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A: Kinetics, Dynamics, Photochemistry, and Excited States

Phase-Transition Temperature of Gold NanorodCoated Nanodroplets to Microbubbles by Pulsed Laser Zhe Zhang, Madison Taylor, Necati Kaval, and Yoonjee C Park J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.9b02566 • Publication Date (Web): 22 May 2019 Downloaded from http://pubs.acs.org on May 30, 2019

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The Journal of Physical Chemistry

Phase-Transition Temperature of Gold Nanorod-Coated Nanodroplets to Microbubbles by Pulsed Laser Zhe Zhang1, Madison Taylor1, Necati Kaval2, Yoonjee C. Park1* 1Department

of Chemical & Environmental Engineering, 2Department of Chemistry, University of Cincinnati, Cincinnati, OH, USA *Corresponding Author: [email protected]

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Abstract Previously, gold nanorod-coated perfluorocarbon nanodroplets have been developed as lightactivated on-demand drug delivery carriers. When gold nanorods on the perfluorocarbon nanodroplets resonate with a laser wavelength, plasmonic heat is generated and vaporizes the nanodroplets to gas bubbles. Optimal laser parameters such as pulse duration, pulse repetition frequency and average power, are critical to effectively trigger the phase-transition of nanodroplets and allow for drug release. This study focused on determining temperature of a gold nanorod-coated perfluorocarbon nanodroplet during phase-transition to a gas bubble using a femtosecond laser. Two integrated experimental and theoretical methods were explored. First, the theoretical temperature was determined by Arrhenius equation and the time it took for the phase-transition to occur, assuming the phase-transition process followed a first-order kinetic model. The activation energy and Arrhenius constant of the phase-transition process were obtained via light transmittance through a nanodroplet suspension at different temperatures. The time required for phase-transition by a femtosecond laser was measured using an optical microscope. The second approach used a classical heat diffusion model. When pulse peak energy was considered in the model, the temperature predicted matched experimental observation of phase-transition temperature threshold while the total energy value failed to predict the temperature threshold. The results suggest the phase-transition mechanism is triggered by the vaporization of the nanodroplets via photothermal heating, which is influenced by the peak energy of laser. It also indicates that optimal laser parameters can be determined by a simple calculation using the classical heat diffusion model and peak energy to control phase-transition.

1. Introduction When a pulsed laser irradiates plasmonic materials, typically noble metals in nanostructure, significantly more heat is generated via plasmonic surface resonance, than when compared to continuous wave (CW) laser 1-2. This phenomenon has been utilized for photothermal therapy to kill specific cells 3-7, or on-demand drug delivery when combined with a drug carrier 4, 7-16. However, most studies determine laser specification based on trial and error methods. In other words, laser parameters, including CW versus pulsed laser, average power, pulse repetition frequency, and pulse duration, have been selected empirically without appropriate models to predict plasmonic heat for their own applications. Theoretical models have been developed to predict the optical heating of gold nanoparticles by pulsed lasers 1, 17-21. Several studies have focused on integrating theoretical models and experiments to investigate the plasmonic heating phenomenon. For example, Hu and Hartland demonstrated energy dissipation of a gold nanoparticle heated by a femtosecond laser by applying a heat transfer model and experimental data measured by pump-probe spectroscopy 2223. However, no study has shown integrated experimental and theoretical methods to calculate laser parameters required for effective trigger of light-activated drug delivery systems. In this


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study, we have developed a method to predict the temperature at the moment of light-activation and to calculate optimal laser parameters. We previously developed gold nanorod-coated perfluorocarbon nanodroplets as a light activated drug delivery system 24. We demonstrated drug release upon pulsed laser irradiation in a precise controlled manner. Pulsed laser causes heat generation from the gold nanorods on the nanodroplet shell and the heat vaporizes the droplet to release the drug from the inside of the droplet (Figure 1). In this study, we performed integrated experimental and theoretical approach to predict the temperature when the vaporization (phase-transition) occurs, in order to fill the gap in knowledge of understanding plasmonic heat required for light activation.

Figure 1. Schematics of phase-transition of a gold nanorod-coated nanodroplet to a micron-sized bubble by pulsed laser, and phase-transition temperature (Tph) of the nanodroplet caused by initial surface temperature of gold nanorod (Ts0).

This study includes two theoretical models to predict the phase-transition temperature. First, a kinetic model was applied to obtain the activation energy and Arrhenius constant for phasetransition based on experimental kinetic data. Second, a classical heat transfer model was used to consider peak energy of the laser, as opposed to average energy, and distance from the gold nanorod to perfluorocarbon nanodroplet surface. Relationships between the phase-transition temperature heated by multiple pulses and pulsed laser parameters were established using a classical heat diffusion model. Finally, we will be able to control the phase-transition with better understanding of the energy required and how heat affects the system. The model can potentially suggest a general solution for determining the necessary parameters for light-activated systems.



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2. Methods 2.1. Gold nanorod-coated nanodroplets The nanodroplets were synthesized using a double emulsion method as described in our previous paper 24. Briefly, the first emulsion was dispersed in liquid perfluoropentane (PF5) or perfluorohexane (PF6) (1.55 mL) (Synquest Laboratories, Alachua, FL, USA) with Krytox (150 uL) (DuPont, USA) as polymer surfactant via probe sonication (Vibra Cell 400, Sonics, Newtown, CT, USA) at amplitude of 20%, 3 min with 10 s on and 20 s pause in an ice bath. The second emulsion was then created by adding liposomes (160 μL at 5.62 μmol/mL) in DI water (1.76 mL) to the first emulsion (80 μL) and probe sonicating in an ice bath in the same manner. The liposome components consisted of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) (Avanti Polar Lipids, Inc., Alabaster, AL, USA), and 1,2-distearoyl-sn-glycero-3phosphoethanolamine-N-[methoxy(polyethylene glycol)-5000] (DSPE-PEG 5K) (Nanocs, Boston, MA, USA), and stearlyamine at 50:15:35 mole ratio. The second emulsion was centrifuged at 6000 rpm (4000 g-force) for 3 min and gold nanorod dispersion (Nanopartz Inc. Loveland, CO) (880 μL) was added to the nanodroplet sediment. The resulting emulsion was then washed three times by centrifugation at 3225 rpm. The gold nanorods used were 10 nm in diameter and 59 nm in length with a concentration of 4.19E+11 per mL according to the manufacturer’s specification data. 2.2 Theoretical Boiling Point of Nanodroplets Determined by Antoine Equation Interfacial Tension Measurement In order to estimate boiling point of our nanodroplets, the Antoine equation was used as mentioned in Sheeran et al. 25. 𝐵

𝑇𝑝ℎ = 𝐴 ― 𝑙𝑜𝑔10𝑃 ―𝐶

(1)

In Equation (1), constant A, B and C for PF5 and PF6 can be found in NIST Chemistry Webbook 26. Pressure, P, is calculated by 𝑃 = 𝑃𝑎𝑡𝑚 +∆𝑃

(2)

2

where Patm is standard atmospheric pressure and ∆𝑃 = 𝛾𝑅. To determine ∆𝑃, we measured interfacial tension 𝛾 using the pendant drop method (KRUSS SC02). A tip of the syringe needle (diameter 1.074 mm) containing the first emulsion was carefully merged into 30 mL of liposome aqueous dispersion in a cuvette (inner dimensions 36 × 36 × 30 mm). Then, a droplet was created in a speed of 0.005 mL/min in the aqueous liposome dispersion at room temperature at atmosphere pressure. The volume of the droplet was 0.5 µL. The nanodroplet size R was measured optically as described in our previous study 24. 2.3. Phase-transition kinetic models An integrated model combining kinetics of droplet disappearance, bubble formation and bubble displacement/disappearance was created. A similar approach is also found in 27. The concentration of nanodroplets (𝐶𝐷) is assumed to follow the first-order rate equation.


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𝑑𝐶𝐷 𝑑𝑡

(3)

= ― 𝑘1𝐶𝐷

where 𝑘1is the rate constant of droplet disappearance (𝑠 ―1). For the concentration of microbubbles (C𝐵), 𝑑𝐶𝐵 𝑑𝑡

𝑣

(4)

= 𝑘1𝐶𝐷 ― 𝑘2𝐶𝐵 ― ℎ ∗ 𝐶𝐵

where 𝑘2 is the rate constant of bubble dissolution by gas diffusion across the shell (𝑠 ―1), 𝑣 is the vertical velocity of microbubbles (cm 𝑠 ―1), 𝑡 is time (s) and ℎ is the distance travelled (cm). However, the last term of bubble displacement was neglected because a small stir bar used interrupted flotation process, resulting in 𝑑𝐶𝐵 𝑑𝑡

= 𝑘1𝐶𝐷 ― 𝑘2𝐶𝐵

(5)

Eqs. (3) and (5) becomes Eqs. (6) and (7), respectively. 𝐶𝐷 = 𝐶𝐷0𝑒 ― 𝑘1𝑡 𝑘1

𝐶𝐵 = 𝐶𝐷0𝑘2 ― 𝑘1(𝑒 ― 𝑘1𝑡 ― 𝑒 ― 𝑘2𝑡)

(6) (7)

where 𝐶𝐷0 is the initial droplet concentration. 2.4. Light transmittance measurement for phase-transition kinetic models Light transmittance was measured to determine concentrations of nanodroplets and microbubbles following Eq. (8). 𝐼 𝐼𝑚𝑎𝑥

= 𝑒 ―𝑙𝛼𝑒𝑓𝑓

(8)

where 𝐼 is the light intensity % measured by a photodetector, 𝐼𝑚𝑎𝑥 was assumed to be 100%, 𝑙 is the path length (1 cm), and 𝛼𝑒𝑓𝑓 is the effective light attenuation coefficient contributed from both nanodroplets and microbubbles: (9)

𝛼𝑒𝑓𝑓 = 𝛼𝐵 + 𝛼𝐷 = 𝜎𝐵𝐶𝐵 + 𝜎𝐷𝐶𝐷 𝛼𝐵 = 𝜎𝐵𝐶𝐵(𝑡)

(10)

𝛼𝐷 = 𝜎𝐷𝐶𝐷(𝑡)

(11)

𝜎𝐵(𝑐𝑚2 𝑏𝑢𝑏𝑏𝑙𝑒 ―1) and 𝜎𝐷 are the extinction cross-section of microbubbles and nanodroplets, respectively, The values of 𝜎𝐵 and 𝜎𝐷 were determined experimentally as described in Supporting Information (Figure S1). Combining Eqs. 6 - 11 yields 𝐼 𝐼𝑚𝑎𝑥

𝑘1

= 𝑒𝑥𝑝( ― 𝑙 ∗ (𝜎𝐵𝐶𝐷0𝑘2 ― 𝑘1(𝑒 ― 𝑘1𝑡 ― 𝑒 ― 𝑘2𝑡) + 𝜎𝐷𝐶𝐷0𝑒 ― 𝑘1𝑡))


(12)


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Then, we used Mathematica (Wolfram Research) to fit I/Imax versus t to obtain rate constants k1 and k2. For experimental measurement, the gold nanorod-coated nanodroplet dispersion (2 mL) was loaded into a glass cuvette and the percentage transmittance was measured using Cary 50 Bio UV-Vis Spectrophotometer for 750 s and temperature was controlled by Cary Single Cell Peltier Accessory (Figure 2A). The measurements were performed at 40, 60, 80 and 95 ⁰C. Temperature was pre-set and constant throughout each measurement. Temperature drop when the sample was inserted was observed, which gradually increased back to the set temperature within 100 s. Changes in light transmittance upon phase-transition were expected because nanodroplets and bubbles have different light attenuation coefficients.

Figure 2 (A) UV-Vis spectrophotometer with temperature control accessory. (B) Schematic of light transmittance test.

2.5 Analysis of Phase-Transition Kinetics using Arrhenius Equation After the determination of kinetic constants 𝑘1 and 𝑘2, the Arrhenius Equation was applied to calculate activation energy 𝐸𝑎 and pre-exponential factor A so that the temperature T of phase transitioned nanodroplets could be determined. To accomplish this, we used both regular plotting method and analytical method. For plotting method, we derived from Arrhenius Equation 𝑘1 = 𝐴𝑒 ―𝐸𝑎/𝑅𝑇

(13)

1

to get linear equation of 𝑙𝑛𝑘1vs. 𝑇 𝑙𝑛𝑘1 = 𝑙𝑛𝐴 ― and the slope is ―

𝐸𝑎 𝑅

𝐸𝑎 𝑅

1

∗𝑇

with intercept 𝑙𝑛𝐴.


(14)

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Values for 𝐸𝑎 and A were also obtained by plugging in different 𝑘1 values at different 𝑇 and solving a series of equations simultaneously. Notice that kinetic constant 𝑘1 depends on temperature, so for each temperature, there exists only one corresponding 𝑘1, and 𝑘1 at that very moment of phase transition can be calculated by equation (6). 𝐶𝐷 = 𝐶𝐷0𝑒 ― 𝑘1𝑡 or 𝐶𝐷/𝐶𝐷0 = 𝑒 ― 𝑘1𝑡

(15)

𝐶𝐷/𝐶𝐷0 can be interpreted as the ratio of nanodroplets that phase-transitioned, and the time 𝑡 can be approximately measured experimentally. With the value of 𝑘1 plugged in Arrhenius equation along with the 𝐸𝑎 and A values obtained previously, we could get the temperature of the very moment of phase transition. The modified version of Arrhenius Equation 28, which is also the more generalized version, was also adopted to calculate plasmonic photothermal phase-transition temperature using activation energy 𝐸𝑎, a stretched exponential term n, along with the pre-exponential factor A of the phasetransition process. 𝑘 = 𝐴𝑇𝑛𝑒 ―𝐸𝑎/𝑅𝑇

(16)

𝐸𝑎, 𝐴, 𝑎𝑛𝑑 𝑛 values were determined by satisfying several criteria and assumptions: (1) It was assumed that the differences of n and A values between PF5 and PF6 are negligible since we have controlled the number of nanodroplets for PF5 and PF6 to be comparable, (2) By plotting 𝑘1 as a function of T, the curve needs to be as close to the curve determined experimentally as possible while maintaining the same trend, (3) A root for the temperature can be found by plugging in the determined n, 𝐸𝑎 and A values using “solver” function in excel. 2.6 Phase-transition by laser and time measurement A concentrated nanodroplet suspension (10 µL) was transferred on a glass slide and then a drop of glycerol was added to immobilize the nanodroplets. This sample was observed at 10x and 40x magnifications using a Zeiss Axioverrt 200 inverted microscope, while it was being irradiated by a Mai Tai femtosecond laser (Spectra Physics) at 80 MHz and 100 fs (Figure 3). The laser wavelength was set at 800 nm and the power varied from 50% to 100%. The region of interest was selected as small as possible in order to decrease the time of scan but large enough to observe the whole phase transition process of a group of nanodroplets. The image and time of

ACS Paragon Plus Environment Figure 3. Schematics of femtosecond pulsed laser scanning with a microscope and image acquisition set up.


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phase-transition process were recorded. The time, t, was used to calculate the rate constant 𝑘1 of phase-transition in Eq. 14 in the previous section.

2.7. Theoretical phase transition temperature predicted by laser peak intensity and heat diffusion model The phase-transition temperature was predicted based on the laser intensity used and a classical heat diffusion model. Gold nanorods irradiated by pulsed laser act as a heat source that release the high energy to the adjacent nanodroplet and surrounding medium. We assumed the heat diffusion is a point thermal explosion similar to several studies reported 1, 22. Heat transfer occurs from the point to an infinite medium in unsteady state because a large amount of peak pulse energy within a very short time period (100 femtoseconds) was absorbed by the gold nanorod and released within a very short period of time (a nanosecond 1). The temperature profile with respect to distance from the point (r) and time (t) is 1∂

( ) ∂𝑇

∂𝑇

𝛼𝑟2∂𝑟 𝑟2 ∂𝑟 = ∂𝑡

(17)

The analytical solution is 𝜀0

𝑇(𝑟,𝑡) =

𝑒𝑥𝑝

3

(4𝜋𝛼𝑡)

2

𝜌𝐶𝑝

― 𝑟2

( )

(18)

4𝛼𝑡

where 𝜀0 is the energy absorbed at the origin, 𝜌 is the density of the medium, 𝛼 is thermal diffusivity of the medium, and 𝐶𝑝 is the specific heat of the medium 1. The physical property values of PF5 and PF6 used in calculations are listed in Table 1.

Table 1. Physical constants used in the study for perfluoropentane (PF5) a, perfluorohaxane (PF6) b, gold and water

Thermal Conductivity, κ (W/m/K) Mass Density, ρ (kg/m3)

PF5 0.05 1630

PF6 0.057 1680

Gold 317 19320

Water 0.6 1000

Specific Heat Capacity, Cp (J/kg/K) Thermal Diffusivity, α (m2/s)

1088 2.82 x 10-8

1050 3.23 x 10-8

129 0.00013

4187 0.143

Absorbance cross section, σabs

NA 1.13 x 10-7 6.36 x 10-9

NA 4.79 x 10-8 8.2 x 10-10

4.6 x 10-17 NA NA NA NA NA

Scattering cross section of bubbles, 𝛔𝐁 (𝐜𝐦𝟐) Scattering cross section of droplets, 𝛔𝐃 (𝐜𝐦𝟐) a

from ref 29 b from ref 30


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We used effective radius (𝑅𝑒𝑓𝑓) for our nonspherical gold nanorod in the classical heat diffusion model calculation in order to take into account spherical point thermal explosion. From, Eq. 19, the effective radius is 10.4 nm. 4

𝑉 = 3𝑅𝑒𝑓𝑓3

(19)

where V is the average volume of our nanodroplet. Thus, temperature at the surface of the nanodroplet, 10.4 nm away from the gold nanorod center, was used as the phase-transition temperature of the nanodroplets. Studies have shown that laser pulse duration is a critical factor of impacting the temperature increment for gold nanorod 1, 21. 𝐸

(20)

𝑃𝑝𝑒𝑎𝑘 = 𝑡𝑑 𝐸=

𝑃𝑎𝑣𝑒

(21)

𝑓

where 𝑃𝑝𝑒𝑎𝑘 is peak power, E the energy per pulse, 𝑡𝑑 the pulse duration, 𝑃𝑎𝑣𝑒 the average power measured by power meter, and f the repetition frequency. We considered 𝑡𝑠 , a short period of time when the power is at the peak power, in order to calculate the peak energy 𝐸𝑝𝑒𝑎𝑘 (Eq. 22). 𝑡𝑠 was obtained assuming the laser intensity profile follows Gaussian distribution and corresponds to 5 fs for power within 95% of the peak power. Then, the peak energy and energy absorbed by gold nanorods within peak intensity duration are (22)

𝐸𝑝𝑒𝑎𝑘 = 𝑃𝑝𝑒𝑎𝑘 × 𝑡𝑠 The energy absorbed by the gold nanorod 𝜀0 is 𝜀0 = 𝜎𝑎𝑏𝑠 × 𝐸𝑝𝑒𝑎𝑘/𝐴 × 𝑡𝑠

(23)

where 𝐸𝑝𝑒𝑎𝑘 is the peak energy derived from peak power, 𝜎𝑎𝑏𝑠 is the optical absorption cross section of the gold nanorod (Supporting Information), and 𝐴 is the laser beam area calculated from the laser beam diameter d. (24)

𝑑 = 1.22𝜆/𝑁𝐴 where wavelength 𝜆 of the laser and NA the numerical aperture (NA = 0.75). The temperature profile after N pulses was expressed as 𝑁―1

𝑗

𝑇𝑁𝑃(𝑡) = ∑𝑗 = 0 𝐺𝑅,𝑔(𝑡 ― 𝑓)

(25)

where f is the repetition frequency, which is 80 MHz in our study 1. Time to scan one pixel is 1.6 µs and under 40 X objective lens, 1 pixel corresponds to 1.76 µm, so for a nanodroplet of average size 500 nm, the times it takes to scan one nanodroplet is 0.46 µs. During 0.46 µs, there are total 36 pulses irradiated to the nanodroplet considering the frequency of 80 MHz of the laser used. Thus, in Eq. (25), the maximum value of N is 36.



We compared the phase-transition temperatures obtained using two methods: (i) the kinetics and (ii) heat diffusion model. In heat diffusion model, laser intensity equation was integrated together with the point explosion models as described above to calculate the temperature inside the nanodroplet at a specific time and location.

3. Results 3.1. Characterization of Nanodroplets Detailed characterization of the nanodroplets is described in our previous publications 24, 31. Briefly, the average size of the nanodroplets measured by optical images and by dynamic light scattering was ~300 ~ 500 nm in diameter. To prove a double emulsion structure of W1/O/W2 visually, we dissolved Rhodamine B dye in W1 phase with drug. The fluorescence signal only came from the inside the nanodroplets, confirming double emulsion structure. Gold nanorods on the nanodroplets were observed via enhanced dark-field imaging and hyperspectral analysis. The characteristic absorption peak near 510 nm was detected at the surface of individual nanodroplets while bare nanodroplets without gold nanorods on the surface did not show any peak 24. 3.2. Theoretical Boiling Point of Nanodroplets Determined by Antoine Equation Interfacial Tension Measurement Interfacial tensions of the PF5 and PF6 nanodroplets were measured by Pendent drop method by using the first emulsion of the nanodroplet as a drop and the aqueous liposome dispersion as a surrounding medium (inset of Figure 4A). The interfacial tension values were determined as 1.14 ±0.25, and 1.59 ± 0.16 mN/m for PF5 and PF6, respectively (n=3, p < 0.05, Figure 4B). Since the interfacial tensions are very close to 0 mN/m, deformation of the drop within a few seconds was observed. Boiling temperatures of each perfluorocarbon droplet determined based on the interfacial tensions and Antoine equation were 31.6 ⁰C and 61.0 ⁰C for PF5 and PF6 nanodroplets, respectively. The boiling temperatures of pefluoropentane and perfluorohexane from database are ~29 ⁰C and 56 ⁰C, respectively 26.


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Figure 4. (A) Interfacial tensions of PF5/PF6 nanodroplet using the pendent drop method. The inset is a representative image of the pendent drop (n=3). (B) Theoretical boiling temperatures of PF5 and PF6 determined by the interfacial tensions measured and Antoine equation.

3.3. Light transmittance measurement and phase-transition kinetic models The light transmittance over 750 s of the nanodroplets at 40, 60, 80, and 95 ⁰C was measured (Figure 5). Measurements at each temperature showed reproducible results after carefully controlling the number density of the nanodroplet across the samples. In general, the curves drop faster as temperature increases for both PF5 and PF6 nanodroplets, indicative of phase-transition occurring faster at higher temperatures. At 40 ⁰C, the kinetics for PF5and PF6 nanodroplets look similar, showing negligible decrease (5%) in %T, indicating that 40 ⁰C is the temperature below the threshold of the phase-transition process of our nanodroplets. This value contradicts the boiling temperature (phase-transition temperature, 𝑇𝑝ℎ) of the PF5 calculated by Antoine equation in the Methods section, which is 31.6 ⁰C. This could be due to metastability of the superheated PF5, which will be discussed in Discussion section. Thus, we excluded the 40 ⁰C data points when determining the phase-transition temperature using the modified Arrhenius equation in Section Analysis of Phase-Transition Kinetics using Arrhenius Equation. However, differences in %T decrease between PF5 and PF6 were noticeable at 60 ⁰C and 80 ⁰C. At 200 s, %T values for PF5 and PF6 are 48.2% and 46.3 % at 60 ⁰C, and 45.4% and 43.8 % at 80 ⁰C, respectively. No difference in the kinetics of PF5 and PF6 from 80 ⁰C was observed. Thus, we



conclude that the temperature values required for phase-transition for PF5 and PF6 are > 60 ⁰C , and > 80 ⁰C, respectively.

Figure 5. Light transmittance kinetics at 40, 60, 80, and 95 ⁰C for PF5 and PF6 nanodroplets.

The rate constants for phase-transition (nanodroplet to microbubble) and bubble dissolution, 𝑘1 and 𝑘2, respectively, were determined by fitting following Eq. 12 (Figure 6A). The values in Figure 6B showed that 𝑘1 increased as temperature increased while 𝑘2 did not depend on temperature, both for PF5 and PF6 nanodroplets. The 𝑘1 values for PF6 were about 3.5 times greater in average than the ones for PF5 across the temperatures tested.


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Figure 6.(A) Representative fittings of light transmittance (B) average k1 and k2 values from the fittings for PF5 and PF6 nanodroplets. The statistical p-values for k1 are: p< 0.05 for 40 °C vs. 60 °C, 80 °C vs. 95 °C for both PF5 and PF6.

3.4. Phase-transition by Laser The phase transition of PF5 nanodroplets was clearly observed and recorded under microscope upon laser irradiation with input power at 52 mW. The representative optical images are shown in Figure 7. The diameters of the nanodroplets and the microbubbles were around 400~500 nm and 1~2 µm, respectively, determined by optical imaging and dynamic light scattering 24, 31. The shortest time available to observe phase-transition was 21 ms because of technical limitation of switching laser to camera. After phase-transition, bubbles started to increase in size and merge with adjacent bubbles over time (arrows in Figure 7). The laser average power at 175 mW was used to trigger phase-transition of PF6 because 52 mW did not cause phase-transition. This indicates heat generated by 52 mW is less than the phase-transition threshold of PF6. The rate constant for the phase-transition, 𝑘1, was determined when time t and the number percentage of phase transitioned nanodroplets at the exact time point is known, based on Eq. 6. Several time points and different percentage were considered when calculating the temperature in the next section.

Figure 7. Representative optical images of phase-transition of perfluorocarbon nanodroplets by femtosecond laser. Arrowed are bubbles merged.

3.5. Analysis of Phase-Transition Kinetics using Arrhenius Equation The activation energy E𝑎 and the pre-exponential factor A for the phase-transition were determined by plotting k1 versus 1/T using Arrhenius equation as described in Methods section Analysis of Phase-Transition Kinetics using Arrhenius Equation (Supporting Information, Figure



S2). The phase-transition temperatures Tph for PF5 and PF6 were calculated using the phasetransition time, 21 ms, obtained from the optical observation in the previous section and Eq.15. The values were negative, -1651.9 K and -865 K for PF5 and PF6, respectively, which indicates that the regular Arrhenius equation failed to predict the temperature. Note that the actual phasetransition time may be shorter than 21 ms 32 and time points shorter than 21 ms were considered when the modified Arrhenius equation was used in the following. The modified Arrhenius equation, Eq. 16, yielded the 𝐸𝑎 , 𝐴, and 𝑛 values in Table 2, and 𝑇𝑝ℎ values in Table 3, with assumption that values for 𝐴 and 𝑛 of both PF5 and PF6 are the same, respectively (Supporting information, Figure S3). Table 2. 𝑬𝒂, A, and n values for the fitted graph and Temperature calculation

A 𝑬𝒂 n

PF5

PF6

1.2 44000 1.2

1.2 47600 1.2


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Table 3. Estimated phase-transition temperature based on the kinetic model PF5 t 21 ms

𝐶𝐷/𝐶𝐷0 0.01 0.1 0.5 0.9

k1 219 110 33 5.02

Tph (K) 1509.5 1317.5 1073.1 824.5

PF6 t 21 ms

𝐶𝐷/𝐶𝐷0 0.01 0.1 0.5 0.9

k1 219 1.10E+02 3.30E+01 5.02E+00

Tph (K) 1599.8 1398.8 1142.1 879.7

The results showed that 𝐸𝑎 for PF6 was higher than for PF5, indicating that higher energy, or greater temperature difference, is required for phase-transition of PF6 than PF5. 𝑇𝑝ℎ values at 21 ms were 1509 K (1236 ⁰C), and 1599 K (1326 ⁰C) when 99% of droplets underwent phasetransition (𝐶𝐷/𝐶𝐷0 = 0.01), for PF5 and PF6, respectively. 𝑇𝑝ℎ for PF6 is 90 K higher compared to PF5, suggesting that under the same temperature, there will be less phase transition for PF6. The 𝑇𝑝ℎ increases significantly to 10209 K and 311105 K when the time becomes 100 μs and 1μs, respectively, for PF5. We calculated with different values of 𝐶𝐷/𝐶𝐷0 because (1) phase-transition process in a bulk condition or in a big volume may be different and (2) we wanted to show the 𝑇𝑝ℎ values highly depend on the 𝐶𝐷/𝐶𝐷0 ratio. Although the 𝑇𝑝ℎ values obtained from the modified Arrhenius equation are positive unlike those obtained from the regular one, 311105 K at 1 μs is unrealistic because it would have affected surrounding materials and generated nanobubbles from water 18, which we have not observed.

3.6. Theoretical phase-transition temperature predicted by laser peak intensity and heat diffusion model At 52 mW average power, the laser peak energy 𝐸𝑝𝑒𝑎𝑘was 1.13 x 10 ―15 𝐽 (Refer to Eq. 23). The values for peak power 𝑃𝑝𝑒𝑎𝑘, energy per pulse 𝐸, and energy input 𝜀0 were summarized in Table 4. When 𝐸𝑝𝑒𝑎𝑘 was used for energy input 𝜀0 in Eq. 18, the maximum temperatures at 10.4 nm away from the center of the gold nanoparticle were 63.4 °C and 63.6 °C for PF5 and PF6, respectively, considering 22 °C as the surrounding temperature. Since each pulse is independent, the temperature increase induced by each pulse was summed to obtain the final temperature after multiple pulses as described by Eq. 25. After 36 pulses by laser scan, the temperatures raised by 4.7 K, or to 68.1 °C, for PF5. This temperature is over the temperature observed in Section Light transmittance measurement and phase-transition kinetic models. For PF6 nanodroplets, with the same power at 52 mW, the temperature increment was ΔT = 46.4 K after 36 pulses, which is below temperature threshold of 80 °C (Figure 8A). The results match our observations



demonstrated in Section Phase-transition by Laser, in that phase-transition did occur at 52 mW for PF5 and not for PF6. When the average power input was 175 mW, the temperature increment predicted for PF6 was ΔT =140.1 K after first pulse and ΔT = 155.9 K after 36 pulses, rendering the final temperature 177.9 °C (Figure 8B). The phase-transition was observed as predicted.

Figure 8. Multi-pulse temperature calculations of PF5 and PF6 nanodroplets with 80 MHz pulsed laser. (a) PF5 (dashed line) and PF6 (solid line) at 52 mW; (b) PF6 at 175 mW.

Table 4. Laser parameters and temperature increment after one pulse Average power (W) Energy per pulse (J)

PF5

PF6

0.052 6.50 x 10-10

0.175 2.19E-09


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Peak power per pulse (W) Beam radius (m) Beam area (𝒎𝟐) peak Intensity I (w/𝒎𝟐) ε0 (J) ΔT (K) after 1st pulse

6.50 x 103 6.50E-07 1.33E-12 4.90E+15 1.13E-15 22.05

2.19E+04 6.50E-07 1.33E-12 1.65E+16 3.79E-15 18.27

4. Discussion According to our light transmittance experiment, the kinetic curves for PF5 at 80 and 95°C are similar each other while the ones for PF6 are different. Thus, our observation concludes that PF5 and PF6 nanodroplets underwent vaporization at temperatures above 60 °C and 80 °C. Resulting in rate constants proportional to temperature rather than a clear threshold is because the nanodroplets have a size distribution 27. Nanodroplets with bigger size undergo phase transition at lower temperature as observed 25. The phase-transition or vaporization temperatures predicted based on the interfacial tensions and Antoine equation were much lower than observed, 31.6 ⁰C and 61.0 ⁰C for PF5 and PF6 nanodroplets, respectively. Temperatures estimated by Sheeran et al. using the same method were ~90 ⁰C and 130 ⁰C for PF5 and PF6, respectively 33. The reason why our estimated values are much lower is because our nanodroplets have very low interfacial tension at ~1.5 mN/m, compared to the value of 51 mN/m used in Sheeran et al. The low value can be due to different surfactants and emulsion inside the nanodroplets. This indicates that the metastabilty of these phase-change agents arises not from the droplet Laplace pressure altering the boiling point, as previously reported, but from the metastability of superheated fluid 27. At the same time, observed values are lower than reported by others, where pure perfluorocarbon was used for nanodroplet formation. Mountford et al 27 reported that pure perfluorobutane (C4F10) nanodroplets vaporized at 75 ⁰C, which is approximately 80−90% of the fluorocarbon critical temperature. Our values are closer to 50% instead of 80~90% of the critical temperatures for PF5 and PF6. We suspect that this is because presence of surfactant and water in our nanodroplets lower the bubble nucleation threshold compared to pure homogeneous nucleation processes 34-35. To determine the phase-transition temperature 𝑇𝑝ℎ of gold nanorod-coated perfluorocarbon nanodroplets when irradiated by pulsed laser, we used two different methods. The first approach used the kinetic model, i.e. rate constants, of the phase-transition process and phase-transition time required by irradiation combined with Arrhenius equation. The 𝑇𝑝ℎ values through the method were overestimated, resulting in ~1500 ⁰C. While we used 23 ms for the time, this is likely longer than the actual time it took for the phase-transition and the 𝑇𝑝ℎ values will be even higher. The overestimation may be due to the assumption that the system followed first order kinetics (Eqs. (3) and (4)) or the failure of the Arrhenius equation when the reaction time is very short.



For the second approach, the classical heat transfer model was used with peak pulse energy to estimate the temperature at the perfluorocarbon droplet surface when considering heat transferred from the gold nanorod. This method resulted in reasonable temperature values ~45 ⁰C and verified the observation where that temperature did not activate PF6 vaporization. Although many studies have tried to use the classical heat transfer model to predict temperature of plasmonic materials, the temperature is either too high or too low compared to observations. The reason is that either pulse energy or average energy of laser was used as energy input, without considering peak energy. We considered the pulse energy distribution and time duration for the peak within one pulse that directly impact the highest temperature achieved by one pulse. Combined with heat transfer distance from the core of the gold nanoparticle to the surface of the perfluorocarbon liquid droplet, we were able to predict temperature values that match our observations. Heat accumulation model also fails to predict the temperature change in our study 36 . 6 13

Q= cm∑𝑑𝑇/𝑑𝑡

where Q represents the energy absorbed by gold nanorod during a pulse instead of the peak time duration, c is the heat capacity, and m is the mass of perfluorocarbon. In this model, we considered the ratio of surface area of a gold nanorod that is contacting perfluorocarbon nanodroplet surface, compared to the whole surface area, to accurately calculate the heat transferred, which is 6/13 18. Note that the classic heat transfer model assumed a point thermal explosion, where the energy transfers to all directions. Assuming heat is accumulated linearly during 36 pulses at 80 MHz, the calculated temperature increase (ΔT) was 6 K for PF5 and 22 K for PF6. This result indicates that phase-transition induced by surface plasmon resonance does not depend on total energy absorbed, but the peak energy absorbed. This also matched our other experimental observation that continuous-wave laser irradiation with the same irradiation duration did not induce phase-transition 37-38.

5. Conclusion We have demonstrated the phase-transition mechanism of nanodroplet coated by gold nanorods triggered by pulsed laser irradiation through integrated experimental and theoretical approach. We have concluded that the phase-transition is due to triggering vaporization of the metastable superheated nanodroplets by photothermal heating influenced by peak energy of laser. Total energy balance based on average power of the laser did not explain the phase-transition of the nanodroplet. More importantly, the phase-transition temperature was successfully predicted by the heat explosion model, suggesting that laser parameters required for phase-transition can be calculated. The phase-transition temperatures estimated using the kinetic model and the time required for phase-transition overestimated the values. The reasons may include inaccuracy of the proposed


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reaction model, technical limitation, and failure of extending Arrhenius equation to predict the temperature change in nanosecond scale. Supporting Information 1.

Determination of scattering cross section and absorption cross section.

2.

Phase-transition temperature determination by Arrhenius equation.

3.

Phase-transition temperature determination by modified Arrhenius equation.

Acknowledgement We would like thank Chet Closson in Live Microscopy Core in College of Medicine, University of Cincinnati, for helping laser activation observation using a microscope. We also would like to thank Yoontaek Oh and Dr. Soryong Chae in Chemical & Environmental Engineering, University of Cincinnati, for allowing us to use his equipment. This study was partially supported by Ohio Lions Eye Research Foundation and NIH KL2 award. References 1. Baffou, G.; Rigneault, H., Femtosecond-pulsed optical heating of gold nanoparticles. Physical Review B 2011, 84 (3), 035415. 2. Anderson, R. R.; Parrish, J. A., Selective photothermolysis: precise microsurgery by selective absorption of pulsed radiation. Science (New York, N.Y.) 1983, 220 (4596), 524-7. 3. Quinn, M. D. J.; Wang, T.; Notley, S. M., Surfactant-exfoliated graphene as a near-infrared photothermal ablation agent. Biomedical Physics & Engineering Express 2018, 4 (2), 025020. 4. Zou, L.; Wang, H.; He, B.; Zeng, L.; Tan, T.; Cao, H.; He, X.; Zhang, Z.; Guo, S.; Li, Y., Current approaches of photothermal therapy in treating cancer metastasis with nanotherapeutics. Theranostics 2016, 6 (6), 762-772. 5. Chen, F.; Cai, W., Nanomedicine for targeted photothermal cancer therapy: Where are we now? Nanomedicine (London, England) 2015, 10 (1), 1-3. 6. Huang, X.; El-Sayed, I. H.; Qian, W.; El-Sayed, M. A., Cancer cell imaging and photothermal therapy in the near-infrared region by using gold nanorods. Journal of the American Chemical Society 2006, 128 (6), 2115-2120. 7. Zharov, V. P.; Mercer, K. E.; Galitovskaya, E. N.; Smeltzer, M. S., Photothermal nanotherapeutics and nanodiagnostics for selective killing of bacteria targeted with gold nanoparticles. Biophysical Journal 2006, 90 (2), 619-627. 8. Jain, P. K.; Lee, K. S.; El-Sayed, I. H.; El-Sayed, M. A., Calculated absorption and scattering properties of gold nanoparticles of different size, shape, and composition: Applications in biological imaging and biomedicine. The Journal of Physical Chemistry B 2006, 110 (14), 7238-7248. 9. Prasad, V.; Mikhailovsky, A.; Zasadzinski, J. A., Inside-out disruption of silica/gold core−shell nanoparticles by pulsed laser irradiation. Langmuir 2005, 21 (16), 7528-7532. 10. Lapotko, D. O.; Lukianova, E.; Oraevsky, A. A., Selective laser nano-thermolysis of human leukemia cells with microbubbles generated around clusters of gold nanoparticles. Lasers in Surgery and Medicine 2006, 38 (6), 631-642.



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