Quantifying the Blue Shift in the Light Absorption of Small Gold Nanoparticles

Transcription

1 C. R. Acad. Bulg. Sci. 70 (2017) [arxiv ] Quantifying the Blue Shift in the Light Absorption of Sall Gold Nanoparticles R. Tsekov, P. Georgiev, S. Sieonova and K. Balashev Departent of Physical Cheistry, University of Sofia, 1164 Sofia, Bulgaria The dependence of the surface plasons resonance (SPR) frequency on the size of gold nanoparticles (GNPs) is experientally studied. The easured data for the SPR frequency by UV-Vis spectroscopy and GNPs diaeter by Dynaic Light Scattering (DLS), Transission Electron Microscopy (TEM) and Atoic Force Microscopy (AFM) are collected in the course of classical citrate GNPs synthesis. The relationship between the GNPs size and the blue shift of the light absorption is presented. They are fitted by an equation with a single free paraeter, the dielectric perittivity of the surrounding edia. Thus, the refractive index of the surrounding edia is deterined, which characterizes the GNPs surface shell. It is well known that the optical properties of etal nanoparticles, such as Au, Ag, Cu, etc., with sizes less than 20 n are deterined by the collective oscillation of valence electrons [1]. These electrons interact with the electric field of the incident radiation, which induces a dipole in the nanoparticle. The optical properties of etal nanoparticles dispersions can be quantified by studying the intensity of the absorption axiu due to surface plason resonance (SPR), easured fro the UV-Vis spectru. The application of the UV-Vis spectroscopy for investigation of gold nanoparticles growth is possible, because the absorption intensity of the SPR axia depends on the nanoparticle size [1-4]. Drude and Lorentz have derived the fundaental laws for the optical properties of bulk etals [5]. Their odels provide the frequency dependence of the dielectric function of a etal. The Drude odel is eployed for description of the dielectric function of etals with free valence electrons such as gold, silver and copper [6]. Johnson and Christy [7] applied the Drude odel for description of the ellipsoetric easureents of the dielectric function of gold, silver and copper fils. Recently, Losurdo et al. [8] easured the ellipsoetric spectra of the GNPs fils and the sizes of the GNPs were characterized by AFM. The experiental results showed dependence of the dielectric function fro the size of GNPs, organized in the fils. The obtained experiental dependence were paraetrized by a cobination of three Lorentzian oscillators. Jenkins et al [9] studied blue shifted narrow localized surface plason resonance (LSPR) fro dipole coupling in GNPs rando arrays. The LSPR width is narrower than that of the single gold nanoparticles. The blue-shifted LSPR is due to the long-range dipole coupling in the gold nanoparticle rando arrays indicated fro siulations using the T-atrix ethod. The absorption of sall gold nanoparticles in solution and extinction cross section for single spherical particle were calculated via the Mie equation [3], where for the dielectric function was used a sei-epirical equation. Accordingly, the theoretical predictions for sall size GNPs (up to 20 n) gave the increase of the intensity of the absorption axia with respect to the increase of the GNPs size. Although this theoretical approach was not capable of explaining the

2 blue shift in the UV-Vis spectra, which is experientally observed in the course of the GNPs synthesis correspondingly to the increasing GNPs size [3, 4]. By taking into account the blue shift we propose a siple relation, where the surface plason resonance frequency is a function of the GNPs size. In order to verify the derived equation for the plason frequency and for the nanoparticles sizes, kinetic data obtained in the course of their synthesis are used. For this purpose, the DLS, TEM and AFM size distributions are analyzed and the SPR frequencies (fro UV-Vis spectra) and corresponding GNPs sizes, could be deterined by the proposed siple equations. Experiental Cheicals and reagents: Analytical grade Tetrachloroauric acid (HAuCl4.3H2O) was purchased fro Panreac Quíica (Spain), Trisodiu citrate (Na3C3H5O(COO)3.2H2O) and Sodiu chloride (NaCl) were obtained fro Siga-Aldrich (Gerany). All solutions were prepared in deionized water. Synthesis of spherical gold nanoparticles: The GNPs synthesis procedure, as previously described [3, 4], was based on citrate ethod [12], one of the best ethods for synthesis of onodisperse spherical GNPs is as follows: 10 l solution of tetrachloroauric acid, containing 5 g gold, was added to 85 l deionized water. The ixture was stirred at 350 rp and heated, and 5 l 1% solution of trisodiu citrate was added as reducing and stabilizing agent. The excess of trisodiu citrate concentration is for stabilizing action foration of citrate shell on nanoparticles surface. The synthesis were perfored at two reaction teperatures, 70 C and 90 C. Experiental ethods: The UV-Vis absorption spectra were easured by spectrophotoeters Thero Scientific Evolution 300 UV-Vis Spectrophotoeter (Fisher Scientific, USA) and Jenway 6400 (Krackeler Scientific Inc., USA). Additional blue shifted UV-Via spectra are published in previous works [3, 4]. The size distribution of gold nanoparticles was deterined by Dynaic Light Scattering (DLS) apparatus Zetasizer Nano ZS (Malvern Instruent Ltd., Malvern, UK). The setup was equipped with 532 n HeNe gas laser and detector optics and an ITT FW 130 photoultiplier and ALV-PM-PD aplifier-discriinator. The orphology and the size of GNPs were deterined by JEM-2100 LaB6 Transission Electron Microscope (JEOL Ltd., Japan), and TEM Philips CM-10, used at 100kV. The saple preparation for AFM iaging is described elsewhere [3, 4]. AFM iaging was perfored on NanoScope V syste (Bruker Inc.) operating in tapping ode in air at roo teperature with silicon cantilevers (Tap300Al-G, Budget Sensors, Innovative solutions Ltd., Bulgaria). The NanoScope software was used for section analysis and particle size deterination [3, 4]. All the ethods were used in the course of the GNPs synthesis as the saples were taken at different reaction tie intervals [3, 4]. The GNPs size distributions fro TEM icrographs and AFM iages were obtained fro analysis of about 200 nanoparticles of each of the saples taken during the synthesis. Experiental observations: The 2D AFM iages, presented in Fig. 1A,D and corresponding 3D AFM iages, were obtained at 30 th and 70 th in fro the GNPs synthesis, perfored at 70 C, after depositing soe aount of the gold suspension on ica support. The particle diaeter were deterined by section analysis, perfored across certain iaged gold nanoparticles on Fig. 1B,E. Representative iages of gold nanoparticles, taken with High Resolution (HR) TEM, are

3 shown in Fig. 1G,H. The figure represents gold nanoparticles synthesized by us at teperature 90 ºC at the final stage of synthesis. The nanoparticles are ostly spherical. Aggregates of nanoparticles could also observed to for when the liited protection ability of sodiu citrate, which serves not only as a reducing agent, but also as a stabilizing one. Fig. 1. (A, D) 2D AFM iages with (B,E) section analysis across the iaged GNPs are z=10 n and z=15 n, (C,F) corresponding 3D AFM iages. The z size of the AFM instruental error is d=±0.2 n. (G, H) HR-TEM icrographs of GNPs at the final stage of growth. The scale bars are 5 n and 20 n. The resolution of the TEM is d=±0.19 n. It is well-known that in the process of GNPs growth the nuber of particles stays nearly constant, equal to the nuber of initial nuclei [3, 9, 13-16]. In agreeent with this postulate it is expected that the extinction cross section of the single GNP. Since the absorbance is proportional to the extinction cross section, this explains the increase of the absorbance with the increase of the nanoparticles size. The blue shift of the absorption axia and the change of the extinction cross section in the course of GNPs growth are presented at Fig. 2A while at Fig 2B are presented the histogras of the GNPs deterined fro AFM (Fig. 2B). Within the instruental error of UV- Vis and AFM data it is possible to quantify the blue shift of the plason axia of the GNPs with diaeters up to 20 n. The coparison of experiental absorption spectra with extinction cross section gives proportionality constant [3]. This constant A/C ext = is very close to one calculated for an idealized case of onodisperse solution of GNPs with spherical shape A/C ext = [3]. This result is in agreeent with well-known forula for absorbance of colloidal suspension A/C ext = N NP L/2.3, where NNP is the nuber of nanoparticles per unit volue and L=1 c the light path length [2, 3]. The observed blue shift is considered to be a function only of GNPs size and not of the nuber of gold nanoparticles, because experiental easured spectra for different concentrations has a constant wavelength (data not shown). The absorption spectra can be described by the equation Eq. (1) giving the relation between the extinction cross section

4 and fitting variables - GNPs size and the wavelength. Here were propose a siple relation between the blue shifted plason absorption axia (wavelength) and the size of GNPs which have sizes saller than 20 n. Fig. 2B represents the AFM size distributions of GNPs corresponding to the absorbance spectra of the sae GNPs saples taken in the course of their synthesis. The curves described the histogra was ade by plotting the nuber of particles with a specified average size as a function of their diaeter d. The ean diaeter, was the value of the axiu of size distribution. It is clear fro the distributions in Fig. 2B that the size distribution does not change appreciably for different saples. The sae conclusions could be ade fro DLS size distributions data (data not shown). Having easured of absorbance spectra, we can relate the to the GNPs size with a siple equation. Fig. 2. (A) Blue shift of the spectra during the citrate synthesis perfored at 70 C and (B) The histogras of the corresponding GNPs size distributions derived fro AFM data. The instruental error of UV-Vis spectrophotoeter wavelength is =±1 n, and the instruental error of AFM for each GNP size deterination is d=±0.2 n. Theoretical Results and Discussions It is well known that incident light excites surface plasons in gold nanoparticles. According to the Mie equation, the extinction cross-section of a single particle is given by [2-4]

5 C 3 d 2 3 3/2 I ext 2 2 ( Re 2 ) I (1) where d is the nanoparticle diaeter, is the light wavelength, is the dielectric constant of the ediu, Re and I are the real and iaginary parts of the dielectric function of etal nanoparticles, respectively. A typical value of the dielectric constant of water is The relevant frequency dependence of the nanoparticle dielectric perittivity is described by the adapted Drude forula [17] 2 ( sp ) 1 2 i (2) where sp is the surface plason frequency and is a daping coefficient. One can easily obtain fro Eq. (2) that. Substituting it in the resonant condition Re 2 0, Re 1 sp / ( ) following fro Eq. (1), yields the frequency ax 2 c / ax of the spectral peak 2 2 sp 2 ax 2 1 (3) where c 300 M/s is the speed of light in vacuu. The dielectric constant relates also the surface plason frequency to p 13.7 PHz for gold. 2 2 sp p / ( 1) to the bulk plason frequency p, which is equal The ean free path of electrons in gold is l 38 n [6]. This eans that in saller gold nanoparticles the dissipation of energy occurs ainly by collisions of electrons on the particle surface, siilar to the Knudsen diffusion. Hence, the corresponding daping coefficient should be proportional to the Feri velocity divided by the particle diaeter d [17]. Since the plason wave vector is inversely proportional to d, the size dependence of the daping coefficient can F F be odelled well by Av / d, where v 1.39 M/s is the Feri velocity for gold. Because the diensionless paraeter A for bulk is 2, the daping coefficient of the bulk gold can be estiated as 2v / l 0.23 PHz. Analyzing further Eq. (1) unveils that the daping F coefficient is approxiately equal to spectru width at half axiu, i.e.. The syetrized width at half axiu of the experiental spectra is plotted in Fig. 3 as a function of the reciprocal GNPs diaeter. In Fig. 3 the experiental data are plotted in accordance to Eq. (3) as open circles refer to synthesis at teperatures 90 C fro TEM (Fig. 4A), DLS (Fig. 4B), and AFM (Fig. 4C) also at 70 C (black circles) [3, 4].

6 Fig. 3. The syetrized width at half axiu PHz of the experiental spectra as a function of the reciprocal particle diaeter 2πvF/d PHz. The data for are obtained fro UV-Vis spectra during the citrate synthesis perfored 90 C (open circles) and 70 C (black circles). The data for GNPs diaeter are obtained fro size distribution axia: (A) TEM; (B) DLS; (C) AFM. The error bars represent the standard deviation. The coparison of slopes and intercepts fro linear fits in Fig. 3 are presented at Table 1. All of the applied experiental ethods: TEM, DLS and AFM gives siilar values fro theoretical fits. Table 1 Linear fit Teperature TEM DLS AFM Slope 90 C Intercept 90 C Slope 70 C 0.79 intercept 70 C 0.21 As is seen, the theoretical prediction describes well the experiental data. Using the relation above, one can replace the daping coefficient with the experientally easured in Eq. (3) to obtain after soe rearrangeents the following equation: 1 (2 1)( 1) 2 2 ax 2 p (4) It shows a fundaental relationship between the resonant frequency ax of the spectral peak 2 2 and the width at half axiu: the su ax is independent on the particle diaeter d. Since decreases with particle size (see Fig. 3), it follows that ax experiences a blue shift with increase of d. In Fig. 4 the experiental data are plotted in accordance to Eq. (4) as open circles refer to synthesizes at teperatures 90 C fro TEM (Fig. 4A). DLS (Fig. 4B), and AFM (Fig. 4C) also at 70 C (black circles) [3, 4]. As is seen, Eq. (4) holds fir and one can calculate the value of the ediu dielectric constant fro 1/ (2 1)( 1) Using the relation n

7 this value can be easily transfored in the relevant refractive index n The easured refractive index of the initial solution is n 1.335, which is close to n of pure water, since the solutions are relatively dilute. Since the value of the refractive index of pure sodiu citrate is n 1.394, the obtained higher value of the refractive index can be attributed to adsorption of citrate anions on the GNPs (c.a. 70%), leading to stabilization of the suspension. Fig. 4. The experientally deterined (ω 2 ax+ 2 )/ω 2 p plotted as a function of the reciprocal particle diaeter 2πvF/d PHz. The eaning of the sybols is the sae as in Fig. 3. The data for are obtained fro UV-Vis spectra during the citrate synthesis perfored at teperature 90 C (open circles) and 70 C (black circles). The data for GNPs diaeter are obtained fro size distribution axia: (A) TEM; (B) DLS; (C) AFM. Conclusions In additional discussion for size and shape there are two plason peaks in the absorbance spectra gold nanorods, fored by growth on spherical citrate stabilized GNPs seeds. The first one corresponds to the so-called transversal plason, localized with respect to the short axis of ellipsoid. It stays constant (525 n) to short axis. The second peak corresponds to the longitudinal plason, localized with respect to the long axis of ellipsoid. With decreasing the aount of spherical citrate stabilized GNPs seeds, the length of ellipsoid is increasing. In this case longitudinal plason is red shifted fro 750 to 980 n with increasing the long axis [18]. The extinction cross section equation for generation of surface plasons in an ellipsoid [1], in difference to sphere, include depolarization factors for the three axes of the ellipsoid. In conclusion the blue shift effect was observed is not to anisotrotropic or tailored GNPs size and shape, or due to aggregation of GNPs. The fundaental Eq. (3), relating the SPR frequency to the GNPs size via the daping paraeter, describes the blue shift of the light absorption. The analytical dependence ( d) ax has only one fitting paraeter, the dielectric perittivity of the surrounding GNPs edia. Thus Eq. (4) was applied for fitting the experiental data extracted fro UV-Vis spectroscopy and AFM iages in the course of GNPs synthesis. Fro the experiental data and the theoretical fit, the refractive index values of the surrounding GNPs edia was deterined, which provides valuable inforation for the adsorption shell (citrate) of the gold nanoparticles.

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