Plasmonic Coupling in Silver Nanocomposite Glasses - The Journal

Article pubs.acs.org/JPCC

Plasmonic Coupling in Silver Nanocomposite Glasses Mariana Sendova† and José A. Jiménez*,‡ †

Optical Spectroscopy & Nano-Materials Lab, New College of Florida, Sarasota, Florida 34243, United States Department of Chemistry, University of North Florida, Jacksonville, Florida 32224, United States

‡

ABSTRACT: This work demonstrates that an enhanced plasmonic response can be attained and tuned for Ag nanocomposite glasses via a real-time in situ control of the plasmonic coupling between closely spaced Ag nanoparticles (NPs). The result is achieved by a two-step modification of Ag NP-doped glasses. First, confined “super-nucleation” domains are induced by highfluence nanosecond laser irradiation promoting photofragmentation of Ag NPs in the matrix. Photoluminescence and Raman scattering spectroscopies are put to use in assessing the effects of laser treatment. Subsequently, a particle regrowth process leading to the development of strongly interacting NPs is activated during an in situ isothermal processing, which also allows for the tuning of the optical response of the material in real time. An important finding is that the post-laser thermal treatment results in a significant narrowing of the Ag NP size distribution as revealed by transmission electron microscopy. Further, valuable insights on the laser-induced “super-nucleation” and NP regrowth process leading to plasmonic coupling are obtained through a quantitative assessment employing the theoretical model for NP aggregates from Quinten and Kreibig, together with the Kolmogorov−Johnson−Mehl−Avrami (KJMA) theory of phase transformations. The activation energy of the post-laser NP regrowth process was estimated at 0.8(±0.1) eV, based on the solid-state precipitation kinetics. The current report is expected to open new avenues of research on plasmon-enhanced processes inside dielectrics with relevance to both fundamental and applied nanoscience.

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INTRODUCTION Silver nanoparticles (NPs) embedded in various optically transparent matrices such as silica films1−3 and glasses4−6 are of great interest to the scientific community due to their potential application in the area of photonics. Glass hosts based on phosphate matrices are exceptionally attractive due to their high metal solubility,4 which allows for the tuning of material optical properties based on the dopants concentration.6 The optical properties of the doped glasses would depend not only on the chemical composition and structure of the matrix, but on the NPs’ morphology, size, and degree of interaction between NPs.7 Moreover, the NP average size and size distribution are products of a dynamic crystal nucleation and growth process leading to the formation of the nanoscale phase of the metal in the solid solution. Therefore, as any other phase transition process, NP growth depends on the degree of supersaturation, nucleation conditions, and most importantly on material processing parameters.6,8 A typical approach to doping glass with metallic NPs is based on having first the metal introduced into the matrix (e.g., in the © 2012 American Chemical Society

form of ions) and subsequently precipitating the NPs during thermal processing (e.g., via chemical reduction processes).6,8−11 On the other hand, laser irradiation has been employed in a variety of treatments aimed for tailoring material properties. Depending on the type of material and the laser wavelength, fluence, and pulse duration, the following modifications have been reported for metal:dielectric composites: particle size reduction;12,13 particle dissolution and bleaching;14,15 formation of luminescent metal clusters;16 NP precipitation;17 and particle shape modification.18,19 The latter is of particular interest, since it has been employed for obtaining anisotropic particle shapes thereby resulting in extended spectral ranges of the plasmonic response of the nanocomposites due to the resonances associated with different axes in the NPs.18,19 An enhanced plasmonic extension covering a broad spectral range from the UV to the visible, Received: May 16, 2012 Revised: July 20, 2012 Published: August 2, 2012 17764

dx.doi.org/10.1021/jp304778z | J. Phys. Chem. C 2012, 116, 17764−17772

The Journal of Physical Chemistry C

Article

cence spectroscopy, and Raman scattering measurements, carried out at room temperature. A CRAIC Technologies QDI 2010 microspectrophotometer (MSP) was used to collect optical extinction spectra. Photoluminescence spectroscopy was carried out with a Photon Technologies International steadystate spectrofluorometer equipped with a Xe lamp. Raman spectra were acquired with a Leica DMLP microscope coupled to a Raman system from Kaiser Optical Systems Inc. The RamanRxn1 analyzer incorporates the thermoelectrically cooled charge-coupled device detector for maximum sensitivity, Invictus near-infrared semiconductor laser operating at 1.58 eV (785 nm) with holographic grating to provide fast, simultaneous full spectral collection of Raman data. The spectral resolution of this Raman system is about 5 cm−1. The MSP was equipped with a Linkam THMS600 heating stage in order to conduct in situ optical extinction measurements of laser-irradiated glasses during HT in air atmosphere.3,6 Measurements were performed with a 10× objective on 50 μm × 50 μm sample areas, and particular attention was given to keep sample position and conditions constant during the fixedtemperature experiments. Samples were heated to the desired temperatures at a rate of 50 deg/min as performed previously for the assessment of the optical evolution of melt-quenched glasses during isothermal treatments.6 The HT temperatures employed were 520, 550, and 580 °C; these were above the glass transition temperature, Tg, of the melt-quenched glass determined to be 508 °C as measured by a differential scanning calorimeter (TA Instruments Q20) at a heating rate of 10 deg/ min. The optical extinction data were collected at 1 h intervals with a total holding time of 8 h. In the text, the conditions are indicated as a subscript for the HT holding time in hours, and a superscript for the temperature, HTTtime. For example, HT580 8 indicates that HT was performed at 580 °C for 8 h. Transmission electron microscopy (TEM) was carried out for NP-doped glasses (i.e., nanocomposite glass prior to laser irradiation, and irradiated glass after the thermal modification), in a JEOL 2010F scanning transmission electron microscope. Specimen preparation was done by scraping films with a diamond pen and subsequent deposition on ultrathin holey carbon-coated copper grids.

and if possible to the infrared, is in fact a desirable output for applications in nonlinear optics,20−22 metal-enhanced spectroscopy,23,24 and solar cells technology.25,26 However, the inherent difficulty in the preparation of anisotropic shapes of NPs, especially when embedded in dielectrics, calls for alternate ways for obtaining such an enhanced plasmonic response. Accordingly, as a novel approach, the clustering of metal NPs and consequent plasmonic coupling has been proposed as a means for the tuning of optical properties at the nanoscale.27,28 Nevertheless, to the best of our knowledge, such plasmonic coupling has not been straightforwardly realized and studied for metallic NPs embedded in a robust inorganic solid-state matrix such as glass. In this work, it is demonstrated how an enhanced plasmonic response can be attained and tuned for Ag nanocomposites, via control over the electrodynamic interactions between closely spaced Ag NPs in a temperature- and time-dependent fashion. Such a result is achieved by a two-step modification of Ag NPdoped glasses, which were prepared by melting and heat treatment (HT) processes. First, confined “super-nucleation”29 domains are induced by fragmentation of Ag NPs photoinduced by high-fluence ns laser irradiation. The adopted term “super-nucleation” (i.e., Müller et al.29) was deemed appropriate herein because of the remarkable effect the laser irradiation shows in producing nonplasmonic Ag particle nuclei. Subsequently, a particle regrowth resulting in strongly interacting NPs is promoted during an in situ isothermal processing, which also allows for the tuning of the optical response of the material in real time.3,6 Furthermore, valuable insights on the laser-induced “super-nucleation” and NP regrowth leading to plasmonic coupling are obtained by a quantitative assessment employing the theoretical model for NP aggregates from Quinten and Kreibig30 together with the Kolmogorov−Johnson−Mehl−Avrami (KJMA) theory of phase transformations.31−33 We believe the current report opens new avenues of research on plasmon-enhanced processes inside dielectrics with relevance to a wide array of applications. Moreover, it also presents a new system for fundamental studies of energy exchange processes and ultrafast relaxation dynamics in coupled NPs, something not yet carried out for interacting NPs embedded in an inorganic solid host.27 This has been mainly because of the inherent difficulty in attaining such type of material up to date, something now feasible as demonstrated in the present study.

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RESULTS AND DISCUSSION Let us begin by describing the Ag nanocomposite glasses which are the subject of this work. In a previous study, it has been established that varying the degree of supersaturation in the phosphate-based glass system by simultaneously changing the silver and tin (reducing agent) concentrations alters the NP nucleation and growth conditions.6 Thus, coupled to a real-time monitoring during thermal processing by in situ optical microspectroscopy, the variation in dopant concentration provided important means for the tuning of material optical properties for photonic applications.6 Herein, the overall metal phase concentration and the matrix chemical composition are kept unaltered, utilizing 4 mol % of both Ag2O and SnO. At this dopant concentration, the glass system has shown a remarkable ability for incorporating relatively large, noninteracting Ag NPs, resulting in significant red shifts in the NPs’ absorption maxima with increasing particle size.6,34 Such outcome is exploited herein in selecting an appropriate sample with plasmon resonance peak near the laser photon energy at 2.33 eV used herein for material modification. Figure 1, trace 1, shows the extinction spectrum of the selected Ag NP-doped glass,34 which exhibits a dipole

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EXPERIMENTAL SECTION Phosphate-based glasses of the P2O5:Al2O3:CaO:SrO:BaO type with an additional 4 mol % of Ag2O along with reducing agent SnO in the same amount were prepared by melting and HT processes.34 An Ag nanocomposite glass (∼0.4 mm thick) exhibiting a surface plasmon resonance (SPR) peak around 2.69 eV was obtained for the present work, which was subsequently subjected to laser irradiation as described below. Further information on the time evolution of material optical properties and NP parameters upon thermal treatments can be found elsewhere.6 Material modification via laser irradiation was achieved by linearly polarized laser pulses from a 5 ns New Wave Research Nd:YAG laser, operating at 2.33 eV (532 nm), 10 Hz, at a laser fluence of 150 mJ/cm2 for 30 min. The laser emission is selected so that the energy is absorbed by Ag NPs in the composite material and not directly by the glass matrix itself, which has a bandgap of ∼4.4. eV.35 The effect of laser irradiation was assessed by optical extinction, photolumines17765



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Figure 1. Optical extinction spectra of Ag nanocomposite glass before (trace 1) and after (trace 2) laser irradiation.

resonance peak around 2.69 eV with a full-width at halfmaximum (fwhm) of about 0.35 eV. The position of such a plasmon absorption peak to fairly lower energy is indicative of the presence of large NPs with size beyond the quasi-static regime of Mie theory.6,34,36 Accordingly, the spectrum also shows the quadrupole resonance mode34,36 at about 3.45 eV. An additional absorption feature is observed around 3.00 eV. Since the relatively low degree of supersaturation employed is known to produce a rather broad NP size range in connection with concurrent nucleation and growth processes,6 the spectral feature around 3.00 eV is believed to be due to the presence of a small-sized NP population in the glass. This is in fact supported by TEM micrographs for such nanocomposite as shown in Figure 2a, with the corresponding particle size histogram presented in Figure 2b. It can be clearly seen that the Ag particles are spherical and have a quite large variation in diameter, d, from 1.9 to 90 nm. The well-expressed bimodal particle size distribution allows for consideration of two particle subsets (small d < 20 nm, and large d > 20 nm particle subsets) on which separate statistical analysis can be performed. The analysis carried out on the smaller particle subset indicates an average diameter of 4.0(±1.4) nm. The average diameter of the large particles appears to be around 55(±19) nm. Following laser irradiation, the plasmonic silver particles vanish as evidenced by the spectrum in Figure 1, trace 2. The photofragmentation of metal NPs resulting in particle size reduction and bleaching of color centers is a well-known phenomenon,12−16,37,38 where in the regime of ns pulse irradiation, it is widely accepted that particle dissociation occurs via the heat-transfer mechanism.12,13,37,38 As will become apparent from the further post-laser HT studies (vide infra), the laser treatment has produced stable nuclei, in the form of small, nonplasmonic particles, or few-atom clusters. The presence of “dissolved” silver atoms expelled from the NPs is also conceivable. As shown by Pyatenko et al.38 for NP colloidal systems, electron ejection as a mechanism of particle size reduction in the regime of irradiation with ns pulses from the second harmonic emission of a Nd:YAG laser is highly unlikely. Accordingly, regarding the nature of the silver fragments, the heating mechanism suggests that these are most likely neutral nonplasmonic species (clusters/atoms). This is in fact supported by the herein reported photoluminescence results as discussed below. Photoluminescence spectroscopy is a well-established nondestructive optical characterization technique capable of revealing reliably the chemical and physical states of ionic

Figure 2. (a) TEM images and (b) the corresponding histogram of Ag nanocomposite for which the extinction spectrum is shown in Figure 1, trace 1. The inset in panel b shows an enlargement of the region corresponding to the larger Ag particles.

silver species in solid-state matrices.3,10,34,35,39,40 Thus, the technique was employed herein in order to further study the nature of the nonplasmonic silver fragments generated by the laser treatment. Figure 3 shows photoluminescence excitation spectra for the glass with extinction spectra in Figure 1, before and after the irradiation, recorded by monitoring emission at 3.54 eV (350 nm). The two excitation spectra appear analogous, with a band maximum around 4.51 eV (275 nm). Such type of excitation peak has been similarly reported by Jiménez et al.34,41−43 for several glasses of the phosphate-based

Figure 3. Photoluminescence excitation spectra for Ag nanocomposite (optical extinction spectra in Figure 1) before (trace 1) and after (trace 2) laser irradiation. The spectra were recorded by monitoring emission at 3.54 eV (350 nm). 17766



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dopants.43 The bands around 1298 and 1187 cm−1 are assigned to asymmetric [νas(PO2)] and symmetric [νs(PO2)] out of chain PO2 stretching, respectively, in the Q2 species. The band around 699 cm−1 is assigned to the in-chain P−O−P symmetric stretch [νs(POP)]. According to refs 44 and 46, a shift in peak position for the νs(POP) and νs(PO2) symmetric stretching vibrations, typically greater than 1 cm−1, can be taken as an indicator of glass structural modification. Therefore, the data presented in Figure 4 suggest that no significant change in glass structure is induced by the ns pulses in the present study. This is likely due to the relatively long pulse duaration employed, the energy of which is predominantly absorbed by the NPs in the matrix. Therefore, the Raman study coupled to the photoluminescence assessment discussed previously indicate that the laser irradiation is merely affecting the NPs in the glass host, inducing their fragmentation into the rather small nonplasmonic neutral silver species, e.g. clusters and/or atoms. As will be subsequently shown, the post-laser HT studies are also consistent with these results. The detailed analysis performed herein on the isothermal SPR band evolution after the laser irradiation provides insights not only on the post-laser mechanism of particle growth, but on the laser-assisted dissolution process itself. The isothermal particle regrowth after the photofragmentation is followed in real time by the evolution of the SPR band. Figure 5 shows the gradual SPR isothermal time evolution for (a) HT520 time, (b) 580 , and (c) HT . On the basis of the band shape, two HT550 time time distinct periods in the SPR evolution were noticed: (i) a first stage exhibiting a single Lorentzian band shape and (ii) a second stage characterized by a double-band spectral envelope. Classified within stage (i) by well-known band shapes typical of noninteracting NPs6 are the lowest traces in Figure 5a−c. These spectra show the first recovered SPR bands just after 550 reaching the HT temperatures of 520 (HT520 0 ), 550 (HT0 ), and 580 °C (HT580 ), where the actual time length of data 0 collection is the temperature ramp-up time, which at a rate of 50 deg/min is around 11 min. After the elapse of the ramp-up time, the temperature is maintained constant and the evolution of the SPR band is monitored at time intervals of 1 h. The bands appeared to be fitted well with a single Lorentzian curve for up to 3 h after reaching 520 °C, and 1 h after reaching 550 °C; at 580 °C, the highest temperature studied herein, only the first SPR band obtained at t = 0 could be fitted with a single Lorentzian line shape (fitting results not shown). Subsequently, a well-pronounced spectral feature appears at the lower energy wing of the SPR band and gradually develops in a temperatureand time-dependent fashion. This relates to stage (ii) mentioned above, and is connected to the real-time evolution of plasmonic coupling between Ag NPs as discussed below in detail. Theoretical calculations performed in the dipolar and quadrupolar approximations for the absorption and elastic scattering of light by various silver particle aggregates reported by Quinten and Kreibig30 have shown double-peak SPR bands. The lowest energy peak is associated with the longitudinal eigenmode and the highest energy peak is associated to the transverse eigenmode of each aggregate. In the current study, the presence of silver particle aggregates is confirmed by TEM as shown in Figure 6a for the sample after HT at 580 °C for 8 h (HT580 8 ). Statistical analysis of particle size was carried out and the corresponding histogram is presented in Figure 6b, overlaid with that for the sample prior to laser irradiation. It is observed that the NPs are quite small and considerably uniform in

system containing 4 mol % of Ag2O and SnO dopants. Herein, a contribution to the excitation band toward the high-energy wing around 4.9 eV is expected owing to electronic transitions in 2-fold-coordinated Sn centers, i.e. from the ground singlet state S0 to the first excited singlet state S1.41 Yet, the peak around 4.51 eV is known to be due to 4d10 → 4d9 5s1 transitions in single Ag+ ions.34,41−43 Other complex ionic 2+ multimeric species Agδ+ n such as the Ag2 centers are known to have dissimilar luminescent properties,35,39,42 none of which have been observed in our experiments either before or after the laser treatment. Therefore, given the similar luminescent properties of the glass before and after laser irradiation, we rule out significant formation of ionic silver clusters as a result of the photofragmentation process. Raman spectroscopy is typically the technique of choice for studying the effects of laser irradiation on the structure of phosphate glasses.44−46 It is well-known that phosphate-based glasses contain PO4 tetrahedra which can be connected via bridging oxygen atoms, i.e. through P−O−P bonds at their corners.47 Depending on the number of bridging oxygen atoms with the neighboring tetrahedra, three types of tetrahedral species can be distinguished: Q1, tetrahedra with one bridging oxygen; Q2, tetrahedra with two bridging oxygens; and Q3, tetrahedra with three bridging oxygen atoms. The phosphate chains in the glass matrix are linked in the network through ionic bonds between nonbridging oxygen terminals and metal cations. Fletcher et al.44,46 have for instance utilized the shift in peak position of several Raman scattering bands associated to distinct tetrahedral species for studying the effects of femtosecond laser pulses in zinc phosphate glasses. Raman scattering spectra were therefore obtained herein in order to assess the possibility of glass matrix modification via the high-fluence ns laser irradiation. Figure 4 shows the spectra obtained for the Ag

Figure 4. Raman scattering spectra for Ag nanocomposite (optical extinction spectra in Figure 1) before (trace 1) and after (trace 2) laser irradiation.

nanocomposite glass (extinction spectra in Figure 1), before and after the laser treatment. Interestingly, analogous to the case of the photoluminescence measurements presented above, the two spectra in Figure 4 appear similar. No significant shift in the position of the bands is observed: Raman scattering bands appear around 699, 1187, and 1298 cm−1 for the glass both before and after the laser treatment. The position of these bands is consistent with the structural study carried out recently by Raman spectroscopy in our group for several glasses of the phosphate-based system containing 4 mol % of Ag2O and SnO 17767



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Figure 5. Real-time SPR band evolution of laser-irradiated glass monitored during HT at 1 h intervals for 8 h at (a) 520, (b) 550, and (c) 580 °C.

Therefore, electrodynamic coupling between the growing particles increases with time, which in turn affects their optical spectra shape and time evolution. The current study attempts a quantitative analysis of the particle growth through the plasmonic coupling in the nanocomposite system under consideration. Through fitting the optical density spectral envelope with two Lorentzians, e.g. Figure 7 inset, the peak positions of the high- and low-energy components were extracted and their separation, ΔE, was plotted in Figure 7 as a function of time for each temperature separately. The theory of light scattering by particle aggregates developed by Gérardy and Auslos49 was applied by Quinten and Kreibig30 to compute the total extinction loss spectra of linear chains of 10 identical nanometer-sized silver spheres with radii of 20 nm embedded under vacuum at varied relative nextneighbor (RNN) distances. The RNN is defined as the nextneighbor particle center-to-center distance, l ,in units of particle radius, r

diameter ranging from 1.5 to 4.9 nm with an average of 2.9(±0.6) nm. In addition, statistical analysis of the particle-toparticle separation, i.e. nearest-neighbor distance (center-tocenter), was carried out. The next-neighbor distance histogram is shown in Figure 6c; an average value of 3.9(±0.9) nm was obtained. The comparison of the statistical particle mean diameter and interparticle distance indicates that for HT580 8 , the particles, on average, are approaching the coalescence point, which can be defined by equating the average value of the distance between the centers of two next-neighbor particles to the average value of the particle diameter. Moreover, the TEM images of the post-laser regrown NPs (HT580 8 ) indicate that the NPs are not uniformly distributed in the glass matrix; they are rather confined in certain areas of the irradiated sample, referred to herein as “super-nucleation” domains. These findings strongly support the main subject of this investigation, namely the spectroscopic analysis of the plasmonic coupling in the samples during the HT following the laser irradiation. within a single “superSignificant particle density at HT580 8 nucleation” domain suggests a strong electrodynamical interparticle interaction revealing itself in broadened and convoluted SPR bands. On the basis of the optical and TEM features, it can be suggested that the laser-assisted NP dissociation creates a large degree of supersaturation for the metallic component, not uniformly throughout the sample, but in volumes restricted to the locality of the dissolved particles only. This is evident from the TEM image in Figure 6a, where random areas without many particles are observed as compared to other densely populated areas. Under such circumstances, diffusion-based growth in a finite volume should take place in order for the supersaturation to be decreased, leading to an increase in particle size.48 Since the nuclei are very close to each other, the next-neighbor distance is comparable to the particle size at HT580 8 , Figure 6, panels b and c, as estimated above.

RNN =

l r

(1)

Therefore, almost-touching spherical NPs have an RNN value around 2. The computed spectra have two local maxima.30 The authors reported the peak energy splitting (separation), ΔE, as a function of the RNN. Their data are summarized in Figure 8 with unfilled circles. Empirically, the RNN vs plasmonic splitting (ΔE) dependence may be described well with a single decaying exponential function (shown as a solid line in Figure 8) with a characteristic exponential factor of 0.3 eV, a preexponential factor of 3.5, and a y-asymptote of 1.9. The correlation coefficient of the fitting curve has a value of +0.998. The largest peak splitting occurs for almost touching spheres (RNN ≈ 2), whereas peak splitting vanishes for RNN > 5.4. At 17768



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Figure 7. Peak-splitting energy as a function of HT holding time for 520 (triangles), 550 (squares), and 580 °C (circles). The inset shows the two Lorentzian component deconvolution of the SPR spectrum collected after 2 h at 580 °C.

Figure 8. The relative next-neighbor distance, RNN (unfilled circles), as a function of the SPR splitting energy, ΔE, according to Quentin and Kreibig;30 the solid line is a first-order exponential decay fit. The square represents an experimental data point from this study. The inset shows the spectrally determined RNN data as a function of HT holding time for 520 (triangles), 550 (squares), and 580 °C (circles), along with the numerical fits (solid lines) with eq 2.

Figure 6. (a) TEM image for Ag nanocomposite after the laser irradiation followed by HT8580. The corresponding particle size distribution histogram is shown in panel b together with the data for the material before laser irradiation for comparison. Panel c shows the histogram of the nearest-neighbor distance distribution after the laser irradiation and HT580 8 .

deconvolution of the HT580 8 spectrum was estimated at around 0.6 eV (the last data point of the 580 °C isotherm, Figure 7, solid circles). Therefore, it may be concluded that the experimental point (Figure 8, solid square symbol) reported herein seems to agree with the theoretical dependence found for the 10-particle chain of the theoretical model from Quinten and Kreibig.30 Thus, an opportunity was provided with the fitted exponential function, the solid line in Figure 8, to be used as a conversion function from the spectroscopically determined peak splitting to the corresponding structural RNN value of the particle aggregates existing at each point in time from the family of isotherms, Figure 7. Shown in the inset of Figure 8 are the isothermal time dependencies of the converted RNN values as discussed above. In turn, each one of the RNN isotherms can be fitted with a correlation factor not smaller than +0.999 to a single decaying exponential function

large RNN values the shape of the SPR becomes like that of noninteracting particles (e.g., lowest traces in Figure 5a−c). Therefore, spectral peak splitting reveals the degree of plasmonic interaction between the next-neighbor particles, which in turn can be measured independently by TEM and characterized by the RNN value defined with eq 1. The solid square point on the same graph represents two independent experimental results (for the x- and y-coordinate values) obtained in this study in the following way. From the TEM analysis (vide supra) on the sample heat-treated at 580 °C for 8 h (HT580 8 ) it was indicated that after irradiation and HT the particles are spherical with average diameter of 2.9(±0.6) nm, and the average center-to-center, next-neighbor distance is 3.9(±0.9) nm. Therefore, it was estimated by eq 1 that the RNN (y-value of the solid square point in Figure 8) is around 2.6(±0.3). In addition, the peak splitting, ΔE, (x-value of the same point) determined experimentally from the SPR band

RNN (t ) = y0 + A e−t / τ

(2)

where y0, A, and τ are parameters determined from the fit. Therefore, particle growth follows first-order kinetics, with a characteristic time τ with values of 143, 190, and 315 min for the 580, 550, and 520 °C isotherms, respectively. The 17769



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uncertainty from the fit in determining τ is 3% for HT580 and 6% for HT550 and HT520. Combining eqs 1 and 2, the following empirical expression for the time dependence of the NP radius, r(t), can be derived r (t ) =

l l = RNN (t ) y0 + A e−t / τ

under isothermal conditions was developed in the late 1930s by Kolmogorov,31 Johnson and Mehl,32 and Avrami33 and is wellknown as the KJMA theory. The isothermal VF data points discussed herein were fit (solid lines, Figure 9) with the KJMA equation (so-called Avrami equation), applied herein for the isothermal conversion process of the nanocomposite system from a nonplasmonic state right after the photofragmentation of NPs, to a plasmonically coupled state due to subsequent noble metal precipitation as

(3)

which in turn is used as an approximation of an isothermal particle volume growth function

n

VF(t ) = 1 − e(−kt )

3

4 4 l Vp(t ) = πr 3(t ) = π 3 (y + A e−t / τ )3 3 0

where k is the overall transformation rate, and n is the Avrami index. The knowledge of the Avrami coefficient, n, is helpful for understanding the mechanism of isothermal phase transformation.50 The three isotherms, Figure 9, are fitted with an Avrami index of 1 (correlation coefficient not less than +0.997) indicating that the NP precipitation kinetics can be described by a simple exponential function. Confined phase transformation processes in which one or more of the initial dimensions is finite tend to follow first-order kinetics, or the equivalent of having an Avrami index of 1.51 In fact, all evidence in this study, as discussed above, points in the direction of nanodomain formation of closely spaced finite-sized nuclei as a direct consequence of the laser-assisted particle dissociation. Therefore, after such a process, the necessary nucleation conditions are established for a confined, phase-transformation process, supporting the empirically established herein Avrami index of 1 and in agreement with TEM, Figure 6a. The investigated NP growth process can be considered as confined to the domains with densely created nucleidefined herein as “super-nucleation” domains. In turn, the localized high density of nonplasmonic nuclei existing prior to the isothermal particle growth resemble the conditions created by the high degree of local supersaturation with all its consequences for the particle growth mechanism and the particle size distribution.6 A similar first-order crystallization kinetics within confining domains was reported and discussed for polymer−carbon nanotube composites and confined diblock copolymers.29,52 Further on, the transformation rate, k, obtained as a fitting coefficient to the VF(t) data points with eq 7, is thermally activated and is assumed to follow Boltzmann−Arrhenius dependency,51

(4)

On the other hand, from eq 4, the maximum particle volume can be defined as the NP volume achieved for long enough time allowing the neighboring particles just to touch each other Vpmax = Vp(t ≫ τ ) =

4 l3 π 3 y0 3

(5)

The particle coalescence process that may happen after this point in time is out of the scope of the current study. The ratio of functions 4 and 5 is used as a characteristic relative volume fraction, VF, accounting for the isothermal NP growth process. Moreover, the isothermal time evolution of the NP volume fraction, VF(t), can be related to the empirically established decaying exponential function, eq 2, which in its own right is an isothermal time-dependent function of the interparticle distance, RNN(t): VF(t ) ≡

Vp(t ) Vpmax

=

⎛ 1 ⎞3 3 y = ⎜ ⎟ 0 ⎝ RNN (t ) ⎠ (y0 + A e−t / τ )3

(7)

y0 3

(6)

Further on, function 6 is utilized to convert the RNN values to VF values. The VF values obtained for each temperature/time data point from the respective RNN values employing eq 6 are plotted in Figure 9 (solid symbols). It is assumed that the time dependence of the experimentally estimated isothermal VF(t) of Ag NPs is directly related to the precipitation processes in the supersaturated solid solution. The theory of precipitation from supersaturated solid solutions

k(T ) = k 0e−Ea / kBT

(8)

where k0 is the pre-exponential coefficient, Ea is the activation energy for the transformation process, kB is Boltzman’s constant, and T is the temperature. An Arrhenius plot for the transformation rate ⎛E ⎞1 ln k = ln k 0 − ⎜ a ⎟ ⎝ kB ⎠ T

(9)

then can be used to determine Ea. The inset of Figure 9 shows a plot of the natural logarithm of the rate constant, k, for each temperature vs T−1, according to eq 9. The data were fitted with a straight line with a strong correlation coefficient of +0.98. From the slope, the overall activation energy of the domain-confined NP growth process is determined to be 0.8(±0.1) eV. Yet, further experiments are desired in order to establish how the laser fluence, photon energy, and pulse duration affect the nonplasmonic nuclei density and the activation energy for their plasmonic phase transformation. In a previous study of the same system with plasmonically noninteracting NPs, prior to any laser modification,48 by

Figure 9. Silver NP relative VF obtained from the RNN values via eq 6 as a function of time for 520 (triangles), 550 (squares), and 580 °C (circles); solid lines are fits with eq 7. The inset shows a plot of the natural logarithm of the rate constant determined from the fits vs the reciprocal absolute temperature (ln k vs T−1), eq 9; the solid line is a linear fit to the data. 17770



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ACKNOWLEDGMENTS Financial support from ARL-W911NF-09-2-0004 is gratefully acknowledged. We thank Kerry N. Siebein from the Major Analytical Instrumentation Center at University of Florida for TEM.

monitoring the isothermal SPR peak shift, the activation energy for the diffusion-based NP growth was estimated at 5.2 eV. Comparing the two activation transformation energies, it can be concluded that the laser-induced confined “super-nucleation” domains lead to a significant reduction of the overall NP growth activation energy, while the initial composition of the glass system remains unchanged. It can be suggested that in the presence of confinement, the achieved high nonplasmonic nuclei density is the main factor lowering the activation energy. Optically, the laser-induced nanodomains change the shape, position, and broaden significantly the SPR band, while narrowing the particle size distribution.

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CONCLUSIONS

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AUTHOR INFORMATION

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REFERENCES

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Plasmonic coupling has been effectively achieved and studied for Ag NPs embedded in a phosphate-based glass system, a robust inorganic solid-state material well suited for further explorations of fundamental and applied nature. The plasmonic coupling was attained by a two-step modification of Ag nanocomposite glasses, namely (1) an initial step of ns laser irradiation at photon energy of 2.33 eV and (2) a subsequent stage of isothermal treatments within the 520−580 °C range. Regarding step 1, absorption, photoluminescence, and Raman scattering spectroscopies were employed in assessing the effects of the laser treatment. The data suggest that the Ag NPs undergo photofragmentation into nonplasmonic Ag clusters and no structural changes are induced in the glass matrix as a result of the laser irradiation. The plasmonic coupling was thermally induced in stage 2 and monitored in situ by the temperature- and time-dependent spectral response. Further, it has been shown that the in situ monitoring of the post-laser SPR band evolution can be utilized as a viable real-time, nondestructive approach to study laser-induced “supernucleation” and the NP regrowth leading to plasmonic coupling. The data were analyzed quantitatively by employing the theoretical model for NP aggregates from Quinten and Kreibig,30 together with the Kolmogorov−Johnson−Mehl− Avrami theory of phase transformations. The analysis yielded an activation energy for the post-laser NP regrowth process of 0.8(±0.1) eV, a value significantly lower than the one estimated previously for the NP growth prior to laser irradiation. Another important finding is that along with the formation of Ag NP aggregates, the particle size distribution has been narrowed significantly. On the other hand, the SPR band has been broadened considerably as a result of electrodynamic interactions between closely spaced NPs, thus charting new avenues for the experimental tuning of plasmonic nanocomposites. These materials may become useful for applications in for instance nonlinear optics and metal-enhanced spectroscopies, as well as for fundamental studies regarding energy exchange processes and NP relaxation dynamics in dielectric-embedded NP aggregates.

Corresponding Author

*Tel.: 1-904-620-1963. Fax: 1-904-620-3535. E-mail: jose. [email protected]. Notes

The authors declare no competing financial interest. 17771



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