Crystal Structure of Ammonium Catena‐polyphosphate IV [NH4PO3]x

Phase‐pure ammonium catena‐polyphosphate IV [NH₄PO₃]_x was synthesized by heating NH₄H₂PO₄ in a tube furnace under an ammonia gas flow. The product contained single crystals of [NH₄PO₃]_x IV appropriate for an X‐ray structure determination enabling structure refinement of this compound. The pseudo‐merohedrally twinned crystals of [NH₄PO₃]_x crystallize in the monoclinic crystal system (P2₁/c, no. 14, a = 2270.3(5), b = 458.14(9), c = 1445.1(3) pm, β = 108.56(3)°, Z = 4, 2264 data, R1 = 0.076). In the unit cell the catena‐polyphosphate chain anions run parallel [010] with a chain‐periodicity P = 2 and a stretching factor f_s = 0.94. The chain anions are interconnected through extensive hydrogen bonding towards the ammonium ions. Due to ‘chemical twinning’ a novel catena‐polyphosphate structure type is realized in [NH₄PO₃]_x IV. The vibrational spectra of [NH₄PO₃]_x IV are reported as well.     

A generalization of Wegscheider's condition. Implications for properties of steady states and for quasi-steady-state approximation

A generalization of Wegschcider's condition concerning equilibrium constants in chemically reacting systems is formulated, which is then proved to be a necessary and sufficient condition for detailed balancing. In order to include a large multitude of rate laws, a generalized mass action kinetics is considered which comprises usual mass action kinetics and all reversible enzyme kinetics and which is consistent with basic postulates of irreversible thermodynamics for ideal mixtures. Reaction systems of arbitrary stoichiometry are considered. They may contain reactants with fixed concentrations, as is characteristic for models of biochemical reaction networks. Existence, uniqueness, and global asymptotic stability of equilibrium states for reaction systems endowed with generalized man action kinetics are proved. Using these results, he generalized Wegscheider condition is shown to be a sufficient criterion for the applicability of the quasi-steady-state approximation.     

Adsorption of a single polymer chain on a surface: A molecular dynamics simulation study

We performed simulations of the physical adsorption of a single globular chain on a surface of hemispherical shape by means of molecular dynamics simulations. For the chain, we took advantage of a united atom model. Interactions within the chain were limited to stretching, bending, and torsional as well as nonbonded interactions between the nonadjacent atoms. The interaction between each chain element and the surface formation are reigned by a Lennard–Jones potential. In this article, we focused on differences in the behavior of the adsorbed globule to the free unadsorbed one particularly in two different zones of the immediate vicinity of the surface. There were strong indications for a localized acceleration of the dynamics as compared with the bulk that appears in an increase of trans–gauche switches. For explanation we came up with an adsorption scenario. Special attention was given to the shift of the percentage of trans and gauche conformations within the globule in dependence on the strength of the adsorption potential that might be related to crystallization or glass transition. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2333–2339, 2001     

Non-contact protein microarray fabrication using a procedure based on liquid bridge formation

Contemporary microarrayers of contact or non-contact format used in protein microarray fabrication still suffer from a number of problems, e.g. generation of satellite spots, inhomogeneous spots, misplaced or even absent spots, and sample carryover. In this paper, a new concept of non-contact sample deposition that reduces such problems is introduced. To show the potential and robustness of this pressure-assisted deposition technique, different sample solutions known to cause severe problems or to be even impossible to print with conventional microarrayers were accurately printed. The samples included 200 mg mL^–1 human serum albumin, highly concentrated sticky cell adhesion proteins, pure high-salt cell-lysis buffer, pure DMSO, and a suspension of 5-μm polystyrene beads. Additionally, a water-immiscible liquid fluorocarbon, which was shown not to affect the functionality of the capture molecules, was employed as a lid to reduce evaporation during microarray printing. The fluorocarbon liquid lid was shown to circumvent hydrolysis of water-sensitive activated surfaces during long-term deposition procedures.     

Maps that are roots of power series

We introduce a class of polynomial maps that we call polynomial roots of powerseries, and show that automorphisms with this property generate the automorphism group in any dimension. In particular we determine generically which polynomial maps that preserve the origin are roots of powerseries. We study the one-dimensional case in greater depth. Funded by Veni-grant of council for the physical sciences, Netherlands Organisation for scientific research (NWO).     

An algebraic multigrid method for high order time-discretizations of the div-grad and the curl-curl equations

We present an algebraic multigrid algorithm for fully coupled implicit Runge–Kutta and Boundary Value Method time-discretizations of the div-grad and curl-curl equations. The algorithm uses a blocksmoother and a multigrid hierarchy derived from the hierarchy built by any algebraic multigrid algorithm for the stationary version of the problem. By a theoretical analysis and numerical experiments, we show that the convergence is similar to or better than the convergence of the scalar algebraic multigrid algorithm on which it is based. The algorithm benefits from several possibilities for implementation optimization. This results in a computational complexity which, for a modest number of stages, scales almost linearly as a function of the number of variables.