J. Phys. Chem. C 2008, 112, 11751–11757
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Effect of Local Heating on the SERS Efficiency of Optically Trapped Prismatic Nanoparticles Matthew D. King, Sushil Khadka, Gary A. Craig, and Michael D. Mason* Department of Chemical and Biological Engineering, Institute for Molecular Biophysics, UniVersity of Maine, Orono, Maine 04469 ReceiVed: April 14, 2008; ReVised Manuscript ReceiVed: June 4, 2008
Local heating of laser trapped metallic nanoparticles results in a gradual decrease in surface-enhanced Raman scattering (SERS) which can be attributed to both photophysical and chemical processes. Initially trapping results in a dramatic increase in Raman signal due to improved excitation and collection efficiencies in the trapping volume, followed by a gradual decay to a stable asymptotic level approximately 20% of the initial maximum value. The underlying processes leading to this decrease in SERS signal include photothermalinduced changes in dielectric properties of the particles and medium, and adsorption/desorption kinetics of the surface molecules. The relatively long apparent decay time seems to suggest that either process occurs on surprisingly long timescales for the thiol capped nanoprisms reported here. Here we present a simple semiempirical description of the observed time dependence of the single nanoparticle Raman intensities simultaneously accounting for both processes. Time series data of total integrated Raman signal supports a simple steady-state thermal equilibrium model which yields an equilibrium temperature change for the particle of T ) 205 ( 7 K and the best-fit time constant of τ ) 0.10 ( 0.05 s, smaller than obtained by other more empirical models. The quality of the fit suggests that desorption kinetics dominate, and that the observed decay cannot be fully explained using a single (average) desorption free energy (∆G). This work demonstrates the dynamic process of SERS from optically trapped prismatic nanoparticles, the utility of single particle measurements, and the effect of local heating on observed Raman scattering efficiency. Introduction The optical scattering properties of small metallic particles have led to their use as pigments in paints and glasses for centuries.1 As the physical dimension of these particles is reduced to the nanoscale ( 50 s). This decrease in signal is consistent with previous SERS measurements of molecules deposited on metallic films and in nanoparticle sols and has been attributed to a number of processes including: thermal annealing (changes in nanoparticle geometry),29 modification of surface molecules (reorientation or removal of analyte molecules),30 lateral particle diffusion in colloidal SERS substrates (decrease in EM coupling between particles),31 and more recently changes in optical properties due to local heating (changes in dielectric properties).32 Though the physical picture behind each of these mechanisms may vary widely, thermal energy is a unifying driving force. In light of the increasing number of studies implicating metallic nanoparticles as an efficient source of optically induced local heating, the application of a time and temperature dependent model is clearly justified. While detailed theoretical descriptions of
Figure 4. Time series of Raman spectra for a single optically trapped nanoparticle or nanoparticle aggregate. The individual spectral acquisition times were 1 s with a delay and read time of approximately 1 s between acquisitions.
temperature dependent ensemble data do exist, they generally address either photophysical or chemical mechanisms.33 Our single particle data, however, exhibit both peak fluctuations on subsecond timescales and a gradual decrease in total signal over the period of tens of seconds suggesting that at the single particle level a description which includes both chemical and optical properties must be considered. In order to better understand the mechanism behind the observed decrease in the SERS signal, we use a simple description. According to previous work,34 the total optical power of the SERS signal from a single nanoparticle can be expressed as
PSERS ) NσadsI(ωL)|A(ωL)|2|A(ωs)|2 ) GCI(ωL)GE
(1)
where N represents the number of surface molecules contributing to the signal, σads is the average Raman cross-section of the surface molecules, I(ωL) is the incident laser intensity and |A(λL)|2 and |A(λs)|2 are the size, shape, and material dependent electromagnetic field enhancement factors (expressed here in terms of angular frequency) at the incident laser and Raman scattering frequencies, respectively.14,15 In this form we are free to separately investigate how the chemical and electric-field SERS contributions may evolve with time and temperature. The chemical contribution to the SERS effect, GC ) Nσads, is still not well understood but is generally believed to result from an electronic coupling of unoccupied molecular orbitals in the N surface molecules with conduction band electrons near the metal surface producing a metal-adsorbate complex. This coupling can result in an approximately 10-102 increase in the total Raman cross-section, but more interestingly, the symmetry rules of the individual modes are differentially modified causing changes in relative peak intensity and the appearance of normally symmetry forbidden transitions (σadsfσads′). This effect can be observed in the single particle Raman spectra, shown in
SERS Efficiency of Optically Trapped Prismatic Nanoparticles
J. Phys. Chem. C, Vol. 112, No. 31, 2008 11755
Figure 6. Average integrated Raman intensity timecourses (N ) 22) and corresponding fit to the complete temperature dependent index of refraction model and resulting residual. Dashed line represents the decrease in SERS signal due only to temperature-induced changes in the electromagnetic enhancement factor, GE.
Figure 5. Representative time evolution of integrated Raman spectral intensity for individual optically trapped thiol-capped nanoprisms.
Figure 3, where NT peaks at 1134, 1264, and 1486 cm-1 are enhanced relative to those present in the neat solution. For molecules which are free to reorient themselves, relative to the nanoparticle surface, dynamic fluctuations in the relative peak intensities are also expected due to changes in local symmetry at the nanoparticle surface. This phenomenon is also visible in the data (Figure 4, t ) 30 and t ) 45), where changes in the relative peak heights at 1062, 1134, 1264, 1371, 1486, and 1616 cm-1 are clearly visible. It is important to point out that while the individual peak intensities may change significantly, the total intensity between sequential spectra only decreases slightly with time. This suggests that the modified total Raman cross section, σads′, is largely unaffected by changes in temperature. Fluctuations in the individual peak intensities clearly provide some insight into the dynamic nature of the adsorbate-nanoparticle interaction. However, when considered separately from the rest of the spectrum they can also obscure how the total Raman activity evolves over time. To avoid this complication, the individual 1 s flattened spectra were integrated in their entirety, and a SERS intensity timecourse was generated for each trapped nanoparticle. Three characteristic intensity timecourses of NT capped nanoprisms are shown in Figure 5. In virtually all cases, the first few time points are representative of the residual background signal (after flattening) and are approximately equal to zero photon counts. Figure 5A shows a timecourse which is representative of approximately half of the particles studied. In this case, a nanoparticle is trapped after a few seconds and subsequently generates a large enhanced NT signal. The intensity decays significantly over the next few seconds and then more slowly for times greater than ∼20 s, eventually settling at some pseudoasymptotic value (∼55 000 photons/s). The remaining particles behaved according to the examples shown in Figure 5B and C. In these measurements an initial peak and subsequent rapid decay, was followed by a larger second peak with decay characteristics similar to that of
Figure 5A. This behavior could be indicative of light induced aggregation of multiple particles, or of a particle which is moving in the focal volume but is not stably trapped and hence not probed by the most intense region of the Gaussian intensity profile. While the former case has been observed by others, the relatively low trapping powers used here (∼5 mW), the comparatively modest increase in signal,35 and the consistency of the maximum observed SERS signal (shown in Figure 6), suggests that aggregation is not significant. In the case of metallic nanoparticles, it is now well-known that the polarizability of conduction electrons leads to an effective focusing of the incident and emitted fields giving rise to signal enhancement factors as large as ∼106.11 There now exist numerous descriptions of this process based on ElectroMagnetic (EM) or Quantum Mechanical (QM) approaches.36 Though less general the former is somewhat more intuitive as a basis for the discussion presented here. In this description, based on Mie scattering, the incident electric field (E0) induces a dipole moment in the nanoparticle which itself becomes a radiator (Ep). The resulting field experienced by the nanoparticle is then a superposition of the incident and dipolar fields (EM ) E0 + Ep). The total field enhancement factor for a given incident wavelength, A(λ), can be expressed as the ratio of the enhanced field to the incident field
A(λ) )
EM(λ) εp - ε0 r ≈ E0(λ) εp + 2ε0 r + d
(
3
)
(2)
where εp and ε0 are the dielectric constants of the nanoparticle and the surrounding medium, respectively, r is the radius of the nanoparticle, and d is the distance from the nanoparticle surface to the analyte molecule.34 The Raman scattering field is similarly enhanced by the presence of the metal particle, but at a slightly shifted frequency corresponding to the individual vibrational transitions. If we assume that the incident and Raman scattering wavelengths are approximately equal, and that the radius of the nanoparticle is large (r ∼ 50 nm) relative to the thickness of the adsorbed molecular surface layer (d < 1 nm), then r/r + d ≈ 1, and we obtain a total electromagnetic enhancement factor (GE)
11756 J. Phys. Chem. C, Vol. 112, No. 31, 2008
GE ) |A(λL)|2|A(λs)|2 ≈
| | εp - ε0 εp + 2ε0
King et al.
4
(3)
where the largest attainable values occur at the plasmon resonance condition where εp ) -2ε0. Changes in εp and ε0, though known, are generally assumed to be small in the high frequency (optical) limit for small changes in temperature, and hence ignored. However, considering the fourth order dependence of Equation 3, and that recent results suggest that under some conditions local temperature increases as large as 1000 K are possible, they can nonetheless have a significant impact on the signal. To include the possible effect of local heating on the SERS signal we employ a simple steady state model. In this case we assume that the thermal dissipation rate of the surrounding matrix (including the water, sample cell, and the entire laboratory) is large relative to the local heating rate, which is proportional to the product of the laser flux and absorption cross section, and that heat transfer from the nanoparticle to the surrounding matrix is nearly instantaneous.37 Under these conditions we expect that, with CW laser heating, some equilibrium temperature will eventually be reached in the direct vicinity of the nanoparticle, consistent with previously reported results.25 The temporal behavior of this process can be modeled simply as the sigmoidal line shape:
T(t) ) T0 + ∆T(1 - e-t⁄τ)
(4)
where T0 is the initial temperature, ∆T is the relative temperature increase at equilibrium, and τ is the characteristic time of the heating process. We can estimate the influence of local temperature on the dielectric constant of surrounding medium, in this case water (ε0 ) εw(T)), using the empirically obtained relationship38
εw(T) ) nw(T)2 ) (A1 + A2T + A3T3)2
(5)
A2, and A3 are constants equal to 1.33455, -5.53 × 10-5, and -1.12 × 10-6, respectively, and we have assumed a negligible dielectric loss factor which is generally true at optical frequencies. The temperature dependence of the real part of dielectric constant of the nanoparticle (εp) is somewhat more complicated. Here we begin with a modified Drude model described previously39
εp(T) ) 1 -
ω2sp 3[ω2 + ωc(T)2]
(6)
where ωspis the nanoparticle plasmon resonance frequency (related to the bulk plasmon frequency, ωp, by ωsp ) ωp/3 for a spherical nanoparticle) and ω is the frequency of the incident radiation. The electron collision damping frequency, ωc(T), is a complicated function consisting of a dominant phonon-electron scattering and a less significant electronelectron scattering term.40 Fortunately, for reasonable temperatures ∼300-1000 K, ωc(T) can be closely approximated by the polynomial function: ωc(T) ) -8.05 × 1012 + 4.24 × 1011T + 8.17 × 107T2, which contributes significantly to εp at elevated temperatures. Additionally, the nanoparticle plasmon frequency, ωsp, exhibits a temperature dependence due to thermal expansion: ωsp(T) ) ωsp,0(1 + γ(T - T0)-1/2, where γ is the volume expansivity (4.26 × 10-5 K-1 for gold), T0 and ωsp,0 are the initial temperature and initial size-dependent plasmon resonance frequency. Though the total contribution of this collection of factors to the dielectric constant may be small, its effect on the SERS enhancement factor is significant.41 The temperature
dependence of εp becomes apparent upon substitution of these expressions into eq 6, yielding
εp(T) ) 1 -
2 ωsp,0
3[ω2 + ωc(T)2](1 + γ(T - T0))
(7)
A final expression for the effect of temperature on the electric field contribution to the SERS enhancement is obtained by first substituting eq 4 (TfT(t)) into eqs 5 and 7, which are then substituted into Equation 3. Furthermore, we assume that the imaginary part of the dielectric constant of water is negligible, and that ∆T(t) ) T(t) - T0. Though, the resulting analytical equation is somewhat cumbersome, and hence not presented here, it is a simple matter for modern computational programs (Mathematica). The data shown in Figure 6 was obtained by averaging a series of individual nanoparticle timecourses, where the maximum integrated SERS signal was used set as the t ) 0 point. In this way all recorded timecourses, including those which exhibit multiple peaks. Remarkably, the intensity variance between timecourses is quite low, indicating the relative homogeneity of the sample and further discounting the probability of uncontrolled aggregation. A fit of eq 3 to the averaged data is shown in Figure 6. In this case the time constant, τ, was initially obtained using a Levenberg-Marquardt method where bothτ and ∆T were allowed to vary. A prefactor (B ) Nσads′I(ωL)) was also included in the fit function such that, at t ) 0, the model and the data were in agreement. The difference between the fit of eq 3 and experimental data are plotted as the residual in Figure 6. The best fit time constant, τ ) 22 ( 5 s, was then fixed and ∆T was set according to previous experimental and theoretical photothermal results for similarly sized gold nanoparticles (∆T ) 275 K), yielding the dashed line in Figure 6 corresponding to only photothermal-induced changes in GE.25 It is immediately evident that temperature induced changes in GE cannot account for the observed decrease in SERS signal at this temperature. In fact, a reasonable fit to the data is only obtained when the equilibrium temperature is raised arbitrarily to∆T ) 2750 K, more than twice the melting temperature for gold. For temperatures and time constants in the range ∆T ) 1-1000 K and τ ) 0.01-100 s, respectively, the largest calculated decrease in GE was less than half of that observed. The ∼5% decrease in signal we estimate for ∆T ) 275 K is consistent with the predicted values of others.32 We assumed above that the molecular cross-section, though modified by the presence of the optically driven nanoparticle surface (σadsfσads′), is itself not expected to significantly decrease the SERS signal with time. However, we have neglected how the molecular composition (N) may be affected by local heating as previously observed.42 If we assume that the population of the surface molecules obeys first-order desorption kinetics, then we can express the time dependence of N as: N(t) ) (N0-Neq)e-kt+N0. Here the rate constant k is derived from kinetic molecular theory and contains adsorption (kads) and desorption (kdes) rate terms; k ) kads[C]+kdes, where [C] is the initial concentration of the NT in the solution (1 µM). The constants, N0 and Neq, represent the initial and equilibrium nanoparticle surface populations, respectively. While the adsorption rate is assumed to be independent of temperature, the rate of desorption is assumed to be Arrhenius-like according to the Eyring equation: kdes ) kBT(t)/h e(-∆G/kBT(t)), where ∆Gis the Gibbs free energy of activation for desorption of the thiol (∆G≈110 kJ/mole),kBand hare the Boltzmann and Planck constants, respectively, and T(t) is again described by the sigmoidal function of eq 4. With this model, using the values
SERS Efficiency of Optically Trapped Prismatic Nanoparticles obtained from the fit of GE (τ ) 22 s,∆T ) 275 K), N(t)would reach a value of 0.5 within the first 10 s and ∼ 0 within 20 s. However, recalling that our values of τ and ∆T were determined only as way to assess the range of possible GE values, we now use them as free fit parameters along with Neq, the equilibrium surface population. The chemical contribution to the SERS signal then becomes: GC ) N(t)σabs′. The complete time (and hence temperature dependent) function can now be fitted to the data where a new scaling factor, B′ ) σads′I(ωL), is used. A fit of the complete signal function: PSERS ) B′N(t)GE, to the average single particle Raman data to is shown in Figure 6. Whereas GE could only account for a fraction of the observed signal decay, the complete function allows for a significant decrease (∼ 80%) in the surface population (N(t)), and shows excellent temporal agreement with our data. Owing to the relative complexity of the model, the best fit coefficients, τ ) 0.1 ( 0.05 s and ∆T ) 205 ( 7 K, show little resemblance to those obtained previously where only the temperature dependence of GE was considered. It should be noted that the extreme sensitivity of the model to the exponential factor in the dissociation constant, kdes, places additional uncertainty on the fit parameters. Specifically, a more accurate experimentally determined value for the distribution of activation energies (∆G) would serve to increase confidence in the fitted parameters. With that said, the values obtained here using literature values for∆G, are in reasonable agreement with both theoretical and experimental values for τ and ∆T. Conclusions Our simple local equilibrium heating model of optically trapped prismatic nanoparticles demonstrates a temperaturedependent reduction in integrated SERS signal as a result of a decrease in the index of refraction of the surrounding medium and changes in the surface population of surface molecules due to desorption. The time-evolution of integrated intensity suggests a slow dynamic process initiated by an initial increase in signal upon optically trapping of nanoparticles followed by a gradual decay to a stable asymptotic intensity value. While the total SERS signal decreases by about 80%, the remaining stabilized signal is still very large for the prismatic nanoparticle system. Local heating of the particles does occur, and the rapid heating times suggested by the model are much less than 1 s. In addition, the apparent shift in the equilibrium constant due to the temperature increase is not sufficient to induce complete desorption. Though not possible by the optical trapping method presented here, further studies investigating whether the SERS signal is recovered after a heating/cooling cycle would be of interest. Our data presented here suggests that optical trapping and simultaneous Raman spectroscopy is an effective method for more detailed characterization of single nanoparticles and surface immobilized molecules, reducing or eliminating the effects of ensemble averaging. Also demonstrated is the relative stability of this system, given the strong perturbation of the optical trap, indicating that the surface modified prismatic nanoparticle system investigated here may have some utility as a local nanoprobe system for Raman imaging applications.
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