Critical discussion of simple adsorption methods used to evaluate the micropore size distribution

The well-known simple adsorption methods used to evaluate the micropore size distribution from low pressure adsorption isotherms were examined by employing model isotherms for slit-like graphite micropores obtained from nonlocal density functional theory. It was shown that in the range of pore sizes from about 0.4 to 0.9 nm, the Horvath Kawazoe (HK) method satisfactorily reproduces the shape of the micropore size distribution, but the pore sizes are underestimated. In the case of micropores wider than 0.9 nm, the method fails as the formation of the monolayer on the pore walls produces a peak corresponding to 0.6 nm micropores on the HK pore size distribution. Therefore, the HK method indicates the presence of microporosity even for nonporous samples. The Dubinin-Astakhov adsorption isotherms were also examined and it was shown that their application to represent local adsorption isotherms for homogeneous pores is questionable. However, the adsorption potential distributions seem to be promising for micropore analysis.Nomenclature A Adsorption potential kJ/mol - C ₁ Constant in Eq. 3 and 4 kJ * nm/mol - C ₂ Constant in Eq. 3 and 4 nm³ - C ₃ Constant in Eq. 3 and 4 nm⁹ - C ₄ Constant in Eq. 3 and 4 - d Adsorbate molecule diameter nm - d _A Adsorbent atom diameter nm - G Change in the Gibbs free energy kJ/mol - J Pore size distribution cm³/(g*nm) - R The universal gas constant = 8.31431 J/(mol * K) - T Absolute temperature K - V Amount adsorbed expressed in cm³ of liquid adsorbate per 1 g of the adsorbent = 0.0015468 * amount adsorbed expressed in cm³ STP/g cm³/g - x Pore width nm - X Differential adsorption potential distribution cm³ * mol/(g*kJ) - Constant defined as nm - p Pressure Pa - p ₀ Saturated pressure = 760 torr = 101325 Pa Pa - P _c Condensation pressure Pa - Degree of pore filling - S _BET BET specific surface area m²/g - S _ex External surface area obtained fromt-plot method m²/g - V _mi Micropore volume obtained fromt-plot method cm³/g - V ₁ Total pore volume cm³/g - E Characteristic energy in the Dubinin-Astakhov equation kJ/mol - n Exponent in the Dubinin-Astakhov equation      

X-ray diffraction (powder), e.s.r. and other spectral studies oftris[methylenebis(diphenylphosphine oxide)]iron(III) perchlorate

Summary Bifunctional methylenebis(diphenylphosphine oxide) (mdpo) on reaction with iron(III) perchlorate forms the complex, [Fe(mdpo)₃](ClO₄)₃ · H₂O. This has been characterized through elemental analysis, i.r., far-i.r., u.v. and visible spectroscopy and by x-ray diffraction, magnetic moment, molar conductance and e.s.r. data. The e.s.r. spectrum consists of five lines with transitions from: ¦–5/2¦–3/2¦–3/2¦–1/2, ¦–1/2¦+1/2¦+1/2¦+3/2 and ¦+3/2¦+5/2 centred at a g-value of 2.00. On the basis of these studies, a chelated octahedral structure has been assigned to the cation, [Fe(mdpo)₃]³⁺.     

Moment Scaling at the Sol-Gel Transition

Two standard models of sol-gel transition are revisited here from the point of view of their fluctuations in various moments of both the mass-distribution and the gel-mass. Bond-percolation model is an at-equilibrium system and undergoes a static second-order phase transition, while Monte-Carlo Smoluchowski model is an off-equilibrium one and shows a dynamical critical phenomenon. We show that the macroscopic quantities can be splitted into the three classes with different scaling properties of their fluctuations, depending on whether they correspond to: (i) noncritical quantities, (ii) critical quantities or to (iii) an order parameter. All these three scaling properties correspond to a single form: M P(M) = ((M – M)/ M), with the values of respectively: = 1/2 (regime (i)), 1/2 and 1 (regime (ii)), and = 1 (regime (iii)). These new scalings are very robust and, in particular, they do not depend on the precise form of an Hamiltonian.     

Average electron momenta in many-electron atoms

In many-electron atoms, the average electron momentum p represents the mean momentum of a single electron when all the electron motions are averaged. If any two electrons are considered simultaneously, however, the average momentum p splits into two different momenta, low momentum p_< and high momentum p_>. For the 102 atoms He through Lr in their ground states, the momenta p_< and p_> are systematically examined at the Hartree–Fock limit level. It is also shown that the sum p_>+p_< and the difference p_>–p_< of the two momenta constitute upper and lower bounds to the electron-pair relative momentum p₁₂=|p₁–p₂| and to the electron-pair center-of-mass momentum P=|p₁+p₂|/2. The tightness of the bounds is discussed for the 102 atoms.     

Approximate upper bounds to the momentum expectation value ratios 〈p 2〉/〈p −1〉 and 〈p〉/〈p −1〉 in atoms

Within an isoelectronic series of atoms, reasonably tight upper bounds on the ratios of the momentum expectation values ;p ²/;p ^–1 and p/p ^–1 respectively have been derived for the first time by using the Dresher's inequality.     

Nachweis von Titan mit Sulfosalicyls?ure und Tetraphenylarsoniumsalz

Zusammenfassung Der durch Ausschütteln des gelben Tetraphenylphosphoniumsalzes der Titan-Sulfosalicylsäure-Verbindung mittels Chloroform geführte Nachweis erlaubt die Erkennung von 0,05 g Titan bei der Grenzkonzentration 120 000 000. Der Nachweis ist spezifisch neben vielen Leicht- und Schwermetallen.     

Comparison of the crystal structures of Co2(X 2O7)·2H2O,X=P and As

Summary Crystals of Co₂(X ₂O₇)·2H₂O,X=P/As were synthesized under hydrothermal conditions. Their crystal structures were determined by single crystal X-ray diffraction:a=6.334(1)/6.531(2),b=13.997(2)/14.206(4),c=7.637(1)/7.615(2)Å, =94.77(2)/94.74(2)°, space group P2₁/n,R=0.032/0.046,R _w=0.028/0.034 for 2423/2042 reflections and 131/119 variables. Within the twoXO₄ tetrahedra connected via a common corner to anX ₂O₇ group the average P-O bond lengths are approximately equal (1.540 and 1.543 Å), but As-O differs significantly (1.685 and 1.696 Å). A comparison with the isotypic Mn and Mg pyrophosphates shows a correlation between the ratio Me-O/X-O and the angle O-X-O.

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Vergleich der Kristallstrukturen von Co₂(X ₂O₇)·2H₂O,X=P und As

Zusammenfassung Kristalle von Co₂(X ₂O₇)·2H₂O,X=P/As wurden unter Hydrothermalbedingungen synthetisiert. Ihre Kristallstrukturen wurden mittels Röntgenbeugung an Einkristallen bestimmt:a=6.334(1)/6.531(2),b=13.997(2)/14.206(4),c=7.637(1)/7.615(2) Å, =94.77(2)/97.74(2)°, Raumgruppe P2₁/n,R=0.032/0.046,R _w=0.028/0.034 für 2423/2042 Reflexe und 131/119 Variable. In den beiden über eine gemeinsame Ecke zuX ₂O₇-Gruppen verknüpftenXO₄-Tetraedern sind die mittleren P-O-Abstände ungefähr gleich (1.540 und 1.543 Å), hingegen differiert As-O signifikant (1.685 und 1.696 Å). Ein Vergleich mit den isotypen Mn- und Mg-Pyrophosphaten zeigt eine Korrelation zwischen dem Quotienten Me-O/X-O und dem WinkelX-O-X.

     

Microwave Spectrum and Dipole Moment of 1,3‐dioxolane in the Hindered‐Pseudorotation States v = 0, 1, 2, and 3

The microwave spectrum of 1,3dioxolane (C₃H₆O₂) in the ground and first three excited states of hindered pseudorotation was studied. The transitions corresponding to the _b, _c, and _a components of the dipole moment were identified. The spectrum was analyzed using numerical diagonalization of the effective rotational Hamiltonian for four interacting states of hindered pseudorotation. The rotational constants, centrifugal distortion constants, the constants of interaction between general rotation and hindered pseudorotation, and the distances between the quasidegenerate vibrational levels ₀₁ = 64840.5, ₁₂ = 122231.7 and ₂₃ = 119732.7 MHz are determined. From the Stark effect of microwave transitions, the dipole moment components (in Debye units) in the hinderedpseudorotation states v = 0, 1, 2, and 3 are determined: 0|_b|0 = 1|_b|1 = 1.22, 2|_b|2 = 1.20, 3|_b|3 = 1.21, 0|_c|1 = 0.77, 2|_c3 = 0.66, and 1|_a|2 = 0.19.     

Two-electron atomic wave functions which satisfy proportionality relations between one-and two-electron moments

Based on momentum- and position-space analyses of the moment operators for two-electron atoms, it is shown that there exists a family of two-electron wave functions which satisfy a proportionality relation, r/ ₁ ^v /r ₁₂ ^v =p/ ₁ ^v /p ₁₂ ^v =2^–v/2, between the one and two-electron moments in position and momentum spaces, where v is an arbitrary number for which the moments are well-defined.     

Texture of Electrolytic Platinum Deposited on Polycrystalline Gold

Platinum deposits of submicron thicknesses on polycrystalline gold substrates subjected to different thermal treatments and characterized by texture 200, 311, and 220 are characterized by methods of x-ray diffractometry and scanning electron microscopy. No deposits prepared in a potentiostatic mode exhibit a pronounced texture or a reliable correlation between a weak texture of a deposit and the substrate texture. Established is the difference of predominant directions of secondary nucleation–growth of deposit on neighboring grains of the substrate. The assumption that the deposit includes fragments the size of a few tens of micrometers with pronounced texture of different directions is substantiated.     

Excited state wave functions

Wave functions and energies were calculated for the 2s, 3p ₀, and 4d ₀ states of the hydrogen atom using the Messmer and Rayleigh-Ritz variational methods with minimization of the second eigenvalue. The wave functions were linear expansions of Gaussian functions and both linear and exponential parameters were varied. Except for the two term expansions, calculated values of the energies and expectation values, r ^–1, r and r ² were within two percent of the true values for both methods.     

Critical behavior and interfacial tension of mixtures of propylene glycol and ethylene glycol oligomers

This investigation presents an analysis of the critical behavior of mixtures of oligomers of propylene glycol, PG₁₇, and ethylene glycol, EG_n, withn=3, 4, 5, 6.4, 8.7, 12.1 and 22.1. The critical coordinates, _c andT _c were determined from the phase diagrams. The critical compositions compare very well with the Huggins-Flory predictions. The interaction parameter _n is around one for EG₃, EG₄ and EG₅ and it increases up to two for the higher oligomers. The break in the interaction parameter also corresponds to a minimum in the critical temperature. The phase diagrams and the interfacial tension were used to get the critical exponents and , respectively. The data were analysed with two approaches. First, from the temperature dependence of the length of the tie-lines and of the interfacial tension up to the upper critical solution temperature, UCST. Second, with the data at 30°C using the critical temperature of the systems as the variable. The first method led to =0.39±0.05 in good agreement with the result of the second method, =0.37±0.04. The exponents for the interfacial tension, , determined with the first method for PG₁₇ with EG_6.4, EG_8.7 and EG_12.1 are =1.66±0.11, 1.46±0.25 and 1.73±0.18, respectively. The second method led to =1.17±0.14. The critical exponents are compared to mean field and ising-3D predictions.     

Zur Kristallographie der Gleitverformung von Wolfram-Einkristallen im Zugversuch

Zusammenfassung Mittels einer speziellen Methode wurden spannungsfreie Wolfram-Einkristall-Zugproben verschiedener Orientierung im Elektronenstrahl-Zonenschmelzofen nach dem floating-zone-Verfahren hergestellt und nachfolgend auf einer Instron-Universalprüfmaschine im Zugversuch bei etwa 2,4%/Min. Dehnungsgeschwindigkeit verformt. Die erhaltenen Spannungs-Dehnungs-Diagramme zeigen eine starke Abhängigkeit des mechanischen Verhaltens der Einkristalle von der jeweiligen Kristallorientierung. Da die beobachteten Gleitspuren an der Oberfläche der Kristalle ausnahmslos als zu {110}-Ebenen gehörend indiziert werden konnten, wurde versucht, für die wirksamen {110}111-Gleitsysteme das kritische Schubspannungsgesetz anzuwenden. Auf Grund der auftretenden Diskrepanz zwischen den zu erwartenden und den tatsächlich gemessenen Spannungswerten bei der Proportionalitätsgrenze wird eine Interpretation des orientierungsabhängigen Abgleitverhaltens bei Wolfram gegeben.

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The crystallography of tungsten single crystal slip deformation in the tensile test

Strain-free tungsten single crystal tensile test specimens of various orientations were grown in an electron beam zone melting furnace using the floating zone method. The specimens were deformed under tension at a stretching rate of approx. 2.4%/min in an Instron Universal Testing Machine. Stress-strain curves show a strong dependence of the mechanical behaviour of the single crystals upon crystal orientation. As the observed slip traces on the surface of the crystals could only be indexed as belonging to {110} slip planes, the critical resolved shear stress law was applied to the active {110} 111 slip systems. In view of the inconsistencies of the measured proportional-limit stresses with the expected values for the different orientations an interpretation of the orientation-dependent slip mechanism for tungsten is proposed.

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Mit 9 Abbildungen     

Augmentation of the Generalised n×n Eigenvalue Equation to a Generalised (n+1)×(n+1) Eigenvalue Equation

Generalised n×n eigenvalue equation B| _i = _i S ^b | _i (i=1,...,n) where B and S ^b are n×n Hermitian matrices while S ^b is in addition positive definite is considered. This equation is augmented to a generalised (n+1)(n+1) eigenvalue equation H| _k = _k S| _k (k=1,...,n+1) where Hermitian matrices H and S represent matrices B and S ^b , respectively, augmented by one additional row and one additional column. It is shown how the eigenvalues _k and the eigenvectors | _k of the augmented eigenvalue equation can be expressed in terms of the eigenvalues _i and the eigenvectors | _i of the original eigenvalue equation. Operation count to obtain by this method all augmented eigenvalues and eigenvectors is of the order O(n ²). Unless matrices involved are of some special kind such as sparse matrices or alike, this operation count is one order of magnitude smaller than operation count required by other presently known methods. In many practical cases operation count to obtain a single selected eigenvalue and/or eigenvector by this method is of the order O(n). In the case of the generalised eigenvalue equation, all other methods usually require again O(n ³) operations, even if only a single eigenvalue and/or eigenvector is required. Thus in many cases of interest operation count to obtain a selected eigenvalue and/or eigenvector by this method is two orders of magnitude smaller than operation count required by other methods.     

Applications of the virtual charge model to the electronic structures and spectra of benzaldehyde and acetophenone

Summary The virtual charge model (Tapia model) in conjunction with the CNDO/S-CI approximation in the frame of SCF-MO theory was employed to study the effects of solvent on the electronic structures and spectra of benzaldehyde and acetophenone molecules. The CNDO/S calculations in presence of solvation indicate a satisfactory interpretation of the medium effects on the electronic structures and spectra of the molecules investigated. The prediction of our MO calculations by means of the Tapia model concerning the solvochromic shifts of n * and * transitions are in accord with the observed trends which indicate a blue shift for the n * band and a red shift for the * band upon a change of solvent from non-polar to polar solvents.

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Anwendung des Virtual Charge-Modells auf die Elektronenstrukturen und Spektren von Benzaldehyd und Acetophenon

Zusammenfassung Das Virtual-Charge-Modell (Tapia-Modell) im Zusammenhang mit der CNDO/S-CI-Näherung im Rahmen der SCF-MO-Theorie wurde zum Studium der Lösungsmitteleffekte auf die Elektronenstrukturen und Spektren von Benzaldehyd und Acetophenon herangezogen. Die CNDO/S-Rechnungen bei Anwesenheit von Solvens erlauben eine befriedigende Interpretation der Mediumeffekte auf Elektronenstrukturen und Spektren der untersuchten Verbindungen. Die aus MO-Rechnungen folgenden Voraussagen ergeben auf Basis des Tapia-Modells solvatochrome Verschiebungen für die n *- und *-Übergänge. Die vorausgesagten Effekte stehen im Einklang mit den experimentell beobachteten Trends: Blauverschiebung für die n *-Bande und Rotverschiebung für die *-Bande beim Wechsel von nichtpolarem zu polarem Lösungsmittel.

     

Arch?ometrische Untersuchungen von r?mischen Ziegeln und Wandplatten

Zusammenfassung Am Beispiel von Ziegel- und Wandplattenbruchstücken einer römischen Wüstung bei Schwarzenholz (Saarland) wird die Auswertung der Analysendaten und der Ergebnisse von Schnittbetrachtungen vorgestellt. Als geeignete Analysenverfahren erweisen sich die Röntgenfluorescenzanalyse und die Atomabsorptionsspektralanalyse. Mit Hilfe der Taxometrie gelingt eine Einteilung der Bruchstücke in die Gruppen Örtliches Material, Blickweiler und Gestempeltes Material. Die Untersuchungsergebnisse gestatten die Bestimmung des mengenmäßigen Anteils verschiedener Produktionen für einen Fundplatz und erlauben somit dem Archäologen Aussagen über wirtschaftliche Zusammenhänge.Für finanzielle Unterstützung danken wir der Stiftung Volkswagenwerk, Hannover.     

Fonctions autocohérentes et intégrales radiales pour les ions de la série du fer

The radial integrals 3d¦r ^k ¦3d, k=–3, –1, 2, 4 and 4p¦r ^k ¦3d, k= 1, 3 for first-row transition-metal ions have been computed from analytical self-consistent field wave functions. The expressions 4p¦r ^k ¦3d allow to compute the oscillator strengths of dipolar electric transitions for an trapped in a crystalline matrix iron group ion. Les intégrales 3d¦r ^k ¦3d, k=–3, –1, 2, 4 et 4p¦r ^k ¦3d, k=1, 3, relatives aux ions de la première série de transition, sont calculées à l'aide de fonctions radiales _3d et _4p , autocohérentes. Les expressions 4p¦r ^k ¦3d permettent d'évaluer les forces d'oscillateur de transitions dipolaires électriques relatives à un ion du groupe du fer engagé dans une matrice cristalline.     

An alternative way to analyze quasi-elastic light scattering data for broadly distributed samples

In Quasi-Elastic Light Scattering (QELS), an apparent average hydrodynamic radius can be calculated from the measuredz-average translational diffusion coefficient D _z by using the Stokes-Einstein equation: withk _B,T and being the Boltzmann constant, the absolute temperature and the solvent viscosity, respectively. It is known thatR _{h, app} is not the same as R _{h z} because , especially when a sample is broadly distributed. In order to obtain R _{h z} instead ofR _{h, app}, an alternative way to analyze QELS data is proposed: at first, we manipulate the measured correlation functionb ^1/2|g ⁽¹⁾(t)| into a new function ; and then, we can analyze this new function to obtain an apparent parameter D_app and an apparent distribution width . We have shown that no matter how broadly a sample is distributed, D_app can be easily reduced to R _{h z} , and is directly related to the distribution width. In this report, besides using a simulated time correlation function, we also used two measured correlation functions of a latex dispersion with a broad particle size distibution and a polystyrene standard with a broad molecular weight distribution to demonstrate this alternative way.     

Coordination of Heterovalent Iron Atoms in SrCo1 – yFeyO3 – zSolid Solutions

Mössbauer spectroscopy was used to study hyperfine interactions on ⁵⁷Fe nuclei of SrCo_{1 – y} Fe _y O_{3 – z} solid solutions (0.2 y 0.8). The ⁵⁷Fe spectra measured in the paramagnetic temperature range look like a superposition of two quadrupole doublets whose parameters correspond to high-spin Fe⁴⁺cations ( = 0.1 mm/s; = 0.4 mm/s) in the anion surrounding with coordination number 5 (tetragonal pyramid) and to Fe³⁺cations ( = 0.3 mm/s; = 0.4 mm/s) in the distorted octahedral environment. The relative number and pattern of distribution of heterovalent cations (Co⁴⁺, Co³⁺, Fe⁴⁺, and Fe³⁺) in the B-sublattice of perovskites were determined. The values of the electronic exchange constants in the solid solutions obtained through Mössbauer spectroscopy were compared with those obtained from thermodynamic calculations. The oxygen penetration in perovskites was found to depend on their composition and structure.