Reciprocally Unambiguous Conformity Between GC Retention Indices and Boiling Points within Two- and Multidimensional Taxonomic Groups of Organic Compounds

It was shown that reciprocally unambiguous conformity between GC retention indices (at least for the commonly used standard nonpolar polydimethylsiloxane liquid phases) and boiling points of organic compounds is typical not only within one-dimensional taxonomic groups (homologous series and/or groups of congeners), but also within two- and multidimensional taxonomic groups (with simultaneous variations of some structural fragments). In all cases, this conformity is described by three-parameter non-linear equations log RI = a log T_b + b (n₁ + Σ k_i n_i) + c, where n₁ is the serial number of homologue within corresponding series and n_i is the number of other structural fragments in the molecules. The coefficients k_i in this equation reflect the relative alterations of molecular polarizabilities and may be estimated as ratios of refractions k_i = R_D(X)/R_D(CH₂), where X are variable structural fragments within a group of congeners, R_D(CH₂) = 4.647 cm³mol⁻¹. The approach under discussion permits precalculation of the retention indices of any organic compounds with known boiling points. The precision of proposed method of RI precalculation is comparable with the contemporary level of interlaboratory reproducibility of experimental RI determination with standard nonpolar liquid phases (5–10 i.u.).     

Generic hypersurface singularities

The problem considered here can be viewed as the analogue in higher dimensions of the one variable polynomial interpolation of Lagrange and Newton. Let x₁,...,x _r be closed points in general position in projective spacePn, then the linear subspaceV ofH ⁰ (⨑ⁿ,O(d)) (the space of homogeneous polynomials of degreed on ⨑ⁿ) formed by those polynomials which are singular at eachx _i, is given by r(n + 1) linear equations in the coefficients, expressing the fact that the polynomial vanishes with its first derivatives at x₁,...,x _r. As such, the “expected” value for the dimension ofV is max(0,h ⁰(O(d))−r(n+1)). We prove thatV has the “expected” dimension for d≥5 (theorem A). This theorem was first proven in [A] using a very complicated induction with many initial cases. Here we give a greatly simplified proof using techniques developed by the authors while treating the corresponding problem in lower degrees.     

Mass transfer in the gas phase during top-blowing with plasma jets

Deoxidation of copper melts by hydrogen has been investigated experimentally by top-blowing with argon-hydrogen plasma jets. The course of the deoxidation process has been described mathematically using kinetic laws. The overall divided course of the process can be examined in live partial steps, which are hydrogen transport within the gas phase, hydrogen transport within the melt, oxygen transport within the melt, reaction between hydrogen and oxygen, and H₂O transport within the gas phase. Based on these five elementary processes, an equation for the velocity of deoxidation has been derived. The values of the rate of deoxidation resulting from this equation, in combination with the mass-transter coefficients valid for this process, have been compared to the experimental data. The results of this study verify those of former investigations on vaporization of elements out of copper melts. The mass-transfer coefficients are the same, when the local activity differences are used as the driving force for mass transport in a system. This means that the surface-renewal theory is valid, when mass-transfer coefficients are defined in this way. This is the case, at least, when metallic melts are subjected to top-blowing by plasma jets.Nomenclature a activity (a _i =x _{i i} ) - A _c (m²) effective mass-transfer area - D(m) characteristic length, such as diameter - D _r(m²/s) diffusion coefficient - H(Cu) oxygen dissolved in copper - k _g (mol/m²s) mass-transfer coefficient in the gas phase [k _g (i) mass-transfer coefficient for speciesi] - k _N (mol/m²s) mass-transfer coefficient in the melt phase - K _i = (x _i /y _i )_eq equilibrium coefficient (distribution coefficient) - n _N (mol) mole number of the melt phase - n _G (mol) mole number of the gas phase - n _i (mol/s) mole flow of speciesi - O(Cu) oxygen dissolved in copper - p(N) momentum flow - t(s) time - T (°C or K) temperature;T _G : in the gas,T _s : in the melt,T ^f : at the phase interface - x _i (mol/mol) concentration in the melt - y _i , (mol/mol) concentration in the gas phase - activity coefficient     

Löwdin correlation energy density of the inhomogeneous electron liquid in some closed-shell molecules at equilibrium geometry

Using existing theoretical studies, we point out that the dominant variable in determining Löwdin correlation energies per electron E _c /N of isoelectronic series of molecules at equilibrium is the total number of electrons. This turns out to be E _c /N = ?0.033 ± 0.003 a.u. for CH₄, NH₃, H₂O and HF (N = 10), and E _c /N = ?0.039 ± 0.007 for some 20 Si-containing molecules in the series SiX _n Y _m . Following earlier work of March and Wind on atoms, some proposals are then made as to a possible explanation of such behaviour. A test is proposed, via low-order Møller–Plesset perturbation theory, as to whether the Löwdin correlation energy density ε _c (r) is, albeit approximately, a local functional ε _c (ρ) of the ground-state density for molecules at equilibrium. Such an LDA assumption would imply that ε _c (ρ) is quantitatively linear in ρ(r), for closed-shell molecules at equilibrium, at least for the light atomic components treated here. This, in turn implies that the dominant effect of the Löwdin correlation energy for closed-shell molecules at equilibrium is merely to shift the chemical potential.     

Heterotri- and -tetrametallic alkoxides of chromium(III) containing aluminium(III), gallium(III) and niobium(V)

CrCl₃ · 3THF reacts with two equivalents of potassium alkoxometallates K{M(OPr ⁱ ) _x } [M = Al(A), Ga(B), x = 4; M = Nb(C), x = 6] to give heterobimetallic chloride isopropoxides [Cr{M(OPr ⁱ ) _x }₂Cl(THF)] [M = Al(A – 1), Ga(B – 1), and Nb(C – 1)], in which the replacement of the chloride with an appropriate alkoxometallate (tetraisopropoxoaluminate, tetraisopropoxogallate, or hexaisopropoxoniobate) results in the formation of novel heterotrimetallic derivatives. The 'single pot synthesis of an heterotetrametallic isopropoxide [Cr{Nb(OPr ⁱ )₆}{Al(OPr ⁱ )₄}{Ga(OPr ⁱ )₄}] (7) has been carried out by the sequential addition of (A), (B), and (C) to a benzene suspension of CrCl₃ · 3THF. Alcoholysis of [Cr{Al(OPr ⁱ )₄}₂{Nb(OPr ⁱ )₆}] (1) and [Cr{Al(OPr ⁱ )₄}₂{Ga(OPr ⁱ )₄}] (5) with t-BuOH has also been studied and the derivatives characterized by elemental analyses, molecular weight determinations, spectroscopic [Electronic, i.r., ²⁷Al-n.m.r.] and magnetic susceptibility studies.     

On the formulation of spin-free quantum chemistry

A set of spin-free functions ?_i(r),i = 1 …? f, is obtained which form the basis of spin-free quantum chemistry. The ?_i(r) show a one-to-one correspondence to antisymmetric space-spin functions Ψ_i(r, σ) with spin functions constructed according to Löwdin's projector operator method.     

The Pyrolysis of Isonitrile Substituted Derivatives of Triosmium Dodecacarbonyl

The pyrolysis of the isonitrile substituted complexes Os₃(CO)_12?x(CNR)x (R = Bu^t, x = 1,2) in refluxing octane has been studied. From these pyrolysis reactions and from the reaction of Os₃(CO)₁₂ with Bu^tNC in refluxing octane the series of hexanuclear complexes Os₆(CO)_18?x(CNBu^t)_x (x = 1?5) has been isolated. The pyrolysis of Os₃(CO)₁₁(CNBuⁿ) also leads to the formation of higher nuclearity clusters and evidence is presented that one product of the reaction is Os₆(CO)₁₇(CNBuⁿ)₂. Possible structures for these isonitrile substituted hexanuclear complexes are discussed in the light of the known structures of Os₆(CO)₁₆(CNBu^t)₂ and Os₆(CO)₁₈(CNC₆H₄Me)₂.     

Non-linear transformations of factors in the generalized standard addition method

Summary Experimental designs and non-linearly transformed factors (concentrations of analytes) have been applied in the Generalized Standard Addition Method (GSAM). The relationship betweenN measured analytical signals,R ⁽¹⁾,...,R su(n), and concentrations of standard additions, c1,..., cn, ofn analytes has been approximated by the following polynomial models:The regression coefficientsB in models (1) are calculated from thesimple formulae^{1, 3, 4}.Functionsf _i ^(l) (e.g. linear, parabolic, exponential, hyperbolic or logarithmic) are selected on the basis of the experimentally determined relationshipsR ^(l) (l=1, ...,N) vs.c _i (i=1, ...,n). An example concerns the flame emission photometric determination of Na and Ca. 2² factorial and uncomplete second-degree modelsR ^(l) have been applied expressed by linear and hyperbolic functionsf _i ^(l). The results of determination of Na by GSAM reveal significant improvement of accuracy as compared with the conventional single-component standard addition method.

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Nicht-lineare Transformation von Faktoren bei der verallgemeinerten Standardadditio nsmethode

Zusammenfassung Statistische Versuchsplanung und nicht-linear transformierte Faktoren (Konzentrationen der zu bestimmenden Substanzen) wurden für die verallgemeinerte Standardadditionsmethode eingesetzt. Die Bezeichnung zwischen N gemessenen analytischen Signalen,R ⁽¹⁾,...,R ^(N) und den Konzentrationen der Standardadditionszugaben C_i,..., C ^N , vonn zu bestimmenden Substanzen wurde durch Polynome des folgenden Typs approximiert: (wobei ). Die Funktionenf _i ^(l) (z. B. lineare, parabolische, exponentielle, hyperbolische oder logarithmische) werden auf Basis experimentell bestimmter Abhängigkeiten festgelegtR ^(l) (l=1,...,N) gegen C _i (l=1,...,N). Als Beispiel wird die Flammenemissionsbestimmung von Na und Ca herangezogen. Dabei wurden ein 2² faktorieller Versuchsplan und ein unvollständiges Polynom der Ordnung 2R ^(l) mit linearen und hyperbolischen Funktionenf _i ^(l) angesetzt. Die Resultate der Na-Be-stimmung zeigen durch die Verwendung der verallgemeinerten Standard-addition signifikante Verbesserungen der Resultate gegenüber der Einkomponenten-Standardaddition.

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The author thanks Doc. dr. hab. A. Parczewski for his helpful discussion and editorial comments during the preparation of this paper.     

Spinodal decomposition and phase separation kinetics in nanoclay–biopolymer solutions

Intensity of light, I(q,t), scattered from homogeneous aqueous solutions, of nanoclay (Laponite) and protein (gelatin‐A), was studied to monitor the temporal and spatial evolution of the solution into a phase‐separated nanoclay–protein‐rich dense phase, when the sample temperature was quenched below spinodal temperature, T_s (=311 ± 3 K). The zeta potential data revealed that the dense phase comprised charge‐neutralized intermolecular complexes of nanoclay and protein chains of low surface charge. The early stage, t < 500 s, of phase separation could be described adequately through Cahn‐Hilliard theory of spinodal decomposition where the intensity grows exponentially, I(q, t) = I₀ exp.(2R(q)t). The wave vector, q dependence of the growth parameter, R(q) exhibited a maxima independent of time. Corresponding correlation length, 1/q_c = ξ_c was found to be ≈75 ± 5 nm independent of quench depth. In the intermediate regime, anomalous growth described by I(q, t) ～ t^α with α = 0.1 ± 0.02 independent of q was observed. Rheological studies established that there was a propensity of network structures inside the dense phase. Isochronal temperature sweep studies of the dense phase determined the melting temperature, T_m = 312 ± 4 K, which was comparable with the spinodal temperature. The stress‐diffusion coupling prevailing in the dense phase when analyzed in the Doi‐Onuki model yielded a viscoelastic correlation length, ξ_v determined from low‐frequency storage modulus, G ′₀ ≈ k_B T/ξ, which was ξ_v ≈ 35 ± 3 nm indicating 2ξ_v ≈ ξ_c. It is concluded that the early stage of phase separation in this system was sufficiently described by linear Cahn‐Hilliard theory, but the same was not true in the intermediate stage. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 555–565, 2010     

On the validity of the Avrami theorem in the case of decelerating growth

It is argued that the use of the Avrami theorem, S(t) = 1−e^−S_x(t), is in principle not allowed when applied to overlapping diffusion zones or, more generally, in all cases where the phantom nuclei overtake the front of their parent nuclei. Via computer simulations the overtake effect is shown to exist and is found to be surprisingly small. The use of a modified Avrami equation, S(t) = FS_x(t)·[1 −e^−S_x(t)], is suggested for such cases and the function F[S_x(t)] pertaining to diffusion-controlled growth is reported.     

Identification of unknown diffusion coefficient in pure diffusive linear model of chronoamperometry. I. The theory

Coefficient identification problem for diffusion equation u _t (x, t) = (D(x)u _x (x, t)) _x arising in chronoamperometry is studied. The adjoint problem approach is developed for the case when the output measured data is given in the form of left/right flux. Analytical formulas for determination of the values D(0), D(L) at the endpoints x = 0; L, of the unknown coefficient D(x), via the solution v(x, t) of the constant coefficient equation v _t (x, t) = D v _xx (x, t) is obtained. The integral identity relating solutions of the forward and corresponding adjoint problems is derived. This integral identity permits one to prove the monotonicity and invertibility of input-output map, as well as formulate the gradient of the cost functional via the solutions of the direct and adjoint problems.     

Trans-methyl-azido-bis(triisopropylphosphin)platin(II), [PtN3(CH3)(PiPr3)2]

Trans-methyl-azido-bis(triisopropylphosphine)platinum(II), [PtN₃(CH₃)(PⁱPr₃)₂] [PtN₃(CH₃)(PⁱPr₃)₂] has been prepared by reductive elimination of ethane from [Pt(CH₃)₃N₃]₄ in the presence of triisopropylphosphine at 80 °C. The complex is characterized by IR and NMR spectroscopy and by crystal structure determination, as well as by ab initio calculations. [PtN₃(CH₃)(PⁱPr₃)₂], which is in trans-configuration here, crystallizes in the monoclinic space group P2₁, Z = 2, and with the lattice dimensions a = 806.9(1), b = 1384.3(1), c = 1093.8(1) pm, β = 94.107(10)°.     

Co(II)-Mediated and microwave assisted coupling between 2,6-diaminopyridine and nitriles. A new synthetic route to N-(6-aminopyridin-2-yl)carboximidamides

The Chinese-lantern-type Co₂(O₂CBu^t)₄{2,6-(NH₂)₂C₅H₃ N}₂ complex reacts with RCN (R = Me or Prⁿ) under microwave irradiation (MWI) to give the mononuclear amidine complexes Co(O₂CBu^t)₂{H₂N(C₅H₃ N)NHC(R)=NH} (R = Me (4a) or Prⁿ (4c)). Under microwave irradiation, the addition of 2,6-diaminopyridine to acetonitrile in the presence of the pivalate complexes Co₂(μ₂-OH₂)(O₂CBu^t)₄(HO₂CBu^t)₄ (1) or [Co(OH)_n(O₂CBu^t)_2−n ]_x (2) afforded complex 4a in higher yield compared to the corresponding reaction performed earlier without MWI. The use of MWI makes it possible to perform analogous reactions with nitriles RCN (R = Et, Prⁿ, or Ph) giving rise to complexes 4b—d, respectively. Compounds 4a—d were characterized by elemental analysis and IR spectroscopy. The structure of complex 4c was established by X-ray diffraction. Amidines H₂N(C₅H₃N)NHC(R)=NH, which formed in the coordination sphere of cobalt(II), were isolated in the free state from methanolic solutions of complexes 4a—d under the action of Na₂S and were characterized by electrospray mass spectrometry and ¹H and ¹³C{¹H} NMR spectroscopy. The reactions of 2-aminopyridine with both complexes 1 and 2 in acetonitrile under microwave irradiation produced the Co(O₂CBu^t)₂(H₂NC₅H₄N)₂ complex. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 35–42, January, 2006.     

Operator technique for obtaining the recursion formulas of characteristic and matching polynomials as applied to polyhex graphs

A simple and efficient method, called an operator technique, for obtaining the recurrence relation of a given counting polynomial, e.g., characteristic P_G(x) or matching M_G(x) polynomial, for periodic networks is proposed. By using this technique the recurrence relations of the P_G(x) and M_G(x) polynomials for the linear zigzag-type and kinked polyacene graphs were obtained. For the lower members of these series of graphs, the coefficients of P_G(x) and M_G(x) polynomials are tabulated.     

Phase separation of off‐critical polymer blends of poly(styrene‐co‐maleic anhydride) and poly(methyl methacrylate). I. Kinetics of spinodal decomposition

The kinetics of phase separation via the spinodal decomposition of poly(styrene‐co‐maleic anhydride)/poly(methyl methacrylate) from a delay time period to late stages were investigated with a light scattering technique. The standard procedure for identifying four stages of spinodal decomposition, based on the characteristics of concentration fluctuations, was clearly introduced with the light scattering method. The spinodal limits were divided into four stages: the delay time, the early stage, the intermediate stage, and the late stage. The validity of the linearized theory was reviewed because it was used as an indicator of the limit of the early stage of spinodal decomposition, which divided the delay time period from the early stage and the early stage from the intermediate stage. The linearized theory fit the experimental results very well after the delay time. The scaled structure function of the melt‐mixed blend was analyzed. The universality of the scale structure function, F(x) = S(q,t)q_m³(t) (where S is the structure function, x is equal to q/q_m, q is the scattering wave vector, q_m is the maximum wave vector, and t is the time in seconds), indicated the late stage of phase separation and divided the late stage from the intermediate stage. The simple normalized scaling function profile for the cluster region proposed by Furukawa described the experimental data very well, whereas the profile for deep quenching, which was recently suggested, showed some discrepancies. As a result of the phase separation, the processing of this blend may be able to be developed to provide the most suitable morphology. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 871–885, 2004     

Conformation of comb‐like liquid crystal polymers in isotropic solution probed by small‐angle neutron scattering

The conformational characteristics of a comb‐like side‐chain liquid crystal polysiloxane (SCLCP), dissolved in deuterated chloroform, were evaluated by small‐angle neutron scattering (SANS) measurements over a wide q range. SANS studies were carried out on specimens with constant backbone length (DP = 198) and variable spacer length (n = 3, 5, and 11), and with constant spacer length (n = 5) and variable DP (45, 72, 127, and 198). The form factor P(q) at high q was analyzed using the wormlike chain model with finite cross‐sectional thickness (R_c) and taking into account the molecular weight polydispersity. The analysis generated values of persistence length in the range l_p = 28–32 Å, considerably larger than that of the unsubstituted polysiloxane chain (l_p = 5.8 Å), with contour lengths per monomer comparable to the fully‐extended polysiloxane backbone (l_m = 2.9 Å). This indicates a relatively rigid SCLCP chain due to the influence of the densely attached mesogenic groups. The SCLCP with n = 11 is more flexible (l_p = 28 Å) than those with n = 3 and n = 5 (l_p = 32 Å). The cross‐sectional thickness increases with spacer length, R_c ～ n^0.21±0.02 (3 ≤ n ≤ 11), and the contour length per monomer decreases with increasing spacer length, l_m ～ n^?0.35±0.01. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2412–2424, 2006     

Synthesis and Crystal Structure of the Azide K4[Re6Sei8(N3)a6]·4H2O; Luminescence,Redox, and DFT Investigations of the [Re6Sei8(N3)a6]4– Cluster Unit

The reaction of K₄[Re₆Seⁱ₈(OH)^a₆] · 8H₂O with NaN₃ in water results in the formation of [Re₆Seⁱ₈(N₃)^a]^4– units that crystallize with K⁺ and H₂O to form K₄[Re₆Seⁱ₈(N₃)^a₆] · 4H₂O [P2₁/c (N°14), a = 9.0595(3) Å, b = 13.2457(4) Å, c = 13.2040(5) Å, β = 94.472(1)°]. In the solid state, the unit is characterized by N₃ linear groups forming bond angles of roughly 120° with the Re₆ cluster. The positions of the ν_as and ν_sy bands as well as N–N–N deformation modes of the N₃ groups are discussed. Luminescence properties of the [Re₆Seⁱ₈(N₃)^a]^4– unit were measured in the solid state and in an acetonitrile solution. The redox potential of the [Re₆Seⁱ₈(N₃)^a]^4–/[Re₆Seⁱ₈(N₃)^a]^3– system was measured in acetonitrile. Experimental results were analyzed in the light of density functional theory calculations.     

Isolatable Organophosphorus(III)–Tellurium Heterocycles

A new structural arrangement Te₃(RP^III)₃ and the first crystal structures of organophosphorus(III)–tellurium heterocycles are presented. The heterocycles can be stabilized and structurally characterized by the appropriate choice of substituents in Te_m(P^IIIR)_n (m=1: n=2, R=OMes* (Mes*=supermesityl or 2,4,6‐tri‐tert‐butylphenyl); n=3, R=adamantyl (Ad); n=4, R=ferrocene (Fc); m=n=3: R=trityl (Trt), Mesor by the installation of a P^V₂N₂ anchor in RP^III[TeP^V(tBuN)(μ‐NtBu)]₂ (R=Ad, tBu).     

Synthesis and Structural Characterization of Divalent Transition Metal Alkynylamidinate Complexes

A series of new alkynylamidinate complexes of selected first and second row transition metals has been synthesized and fully characterized. Treatment of MCl₂ precursors (M=Mn, Fe, Co) with 2 equiv. of the lithium alkynylamidinates Li[c-C₃H₅−C≡C−C(NR′)₂] ⋅ THF (R′=ⁱPr (2), Cy (cyclohexyl) ( 2 )) afforded a series of binuclear complexes of the type M₂[c-C₃H₅−C≡C−C(NR)₂-κN:κN′]₂[c-C₃H₅−C≡C−C(NR)₂-κ²N,N′]₂ ( 3 : M=Mn, R=Cy; 4 a : M=Fe, R=ⁱPr; 4 b : M=Fe, R=Cy; 5 : M=Co, R=ⁱPr) with no significant metal-metal bonding. In marked contrast, a similar reaction of CrCl₂ with 2 equiv. of 1 afforded the homoleptic dinuclear chromium(II) complex Cr₂[c-C₃H₅−C≡C−C(NⁱPr)₂-κN:κN′]₄ ( 6 ) which supposedly comprises a Cr−Cr quadruple bond. Complex 6 could also be prepared in a more rational way and in better yield (61 %) by using dichromium(II) tetraacetate, Cr₂(OAc)₄, as starting material. Related reactions employing dimolybdenum(II) tetraacetate, Mo₂(OAc)₄, and 2 or 3 equiv. of 1 afforded the mixed-ligand paddle wheel-type complexes trans-Mo₂(OAc-κO:κO′)₂([c-C₃H₅−C≡C−C(NⁱPr)₂-κN:κN′]₂ ( 7 ) and Mo₂(OAc-κO:κO′)([c-C₃H₅−C≡C−C(NⁱPr)₂-κN:κN′]₃ ( 8 ). All title compounds were structurally characterized through single-crystal X-ray diffraction and spectroscopic techniques (NMR, IR, Raman).