Lattice-Boltzmann simulations of the dynamics of polymer solutions in periodic and confined geometries

A numerical method to simulate the dynamics of polymer solutions in confined geometries has been implemented and tested. The method combines a fluctuating lattice-Boltzmann model of the solvent [Ladd, Phys. Rev. Lett. 70, 1339 (1993)] with a point-particle model of the polymer chains. A friction term couples the monomers to the fluid [Ahlrichs and Dunweg, J. Chem. Phys. 111, 8225 (1999)], providing both the hydrodynamic interactions between the monomers and the correlated random forces. The coupled equations for particles and fluid are solved on an inertial time scale, which proves to be surprisingly simple and efficient, avoiding the costly linear algebra associated with Brownian dynamics. Complex confined geometries can be represented by a straightforward mapping of the boundary surfaces onto a regular three-dimensional grid. The hydrodynamic interactions between monomers are shown to compare well with solutions of the Stokes equations down to distances of the order of the grid spacing. Numerical results are presented for the radius of gyration, end-to-end distance, and diffusion coefficient of an isolated polymer chain, ranging from 16 to 1024 monomers in length. The simulations are in excellent agreement with renormalization group calculations for an excluded volume chain. We show that hydrodynamic interactions in large polymers can be systematically coarse-grained to substantially reduce the computational cost of the simulation. Finally, we examine the effects of confinement and flow on the polymer distribution and diffusion constant in a narrow channel. Our results support the qualitative conclusions of recent Brownian dynamics simulations of confined polymers [Jendrejack et al., J. Chem. Phys. 119, 1165 (2003) and Jendrejack et al., J. Chem. Phys. 120, 2513 (2004)].     

Non-Template-Centered, Closed Tetravanadium Phosphate and Phosphonate Clusters

Tetranuclear V(III) complexes, [HB(pz)(3)](4)V(4)(&mgr;-C(6)H(5)OPO(3))(4) (I), its acetonitrile solvate (I.4CH(3)CN), and [HB(pz)(3)](4)V(4)(&mgr;-O(2)NC(6)H(4)OPO(3))(4).4C(7)H(8).H(2)O (II), and tetranuclear vanadyl complexes, (t-Bupz)(4)V(4)O(4)(&mgr;-C(6)H(5)PO(3))(4).2H(2)O (III) and (t-Bupz)(5)V(4)O(4)(&mgr;-C(6)H(5)PO(3))(4).4CH(3)CN.0.6 H(2)O (IV), have been prepared and characterized by spectroscopic, magnetic, and electrochemical methods (pz = pyrazole, t-Bupz = tert-butylpyrazole). The use of organic solvents and bulky organic groups as ancillary ligands leads to formation of neutral species instead of the anionic clusters commonly found in the hydrothermal synthesis of vanadium organophosphate/phosphonate systems. Complexes I.4CH(3)CN and IV have also been characterized by single-crystal X-ray diffraction. Crystal data: I.4CH(3)CN, triclinic, P&onemacr;, a = 15.495(3) ?, b = 17.000(3) ?, c = 17.949(4) ?, alpha = 89.17(3) degrees, beta = 86.00(3) degrees, gamma = 78.60(3) degrees, Z = 2; IV, triclinic, P&onemacr;, a = 15.541(3) ?, b = 16.340(2) ?, c = 19.069(5) ?, alpha = 83.58(2) degrees, beta = 79.67(2) degrees, gamma = 63.68(1) degrees, Z = 2. Both are closed clusters, the core structure of the first consisting of a cubane-like arrangement of metal octahedra and phosphate tetrahedra and the core structure of the second consisting of a distorted, collapsed variant of the first. Unlike other vanadium phosphate clusters, these compounds form in the absence of a central, templating agent. As such they represent the simplest form of a closed cluster in which steric forces and cluster connectivity requirements play the primary role in organizing the cluster framework.     

Synthesis,spectroscopy, and structures of 2-bromo-1-bromoimino-3-oxo-isoindoline(III) and 1-bromoimino-3-oxoisoindoline(IV)

The title compounds have been synthesized, characterized by spectroscopic and analytical methods, and the complete structure of (IV) determined by single-crystal X-ray methods. Compound (IV) is monoclinic:a=13.891(3),b=4.935(2),c=12.499(2)Å,=112.10(1) deg,P2₁/n,Z=4. The structure was determined by the heavy-atom method, and refined by full-matrix least squares onF toR=4.6%, with 1283 reflexions for whichI3 (I). The structure (IV) was confirmed, and the molecule was shown to be planar to within 0.01 Å.     

Crystal and molecular structure of 3-(2-(1,10-phenanthrolyl))-5,6-diphenyl-1,2,4-triazine-chloroaquotriphenyltin(IV) (1:1)

3-(2-(1,10-Phenanthrolyl))-5,6-diphenyl-1,2,4-triazine-chloroaquotriphenyl-tin(IV) (1:1) crystallizes in the orthorhombic system:a=19.195,b=9.144,c=21.642 Å,Z=4, space groupPca2₁ (No. 29). The structure was determined using the procedure for difference structures (Dirdir) with CuK diffractometer data, and refined by block-diagonal least squares toR=0.031 for 3287 observed reflections. The tin atom is 5-coordinate with the three phenyl groups forming the equatorial plane. A chlorine atom and a water molecule complete the coordination. The triazine moiety does not coordinate directly to the metal atom. The only interaction is due to two N H-O hydrogen bonds formed between two nitrogen atoms from the ligand and the water molecule.