Abstract
Heterogeneous condensed-state processes take place at interfaces of different phases. In general, the surfaces are not perfectly flat and their properties are not homogeneous: they are mostly rough with many irregularities and inhomogeneities. Surface geometric inhomogeneity is reflected in its chemical inhomogeneity. For the description of the structure of physical objects with inhomogeneous properties (roughness, mass density, heat density, etc.), the methods of fractal geometry can be applied (Šesták J, Science of heat and thermophysical studies: a generalized approach to thermal analysis. Elsevier, Amsterdam, 2005). The word “fractal” originates from the Latin word “fractus,” meaning broken. It is indicated that fractals are widespread and that the fractal geometry is the geometry of Nature (Barnsley MF, Fractals everywhere. Academic, New York, 1993). Classical geometry provides a first approximation to the structure of physical objects; it is the language that we use to communicate the designs of technological products and, very approximately, the forms of natural creations. Fractal geometry is an extension of classical geometry. It can be used to make precise models of physical structures of rough surfaces, disordered layers on surfaces and porous objects (such as heterogeneous catalysts). Furthermore, gels, soot, and smoke, and most macromolecules, are also fractals (Sadana A, Engineering biosensors: kinetics and design applications. Academic, New York, 2002).
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References
Šesták J (2005) Science of heat and thermophysical studies: a generalized approach to thermal analysis. Elsevier, Amsterdam
Barnsley MF (1993) Fractals everywhere. Academic, New York
Sadana A (2002) Engineering biosensors: kinetics and design applications. Academic, New York
Mandelbrot B (1983) The fractal geometry of nature. Macmillan, New York
Atkins PW (1998) Physical chemistry. Oxford University Press, Oxford
Zmeskal O, Nezadal M, Buchnicek M (2004) Field and potential of fractal–Cantorian structures and El Naschie‘s E- infinite theory. Chaos Solitons Fractals 19:1013–1022
Zmeskal O, Buchnicek M, Vala M (2005) Thermal properties of bodies in fractal and cantorian physics. Chaos Solitons Fractals 25:941–954
Zmeskal O, Vala M, Weiter M, Stefkova P (2009) Fractal-cantorian geometry of space-time. Chaos Solitons Fractals 42:1878–1892
Šesták J, Kratochvil J (1973) Rational approach to thermodynamic processes and constitutive equation. J Therm Anal 5:193–201
Šimon P (2006) Considerations on the single-step kinetics approximation. J Therm Anal Calorim 82:651–657
Šimon P (2007) The single-step approximation: attributes, strong and weak sides. J Therm Anal Calorim 88:709–715
Ozao R, Ochiai M (1993) Fractal nature and thermal analysis of powders. J Therm Anal 40:1331–1340
Avrami M (1939) Kinetics of phase change. I. General theory. J Chem Phys 7(12):1103–1112
Avrami M (1940) Kinetics of phase change. II. Transformation–time relations for random distribution of nuclei. J Chem Phys 8(2):212–224
Avrami M (1941) Kinetics of phase change. III. Granulation, phase change, and microstructure. J Chem Phys 9(2):177–184
Jena SK, Chaturvedi MC (1992) Phase transformations in materials. Prentice Hall, Upper Saddle River
Kemeny T, Šesták J (1987) Comparison of crystallization kinetics determined by isothermal and nonisothermal evaluation methods. Thermochim Acta 110:113–129
Flynn JH (1997) The “temperature integral:” its use and abuse. Thermochim Acta 300:83–92
Kaye BH (1994) A random walk through fractal dimensions. VCH, Weinheim
Rothschild WG (1998) Fractals in chemistry. Wiley, New York
Avnir D (1989) Fractal approach to heterogeneous chemistry. Wiley, New York
Kopelman R (1988) Fractal reaction kinetics. Science 241:1620–1626
Ochiai M, Ozao R (1992) Fundamental properties in fractal nature and thermal analysis of powders. J Therm Anal 38:1901–1910
Ochiai M, Ozao R (1992) Thermal analysis and self-similarity law in particle size distribution of powder samples. Part 1. Thermochim Acta 198:279–287
Ozao R, Ochiai M (1992) Thermal analysis and self-similarity law in particle size distribution of powder samples. Part 2. Thermochimica Acta 198:289–295
Lazarev VB, Izotov AD, Gavrichev KS, Shebershneva OV (1995) Fractal model of heat capacity for substances with diamond-like structures. Thermochimica Acta 269/270:109–116
Segal E (1998) Fractal approach in the kinetics of solid-gas decompositions. J Therm Anal 52:537–542
Segal E (2000) Fractal approach in the kinetics of solid-gas decompositions. Part II. J Therm Anal 61:979–984
Holeček M (2000) Scale axis, fractals and some thermal phenomena. J Therm Anal 60:1093–1100
Kalinin SV, Vertegel AA, Oleynikov NN, Tretyakov YD (1998) Kinetics of solid state reactions with fractal reagent. J Mater Synth Proc 6:305–309
Vlad O, Popa VT, Segal E, Ross J (2005) Multiple rate-determining steps for non-ideal and fractal kinetics. J Phys Chem B 109:2455–2460
Šesták J (2005) Modeling reaction mechanism: the use of Euclidian and fractal geometry. In: Science of heat and thermophysical studies: a generalized approach to thermal analysis. Elsevier, Amsterdam, pp 277–345
Šesták J (2012) Rationale and fallacy of thermoanalytical kinetic patterns: how we model subject matter. J Therm Anal Calorim doi:10.1007/s10973-011-2089-1, published online 21, December 2011 (in press)
Kalva Z, Sestak J, Mareš JJ, Stávek J (2009) Transdisciplinarity of diffusion including aspects of quasiparticles, quantum diffusion and self-organized reactions periodicity. In: Šesták J, Holeček M, Málek J (eds) Some thermodynamic, structural and behavioral aspects of materials accentuating non-crystalline states. OPS-ZCU, Pilsen
Kalva Z, Šesták J (2004) Transdisciplinary aspects of diffusion and magnetocaloric effect. J Therm Anal Calorim 76:67–74
Jesenák V (1985) Philosophy of the mechanism of diffusion controlled processes. Thermochim Acta 92:39
Jesenák V (1985) Thermal effects of oscillating solid-state reactions. Thermochim Acta 85:91
Avramov I, Höche T, Rüssel C (1999) Is there a crystallization pendulum? J Chem Phys 110(17):8676–8678
Elliot RS (1989) Eutectic solidification processing: crystalline and glassy alloys. Butterworth, London
Šesták J (2004) Disequilibria and dendritic growth. In: Heat, thermal analysis and society. Nucleus, Hradec Kralove
Mareš JJ, Šesták J, Hubík P (2011) Transport constitutive relations, quantum diffusion and periodic reactions. In: Šesták J, Mareš JJ, Hubík P (eds) Glassy, amorphous and nano-crystalline materials, Berlin, Springer, pp 227--244
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Šimon, P., Zmeškal, O., Šesták, J. (2012). Fractals in Solid-State Processes. In: Šesták, J., Šimon, P. (eds) Thermal analysis of Micro, Nano- and Non-Crystalline Materials. Hot Topics in Thermal Analysis and Calorimetry, vol 9. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3150-1_12
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