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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Lower and upper bounds are derived for the decay and transitions of quantum states, evolving under a

The concept of fractal dimension D of surfaces, advanced as natural measure of surface irregularity in part I of this series, is shown to apply to a remarkable variety of adsorbents: graphites, fume silica, faujasite, crushed glass, charcoals, and silica gel. The D values found for these examples vary from two to almost three (for smooth and very irregular surfaces, respectively), thus covering the whole possible range. They quantify the intuitive picture that surface inhomogeneities are minor, e.g., in graphites, but dominant, e.g., in charcoal. The analysis is based on adsorption data, with main focus on adsorbates of varying molecular cross section. They include N2, alkanes, polycyclic aromatics, a quaternary ammonium salt, and polymers. The straight-line plots so obtained confirm also a number of reported on-surface conformations of specific adsorbates. The converse method to get D from varying the size of adsorbent particles is exemplified for fume silica and crushed glass.