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Coherent acoustic vibration of metal nanoshells C. Guillona, P. Langota, N. Del Fattia,b, and F. Vall´eea,b a Centre de Physique Mol´eculaire Optique et Hertzienne CNRS and Universit´e Bordeaux I, 351 cours de la Lib´eration, 33405 Talence, France and b Laboratoire de Spectrom´etrie Ionique et Mol´eculaire 7 CNRS and Universit´e Lyon I, 43 Bd. du 11 Novembre 1918, 69622 Villeurbanne, France 0 0 A. S. Kirakosyan and T. V. Shahbazyan 2 Department of Physics and Computational Center for Molecular Structure and Interactions, n Jackson State University, P.O. Box 17660, Jackson, Mississippi 39217, USA a J T. Cardinal and M. Treguer 0 Institut de Chimie de la Mati`ere Condens´ee de Bordeaux 1 CNRS and Universit´e Bordeaux I, 87 Av. du Dr. Albert Schweitzer, 33608 Pessac, France (Dated: February 3, 2008) ] l l Using time-resolved pump-probe spectroscopy we have performed the first investigation of the a vibrational modes of gold nanoshells. The fundamental isotropic mode launched by a femtosecond h pumppulsemanifestsitselfinapronouncedtime-domainmodulationofthedifferentialtransmission - s probed at the frequency of nanoshell surface plasmon resonance. The modulation amplitude is e significantly stronger and the period is longer than in a gold nanoparticle of the same overall size, m inagreement withtheoreticalcalculations. Thisdistinctacoustical signatureofnanoshells provides . a new and efficient method for identifying these versatile nanostructures and for studying their t a mechanical and structuralproperties. m - d Metal nanoshells – metal shells grown on dielectric Time-resolved optical techniques are powerful tools n spheres – are among the highlights of nanostructures for investigating the low-frequency vibrational modes of o with versatile optical and mechanical properties [1]. As nanostructures. They have been applied to the study c for fully metallic nanoparticles, absorption and scatter- of the acoustic properties of semiconductor and metal [ ing of light by nanoshells are dominated by the surface nanoparticles [15, 16, 17, 18] and have recently been ex- 1 plasmon resonance (SPR) [2]. However, they offer wide tended to bimetallic particles [19, 20]. In these exper- v new possibilities of controlling the SPR characteristics, iments, vibrational modes are impulsively excited as a 4 such as its frequency position, by varying, for instance, result of rapid expansion of metal particle induced by 2 the shell thickness vs. overall size, or the constituent absorptionof a femtosecond pump pulse [15, 21]. In this 2 materials [3, 4]. Furthermore, recent measurements of process,theenergyinitiallyinjectedintotheelectrongas 1 0 scatteringspectraofsinglenanoshells[5,6]indicateden- is quickly damped to the lattice on the time scale of the 7 hancedsensitivitytotheirenvironmentandnarrowingof electron-phononenergytransfer,about1-2picosecondin 0 their resonance lineshape as compared to solid gold par- noble metals. Due to lattice anharmonicity, this lattice / ticles [7]. These unique tunability and characteristics of heating leads to an isotropic force on ions triggering in- t a nanoshells optical properties spurred a number of pro- phase dilation of each particle that subsequently under- m posals for their applications including in optomechanics goes radial contractions and expansions around its new - [8], sensing [9, 10], and drug delivery [11, 12]. equilibrium size. The periodic change in nanoparticle d volume translates into a modulation in time of the elec- n While the optical response of nanoshells has been ex- tronicproperties. Thiscanbedetectedbyatime-delayed o tensively studied, much less is known about their acous- c probe pulse monitoring the concomitant modulation of tical properties. In fact, the low frequency vibrational : the wavelength of the SPR [15]. The triggered initial v modesofnanostructuresbearaunique signatureoftheir expansion being homogeneous, the modulation is dom- i X structural and mechanical properties directly reflecting inated by the fundamental breathing mode that closely the impact of confinement on the ionic movement. This r corresponds to particle expansion as a whole. a is incontrastto the opticalfrequency domainwhosefea- tures are determined by the electronic response. The vi- Using time-domain spectroscopy, we have performed bratinalmodesthusconstituteadditionalsourceofinfor- the first investigation of acoustic vibrational modes in mation that could be particularly important in the case metal nanoshells. As in fully metallic particles, we ob- ofcomplexsystems. Thisisespeciallythecaseforhybrid served in nanoshells a pronounced time-modulation of orlayeredsystemswithstructurallydistinctconstituents, the measured probe differential transmission indicating suchasnanoshells[13,14]. Due to theirstructuralsensi- coherent excitation of the fundamental breathing mode. tivity, vibrational modes are also expected to constitute The modulation amplitude is significantly stronger and acoustic signatures permitting further nanoshellidentifi- its period is considerably longer than those in pure gold cation, complementary to the optical one. nanospheres of the same size. At the same time, the 2 dampingtime oftheoscillationsismuchshorterthanfor at 860 nm with a 80 MHz repetition rate. Part of the gold particles suggesting a faster energy transfer from pulse train is selected to create the pump pulses. Ab- nanoshells to the surrounding medium. Such distinct sorption in this spectral range being dominated by the signatures allow unambiguous identification of nanoshell broadSPRofthenanoshells,theyarepredominantlyex- acoustic vibration and separation of their contribution cited. The pump induced transient change of the sam- from that of possibly present other entities in a colloidal ple transmission ∆T is detected at the same wavelength solution. These results are consistent with theoretical around the nanoshell SPR using the remaining part of analysis of vibrational modes in nanoshells. the beam. This probe wavelength permits further selec- Experiments were performed in colloidal solution tion of the nanoshells that thus dominate the detected of Au S-core/Au-shell nanoshells prepared using the ∆T/T signal. This has been confirmed by the fact that 2 method described in Ref. [1]. Both nanoshells and gold pure gold nanoparticle colloidal solutions yield an unde- nanoparticles are simultaneously synthesized, as shown tectable signal in this pump-probe configuration. The by the linear absorption spectra of the colloidal solution twobeams werefocussedona30µmdiameterfocalspot (Fig. 1). It exhibits two characteristic bands centered and the pump beam average power was about 100 mW. around 700 and 530 nm that have been associated to Measurements were performed with a standard pump- SPR in core-shell nanoparticles and gold nanospheres, probesetupwithmechanicalchoppingofthepump-beam respectively [1, 22]. This assignement is confirmed by and locking detection of ∆T. the spectral displacement of the former band during The measured time-dependent transmission change nanoshell growth, while, in contrast, the spectral po- shows a fast transient, ascribed to photoexcitation of sition of the latter remains almost unchanged as ex- nonequilibrium electrons and their cooling via electron- pected for small nanospheres [1]. This is further corrob- lattice energy transfer (Fig. 2). The observed kinetics is orated by TEM measurements showing the presence of consistentwiththatpreviouslyreportedingoldnanopar- largenanoparticles(meanradiusR inthe 14nmrange) ticlesandfilmsforsimilarexcitationconditions[23]. This 2 that have been identified as nanoshells, and of smaller signal is followed by pronounced oscillations that can be ones (mean size of about 4 nm) identified as pure gold reproduced by a phenomenological response function: [1, 14]. The nanoshell SPR energy is determined by the ratio of the inner to outer radius R1/R2; the latter was R(t)=Aexp(−t/τ)cos[2πt/Tosc−ϕ] . (1) thusestimatedbyfittingtheexperimentalspectrumwith using a period T ≈ 38 ps and a decay time τ ≈ 60 ps A(ω) = P A (ω)+P A (ω), where P and P are the osc p p s s p s for the nanoshells of Fig. 2(a). Such long probe-delay volumefractionsofnanoparticlesandnanoshells,respec- response is similar to that reported in fully metallic tively, and A (ω) are the corresponding absorbances p,s nanoparticles [15, 16, 17, 18], but the measured period [1]. For the investigated nanoshells, R ranges from 9 1 of the oscillations is by far too long to ascribe them to to 10.3 nm with a shell thickness d = R −R of 2.5 to 2 1 the residual fully metallic small nanoparticles. We thus 3.7 nm, i.e., R /R ranges from 0.78 to 0.73 nm. 1 2 ascribedthemtotheacousticvibrationofthenanoshells. 0.8 Furthermore,theiramplituderelativetothatoftheshort nanoparticles timedelayelectronicsignal,ismuchlargerthaninmetal ts) R1 nanospheres (about 75% as compared to 10% [15]). The ni 0.6 measuredperiodisalsomuchlonger(about4times)than u thatpredictedforsolidAunanospheresofthesameover- rb. nanoshells R2 all size, about 9 ps for R2 = 13.5 nm. Furthermore, the a ( 0.4 phaseoftheoscillationϕ≈1.1issignificantlylargerthan ce predicted for a purely displacive type of excitation in a n harmonic oscillator model (about 0.2). As this phase is a b a signature of the excitation mechanism, this suggest a or 0.2 s modifiedlaunchingprocessascomparedtothebreathing b A mode of nanospheres [21]. Measurements performed in different nanoshells show 0.0 400 500 600 700 800 900 1000 similar behaviors with an almost linear increase of Wavelength (nm) the oscillation period with the outer nanoshell size R2 [Fig. 2(b)]. The effective decay time τ of the oscilla- tions can also be extracted from the time-domain data. FIG. 1: Measured linear absorption spectrum of Au2S/Au It varies from30 to 60 ps for the three investigatedsam- core/shellparticlesinwaterfortwodifferentsizes,withR1 = 9.0 nm inner radius and R2 = 11.5 nm outer radius (solid ples (30, 60 and 42 ps in increasing order of R2), but line), andfor R1 =11.5 nmand R2 =13.5 nm (dashed line). conversely to the period, no systematic variation with Inset: schematic geometry of a nanoshell. the nanoshell size is experimentally found. This sug- geststhat,asfornanospherecolloidalsolutions,inhomo- Time resolved measurements were performed using a geneous relaxationdue to the particle size and structure femtosecondTi:sapphireoscillatordelivering20 fs pulses fluctuations dominatesoverthe homogeneousonedue to 3 1.2 derivative over r. Matching u and σ at r = R ,R rr 1 2 (a) yields the equations for the eigenvalues 0.8 T / T 0.4 ξκcot(ξξκ2κ+2 φ)−1 − (ξκ/αc)cηocξt(2ξκκ2/αc)−1 +χc =0, ξ2 η ξ2 D 0.0 + m +χ =0, (4) ξcot(ξ+φ)−1 1+iξ/α m m -0.4 0 20 40 60 80 where ξ =kR2 =ωR2/cL and κ=R1/R2 are shorthand notationsforthenormalizedeigenenergiesandaspectra- Time delay (ps) tio, respectively. The parameters 45 (b) α =c(i)/c(s), η =ρ(i)/ρ(s), χ =4(β2−η δ2), i L L i i s i i ) 40 βi =cT(i)/cL(i), δi =cT(i)/c(Ls), (5) s p ( 35 characterize the metal/dielectric interfaces (i = c,s,m sc stand for core, shell, and outer medium). From Eq. (4), o T 30 the ideal case of a nanoshell in vacuum is obtained by setting α = α = η = η = 0 and χ = χ = 4β2; 25 c m m c c m s 11 12 13 14 15 in the thin shell limit, 1−κ = d/R2 ≪ 1, we then re- R2 (nm) cover the well known result ξ0 = 2βs 3−4βs2 [26]. For a nanoshell in a dielectric medium, the eigenvalues are p complex reflecting energy exchanges with the environ- FIG. 2: (a). Time-dependentdifferential transmission ∆T/T ment, ξ = ωR /c + iγR /c , where ω = 1/T and measured inAu2S/Aunanoshells in waterwith nearinfrared 2 L 2 L osc γ = 1/τ are the mode frequency and damping rate, re- pump and probe pulses is shown together with a fit using spectively. Eq. (1). The inner and outer radii are R1 = 10.3 and R2 = 13.5 nm, respectively. (b) Oscillation period Tosc measured Thisgeneralmodelprovidesanequilibriumdescription in different Au2S/Au nanoshells as a function of their outer ofthenanoshellacousticresponse. However,underultra- radius R2. The aspect ratio R1/R2 is 0.78, 0.76 and 0.74, in fast excitation, the role of the dielectric core is expected increasing R2 order. The line is a fit assuming that Tosc is to diminish. Indeed, the dielectric core is not directly proportional to R2. affected by the pump pulse, but experiences thermal ex- pansion as a result of heat transfer from the metal shell. At the same time, this expansion is much weaker than matrix-water coupling [16, 24]. that of the metal, so that when new equilibrium size To further correlate the observed oscillation mode is established, the core is almost fully disengaged from with the nanoparticle structure, we have theoretically the shell. This should be contrasted to bimetallic parti- analyzed the radial vibrational modes of a spherical cles where the core remains engaged after the expansion nanoshell in a dielectric medium. The motion of andthuscontributestotheacousticalvibrationspectrum nanoshell boundaries is determined by the radial dis- [19, 20]. placement u(r) that satisfies the Helmholtz equation (at To take into accountthis effect, calculations were per- zero angular momentum) formed for gold nanoshells with disengaged core [η = 0 c ′ in Eq. (4)]. The calculated frequency, ω, and damping 2u u′′+ +k2u=0, (2) rate,γ =1/τ,areplottedinFig.3versustheaspectratio r R /R ,forthefundamentalbreathingmodeofnanoshells 1 2 where k = ω/c is the wave-vector. In the presence of immersed in water. The data are normalized in units of L core and outer dielectric medium, the boundary condi- c /R sothatthecorrespondingcurvesforsolidnanopar- L 2 tions impose that both the displacement u(r) and the ticles are horizontal lines starting at R /R = 0. The 1 2 radial diagonal component of the stress tensor, soundvelocitiesandthedensityweretakenasc(s) =3240 L σrr =ρ c2Lu′+(c2L−2c2T)2ru , (3) mc(Lm/s),=c(Ts1)4=901m20/0s,mc(T/ms,)ρ=(s)0,=an1d97ρ0(0mk)g=/m1300f0orkAg/um,3afnodr (cid:20) (cid:21) water. are continuousatthe core/shelland shell/mediuminter- The computed frequency of the fundamental mode is faces (ρ and cL,T are, respectively, density and longitu- significantly smaller for nanoshells as compared to gold dinal/tranverse sound velocities). In the core, shell, and particles of the same overall size (Fig. 3). It is about 2 medium regions, solutions are, respectively, of the form times smaller for R /R = 0.5 and further decreases to ′ ′ ′ 1 2 u∼ sin(kr)/r ,u∼ sin(kr+φ)/r ,andu∼ eikr/r , about a factor of 3 for thin nanoshells. In contrast, the where φ is the phase mismatch and prime stands for aspect ratio dependence of the computed damping rate (cid:2) (cid:3) (cid:2) (cid:3) (cid:2) (cid:3) 4 ρ(m)/ρ(s) ≪1, Eq. (6) further simplifies to (a) 3.0 α η 4α β2 x2 cL x2−1= m m m m − , (7) 2.0 ξ (1−κ) ξ α /ξ −ix / 0 " 0 m 0 # 2 R 1.0 where x = ξ/ξ0 and we used χm − χc = −4ηmα2mβm2 w and χm/χc = 1 − ηmβm2 . Two regimes can now be 0.0 clearly identified, governed by the ratio ηm/(1 − κ) = (b) R2ρ(m)/dρ(s) ≈ Mm/Ms, where Ms is the metal shell 0.3 mass,andMm is the mass ofoutermedium displacedby L cccc the core-shell particle. Explicit expressions can be ob- c / 0.2 ssss tained for the cases of “heavy” and “light” shells. For R 2 a “heavy shell”, Ms ≫ Mm, the complex eigenvalue is 0.1 mmmm given by g λ α +iξ ξ ≃ξ − m 0 −4α β2 , (8) 0.0 0.2 0.4 0.6 0.8 1.0 0 2 (α /ξ )2+1 m m R / R (cid:20) m 0 (cid:21) 1 2 where ξ is the eigenvalue for a nanoshellin vacuumand 0 λ=α η /ξ (1−κ). In a good approximation, the real m m 0 part is simply ξ′ ≃ ξ , and is thus independent of the FIG.3: Calculatedfrequency(a)anddampingrate(b)ofthe 0 medium or aspect ratio, in agreement with the full cal- fundamental breathing mode of a gold nanoshell with disen- culation for R /R ≤0.9 (Fig. 3). In contrast the imag- gagedcoreinwaterversusitsaspectratioR1/R2. Thedashed 1 2 line in (a) is for a gold nanoshell in vacuum. The horizontal inary part, although small (ξ′′ ≪ξ′), is only non-zero in dotted lines show the normalized frequency and damping for presence of a matrix and thus depends on both. Putting a gold nanosphere of the same overall size (radius R2). The all together, we obtain in the “heavy shell” regime insetindicatesmechanicalmovementassociatedtothefunda- mental mode (thin arrows) and the energy damping mecha- 2c(s)β c(m) 2η β2(3−4β2) ω ≃ L s 3−4β2, γ ≃ L m s s . nism to theenvironment (thick arrows). R s d α2 +4β2(3−4β2) 2 m s s p (9) Asdiscussedabove,herethe dampingrateisdetermined by the shell thickness rather than by the overall size. In is non-monotonic. A minimum is reached at R /R = 1 2 theoppositecaseofa“lightshell”,M ≪M ,theeigen- 0.4, followed by a large increase for thin shells that can s m value is given by ξ ≃2α β 1−β2 −iβ , yielding be understood on the basis of energy consideration: the m m m m depositedenergyisproportionaltothenanoshellvolume, ω ≃2c(m)/R , γ(cid:0)p≃ωc(m)/c(m). (cid:1) (10) V, while the efficiency of energy exchange is determined T 2 T L by the surface area, A. Then, the characteristic time Note that for a light nanoshell in water (c(w) = 0) the of energy transfer from the shell to the outer medium T limiting frequency vanishes. In the crossover region, the is τ ∼ V/Ac(m) ∝ d/c(m), as opposed to the R/c(m) L L L nanoshellfrequencyissignificantlylowerthaninvacuum dependenceforsolidparticles[25]. Withfurtherdecrease (Fig. 3). of the nanoshell thickness, a sharp change in behavior The above theoretical analysis of the nanoshell vibra- is seen for both ω and γ, indicating a crossover to an tional modes is consistent with experimental data. In overdamped regime (Fig. 3). In this thin shell limit, the the aspect ratio of interest, R /R ≈ 0.75, the funda- 1 2 spectrum of vibrational modes is mostly determined by mental mode period is considerably longer than for a the energy exchange with environment, as shown by the pure metal particle of same overall size. For the investi- largedeviationof the computedfrequency for a wateror gated particles, the aspect ratio R /R lies in the range 1 2 vacuum environment for R /R ≥0.9 (Fig. 3). 1 2 where the normalized frequency ωR /c varies weakly 2 L The behavior for the thin shell regime can be better so the period is almostproportionalto R2, in agreement analyzedusing approximatedanalyticalsolutionsfor the withthe experimentaldata[Fig.2(b)]. Adeviationfrom vibrations frequency and damping. For 1−κ=d/R2 ≪ a simple R2 dependence towards longer Tosc is appar- 1, Eqs. (4) (with η =0) reduces to ent for the nanoshell with largest aspect ratio (smallest c R ), in agreementwith the calculatedvibrationalmodes 2 spectra. However, the measured period for a nanoshell χc χ −χ +αmηmξ2 = χ +αmηmξ2 ξ2−χ ξ2. in Fig. 2(a), Tosc ≈ 38 ps is larger by about a factor 1−κ m c α −iξ m α −iξ 0 c of 2 than that calculated for the ideal nanoshell. This (cid:18) m (cid:19) (cid:18) m (cid:19) (6) discrepancy could be attributed to structural inhomo- In the typical case when the metal shell density is much geneity of the metal shell. Its porous (“bumpy”) struc- higher than that of the surrounding medium, i.e., η = turewithintersticesincreasesthesurfacetovolumeratio m 5 and, thus, moves the vibrational modes towards that of role[16,24]. Thisstatisticaleffectthatreflectstheparti- effectively thinner nanoshells. Importantly, such struc- clesize,shapeandstructuredistributionisalsoprobably tural defects drive nanoshell acoustical response away at the origin of the sample to sample fluctuations of the from solid nanoparticle, as long as the shell is contin- measured damping rate. uous. Note that clusterization or aggregation processes In summary, using a time-resolved pump-probe tech- that effectively break the shell geometry will results in nique,wehaveinvestigatedtheacousticvibrationofgold an increase, as compared to ideal shell, of the vibration nanoshells in colloidal solution. The results clearly show frequencycontrarytotheexperimentallyobservedreduc- oscillationswithaperiodinthe40psrange,muchlonger tion. This specific acoustic response can thus be used than expected for pure gold nanospheres. In agreement to unambiguously distinguish different nanoobjects pro- with our theoretical model, they have been ascribed to ducedduringnanoparticlesynthesis,suchasnanoparticle fundamental breathing vibration of the gold nanoshells, clusters and nanoshells. whose acoustic signature is thus observed here for the The computed damping rate τ is smaller than the ex- first time. Note that such low frequency vibrational perimental one by almost a factor of 1.5. A similar dis- modes (in the 1 cm−1 range) are extremely difficult to crepancyhasbeenreportedfornanospherecolloidalsolu- observe using spontaneous Raman spectroscopy. These tions[15]. Intheoreticalmodels,computationismadefor results stress the importance of time-resolved studies of one nanoparticle with a given mean geometry. Damping acousticvibrationalmodesasanewandpowerfultoolfor is then associated to energy transfer to the surround- unambiguous determination of the structure of synthe- ing medium and is thus weak in the case of a water sized nanoobjects via their specific acoustic properties. matrix. As a large number of nanoparticles is simul- C.G.,P.L.,N.D.FandF.V.acknowledgefinancialsup- taneously investigated inhomogeneous damping due to portby ConseilR´egionald’Aquitaine. A.S.K andT.V.S. dephasing of the coherently excited acoustic oscillations acknowledgefinancialsupportbyNationalScienceFoun- of the nanoparticles is thus expected to play a dominant dation and by National Institute of Health. [1] R.D.Averitt,D.SarkarandN.J.Halas,Phys.Rev.Lett. Klar, J. Feldmann, B. Fieres, N. Petkov, T. Bein, A. 1997, 78, 4217. Nichtl, and K. Krzinger, Nano Lett. 2005, 5, 811. [2] U. Kreibig and M. Vollmer, Optical properties of metal [15] N. DelFatti, C. Voisin, F.Chevy,F.Vall´ee, and C. 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