Advantage of the universal equation over the linear equation for the calculation of retention parameters of homologous series in capillary chromatography

A procedure is suggested for preparation of reproducible and stable galss capillary Apiezon LH+KF columns for the determination of organic compounds containing different functional groups. The advantage of the universal equation over the linear equation for calculation of retention indices for any homologs, including the first members of the series, is shown using the following five homologous series as examples: fatty acid methyl esters, methyl ketones, secondary and tertiary aliphatic amines, and N-alkyl piperidines. The accuracy of the calculation enables the universal equation to be used in computer-assisted identification.     

Prediction of the retention indices of methyl pyridines and pyrazines in capillary gas chromatography based on the non-linear additivity of the sorption energy

Summary Methylbenzenes, pyridines and pyrazines were investigated on fused-silica and glass capillary columns coated with SE-30 and PEG-40M/KF liquid phases, at two temperatures, 80° and 110°C. The contribution of the methylene groups to the partial molar free sorption energy was determined for methylpyridines and pyrazines. Equations are proposed for the calculation of the retention indices of methyl pyridines and pyrazines. These equations are based on the ortho- and α-effects of the methyl groups. The predicted indices have been experimentally tested for six dimethyl- and trimethylpyridines, and four methylpyrazines. Good accuracy of the calculation permits to use this method for the identification of methylpyridines and pyrazines in complex mixtures. Enlarged text of the paper presented at the Eighth International Symposium on Capillary Chromatography, Riva del Garda, Italy, May 19–21, 1987.     

The system of universal retention indices and aspects of its application in gas chromatography

Summary The universal retention index has been developed on the basis of a critical analysis of the forms of chromatographic retention data presentation. Methods are presented for the determination of the universal retention index. The advantages of the universal retention index system in the evaluation of the selectivity and classification of stationary phases and in the determination of the composition of binary and polynary stationary phases are discussed. The thermodynamic aspect of the suggested system of chromatographic retention data presentation is also considered.     

Nonlinear variation of sorption parameters of n-alkane homologsl in temperature-programmed gas chromatography (tpgc) and new equation for calculation of retention indixces

It has been demonstated that the considaerable difference in temperature increments of sorption parameters of n-alkanes under isothermal conditions is the main reason for nonlinear dependence of sorption parameters on molecular mass of homolog in temperaturre programmed gas chromatography (TPGC). A new nonlinear 4th parameter equation has been given for calculation of the retention indices. Coefficients of the equation are calculated from n-alkanes. The equation allows extrapolation and interpolation calculations of retention indices under TPGC conditions with experimental precision. The results obtained; for fatty acidkl methyl esters demonstrate the advantage of ovr equation in comparison with van den Dool and Kratz's equation.     

Effect of competing binding modes on retention in chromatography and capillary electrophoresis. A theoretical consideration

A mathematical formalism has been developed to describe equilibrium in a system involving a single selector and a selectand molecule capable of binding to this selector by different modes. The generalization of this model to a multiselector system has also been considered. Applications of the developed equations in chromatography and CE are discussed.     

An equation for the calculation of retention indices in temperature-programmed gas chromatography with allowance for the nonlinear variation of the retention parameters ofn-alkanes

In view of the nonlinear variation of the temperature increments ofn-alkanes found previously, the accuracy of the calculations of the retention indices (I _pr) of substances in temperature-programmed capillary gas chromatography carried out in terms of six known equations was verified. A new four-parameter equation was proposed, and a general method for the calculation of its coefficients, suitable for all stationary phases, based on the adjusted retention times ofn-alkanes was suggested. The coefficients of the equation for 12 temperature variation programs were determined. Using the homologous series of methyl esters of fatty acids as an example, it was shown that the proposed equation ensures the minimum error of determination ofI _pr under various conditions. The equation also makes it possible to carry out interpolation and extrapolation calculations. The coefficients of the equation are found using the least-squares method based on data for any 4–5 referencen-alkanes. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 323–327, February, 1997.     

Temperature changes of sorption parameters of di-n-alkylketones and methylcyclohexanones in capillary gas chromatography

The gas chromatographic behavior of di-n-alkylketones and isomeric methylcyclohexanones at variable temperatures in the isothermal runs has been studied using three capillary columns coated with SE-30, OV-225, and PEG-40M/KF stationary phases. The retention indices and their temperature increments were determined, and the partial molar free energies of the compounds under study were calculated. A linear dependence of the values of the partial molar free energy of sorption on the homologue number in di-n-alkylketones is not observed for the first member on the nonpolar SE-30 phase and for the third member on the polar OV-225 and PEG-40M/KF phases. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 328–332, February, 1997.     

Revisiting the problem of correcting retention parameters for pressure and temperature in gas chromatography

Summary It has been shown [1, 2] that the compressibility correction factor equals the ratio of gas pressure at the column outlet to the average pressure in the column,j=p _o /p _c , and, therefore, by multiplying by this factor, all experimentally measured retention volumes and flow rates are converted from ambient pressure to the average pressure in the column. This makes retention volumes corrected in this way independent of pressure. In contrast, correcting retention times for gas compressibility has no physical meaning and terms such as “corrected retention time” and “net retention time” should not be used. Similarly, recalculating corrected retention volumes to a standard temperature of 273 K appears to provide a thermodynamically sound basis for comparison of data obtained at different temperatures. In reality, it distorts actual relationships and should not be used. Presented at: Balaton Symposium on High-Performance Separation Methods, Siófok, Hungary, September 3–5, 1997.     

糖类化合物亲水作用色谱保留行为评价

以糖类化合物为研究对象,系统评价了其在亲水模式下的色谱保留行为。分别考察了流动相、固定相和缓冲盐等对糖类化合物保留的影响,建立了糖类化合物在亲水模式下的保留方程。结果表明,糖类化合物随着流动相中乙腈比例的降低,保留时间减小;随着缓冲盐浓度的增加,保留时间增加;同时,糖类化合物的保留行为还会受到有机溶剂种类和固定相类型的影响;其保留行为可使用顶替吸附-液相相互作用模型定量描述。将该模型进一步用于实际样品中糖类化合物保留行为的预测,获得了较好的实验结果,预测保留时间与实测保留时间的相对误差小于0.3%。对糖类化合物亲水模式下的保留行为进行了系统的评价和定量描述,该研究结果将有助于糖类化合物亲水作用色谱分离方法的发展。     

On the linearity of the energy of activation in theEyring theory of kinetics

Summary A result obtained earlier implies that — if theEyring theory is correct — the energy of the transition state is less thanU+E _a whereU is the sum of the internal energies of the chemical reactants andE _a is the energy of activation. The energy of the transition state for the forward reaction is not equal to that of the inverse reaction; it varies linearly with the temperature.

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Zur Linearität der Aktivierungsenergie in derEyringschen Theorie

Zusammenfassung Aus einem früher erhaltenen Ergebnis folgt, daß — Richtigkeit derEyring-Theorie vorausgesetzt — die Energie des Übergangszustands geringer ist alsU+E _a (U: Summe der inneren Energien der Reaktanden;E _a: Aktivierungsenergie). Die Energie des Übergangszustands ist für Hin- und Rückreaktion unterschiedlich und hängt linear von der Temperatur ab.

     

Calculation of the thermondynamic values of alkylthiazoles from the Kovats retention indices on the basis of the non-linear additivity principle

Summary Retention indices and their energy equivalents were determined for ten alkylthiazoles analysed on the stationary phases Apiezon L, Triton X-305 and Carbowax 1000. It was found that the energy contributions of identical alkyl groups to the partial molar free energy of sorption of a molecule are not equivalent. Smaller energy contribututions are due to the α-position of alkyl groups with respect to the heteroatoms in the thiazole ring (α-effect). This effect was most pronounced for 2-alkylthiazoles. Higher sorption energies were found for dimethylthiazoles with two methylgroups in a vicinal position. The retention indices were predicted for ten other di- and tri-substituted methyl, ethyl and propyl thiazoles on the basis of the so-called α- and ortho-effects. The predicted values are in good agreement with the experimentally determined values. Dedicated to Prof. Dr. E. sz. Kováts (Ecole Polytechnique Fédérale de Lausanne) on the occasion of his sixtieth birthday.     

Molecular dynamics simulations of monoclinic calcium apatites: A universal equation of state

Molecular dynamics simulations of monoclinic (P2₁/b) hydroxy- and chlorapatite were undertaken in the range 498 K < T < 1298 K, and for pressures up to 7.5 GPa. The all-atom Born–Huggins–Mayer force field, that had been previously used to successfully describe the room temperature isotherms of both compounds, was also used in this work. The isothermal sets of p–V data generated by simulation were each fitted to the three-parameter form of the isothermal Parsafar and Mason equation of state (EoS) with an accuracy better than 0.07%. Taking the temperature dependence of the coefficients into account, it was found that the MD data are satisfactorily reproduced by the universal EoS. The isothermal compressibility coefficient dependence with pressure can be described by a linear relation.     

Variation in the sorption energy of esters ofn-perfluoroalkanoic acids on chromatographic phases of different polarity

The contributions of methylene and difluoromethylene units of six homologous and six pseudohomologous series of esters ofn-perfluoroalkanoic acids to the differential molar free energy, enthalpy, and entropy of sorption on stationary phases of different polarities in glass capillary columns under isothermal conditions were calculated. The features observed characterize the peculiarities of the sorption of esters of polyfluorinated carboxylic acids on phases of different polarities and make it possible to estimate the enthalpy and entropy contributions to the energy of sorption of the esters, the effect of the temperature of the analysis and the length of the alkyl or polyfluoroalkyl chain on the retention parameters of the compound analyzed. The inversion of the retention order of trifluoroacetates and pentafluoropropionates in XE-60 nitrile-containing phase was found.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 12, pp. 2051–2055, December, 1993.     

Isoelectronic changes in energy of quark atoms and molecules via the Levy equation

Summary Z-transition state calculations based on the Levy equation suggest that the isoelectronic changes in energy of quark atoms,Q, (ordinary atoms with extra nuclear charge in units of ±1/3 and/or ±2/3) can be expressed quantitatively in terms of the electrostatic potential at the nucleus of an isoelectronic ordinary atom. Numerical tests within the local density functional theory are presented for the quark atoms of Li-F. Theab initio MO (molecular orbital) calculations using STO-5G basis on the C₂ molecule and its quark derivatives lead to similar conclusions.     

Water sorption in poly(zwitterions) of the ammonioalkoxydicyanoethenolate type

Water sorption by amorphous (meth)acrylic poly(zwitterions)-bearing quaternary ammonioalkoxydicyanoethenolate side groups , dipole moment μ(D) = 25.9 and 30.8 for p = 2 and 3, respectively was studied at 23°C over a broad range of water activity a (0.14–0.98). Water diffusion is nearly Fickian (D_s = 5.9 10^?7 cm².s^?1 for a = 0.63) and the sorption isotherms may be quantitatively analyzed according to the Guggenheim-Anderson-De Boer equation for a multilayer process characterized by a number of site-bound water molecules per monomeric unit, n_m ? 0.7. The Flory χ interaction parameter is a strongly increasing function of the water content in the glassy hydrated systems and it always remains higher than 0.75. Clustering of water molecules (Zimm-Lundberg theory) is never observed. Differential scanning calorimetry allows to quantify nonfreezable bound water (type I) of strong plasticization efficiency, n(I) = 2.8 mol. of water per monomeric unit, and it points out the quasisimultaneous emergence of low amounts of freezable bound water (type II) crystallizing at ?40°C and melting at ?1°C and of bulkfree water (type III, n(II)/n(III) ? 0.1). All these typical features distinguish these rather hydrophobic poly(zwitterions) from their hydrophilic homologues of the quaternary ammoniopropanesulfonate type . © 1995 John Wiley & Sons, Inc.     

A detailed study of the viscoelastic nature of vapor sorption and transport in a cellulosic polymer. I. Origin and physical implications of deviations from Fickian sorption kinetics

Various aspects of the kinetics of sorption of acetone vapor by cellulose acetate films at 30°C have been studied in detail, the principal aim being to understand more thoroughly the physical nature and causes of non-Fickian behavior in this and other similar polymer-micromolecular penetrant systems. Particular attention was given to the changes in sorption (including absorption, desorption, and resorption) kinetics caused by (a) systematic variation of the vapor pressure of acetone in different ways and (b) changes in membrane thickness. It has been shown that both viscous volume swelling relaxation and longitudinal differential swelling stress effects must be invoked, in order to explain fully the observed behavior. Detailed analysis of two-stage sorption kinetics indicated (1) reasonable agreement between estimates of the diffusion coefficient reported by different authors, as long as a consistent analysis of the first stage is used, although the significance of the values given is open to some doubt, because the said first stage is found not to be free of non-Fickian features; and (2) reasonable conformity of the second stage to a first-order volume relaxation process (except a long times), with a relaxation frequency strongly dependent on the width of the concentration interval covered by the sorption experiment (and hence on the applied “osmotic stress”). The close similarity of second-stage sorption to nonlinear viscoelastic creep behavior, previously found in the cellulose-water system was confirmed and is taken further here, by demonstrating semiquantitative agreement between the corresponding “elastic swelling” and mechanical bulk moduli. ©1995 John Wiley & Sons, Inc.     

Gas chromatographic determination of the free energy of sorption of methylene units ofN-alkylsubstituted six-membered cyclic amines

The free energy of sorption of methylene units, G(CH₂), for the homologous series ofN-alkylsubstituted morpholines, thiomorpholines, piperidines and 2-methyl-, 3-methyl-, 4-methyl- and 2,6-dimethylpiperidines was determined. It was shown that the dependence of these values on the number of CH₂ units in the carbon chain is not linear. Universal equations for calculating the values of the energy contribution depending on the number of CH₂ units in the carbon chain were obtained. Abnormally high values of free energy of sorption of the first CH₂ unit were found in all series studied and reasons for the anomaly are discussed.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 437–439, March, 1994.This work was made possible by the financial support of Russian Foundation for Basic Research, project No. 93-03-4969,