Chemistry in noninteger dimensions between two and three. I. Fractal theory of heterogeneous surfaces

Journal of Chemical Physics - Tập 79 Số 7 - Trang 3558-3565 - 1983
Peter Pfeifer1,2, David Avnir3
1Fakultät für Chemie, Universität Bielefeld, D 4800 Bielefeld, Federal Republic of Germany
2The Fritz Haber Research Center for Molecular Dynamics, The Hebrew University of Jerusalem, Jersusalem 91904, Israel
3Department of Organic Chemistry, The Hebrew University of Jerusalem, Jersusalem 91904, Israel

Tóm tắt

In this, the first of a series of papers, we lay the foundations for appreciation of chemical surfaces as D-dimensional objects where 2≤D<3. Being a global measure of surface irregularity, this dimension labels an extremely heterogeneous surface by a value far from two. It implies, e.g., that any monolayer on such a surface resembles three-dimensional bulk rather than a two-dimensional film because the number of adsorption sites within distance l from any fixed site, grows as lD. Generally, a particular value of D means that any typical piece of the surface unfolds into mD similar pieces upon m-fold magnification (self-similarity). The underlying concept of fractal dimension D is reviewed and illustrated in a form adapted to surface-chemical problems. From this, we derive three major methods to determine D of a given solid surface which establish powerful connections between several surface properties: (1) The surface area A depends on the cross-section area σ of different molecules used for monolayer coverage, according to A∝σ(2−D)/2. (2) The surface area of a fixed amount of powdered adsorbent, as measured from monolayer coverage by a fixed adsorbate, relates to the radius of adsorbent particles according to A∝RD−3. (3) If surface heterogeneity comes from pores, then −dV/dρ∝ρ2−D where V is the cumulative volume of pores with radius ≥ρ. Also statistical mechanical implications are discussed.

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Tài liệu tham khảo

1983, Nouv. J. Chim., 7, 71

1983, Surf. Sci., 126, 569, 10.1016/0039-6028(83)90759-8

1972, Essays Phys., 4, 43

1979, Sci. Am., 241, 140

1980, Phys. Rev. Lett., 45, 1456, 10.1103/PhysRevLett.45.1456

1964, J. Phys. Chem., 68, 2562, 10.1021/j100791a029

1967, J. Coll. Interface Sci., 23, 577, 10.1016/0021-9797(67)90204-4

1981, Rev. Mod. Phys., 53, 199, 10.1103/RevModPhys.53.199

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Journal of Chemical Physics

Tập 79 Số 7

3558-3565

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