Abstract
The multifractal approach has been employed to quantitatively analyze an intact glassy polymer (polystyrene) surface and that deformed in an atomic force microscope. An algorithm has been described in detail for constructing generalized fractal dimension spectra. These spectra have been shown to provide information that reasonably reflects the properties of the studied reliefs of a polystyrene surface.
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Herminghaus, S., Jacobs, K., and Seemann, R., Eur. Phys. J. E, 2001, vol. 5, p. 534.
De Gennes, P.-G., Scaling Concepts in Polymer Physics, Ithaca: Cornell Univ. Press, 1979.
Grosberg, A.Yu. and Khokhlov, A.R., Statistical Physics of Macromolecules, Ithaca: AIP, 1994.
Doi, M. and Edvards, S.F., The Theory of Polymer Dynamics, Oxford: Clarendon, 1986.
Blavatska, V., von Ferber, C., and Holovatch, Yu., Philos. Mag., 2008, vol. 88, p. 4085.
Fractals in Physics, Pietronero, L. and Tosatti, E., Eds., Amsterdam: North-Holland, 1986.
Bliznyuk, V.N., Burlakov, V.M., Assender, H.E., Briggs, G.A.D., and Tsukahara, Y., Macromol. Symp., 2001, vol. 167. p. 89
Havlin, S. and Ben-Avraham, D., J. Phys. A: Math. Gen., 1982, vol. 15, p. L311.
Muthukuma, M., J. Chem. Phys., 1985, vol. 63, p. 3161.
Cates, M.E., Phys. Rev. Lett., 1984, vol. 53, p. 926.
von Ferber, C. and Holovatch, Yu., Europhys. Lett., 1997, vol. 39, p. 31.
Monthus, C. and Garel, Th., Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top., 2007, vol. 75, p. 051122.
Mills, S.L., Lees, G.C., Liauw, C.M., and Lynch, S., Polym. Test., 2002, vol. 21, p. 941.
Mills, S.L., Lees, G.C., Liauw, C.M., and Lynch, S., Macromol. Mater. Eng., 2004, vol. 289, p. 864.
Mills, S.L., Lees, G.C., Liauw, C.M., Rothon, R.N., and Lynch, S., J. Macromol. Sci. B, 2005, vol. 44, p. 1137.
Gu, G.-F. and Zhou, W.-X., Phys. Rev. Lett., 2006, vol. 74, p. 061104.
Liu, Ch., Jiang, X.-L., Liu, T., Zhao, L., Zhou, W.-X., and Yuan, W.-K., Appl. Surf. Sci., 2009, vol. 255, p. 4239.
Balankin, A.S. and Bugrimov, A.L., Vysokomol. Soedin., Ser. A, 1992, vol. 34, p. 129.
Balankin, A.S. and Bugrimov, A.L., Vysokomol. Soedin., Ser. A, 1992, vol. 34, p. 135.
Balankin, A.S., Izotov, A.D., and Lazarev, V.B., Neorg. Mater., 1993, vol. 29, p. 451.
Balankin, A.S., Izotov, A.D., and Novikov, V.U., Inorg. Mater., 1999, vol. 35, p. 1047.
Balankin, A.S., Phys. Lett. A, 1996, vol. 210, p. 51.
Balankin, A.S., Phys. Rev. B, 1996, vol. 53, p. 5438.
Blumen, A. and Jurjiu, A., J. Chem. Phys., 2002, vol. 116, p. 2636.
Magonov, S.N., Polym. Sci., Ser. B, 1996, vol. 38, p. 34.
Leung, O.M. and Goh, M.C., Science (Washington, D.C.), 1992, vol. 255, p. 64.
Meyers, G.F., DeKoven, B.M., and Seitz, J.T., Langmuir, 1992, vol. 8, p. 2330.
Yang, A.C.M., Terris, B.D., and Runz, M., Macromolecules, 1991, vol. 24, p. 6800.
Albrecht, T.R., Dovek, M.M., Lang, C.A., Grutter, P., Quate, C.F., Kuan, S.W.J., Frank, C.W., and Pease, R.F.W., J. Appl. Phys., 1988, vol. 64, p. 1178.
Drake, B., Prater, C.B., Weisenhorn, A.L., Gould, S.A.C., Albrecht, T.R., Quate, C.F., Cannel, D.S., Hansma, H.G., and Hansma, P.K., Science (Washington, D. C.), 1989, vol. 243, p. 1586.
Jing, J., Henriksen, P.N., and Wang, H., J. Mater. Sci., 1995, vol. 30, p. 5700.
Mizes, H.A., Lon, K.G., Miller, R.J.D., Ahuja, S.K., and Grabowski, E.F., Appl. Phys. Lett., 1991, vol. 59, p. 2901.
Schmidt, R.H., Haungstad, G., and Gladfelter, W.L., Langmuir, 2003, vol. 19, p. 898.
Berger, R., Cheng, Y., Forch, R., Gotsmann, B., Gutmann, J.S., Pakula, T., Rietzler, U., Schartl, W., Schmidt, M., Strack, A., Windeln, J., and Butt, H.-J., Langmuir, 2007, vol. 23, p. 3150.
Ge, S., Pu, Y., Zhang, W., Rafailovich, M., and Sokolov, J., Phys. Rev. Lett., 2000, vol. 85, p. 2340.
Goldbeck-Wood, G., Bliznyuk, V.N., Burlakov, V.M., Assender, H.E., Briggs, G.A.D., Tsukahara, Y., Anderson, K.L., and Windle, A.H., Macromolecules, 2002, vol. 35, p. 5283.
Bliznyuk, V.N., Assender, H.E., and Briggs, G.A.D., Macromolecules, 2002, vol. 35, p. 6613.
Wang, X.P., Loy, M.M.T., and Xiao, X., Nanotechnology, 2002, vol. 13, p. 478.
Tsui, O.K.S., Wang, X.P., Ho, J.Y.L., and Xiao, X., Macromolecules, 2000, vol. 33, p. 4198.
Mandelbrot, B.B., The Fractal Geometry of Nature, New York: W.H. Freeman, 1982.
Feder, E., Fractals, New York: Plenum, 1988.
Roldughin, V.I., Usp. Khim., 2003, vol. 72, p. 931.
Roldughin, V.I., Usp. Khim., 2003, vol. 72, p. 1028.
Vysotskii, V.V. and Roldughin, V.I., Colloid J., 1998, vol. 60, p. 673.
Roldughin, V.I. and Vysotskii, V.V., Prog. Org. Coat., 2000, vol. 39, p. 81.
Filonov, A.S. and Yaminskii, I.V., Rukovodstvo pol’zovatelya paketa programmnogo obespecheniya dlya upravleniya skaniruyushchim zondovym mikroskopom i obrabotki izobrazhenii “FemtoSkan-001”. Versiya 2.16 (User’s Guide of Program Package for Control of Scanning Probe Microscope and Image Processing FemtoScan-001. Version 2.16), Moscow: Tsentr Perspektivnykh Tekhnologii, 1999.
Chhabra, A.B. and Jensen, R.V., Phys. Rev. Lett., 1989, vol. 62, p. 1327.
Chhabra, A.B., Meneveau, C., Jensen, R.V., and Screenivasan, K.R., Phys. Rev. A, 1989, vol. 40, p. 5284.
Pavlov, A.N. and Anishchenko, V.S., Usp. Fiz. Nauk, 2007, vol. 177, p. 859.
Bozhokin, S.V. and Parshin, D.A., Fraktaly i mul’tifraktaly (Fractals and Multifractals), Izhevsk: NITs Regulyarnaya Khaoticheskaya Dinamika, 2001.
Johannsmann, D., Eur. Phys. J. E, 2002, vol. 8, p. 257.
Forrest, J.A., Dalnoki-Veress, K., Stevens, J.R., and Dutcher, J.R., Phys. Rev. Lett., 1996, vol. 77, p. 2002.
Hall, D.B., Hooker, J.C., and Torkelson, J.M., Macromolecules, 1997, vol. 30, p. 667.
Kajiyama, T., Tanaka, K., Satomi, N., and Takahara, A., Macromolecules, 1998, vol. 31, p. 5150.
Dement’eva, O.V., Zaitseva, A.V., Kartseva, M.E., Ogarev, V.A., and Rudoy, V.M., Colloid J., 2007, vol. 69, p. 278.
Frichsen, J., Kanzow, J., Schurmann, U., Dolgner, K., Gunther-Schade, K., Strunskus, T., Zaporojtchenko, V., and Faupel, F., Macromolecules, 2004, vol. 37, p. 1831.
Teichroeb, J.H. and Forrest, J.A., Phys. Rev. Lett., 2003, vol. 91, p. 016104.
Kimura, K., Kobayashi, K., Yamada, H., Horiuchi, T., Ishida, K., and Matsushige, K., Eur. Polym. J., 2004, vol. 40, p. 933.
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Original Russian Text © V.M. Sukhov, V.M. Rudoy, 2014, published in Kolloidnyi Zhurnal, 2014, Vol. 76, No. 1, pp. 92–102.
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Sukhov, V.M., Rudoy, V.M. Multifractal analysis of nanodeformation of glassy polymer surface. Colloid J 76, 85–95 (2014). https://doi.org/10.1134/S1061933X1401013X
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DOI: https://doi.org/10.1134/S1061933X1401013X