Packed uniform sphere model for solids: interstitial access opening sizes and pressure deficiencies for wetting liquids with comparison to reported experimental results

Mathematical relationships have been developed to describe the pressure deficiencies required for drainage and removal of wetting liquids through the access openings to the interstitial void space for a model comprised of uniform packed solid spheres. Access openings and associated pressure deficiencies are defined in terms of the packing and radius of the spheres, using a circular arc approximation for the liquid-vapor portion of the perimeter of the opening. This allows determination of equivalent particle radius rather than equivalent cylindrical pore radius within a porous solid sample by use of standard pressure, porosity and desorption data. For a known particle size and porosity, it allows comparison and prediction of drainage of wetting liquids and pressures required for removal of the liquid from compacted materials and collections of random packed spherical particles. Comparisons are made to experimental packing of spheres. Sorption isotherms for a volatile wetting liquid are presented, covering the access to the interstitial void space, the pendular liquid ring between adjacent touching spheres and the monolayer surface area. The larger size of the interstitial void space compared to the size of the access opening leads to lower imbibition pressures and hysteresis for both volatile and nonvolatile wetting liquids. The relationship to mercury porosimetry and the adjustment for contact angles other than 0 degrees and 180 degrees are discussed.     

Small exponent asymptotics

We study the surprisingly complicated asymptotic character ofa simple first-order differential equation, which involves aterm with a low exponent of the dependent variable. While numericalsolutions and straightforward asymptotic expansions indicatea clearly defined boundary layer type transition, we find thatthe correct asymptotic structure involves a 'hidden' boundarylayer, and that a straightforward approach cannot discern this.     

Direct frequency comb measurements of absolute optical frequencies and population transfer dynamics

A phase-stabilized femtosecond laser comb is directly used for high-resolution spectroscopy and absolute optical frequency measurements of one- and two-photon transitions in laser-cooled 87Rb atoms. Absolute atomic transition frequencies, such as the 5S1/2 F=2-->7S1/2 F"=2 two-photon resonance measured at 788,794 768,921 (44) kHz, are determined without a priori knowledge about their values. Detailed dynamics of population transfer driven by a sequence of pulses are uncovered and taken into account for the measurement of the 5P states via resonantly enhanced two-photon transitions.     

Time-domain differentiation of terahertz pulses

We report on the time-domain differentiation of light waves by metallic transmission gratings. Time-resolved terahertz experiments show that the first time derivative of an arbitrary waveform can be achieved by use of gratings of subwavelength period. The results are in accord with classical diffraction theory and may permit novel applications for tailoring few-cycle light pulses and ultrahigh-frequency optoelectronics.     

Structure and magnetism of the tetra-copper(II)-substituted heteropolyanion [Cu(4)K(2)(H(2)O)(8)(alpha-AsW(9)O(33))(2)](8-)

The novel heteropolyanion [Cu(4)K(2)(H(2)O)(8)(alpha-AsW(9)O(33))(2)](8)(-) (1) has been synthesized and characterized by IR spectroscopy, elemental analysis, and magnetic studies. Single-crystal X-ray analysis was carried out on [K(7)Na[Cu(4)K(2)(H(2)O)(6)(alpha-AsW(9)O(33))(2)].5.5H(2)O](n)(K(7)Na-1), which crystallizes in the tetragonal system, space group P42(1)m, with a = 16.705(4) A, b = 16.705(4) A, c = 13.956(5) A, and Z = 2. Interaction of the lacunary [alpha-AsW(9)O(33)](9)(-) with Cu(2+) ions in neutral, aqueous medium leads to the formation of the dimeric polyoxoanion 1 in high yield. Polyanion 1 consists of two alpha-AsW(9)O(33) units joined by a cyclic arrangement of four Cu(2+) and two K(+) ions, resulting in a structure with C(2)(v)() symmetry. All copper ions have one terminal water molecule, resulting in square-pyramidal coordination geometry. Three of the copper ions are adjacent to each other and connected via two micro(3)-oxo bridges. EPR studies on K(7)Na-1 and also on Na(9)[Cu(3)Na(3)(H(2)O)(9)(alpha-AsW(9)O(33))(2)].26H(2)O (Na(9)-2) over 2-300 K yielded g values that are consistent with a square-pyramidal coordination around the copper(II) ions in 1 and 2. No hyperfine structure was observed due to the presence of strong spin exchange, but fine structure was observed for the excited (S(T) = 3/2) state of Na(9)-2 and the ground state (S(T) = 1) of K(7)Na-1. The zero-field (D) parameters have also been determined for these states, constituting a rare case wherein one observes EPR from both the ground and the excited states. Magnetic susceptibility data show that Na(9)-2 has antiferromagnetically coupled Cu(2+) ions, with J = -1.36 +/- 0.01 cm(-)(1), while K(7)Na-1 has both ferromagnetically and antiferromagnetically coupled Cu(2+) ions (J(1) = 2.78 +/- 0.13 cm(-)(1), J(2) = -1.35 +/- 0.02 cm(-)(1), and J(3) = -2.24 +/- 0.06 cm(-)(1)), and the ground-state total spins are S(T) = 1/2 in Na(9)-2 and S(T) = 1 in K(7)Na-1.