CO(2) Fixation by Novel Copper(II) and Zinc(II) Macrocyclic Complexes. A Solution and Solid State Study

Solutions containing Zn(II) and Cu(II) complexes with [15]aneN(3)O(2) rapidly adsorb atmospheric CO(2) to give {[ZnL](3)(&mgr;(3)-CO(3))}.(ClO(4))(4) (2) and {[CuL](3)(&mgr;(3)-CO(3))}.(ClO(4))(4) (4) complexes. The crystal structures of both complexes have been solved (for 2, space group R3c, a, b = 22.300(5) ?, c = 17.980(8) ?, V = 7743(4) ?(3), Z = 6, R = 0.0666, R(w)(2) = 0.1719; for 4, space group R3c, a, b = 22.292(7) ?, c = 10.096(8) ?, V = 7788(5) ?(3), Z = 6, R = 0.0598, R(w)(2) = 0.1611), and the spectromagnetic behavior of 4 has been studied. In both compounds a carbonate anion triply bridges three metal cations. Each metal is coordinated by one oxygen of the carbonate, three nitrogens, and an oxygen of the macrocycle; the latter donor weakly interacts with the metals. Although the two compounds are isomorphous, they are not isostructural, because the coordination geometries of Zn(II) in 2 and Cu(II) in 4 are different. The mixed complex {[CuZn(2)L(3)](&mgr;(3)-CO(3))}.(ClO(4))(4) has been synthesized. X-ray analysis (space group R3c, a, b = 22.323(7) ?, c = 17.989(9) ?, V = 7763(5) ?(3), Z = 6, R = 0.0477, R(w)(2) = 0.1371) and EPR measurements are in accord with a &mgr;(3)-carbonate bridging one Cu(II) and two Zn(II) ions in {[CuZn(2)L(3)](&mgr;(3)-CO(3))}(4+). Both the Zn(II) and Cu(II) cations exhibit the same coordination sphere, almost equal to that found in the trinuclear Zn(II) complex 2. The systems Zn(II)/L and Cu(II)/Lhave been studied by means of potentiometric measurements in 0.15 mol dm(-)(1) NaCl and in 0.1 mol dm(-)(3) NaClO(4) aqueous solutions; the species present in solution and their stability constants have been determined. In both systems [ML](2+) species and hydroxo complexes [M(II)LOH](+) (M = Zn, Cu) are present in solution. In the case of Cu(II), a [CuL(OH)(2)] complex is also found. The process of CO(2) fixation is due to the presence of such hydroxo-species, which can act as nucleophiles toward CO(2). In order to test the nucleophilic ability of the Zn(II) complexes, the kinetics of the promoted hydrolysis of p-nitrophenyl acetate has been studied. The [ZnLOH](+) complex promotes such a reaction, where the Zn(II)-bound OH(-) acts as a nucleophile to the carbonyl carbon. The equilibrium constants for the addition of HCO(3)(-) and CO(3)(2)(-) to the [ZnL](2+) complex have been potentiometrically determined. Only [ML(HCO(3))](+) and [ML(CO(3))] species are found in aqueous solution. A mechanism for the formation of {[ML](3)(&mgr;(3)-CO(3))}.(ClO(4))(4) is suggested.     

Electronic structure of paramagnetic clusters of transition metal ions. 3. Magnetic properties and scattered wave description of the electronic structure of the hexanuclear octahedral cluster [Fe6(μ3−S)8(PEt3)6] (BPh4)2

Spin-polarized Xα–SW calculations of [Fe₆(μ₃?S)₈(PH₃)₆]²⁺ as a model of the cluster [Fe₆(μ₃?S)₈(PEt₃)₆] (BPh₄)₂ have been performed. The highest occupied energy levels are well separated from empty levels, and up to a maximum of eight electrons can be unpaired, giving a maximum spin state with S = 4. This electronic state is consistent with the magnetic data of [Fe₆(μ₃?S)₈(PEt₃)₆](BPh ₄)₂, which have been interpreted using the Heisenberg–Dirac–Van Vleck exchange spin Hamiltonian. The S = 4 state arises from the magnetic coupling between five low-spin (S_i = 1/2) and one intermediate-spin (S = 3/2) iron(III) center. © 1994 John Wiley & Sons, Inc.     

Thermodynamic equilibrium in dielectric fluids

Summary A rigorous deduction of the thermodynamic-equilibrium condition is provided for a homogeneous, uncharged and linear dielectric fluid contained in an electrostatic field. Contrary to the previous ones, this deduction does not postulate the existence of a mechanical stress tensor and of a body force density in the polarized fluid. Then, the equilibrium condition is employed to obtain the mass density distribution of the fluid and to present a correct proof of the well-known formula for the attractive force between the plates of a plane-parallel capacitor immersed in the fluid.     

Thermal-wave heat conduction in a solid cylinder which undergoes a change of boundary temperature

The propagation of thermal waves in a solid cylinder which undergoes a change of its boundary temperature is studied by assuming the validity of Cattaneo-Vernotte's constitutive equation for the heat flux. The hyperbolic energy equation, together with its boundary and initial conditions, is written in a dimensionless form and solved analytically by the Laplace transform method. It is shown that, if the boundary temperature undergoes a step change, the temperature field presents singularities. On the other hand, no singularity is present if the temperature change is achieved by a continuous monotonic evolution of the boundary temperature. However, even in this case, the absolute value of the temperature change in internal points of the cylinder can be greater than that prescribed at the boundary.     

Non-fourier heat conduction in a plane slab with prescribed boundary heat flux

The non-stationary heat conduction in an infinitely wide plane slab with a prescribed boundary heat flux is studied. An arbitrary time dependent boundary heat flux is considered and a non-vanishing thermal relaxation time is assumed. The temperature and the heat flux density distributions are determined analytically by employing Cattaneo-Vernotte's constitutive equation for the heat flux density. It is proved that the temperature and the heat flux density distributions can be incompatible with the hypothesis of local thermodynamic equilibrium. A comparison with the solution which would be obtained by means of Fourier's law is performed by considering the limit of a vanishing thermal relaxation time.     

Magnetostatic stresses on a superconductor in a dielectric fluid

Summary The stresses which act on the surface of a superconductor surrounded by an isotropic dielectric fluid at rest are evaluated. Moreover, it is proved that there exists an infinite set of second-order tensors which yield these stresses. The magnetic Helmoltz stress tensor belongs to this set.     

A rigorous treatment of the phase rule

Summary After a critical analysis of the literature, the traditional formulation of the phase rule proposed by Gibbs is stated in a different form and is proved rigorously, together with Gibbs' conjecture on the maximum number of coexisting phases. A new statement of Gibbs' phase rule is proved for closed systems. Then, Hatsopoulos-Keenan's formulation of the phase rule is restated and proved, both for open and for closed systems. The whole treatment of the phase rule presented in this paper holds both in the presence and in the absence of chemical reactions.     

Can the definition of mechanical stress tensor be applied to a dielectric fluid in an electrostatic or magnetostatic field?

Summary It is proved that, for an uncharged and linear dielectric fluid at rest and in local equilibrium in an electrostatic or magnetostatic field, the definition of stress tensor employed in continuum mechanics is inconsistent with the assumption that the stress tensor depends only on the local values of mass density, temperature, electric- or magnetic-field components and the derivatives of these quantities with respect to space and time.     

Mechanical stress tensor for a fluid in a magnetostatic field

Summary Two constraints on the form of the mechanical stress tensor for an uncharged and linear dielectric fluid at rest in a magnetostatic field are determined. Moreover, it is shown that the stress tensor proposed by Helmholtz, that proposed by Einstein-Laub and that proposed by Liu-Müller are unacceptable as mechanical stress tensors for a dielectric fluid in the conditions stated above.     

Heat conduction in a cylinder crossed by an electric current with skin effect

The steady periodic temperature distribution in an infinitely long solid cylinder crossed by an alternating current is evaluated. First, the time dependent and non-uniform power generated per unit volume by Joule effect within the cylinder is determined. Then, the dimensionless temperature distribution is obtained by analytical methods in steady periodic regime. Dimensionless tables which yield the amplitude and the phase of temperature oscillations both on the axis and on the surface of copper or nichrome cylindrical electric resistors are presented.

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Wärmeleitung in einem stromdurchflossenen Zylinder unter Berücksichtigung des Skin-Effektes

Zusammenfassung Es wird die periodische Temperaturverteilung für den eingeschwungenen Zustand in einem unendlich langen, von Wechselstrom durchflossenen Vollzylinder ermittelt. Zuerst erfolgt die Bestimmung der zeitabhängigen, nichgleichförmigen Energiefreisetzung pro Volumeneinheit des Zylinders infolge Joulescher Wärmeentwicklung und anschließend die Ermittlung der quasistationären Temperaturverteilung auf analytischem Wege. Amplitude und Phasenverzögerung der Temperaturschwingungen werden für die Achse und die Oberfläche eines Kupfer- oder Nickelchromzylinders tabellarisch in dimensionsloser Form mitgeteilt.

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Nomenclature A integration constant introduced in Eq. (2) - ber, bei Thomson functions of order zero - Bi Biot numberhr ₀/ - c speed of light in empty space - c ₁,c ₂ integration constants introduced in Eq. (46) - c _p specific heat at constant pressure - E electric field - E _z component ofE alongz - E time independent part ofE, defined in Eq. (1) - f function ofs and defined in Eq. (11) - g function ofs and defined in Eq. (37) - h convection heat transfer coefficient - H magnetic field - i imaginary uniti=(–1)^1/2 - I electric current - I _eff effective electric currentI _eff=I/2^1/2 - Im imaginary part of a complex number - J _n Bessel function of first kind and ordern - J electric current density - q _g power generated per unit volume - time average of the power generated per unit volume - time averaged power per unit length - r radial coordinate - R electric resistance per unit length - r ₀ radius of the cylinder - Re real part of a complex number - s dimensionless radial coordinates=r/r ₀ - s, s integration variables - t time - T temperature - time averaged temperature - T _f fluid temperature outside the boundary layer - time average of the surface temperature of the cylinder - u, functions ofs, and defined in Eqs. (47) and (48) - W Wronskian - x position vector - x real variable - Y _n Bessel function of second kind and ordern - z unit vector parallel to the axis of the cylinder - z axial coordinate - · modulus of a complex number - equal by definition Greek symbols amplitude of the dimensionless temperature oscillations - electric permittivity - dimensionless temperature defined in Eq. (16) - ₀, ₁, ₂ functions ofs defined in Eq. (22) - thermal conductivity - dimensionless parameter=(2)^1/2 - magnetic permeability - ₀ magnetic permeability of free space - function of defined in Eq. (59) - dimensionless parameter=c _p/() - mass density - electric conductivity - dimensionless time=t - phase of the dimensionless temperature oscillations - function ofs:= ₁+i ₂ - angular frequency - dimensionless parameter=()^1/2 r ₀