Article pubs.acs.org/JPCC
Surface Plasmon Polariton Propagation and Coupling in Gold Nanostructures Kuai Yu, Mary Sajini Devadas, Todd A. Major, Shun Shang Lo, and Gregory V. Hartland* Department of Chemistry and Biochemistry, University of Notre Dame, Notre Dame, Indiana 46556-5670, United States S Supporting Information *
ABSTRACT: Surface plasmon polariton (SPP) propagation in chemically synthesized gold nanobars was investigated using scanning transient absorption microscopy. The SPP propagation lengths were correlated to the size and shape of the nanobars, which were determined by atomic force microscopy. The average propagation length was found to be 12 ± 4 μm, and the measured values were independent of the excitation polarization. Finite element calculations were performed for gold nanobars in the presence of a glass substrate to model the experimental results. Comparison between the experimental and theoretical results shows that both bound and leaky SPP modes can be excited. The leaky mode is detected in the larger nanobars (widths greater than 500 nm), and the bound mode is detected in smaller nanobars. Highly directional and efficient plasmon coupling between a gold nanobar and a nearby gold nanoplate was also observed in the experiments.
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wires30 and carrier diffusion in semiconductor nanowires.31,32 This technique provides a simple and repeatable way of interrogating SPP propagation in metal nanostructures and electron/hole migration in semiconductor nanostructures with ultrafast time resolution and diffraction limited spatial resolution. In this study, we investigated SPPs propagation in gold nanobars (nanowires with roughly rectangular cross sections) supported on a glass substrate using scanning transient absorption microscopy. The SPPs were launched by focusing an 800 nm pump beam at one end of the nanobar with a microscope objective.33 Transient absorption images were generated by spatially scanning the probe beam relative to the pump with a galvanometer scanner. The size and shape of the nanobars were determined by atomic force microscopy (AFM) to correlate dimensions with the SPP propagation distances. The measured propagation lengths for the gold nanobars were found to be 11.3 ± 3.1 μm and 12.3 ± 4.1 μm (error equals standard deviation) for pump laser polarizations parallel and perpendicular to the long axis of the nanobar, respectively. The size and shape dependent propagation lengths, and the polarization independent properties for the gold nanobars on a glass substrate were quantitatively understood by comparing experiments with finite element calculations. This comparison shows that for nanobars with large sizes (widths >500 nm) the leaky SPP mode is detected in
INTRODUCTION Surface plasmon polaritons (SPPs) are electromagnetic waves that propagate along metal−dielectric interfaces.1 They are highly confined along the metal’s surface and provide a promising route to transmit or direct optical signals in subwavelength dimensions. Noble metal nanostructures have been demonstrated to support SPPs at visible and near-IR frequencies.2−4 Among the various plasmonic waveguide nanostructures,5−9 chemically synthesized gold and silver nanowires have been shown to provide longer propagation lengths compared to lithographically defined metal nanostructures,10−13 because of their high crystallinity and smooth surfaces. The detection and imaging of SPPs propagation can be accomplished using techniques such as scanning near-field optical microscopy14−16 and photoemission electron microscopy17 or by utilizing fluorescent dyes or quantum dots to map the SPP near-field intensity.18−21 All these techniques have limitations, however. Near-field techniques are usually very complicated to implement compared to far-field techniques. Meanwhile, the use of fluorescent reporter molecules can affect the intrinsic properties of the SPP modes,19 although these effects can be minimized by using low concentrations of molecules.21 Far-field scattering microscopy22−27 and leakage radiation microscopy28,29 are less expensive and easier to implement. However, it is difficult to obtain quantitative decay length information from these techniques, due to the presence of scatter from the laser source. Recently, a variation of transient absorption microscopy, where the probe laser is spatially scanned independent of the pump laser, has been demonstrated for measuring SPP propagation in gold nano© 2014 American Chemical Society
Received: February 14, 2014 Revised: March 27, 2014 Published: March 31, 2014 8603
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frequency (400 kHz) modulation of the pump beam was used to extract the small change in reflectivity ΔR of the probe beam induced by the pump. For imaging SPPs propagation, the probe beam was spatially scanned relative to the pump beam using a two-dimensional galvano-scanner. Typically, a 20 × 20 μm2 image was recorded. A 4f system was constructed before the microscope using two 250 mm focal length lenses to direct the probe beam to the back aperture of the objective. The intensities of the pump and probe beams were controlled through half-waveplate/polarizer combinations, while their polarizations were set using half- or quarter-waveplates. The pump beam was linearly polarized and was adjusted to be either parallel or perpendicular to the long axis of the nanobar, while the probe beam was circularly polarized. The pump and probe powers were kept below 800 μW and 200 μW, respectively. Under those conditions, the signal is stable and no melting or reshaping of the nanobars was observed, as confirmed by AFM measurements.
the transient absorption measurements, while for smaller size nanobars the bound SPP mode is detected. We also observed an efficient plasmon coupling between a nanobar and a nearby nanoplate separated by ca. 300 nm. Finally, we demonstrated that both the propagation lengths and coupling efficiency decrease when the surrounding medium is changed from air to microscope immersion oil.
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MATERIALS AND METHODS The gold nanobars used in this study were chemically synthesized, and the detailed synthesis procedure is given in the Supporting Information. Scanning electron microscopy (SEM) images of the gold nanobars are shown in Figure S1. The cross-sectional shapes are mainly rectangular with small aspect ratios (AR = width/height), mixed with a few nanobars with pentagonal and hexagonal cross sections. The gold nanobars have smooth and clean surfaces and irregular end shapes. For single particle experiments, the sample was first centrifuged to remove excess surfactant in solution, and then spin-coated onto a clean glass coverslip. The dimensions of the nanobars examined in the transient absorption experiments were measured by AFM. The size distributions extracted from the AFM measurements are 600 ± 220 nm, 380 ± 140 nm, and 15 ± 4 μm for the width, height, and length, respectively, as shown in Supporting Information Figure S2 (errors equal standard deviation). The scanning transient absorption microscopy setup is shown schematically in Figure 1 and has been described
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RESULTS AND DISCUSSION Figure 2 shows transient absorption images of SPP propagation in a representative gold nanobar. Figure 2a displays the scattered light image of the nanobar, and the corresponding AFM image is shown in Figure 2b. Transient absorption images showing SPP propagation using parallel and perpendicular excitation polarization are presented in Figure 2c and d, respectively. The SPPs are launched by focusing the 800 nm excitation beam at the end of the nanobar, indicated by the arrows in Figure 2, and the images are obtained by scanning the probe beam over the nanobar while the pump beam is held fixed. Note that the pump and probe beams are temporally overlapped for all the plasmon propagation imaging measurements, in order to maximize the signal. In noble metal nanostructures, SPPs propagate at approximately half the speed of light at 800 nm;11,21 therefore, we expect essentially instantaneous propagation of the SPP along the nanobar within the time resolution of our experimental setup (∼300 fs). This was verified by recording transient absorption traces for a long (∼25 μm) nanobar with the probe beam positioned at different points (Supporting Information, Figure S3). The traces show very slight differences in the rise time of the signal, which means that timing between the pump and probe pulses does not affect our measurements of the SPP field strength. The signals in Figure 2c and d decay along the nanobar because of a reduction of the SPP field strength by leakage radiation and/or Joule losses.6,14 The line profiles of the signal intensity (on a log scale) along the long axis of the nanobar are shown in Figure 2e and f. The signal intensity is lower with perpendicular excitation, due to less efficient launching of the SPPs in the nanobar.18 The propagation lengths obtained by fitting the line profiles are 16.7 ± 0.8 μm for parallel excitation and 16.4 ± 1.0 μm for perpendicular excitation. The uncertainties were determined from 10 repeated measurements of the same particle. The pump laser polarization and size dependence of the SPP propagation lengths for more than 40 gold nanobars are presented in Figure 3. Figure 3a shows a plot of the SPP propagation length for perpendicular excitation versus that for parallel excitation. For each nanobar, the propagation lengths for the two polarizations are very similar: the average values are 11.3 ± 3.1 μm and 12.3 ± 4.1 μm for the parallel and perpendicular polarization excitation, respectively (errors equal standard deviation). This lack of sensitivity to excitation
Figure 1. Schematic diagram of the scanning transient absorption microscopy setup. BS: beam splitter; FI: Faraday isolator; BE: beam expander; DM: dichroic mirror; Pol: polarizer; λ/4 and λ/2: quarterand half-waveplates, respectively; APD: avalanche photodiode; LIA: lock-in amplifier; AOM: acousto-optic modulator.
earlier.30 The instrument is based on a Ti:sapphire oscillator/ OPO laser system (80 MHz repetition rate) that provides nearIR (800 nm) pump and visible (570 nm) probe beams. The timing between the pump and probe pulses was controlled by a translation stage, and the two beams were combined with a dichroic mirror, and then focused at the sample with a high numerical aperture oil immersion objective (NA = 1.3). Propagating SPP modes were excited by focusing the near-IR pump beam at the end of a nanobar. The SPPs travel down the wire, and as they move they lose energy through radiative losses or by creation of electron−hole excitations. The electron−hole excitations produce a transient signal that is monitored by the visible probe beam.34 The experiments were performed in reflection mode, with an avalanche photodiode (APD) to detect the probe. A lock-in amplifier in conjunction with high 8604
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Figure 2. SPP propagation in a representative gold nanobar. (a) Scattered white light image of the gold nanobar, and (b) the corresponding AFM image. The dimensions of the nanobar determined from the AFM measurements are 450 nm × 250 nm × 15 μm (width × height × length). (c and d) Transient absorption images with pump excitation parallel and perpendicular to the long axis of the nanobar, respectively. The pump beam is spatially fixed on the end of the nanobar, as indicated by the arrows. (e and f) Line profiles of the signal extracted from the images in parts c and d. Note that the intensities are on a log scale. A fit to the linear portion (red lines) gives an estimate of SPP propagation length.
Figure 3. Polarization and particle size dependent SPP propagation. (a) Correlation of the SPP propagation under parallel and perpendicular excitation. Error bars are determined from repeated experiments. The dash-dotted line corresponds to L∥ = L⊥. Parts b and c show the particle height and width dependence of the SPP propagation distance under parallel excitation. The different colored symbols separate the small nanobars from the larger onessee text for details. The shadowed area in part c shows the calculated leaky mode propagation distance for nanobars with aspect ratio between 1 and 2 and a radius-of-curvature of 10 nm. The two green lines show the calculated bound mode propagation distance for nanobars with an aspect ratio of 1 and radius-of-curvatures between 10 and 100 nm.
polarization is not due to the symmetry of the structure,35 which is broken by the glass substrate in our study. Rather, we attribute the polarization independence to the fact that the same SPP modes are excited in both experiments, as will be discussed below. The nanobar length dependence of the SPP propagation is shown in Supporting Information Figure S4. The SPP data does not show any significant dependence on length, which indicates that reflections at the end of the nanostructures do not affect our results.29 Parts b and c of Figure 3 show the dependence of the SPP propagation length for parallel excitation on the height and width of the nanostructure. This data has been divided into two groups: larger nanobars (heights greater than 300 nm and widths greater than 500 nm, solid black symbols in Figure 3) and smaller nanobars (red symbols in Figure 3). The larger nanobars show a moderate increase in propagation length with dimensions, while the smaller nanobars have longer propagation lengths, but do not show an obvious trend with dimensions. In the following we explain these observations. According to waveguide theory, supported metal nanowires with diameters of a few hundred nanometers can support
several SPP modes; these are categorized into bound and leaky modes.27,36 The bound mode is localized at the substrate− metal interface, while the leaky mode is localized at the air− metal interface. In general, the propagation constant of the leaky mode decreases as the dimensions become smaller, which means that the mode becomes leakier as the propagation length decreases.36 Previous measurements and modeling have demonstrated that both the bound and leaky modes can be excited by parallel and perpendicular polarizations in chemically synthesized nanowires.26 Because both the bound and leaky modes suffer Joule losses in the metal, they can be imaged by the transient absorption technique (which detects excited electron−hole pairs produced by dephasing of the SPP modes). However, the transient absorption images and line profile analysis presented above will predominantly provide information about the SPP mode with the longer propagation length. To obtain quantitative information about SPP propagation in our experiments, the Au nanobars were modeled using finite element methods implemented with COMSOL Multiphysics.24,26,27,29,35 In this study, we simulated infinitely long gold nanowires with a rectangular cross section. The height and 8605
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Figure 4. Supported plasmon modes. (a) Intensity profiles of three lowest order SPP modes supported by a gold nanobar with AR = 1 on a glass substrate. (b) Phase constant β and (c) propagation length L as a function of width in gold nanobars with different aspect ratios. The blue circle in panel c shows the range of propagation lengths measured for the larger nanobars.
except for a sign change in the E(1,1) mode). The E(1,1) mode has a cutoff at an edge length of around 800 nm. Similar to the SPP modes supported by circular metallic nanowires,26 for a vertically propagating laser beam in our scheme (see Figure S6), the E(0,0) and E(1,0) modes can be excited by light polarized parallel to the long axis of the nanobar, while the E(0,1) and E(1,1) modes can be excited by perpendicularly polarized light. The presence of the glass substrate breaks the symmetry of the structure and the corresponding supported mode profiles. The substrate effect can be qualitatively interpreted using an “image charge” picture.27 The primary SPP modes (E(0,0), E(1,0), E(0,1), and E(1,1)) hybridize with the image charges in the substrate surface, leading to a new set of SPP modes as shown in Figure 4a (denoted as H0, H1, and H2). As elaborated by Xu et al.,27 the H0 mode comes from an in-phase coupling between the E(0,0) and E(1,0) modes and is a bound mode with the electric field confined in the substrate region. On the other hand, the H2 mode comes from an out-of-phase coupling between the E(0,0) and E(1,0) modes, with the electric field leaking into the air region. Since the E(0,0) and E(1,0) modes can be excited by parallel polarized light, so can the H0 and H2 modes. Similarly, the H1 mode comes from coupling between the E(0,1) and E(1,1) modes and, therefore, can be excited by perpendicularly polarized light. Plots of the phase constant β and propagation distance L as a function of nanobar width are shown in Figure 4b and c, respectively, for substrate supported nanobars with different aspect ratios. For the H0 mode, the phase constant β is almost constant, and the propagation length L only increases slightly from 8 to 10 μm for widths between 200 and 1000 nm. Changing the aspect ratio has a negligible effect on the propagation distance for the bound mode. For the leaky mode H2, the propagation lengths are quite sensitive to the dimensions. The propagation distance increases with increasing width at a set aspect ratio. On the other hand, for a set width, the propagation distance increases with decreasing aspect ratio
width of the cross sections were chosen to be in the range of sizes measured in the AFM experiments, and the aspect ratio of the cross section was varied between 1 and 2. The nanobars are supported on a glass substrate with a refractive index of 1.5. The relative permittivity of gold was taken from Johnson and Christy, and set to εr = −24.13 + 1.51i for 800 nm wavelength.37 In order to perform a finite element analysis of the waveguide structure, the infinite air and glass substrate that surrounds the metal core has to be truncated. A circular perfectly matched layer was used as the boundary conditions to reduce reflections. The calculation domains were discretized in a mesh of small finite triangular elements. A high mesh density and a large calculation domain were used to ensure the convergence of the calculated propagation constant, which is defined by a complex wave vector k0 = β + iα, with β and α being the phase and attenuation constants, respectively. The propagation constants for the different modes were obtained from the finite element calculations through mode analysis. The propagation length L is obtained by L = 1/(2α).27,29 Note that, in all calculations, the corners of the metal core are rounded to avoid abrupt structural discontinuities that can lead to artifacts in the finite element analysis.35 A radius-of-curvature of 10 nm was used for the majority of the calculations.27,29,35 To understand the supported SPP modes in rectangular gold nanobars on a glass substrate, we first identified the supported modes in the nanobar embedded in a homogeneous medium. The intensity profiles of the four fundamental SPPs modes (E(0,0), E(1,0), E(0,1), E(1,1)) for a Au nanobar in air are shown in Supporting Information Figure S5, and the corresponding phase constant β and propagation length L are shown in Figure S6. We label the modes according to the nomenclature described by Berini and Bozhevolnyi.35,38 The E(1,0) and E(0,1) modes correspond to charge oscillations in the vertical and horizontal plane, respectively, and the E(0,0) and E(1,1) modes are axially symmetric (the charge oscillations remains unchanged after a 90° rotation around the nanobar long axis, 8606
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Figure 5. SPP propagation and coupling. (a) Scattered light image of the gold nanostructure. (b) AFM image of the nanostructure and an enlarged AFM image of the gap. (c and d) Transient absorption images with pump excitation parallel and perpendicular to the nanobar long axis, respectively. (e and f) The corresponding SPP propagation line profiles (blue lines) along the nanobar axis and across the gold plate extracted from parts c and d. Fits to the linear portions (red lines) in both the gold nanobar and the plate give estimates of the SPP propagation lengths.
The calculated propagation distances for the bound (H0) mode in nanobars with widths smaller than 500 nm are slightly shorter than those determined in our measurements. We attribute this to a corner rounding effect. For the leaky H2 mode, the calculated propagation lengths are relatively insensitive to the radius of curvature of the corners, see Figure S8 in the Supporting Information. However, the calculated propagation lengths for the bound H0 mode increase with increasing radius of curvature at the corners. For example, for a nanobar with an edge length of 300 nm, the calculated propagation length for the bound mode is 8 μm for a radius of curvature of 10 nm, and 15 μm for a radius of curvature of 100 nm. The green lines in Figure 3c show the calculated propagation lengths for the H0 mode for nanobars with different radii of curvatures at the corners. These lines essentially capture the spread of propagation lengths measured for the smaller nanobars, implying that the variation in propagation lengths for these nano-objects is due to corner rounding effects. Note that nanoparticles with pentagonal and hexagonal cross sections are also present in our samples. The plasmon propagation lengths for these different shapes are very similar to those for the rectangular gold nanobars with identical sizes; see Figure S9 in the Supporting Information. We now examine the polarization dependence of the experiments. From the calculations, only the H1 mode should be excited by perpendicularly polarized light. However, there is a cutoff for this mode at around 800 nm size, which is larger than most of the nanobars interrogated in our experiments. Thus, we think that the signal in the perpendicular excitation experiments is due to the H0 and H2 modes, and that these modes are excited due to the irregular end geometries of the
(i.e., as the height is increased while maintaining the width constant). This is because the electrical field tends to be confined in the air region with increasing particle size, which reduces the Joule losses in metal nanostructures.27 In Figure 4 the dashed blue curve shows the range of measured propagation lengths for the larger nanobars in our experiments (widths greater than 500 nm, black symbols in Figure 3b and c). Thus, the calculated results for the leaky mode H2 capture the observed propagation lengths for the larger nanobars, which implies that the leaky mode is the dominant mode detected in these nanostructures. For nanobars with widths smaller than 500 nm, the leaky mode is damped quickly due to Joule losses.36 The propagation lengths for the smaller nanobars are shown in Figure 3b and c as the red symbols. These experimental data are consistent with the calculated values for the bound mode H0, which shows that the bound mode is the dominant mode detected for the smaller nanobars. The assignment that the larger nanobars support the leaky mode and the smaller nanobars support the bound mode is confirmed by the scattered light patterns created by the SPP modes (see Supporting Information Figure S7). In the larger nanobar in this figure, leakage radiation is visible in the form of two lines located on either side of the nanobar,28,29 while for the smaller nanobar the SPP mode only couples to far field emission at the end facets.10−12,25 It is important to note that we believe that both the bound and leaky modes are excited in our experiments for all the nanobars, but the transient absorption images display the mode with the longer propagation length. Thus, the line profiles report on the leaky mode for the larger nanobars, and the bound mode for the smaller nanobars. 8607
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nanobars, which can be seen in the AFM and SEM images.24 This explains why the propagation lengths are identical for the parallel and perpendicular polarization experiments but the signal is weaker for perpendicular excitation. During the course of these experiments, SPP coupling between two nearby nanostructures was also observed. Figure 5a and b show scattered light and AFM images of a nanobar in close contact with a nanoplate. The dimensions of the nanobar determined from the AFM measurements are 600 nm × 500 nm × 11 μm, and the nanoplate is 50 nm high and separated from the gold nanobar by ca. 300 nm. Figure 5b shows an enlarged view of the gap structure. SPP modes in the nanobar were launched by excitation at the point indicated by the arrows. Under both parallel and perpendicular excitation, SPPs are excited and propagate along the nanobar, as shown in Figure 5c and d. The corresponding propagation distances are analyzed in Figure 5e and f, respectively. The SPP propagation distance (∼12.5 μm) in the gold nanobar is consistent with the calculation in Figure 4. Interestingly, the images show that the SPPs travel across the gap and propagate in the gold nanoplate. Note that in principle these measurements could give an estimate of the SPP coupling efficiency between the two nanoobjects. However, the transient absorption response of the nanobar and nanoplate will be different, which means that the signal intensity cannot be used to determine the coupling efficiency in this case. The transient absorption images also show that the propagating SPPs in the nanoplate are highly directional. This directionality in the motion of the SPPs in the nanoplate is reminiscent of the directional SPP emission discussed in ref 28; it is a consequence of the fact that the end facets do not act like a point dipole. In addition to the size and shape effect for SPP propagation, the surrounding environment also changes the propagation properties. This was examined by changing the surrounding environment from air to microscope immersion oil. The SPP propagation and coupling for the nanostructures in Figure 5 are displayed in Supporting Information Figure S10. The SPP propagation and coupling are severely damped with immersion oil. The COMSOL calculations presented in Figure S11 show that the propagation lengths of all the supported modes are decreased compared to the nanobars in air. The measured propagation length of 5.4 μm for the nanobar in Figure S10 is in good agreement with the calculated value of ∼6 μm.
Compared to the previously studied chemically synthesized gold nanowires and lithographically defined gold stripes,5,18,19,21,38 the gold nanobars in our work share both the high crystallinity and smooth surfaces of the chemically synthesized structures and the larger geometry of the stripes. This creates nano-objects with long SPP propagation distances, matching the values calculated from the tabulated dielectric constants of gold.37 Thus, these structures may find applications as components for plasmonic waveguides.
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ASSOCIATED CONTENT
S Supporting Information *
Synthesis of gold nanobars, size distribution, SPP dynamics, length dependent SPP propagation, SPP mode profiles of gold nanobars in a homogeneous environment, SPP propagation images, corner rounding effect, cross-sectional shape effect, and environment effect on the properties of SPP propagation. This material is available free of charge via the Internet at http:// pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was supported by the National Science Foundation (CHE-1110560), the Office of Naval Research (Award No.: N00014-12-1-1030), and the University of Notre Dame Strategic Research Initiative.
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REFERENCES
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SUMMARY AND CONCLUSIONS We have used scanning transient absorption microscopy to examine SPP propagation in chemically synthesized gold nanobars on a glass substrate. The nanobars are crystalline and show SPP propagation lengths of ∼12 μm, independent of the excitation polarization. The dependence of the propagation length on dimensions was determined by correlating the optical experiments with AFM measurements. Analysis of the nanobar SPP modes by finite element calculations shows that the leaky mode is detected in the large nanostructures, while the bound mode is detected in the smaller nanostructures. The combination of finite element analysis and transient absorption experiments thus allows us to fully characterize the SPP modes in these systems. We have also observed highly directional SPP propagation and efficient coupling between a gold nanobar and a nearby nanoplate separated by ∼300 nm. Finally, we demonstrated that the propagation length and coupling efficiency are decreased by increasing the refractive index of the surrounding, namely from air to oil. 8608
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dx.doi.org/10.1021/jp501629w | J. Phys. Chem. C 2014, 118, 8603−8609
