refrigeration of hydrothermal nanocrystals in physiological media

Paden B. Rodera,1, Bennett E. Smithb,1, Xuezhe Zhoua,1, Matthew J. Cranec, and Peter J. Pauzauskiea,d,2

aDepartment of Materials Science & Engineering, University of Washington, Seattle, WA 98195; bDepartment of Chemistry, University of Washington, Seattle, WA 98195; cDepartment of Chemical Engineering, University of Washington, Seattle, WA 98195; and dFundamental & Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, WA 99354

Edited by Qihua Xiong, Nanyang Technological University, Singapore, Singapore, and accepted by the Editorial Board October 13, 2015 (received for review June 9, 2015) Coherent laser radiation has enabled many scientific and techno- contrast with anti-Stokes processes, optomechanical laser refrig- logical breakthroughs including Bose–Einstein condensates, ultra- eration has also been demonstrated based on a novel mechanism fast spectroscopy, superresolution optical microscopy, photothermal of angular momentum transfer between a circularly polarized laser therapy, and long-distance telecommunications. However, it has and a birefringent crystal (23). remained a challenge to refrigerate liquid media (including phys- To date, laser refrigeration of nanocrystals in aqueous media iological buffers) during laser illumination due to significant back- has not been reported stemming primarily from the large NIR ground solvent absorption and the rapid (∼ps) nonradiative α j ∼ optical absorption coefficient of water ( H2O 975 nm 0.5/cm) (24). vibrational relaxation of molecular electronic excited states. Here It has remained an open question whether these known cooling we demonstrate that single-beam laser trapping can be used to materials could act to refrigerate aqueous media and undergo induce and quantify the local refrigeration of physiological media hypothesized cold Brownian motion (CBM) (25, 26), or whether by >10 °C following the emission of photoluminescence from solvent heating from the background absorption coefficient of upconverting fluoride (YLF) nanocrystals. A simple, water would overwhelm the cooling of individual YLF crystals. low-cost hydrothermal approach is used to synthesize polycrystalline Furthermore, it is not obvious a priori that YLF crystals made particles with sizes ranging from <200 nm to >1 μm. A tunable, near- through hydrothermal processing would have sufficiently low infrared continuous-wave laser is usedtoopticallytrapindividualYLF background impurity levels to achieve laser cooling (27, 28). In crystals with an irradiance on the order of 1 MW/cm2.Heatistrans- this work, we demonstrate the local laser refrigeration of hydro- ported out of the crystal lattice (across the solid–liquid interface) by + thermal YLF nanocrystals dispersed within several different anti-Stokes (blue-shifted) photons following upconversion of Yb3 aqueous media including deionized water, heavy water (D2O), electronic excited states mediated by the absorption of optical and physiological electrolytes. Refrigeration >10 °C below am- phonons. Temperatures are quantified through analysis of the bient conditions is observed in PBS following anti-Stokes pho- cold Brownian dynamics of individual nanocrystals in an inhomo- toluminescence from optically trapped (29), rare-earth–doped YLF geneous temperature field via forward light scattering in the back nanocrystals undergoing CBM. focal plane. The cold Brownian motion (CBM) analysis of individual YLF crystals indicates local cooling by >21 °C below ambient con- Results and Discussion 3+ ditions in D2O, suggesting a range of potential future applications Pioneering efforts to cool Yb :YLF materials in vacuo have including single-molecule biophysics and integrated photonic, relied on the growth of high-purity YLF single crystals using an electronic, and microfluidic devices. Significance laser refrigeration | nanocrystal | hydrothermal | physiological | anti-Stokes

Although the laser refrigeration of bulk crystals has recently dvances in cryogenic sciences have enabled several obser- shown to cool below cryogenic temperatures (∼90 K) in vac- Avations of new low-temperature physical phenomena including uum, to date the laser refrigeration of physiological media has – superconductivity (1), superfluidity (2), and Bose Einstein con- not been reported. In this work, a low-cost hydrothermal densates (3). Heat transfer is critical in numerous fields of science synthetic approach is used to prepare nanocrystals that are and technology including thermal management within integrated capable of locally refrigerating physiological buffers (PBS, microelectronics (4–6), photonic (7, 8) and microfluidic (9) cir- DMEM) upon near-infrared illumination. Optical tweezers are cuits, and the regulation of metabolic processes (9–11). In 1929, used in tandem with cold Brownian motion analysis to observe + Pringsheim (12) proposed that solid-state materials could experi- the refrigeration of individual (Yb3 )-doped nanocrystals >10 °C ence refrigeration if they exhibited biased emission of anti-Stokes below ambient conditions. The ability to optically generate (blue-shifted) radiation relative to a fixed optical excitation wave- local refrigeration fields around individual nanocrystals prom- length. Epstein et al. (13) experimentally demonstrated this concept ises to enable precise optical temperature control within in- first in 1995 using rare-earth–doped fluoride glass materials. Optical tegrated electronic/photonic/microfluidic circuits, and also refrigeration of a condensed phase with a rhodamine dye by anti- thermal modulation of basic biomolecular processes, including Stokes radiation has previously been reported (14–16) but the the dynamics of motor proteins. results remain controversial (17, 18). More recently, it has been + shown that rare-earth–doped yttrium (Yb3 : Author contributions: P.J.P. designed research; P.B.R., B.E.S., X.Z., and M.J.C. performed research; P.B.R., X.Z., and P.J.P. contributed new reagents/analytic tools; P.B.R., B.E.S., YLF) crystals grown in high-temperature Czochralski reactors X.Z., M.J.C., and P.J.P. analyzed data; and P.B.R., B.E.S., X.Z., and P.J.P. wrote the paper. ∼ (19) can be cooled to cryogenic temperatures ( 90 K) (20) in The authors declare no conflict of interest. vacuo using continuous-wave near-infrared (NIR) laser excita- This article is a PNAS Direct Submission. Q.X. is a guest editor invited by the Editorial tion. Furthermore, the laser refrigeration of doped yttrium alu- Board. 3+ minum garnet (Yb :YAG) materials has recently been reported in 1P.B.R., B.E.S., and X.Z. contributed equally to this work. air at atmospheric pressure (21). Anti-Stokes photoluminescence 2To whom correspondence should be addressed. Email: [email protected]. has also been reported (22) to cool cadmium sulfide (CdS) nano- This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. ribbons in vacuo by as much as 40 °C below room temperature. In 1073/pnas.1510418112/-/DCSupplemental.

15024–15029 | PNAS | December 8, 2015 | vol. 112 | no. 49 www.pnas.org/cgi/doi/10.1073/pnas.1510418112 Downloaded by guest on September 28, 2021 Fig. 1. Synthesis and characterization of YLF crystals. (A) Schematic of Scheelite crystal structure of YLF with I41/a space group symmetry. (B) SEM image of 3+ 3+ a faceted (Yb )0.1(Y )0.9 LiF4 particle exhibiting TTB morphology. (Scale bar, 1 μm.) (C) Powder XRD pattern of YLF crystals following hydrothermal synthesis indicating a pure Scheelite crystal phase. (Inset) Schematic of TTB morphology relative to YLF’s unit cell. (D) Bright-field TEM image of an in- + dividual Yb3 :YLF grain. (Scale bar, 200 nm.) (Inset) High-resolution TEM image taken from the indicated region. (Scale bar, 2 nm.) (E) HAADF image of the YLF grain in B showing regions of high contrast suggesting the presence of polycrystalline domains. (Inset) SAED from the indicated region. (F)X-ray fluorescence compositional-analysis spectrum of an individual YLF crystal taken within the TEM confirming the elemental crystalline composition in- cludingY,Yb,andFspecies. SCIENCES APPLIED PHYSICAL

air- and moisture-free Czochralski process (30). In the experi- to pump the E4–E5 resonance and subsequently cannot initiate ments reported here, a low-cost modified hydrothermal synthesis upconversion-mediated cooling (Fig. 3B). + (31) of Yb3 :YLF is used to prepare crystals shown in Fig. 1. The CBM analysis discussed above is limited to reporting local Scanning electron microscopy (SEM) reveals that YLF crystals solvent temperatures, but it does not provide information on the exhibit a truncated tetragonal bipyramidal (TTB) morphology (Fig. internal lattice temperature of optically trapped YLF nanocrystals. + 1B). X-ray diffraction shows that the YLF crystal has a Scheelite It is well known that codoping YLF crystals with both Yb3 and + structure (Fig. 1C). Bright-field/high-angle annular-dark-field Er3 ions leads to a thermalized Boltzmann distribution between 2 4 3+ (HAADF) transmission electron microscope (TEM) imaging (Fig. the E2 ( H11/2) and E1 ( S3/2) manifolds of Er and an intense 1 D and E) and electron diffraction suggest that the TTB materials green upconversion emission that is visible to the unaided eye are polycrystalline and likely form through an oriented attachment (showninFig.4A). This upconversion process is enabled by the (32) process of nanocrystalline grains (Fig. 1E, Inset). long (ms) photoluminescence lifetimes from the rare-earth point A home-built laser trapping instrument (shown in Fig. 2) was defects (35). It has also been shown that this upconverted + + used to observe the Brownian dynamics of individual Yb3 :YLF photoluminescence from Er3 mayalsobeusedtoinfertem- nanocrystals. The laser trap setup is outlined in Materials and perature changes through ratiometric thermometry by analysis Methods, and the CBM temperature analysis is described in SI of the photoluminescence emission from different Boltzmann Appendix, section A. Briefly, the single-beam laser trap was used thermal populations (36) given by the equation to extract the surrounding local temperature profile of YLF parti-   cles through observations of forward-scattered laser radiation pro- I −ðE − E Þ 2 ∝ exp 2 1 . [1] files that are processed to yield both the calibrated power spectral I1 kbT density and diffusion coefficient for individual YLF crystals (33). 3+ 3+ The laser refrigeration of 10% (mol%) Yb :YLF (i.e., 10% Yb In brief, changes in the ratio of the integrated emission bands I2 3+ ions, 90% Y ions) nanocrystals by more than 10 °C in PBS and and I1 that stem from transitions between energy states E2 and ’ Dulbecco s modified Eagle medium (DMEM) was observed at a E1, respectively, and a common ground state are directly corre- trapping wavelength of λ = 1,020 nm (Table 1). To minimize fluid lated to a change in the particle’s temperature. Furthermore, it heating at control NIR trapping wavelengths (λ = 975 nm and has been recently reported that strong visible upconversion in 1,064 nm), experiments discussed below were performed in D2O, rare-earth codoped nanocrystals can be used for efficient biological unless explicitly stated otherwise, due to its low absorption com- imaging and labeling (37). pared with H2O(34). Photoluminescence spectroscopy of optically trapped YLF A bright-field micrograph for a characteristic optically trapped nanocrystals provides a unique capability of observing particle- + Yb3 :YLF crystal is shown in Fig. 3A. The dependence of laser to-particle variability within an ensemble (38). For the codoped + + refrigeration on the trapping laser’s pump wavelength is shown 2%Er3 , 10%Yb3 :YLF particles reported, substantial fluctu- + in Fig. 3C, where YLF crystals doped with 10% Yb3 are ob- ations in upconversion photoluminescence were observed, indi- served to cool from 19 °C at a 5.9-MW/cm2 trapping irradiance to cating that ensemble calibrations are inapplicable to quantitative 4 °C at a 25.5-MW/cm2 trapping irradiance when trapped with ratiometric temperature measurements of individual nanocrys- λ = 1,020 nm, which is resonant with ytterbium’sE4–E5 transi- tals (SI Appendix, section B). However, ratiometric thermometry + tion shown in Fig. 3B. The same Yb3 :YLF crystals are shown to can still be used during laser trapping experiments to make heat from 40 °C to 47 °C when trapped at the same respective qualitative observations of temperature changes as the trapping irradiances with λ = 1,064 nm, which is energetically insufficient irradiance is increased, as shown in Fig. 4 B and C.The

Roder et al. PNAS | December 8, 2015 | vol. 112 | no. 49 | 15025 Downloaded by guest on September 28, 2021 Fig. 2. Schematic of laser trapping instrument. An optically trapped YLF crystal in an aqueous fluid chamber. A piezostage driven at 32 Hz produces a peak in

the quadrant photodiode (QPD) power spectrum which is used to extract a calibrated diffusion constant. The particle’s temperature (Tp) and local tem- perature profile is then extracted using CBM analysis.

decrease (increase) in the logarithmic ratio of I2 to I1 (Fig. 4 B discontinuity at the particle’s surface from the Kapitza resistance and C) with increasing irradiance reflects a decrease (increase) (44)], which is given by (45) in the internal lattice temperature (39), which agrees well with R À Á the observed temperature changes measured via laser trapping light TðrÞ = T + T − T , [2] scattering temperature analysis (Fig. 4D). Specifically, laser trapping 0 r p 0 + analysis of the particles’ CBM indicates that codoped 2%Er3 , + 3 Δ = − ± where T0 is the bath temperature of the medium. Given that the 10%Yb :YLF undergoes laser refrigeration ( T 4.9 2.8 °C) 3+ λ = Δ = ± average radius of the Yb :YLF particles trapped at λ = 1,020 nm when trapped at 1,020 nm and heating ( T 21.8 10.11 °C) = ± = = when trapped at λ = 975 nm. Furthermore, it has been proposed in Fig. 3C is Ravg 764 293 nm, T0 25 °C, and Tp,avg 3.4 °C at 25.5-MW/cm2 irradiance, the distance away from the particle recently that codoping YLF crystals with other upconverting rare- where the temperature increases to within 1% of T is 6.9 μm earth ions can enhance cooling through energy transfer enhanced 0 (Fig. 2). However, this treatment assumes that the local temper- cooling (40). ature profile around the cold particle behaves according to Eq. 2. These results illustrate the potential of using singly- and Furthermore, it is also conceivable that the region around the codoped YLF nanocrystals as a platform for precision circuit cold particle is surrounded by a hot corona that slowly diminishes cooling, physiological refrigeration, biological imaging, and in situ to the base temperature of the solvent. ratiometric thermometry. Potential applications for these mate- In the future it can be envisioned that the refrigeration of rials include precision temperature control in integrated electronic particle ensembles and local mapping of the surrounding solvent – (4 6), photonic (7, 8), and microfluidic (9) circuits, as well as temperature profile can be achieved through the generation of – triggering and probing fundamental metabolic processes (9 11). multiple laser traps, via either holographic phase masks (46) or In particular, the ability to measure and to modulate temper- galvo-steering mirrors (47), to bring a temperature-sensing par- ature could enable the investigation of the kinetics and tem- ticle into close proximity to a cooling YLF particle. Future perature sensitivity of cellular processes, including ion channel synthetic efforts with YLF host crystals will be directed at con- actuation (41), conformational folding dynamics of RNA (42), trolling the grain size and morphology in pursuit of morphology- and dynamic stepping motion of molecular myosin (V) motor dependent cavity resonances (48) that can increase the optical proteins (43). Analyzing the CBM of a nanocrystal dispersed in a liquid 3+ phase to measure the nanocrystal’s temperature also provides Table 1. Local cooling of Yb -doped YLF crystals in various 2 = the unique capability to predict the local temperature gradient in media at an irradiance of 25.5 MW/cm , where T0 25 °C

the medium surrounding the trapped nanocrystal. Because the Solvent ΔT = (Tp − T0), °C ΔTSD,°C aspect ratio of the truncated tetragonal bipyramid morphology − encountered for YLF crystals is near unity, we approximate the D2O 15.0 4.1 − radius R of the particles using an equivalent-sphere model and DI water 14.7 3.8 − can extract the local temperature field a distance r from the PBS 14.9 4.3 DMEM −11.2 6.3 particles’ surface [at temperature Tp, excluding the temperature

15026 | www.pnas.org/cgi/doi/10.1073/pnas.1510418112 Roder et al. Downloaded by guest on September 28, 2021 SEM Characterization. Secondary electron images were taken on an FEI Sirion at an accelerating voltage of 5 keV.

XRD Characterization. Powder X-ray diffraction (XRD) patterns are obtained on a Bruker F8 Focus Powder XRD with Cu K (40-kV, 40-mA) irradiation (λ = 0.154 nm). The 2θ angle of the XRD spectra is from 10° to 70° and the scanning rate is 0.01° s−1. The one minor unlabeled peak in the XRD spectra at 2θ = 44.9° is attributed to a small amount of unreacted LiF precursor [(200) peak].

Laser Trapping Description. The laser tweezer setup is a modified modular optical tweezer kit (Thorlabs, OTKB), where the original condenser lens has been replaced with a 10× Mitutoyo condenser (Plan Apo infinity-corrected long WD objective, stock no. 46–144). The 100× objective focusing lens has a numerical aperture of 1.25 and a focal spot of 1.1 μm. The quadrant pho- todiode (QPD) and piezostage were interfaced to the computer through a DAQ card (PCIe-6361 X series, National Instruments) and controlled through modified MATLAB software (Thorlabs). Experimental chambers were prepared as follows. Several microliters of the nanocrystal/aqueous medium dispersion were transferred by a pipette into a chamber consisting of a glass slide and glass coverslip. The edges of the glass slide and the glass coverslip were then sealed with a 150-μm-thick adhesive spacer (SecureSeal Imaging Spacer, Grace Bio-laboratories). Nanocrystals were trapped at the center (∼75 μmfromthe surface) of the temperature-controlled perfusion chamber (RC-31, Warner In-

struments) and held at T0 = 25 °C while voltage traces were recorded at the QPD for 3 s at a sample rate of 100 kHz. The QPD voltage signal was calibrated by oscillating the piezostage at 32 Hz and an amplitude of 150 nm peak-to- peak during signal acquisition, as outlined in ref. 49. Trapping data were ac- 3+ Fig. 3. Laser refrigeration of optically trapped YLF microcrystals. (A) Optical quired using a diode-pumped solid-state Yb :YAG thin-disk tunable laser micrograph of an optically trapped YLF crystal. (Scale bar, 3 μm.) (B) Crystal- (VersaDisk 1030–10, Sahajanand Laser Technologies) at a wavelength of 1,020 + SCIENCES field energy level configuration of Yb3 dopant ions and used cooling nm, a 975-nm pigtailed fiber Bragg grating stabilized single-mode +

3 APPLIED PHYSICAL scheme. (C) Extracted temperature (Tp) of optically trapped particles in D2O (PL980P330J, Thorlabs), as well as a solid-state Nd :YAG 1,064-nm (BL-106C, + as determined using the outlined CBM analysis. Yb3 -doped YLF particles are Spectra-Physics) at an irradiance of 5.9, 10.7, 14.6, 21.2, and 25.5 MW/cm2.Each shown to cool when trapping wavelength is resonant with the E4–E5 tran- YLF cooling data point in Fig. 3C in the article represents an average of six sition (λ = 1,020 nm) but heat when the trapping wavelength is below the individual particles with an average radius of 764 nm with an SD of 293 nm. transition (λ = 1,064 nm). Magnitudes of cold Brownian temperature changes presented in Table 1 were determined using methods outlined in ref. 33. Silica beads (SS04N/9857, Bangs Laboratories) were used for their monodisperse size distribution (1,010-nm 3+ diameter), and they have shown to minimally heat when trapped with a laser absorption of Yb and reduce the irradiance required to ob- tweezer at NIR wavelengths (50). Electromagnetic simulations of the in- serve the laser refrigeration of physiological media. Furthermore, teraction of the trapping laser with an YLF TTB were also performed to predict the low-cost hydrothermal approach reported here could be used the stable trapping configurations of optically trapped YLF particles, detailed to synthesize novel phases for host crystals (such as β-NaYF4) that cannot be grown through single-crystal Czochralski methods. Materials and Methods YLF Synthesis. The following synthesis was performed following modifications

to Lu et al. (31). Yttrium oxide (Y2O3), ytterbium oxide (Yb2O3), and erbium oxide (Er2O3) are of 99.99% purity and used as purchased from Sigma-Aldrich. Yttrium nitrate (Y(NO3)3), ytterbium nitrate (Yb(NO3)3), and erbium ni- trate (Er(NO3)3) are obtained by dissolving the oxide in concentrated nitric acid at 60 °C while stirring for several hours until excess nitric acid is removed. The residual solid is then dissolved in Millipore deionized (DI) water to achieve a stock concentration of the respective nitrate. Lithium fluoride (LiF), nitric acid

(HNO3), ammonium bifluoride (NH4HF2), and EDTA are analytical grade and used directly in the synthesis without any purification. The following prepa- 3+ 3+ ration uses the synthesis of 2%Er ,10%Yb :LiYF4 as an example. For this synthesis, 7.04 mL of 0.5M Y(NO3)3, 0.8 mL of 0.5M Yb(NO3)3, and 0.16 mL of 0.5M Er(NO3)3 are mixed with 1.17g EDTA in 5 mL Millipore DI water at 80 °C while stirring for 1h. This is solution A. Subsequently, 0.21g of LiF and 0.68g of

NH4HF2 are dissolved in 7 mL Millipore DI water at 70 °C while stirring for 1h to form solution B. Solutions A and B are mixed together while stirring for 20 min to form a homogeneous white suspension which is then transferred to a 23-mL Teflon-lined autoclave and heated to 220 °C for 72 h. After the autoclave cools Fig. 4. Upconversion and ratiometric thermometry of codoped YLF. (A) Bright- 3+ 3+ 3+ 3+ to room temperature, the 2%Er ,10%Yb :LiYF4 particles can be recovered by field optical micrograph showing a codoped 2%Er ,10%Yb :YLF particle in centrifuging and washing with ethanol and Millipore DI water three times. Brownian motion (Top Left) and a dark-field optical micrograph of the crystal The final white powder is obtained by calcining at 300 °C for 2 h. Using the when trapped with λ = 1,020 nm (Bottom Left). (Scale bar, 4 μm.) Upconverted 3+ same method, 10%Yb :LiYF4 particles are achieved. photoluminescence can be seen with the unaided eye (Right). (B)Photo- luminescence spectra of the corresponding dark-field image showing the in- 3+ TEM Characterization. Bright-field and scanning TEM HAADF images were tegration regions I2 and I1, representing emission from Er energy states E2 2 4 4 taken on an FEI Tecnai G2 F20 at an accelerating voltage of 200 keV. Select ( H11/2)andE1 ( S3/2) to the ground state Eground ( I15/2), respectively. area electron diffraction (SAED) images were taken with a camera length of (C) Natural logarithm of the ratio I2/I1 showing a linear increase (Top)with 490 mm. Energy-dispersive X-ray spectroscopy spectra were obtained with a 60-s laser irradiance at λ = 975 nm and a linear decrease (Bottom) with laser ir- acquisition time. The spectra were then processed by subtracting the back- radiance at λ = 1,020 nm. (D) Laser refrigeration of the codoped YLF crystal ground and smoothing the peaks. analyzed in C measured via CBM analysis at an irradiance of 25.5 MW/cm2.

Roder et al. PNAS | December 8, 2015 | vol. 112 | no. 49 | 15027 Downloaded by guest on September 28, 2021 3+ in SI Appendix, section E. Lastly, visible emission of Er from Er/Yb codoped temperature Tp [excluding the temperature discontinuity at the particle’s trapped YLF host crystals was detected using an Acton SpectraPro 500i spec- surface from the Kapitza resistance (44)]. An alternative CBM temperature analysis

trograph with a Princeton liquid-nitrogen-cooled Si detector. using a semiphenomenological expression for DCBM that approximately accounts for higher-order terms in ΔT (equation 15 of the supporting online materials of CBM Temperature. Power spectra from the QPD voltage traces were processed Chakraborty et al. (25)] yields consistent results, indicating that these higher-order according to Berg-Sorensen and Flyvbjerg (51) and used to calibrate the QPD corrections are negligible, for our purposes. For the experiments reported here, the traces following the method of Tolic-Norrelykke et al. (49). An experimental VFT viscosity parameters were fit to experimental data and are as follows: diffusion coefficient was then extracted by fitting the characteristic function for the experimental power spectra derived in Berg-Sorensen and Flyvbjerg D2O (51). Given that the temperature of the trapped particle is significantly −5 different from the temperature sufficiently far from the laser focus, the η∞ = 3.456 · 10 Pa · s particle–trap system is not isothermal and behaves according to non- equilibrium dynamics. Thus, equating the experimental diffusion coefficient A = 478.6 K to nonisothermal Brownian dynamics necessitates the application of CBM, as = derived by Chakraborty et al. (25). The CBM diffusion coefficient is then TVFT 160 K, related to the CBM temperature by and k T = b CBM DCBM γ ð Þ, [3] DI water, PBS, DMEM CBM T η = · −5 · where DCBM is the CBM diffusion coefficient, kb is Boltzmann’s constant, TCBM ∞ 2.664 10 Pa s γ ð Þ is the CBM temperature, and CBM T is the CBM Stokes drag. To the leading A = 536.5 K order of the temperature increment or decrement ΔT = (Tp − T0), the tem- perature dependence of the viscosity on T can be neglected, giving the CBM = effective temperature (25) TVFT 145.5 K.

5 VFT viscosity parameters for DI water, PBS (0.01M, pH 7.4; Sigma P5368), and T = T + ΔT. [4] × – CBM 0 12 DMEM (1 , high glucose, pyruvate; Life Technologies cat. no. 11995 065) were assumed to be equivalent because it has been reported that water To account for the solvent viscosity temperature dependence, we follow the viscosity can be used for purposes of modeling particle transport in non–serum- methods of ref. 52 and use the Vogel–Fulcher–Tammann–Hesse (VFT) law containing media (53). with the viscosity functional form ηðTÞ = η∞exp½A=ðT − TVFT Þ. The CBM Stokes drag is given by ACKNOWLEDGMENTS. The authors thank Klaus Kroy of Leipzig University for discussion of CBM analysis, John W. Cahn for discussion of YLF crystallog- γ ð Þ = π η ð Þ CBM T 6 R CBM T , [5] raphy, and E. James Davis for manuscript comments and providing an optical spectrometer with LN -cooled detector. This research was made possible by a η ð Þ 2 where R is the particle radius, and CBM T is the temperature-dependent grant from the Air Force Office of Scientific Research Young Investigator Pro- CBM viscosity that is related to the viscosity of the solvent at room tem- gram (Contract FA95501210400), start-up funding from the University of η perature, 0,by Washington, as well as a capital equipment donation from the Lawrence Liver-     more National Laboratory. P.B.R. thanks the National Science Foundation for a η 193 η ΔT Graduate Research Fellowship under Grant DGE-1256082. M.J.C. was sup- 0 ≈ 1 + ln 0 η ðTÞ 486 η∞ ðT − T Þ ported by the Department of Defense through the National Defense Science CBM    0 VFT    2 and Engineering Graduate Fellowship Program. P.J.P. gratefully acknowledges 56 η 12,563 η ΔT ’ − ln 0 − ln2 0 . [6] support from both the US Department of Energy s Pacific Northwest National 243 η∞ 118,098 η∞ ðT0 − TVFT Þ Laboratory (PNNL) and the Materials Synthesis and Simulation Across Scales (MS3) Initiative, a Laboratory Directed Research and Development (LDRD) Eqs. 4–6 are then used in Eq. 3 to obtain DCBM, which is subsequently com- program at the PNNL. The PNNL is operated by Battelle under Contract DE- pared with the experimental diffusion coefficient to determine the particle AC05-76RL01830.

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