An algebraic method that includes Gibbs minimization for performing phase equilibrium calculations for any number of components or phases

The most widely used technique for performing phase equilibria calculations is the K-value method (equality of chemical potentials). This paper proposes a more efficient algorithm to achieve the results that includes Gibbs minimization when we know the number of phases. Using the orthogonal derivatives, the tangent plane equation and mass balances, it is possible to reduce the Gibbs minimization procedure to the task of finding the solution of a system of non-linear equations. Such an operation is easier and faster than finding tangents or areas, and appears to converge as fast as the K-value method. Examples illustrate application of the new technique to two and three phases in equilibrium for binary and ternary mixtures.     

Solid-state structures of cis- and trans-1-cyclohexyl-2-phenyl-3-(p-toluyl)aziridines

Solid-state structures have been determined for cis- and trans-1-cyclohexyl-2-phenyl-3-(p-toluyl)aziridines using single-crystal X-ray diffraction techniques. The cis isomer crystallizes in the centrosymmetric monoclinic space group P2₁/c (No. 14), with a = 18.669(3)Å, b = 5.709(1)Å, c = 17.412(2)Å, β = 96.29(1)° and Z = 4; the trans isomer crystallizes in the noncentrosymmetric orthorhombic space group Pna2₁ (No. 33), with a = 17.089(2)Å, b = 18.729(3)Å, c = 5.749(1)Å and Z = 4. Full-matrix least-squares refinement of the structural parameters led to the following final agreement factors: R₁ (unweighted, based on F) = 0.040 and R₂ (weighted, based on F) = 0.054 for the 2592 independent reflections of the cis isomer having 2θ_MoK¯α <55° and I>3σ₁, and R₁ = 0.033 and R₂ = 0.031 for the 1504 independent reflections of the trans isomer having 2θ_MoK¯α <55° and I>3σ₁. The statistically significant differences that exist between the two isomers for two bond lengths and ten bond angles (p < 0.05) appear to be the direct result of the p-toluyl group orientation with respect to the cyclohexyl and phenyl substituents. In the cis isomer it is anti with respect to the N-cyclohexyl group and cis with respect to the phenyl group, whereas in the trans isomer it is syn with respect to the N-cyclohexyl and trans with respect to the phenyl group. Three-ring to carbonyl hyperconjugation is correlated with stereoelectronic interactions in the trans isomer. Bonding, determined by X-ray and nmr studies, is discussed for the three-membered aziridine ring proper; while bonding, determined by X-ray studies, is discussed for substituents of the aziridine ring. These aziridinyl ketone compounds are of importance as potential mammalian DNA alkylating anti-tumor agents in solid-state solid-state systems. To date only a trans isomer has demonstrated this biological activity in tumor-bearing rats.     

Probing the contribution of electronic coupling to the directionality of electron transfer in photosynthetic reaction centers

Subpicosecond transient absorption studies are reported for a set of Rhodobacter (R.) capsulatus bacterial photosynthetic reaction centers (RCs) designed to probe the origins of the unidirectionality of charge separation via one of two electron transport chains in the native pigment-protein complex. All of the RCs have been engineered to contain a heterodimeric primary electron donor (D) consisting of a bacteriochlorophyll (BChl) and a bacteriopheophytin (BPh). The BPh component of the M heterodimer (Mhd) or L heterodimer (Lhd) is introduced by substituting a Leu for His M200 or His L173, respectively. Previous work on primary charge separation in heterodimer mutants has not included the Lhd RC from R. capsulatus, which we report for the first time. The Lhd and Mhd RCs are used as controls against which we assess RCs that combine the heterodimer mutations with a second mutation (His substituted for Leu at M212) that results in replacement of the native L-side BPh acceptor with a BChl (beta). The transient absorption spectra reveal clear evidence for charge separation to the normally inactive M-side BPh acceptor (H(M)) in Lhd-beta RCs to form D+H(M)- with a yield of approximately 6%. This state also forms in Mhd-beta RCs but with about one-quarter the yield. In both RCs, deactivation to the ground state is the predominant pathway of D decay, as it is in the Mhd and Lhd single mutants. Analysis of the results indicates an upper limit ofV2L/V2m < or = 4 for the contribution of the electronic coupling elements to the relative rates of electron transfer to the L versus M sides of the wild-type RC. In comparison to the L/M rate ratio (kL/kM) approximately 30 for wild-type RCs, our findings indicate that electronic factors contribute approximately 35% at most to directionality with the other 65% deriving from energetic considerations, which includes differences in free energies, reorganization energies, and contributions of one- and two-step mechanisms on the two sides of the RC.     

Bis(m-phenylene)-32-crown-10-based cryptands, powerful hosts for paraquat derivatives

Four new bis(m-phenylene)-32-crown-10-based cryptands with different third bridges were prepared. Their complexes with paraquat derivatives were studied by proton NMR spectroscopy, mass spectrometry, and X-ray analysis. It was found that these cryptands bind paraquat derivatives very strongly. Specifically, a diester cryptand with a pyridyl nitrogen atom located at a site occupied by either water or a PF(6) anion in analogous complexes exhibited the highest association constant K(a) = 5.0 x 10(6) M(-1) in acetone with paraquat, 9000 times greater than the crown ether system. X-ray structures of this and analogous complexes demonstrate that improved complexation with this host is a consequence of preorganization, adequate ring size for occupation by the guest, and the proper location of the pyridyl N-atom for binding to the beta-pyridinium hydrogens of the paraquat guests. This readily accessible cryptand is one of the most powerful hosts reported for paraquats.     

Frequency-Dependent Streaming Potentials

An experimental apparatus and data acquisition system was constructed to measure the streaming potential coupling coefficients as a function of frequency. The purpose of the experiments was to measure, for the first time, the real and imaginary portion of streaming potentials. In addition, the measured frequency range was extended beyond any previous measurements. Frequency-dependent streaming potential experiments were conducted on one glass capillary and two porous glass filters. The sample pore diameters ranged from 1 mm to 34 μm. Two frequency-dependent models (Packard and Pride) were compared to the data. Both Pride's and Packard's models have a good fit to the experimental data in the low- and intermediate-frequency regime. In the high-frequency regime, the data fit the theory after being corrected for capacitance effects of the experimental setup. Pride's generalized model appears to have the ability to more accurately estimate pore sizes in the porous medium samples. Packard's model has one unknown model parameter while Pride's model has four unknown model parameters, two of which can be independently determined experimentally. Pride's additional parameters may allow for a determination of permeability. Copyright 2001 Academic Press.     

Organic sonochemistry. Ultrasound-promoted coupling of organic halides in the presence of lithium wire

Alkyl, aromatic, benzylic and benzoyl halides have been successfully coupled in good yields using lithium wire suspended in tetrahydrofuran and ultrasound.     

Synthesis with migrating phenylthio groups: connective routes to 2-phenylthioallyl alcohols and 2-phenylthio enones

The title compounds may be made from bis(phenylthio) acetals and aldehydes by routes involving PhS migration.     

All torsion-free spherical vacuum solutions of the quadratic Poincaré gauge theory of gravity

We find all torsion-free, spherically symmetric, vacuum solutions to the theory of gravity recently proposed by Hehl, Ne'eman, Nitsch, and von der Heyde. There are three classes of solutions: (A) the Schwarzschild metrics with arbitrary mass,M, and arbitrary cosmological constant, ; (B) the Nariai-Bertotti metrics with arbitrary positive cosmological constant, ; and (C) the conformally flat metrics whose conformai factor is ²/ ² where is a function of only the time coordinate , and the radial coordinate, and satisfies the wave equation in these variables. Hence there is no Birkhoff theorem for this theory. In fact, solutions (C) include some asymptotically flat but nonstationary solutions. On the other hand, solutions (A) include a gravitational confinement potential, as was sought by Hehl et al., since when <0, the weak field limit of the Schwarzschild metric becomes a harmonic oscillator potential. We also discuss the relationship of this theory to the Eddington theory, the Lichnerowicz-Kilmister-Newman-Yang theory, the Nordström theory and the Einstein theory with a cosmological constant.     

Mössbauer study of the three-coordinate planar Fe(II) thiolate complex [Fe(SR)(3)](-) (R = C(6)H(2)-2,4,6-tBu(3)): model for the trigonal iron sites of the MoFe(7)S(9):homocitrate cofactor of nitrogenase

The cofactor (M-center) of the MoFe protein of nitrogenase, a MoFe(7)S(9):homocitrate cluster, contains six Fe sites with a (distorted) trigonal sulfido coordination. These sites exhibit unusually small quadrupole splittings, Delta E(Q) approximately 0.7 mm/s, and isomer shifts, delta approximately 0.41 mm/s. M?ssbauer and ENDOR studies have provided the magnetic hyperfine tensors of all iron sites in the S = 3/2 state M(N). To assess the intrinsic zero-field splittings and hyperfine parameters of the cofactor sites, we have studied with M?ssbauer spectroscopy two salts of the three-coordinated Fe(II) thiolate complex [Fe(SR)(3)](-) (R = C(6)H(2)-2,4,6-tBu(3)). One of the salts, [Ph(4)P][Fe(SR)(3)] x 2MeCN x C(7)H(8), 1, has a planar geometry with idealized C(3h) symmetry. This S = 2 complex has an axial zero-field splitting with D = +10.2 cm(-1). The magnetic hyperfine tensor components A(x) = A(y) = -7.5 MHz and A(z) = -29.5 MHz reflect an orbital ground state with d(z(2)) symmetry. A(iso) = (A(x) +A(y) +A(z))/3 = -14.9 MHz, which includes the contact interaction (kappa P = -21.9 MHz) and an orbital contribution (+7 MHz), which is substantially smaller than A(iso) approximately -22 MHz of the tetrahedral Fe(II)(S-R)(4) sites of both rubredoxin and [PPh(4)](2)[Fe(II)(SPh)(4)]. The largest component of the electric field gradient (EFG) tensor is negative, as expected for a d(z(2)) orbital. However, Delta E(Q) = -0.83 mm/s, which is smaller than expected for a high-spin ferrous site. This reduction can be attributed to a ligand contribution, which in planar complexes provides a large positive EFG component perpendicular to the ligand plane. The isomer shift of 1, delta = 0.56 mm/s, approaches the delta-values reported for the six trigonal cofactor sites. The parameters of 1 and their importance for the cofactor cluster of nitrogenase are discussed.     

Development of a systems analysis approach for resolving the structure of biodegrading soil systems

An experimental and mathematical method is developed for the microbial systems analysis of polyaromatic hydrocarbon (PAH)-degrading mixed cultures in PAH-contaminated “town gas” soil systems. Frequency response is the primary experimental and data analysis tool used to probe the structure of these complicated systems. The objective is to provide a fundamental protocol for evaluating the performance of specific mixed microbial cultures on specific soil systems by elucidating the salient system variables and their interactions. Two well-described reactor systems, a constant volume stirred tank reactor (CSTR) and a plug flow differential volume reactor, are used in order to remove performance effects that are related to reactor type as opposed to system structure. These two reactor systems are well-defined systems that can be described mathematically and represent the two extremes of one potentially important system variable, macroscopic mass transfer. The experimental and mathematical structure of the protocol is described, experimental data is presented, and data analysis is demonstrated for the stripping, sorption, and biodegradation of napththalene.