J. Phys. Chem. C 2010, 114, 6989–6993
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Surface Plasmon Response for Anisotropic Silver Particles with Dimensions Below the Electrostatic Limit Stuart T. Gentry* and Mark W. Bezpalko Department of Chemistry and Biochemistry, La Salle UniVersity, 1900 W. Olney AVenue, Philadelphia, PennsylVania, 19141 ReceiVed: January 18, 2010; ReVised Manuscript ReceiVed: March 12, 2010
A seeded process based on the staged addition of sodium borohydride and hydroquinone with silver nitrate was used to form aqueous nanocolloids consisting of a mixture of quasi-spherical and tabular structures. All of the dimensions for these particles were less than the 40 nm limit that marks the transition in spherical particles from a single surface plasmon peak to a broad multipolar signal. Despite the size being below the electrostatic limit, the small tabular particles retained the unique shape of the optical response seen with particles that are large with respect to the optical wavelength. This retention of response shape across the transition from electrostatic to electrodynamic conditions stands in marked contrast to the large change in response seen with spherical particles. The results are explained with respect to the geometry of the resultant induced electrical field across the particles. There is a long history of interest in noble-metal nanoparticles going back to Michael Faraday’s treatise on gold sols in 1857.1 These particles were originally assumed to be spherical, but in 1954, Turkevich, Garton, and Stevenson published micrographs showing the presence of triangular gold particles intermixed with the expected spheres.2 In recent years, nonspherical particles have received a great deal of new interest due to the impact that particle morphology has on Raman spectroscopy, chemical sensors, and catalysis.3 With all of this interest in metallic nanosols, there remains one area that is poorly documented. That is the optical response of nonspherical particles when all the dimensions of the particles are below the critical electrostatic limit. It is known that the optical response of spherical particles undergoes a sharp transition in behavior when particles are either above or below a critical size limit. What is missing is information on whether anisotropic particles show a similar transition. This paper will present data that show that the plasmon behavior of small nonspherical particles is very different than that of their spherical counterparts. The optical response of anisotropic particles does not collapse into one well-defined resonance peak like it does for spheres when the particle size drops to a level that is well below the wavelength of the applied light. Background The optical response of spherical nanosols is well-understood. Mie theory4 correctly predicts the presence of a critical size limit that controls the plasmon signal. This limit is ca. 40 nm in diameter for silver particles in water. For particles below this limit, the applied optical field is uniform across the breadth of the particle and the free electrons in the metal move as a single electron cloud in resonance with the light. These electrostatic (ES) conditions5 generate a characteristic single, sharp peak in the optical response of the particle (Figure 1). So long as the diameter of the particles is kept below this critical size, the wavelength of the plasmon resonance is independent of particle * To whom correspondence should be addressed. E-mail: gentry@ lasalle.edu. Phone: 215-951-1259. Fax: 215-951-1772.
Figure 1. Theoretical calculations on silver spheres in water, with diameters of 20, 40, and 100 nm. Calculations are based on Mie theory.
diameter. For particles larger than this critical size, however, the applied optical electric field begins to vary substantially in magnitude and phase from one end of the particle to the other.6 Consequently, under these electrodynamic (ED) conditions, the electron cloud no longer oscillates as a single dipole unit. The result is that the dipole peak shifts to longer wavelengths while quadrupole and octupole peaks begin to emerge at higher energies. This plasmon behavior changes significantly when one switches from spherical to anisotropic sols. There is no closedform solution to Maxwell’s equations for nonspherical particles, but a number of computational approaches exist for modeling their optical response.7 In almost all cases, however, the published work has concentrated on particles having at least one of the dimensions of the particle being much larger than the spherical electrostatic limit. This implies the presence of a longitudinal plasmon mode that can be distributed across a distance that is large relative to the wavelength of light, similar to large spherical particles. Figure 2 shows experimental data that is typical of large nonspherical particles. On the basis of the literature, the red shifted peak at 902 nm is attributed to a longitudinal (in-plane) dipole mode. The small, sharp peak at
10.1021/jp1004902 2010 American Chemical Society Published on Web 03/25/2010
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Figure 3. Experimental extinction spectrum and TEM for bimodal particles. Particles were formed from addition of sodium citrate prior to seed formation. The inset was taken from the centrifuge supernatant at the same scale as the rest of the TEM. Anisotropic particles have a 6 nm plate thickness and a 25-30 nm face dimension.
Figure 2. Experimental extinction spectra for spherical and triangular nanoprism particles. Spectra are taken from ref 8. The diameters of the spherical particles (a) are 10-11 nm, whereas the dimensions of the triangular particles (b) are 8 nm in thickness and 80-150 nm in edge length. The spherical particles were made with 0.020 mol fraction of BH4 and pH 7 buffer, whereas the nanoprisms were prepared with 0.002 mol fraction of BH4 and slightly acidic pH.
334 nm is characteristic of tabular particles and has been assigned by others as a transverse (out-of-plane) quadrupole signal. There are also overlapping peaks around 400 nm corresponding to longitudinal-quadrupole and transverse-dipole modes, as well as a signal from residual spherical particles. Despite all of this published work, there is very little data on the plasmon response of small, nonspherical particles. Of particular interest in this paper is whether anisotropic particles demonstrate a critical size-dependent transition in their optical response similar to that seen with the spherical particles in Figure 1. We will present experimental data on tabular (flat) particles that have all of their in-plane and out-of-plane dimensions below the spherical electrostatic limit. We will show that the plasmon extinction spectrum for these nanoplate particles retains the same general shape as that seen with large nanoprisms, albeit shifted in wavelength and intensity. There is no collapse of the broad multipolar signal into a single resonance peak when going to small nonspherical particles. This is true even though the dimensions for the small particles are much smaller than the wavelength of light. Experimental Section Sample Preparation. The experimental samples were prepared using a seeded process described in greater detail in ref 8. It consists of a first stage of 0.2 mM aqueous AgNO3 (prepared as a 1.0 mM stock solution) and low-level addition (0.002 mol fraction relative to Ag) of NaBH4 (0.1 mM solution prepared fresh each day, adjusted to pH 7-7.5, and kept chilled in ice water). After a 2 min hold time, the particles were grown out to full size using 1.0 mol fraction of hydroquinone (HQ) as the reducing agent (prepared fresh each day as a 0.05 M solution). Sodium citrate (1.0 mol fraction, 1.0 mM stock solution) was used as the colloidal stabilizer. The stabilizer was added either prior to seed formation or after the seed had been allowed to equilibrate, but before the HQ addition. All chemicals were reagent grade and used as received from the supplier without additional purification. Glassware was soaked in concentrated HNO3 and rinsed multiple times in water. Samples
were stored in the dark during particle formation to ensure that there was no UV-induced reaction.9 Instruments. The plasmon extinction spectra were recorded using an Hitachi U-2910 UV/vis spectrometer. This instrument was run in absorption mode but actually measured the optical extinction because plasmons both absorb and scatter incident light. Transmission electron micrographs were recorded in the bright-field mode using a Phillips CM12 scanning/transmission electron microscope at the U.S. Dept. of Agriculture’s Eastern Regional Research Center. Samples were evaporated on carbonized copper grids, and the microscope was operated at 80 kV. Particle diameters were determined by analyzing the micrographs using ImageJ, a Java program developed at the National Institute of Mental Health.10 The transverse widths of the nanoprisms were determined from micrographs of large aggregatessformed during drying on the TEM gridsmeasuring the widths of particles situated edge-on to the electron beam. Calculations. Theoretical calculations were performed using MiePlot, a software package developed by P. Laven.11 Calculations were based on the program’s optical constant data for silver tabulated by Johnson and Christy.12 The program used optical data for water compiled by Segelstein.13 Results The study of small anisotropic particles below the spherical electrostatic limit is experimentally challenging. It is difficult to control the formation and resultant morphology of such small, nascent particles. Larger particles have the advantage of being able to fill in defects and form more energetically favored structures as they grow in size.8 Furthermore, once small anisotropic particles are formed, they are unstable due to increased Ostwald ripening. The small particles begin to immediately reform, with a substantial degradation in signal seen within 30-60 min (see Figure S8, Supporting Information). By contrast, large nanoprisms like those in Figure 2 are stable over the course of weeks. Because of the aforementioned difficulties, we used two different approaches to study small silver nanoplate sols. Neither experiment is as clean as one would like because of the inherent problems with small particles, but they lead to consistent results and are similar to recent published theoretical calculations. The first approach that was used was to add citrate stabilizer to the formulation prior to seed formation. This generates a distribution of two different types of particles. The micrographs in Figure 3 show quasi-spherical solids with diameters centered around 15-25 nm. These are manifest in the TEM as opaque shapes with multiple domains. The TEM also shows a second
Surface Plasmon Response for Anisotropic Ag Particles
Figure 4. Centrifuged samples. Bimodal samples from Figure 3 were spun for 25 min at 12 000 rpm and a spinning diameter of 5 in. The pellet sample was redispersed in water following centrifugation. The TEM shows the pellet to be concentrated in spherical particles while the supernatant is mixed, but rich in nanoplate particles.
set of particles, seen as translucent uniformly shaded solids, that are tabular with a plate thickness of ca. 6 nm. The flat faces have a variety of geometries, ranging from circular to triangular, but in all cases, the longitudinal diameters (centered around 20-30 nm) are below the 40 nm spherical electrostatic limit. The population ratio between spherical and nonspherical particles for the sample shown in Figure 3 was 64:36, respectively, as defined on the basis of the number of particles of each. (See Figure S3 in the Supporting Information for further information on the particle size distributions for Figure 3.) The optical response in Figure 3 is a bimodal signal with peaks at 400 and 540 nm. It may not seem surprising that two sets of particles should give rise to two sets of optical peaks. It should be remembered, however, that if anisotropic particles responded in the same way to the electrostatic limit as spherical particles, then one would have expected only one peak at 400 nm wavelength whether or not the small particles had two different morphologies. It would take spherical particles larger than 100 nm in diameter to give a second extinction peak at a wavelength of 500-600 nm. Repeated TEM studies of particles like those in Figure 3 clearly show that there are no such large particles in the sample. An alternative explanation would have been that the 540 nm peak was due to chains or other aggregations of small particles.14 There is no TEM evidence for structures of this sort in the dispersed colloids (see Figure S9, Supporting Information). Instead, the peak at 540 nm is due to small, individual, nanoplate particles in the sample even though they are below the electrostatic/electrodynamic transition threshold for spherical particles. To help clarify the difference in plasmon response for the two types of particles, we centrifuged the samples (Figure 4). This generated a supernatant that was rich in anisotropic particles, while the pellet (sediment) was primarily composed of spherical particles. (See Figures S4 and S5 in the Supporting Information for corresponding micrographs.) Unfortunately, differential centrifugation is not sufficiently selective to completely separate nanoplate particles from spherical onessthere is not a large enough difference in relative mass or shape factors to achieve complete separation. However, it is possible to mathematically extract the signal of the nanoplate particles from the data. This can be done by subtracting the signal from the spherical-rich pellet from the anisotropic-rich supernatant signal. We used a weighting factor of 0.71 for subtracting the pellet data from the supernatant. (This factor has little physical meaning because the pellet was redispersed in water to an arbitrary concentration following centrifugation.) Figure 5 shows the resultant signal that is due to just the anisotropic particles. Figure 5 is somewhat surprising. If anisotropic particles responded in the same way to the electrostatic limit as spherical
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Figure 5. Extracted extinction response for anisotropic particles. The curve is the result of subtracting the pellet signal from the supernatant signal. The normalized pellet signal was multiplied by a weighting factor of 0.71 prior to subtraction. Peaks are at 333, 398, and 523 nm.
particles do, then one would expect small anisotropic particles to exhibit a single well-defined peak at 400 nm. The particles in Figure 5 are below the limit where the optical field is uniform across the particle, and one would expect the free-electron cloud to oscillate in resonance with the optical dipole. Even in the absence of the mathematical treatment in Figure 5, it is clear in Figure 4 that there is a large red shifted primary signal at 523 nm and a small sharp higher-order blue shifted peak at 333 nm that are not seen with similarly sized spherical particles. We recognize that the mathematical manipulation of the data in Figure 5 raises questions about the level of confidence in the interpreted results. We, therefore, also pursued a second approach to study small anisotropic particles. This was based on looking at the early particle development when forming large triangular nanoplates like those in Figure 2. These large nanoprisms are prepared by moving the addition of the citrate stabilizer to a point after the formation of the seed rather than prior to it. This small change in experimental procedure changes the size and number of particles and, consequently, generates triangular nanoprisms that have edge lengths on the order of 80-150 nm. These prisms grow via continuous addition of silver to the anisotropic seed particles rather than through accretion of smaller particles.8 Figure 6 shows the early stage development of large nanoprisms of the type shown in Figure 2. What one sees is that, as the particles first begin to grow from their initial seeds, the early stage extinction peak immediately starts to shift to the red. This gradual shift begins at times as early as 1 min. By 5 min, the signal is sufficient to discern the characteristic shape seen with larger nanoprisms (red shifted primary peak above 500 nm and a 333 nm transverse quadrupole peak) even though the particles are still only 20-40 nm in face diameter.8 (See Figure S11 in the Supporting Information for particle size distribution data.) Continued growth beyond 5 min causes a smooth continuation of the red shift until the nanoprisms reach a final peak value greater than 800 nm. The early stage flat particles initially have a mixture of face geometries similar to the samples in Figure 3, but they transition to well-defined triangular faces as they grow to 100 nm in size after 1 h. What is notably absent from the 1-5 min data in Figure 6 is any indication of the initial formation of a single fixed-wavelength dipole resonance peak like that seen with spherical particles below 40 nm. This experiment is cleaner in concept than the data in Figures 3 and 5 because there is a much smaller fraction of residual spherical particles in Figure 6. Unfortunately, the signal-to-noise ratio of the early stage particles in Figure 6 is poor because the desired result of generating large final particles requires having a much smaller number of initial seed particles present in the system. Despite the differences in procedure, the results of Figure 6 are consistent with those in Figure 5. Both show
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Figure 6. Time-development of optical response for the grow-out of triangular nanoprisms. Samples are similar to the nanoprisms in Figure 2, with ∼100 nm triangular edge lengths after full grow-out at 1 h. At earlier times, particles are less defined in their face geometry but are still resolvable nanoplate particles in the TEM at times as early as 5 min of growth (20-40 nm face dimensions) The two sets of graphs are the same sample but drawn with different extinction scales for the y axis.
longitudinal dipole peaks at wavelengths greater than 500 nm and characteristic transverse quadrupole peaks at ca. 330-340 nm even though the particle dimensions are less than 40 nm in size. It is interesting that the blue shifted peak at ca. 334 nm remained at a fixed wavelength as we changed the dimensions of the edge face from 20-150 nm. At the same time as the 334 nm peak remained fixed, the primary peak red shifted in wavelength from 500 to 900 nm. We speculate that the fixed nature of this transverse peak is due to all of our experimental samples having similar plate thicknesses of 6-8 nm even though the face dimensions of the nanoplates underwent large changes. It would be interesting to pursue this question further with subsequent theoretical work, but this line of investigation is outside the scope of the current experimental paper. Furthermore, it is the continuity of the 334 nm peak across our span of samples that allows us to extend the assignment made by others for that peak in large particles as being a transverse quadrupole plasmon mode and maintain the same assignment to small nanoplates below the electrostatic limit. Discussion To our knowledge, this is the first publication of experimental data on nonspherical silver particles (not clusters) where all of the dimensions are less than the spherical electrostatic limit of 40 nm. The theoretical literature is similarly limited. The one exception found for nonspherical sub-ES-limit particles was a recent theoretical article by Yang et al.15 This paper focused on large particles but also included one set of discrete dipole approximation (DDA) calculations on small triangular nanoprisms. These calculations had a plate thickness of 5 nm and an edge length of 25 nm. If one replots Yang’s data in units of wavelength rather than eV, one obtains an optical response similar to that seen experimentally in Figures 5 and 6 (see Figure S12, Supporting Information). It should be noted that compu-
Gentry and Bezpalko tational techniques, such as DDA, are limited when it comes to small particles due to the increasing contribution of quantum effects at the surface of very small particles.16 The similarity of our experimental data for large and small anisotropic particles when comparing Figure 2 to Figures 5 and 6 demonstrates that size has a more limited role in controlling the optical extinction response of nanoplate particles than it does for spherical ones. This is not to ignore the importance of size on the wavelength location of the primary peak in anisotropic particles. It has been shown that the extinction peak can be pushed well into the infrared region of the spectrum by continuing to increase the edge length dimensions of triangular nanoprisms.17 Rather than looking at the absolute peak location, we are focused instead on the general shape of the response. The insensitivity in the shape of the spectrum (red shifted primary peak with a fixed blue shifted quadrupole response) for nanoplate particles stands in sharp contrast to spherical particles whose response morphs from a broad multipolar peak to a single, size-independent, sharp peak when size is reduced from above to below the ES limit. This difference between spherical and anisotropic particles highlights the importance that the geometry of the induced surface field has on the plasmon signal. This induced field arises from the oscillating excess and depletion of electron surface density that builds on opposing sides of the particles when exposed to an external optical field. It is this buildup of surface electron density and their associated induced electric field that generates surface plasmons. Tabular particles undergo this same creation of an induced electric field. In the case of small flat particles, however, the geometry of the overall induced field is that of two parallel plates rather than a dipole field distributed around the surface of a sphere as is the case for Mie theory. It is our premise that this difference in the geometries of the induced field is what generates the differences in the dependence on size for the optical resonance signals seen in spherical versus anisotropic small particles. The dependence of the extinction response on the parallel-plate induced field is able to survive the change in applied optical field from the electrostatic limit (optical field is constant across the particle) to the electrodynamic regime (particle large enough that the applied optical field begins to vary in magnitude and phase from one end of the particle to the other). It may be that the small transverse plate thickness of both large and small triangular nanoprisms plays a major role in defining parallel-plate induced fields, even though it is the longitudinal edge length that most attracts ones initial visual attention. As a final note, this paper has focused on discussing the response of the optical extinction signal to changes in morphology. The shape of the signal was somewhat insensitive to the actual experimental geometry of the flat face, that is, circular, hexagonal, truncated triangular, or fully triangular. Theoretical work by others has explored the full impact that face morphology has on large nanoplates when comparing well-defined triangles, truncated triangles, hexagons, and circular discs.7 In general, the peak of the extinction signal will shift back and forth in wavelength, depending on morphology, but one sees the same general response in the extinction spectrum for the different face geometries of flat particles. What the theoretical papers show, in addition, however, is large differences in the local electric field gradients as a function of face geometry. For example, the local fields at sharp vertices in well-defined triangular nanoprisms are greatly enhanced over those along the faces of the prisms or at the vertices of truncated triangles.
Surface Plasmon Response for Anisotropic Ag Particles These variations in local electric field gradients can have a large impact on the use of nanoparticles as catalysts and their use in surface enhanced raman spectroscopy (SERS), but the variations in local gradient have less impact on the UV/vis extinction spectra discussed here. Summary It is not surprising that Mie theory demonstrates a critical transition that depends on the size of spherical particles as compared to the wavelength of the interacting electromagnetic radiation. What is surprising, however, is that anisotropic particles do not show a similar transition. This paper has demonstrated that nanoplate particles are somewhat insensitive to a transition from electrostatic conditions (particle dimensions small relative to the wavelength of the applied optical field) to electrodynamic conditions (applied optical field varies significantly in magnitude and phase across the particle). The peak location can vary from 500 nm to greater than 1000 nm in wavelength, depending on the size of the tabular crystal face. At the same time, however, the general shape of the extinction response remains roughly the same. This difference in the dependence on particle size for spherical versus nanoplate anisotropic particles points out the large impact that the geometry of the induced surface electric field can have on optical extinction. Although small nanoplates do not seem to have the same potential for applications to other scientific fields as do large nanoplates and nanoprisms, the study of small anisotropic particles does add to our body of knowledge associated with understanding the phenomenon of surface plasmon generation. Acknowledgment. The authors wish to acknowledge the guidance and open access to instrumentation offered by Dr. Peter Cooke at the USDA Eastern Regional Research Center in Philadelphia, PA. We also wish to thank Dr. Kevin L. Shuford (Drexel University) for his insights on the strengths and
J. Phys. Chem. C, Vol. 114, No. 15, 2010 6993 limitations inherent with the computational modeling of plasmon performance. Supporting Information Available: Additional experimental data is included in the Supporting Information that accompanies this paper. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Faraday, M. Philos. Trans. R. Soc. London 1857, 147, 145. (2) Turkevich, J.; Garton, G.; Stevenson, P. C. J. Colloid Sci. 1954, 1, 26. (3) Xia, Y.; Xiong, Y.; Lim, B.; Skrabalak, S. E. Angew. Chem., Int. Ed. 2009, 48, 60. (4) Mie, G. Ann. Phys. 1908, 25, 377. (5) Kelly, K. L.; Coronado, E.; Zhao, L. L.; Schatz, G. C. J. Phys. Chem. B 2003, 107, 668. (6) Link, S.; El-Sayed, M. A. J. Phys. Chem. B 1999, 103, 8410. (7) (a) Jensen, T.; Kelly, L.; Lazarides, A.; Schatz, G. C. J. Cluster Sci. 1999, 10, 295. (b) Maillard, M.; Huang, P.; Brus, L. Nano Lett. 2003, 3, 1611. (c) Sosa, I. O.; Noguez, C.; Barrera, R. G. J. Phys. Chem. B 2003, 107, 6269. (d) Jing, A.; Tang, B.; Ning, X.; Zhou, J.; Xu, S.; Zhao, B.; Weiqing, X.; Corredor, C.; Lombardi, J. R. J. Phys. Chem. C 2007, 111, 18055. (e) Wiley, B.; Sun, Y.; Mayers, B.; Xia, Y. Chem.sEur. J. 2005, 11, 454. (8) Gentry, S. T.; Levit, S. D. J. Phys. Chem. C 2009, 113, 12007. (9) Gentry, S. T.; Fredericks, S. J.; Krchnavek, R. Langmuir 2009, 25, 2613. (10) http://rsb.info.nih.gov/ij (accessed 2/14/09). (11) Laven, P. MiePlot V3.5.01; accessed at www.philiplaven.com, 2009. (12) Johnson, P. B.; Christy, R. W. Phys. ReV. B 1972, 16, 4370. (13) Segelstein, D. The Complex Refractive Index of Water. M.S. Thesis, University of Missouri, Kansas City, 1981. (14) (a) Yang, Y.; Shi, J.; Tanaka, T.; Nogami, M. Langmuir 2007, 23, 12042. (b) Zhao, L. Z.; Kelly, K. L.; Schatz, G. C. J. Phys. Chem. B 2003, 107, 7343. (15) Yang, P.; Portales, H.; Pileni, M.-P. J. Phys. Chem. C 2009, 113, 11597. (16) Private communication with Kevin L. Shuford, Drexel University, 2009. (17) Bastys, V.; Pastoriza-Santos, I.; Rodriguez-Gonzalez, B.; Vaisnoras, R.; Liz-Marzan, L. M. AdV. Funct. Mater 2006, 16, 766.
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