Comments on the mean spherical approximation for hard-core and soft potentials and an application to the one-component plasma

The thermodynamic properties of the mean spherical (MSA), Percus-Yevick (PY), and hypernetted-chain (HNC) approximations are derived by a simple and unified approach by considering the RPA free-energy functionalF and employing an Ewald-type identity. It is demonstrated that with decreasing relative contribution of the hard-core insertion to the thermodynamic functions, the MSA changes its nature from PY-like to HNC-like, withF changing its role from excess pressure to excess free energy, respectively. It is found that the condition of continuity of the MSA pair functions is equivalent to a stationarity condition forF and leads to thermodynamic consistency between the virial and energy equations of state for the (thus defined) soft-MSA (SMSA), withF playing the role of the excess free energy. It is shown that the PY-compressibility and virial equations of state forD-dimensional hard spheres may be simply obtained one from the other without knowing any details of the solution of the model. Using this relation we find an indication that the PY approximation for hard spheres becomes less accurate with increasing dimensionality. A general variational formulation is presented for the application of the MSA for soft potentials, and results for the one-component plasma are discussed and extended.On sabbatical leave from the Nuclear Research Center-Negev, P.O. Box 9001, Beer Sheva, Israel.     

钙的加入对含锆熔铁型氨合成催化剂性能的影响

近年来，对于熔铁型氨合成催化剂在不断通过加入新的助剂来改善其性能。本文用Mossbauer谱等手段分析与研究加入钙后对含锆催化剂的影响。     

On fluctuations in μ-space

A master equation is derived microscopically to describe the fluctuating motion of the particle density in . space. This equation accounts for the drift motion of particles and is valid for any inhomogeneous gas. The Boltzmann equation is obtained from the first moment of this equation by neglecting the second cumulant (the pair correlation function). The successive moments form coarse-grained BBGKY-like hierarchy equations, in which small spatial regions with r_ij < the force range are smeared out. These hierarchy equations are convenient for investigating the nonequilibrium long-range pair correlation function, which arises mainly from sequences of isolated binary collisions and gives rise to the much-discussed long-time tail and the logarithmic term in the density expansion of transport coefficients. It is shown to have a spatial long tail, like the Coulombic potential, in a steady laminar flow. The stochastic nature of the nonlinear Boltzmann-Langevin equation is also investigated; the random source term is found to be expressed as a linear superposition of Poisson random variables and to become Gaussian in special cases.     

The molecular structure of gaseous bis(hexamethydisilylamido)mercury(II), Hg{N(Si(CH3)3)2}2, as determined by electron diffraction

Gaseous bis(hexamethydisilylamido)mercury(II), Hg{N(SiMe₃)₂)₂}₂, has been studied by electron diffraction at a nozzle temperature of ca 390 K.

The diffraction data are consistent with a model consisting only of monomers. By assuming the NHgN chain to be linear and the HgHSi₂ fragments to be planar, an equilibrium conformer with a staggered Si₂NHgNSi₂ skeleton of D_ad-symmetry may be brought into a nice agreement with the observed diffraction data. The relatively large value of the vibrational amplitude of the inter-ligand SiSi distance, 0.26(12) A, indicates that the ligands undergo large amplitude vibrations about the NHgN axis. Steric considerations as well as the magnitude of the rotational barrier as estimated from the diffraction data (ca. 2 kcal mol⁻¹) show that this motion is hindered. A model with an eclipsed, co-planar Si₂NHgNSi₂ backbone of D_adsymmetry could not satisfactorily be brought into agreement with the observed diffraction data.

The values of some relevant key-parameters are: r_a(Hg---N) = 2.01(2) A, r_a(Si---N) = 1.732(9) A, r_a(Si---C) = 1.883(6) A;HgNSi = 116.0(1.0)°, SiNSi = 128.0(2.0)°, NSiC= 111.8(1.2)° and SiCH = 111.0(2.0)°. The trimethylsilyl groups are twisted 25(3)° away from their references positions typified by one Si---C bond of each such group eclipsing the adjacent Hg---N bond, in such a way that the overall symmetry of the model is lowered from D_ad to S₄.     

Lipophilicity determination of some photosynthetic pigments by reversed-phase thin-layer chromatography. The effect of support and the organic phase in the eluent

Summary The lipophilicity of some photosynthetic pigments was determined by reversed-phase thin-layer chromatography using silica, alumina, cellulose, polyamid and diatomaceous earth as supports and acetone and ethanol as organic mobile phase. The R_M value of each compound linearly decreased with increasing concentration of the organic modifier. The supports exerted high impact on the separation: no acceptable separation was achieved on cellulose, polyamid, alumina and diatomaceous earth supports while silica supports produced the best separation. The retention of photosynthetic pigments depended on the origin of silica and on the type of organic mobile phase.     

Location of saddle points and minimum energy paths by a constrained simplex optimization procedure

Two methods are proposed, one for the location of saddle points and one for the calculation of steepest-descent paths on multidimensional surfaces. Both methods are based on a constrained simplex optimization technique that avoids the evaluation of gradients or second derivative matrices. Three chemical reactions of increasing structural complexity are studied within the PRDDO SCF approximation. Predicted properties of reaction hypersurfaces are in good overall agreement with those determined by gradient minimization and gradient following algorithms in connection with various ab initio SCF methods. Computational efforts required by the new procedures are discussed.     

Liquid fluidized bed starter culture ofTrichoderma reesei for cellulase production

A starter culture ofTrichoderma reesei (Rut-C30) prepared in a liquid fluidized bed reactor (LFBR) gave better growth and greater cellulase production in submerged fermentation than a conventional shake flask inoculum. The LFBR starter was prepared by first coatingT. reesei spores to 0.25 mm size corncob (1.0x10⁸g^-1) in a medium containing 1.0% corncob, 0.5 gL^-1 xylose and 0.1 gL^-1 lactose in a balanced salt solution, then fluidizing the particles in the LFBR for 36 h to allow germination of the spores, and covering the particles with an approx 30 μm thick biofilm. This biofilm that developed in constant adherence to the lignocellulosic carrier, apparently became well adapted to grow rapidly on insoluble cellulose substrates (Solca Floc), and had the enzymes of the cellulase complex induced for increased cellulase production. The LFBR starter used in a stirred tank reactor (STR) gave 15 gL^-1 biomass production and 6.5 IU mL^-1 overall cellulase activity with a volumetric productivity of 64 IU L^-1h^-1 in a 5 d fermentation, compared with a 7 d shake flask inoculum that gave 11 gL^-1 biomass and 3.2 IU mL^-1 cellulase activity, with a volumetric productivity of 31IU L^-1h^-1. The LFBR starter culture retained its viability in dry storage for 6–9 mo.     

Biocatalytic synthesis of polymers. III. Formation of a high molecular weight polyester through limitation of hydrolysis by enzyme-bound water and through equilibrium control

Enzyme-catalyzed preparation of polymers offers several potentially valuable advantages over the usual polymerization procedures and has been studied for several years. A significant limitation on the polyesters prepared to date has been the low molecular weights achieved. The present studies have established that, in the polycondensation of bis(2,2,2-trifluoroethyl) glutarate with 1,4-butanediol using porcine pancreatic lipase as the catalyst, this limitation arises from at least two sources: hydrolysis of activated ester end groups by water introduced along with the enzyme and the polymerization's reaching equilibrium despite using the poorly nucleophilic 2,2,2-trifluoroethanol as the leaving group. Evidence is also developed that the presence of trifluoroethanol accelerates the release of the enzyme-bound water which hydrolyzes the activated ester end groups. The hydrolysis could be avoided by choosing a relatively high-boiling solvent, such as bis(2-ethoxyethyl) ether, then removing the trifluoroethanol by placing the reaction mixture under vacuum periodically or by drying the enzyme rigorously. The vacuum method also removed the limitation on molecular weight resulting from the reaction's reaching equilibrium. A further improvement in the molecular weight to nearly 40,000 daltons, well within the range that is technically interesting, was achieved by using 1,2-dimethoxybenzene or 1,3-dimethoxybenzene as the polymerization solvent. © 1995 John Wiley & Sons, Inc.     

Sample evaporation in conventional split/splitless GC injectors. Part 3: Retaining the liquid in the vaporizing chamber

As most sample liquids tend to pass through an empty injector insert at a speed which is too high to enable complete evaporation, movement of the liquid must be arrested before it reaches the column entrance. Stopping the liquid means deposition on to a surface; this, however, is possible only after the temperature of the surface has been cooled to (or below) the boiling point of the liquid (solvent). The performance of different means of stopping the liquid has been tested visually (by the method described in Part 2). Baffles on the wall of the injector insert had hardly any effect on evaporation: the band of liquid leaving the syringe needle performed a perfect slalorn around them. The inverted cup proved more efficient, but the best performance was obtained from a light plug of glass wool: owing to its low thermal mass, the first fibers to be met by the liquid are immediately cooled to the solvent boiling point, allowing the liquid to wet it. The sample liquid is sucked up by the glass wool, from where the sample evaporates relatively slowly, often over a period of several seconds.     

On the statistical independence of various column contributions to band broadening. Part 1: Second moment contributions from statistically independent,longitudinal diffusion in both phases

The total length-based second moment contribution from longitudinal sample diffusion in both phases on a column, σD , is derived by adding individual partial differential contributions to a partial differential equation accounting for the longitudinal diffusion processes only. Although each diffusion-dispersed sample part is equilibrated between two phases, the resulting σ,D (= 2D _mt _m + 2D _st _s) can be interpreted as the sum of two independent contributions in accordance with the variance addition rule. (D _m and D _s are the mean diffusion coefficients and t _mand t _s the mean residence times of the sample in the mobile and stationary phases, respectively.) The same σD expression is derived from the random walk model of Giddings by treating the diffusional process in each phase as statistically independent of the other processes. Under these conditions the broadening contribution from longitudinal diffusion in the mobile phase is shown to be independent of the velocity profile.