On the statistical independence of various column contributions to band broadening. Part 3: Independent treatment of longitudinal diffusion in the plate model

It is shown theorectically that the classical formula for calculating the theoretical plate number from squared first central moment, t , and second central moment, σ², according to n _theor = t /σ² is valid only when the capacity ratio, k approaches infinity. The general relation between the classical experimental HETP value, H = L/nm _theor, and the underlying true theoretical plate height, ΔL, is found to be when (σ′)² is the total column contribution to band broadening, L is the column length, D _m is the average diffusion coefficient of the sample component in the mobile phase, D _s is its value in the stationary phase, and u is the average linear velocity of the mobile phase. The mobile phase displacement, as well as the mass exchange process, is assumed to be continuous, but the application of the plate concept conditions leads to a mass balance equation that can be interpreted as belonging to a modified discontinuous plate model. The contributions 2D _m/u and k 2 D _s/u from longitudinal sample diffusion in the mobile and stationary phases, respectively, are consistent with the assumption that the processes are statistically independent, although the common solution technique of the differential equations does not take full account of this independence.     

Theoretical determination of optimum composition of the binary mobile phase for distribution of substances in thin-layer chromatography

The measure of the distribution of a mixture of substances in TLC with a binary mobile phase is expressed as ΔRM which represents the difference between the R_M values of substances i and j on use of the binary solvent 1 + 2 as the mobile phase. The possibility of determining its maximum value at an optimum composition of the binary mobile phase is demonstrated in this paper. This value can calculated from experimental and theoretical functions R_M1,2 = f(Φ₁) of substance i and j. More simply, ΔRM can be calculated theoretically from easily measurable adsorption parameters of excess adsorption isotherms and from chromatographic parameters obtained for pure solvents. The ΔRM value calculated theoretically can be utilized in a pilot technique for determination of the optimum composition of the mobile phase in gradient liquid chromatography.     

Influence of solvent strength in possible optimization of adsorption thin-layer chromatography

Considerations of TLC process optimization have been based on the thermodynamic theory of adsorption from multicomponent solvents using experimental and theoretical R_{M1, 2} = f (Φ₁) relationships. It was found that a relationship exists between the A_z parameter (log k where k is the partition coefficient of the substance chromatographed) of the above theory and pK_a values of substances as well as the solubility parameter δ of the mobile phase components. Analysis of the A_z values of substances shows that a slight variation therein is associated with lower selectivity of chromatographic separation.     

On the estimation of extra-column contributions to band broadening through measurements on an authentic chromatogram

The time constant, τ, is determined from the tail of an authentic HPLC peak through a plot of In U versus time, t, according to the relation expected at low recorder deflexions, U. The value obtained, τ = 2.43 s, is one order of magnitude larger than an ordinary recorder time constant, which is quite normal for LC detectors. It agrees with the value, τ = 2.44 s, needed theoretically to distort a Gaussian-shaped peak so as to obtain the experiment-ally found second moment, σ² = 11.13 s,² and the experimental difference between first moment t and peak retention time t_max, t – t_max = 0.78 s. The determination is therefore regarded as a demonstration of the variance addition rule where σ is the second moment of the non-distorted peak. The column contribution version is also considered. This equation was appliied earlier to an estimation of extra-column contributions to band broadening with the aid of the “abt” concept. An explicitly k-(capacity ratio)-dependent expression for the mass exchange contribution, σ is derived from Golay's equation for capillary columns, but the validity of the Golay equation is under discussion.     

The proton affinity and the structure of protonated species of methylsilane

An ab initio LCAO-MO-SCF calculation was made on the proton affinity (PA ) of methylsilane (CH₃SiH₃) by using STO -3G, MIDI -1, and MIDI -1* basis sets. Three types of protonated methylsilane are taken into account, and their geometrical parameters are optimized. The calculated PA of CH₃SiH₃ is 160.5 kcal/mol, which exceeds that of SiH₄ by 11.5 kcal/mol. The protonated species (I) which refers to Si—C bond protonation is shown to be most favorable, and to be a weak σ-complex between CH₄ and SiH. Other two species are also σ-complexes between H₂ molecule and SiH₃CH or CH₃SiH, and similar to CH, SiH, GeH, and C₂H.     

On the applicability of the “abt” concept

Kaiser's “abt” concept rests on the experimental establishment of a linear relation between band width at half height, b_0.5, and capacity ratio, k, according to His column specification quantity, h_real, is dependent on the square of the slope a, obtained from a linear regression analysis based on this relation. It is shown in the present paper that an improvement of the experimental conditions leading to a lower extra-column contribution to band broadening, b, introduces a tendency towards a negative curvature in the plot at low k values. The mean slope increases, and an uncritical linear regression would yield an h_real-value which is higher than before and which would be in the opposite direction to the requirements of a reliable column specification. Generally the linear regression analysis has to be moved to higher k regions in cases of curvature, especially as it is also shown that h_real is an estimation of the traditional HETP value, H∞, that would be obtained when k approaches infinity. This theoretically expected relation is a strong motivation for the use of h_real as a column specification, since the b_0.5-value associated with H∞ is expected to be practically independent of b.     

Über geordnete Perowskite mit Kationenfehlstellen. XI. Verbindungen vom Typ ABB□1/4WVIO6 ≙ ABIIB□WO24 mit AII,BII = Ba,Sr

On Ordered Perovskites with Cationic Vacancies. XI. Compounds of Type A B B □_1/4W^VIO₆ ? A B^IIB □W O₂₄ with A^II, B^II = Ba, Sr Depending on the ionic radii of the two and three valent cations in the perovskites of type ABB □_1/4W^VIO₆ ?; AB^IIB □WO₂₄ order disorder phenomena are present. The results of the x-ray and vibrational spectroscopic investigations as well as the diffuse reflectance spectra and the visible photoluminescence are reported.     

Schwingungsspektren und Kraftkonstanten der Übergangsreihe O2PF—S2PF— S2P(CH3)

Vibration spectra and force constants of the series O₂PF — S₂PF — S₂P(CH₃). The vibrational spectra of OSPF, S₂PF, S₂PF(CH₃) and S₂P(CN) are reported and discussed with O₂PF and S₂P(CH₃). On the basis of a simplified valence-force-field the force constants are calculated and the bonding relations are discussed. In the ions, f PF is lower than in corresponding molecules. The ionic charge is distributed over nearly all atoms of the ions.     

Über geordnete Perowskite mit Kationenfehlstellen. X. Verbindungen vom Typ ABB□1/4MVIO6 ≙ ABIIB□MO24 mit AII,BII = Ba,Sr, Ca und MVI = U,W

On Ordered Perovskites with Cationic Vacancies. X. Compounds of Type A B B □_1/4M^VIO₆ ? A B^IIB □M O₂₄ with A^II, B^II = Ba, Sr, Ca and M^VI = U, W Perovskites of type Ba₈B^IIB₂^III□UO₂₄ show polymorphic phase transformations of order disorder type. An 1:1 ordered orthorhombic HT form is transformed into a higher ordered LT modification with a fourfold cell content (four formula units Ba₈B^IIB□U₄O₂₄), compared to cubic 1:1 ordered perovskites A₂BMO₆. In the series Ba₈BaB□W₄O₂₄ and Sr₈SrB□W₄O₂₄ different ordering phenomena are observed. In comparison with 1:1 ordered cubic perovskites A₂BMO₆, the cell contains eight formula units AB^IIB□W₄O₂₄. The higher ordered cells with U^VI and W^VI are face centered, which has its origin in an ordering of cationic vacancies.     

19F-NMR-spektroskopischer Nachweis und statistische Untersuchung zur Bildung der gemischten Clusteranionen [(Mo6ICl)F]2−, n = 0–7, und Darstellung von (TBA)2[(Mo6I)F]

¹⁹F NMR Spectroscopic Evidence and Calculation of the Statistical Formation of Mixed Cluster Anions [(Mo₆I Cl )F ]^2?, n = 0–7, and Preparation of (TBA)₂[(Mo₆I )F ] The octa-μ₃-iodo-hexafluoro-hexamolybdate(2?)ion [(Mo₆I)F]^2? is prepared for the first time. The system of the 21 innersphere mixed clusters (Mo₆ICl)⁴⁺, n = 0–7 is formed by exchange of innersphere bound Clⁱ against outersphere bound I^a on tempering solid [(Mo₆Cl)I] at 400°C. Prolonged tempering leads to increasing average n values of the mixture, which is converted into the tetrabutylammonium salt (TBA)₂[(Mo₆ICl)F]. Using increments of chemical shifts and integral peak intensities the 54 ¹⁹F-nmr signals of the 21 species (compound n = 8 is absent) are assigned and confirmed by the 2 D-¹⁹F/¹⁹F-COSY spectrum. From the measured intensities the distribution of the different compounds is determined and proves significant deviation from statistical occupation, revealing the preference of isomers with iodine atoms occupying edges of the innersphere cube and discrimination of those sharing diagonals of the faces. Moreover all compounds with n = 3 and 4 are present overaverage in comparison to the others.     

Magnesium chloride supported high mileage catalysts for olefin polymerization. XII. Polymerization of ethylene

Polymerizations of ethylene by the MgCl₂/ethylbenzoate/p-cresol/AlEt₃ TiCl₄-AlEt₃/methyl-p-toluate (CW-catalyst) have been studied. The initially formed active site concentration, [Ti] has a maximum value of 50% of total titanium at 50°C and lower values at other temperatures. The Ti decays rapidly to Ti sites with conc. ca. 10 mol %/mol Ti. The rate constants for four chain transfer processes have been obtained at 50°C: for transfer with AlEt₃, k = 2.1 × 10^?4 s^?1 and k = 4.8 × 10^?4 s^?1; for transfer with monomer, k = 3.6 × 10^?3 (M s)^?1 and K = 8.3 × 10^?3 (M s)^?1; for β-hydride transfer, k = 7.2 × 10^?4 s^?1 and k = 4.9 × 10^?4 s^?1; and transfer with hydrogen, k = 4.0 × 10^?3 torr^1/2 s^? and k = 5.1 × 10^?3 torr^1/2 s^?1. The rate constants for the termination assisted by hydrogen is k = 1.7 (M^1/2 torr^1/2 S)^?1. If monomer is assisting termination as was observed for propylene polymerization, then k = 7.8 (M^3/2 s)^?1. Values of all the rate constants can be higher or lower at other temperatures. Detailed comparisons were made with the results of propylene polymerizations. There are more than four times as many Ti active sites for ethylene polymerization than there are for stereospecific polymerization of propylene; the difference is more than a factor of two for the Ti sites. Certain rate constants are nearly the same for both monomers while others are markedly different. Some of the differences can be explained by stereoelectronic effects.     

The role of d orbitals in tetrahedral hybrid orbitals of oxy-ions

The hybrid orbitals of tetrahedral oxy-ions containing some d character have been calculated by maximum overlap method. The d characters of hybrid orbitals increase in the order of SiO, PO, SO, ClO, and decrease in order of GeO, AsO, SeO, BrO. The bond strengths are also obtained for these ions. The hybrid Orbital of VO, CrO, and MnO are of the type d³s as the result of calculation.     

Low Valence States of Metal Chelates. V. Tris(1,10-phenanthroline)cobalt(II) and bis(2,9-dimethyl-1,10-phenanthroline)cobalt(II) perchlorates

D. C. polarography and cyclic voltammetry were used for investigating the reduction processes of the tris(1,10-phenanthroline)cobalt(II) and bis(2,9-dimethyl-1, 10-phenanthroline)-cobalt(II) perchlorates in 0.1 M solutions of tetraethylammonium perchlorate in acetonitrile. The first complex gave a four-step reduction wave; the first two steps were found to be diffusion controlled and reversible reductions from Co(phen)⁺ to Co(phen)₃⁺ to Co(phen) to Co(phen;) occured. The second complex gave a six-step reduction wave; the first three steps were found to be diffusion controlled and were to be considered as successive reversible reductions from Co(2, 9dm-phen)⁺ to Co(2, 9dmphen), from Co(2, 9dmphen) to Co(2, 9dmphen)₂ and from Co(2, 9dmphen)₂ to Co(2, 9dmphen).     

Structure and Bonding in Cyclic Sulfur-Nitrogen Compounds—Molecular Orbital Considerations

The molecular structures of monocyclic sulfur-nitrogen ring systems, such as S₂N₂, S₃N, S₄N and S₅N, can be considered as examples of electron rich (4n + 2)π systems. The structures of S₄N₄, S₄N, P₄S₄, As₄S₄ and the bicyclic structures S₄N, S₄N as well as S₅N₆ can be rationalized on the basis of a planar tetrasulfur tetranitride with 12π electrons.     

Ab initio MO calculations on the stability of the CF,PF, SF,and MoF ions with the F1s core hole

For the CF, PF, SF, and MoF ions appearing after the F1s photoionization, the possibility of dissociation has been shown by the ab initio MO LCAO method within the Z + 1 core equivalent model. According to the calculations, the decay channel AF → AF + F(1s¹2p⁶) is energetically open for the ions. So the interpretation of the gas-phase emission FKα spectra, in which the bands are assigned to the discrete transition energies, can be unacceptable for these ions. The conditions and signs of such failure are discussed.     

Extended basis CNDO calculations of linear and nonlinear electric susceptibilities of some molecular dianions and carbonions using coupled Hartree–Fock perturbation theory

The results of calculating the average polarizabilities, first and second hyperpolarizabilities and molar Kerr constants of C₅H, C₆H, 2-C₁₀H, 2-C₁₄H, C₈H and C₈H are reported. The main elements of our computational scheme are McWeeny's coupled Hartree–Fock perturbation theory and an extended basis CNDO wave function. It is shown that the studied anions have nonlinearities within the same order of magnitude as their respective uncharged parent molecules. The Kerr constants of these anions are analyzed and the contribution of the various terms is appraised.     

Zur Kristallstruktur von OMF (M = Sb,Ru, Pt,Au)

On the Crystal Structure of O MF (M = Sb, Ru, Pt, Au) OMF (M = Sb, Ru, Pt, Au) were obtained again, but for the first time investigated by X-ray methods. Colourless OSbF and the rubyred compounds ORuF and OPtF crystallize isostructural in space group Ia3 -T_h⁷ (Nr. 206) with a = 1016(1) pm (Sb), a = 1002.6(9) pm (Ru) and a = 1003.6(9) pm (Pt), Z = 8. Yellow OAuF crystallizes trigonal-rhombohedric in space group R3 -D₃₂⁶ (Nr. 148) with a = 775.9(3) pm, c = 711.7(4) pm, Z = 3.     

63Cu-NMR.-Untersuchungen von Kupfer (I)-Tetrapyridin-und Kupfer (I)-Tetraacetonitrilsolvaten

⁶³Cu-NMR.-Spectra of Cu(CH₃CN)₄X (X = ClO, BF, PF) and Cu(C₅H₅N)₄X (X = ClO, BF) in solution are reported at different temperatures and concentrations. The influence of temperature on the linewidth and chemical shift indicates an equilibrium of Cu(CH₃CN) and Cu(C₅H₅N) with another complex of lower symmetry. The preferential solvation of Cu (I) by pyridin in a mixture acetonitrile/pyridine is clearly shown.     

Darstellung,Schwingungsspektrum und Kristallstruktur von (n‐Bu4N)2[(W6Cl)F] · 2 CH2Cl2 und 19F‐NMR‐spektroskopischer Nachweis der gemischten Clusteranionen [(W6Cl)FCl]2–, n = 1–6

Synthesis, Vibrational Spectra, and Crystal Structure of ( n ‐Bu₄N)₂[(W₆Cl )F ] · 2 CH₂Cl₂ and ¹⁹F NMR Spectroscopic Evidence of the Mixed Cluster Anions [(W₆Cl )F Cl ]^2–, n = 1–6 The reaction of (n‐Bu₄N)₂[(W₆Cl)Cl] with CF₃COOH in dichloromethane gives intermediately a mixture of the cluster anions [(W₆Cl)(CF₃COO)Cl]^2–, n = 1–6. By treatment with NH₄F the outer sphere coordinated trifluoracetato ligands are easily substituted and the components of the series [(W₆Cl)FCl], n = 1–6 are formed and characterized by their distinct ¹⁹F NMR chemical shifts. An X‐ray structure determination has been performed on a single crystal of (n‐Bu₄N)₂[(W₆Cl)F] · 2 CH₂Cl₂ (orthorhombic, space group Pbca, a = 15.628(4), b = 17.656(3), c = 20.687(4) Å, Z = 4). The low temperatur IR (60 K) and Raman (20 K) spectra are assigned by normal coordinate analysis based on the molecular parameters of the X‐ray determination. The valence force constants are f_d(WW) = 1.89, f_d(WF) = 2.43 and f_d(WCl) = 0.93 mdyn/Å.     

Oxidation of thallium(I) by hexacyanoferrate(III) in aqueous acetic acid

The hexacyanoferrate(III)-thallium(I) reaction in aqueous acetic acid containing large concentrations of hydrochloric acid is considerably accelerated both by hydrogen and chloride ions as well as increasing acetic acid in the medium. The experimental results obey the rate law (1) where β₁ to β₆ are the cumulative stability constants of the species TlCl, TlCl, TlCl, HFe(CN), H₂Fe(CN) and H₃Fe(CN)₆ respectively and k_a and k_b are the rate constants associated with the mono- and di-protonated oxidant species. The main active species are H₂Fe(CN) and TlCl.