is optically trapped and rotated within a microchamber by a circularly polarized 808 nm laser beam. The microchamber is placed on a stage at a constant temperature of 20 °C. The absence of any relevant laser-induced heating has been confirmed from the analysis of both the Er³⁺ luminescence and the rotation dynamics, as described in Section S6 (Supporting Information) (Figure S5, Supporting Information). Initially, the microchamber was filled with water. At a specific timepoint, a second liquid – consisting of a viscous solution of polyacrylamide (PAM) in water with a viscosity of 1.88 mPa·s also at a temperature of 20 °C – was injected into the chamber through one of its inlets. Details about the injection procedure and solution properties can be found in the Experimental Section, and the emission spectra of the rotating UCP is shown in Section S7 (Supporting Information) (Figure S6, Supporting Information). Time evolution of local temperature and viscosity before, during, and after the diffusion of the viscous solution was determined from the ratiometric analysis of both green and red bands, respectively, as explained in Sections 2.2 and 2.3. The time evolution of the local temperature (Figure 4b) reveals an average temperature of 19.9 °C, in very good agreement with the temperature set externally in the microchamber (20 °C). Statistical analysis of experimental data reveals a temperature uncertainty, estimated from the standard deviation of temperature readouts, of ±1.5 °C. Note that the diffusion of the viscous PAM solution does not lead to any noticeable change in the temperature sensed by the particle within the abovementioned uncertainty. This was, indeed, expected as the injected viscous medium was at the same temperature as the water initially filling the microchamber. Figure 4b reveals that any change in local viscosity cannot be correlated with temperature and, thus, should be caused by the diffusion of the viscous medium through the chamber. Figure 4c includes the time fluctuation of the intensity ratio R_r before (blue) and after (pink) the viscous medium has fully mixed with the water within the chamber. When the viscous liquid diffuses along the chamber there is a slow-down of the particle spinning, indicating an increment in local viscosity. The time evolution of local viscosity was determined from the Fourier analysis of the R_r versus time (Figure 4d) at different time points after the injection of viscous liquid. This analysis showed an initial viscosity between 0.9 and 1.0 mPa·s (expected for pure water), followed by a rapid increase to an average value of 1.2 mPa·s upon intermixing of water with the PAM solution. As expected, the latter value is lower than the one of the PAM solution (1.88 mPa·s), due to the dilution of the polymer solution in pure water.

Once the ability of a rotating UCP for decoupled measurement of temperature and viscosity has been demonstrated, we applied this method to determine the temperature dependence of viscosity of an aqueous solution of PAM using the set-up represented in Figure 5a. An individual UCP was optically trapped and rotated within a microchamber by using a focused 808 nm laser beam. The microchamber was filled with a polyacrylamide (PAM) solution whose viscosity versus temperature curve is unknown. The (negligible) effect of PAM on the spectroscopic properties of our UCP are discussed in Supporting Information (Section S8 and Figure S7, Supporting Information). The polarized luminescence generated by this UCP was registered to achieve simultaneous reading of both temperature and viscosity. Local temperature was varied by using an additional single-mode diode laser operating at 1450 nm (radiation highly absorbed by water) that is coupled to the experimental system and that overlaps with the 808 nm trapping laser. The laser beam radius at the focus of the 808 and 1450 nm radiation within the chamber were estimated to be 0.7 and 1.1 µm, respectively. The power of the 808 nm laser was kept constant (70 mW, corresponding to 4.5 MW cm⁻²) during the experiment to ensure a constant optical torque. On the other hand, the 1450 nm laser power was varied between 0 and 30 mW (from 0 to 0.8 MW cm⁻²) to change the local temperature of the fluid. For each value of the 1450 nm laser power, we analyzed the green and red bands luminescence to determine the local temperature and viscosity, respectively (see Figure 5b). As expected, and in agreement with previous works, the local temperature increases linearly with the 1450 nm laser power while the local viscosity decreases due to the local heating. Combining the data shown in Figure 5b, we obtained the temperature-induced reduction in the local viscosity of the polyacrylamide solution (Figure 5c). The experimental data can be compared with previous reports on the temperature dependence of the viscosity of similar solutions.^[43] A reasonably good agreement between our data and those obtained by rheological measurements using a viscometer (solid line in Figure 5c) is observed, which clearly confirms the validity of our approach for simultaneous measurement of the temperature and the viscosity.