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

https://www.tau.ac.il/%7Eklafter1/258.pdf

The random walk's guide to anomalous diffusion: a fractional dynamics approach

Polymer/layered silicate nanocomposites: a review from preparation to processing

A family of highly ordered mesoporous (20−300 A) silica structures have been synthesized by the use of commercially available nonionic alkyl poly(ethylene oxide) (PEO) oligomeric surfactants and poly(alkylene oxide) block copolymers in acid media. Periodic arrangements of mescoscopically ordered pores with cubic Im3m, cubic Pm3m (or others), 3-d hexagonal (P63/mmc), 2-d hexagonal (p6mm), and lamellar (Lα) symmetries have been prepared. Under acidic conditions at room temperature, the nonionic oligomeric surfactants frequently form cubic or 3-d hexagonal mesoporous silica structures, while the nonionic triblock copolymers tend to form hexagonal (p6mm) mesoporous silica structures. A cubic mesoporous silica structure (SBA-11) with Pm3m diffraction symmetry has been synthesized in the presence of C16H33(OCH2CH2)10OH (C16EO10) surfactant species, while a 3-d hexagonal (P63/mmc) mesoporous silica structure (SBA-12) results when C18EO10 is used. Surfactants with short EO segments tend to form lamellar mesost...

Nonionic Triblock and Star Diblock Copolymer and Oligomeric Surfactant Syntheses of Highly Ordered, Hydrothermally Stable, Mesoporous Silica Structures

This review summarizes recent developments in the theory of spin glasses, as well as pertinent experimental data. The most characteristic properties of spin glass systems are described, and related phenomena in other glassy systems (dielectric and orientational glasses) are mentioned. The Edwards-Anderson model of spin glasses and its treatment within the replica method and mean-field theory are outlined, and concepts such as "frustration," "broken replica symmetry," "broken ergodicity," etc., are discussed. The dynamic approach to describing the spin glass transition is emphasized. Monte Carlo simulations of spin glasses and the insight gained by them are described. Other topics discussed include site-disorder models, phenomenological theories for the frozen phase and its excitations, phase diagrams in which spin glass order and ferromagnetism or antiferromagnetism compete, the Ne\'el model of superparamagnetism and related approaches, and possible connections between spin glasses and other topics in the theory of disordered condensed-matter systems.

Spin glasses: Experimental facts, theoretical concepts, and open questions

Use of amphiphilic triblock copolymers to direct the organization of polymerizing silica species has resulted in the preparation of well-ordered hexagonal mesoporous silica structures (SBA-15) with uniform pore sizes up to approximately 300 angstroms. The SBA-15 materials are synthesized in acidic media to produce highly ordered, two-dimensional hexagonal (space group p6mm) silica-block copolymer mesophases. Calcination at 500°C gives porous structures with unusually large interlattice d spacings of 74.5 to 320 angstroms between the (100) planes, pore sizes from 46 to 300 angstroms, pore volume fractions up to 0.85, and silica wall thicknesses of 31 to 64 angstroms. SBA-15 can be readily prepared over a wide range of uniform pore sizes and pore wall thicknesses at low temperature (35° to 80°C), using a variety of poly(alkylene oxide) triblock copolymers and by the addition of cosolvent organic molecules. The block copolymer species can be recovered for reuse by solvent extraction with ethanol or removed by heating at 140°C for 3 hours, in both cases, yielding a product that is thermally stable in boiling water.

Triblock copolymer syntheses of mesoporous silica with periodic 50 to 300 angstrom pores

Block copolymers are macromolecules composed of sequences, or blocks, of chemically distinct repeat units. The development of this field originated with the discovery of termination-free anionic polymerization, which made possible the sequential addition of monomers to various carbanion-ter­ minated ("living") linear polymer chains. Polymerization of just two dis­ tinct monomer types (e.g. styrene and isoprene) leads to a class of materials referred to as AB block copolymers. Within this class, a variety of molec­ ular architectures is possible. For example, the simplest combination, obtained by the two-step anionic polymerization of A and B monomers, is an (A-B) dioblock copolymer. A three-step reaction provides for the preparation of (ABA) or (BAB) triblock copolymer. Alternatively, "living" diblock copolymers can be reacted with an n-functional coupling agent to produce (A-B)n star-block copolymers, where n = 2 constitutes a triblock copolymer. Several representative (A-B)n block copolymer architectures

Block Copolymer Thermodynamics: Theory and Experiment

Block copolymers are all around us, found in such products as upholstery foam, adhesive tape and asphalt additives. This class of macromolecules is produced by joining two or more chemically distinct polymer blocks, each a linear series of identical monomers, that may be thermodynamically incompatible (like oil and vinegar). Segregation of these blocks on the molecular scale (5–100 nm) can produce astonishingly complex nanostructures, such as the “knitting pattern” shown on the cover of this issue of PHYSICS TODAY. This striking pattern, discovered by Reimund Stadler and his coworkers, reflects a delicate free‐energy minimization that is common to all block copolymer materials.

Block Copolymers—Designer Soft Materials

Recent years have brought exciting theoretical advances to understanding the behavior of macromolecular systems under nonequilibrium conditions. Developments in diffusion-controlled reactions of polymers are bringing molecular insights to reactive blending technologies, and improved theories relating to associating polymers should aid in the design of thickening agents and coatings. Recent progress in molecular theories of flow and deformation may facilitate the design of branched polymers with tailored rheological properties and improved adhesives.

The theory of polymer dynamics

The effect of composition fluctuations on the microphase separation transition in diblock copolymers is investigated. Such fluctuation corrections, which were neglected in the mean field treatment of Leibler, are found to be significant for the molecular weights usually encountered. The analysis is facilitated by reducing the block copolymer Hamiltonian to a form previously studied by Brazovskii. Our principal results are the following: (i) A symmetric diblock copolymer is predicted to undergo a first order phase transition at a larger value of χN than the second order transition found by Leibler. The Flory interaction parameter is denoted χ and N is the number of statistical segments per chain. The location of the transition is predicted to be at (χN)t=10.495+41.022 N−1/3, where the peak in the scattering function attains its maximum value of 0.12328 N1/3. (ii) We find windows in composition, with finite width, through which it is possible to pass from the disordered phase to each of the ordered micropha...

Glenn H. Fredrickson

Papers

Triblock copolymer syntheses of mesoporous silica with periodic 50 to 300 angstrom pores

Block Copolymer Thermodynamics: Theory and Experiment

Block Copolymers—Designer Soft Materials

The theory of polymer dynamics

Fluctuation effects in the theory of microphase separation in block copolymers