Thermal properties of nanofluids using hydrophilic and hydrophobic LiYF4:Yb/Er upconverting nanoparticles

Luminescent nanoparticles have shown great potential for thermal sensing in bio-applications. Nonetheless, these materials lack water dispersibility that can be overcome by modifying their surface properties with water dispersible molecules such as cysteine. Herein, we employ LiYF4:Er3+/Yb3+ upconverting nanoparticles (UCNPs) capped with oleate or modified with cysteine dispersed in cyclohexane or in water, respectively, as thermal probes. Upconversion emission was used to sense temperature with a relative thermal sensitivity of ∼1.24% K−1 (at 300 K) and a temperature uncertainty of 0.8 K for the oleate capped and of 0.5 K for cysteine modified NPs. To study the effect of the cysteine modification in the heat transfer processes, the thermal conductivity of the nanofluids was determined, yielding 0.123(6) W m−1 K−1 for the oleate capped UCNPs dispersed in cyclohexane and 0.50(7) W m−1 K−1 for the cysteine modified UCNPs dispersed in water. Moreover, through the heating curves, the nanofluids' thermal resistances were estimated, showing that the cysteine modification partially prevents heat transfer.


Structural characterization
Powder X-Ray Diffraction experiments were conducted on a Bruker-AXS D2 Phaser diffractometer with Cu Kα radiation (λ = 1.5418Å) from 10° to 60° at a scanning rate of 5° min −1 .Figure S1 shows the obtained XRD patterns for the oleate capped UCNPs which presents narrow peaks in great agreement with the LiYF 4 tetragonal phase (JCPDS #81-2254) 1 , with no extra peaks observed.The Fourier Transform Infrared spectroscopy (FTIR) was performed on a Shimadzu IRPrestige-2.All spectra were recorded with 20 scans and 2.0 cm −1 resolution in the 4000-400 cm −1 window.All samples were prepared as KBr pellets.Figure S2 presents the FTIR spectrum for the oleate capped UCNPs, showing typical oleic acid bands, attributed to stretching of CH 2 groups (at 2920 cm −1 and 2850 cm −1 ) and -COO-groups (at 1560 cm −1 and 1460 cm −1 ).A wide and rather intense band near 3500 cm −1 was attributed to OH stretching of unbound oleic acid COOH groups that were not washed away [2][3][4] .After cysteine modification, C-N and N-H stretching appears at 1146 cm −1 and 1208 cm −1 and a C=O vibration at 1680 cm −1 , characteristic of cysteine 5 .

Determination of UCNP and nanofluid properties
The absorption coefficient, (in ), of an absorbing species J in the (nano)fluid is where is the absorbance of species J using the solvent as the reference and is the optical Figure S3 -Visible NIR room temperature absorption spectra of the oleate capped and cysteine modified LiYF 4 :Yb3%,Er0.025%nanoparticles.
The molar extinction coefficient, (in M −1 m −1 ) at 980 nm is calculated through the following equation: where is the absorbance at 980 nm, and corresponds to the molar concentration of J-  (980)   absorbing species.
The absorption cross section, (in ), of a single absorber J in solution is is the number density of J-th absorbers in (# of absorbers-J) . For a solution of absorbers    -3 with concentration (in ), is where (in ) is the mass of the absorber-J.

𝑚 𝐽 𝑚𝑔
Both the oleate capped-and cysteine modified-LiYF 4 nanoparticles have a square (or tetragonal) bipyramid shape with small diagonal, , long diagonal , and its volume, , is given by: The number of nanoparticles exposed to the laser was calculated from the concentration of nanoparticles in the dispersion, volume of nanoparticles and volume of the cylinder formed by the incident laser on the cuvette.The number of UCNPs, , and of solvent molecules, , exposed to the laser beam are where (in ) is the number density of NPs, (in ) is the number density of solvent, (in ) is the area of the laser spot, and (in ) is the optical path length.
It was also considered that the modification of oleic acid with cysteine did not alter significantly the oleic acid surface area, considered 0.4 nm 2 6 or the coverage of ligands in the surface of the nanoparticle.From the oleic acid covered area and oleic acid surface area, the number of oleic acid molecules at the surface of the nanoparticles was calculated.With this, it was possible to calculate the mass of oleic acid in each nanoparticle.For the cysteine-modified oleic acid, an analogous procedure was used, but with the molecular weight of the modified oleic acid.
The weight of the cysteine-modified oleic acid was calculated from the sum of oleic acid and cysteine molecular weights.The total mass of the particle plus ligands was calculated from the sum of the mass of one particle and the total mass of ligands in the particles.
The area of the nanoparticle covered with oleic acid must be accounted in the molecular weight of each UCNP.To measure the number of oleic acid molecules attached to each nanoparticle, the thermogravimetric analysis (TGA) was used.Figure S4 shows the TGA profile of the sample, which shows a mass loss of 2.46 % between 280 o C and 400 o C 6,7 , which represents the loss attributed to the oleic acid bonded to the nanoparticle.Considering the initial mass of 13.4350 mg, the calculated number of molecules of oleic acid was 7.0×10 17 molecules and using the oleic acid area, the total coverage of the particle was considered 40%, which is in agreement with the literature 6 .

Optical characterization and thermometric characterization of the luminescent thermometers
Figure S5 -Normalized emission spectra acquired upon 980 nm excitation (229 W cm −2 ) for each of the nanofluids.The Er 3+ transitions are labeled.
To verify the capability of the system to be a primary thermometer, upconversion emission spectra were obtained for temperatures ranging from 293 K to 317 K.The intensity parameter Δ was defined as the intensity ratio between 2 H 11/2 → 4 I 15/2 and 4 S 13/2 → 4 I 15/2 transitions of Er 3+ .

Figure S6 -Temperature-dependence of the upconversion emission spectra of oleate capped
UCNPs dispersed in cyclohexane upon irradiation with 980 nm laser (172 W cm −2 ).
To calculate , one representative spectrum was plotted, and each one was fitted to a Gaussian ∆ distribution.The signal was converted from wavelength to energy units to fit Gaussian functions to the spectrum applying where is the energy in units of cm −1 , and is the wavelength in nm units.The Jacobian  To obtain the value of , the emission spectra were recorded in different power densities and ∆ 0 a linear dependence of the intensity parameter with the laser power density.The intercept of ∆ the linear fit was taken as , as presented in each one of the graphs and showed in Table S1.With all these parameters (Table S1), it was possible to calculate the temperature using the Δ, the following equation was used 8 : where is the Boltzmann constant, is the energy difference between the barycenter of the   ∆ two emissions, is the temperature of null laser-induced heating, and is the intensity

Relative Thermal Sensitivity and Temperature Uncertainty
To assess the thermometer performance, two figures of merit were calculated, the relative thermal sensitivity and the temperature uncertainty.The relative thermal sensitivity indicates the relative change of per degree of temperature change, and is defined by: where is the separation between the thermally coupled energy levels, is the Boltzmann Δ   constant, is the absolute temperature, and is the thermometric parameter.The error related  Δ to the sensitivity ( ) was derived from the errors of the parameters used in the calculation, as defined by: where is the error in .The temperature uncertainty is the temperature resolution, i.e.,

𝛿Δ𝐸 Δ𝐸 𝛿𝑇
the smallest temperature change that can be detected in a given measurement.The uncertainty of the thermometer temperature is given by: where is the relative error in the thermometric parameter.obtained when the nanofluids were irradiated with a 980 nm laser (200-250 W cm −2 ).For lower power densities, the luminescent thermometer presented a higher error and scattered.
was used to rescale the intensity values as a function of energy units: as a function of energy and wavelength, respectively.Then,() ()the barycenter of each transition was calculated by a weighted arithmetic mean and the energy difference was calculated.The values calculated were 777 ± 44 cm −1 and 775 ± 35 cm −1 for the oleate capped and cysteine modified UCNPs, respectively.

∆ 0 Figure S8 -
Figure S8 -Dependency of the Δ intensity parameter with the laser power density used to calculate Δ 0 for (a) oleate capped UCNPs and (b) cysteine modified UCNPs.

Figure S9 -
Figure S9 -Thermometric performance of the nanofluids upon 980 nm excitations.(a) Relative thermal sensitivity of the oleate capped UCNPs and cysteine modified UCNPs.The shadowed area corresponds to the respective error calculated using Equation S11.(b) Temperature uncertainty of the nanothermometers.

Figure S10 -
Figure S10 -Temperature profiles of the (a-c) oleate capped UCNPs dispersed in cyclohexane and (d-f) cysteine modified UCNPs dispersed in water, measured by the immersed thermocouple (grey dots) and luminescent thermometer (colored dots).The curves were