Wolfram

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Comparison of Differently Bound Molecules in the Gel and Subgel Phases of a Phospholipid Bilayer System

The thermal behavior associated with the melting of ice was investigated by differential scanning calorimetry (DSC) for the gel and L-subgel phases of dipalmitoylphosphatidylcholine (DPPC)-water system of varying water contents up to a full hydration. By calorimetric analysis previously developed by us, the numbers of differently bound water molecules were estimated, and used to construct water distribution diagrams (i.e., a plot of the cumulative numbers of these water molecules vs. water content) for the two phases. A comparison of the diagrams revealed the critical role of interlamellar water which changes from freezable to non-freezable one in a conversion of the gel to the L-subgel phase by the thermal annealing. This revised version was published online in July 2006 with corrections to the Cover Date.     

Theory of the steady-state current of a redox couple at interdigitated array electrodes of which pairs are insulated electrically by steps

The possibility of constructing an interdigitated array electrode (IDA) with a submicrometre gap is proposed in which adjacent microband electrodes are separated from each other by an insulated step. Then the IDA is an assembly of protrusive and hollow microband electrodes. The unit model of the IDA consisted of half of the lower (hollow) microband electrode, an insulated step and half of the upper (protrusive) microband electrode with a finite thickness on the step. The boundary value problem involving the two-dimensional Laplace equation is presented for redox cycling at the IDA under diffusion control and is solved numerically by a boundary element method. The steady-state current was computed as a function of the height of the step and the thickness of the upper electrode. It was larger than the current at the ordinary IDA, partly because the true electrode area was larger than the area of the ordinary IDA. The current varied linearly with the logarithm of the step height. It was expressed by a simple approximate equation in order to facilitate prediction of its numerical value.     

A generating function for sums of multiple zeta values and its applications

A generating function for specified sums of multiple zeta values is defined and a differential equation that characterizes this function is given. As applications, some relations for multiple zeta values over the field of rational numbers are discussed.

     

Spontaneous emulsification at oil–water interface by tetraalkylammonium chloride

Water droplets were formed spontaneously at the interface of the 2-nitrophenyloctyl ether and aqueous phases on the oil phase side when the oil contained tetraalkylammonium chloride without surfactants. The droplets, less than some micrometers in diameter, gathered at the interface. The number density of the droplets was proportional to the concentration of tetraethylammonium chloride, and hence this salt should be responsible for the formation of the droplets as a surfactant. When positive voltage was applied to the aqueous phase against the oil, the droplets departed from the interface toward the oil bulk. The droplets should be negatively charged by chloride. The adsorption model of the salt was suggested, in which chloride is immobilized at the interface on the aqueous side electrostatically with tetraethylammonium ion on the oil side.     

From Infinite Chains according to 1∞[Zr(S2O7)4/2] in Zr(S2O7)2 to the unprecedented [Zr(S2O7)4]4– Anion in Ag4[Zr(S2O7)4]

The reaction of ZrCl₄ with oleum (65 % SO₃) in the presence of Ag₂SO₄ at 250 °C yielded colorless single crystals of Zr(S₂O₇)₂ [orthorhombic, Pccn, Z = 4, a = 709.08(6) pm, b = 1442.2(2) pm, c = 942.23(9) pm, V = 963.5(2) × 10⁶ pm³]. Zr(S₂O₇)₂ shows Zr⁴⁺ ions in an eightfold distorted square antiprismatic coordination of oxygen atoms belonging to four chelating disulfate units. Each S₂O₇^2– ion is connected to a further Zr⁴⁺ ion leading to chains according to ¹_∞[Zr(S₂O₇)_4/2]. The same reaction at a temperature of 150 °C resulted in the formation of Ag₄[Zr(S₂O₇)₄] [monoclinic, C2/c, Z = 4, a = 1829.35(9) pm, b = 704.37(3) pm, c = 1999.1(1) pm, β = 117.844(2)°, V = 2277.6(2) × 10⁶ pm³]. Ag₄[Zr(S₂O₇)₄] exhibits the unprecedented [Zr(S₂O₇)₄]^4– anion, in which the central Zr⁴⁺ cation is coordinated by four chelating disulfate units. Thus, in Ag₄[Zr(S₂O₇)₄] the ¹_∞[[Zr(S₂O₇)_4/2] chains observed in Zr(S₂O₇)₂ are formally cut into pieces by the implementation of Ag⁺ ions.