TY - JOUR
T1 - Chemistry in noninteger dimensions between two and three. I. Fractal theory of heterogeneous surfaces
AU - Pfeifer, Peter
AU - Avnir, David
PY - 1983
Y1 - 1983
N2 - 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 a 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.
AB - 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 a 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.
UR - http://www.scopus.com/inward/record.url?scp=0011836746&partnerID=8YFLogxK
U2 - 10.1063/1.446210
DO - 10.1063/1.446210
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AN - SCOPUS:0011836746
SN - 0021-9606
VL - 79
SP - 3558
EP - 3565
JO - The Journal of Chemical Physics
JF - The Journal of Chemical Physics
IS - 7
ER -