David Avnir

Multiple Resolution Texture Analysis and Classification

Textures are classified based on the change in their properties with changing resolution. The area of the gray level surface is measured at serveral resolutions. This area decreases at coarser resolutions since fine details that contribute to the area disappear. Fractal properties of the picture are computed from the rate of this decrease in area, and are used for texture comparison and classification. The relation of a texture picture to its negative, and directional properties, are also discussed.

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

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 cov...

Recent bio-applications of sol-gel materials

This review is devoted to the most recent developments (2000–2005) of sol–gel materials at the interface with biology. In the context of bioencapsulation in mineral hosts, novel synthetic approaches have been designed, allowing the immobilization of numerous proteins, enzymes and immune molecules as well as poly-saccharides, phospholipids and nucleic acids. These efforts have led to the development of new biosensors and bioreactors. A similar trend was also observed for whole cell encapsulation, survival periods over several weeks now being achieved. This has opened the possibility of designing hybrid hosts for cell-based biosensing and bioproduction, ultimately allowing the development of artificial organs. Indeed, applications of sol–gel processes are not restricted to bioencapsulation, as demonstrated by recent progress in drug release systems and bioactive materials. Finally, the considerable efforts devoted to the biomimetic elaboration of mineral structures suggest that they might be the key for future development of improved sol–gel materials for bio-applications.

Chemistry in noninteger dimensions between two and three. II. Fractal surfaces of adsorbents

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.

Biochemically active sol-gel glasses: The trapping of enzymes ☆

Abstract We describe the preparation and properties of a biochemically active sol-gel glass, obtained by trapping the enzyme alkaline phosphatase (ALP) in a polymerizing tetramethoxysilane. The immobilized purified ALP from bovine intestinal mucosa had a 30% activity yield and an improved stability to thermal deactivation compared to a solution. The composite bioactive glass was preserved in water at room temperature for two months without loosing activity. A non-Michaelis-Menten kinetics was observed. The concept of preparing bioactive materials by the sol-gel method seems to be general. Thus, other enzymes (chitinase, aspartase, β-glucosidase) were successfully trapped.

Organic fluorescent dyes trapped in silica and silica-titania thin films by the sol-gel method. Photophysical, film and cage properties

Abstract The sol-gel process is utilized to solve the notorious problem of incorporating an organic dye in an inorganic oxide thin film. Fluorescent thin films are prepared by this low temperature process with the aid of a surface active agent, with good homogeneity and reproducability. A variety of organic fluorescent molecules are embeded either in silica or in silica-titania films. The dye molecules are not leached out by water. Absorption and emission spectra, enhanced photostability, longer lifetimes and energy transfers between the trapped dye molecules are described and discussed in terms of the effects of molecule matrix-isolation on these properties. Potential uses of the special thin films are numerous, e.g., as laser or solar light guides.

Is the Geometry of Nature Fractal

The notion of the abundance of fractals is critically re-examined in light of surprising data regarding the scaling range in empirical reports on fractality.

Surface geometric irregularity of particulate materials: The fractal approach

Abstract Surface geometric irregularities of a wide variety of particulate materials are determined by applying the fractal theory of surface science (P. Pfeifer and D. Avnir, J. Chem. Phys. 79, 3558 1983). Reanalysis and reinterpretation of previously published experimental data, revealed the following surface-fractal dimensions, all falling in the expected range 2.0 to 3.0, for the following materials: periclase—1.95; a number of quartzes—2.02 to 2.21; iron oxide—2.59; porous silica gel—3.0; coal dusts—2.33 and 2.53; six carbonate rocks—2.16 to 2.97; seven types of soils—2.19 to 2.99; a number of crushed rocks from nuclear test site—2.7 to 3.0. We describe in detail the method by which these fractal dimensions were determined, i.e., studying the dependence of monolayer values (n) on particle radii (R): n ∝ RD-3. Interestingly, several authors had presented their experimental results as log n vs log R, yet no explanation was offered to the straight lines obtained; the notion of self-similarity (fractal surfaces) fits nicely in all these studies. The various features of our approach are described in connection with the analyzed examples, e.g., we exemplify estimation of particle diameters by this approach. Attention is given to the question of range of self-similarity. It is suggested that materials with fractal surfaces were formed in general by an iterative mechanism. Based on the massive list of fractal surfaces found (D. Avnir, D. Farin, and P. Pfeifer, Nature (London) 308, 261, 1984), this is probably the operative mechanism for the majority of natural and synthetic materials.

The Limited Scaling Range of Empirical Fractals

The notion of the abundance of fractals is critically re-examined in light of surprising data regarding the scaling range in empirical reports on fractality.

Doped sol-gel glasses as chemical sensors☆

Abstract It is reported that by trapping suitable analytical reagents, porous sol-gel glasses can be used for the preparation of a wide variety of chemical-sensing materials. The key to the successful preparation of these materials is based on the observation that a substantial fraction of the trapped molecules is exposed to the liquid or gaseous intra-pore volume. The glass matrix thus serves as a solid support for analytical reagents which interact with analyzates present in the adjacent phase. The phenomenon is quite general, and has been demonstrated for a variety of color tests for metal cations, proton (pH indication), anions, and organic molecules.