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Photoacoustic Signal Generation in Gold Nanospheres in Aqueous Solution: Signal Generation Enhancement and Particle Diameter Effects Genny A Pang, Jan Laufer, Reinhard Niessner, and Christoph Haisch J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b09374 • Publication Date (Web): 09 Nov 2016 Downloaded from http://pubs.acs.org on November 15, 2016

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The Journal of Physical Chemistry

Photoacoustic Signal Generation in Gold Nanospheres in Aqueous Solution: Signal Generation Enhancement and Particle Diameter Effects Genny A. Pang1*, Jan Laufer2,3, Reinhard Niessner1, Christoph Haisch1 1

Chair for Analytical Chemistry and Institute of Hydrochemistry, Technische Universität München, Marchioninistrasse 17, D-81377 Munich, Germany 2

Institut für Optik und Atomare Physik, Technische Universität Berlin, Straße des 17. Juni 135, D-10623 Berlin, Germany

3

Institut für Radiologie, Charité – Universitätsmedizin Berlin, Charitéplatz 1, D-10117 Berlin, Germany

*Marchioninistrasse 17, 81377 München Tel.: +49 (0)89 2180 78250, Fax: +49 (0)89 2180 78255 Mail: [email protected]

1 ACS Paragon Plus Environment


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ABSTRACT Gold nanoparticles can be used as an exogenous contrast agent for biomedical photoacoustic (PA) imaging. The generation of PA signals in monodispersed gold nanosphere suspensions (diameters 20 to 150 nm) from pulsed-laser excitation (5 ns pulse width, wavelength 532 nm) was investigated experimentally and compared to signals measured in solutions of a homogeneous molecular absorber. The PA signal amplitude was found to increase linearly with excitation fluence for the homogeneous absorber and the nanospheres up to 80 nm in diameter. By contrast, the signal amplitude was found to increase quadratically with respect to fluence for larger nanospheres. In the linear regime, the PA signal amplitude in gold nanosphere suspensions was found to be on average 26% higher than that in the homogeneous absorber with identical absorption coefficient, which were measured using an integrating sphere. Furthermore, in suspensions with identical absorption coefficient, no dependence of the PA signal amplitude on nanosphere diameter was found in the linear regime, entailing that suspensions with identical extinction coefficient display a decreasing trend in PA signal amplitude with increasing nanosphere diameter due to increasing contribution of scattering. This study presents experimental evidence of some of the physical phenomena governing the photoacoustic signal generation in gold nanosphere suspensions, which may inform approaches to molecular biomedical PA imaging.


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INTRODUCTION The use of gold nanoparticles as exogenous contrast agents in biomedical photoacoustic (PA) imaging has been investigated in a number of studies1-5. The high absorption cross section of gold nanoparticles, due to their surface plasmon resonance, provides strong PA contrast. Combined with particle functionalization, this contrast can be used to visualize target tissues, such as tumors. Although previous studies1-5 have demonstrated the enhanced contrast in a qualitative manner when gold nanoparticles are employed, much is still left unknown about the processes involved in the PA signal generation. Improving this knowledge could facilitate molecular and quantitative PA imaging approaches using nanoparticles, and also enable researchers to optimize nanoparticle design for specific applications. Photoacoustic imaging in biomedicine is based on the conversion of absorbed radiant energy from a modulated light source to measurable acoustic energy due to thermoelastic expansion of the absorbing medium. Provided the condition of thermal and stress confinement is fulfilled, PA excitation of turbid media is typically assumed to generate an initial PA pressure, p0, at a given position, r, directly related to the local absorption coefficient, , and the local optical fluence, Φ, , ′, which depends on the absorption and scattering properties of the tissue. The relationship is governed by the expression

= Γ Φ, , ′

(1)

where Γ = / is the Grüneisen parameter of the tissue, normally assumed to be that of water, where is the volume thermal expansion coefficient, the speed of sound, and the specific heat capacity6. When gold nanoparticles are used as PA contrast agents, the absorbed energy by the nanoparticles can lead to thermal expansion locally within the particle, and also in



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the surrounding fluid, to which the absorbed energy is transferred, as illustrated in Figure 1a. Thermoelastic expansion of the nanoparticle has been thought to be only a second order effect in the PA signal generation7-9. For aqueous suspensions of gold nanospheres on the order of ten to one hundred nanometers in diameter, the thermal diffusion time for energy transfer from the nanosphere to water is on the order of nanoseconds, calculated by = ! ⁄24χ%& , where ! is the nanosphere diameter and χ%& is the thermal diffusivity of water10. As illustrated in Figure 1b , thermal diffusion occurs on a time scale on the same order of magnitude as the typical PA excitation pulse duration, but shorter than the characteristic time scales for thermal and stress relaxation in water (&(,%& = ) ⁄4*%& and &,%& = )⁄,%&, respectively, with characteristic dimension ) = 1⁄ )6. Thus, the condition of thermal and stress confinement in the particle suspension is not satisfied, and Equation (1) does not directly describe the generated PA signal from pulsed laser excitation of gold nanospheres. The time scale for thermal and stress relaxation in within the gold particle (analogously defined as &(,,- = ! .4*,- and &,,- = ! ⁄,,- , respectively) occur on the picosecond time scale and can be neglected.


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Figure 1. (a) Energy conversion pathways during PA excitation of a colloidal suspension of nanospheres. (b) Time scales in the PA signal generation aqueous suspensions of gold nanoparticles of different diameters, and a comparison of the characteristic time scales of stress and thermal confinement in a homogeneous absorbing aqueous solution with absorption coefficient µa = 4 cm-1.

A theoretical description of the initial PA pressure in a nanoparticle suspension is also complicated by additional phenomena that have been observed in heterogeneous nanoparticle suspensions. For example, the PA signal amplitude in a gold nanosphere suspension of a given optical density has been found to decrease with increasing nanosphere diameter and increasing scattering11. Furthermore, the high absorption cross section of a nanoparticle can lead to significant temperature rises confined to a nanoscale volume near the particle surface that can cause non-linearity of the signal amplitude with respect to the excitation fluence due to the temperature dependence of the thermal expansion coefficient of water7, 12. While the aforementioned experimental studies demonstrate that particle size and non-uniform heating can be important in PA excitation of particle suspensions, many fundamental questions about the PA



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signal generation process remain unanswered, including the influence of a spatial heterogeneity of material properties, i.e. when solid nanoparticles are suspended in liquid, on the PA signal. Furthermore, little is known about the dependence of the absorbed-energy-to-PA-pressure conversion efficiency on nanosphere diameter, optical scattering, and excitation fluence. This study investigates these relationships experimentally, through PA excitation of aqueous gold nanosphere suspensions of nanosphere sizes from 20 nm to 150 nm in diameter, and a comparison of the results to the PA signal amplitude generated in a homogeneous absorbing aqueous solution. The optical absorption properties of all samples were measured using an integrating sphere to be able to directly compare the PA signal amplitude with the absorbed radiant energy. Finally, we examine the influence of nanosphere diameter on the non-linearity of the PA signal with respect to the excitation fluence, and compare the results a theoretical model describing the temperature rises in nanoscale volumes that occur during pulsed-laser heating of gold nanosphere suspensions. EXPERIMENTAL SECTION Photoacoustic Setup. Time-resolved PA signals were acquired using a custom-made backward mode sensor head13. A schematic of the PA sensor head and the optical setup is provided in Figure 2. The sensor head consists of a 5-mm diameter circular 25-µm-thick piezoelectric poly(vinylidene) fluoride (PVDF) foil that was coupled to the bottom of a transparent glass prism with conductive epoxy. The calculated frequency response of the acoustic sensor is broadband with a cutoff frequency near 400 MHz14. The piezoelectric foil was integrated into a BNC socket to eliminate electromagnetic interference, and the output of the BNC socket was fed into a high speed current amplifier (Gain 50 kV/A, Bandwidth: 100 MHz, HCA-100M-50K-C, FEMTO®, Berlin, Germany) and the amplified output signal was read by a two-channel digitizing 6 ACS Paragon Plus Environment

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oscilloscope (Tektronix TDS 620A). The PA excitation was achieved by illuminating the sample through the base of the prism, on the same side as the acoustic detection, i.e. in PA backward mode. The sample was placed onto a 1-mm-thick clear silicon layer, which was acousticallycoupled to the prism with water. The purpose of the silicon layer was to prevent contamination on the prism surface from affecting the signal. Experiments were performed with a 300 µL volume of the sample resting on the silicon surface. PA excitation pulses at a wavelength of 532 nm were provided by a Q-switched, frequency-doubled Nd:YAG laser (Surelite 10-I, Continuum, Santa Clara, CA) with a pulse width (fwhm) of 5 ns (/0- ) and a repetition rate of 10 Hz. The laser output was guided to the PA sensor head using a series of mirrors and apertures and a planocave lens (f = -40 mm). A 3 mm aperture was placed downstream of the planocave lens to truncate the Gaussian beam such that only the central and most uniform portion of the beam arrived at the PA sensor head. The beam diameter at the sample surface was 4 mm and fit entirely within the sample surface. The laser energy was controlled by adjusting the Q-switch delay of the laser, leading to a pulse energy at the sample surface of the PA sensor ranging from 100 µJ to 800 µJ. A part of the beam upstream of the diverging lens was diverted with a beam splitter onto a pyroelectric energy probe (Laser Probe RjP-735, Utica, NY), and the pulse energy was measured using a universal radiometer (Laser Probe Rm-6600, Utica, NY). The analog output of the radiometer was fed to the second channel of the digitizing oscilloscope in order to normalize the PA signal amplitude with respect to pulse energy fluctuations.



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Figure 2. Schematic of the backward-mode PA sensor head and the optical setup.

The PA signal and the pulse energy data from the oscilloscope were acquired using LabVIEW. Each saved data trace was averaged over 50 pulses. Five consecutive data traces were saved for each measurement. Absorbing Samples (Gold Colloid and Aqueous Dye). The nanoparticle samples were gold nanosphere colloid of diameter 20 nm, 40 nm, 60 nm, 80 nm, 100 nm, and 150 nm in water (BBI Solutions, Cardiff, UK). The optical extinction coefficient (µe), which is the sum of the absorption and scattering coefficients (i.e. µe = µa + µs), of the purchased concentration of each nanosphere suspension was measured in a 10 mm cuvette using a UV/Vis Spectrometer (Specord 250 Plus, Analytik Jena AG, Jena, Germany), and the respective µe for diluted and concentrated samples were assumed to scale proportionally to concentration. The fraction of optical extinction due to absorption (µa/µe) for a sample of each nanosphere diameter was measured using an integrating sphere (Labsphere, North Sutton, NH USA). Details of the µa/µe measurements are provided in the Supplementary Information. In addition to the gold nanosphere colloid samples, absorbing nonfluorescent aqueous dye solutions were prepared using red textile dye (Sirius® 8 ACS Paragon Plus Environment

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Supra Red F4BL) and distilled water, the optical coefficients of which were also measured using the UV/Vis Spectrometer and integrating sphere. For the investigations of the effect of nanosphere diameter on the PA signal amplitude, suspensions of each of the nanosphere diameters at three concentrations were prepared. For the 20 nm, 40 nm, and 60 nm diameter suspensions, the undiluted samples provided the highest concentration, and each was diluted to two additional samples of 67% and 33% of the original concentration using deionized water. The 80 nm, 100 nm, and 150 nm diameter suspensions were concentrated to samples of higher µa by removing a portion of the supernatant after the nanosphere colloid naturally settled. The settled colloid samples were then redispersed, and the concentrated suspensions were each diluted to two additional samples of 67% and 33% of their concentration with deionized water to form the rest of the nanosphere samples. An aqueous dye solution was prepared with µe = 4 cm-1, and three additional solutions were diluted to 75%, 50%, and 25% of the original concentration. For the investigations of the dependence of PA signal amplitude on laser fluence, the samples of each nanosphere diameter and the aqueous dye solution were diluted with deionized water to normalize the absorption coefficient to µa = 2.0 cm1

.

RESULTS AND DISCUSSION PA Signal Amplitude as a Function of Concentration. A representative set of PA signals acquired in the three concentrations of the 20 nm diameter gold nanosphere suspension using a laser excitation fluence of 2 mJ/cm2 is shown in Figure 3a. We define the PA signal amplitude as the initial peak amplitude, which occurs at 4.54 µs after the laser pulse, corresponding to the time required for the PA wave to travel through the silicon layer and the glass prism to the detector. The PA signal amplitude increases with µe, which is proportional to gold nanosphere 9 ACS Paragon Plus Environment


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concentration. Figure 3a also shows that the PA signal measured in water is dominated by noise due to the low absorption coefficient of water at 532 nm. Figure 3b shows the dependence of the PA signal amplitude on µe, measured in the three concentrations of the 20 nm nanosphere suspension, with each measurement repeated three times. Each measurement repetition involved a new sample with the same optical properties placed onto the PA sensor head. The error bars indicate the standard deviation of the signal for the measurement condition shown. All signals reported throughout this manuscript were normalized by the pyroelectric energy meter reading to correct for small fluctuations in pulse energy. A linear trend fits the measured PA signal amplitude increase with µe within the uncertainty limits of the measurements. The repeatability of the measurements suggests that the particle suspensions were uniform, and the low standard deviation of the measurement within the consecutive data traces captured indicates that photoacoustic excitation did not cause any significant changes in the particle suspension (i.e. no measureable effect of agglomeration).

Figure 3. (a) Representative PA signals acquired in a suspension of 20 nm diameter gold nanospheres at different concentrations yielding optical extinction coefficients of µe = 2.4 cm-1, 1.6 cm-1 and 0.8 cm-1 at 532 nm; the excitation fluence was 2 mJ/cm2; the signals are 50 pulse averages; the signal from water is also shown for


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comparison. (b) PA signal amplitude in 20 nm diameter gold nanosphere suspensions as a function of µe; error bars indicate the standard deviation of five consecutive data traces, and the three measurement repetitions illustrate the repeatability of the data.

Effect of Nanosphere Diameter on PA Signal Amplitude: Low Fluence Case. Figure 4a shows the PA signal amplitude generated in gold nanosphere suspensions of all nanosphere sizes as a function of µe at a comparatively low fluence of 2 mJ/cm2, which we refer to as low fluence. The PA signal amplitude increases linearly with µe (i.e. increasing concentration). For samples at identical µe, the suspensions containing larger nanospheres systematically feature a lower PA signal amplitude.

Figure 4. Results of PA signal generation in gold nanosphere suspensions at a fluence of 2 mJ/cm2. (a) PA signal amplitude as a function of µe for all gold nanosphere suspensions. The error bars indicate the standard deviation of the signal within three measurement repetitions. (b) The extinction-normalized PA signal as a function of nanosphere diameter for the nanosphere suspensions and the aqueous dye solution; the error bars indicate the standard deviation in three measurement repetitions and different sample concentrations. The ratio of absorption to extinction coefficient (µa/µe) at 532 nm for each nanosphere diameter is also shown as measured using an integrating sphere and as predicted by Mie Theory.



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Figure 4b shows the each measured PA signal normalized by the corresponding µe of the sample to obtain an extinction-normalized PA signal for each nanosphere diameter. The extinction-normalized PA signal from the aqueous dye solution is also shown in Figure 4b for comparison. The extinction-normalized PA signal decreases with increasing nanosphere diameter at low fluence excitation. This can be expected since the contribution of scattering to optical extinction increases with nanosphere diameter, thus reducing µa/µe, the relative contribution of absorption. Figure 4b also shows the µa/µe of the nanosphere suspensions as measured in the integrating sphere, and the predicted µa/µe from Mie Theory, computed with a wavelength of 532 nm and a medium refractive index of 1.33 using the Mie Scattering Matlab calculator from Metwally et al.15, which is based on the theory presented in Bohren and Huffman16. Our measured values for µa/µe are in close agreement with the values predicted from Mie Theory. Moreover, the decreasing µa/µe with increasing nanosphere diameter matches the trend of decreasing extinction-normalized PA signal with increasing nanosphere diameter, supporting the reasoning that increased scattering contribution to extinction lowers the PA signal amplitude. Minor discrepancies between our measured µa/µe and that calculated by Mie Theory are seen for the larger nanosphere diameters, and may be due to the fact that the Mie Theory calculation is for a single particle while the measured values account for multiple scattering incidences and absorption of backscattered light, describing the total absorption and extinction in the actual nanosphere suspension. From Figure 4b, it is also evident that the 20 nm diameter nanospheres, which have very low scattering (measured 94% of the extinction due to absorption), generate an extinctionnormalized PA signal 20% higher than the non-scattering aqueous dye solution. Integrating sphere measurements confirmed that the aqueous dye solution was non scattering. The higher PA


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signal amplitude form the 20 nm diameter nanosphere suspension can be further appreciated from the results of a two sample T-Test to statistically compare the extinction-normalized PA signals (see Table 1), which show that the PA signal amplitude from the 20 nm diameter nanosphere is statistically different (p = 0.083%) from the signal from the aqueous dye solution. The discrepancy between the PA signal amplitude from the 20 nm gold nanosphere suspension and the aqueous dye solution is discussed further after examining the absorption-normalized PA signals. Table 1. P-value results from a two sample T-test of the extinction-normalized PA signal output for an excitation laser fluence of 2 mJ/cm2 (data from Figure 4b). Pairs with P-value greater than 50% are colored red, pairs with Pvalue 5-50% are colored blue, and pairs with P-value less than 5% are colored green.

P-value: Extinction-normalized Photoacoustic Signal (PA Signal / µe) Liquid Dye 20 nm 40 nm 60 nm 80 nm

8.4x10

-04

20 nm 1

40 nm

60 nm

80 nm -03

100 nm

0.31

0.025

9.8x10

1

0.14

0.060

1.0x10

1

0.63

2.9x10

1

8.8x10

2.4x10

100 nm

1

150 nm

-05 -04 -03 -03

150 nm 3.4x10 1.3x10 2.1x10 5.4x10

-05 -04 -03 -03

0.51 1

Figure 5a illustrates the relationship between the signal amplitude and the absorption coefficient. It shows the amplitude as a function of the corresponding µa, which was determined by multiplying the extinction coefficient by the measured µa/µe. There is negligible dependence of the PA signal amplitude on the nanosphere diameter. Moreover, the signal amplitudes generated in all the nanosphere suspensions are systematically higher than those generated in the aqueous dye solution. Figure 5b shows the absorption-normalized PA signal amplitude for the aqueous dye solution and the nanosphere suspensions as a function of nanosphere diameter. Absorption normalization was achieved by dividing each PA signal amplitude by the 13 ACS Paragon Plus Environment


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corresponding µa. Each nanosphere suspension produced an absorption-normalized PA signal on average 26% higher than that from the aqueous dye solution. A possible explanation for this difference is a finite contribution of thermoelastic expansion of the solid gold particle to the PA signal. This signal generation pathway is shown in Figure 1, which has previously been thought to be only a second order effect in PA signal generation in nanosphere suspensions7-9. The current results indicate that a this second order effect makes a constant non-negligible contribution to the photoacoustic signal. This phenomena will be discussed further in later sections of this paper.

Figure 5. Results of PA signal generation in gold nanosphere suspensions at a fluence of 2 mJ/cm2. (a) PA signal amplitude as a function of µa for all gold nanosphere suspensions and the aqueous dye solution. (b) The absorptionnormalized PA signal as a function of nanosphere diameter for the nanosphere suspensions and the aqueous dye solution. The dotted black line shows the average of the nanosphere signals, 26% higher than the aqueous dye signal (shown also as dotted red line).

Table 2 shows the results of a two sample T-Test carried out comparing the absorptionnormalized PA signals from the different sized nanospheres and the aqueous dye. In contrast to the extinction-normalized PA signals (Table 1), signals from all nanosphere suspensions do not differ significantly regardless of nanosphere diameter. However, the PA signals from each 14 ACS Paragon Plus Environment

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nanosphere suspension is significantly statistically different from the signal of the aqueous dye solution. Table 2. P-value results from a two sample T-Test of the absorption-normalized PA signal for an excitation laser fluence of 2 mJ/cm2 (data from Figure 5b). Pairs with P-value greater than 50% are colored red, pairs with P-value 5-50% are colored blue, and pairs with P-value less than 5% are colored green.

P-value: Absorption-normalized Photoacoustic Signal (PA Signal / µa) Liquid Dye 20 nm 40 nm 60 nm 80 nm 100 nm 150 nm

4.4x10 1.1x10 6.3x10 4.8x10 1.8x10 1.6x10

-05 -04 -04 -04

20 nm

40 nm

60 nm

80 nm

100 nm

150 nm

1

0.63

0.52

0.70

0.85

0.38

1

0.83

0.97

0.85

0.26

1

0.87

0.73

0.22

1

0.89

0.28

1

0.35

-03 -03

1

Effect of Nanosphere Diameter on PA Signal Amplitude: High Fluence Case. The results for PA experiments carried out with a fluence of 5 mJ/cm2, which is referred to as high fluence excitation in this paper, are shown in Figure 6. Similar to the low fluence case, the extinctionnormalized PA signal was found again to exhibit a dependence on nanosphere diameter. An exception was observed for the 150 nm diameter nanosphere suspension, where the extinctionnormalized PA signal was found to be greater than expected. The main differences between the low and high fluence cases can be seen in the PA signal amplitude generated in 100 nm and 150 nm diameter nanosphere suspensions, where the extinction-normalized PA signal is significantly higher with respect to the other nanosphere diameters and the aqueous dye solution, as compared to the low excitation fluence case. Moreover, these data do not follow the trend of µa/µe of the nanospheres (Figure 6b) like in the low excitation fluence case (Figure 4b). At high fluences, the 20 nm diameter nanospheres were found again to generate an extinction-normalized PA signal that is on average 20% higher than the non-scattering aqueous dye solution, shown in Figure 6b. 15 ACS Paragon Plus Environment


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This finding indicates that the relative contribution of the gold nanospheres to the PA signal amplitude is not fluence dependent up to 5 mJ/cm2.

Figure 6. Results of PA signal generation in gold nanosphere suspensions at a fluence of 5 mJ/cm2. (a) PA signal amplitude as a function of µe for all gold nanosphere suspensions and the aqueous dye solution. (b) The extinctionnormalized PA signal as a function of nanosphere diameter for the nanosphere suspensions and the aqueous dye solution, and µa/µe at 532 nm for each nanosphere diameter.

Figure 7a shows the PA signal amplitude for all the samples as a function of µa, for the high fluence case. Unlike the results obtained at low fluence (Figure 5a), the PA signal amplitude is dependent on nanosphere diameter with the 100 nm and 150 nm nanospheres exhibiting a significantly higher signal amplitude compared to the low fluence case. The PA signal amplitude from the aqueous dye solution is again lower than that generated in all nanosphere suspensions Figure 7b shows the absorption-normalized PA signal as a function of nanosphere diameter for the high fluence case. Comparison of Figure 5b and Figure 7b suggests that for nanospheres of diameter less than 80 nm, the absorption-normalized PA signal amplitude measured in gold nanosphere suspensions is on average 26% higher than that measured in the aqueous dye solution for both the low and high fluence excitation. However, for nanospheres with a diameter of 100 nm and 150 nm, the absorption-normalized PA signal shows a much greater amplitude at high 16 ACS Paragon Plus Environment

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fluence compared with that measured in the aqueous dye solution and the suspensions of smaller diameter nanospheres. This observation can be explained by a non-linearity of the PA signal with respect to fluence for larger particle suspensions, which is discussed in the following section.

Figure 7. Results of PA signal generation in gold nanosphere suspensions at a fluence of 5 mJ/cm2. (a) PA signal amplitude as a function of µa for all gold nanosphere suspensions and the aqueous dye solution. (b) The absorptionnormalized PA signal as a function of nanosphere diameter for the nanosphere suspensions and the aqueous dye solution. The dotted black line shows the value 26% higher than the aqueous dye signal (shown also as dotted red line).

Signal Non-linearity as a Function of Nanosphere Size. The relationship between PA signal amplitude and excitation fluence was directly studied using nanosphere suspensions and an aqueous dye solution, all with the same absorption coefficient µa = 2.0 cm-1. Figure 8a shows the dependence of the PA signal amplitude on the laser excitation fluence for each sample. The aqueous dye solution exhibits a linear dependence of the signal amplitude on fluence, as expected from Equation (1). For each suspension with nanospheres of 20 nm to 80 nm in diameter, the PA signal amplitude also shows a linear dependence on fluence, marginally above the linear fit to the aqueous dye data and consistent with the observations in Figure 5 and Figure 7. By contrast, the PA signal amplitude measured from the 100 nm and 150 nm diameter 17 ACS Paragon Plus Environment


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nanosphere suspensions shown Figure 8a is clearly seen to be non-linear with fluence. Moreover, for fluences above 2 mJ/cm2, the PA signal amplitude begins to deviate significantly from that measured in the other nanosphere suspensions. The non-linearity of the PA signal with fluence for 100 nm and 150 nm diameter nanosphere suspensions explains the trend seen in PA signals excited using a fluence of 5 mJ/cm2 (Figure 6 and Figure 7), where the absorption-normalized PA signal is found to be greater than expected for large diameter particles.

Figure 8. (a) PA signal amplitude as a function of fluence for gold nanosphere suspensions and an aqueous dye solution of identical µa (2.0 cm-1). Error bars indicate the standard deviation of the signal within several measurement repetitions. Dotted green line shows a quadratic fit to the 150 nm data. (b) Deviation of the PA signal from the “Liquid Dye Linear Fit” shown in Figure 8a. Dotted green line shows a linear fit to the 150 nm data.


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Figure 8b shows the deviation of the PA signal amplitude from linearity for all nanosphere diameters and the aqueous dye solution as a function of fluence, computed by dividing the PA signal amplitude by the respective value of the linear fit to the aqueous dye data. The deviation of the PA signal amplitude measured in 100 nm and 150 nm diameter nanosphere suspensions increases linearly with fluence, indicating that the PA signal amplitude for these particles displays a quadratic dependence on fluence instead of a linear one. This is also illustrated in Figure 8a by the dotted green line, which is the quadratic fit to the 150 nm nanosphere suspension data. For the nanosphere suspensions used for the measurements in Figure 8a, only the absorption coefficient is held constant, meaning that the particle density is not identical for each of the nanosphere sizes. However, from all our experimental results, we found no dependence of the linearity of the PA signal with fluence on the density of the nanosphere suspensions. Comparison to Previous Experimental Studies. The effect of nanosphere diameter on the PA signal amplitude has been previously investigated by Fukasawa et al.11 In Figure 9, the data obtained in this study are compared to their work, showing the extinction-normalized PA signal, normalized by the respective signal of the 20 nm diameter nanosphere suspension to enable comparison of PA signal amplitudes from different experimental setups. The data from Fukasawa et al. exhibit the same qualitative trend of decreasing PA signal amplitude with increasing nanosphere diameter. However, their data exhibits a sharper signal decrease with nanosphere diameter than measured in this study. This may be explained by the fact that the ratio µa/µe for gold nanospheres at a laser wavelength of 560 nm used by Fukasawa et al. is lower compared to that at 532 nm. The difference in the decrease of the PA signal amplitude with nanosphere diameter is in qualitative agreement with Mie Theory computed µa/µe as a function 19 ACS Paragon Plus Environment


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of nanosphere size for the two excitation wavelengths, as shown in Figure 9 with the respective data for comparison.

Figure 9. The extinction-normalized PA signal for each size of nanosphere in suspension, divided by the respective value from the 20 nm diameter nanosphere suspension; the error bars on the current work indicate the variation in three measurement repetitions and different sample concentrations. Shown in comparison is the respective data from Fukasawa et al.11 who used an excitation fluence of 12.7 mJ/cm2 and laser wavelength of 560 nm. Also shown is the ratio µa/µe as predicted from Mie Theory.

In gold nanosphere suspensions, the fraction of the PA signal attributed to thermoelastic expansion of the gold nanospheres has not previously been directly studied, but can be estimated from available literature data with a few assumptions. At a temperature of 4°C (Figure 10a), the thermal expansion coefficient of water is zero. Hence, any PA signal from a aqueous gold nanosphere suspension measured at this suspension temperature is suggested to arise solely from the heat within the gold nanospheres11. PA experiments of aqueous gold nanosphere suspensions reported in the literature8-9, 11-12 show that the signal amplitude generated at a suspension temperature of 4°C is 4% to 46% of the room-temperature-generated PA signal, suggesting that this percentage of the room-temperature PA pressure originates solely from thermoelastic expansion of gold. This percentage is, however, only an upper limit to the fraction of the PA 20 ACS Paragon Plus Environment

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pressure originating from thermoelastic expansion of gold, because rapid heating of water in the immediate vicinity of the gold nanosphere can occur during PA excitation of nanosphere suspensions with initial temperature of 4°C, which would lead to a non-zero thermal expansion coefficient in these nanoscale volumes of water. This would cause a measureable PA signal generated in the initially 4°C water12. The magnitude of these temperature rises in nanoscale volumes is dependent on nanosphere diameter and excitation fluence, which perhaps explains the large discrepancy in the literature of the ratio of the PA signal generated at a suspension temperature of 4°C to the room-temperature generated signal. Although gold has a relatively low thermal expansion coefficient relative to water, the Grüneisen parameter of gold is larger because of the high speed of sound and low heat capacity of gold (Table 3). Therefore, it is reasonable to conclude that absorbed radiant energy by gold converted to acoustic energy will create a PA wave with higher initial pressure than the same amount of absorbed energy in water. Therefore, our findings that a gold nanosphere suspension will generate a PA pressure approximately 26% higher than a homogeneous aqueous dye solution absorbing the same amount of radiant energy, because of thermoelastic expansion in gold, is at least qualitatively consistent with the given literature. Table 3. Volumetric thermal expansion coefficient (β), speed of sound (cs), specific heat capacity (CP) and Grüneisen parameter (Γ) for water and gold at 25°C.17

Properties of Water and Gold -4

β (10 K-1)

cs (m/s)

CP (J/kg-K)

Γ

Water

2.5

1500

4180

0.13

Gold

0.43

3240

129

3.5



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A few experimental studies7, 12 have investigated PA excitation of both gold nanosphere solutions and homogeneous liquids. However, these studies do not enable direct analysis of the contribution of thermoelastic expansion of solid gold nanosphere inclusions to the overall PA signal amplitude. Egerev and Oraevsky7 excited PA signals in 200 nm diameter gold nanospheres at 532 nm with laser pulses of fluences from 30 mJ/cm2 to 100 mJ/cm2 and compared the behavior of the PA signals from a gold nanosphere suspension to that of a homogeneous fluid (water). The absorption coefficient of the nanosphere suspension was not reported. Therefore, no quantitative comparison can be made to determine the contribution of thermoelastic expansion of gold nanospheres to the PA signal amplitude. A significant result from their study was to demonstrate that the PA signal amplitude increases non-linearly with fluence, similar to the behavior seen from the 100 nm and 150 nm diameter nanospheres in the current work. They also showed that in the absence of gold nanospheres (during PA excitation of water) the relationship between PA signal amplitude and fluence is linear. Simandoux et al.12 presented comparable magnitudes for PA signal amplitudes measured from an organic blue dye solution and from a 40 nm diameter gold nanosphere suspension, both diluted to a similar optical density. Their intent was to study the linearity of the signals with increasing fluence, and therefore, an accurate comparison of the signal magnitudes from the gold nanosphere suspension and the organic dye from their data is not possible. Simandoux et al. observed a non-linear relationship between PA signal amplitude and fluence in gold nanosphere suspensions, but only in a suspension temperature of 4°C. At a suspension temperature of 20°C, they found the PA signal to be linear with fluence, just as seen in the current work. For experiments carried out at room temperature in the literature and the current work, non-linear behavior has only been observed for larger nanosphere diameters.


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Comparison to Theoretical Models. The PA wave generation from a gold nanosphere in water was computationally solved by Prost et al.18 using an analytical Green’s function solution to the temperature field in water, accounting for laser heating and convection, and a finite-difference time-domain algorithm to solve the thermoelastic wave generation problem. From their computed photoacoustic waveforms in the linear regime for a laser pulse duration of 5 ns and nanosphere diameter of 40 nm, the amplitude of the PA waveform generated with thermal expansion in both water and gold is approximately 2% higher than the signal amplitude computed with no thermal expansion in gold. According to their model, the discrepancy between the amplitude of the PA waveform generated with thermal expansion in both water and gold, and that obtained with only thermal expansion in water increases with increasing nanosphere diameter. The results from our study showing a higher PA signal amplitude in gold nanosphere suspensions, in comparison to an aqueous solution with the same absorption properties, are in qualitative agreement with this observation from the model of Prost et al. The quantitative discrepancy between our experimental results and the model of Prost et al. of the contribution of thermal expansion of gold to the PA signal amplitude could be explained in that their model neglects coupling of the temperature and wave equation and assumes a temperature continuity at the gold-water interface (no interfacial thermal resistance). The coupling effect between the temperature and wave equation is not expected to lead to significant changes in the temperature profile19, but interfacial thermal resistance can lead to a temperature discontinuity at the goldwater interface, which would lower the peak temperature of the surrounding water15. Therefore, the results of Prost et al.18 indicate only a lower bound for the relative contribution of the thermoelastic expansion of gold to the overall PA pressure. In their model, Prost et al. also accounted for temperature rises in nanoscale volumes in gold nanosphere suspensions that lead



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to an increase in the thermal expansion coefficient of water. The higher PA signal amplitude in gold nanosphere suspensions, as compared to a homogeneous absorbing aqueous dye solution, found in our data could also be partially due to this phenomena of temperature rise in nanoscale volumes. However, this phenomena is likely not the primary contributor to the increase in PA signal amplitude in gold nanosphere suspensions (as compared to a homogeneous absorbing aqueous dye), because we found the PA signal increase to be independent nanosphere diameter at low fluence excitation, and the magnitude of the temperature rise in nanoscale volumes is dependent on the nanosphere diameter. Several models have been proposed to predict the temperature changes in a gold nanosphere and the surrounding water after excitation by a pulsed laser10, 15, 18. An early model proposed by Copland et al.10 assumed a temperature continuity at the gold/water interface and a square laser pulse profile. They accounted for simultaneous absorption and heat diffusion through and exponential heating decay with known heat diffusion time. More recently, Prost et al.18 proposed a model that assumed a temperature continuity at the gold-water interface, a Gaussian-shaped source term, and account for the simultaneous heating and cooling of the particle through the Green’s function as the solution to a delta excitation. Metwally et al.15 numerically solved the differential equations for heat diffusion with a Gaussian-shaped source term, and allowed a finite interfacial thermal resistance at the gold-water interface to be accounted for, which would lead to a temperature discontinuity at the interface. The temperature changes in the water surrounding the gold nanosphere can raise the volumetric thermal expansion coefficient (Figure 10a), and thus the Grüneisen parameter. The peak temperature rise of the water surrounding a nanosphere excited by a 5 ns laser pulse with a fluence of 2 mJ/cm2 was calculated using the models of Prost et al.18 and Metwally 24 ACS Paragon Plus Environment

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et al.15. Figure 10b shows the dependence of the peak water temperature rise on the nanosphere diameter. Also shown is the influence of the presence of an interfacial thermal resistance of g = 150 MW/m2-K using the model of Metwally et al. At a fluence of only 2 mJ/cm2, the peak temperature change in the water surrounding the literature can reach over 80°C for nanospheres of 60 nm and 80 nm in diameter. Assuming an ambient suspension temperature of 20°C, this indicates that the water temperature may exceed 100°C. However, cavitation bubbles around the nanosphere are not expected to be formed because the theoretical temperature threshold for generation of cavitation bubbles in water is the spinodal temperature of 277°C15, at which the second derivative of Gibbs free energy is zero. The fluence threshold for cavitation bubble generation was found to be greater than 50 mJ/cm2 for nanosecond pulses and for nanosphere diameters comparable to those studied in this work7, 20-21. Therefore, the non-linearity observed is unlikely to be due to the formation of cavitation bubbles. High-temperature heating in a nanoscale volume, however, would nevertheless be expected to lead to non-linearity of PA signal amplitude as a function of fluence, because the local temperature, and thus the thermal expansion coefficient and Grüneisen parameter, depend on the fluence.

Figure 10. Model predictions of PA signal generation in gold nanoparticles. (a) Temperature dependence of the volumetric thermal expansion coefficient of water relative to its value at 20°C. (b) Calculated peak water



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temperatures after pulsed laser heating by a 2 mJ/cm2 fluence beam at 532 nm with pulse width 5 ns as calculated by the models of Prost et al.18 and Metwally et al.15 with and without interfacial thermal resistance. (c) Predicted deviation from linearity of the PA signal with respect to fluence based on the thermoelastic wave equation from Prost et al.18 and the space- and time-resolved temperature field from the algorithm of Metwally et al.15

The peak water temperature shown in Figure 10b occurs for a short instant, and only in a thin volume surrounding the nanosphere. Therefore, the wave equation with a temperaturedependent thermal expansion coefficient must be solved coupled with the complete temperature profile in time and space to account for the effect of the temperature rise on the PA signal. For conditions representative of the current experiments, we numerically solved the thermoelastic equations with spherical symmetry from Prost et al.18 using the finite-difference time-domain algorithm described by them, coupled with the space- and time-resolved temperature profile computed from the numerical solution algorithm of Metwally et al.15, assuming an interfacial thermal resistance of g = 150 MW/m2-K. Details of the calculations and representative temperature profiles along with sample solutions of the thermoelastic equations with and without assuming a temperature-dependent thermal expansion coefficient are presented in the Supplementary Information. Figure 10c shows the resulting expected deviation of the PA pressure from linearity, which we calculated as the ratio of the simulated PA pressure using the temperature-dependent thermal expansion coefficient of water to the simulated PA pressure using the fixed thermal expansion coefficient of water at 20°C. Based on the simulations, the largest deviation from linearity is expected for nanospheres of 80 nm diameter. From our experimental data in Figure 8, however, no significant deviation of the PA signal from linearity was found for nanospheres of 80 nm in diameter, and significant deviations from linearity were only seen for nanospheres of 100 nm and 150 nm.


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The models12, 15 for predicting the non-linearity of the PA signal with respect to fluence, shown in Figure 10c, are for a single nanosphere with the PA pressure recorded at a single point source in space. Therefore, these models may be limited in predicting the experimentally recorded PA pressure, which can include PA signal integration from an ensemble of a nanospheres, and integration of point sources of PA pressure over a finite acoustic sensor surface area. Another consideration that can influence the recorded PA pressure is the frequency response of the acoustic transducer. Simandoux et al.12 suggested that the non-linear contribution of the PA signal is centered at a much higher frequency than their detection frequency, because the signal arises from a very thin heated region surrounding the nanosphere. While the PA wave from a single nanoscale source volume would theoretically generate a high frequency signals outside our detection bandwidth, further investigation is necessary to determine the signal properties after integration of the PA waves from all nanosphere sources in a suspension. Based on the currently available information in the literature, it is uncertain whether our experimental finding of non-linearity are different from the theoretical prediction because of the bandwidth or geometry of the acoustic sensor, or of other physical phenomena not accounted for in the models, such as thermal interaction within an ensemble of particles, or a higher interfacial thermal resistance, which can influence the temperature profile of the water surrounding the nanosphere significantly differently than predicted by the available theories. CONCLUSION The current experimental study indicates that the PA signal amplitude in a gold nanosphere suspension is higher than that from a homogeneous absorbing aqueous solution of equal µa by approximately 26%. This enhancement of the PA signal amplitude in the gold nanosphere suspension can be attributed to differences in the spatial heterogeneity of material 27 ACS Paragon Plus Environment


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properties, where the solid gold nanospheres present nanoscale inclusions of higher Grüneisen parameter. The PA signal amplitude is, therefore, not a direct indicator of the absorbed radiant energy. Our results also show that for suspensions of nanospheres with large diameter (100 nm and 150 nm), the PA signal amplitude increases quadratically with fluence. This is due to temperature rises in nanoscale volumes in the fluid, which further enhance the PA signal amplitude compared to a homogeneous dye solution of the same absorption properties. Although theoretical models describing the temperature changes in nanoscale volumes predict significant non-linear behavior for nanosphere diameters 60 to 80 nm, this was not observed in our data. We find only the nanospheres of 100 nm and 150 nm in diameter exhibit non-linear behavior, while the nanospheres 60 to 80 nm in diameter still show linear behavior. Further studies are needed to determine whether this discrepancy is due to shortcomings in the theory to predict the temperature field in the nanosphere suspension or a result of limitations in the experimental setup related to bandwidth or active area of the acoustic sensor. In any case, our experimental results demonstrate key dependencies of the PA signal amplitude on absorption, nanosphere size, and excitation fluence, and these results should be taken into account by those employing nanospheres in PA imaging. This study adds new evidence to our understanding of the processes involved in the generation of PA signals in gold nanosphere suspensions. The findings can be applied to advance the application of nanospheres as contrast agents in PA imaging in biomedicine, and may facilitate their future application of nanoparticle contrast agents in molecular and quantitative PA imaging studies. ASSOCIATED CONTENT 28 ACS Paragon Plus Environment

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The experimental procedure and data analysis for measurement of the optical absorption properties of the nanosphere suspensions, and representative calculations of temperature and PA pressure from models describing the pulsed-laser excitation of a gold nanosphere are available as Supporting Information. AUTHOR INFORMATION *Marchioninistrasse 17 81377 München Tel.

+49 (0)89 2180 78250

Fax

+49 (0)89 2180 78255

Mail

[email protected]

ACKNOWLEDGEMENTS G. A. Pang acknowledges funding provided by an Alexander von Humboldt Fellowship for Postdoctoral Researchers. The authors thank Adrian Rühm, Max Aumiller, Max Eisel for experimental assistance with the integrating sphere measurements. REFERENCES 1.

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