Three parallel algorithms for classical molecular dynamics are presented. The first assigns each processor a fixed subset of atoms; the second assigns each a fixed subset of inter-atomic forces to compute; the third assigns each a fixed spatial region. The algorithms are suitable for molecular dynamics models which can be difficult to parallelize efficiently—those with short-range forces where the neighbors of each atom change rapidly. They can be implemented on any distributed-memory parallel machine which allows for message-passing of data between independently executing processors. The algorithms are tested on a standard Lennard-Jones benchmark problem for system sizes ranging from 500 to 100,000,000 atoms on several parallel supercomputers--the nCUBE 2, Intel iPSC/860 and Paragon, and Cray T3D. Comparing the results to the fastest reported vectorized Cray Y-MP and C90 algorithm shows that the current generation of parallel machines is competitive with conventional vector supercomputers even for small problems. For large problems, the spatial algorithm achieves parallel efficiencies of 90% and a 1840-node Intel Paragon performs up to 165 faster than a single Cray C9O processor. Trade-offs between the three algorithms and guidelines for adapting them to more complex molecular dynamics simulations are also discussed.

Fast parallel algorithms for short-range molecular dynamics

Although gold is the subject of one of the most ancient themes of investigation in science, its renaissance now leads to an exponentially increasing number of publications, especially in the context of emerging nanoscience and nanotechnology with nanoparticles and self-assembled monolayers (SAMs). We will limit the present review to gold nanoparticles (AuNPs), also called gold colloids. AuNPs are the most stable metal nanoparticles, and they present fascinating aspects such as their assembly of multiple types involving materials science, the behavior of the individual particles, size-related electronic, magnetic and optical properties (quantum size effect), and their applications to catalysis and biology. Their promises are in these fields as well as in the bottom-up approach of nanotechnology, and they will be key materials and building block in the 21st century. Whereas the extraction of gold started in the 5th millennium B.C. near Varna (Bulgaria) and reached 10 tons per year in Egypt around 1200-1300 B.C. when the marvelous statue of Touthankamon was constructed, it is probable that “soluble” gold appeared around the 5th or 4th century B.C. in Egypt and China. In antiquity, materials were used in an ecological sense for both aesthetic and curative purposes. Colloidal gold was used to make ruby glass 293 Chem. Rev. 2004, 104, 293−346

Gold nanoparticles: assembly, supramolecular chemistry, quantum-size-related properties, and applications toward biology, catalysis, and nanotechnology.

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Self-assembled monolayers of thiolates on metals as a form of nanotechnology.

Fundamentals of Plasmonics.- Electromagnetics of Metals.- Surface Plasmon Polaritons at Metal / Insulator Interfaces.- Excitation of Surface Plasmon Polaritons at Planar Interfaces.- Imaging Surface Plasmon Polariton Propagation.- Localized Surface Plasmons.- Electromagnetic Surface Modes at Low Frequencies.- Applications.- Plasmon Waveguides.- Transmission of Radiation Through Apertures and Films.- Enhancement of Emissive Processes and Nonlinearities.- Spectroscopy and Sensing.- Metamaterials and Imaging with Surface Plasmon Polaritons.- Concluding Remarks.

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Plasmonics: Fundamentals and Applications

The interest in nanoscale materials stems from the fact that new properties are acquired at this length scale and, equally important, that these properties * To whom correspondence should be addressed. Phone, 404-8940292; fax, 404-894-0294; e-mail, mostafa.el-sayed@ chemistry.gatech.edu. † Case Western Reserve UniversitysMillis 2258. ‡ Phone, 216-368-5918; fax, 216-368-3006; e-mail, burda@case.edu. § Georgia Institute of Technology. 1025 Chem. Rev. 2005, 105, 1025−1102

Chemistry and properties of nanocrystals of different shapes.

Measurement of the fractal dimension, $D$, of colloidal aggregates of small silica particles is reported. We observe power-law decay of the structure factor $[S(k)\ensuremath{\sim}{k}^{\ensuremath{-}D}]$ by both light and x-ray scattering showing that the aggregates are fractal. $D$ is found to be 2.12\ifmmode\pm\else\textpm\fi{}0.05, which is intermediate between recent numerical results for the kinetic models of diffusion-limited aggregation ($D=2.5$) and cluster aggregation ($D=1.75$), but is rather close to the value for lattice animals ($D=2.0$), which are equilibrium structures.

Fractal geometry of colloidal aggregates

We have observed visible light emission from nanosize gold clusters. Liquid chromatographic analysis of the metal clusters shows that relatively intense photoluminescence occurs only when the size of the metal nanocluster is sufficiently small (<5 nm). The emission is strongly Stokes shifted and is assigned to radiative recombination of Fermi level electrons and sp- or d-band holes. The electron and/or hole states are perturbed by surface states, as indicated by the dependence of the emission spectrum on the nature of the cluster surface. Finally, we found that large, nonemitting gold clusters can also be made luminescent by partial dissolution using KCN.

Photoluminescence from nanosize gold clusters

The concepts of dilation symmetry and the fractal dimension are introduced, and from these basic concepts scattering functions are computed for surface and mass fractals. It is then shown how the fractal structure of various random media has been elucidated from scattering measurements, and how these observations relate to specific models of fractal geometry. Examples include colloidal aggregates, gels, soot and the fractal porosity of rocks of various sorts.

Scattering from fractals

Viscoelastic measurements on gels near the gel point show power-law frequency and time dependences. Using a percolation model, we find that viscoelastic properties are described by the universal exponent /Delta/= d/nu//(d/nu/+k) where k is the viscosity exponent, /nu/ is the correlation-length exponent, and d is the dimension of space. This expression leads to a theory for the critical growth of the equilibrium shear modulus beyond the gel point, and the steady-state creep compliance beneath the gel point. Viscoelastic data are given for epoxy resins.

Viscoelasticity of near-critical gels.

Near the sol-gel transition, gelling systems exhibit an extremely slow relaxation of thermally driven density fluctuations. We have made a detailed quasielastic light scattering study of the decay of density fluctuations in reacting silica sol-gels in the pre- and post-gel regimes, and at the gel point. In the pre-gel regime the dynamic structure factor {ital S}({ital q},{ital t}) for the branched polymer melt has a stretched exponential tail whose characteristic time diverges at the gel point. This {ital critical} {ital slowing} {ital down} is due to the divergence of the average cluster size and is distinct from the usual critical slowing down observed in second-order thermodynamic phase transitions, since the initial decay rate of {ital S}({ital q},{ital t}) is nondivergent at the gel point. In fact, at the gel point, {ital S}({ital q},{ital t}) becomes a power law, indicating a fractal time set in the scattered field. These observations are accounted for by considering the dynamics of percolation clusters, and in this connection the analogy to viscoelasticity is described. Beyond the gel point {ital S}({ital q},{ital t}) remains a power law, but the amplitude of the relaxing part of the intensity autocorrelation function diminishes. Finally, the dynamics of clusters dilutedmore » from the reaction bath is studied, and a crossover from power law to stretched exponential decay of {ital S}({ital q},{ital t}) is observed. It is shown that at infinite dilution the long-time tail of the correlation function describes the internal modes of a single percolation cluster.« less

James E. Martin

Papers

Fractal geometry of colloidal aggregates

Photoluminescence from nanosize gold clusters

Scattering from fractals

Viscoelasticity of near-critical gels.

Decay of density fluctuations in gels.