Abstract
Spectra of absorption (400–800 nm) by the aggregates of colloidal gold (5, 15, and 30 nm in diameter) and silver (20 nm in diameter) particles were studied experimentally and theoretically. It was revealed that, during fast aggregation corresponding to the diffusion-limited cluster aggregation (DLCA), the pattern of spectra is dependent on the size of primary particles. Spectra with the additional absorption maximum in the red region are observed for 15 and 30 nm gold and 20 nm silver particles, while the absorption spectrum for 5 nm particles is characterized by only one maximum shifted to the red region. The slow aggregation resulted in a decrease in plasmon absorption peak with no marked shift to the red region and to the broadening of long-wave absorption wing. From data on electron microscopy, typical branched DLCA-clusters were formed during fast aggregation, whereas small compact aggregates and a noticeable number of single particles were observed in a system during slow aggregation. The computer model of the diffusion-limited cluster-cluster aggregation was used to explain these results. Optical properties of aggregates were calculated using coupled dipole method (CDM or DDA) and the exact method of a multipole expansion. Corrections for the size effect were introduced into the bulk optical constants of metals for nanosized particles. It was shown that a modified version of DDA (Markel et al.,Phys. Rev. B, 1996, vol. 53, no. 5, p. 2425) allows us to explain the pattern of experimental spectra of DLCA-aggregates and their dependence on a monomer size. The exact method was applied to calculate the extinction cross sections of metallic aggregates demonstrating strong electrodynamic interaction between particles. The number of higher multipoles that are required to adequately describe this interaction is much larger than the number of terms of an ordinary Mie series and is the main obstacle to the exact calculation of the spectra of metallic aggregates with a large number of particles.
Similar content being viewed by others
REFERENCES
Bohren, C.F. and Huffman, D.R., Absorption and Scattering of Light by Small Particles, New York: Wiley, 1983. Translated under the title Pogloshchenie i rasseyanie sveta malymi chastitsami, Moscow: Mir, 1986.
Shalaev, V.M. and Shtokman, M.I., Zh. Eksp. Teor. Fiz., 1987, vol. 92,no. 2, p. 509.
Markel', V.A., Muratov, L.S., and Shtokman, M.I., Zh. Eksp. Teor. Fiz., 1990, vol. 98,no. 3, p. 819.
Markel, V.A., Shalaev, V.M., Stechel, E.B., et al., Phys. Rev. B, 1996, vol. 53,no. 5, p. 2425.
Rautian, S.G., Safonov, V.P., Chubakov, P.A., et al., Pis'ma Zh. Eksp. Teor. Fiz., 1988, vol. 47,no. 4, p. 200.
Butenko, A.V., Chubakov, P.A., Danilova, Yu.E., et al., Z. Phys. D, 1990, vol. 17, p. 283.
Shalaev, V.M., Poliakov, E.Y., and Markel, V.A., Phys. Rev. B, 1996, vol. 53,no. 5, p. 2437.
Tsai, D.R., Kovacs, J., Wang, Zh., et al., Phys. Rev. Lett., 1994, vol. 72,no. 26, p. 4149.
Karpov, S.V., Popov, A.K., Rautian, S.G., et al., Pis'ma Zh. Eksp. Teor. Fiz., 1988, vol. 48,no. 10, p. 528.
Safonov, V.P., Shalaev, V.M., Markel, V.A., et al., Phys. Rev. Lett., 1998, vol. 80,no. 5, p. 1102.
Bruning, J.H. and Lo, Y.T., IEEE Trans. Antennas Propag., 1971, vol. AP-19, p. 378; p. 391.
Borghese, F., Denti, P., Toscano, G., and Sindoni, O.I., Appl. Opt., 1979, vol. 18,no. 1, p. 116.
Gerardy, J.M. and Ausloos, M., Phys. Rev. B, 1982, vol. 25,no. 6, p. 4204.
Mackowski, D.W., J. Opt. Soc. Am. A, 1994, vol. 11,no. 11, p. 2851.
Fuller, K., J. Opt. Soc. Am. A, 1994, vol. 11,no. 12, p. 3251.
Xu, Y.-L., Appl. Opt., 1995, vol. 34,no. 21, p. 4573.
Mackowski, D.W. and Mishchenko, M.I., J. Opt. Soc. Am. A, 1996, vol. 13,no. 11, p. 2266.
Xu, Y.-L., Appl. Opt., 1997, vol. 36,no. 36, p. 9496.
Purcell, E.M. and Pennypacker, C.R., Astrophys. J., 1973, vol. 186,no. 2, p. 705.
Ravey, J.-C., J. Colloid Interface Sci., 1974, vol. 46, p. 139.
Jones, A.R., Proc. Roy. Soc. London, Ser. A, 1979, vol. 366, p. 111.
Chiappetta, P., J. Phys. A: Math. Gen., 1980, vol. 13, p. 2101.
Draine, B.T., Astrophys. J., 1988, vol. 333,no. 2, p. 848.
Draine, B.T. and Flatau, P.J., J. Opt. Soc. Am. A, 1994, vol. 11,no. 4, p. 1491.
Lumme, K. and Rahola, J., Astrophys. J., 1994, vol. 425, p. 653.
Lakhtakia, A. and Mulholland, G.W., J. Res. Natl. Inst. Stand. Technol., 1993, vol. 98,no. 6, p. 699.
Quinten, M. and Kreibig, U., Surf. Sci., 1986, vol. 172,no. 3, p. 557.
Quinten, M. and Kreibig, U., in Optical Particle Sizing: Theory and Practice, Gouesbet, G. and Grehan, G., Eds., New York: Plenum, 1988, p. 249.
Quinten, M., Schönauer, D., and Kreibig, U., Z. Phys. D, 1989, vol. 12, p. 521.
Quinten, M. and Kreibig, U., Appl. Opt., 1993, vol. 32,no. 30, p. 6173.
Kahlau, T., Quinten, M., and Kreibig, U., Appl. Phys. A, 1996, vol. 62, p. 19.
Dykman, L.A. and Bogatyrev, V.A., Biokhimiya, 1997, vol. 62,no. 5, p. 411.
Schalkhammer, T., Chem. Monthly, 1998, vol. 129,no. 10, p. 1067.
Collier, C.P., Vossmeyer, T., and Heath, J.R., Ann. Rev. Phys. Chem., 1998, vol. 49, p. 371.
Khlebtsov, N.G., Bogatyrev, V.A., Dykman, L.A., and Mel'nikov, A.G., Kolloidn. Zh., 1995, vol. 57,no. 3, p. 412; Erratum: Kolloidn. Zh., 1996, vol. 58, no. 1, p. 144.
Khlebtsov, N.G., Bogatyrev, V.A., Dykman, L.A., and Melnikov, A.G., J. Colloid Interface Sci., 1996, vol. 180, p. 436.
Khlebtsov, N.G., Bogatyrev, V.A., Dykman, L.A., and Mel'nikov, A.G., Opt. Spektrosk., 1996, vol. 80,no. 1, p. 128.
Tsar'kova, L.A. and Lopatina, L.I., Kolloidn. Zh., 1998, vol. 60,no. 5, p. 698.
Kerker, M., J. Colloid Interface Sci., 1985, vol. 105,no. 2, p. 297.
Karpov, S.V., Popov, A.K., Slabko, V.V., and Shevnina, G.B., Kolloidn. Zh., 1995, vol. 57,no. 2, p. 199.
Karpov, S.V., Bas'ko, A.L., Koshelev, S.V., et al., Kolloidn. Zh., 1997, vol. 59,no. 6, p. 765.
Danilova, Yu.E. and Safonov, V.P., Fractal Reviews in the Natural and Applied Sciences, Novak, M.M., Ed., London: Chapman and Hall, 1995, p. 101.
Danilova, Yu.E., Rautian, S.G., and Safonov, V.P., Izv. Russ. Akad. Nauk, Ser. Fiz., 1996, vol. 60,no. 3, p. 56.
Meakin, P., Ann. Rev. Phys. Chem., 1988, vol. 39, p. 237.
Khlebtsov, N.G. and Mel'nikov, A.G., Kolloidn. Zh., 1998, vol. 60,no. 6, p. 843.
Born, M. and Wolf, E., Principles of Optics, Oxford: Pergamon, 1968, 4th ed. Translated under the title Osnovy optiki, Moscow: Nauka, 1973.
Goedecke, G.H. and O'Brien, S.G., Appl. Opt., 1988, vol. 27,no. 12, p. 2431.
Draine, B.T. and Goodman, J., Astrophys. J., 1993, vol. 405,no. 2, p. 685.
Danilova, Yu.E., Localization of Optical Excitation in Colloidal Aggregates of Silver, Cand. Sci. (Phys.-Math.) Dissertation, Novosibirsk: Inst. Automatics and Electrometry, Siberian Division, Russian Academy of Sciences, 1999.
McClain, W.M. and Ghoul, W.A., J. Chem. Phys., 1986, vol. 84,no. 12, p. 6609.
Singham, M.K., Singham, S.B., and Salzman, G.C., J. Chem. Phys., 1986, vol. 85,no. 7, p. 3807.
Quinten, M., Z. Phys. B: Condens. Matter, 1996, vol. 101, p. 211.
Gouesbet, G. and Grehan, G., J. Opt. (Paris), 1982, vol. 13, p. 97.
Gouesbet, G., Maheu, B., and Grehan, G., J. Opt. (Paris), 1985, vol. 16, p. 83.
Xu, Y.-L., J. Comput. Phys., 1998, vol. 139, p. 137.
Wilkinson, J.H. and Reinsch, C., Handbook for Automatic Computation. Linear Algebra, Berlin: Springer, 1974.
Flatau, P.J., Opt. Lett., 1997, vol. 22,no. 16, p. 1205.
Waterman, P.C., Phys. Rev. D, 1971, vol. 3,no. 4, p. 825.
Frens, G., Nature Phys. Sci., 1973, vol. 241,no. 105, p. 20.
Bogatyrev, V.A., Dykman, L.A., and Shchegolev, S.Yu, RF Patent 2 013 374, Byull. Izobret., 1994, no. 10, p. 1.
Fabrikanos, A., Athanassiou, S., and Lieser, K.H., Z. Naturforsch., 1963, vol. 18, p. 612.
Khlebtsov, N.G., Appl. Opt., 1996, vol. 35,no. 21, p. 4261.
Lin, M.Y., Lindsay, H.M., Weitz, D.A., et al., Nature, 1989, vol. 339,no. 6223, p. 360.
Jullien, R., New J. Chem., 1990, vol. 14,no. 3, p. 239.
Xu, Y.-L., private communication.
Mishchenko, M.I., Travis, L.D., and Mackowski, D.W., J. Quant. Spectrosc. Radiat. Transf., 1996, vol. 55,no. 5, p. 535.
Varshalovich, D.A., Moskalev, A.N., and Khersonskii, V.K., Quantum Theory of Angular Momentum, Singapore: World Scientific, 1988.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Khlebtsov, N.G., Dykman, L.A., Krasnov, Y.M. et al. Light Absorption by the Clusters of Colloidal Gold and Silver Particles Formed During Slow and Fast Aggregation. Colloid Journal 62, 765–779 (2000). https://doi.org/10.1023/A:1026643111821
Issue Date:
DOI: https://doi.org/10.1023/A:1026643111821