This paper describes the first synthesis of a new class of topological macromolecules which we refer to as “starburst polymers.” The fundamental building blocks to this new polymer class are referred to as “dendrimers.” These dendrimers differ from classical monomers/oligomers by their extraordinary symmetry, high branching and maximized (telechelic) terminal functionality density. The dendrimers possess “reactive end groups” which allow (a) controlled moelcular weight building (monodispersity), (b) controlled branching (topology), and (c) versatility in design and modification of the terminal end groups. Dendrimer synthesis is accomplished by a variety of strategies involving “time sequenced propagation” techniques. The resulting dendrimers grow in a geometrically progressive fashion as shown: Chemically bridging these dendrimers leads to the new class of macromolecules—”starburst polymers” (e.g., (A)n, (B)n, or (C)n).

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A new class of polymers: Starburst-dendritic macromolecules

The density of states on a fractal is calculated taking into account the scaling properties of both the volume and the connectivity. We use a Green's function method developed elsewhere which utilizes a relationship to the diffusion problem. It is found that proper mode counting requires a reciprocal space with new intrinsic fracton dimensionality d = 2 d/(2 + δ). Here, d is the effective dimensionality, and δ the exponent giving the dependence of the diffusion constant on distance. For example, we find for percolation clusters d = 4/3 within the numerical accuracy available, independent of the Euclidean dimensionality d. Crossover to normal behaviour at low frequencies is discussed for finite fractals and for percolation above the percolation threshold pc. Relevance to experimental results on proteins is also discussed.

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Density of states on fractals : « fractons »

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...

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

Diffusion in disordered systems does not follow the classical laws which describe transport in ordered crystalline media, and this leads to many anomalous physical properties. Since the application of percolation theory, the main advances in the understanding of these processes have come from fractal theory. Scaling theories and numerical simulations are important tools to describe diffusion processes (random walks: the 'ant in the labyrinth') on percolation systems and fractals. Different types of disordered systems exhibiting anomalous diffusion are presented (the incipient infinite percolation cluster, diffusion-limited aggregation clusters, lattice animals, and random combs), and scaling theories as well as numerical simulations of greater sophistication are described. Also, diffusion in the presence of singular distributions of transition rates is discussed and related to anomalous diffusion on disordered structures.

Diffusion in disordered media

In this letter we report that, at the molecular-size range, the surfaces of most materials are fractals, that is, at this range, surface geometric irregularities and defects are characteristically self-similar upon variations of resolution. The whole range of fractal dimension1, 2⩽D<3, is found in the many examples presented. Two representative examples, namely adsorption of polystyrene on alumina and adsorption of krypton on dolomite are discussed in some detail. Our findings suggest a simple solution to the problem of quantifying the degree of surface irregularity2,3 at a resolution which is of relevance to many aspects of surface science. The results provide a general explanation for phenomenological links between various surface parameters, and we derive a set of equations of use in predicting surface variables.

Molecular fractal surfaces

Electron spin relaxation measurements on low-spin ${\mathrm{Fe}}^{3+}$ in several proteins show that they occupy a space of fractal dimensionality $d=1.65\ifmmode\pm\else\textpm\fi{}0.04$, in conformity with the dimensionality $d=\frac{5}{3}$ of a self-avoiding random walk. Analysis of myoglobin x-ray data independently confirms this fractal dimension.

Fractal Form of Proteins

Protein conformation from electron spin relaxation data

Multilayered Co/Pd thin films were prepared by sequential electron‐beam evaporation of Co and Pd onto Si substrates at room temperature. The thicknesses of the Co sublayer and of the Pd sublayer were varied between 2.0–10.3 and 4.5–22.3 A, respectively. As the Pd sublayer thickness was varied at constant Co thickness, broad maxima in the saturation magnetization Ms and intrinsic perpendicular anisotropy energy Ku were observed at a Pd thickness of about 10 A. At this maximum, Ms per Co volume is larger than the saturation magnetization of bulk Co. This is believed to be caused by the polarization of the Pd atoms within about 10 A of the Co layer. Ku and Ms per Co volume both decrease with increasing Co layer thickness.

Magnetization and anisotropy of Co/Pd multilayer thin films

Photoselective vaporization prostatectomy: experience with a novel 180 W 532 nm lithium triborate laser and fiber delivery system in living dogs.

Various aspects of multiple-channel light transmitting systems are disclosed. The system may include a multiple-wave length light source, a demultiplexer; a modulator, and a wavelocker. The wavelocker is configured to drive the light source such that said multiple wavelengths coincide with the ITU grid. The system may also include other elements including a locker or a mode-locking servo, where the servo is configured to adjust the mode locking method frequency to coincide with the spacing of the ITU grid. Further additional elements may include an optical amplifier or an equalizer. The equalizer may include a filter whose transmission function varies with wavelength.

Douglas G. Stinson

Papers

Fractal Form of Proteins

Protein conformation from electron spin relaxation data

Magnetization and anisotropy of Co/Pd multilayer thin films

Photoselective vaporization prostatectomy: experience with a novel 180 W 532 nm lithium triborate laser and fiber delivery system in living dogs.

Multi-wavelength transmitter