Analysis of the equations for the temperature dependence of the retention index. II. Physico-chemical meaning of the parameters

A general expression for the meaning of various parameters from the retention index-temperature equations was found. This is a linear combination of two solute dependent factors consisting of differences of enthalpies and respective entropies of solution, between the solute and the reference inferior n-alkane. The particular coefficients for each parameter are stationary phase dependent factors. They were calculated from methylene contributions to the thermodynamic functions of solution in SE-30 and Carbowax-20M, revealing the influence of the used temperature range. A short review of structural influences on dI/dT is included.     

Modeling the combined effect of temperature and organic modifier content on reversed-phase chromatographic retention. Effectiveness of derived models in isocratic and isothermal mode retention prediction

Models considering simultaneously mobile phase organic content and column temperature were developed in this study by an extension of different equations describing the influence of temperature on solute retention. This extension was achieved by two methods: a semi-thermodynamic and a direct combination of equations expressed separately the dependence of the retention upon each of these factors. The above approaches gave a great number of expressions for the logarithm of the solute retention factor in terms of both temperature and organic content in the mobile phase, ln k(T,phi), determined from the dependence of the standard enthalpy of the retention process on T. From the final expressions of ln k(T,phi) we tested only those with the minimum number of adjustable parameters, i.e. those that correspond to a constant standard enthalpy of the retention process. For this test we examined the retention behaviour of a sample of alkylbenzenes in aqueous acetonitrile eluents. These compounds exhibit ln k versus 1/T plots with a very small curvature. We found that a new equation for ln k(T,phi) based on the adsorption model for retention performs better than all the others. The average percentage prediction error ranges from 0.7 to 1.4%.     

Activity coefficients for the system NaCl+Na2SO4+H2O at various temperatures. Application of Pitzer's equations

The mean activity coefficients of NaCl in the system NaCl+Na₂SO₄+H₂O at various compositions were determined in the temperature range 5–45°C from the emf of potentiometric cells. By processing the results using Pitzer's equations the mixing parameters describing the non-ideal behavior of electrolytes were calculated. The temperature coefficients of the mixing parameters were determined and found not to be significant. The mixing parameters and temperature coefficients calculated for the binary mixture can be used to describe the behavior of multicomponent systems containing NaCl and Na₂SO₄, and eventually sea water.     

反相液相色谱中同系物体系实验点与预测方程参数间的匹配研究

以波相色谱中溶质计量置换统一保留模型（SDM-R）的二参数、三参数和四参数方程为基础,研究了在预测同系物保留值时实验点与预测方程参数间的匹配关系。用两个实验点,分别以二、三和四参数方程对反相色谱中同系物保留值进行预测,发现预测值与实验值基本相符,但以二参数方程预测结果为最佳。又与其它保留方程的预测结果进行了比较,证实了上述结论。当实验点数增加到4～5个时,多参数方程预测同系物的准确度增加,且明显高于二参数方程。同时还讨论了方程中各参数与同系物碳数间的线性关系,发现二参数方程中的参数遵循同系物变化规律。     

Contribution to linearly programmed temperature gas chromatography. Further application of the Van den Dool-Kratz equation, and a new utilization of the Sadtler retention index library

Programmed temperature retention indices (PTRIs) calculated according to the equations of Van den Dool and Kratz, Golovnya and Uraletz, and Erdey et al. (also referred to as Antoine's integrated equation) are used in this work. Precalculation of isotherm retention indices from the results of a linearly programmed temperature GC is also presented. Deviations between experimental and calculated isothermal retention indices are below 2 retention index units. A relative "volatility" retention index is defined, as a function of the "volatilities"of the solute and the bracket reference n-alkanes. The comparison of the "volatility" retention indices with the PTRIs obtained with the other above equations shows absolute deviations of up to 4 retention index units. Based on an earlier "equivalent" temperature concept and on Tekler's proviso, a novel way for the utilization of Sadtler's retention index database, which takes advantage of the 3 data supplied by the library, is proposed.     

Lattice-fluid model for gas-liquid chromatography

Lattice-fluid models describe molecular ensembles in terms of the number of lattice sites occupied by molecular species (r-mers) and the interactions between neighboring molecules. The lattice-fluid model proposed by Sanchez and Lacombe (Macromolecules, 1978;11:1145-1156) was used to model specific retention volume data for a series of n-alkane solutes with n-alkane, polystyrene, and poly(dimethylsiloxane) stationary liquid phases. Theoretical equations were derived for the specific retention volume and also for the temperature dependence and limiting (high temperature) values for the specific retention volume. The model was used to predict retention volumes within 10% for the n-alkanes phases; 22% for polystyrene; and from 20 to 70% for PDMS using no adjustable parameters. The temperature derivative (enthalpy) could be calculated within 5% for all of the solutes in nine stationary liquid phases. The limiting value for the specific retention volume at high temperature (entropy controlled state) could be calculated within 10% for all of the systems. The limiting data also provided a new chromatographic method to measure the size parameter, r, for any chromatographic solute using characteristic and size parameters for the stationary phase only. The calculated size parameters of the solutes were consistent, i.e. independent of the stationary phase and agreed within experimental error with the size parameters previously reported from saturated vapor pressure, latent heat of vaporization or density data.     

Modified Dubinin-Radushkevich/Dubinin-Astakhov adsorption equations

The Dubinin-Radushkevich/Dubinin-Astakhov (DR/DA) adsorption equations have been modified with the aim to eliminate the thermodynamic incorrect behavior of these equations in the Henry region and in the vicinity of the equilibrium saturated vapor pressure. The expressions for heat and entropy of adsorption are obtained from the proposed modified DR/DA equations. These new equations, which do not include additional empirical parameters, have been evaluated on adsorption systems measured over a wide range of pressure and temperatures. The temperature dependence of the parameters has been analyzed.     

Empirical correlation equations describing retention data of hydrocarbons on dinonylphatalate and polyethyleneglycol 4000

Summary Relative retention data and Kováts retention indices were measured for several hydrocarbons (mainly for alkylbenzenes) on dinonylphtalate and polyethylenelycol 4000 stationary phase. Correlations were searched between these retention data and the following physical (boiling point, molrefraction, molvolume) and topological (connectiviity index and general index of molecular complexity) properties of solutes. The best fitting equations was choosen among more than 150 equations involving linear, quadratic, exponential, two variables linear and quadratic dependence of retention data and the properties mentioned as well as their inverses.     

Comparative analysis of HPLC retention: A thermodynamic approach to the interpretation of correlation equations

That correlation equations in the method of comparative analysis of chromatographic retention are linear was explained by the fact that relationships between the Gibbs energies are linear. The specifics of the application of the thermodynamic approach to an analysis of the retention of substances under conditions of reversed-phase partition chromatography were discussed. It was shown that a similar approach can be applied to an analysis of incremental relationships for the retention of three substances.     

The absolute retention index in chromatography. Part 1

A definition for an absolute retention index is given. This index is independent of whether the process is isothermal or temperature programmed. The relation between this index and Kovats's index is discussed. General equations are derived for the retention times of homologous series, from which the position of the air peak or missing members can be determined. Methods used in the literature for air peak determination are improved and extended to other cases of interest. The retention index in temperature programmed chromatography is reexamined in the light of recent publications on temperature programming.     

The use of recurrent equations in chromatography

Recurrent equations A(x + k) = aA(x) + b were shown to be applicable to the approximation not only of virtually arbitrary properties of organic compounds (A) in homologous series (A = n _C, k = 1 or 2) but also of the dependences of chromatographic retention parameters on the number of carbon atoms in homologue molecules (A = t _R). The same equations described the temperature dependences of retention times of arbitrary compounds under isothermal separation conditions in gas chromatography (x = T, k = ΔT = const) and the dependences of retention times on the concentration of an organic solvent as an eluent component (x = C, k = ΔC = const) under isocratic separation conditions in high performance liquid chromatography.     

Retention models for programmed gas chromatography

The models proposed by many authors for the prediction of retention times and temperatures, peak widths, retention indices and separation numbers in programmed temperature and pressure gas chromatography by starting from preliminary measurements of the retention in isothermal and isobaric conditions are reviewed. Several articles showing the correlation between retention data and thermodynamic parameters and the determination of the optimum programming rate are reported. The columns of different polarity used for the experimental measurement and the main equations, mathematical models and calculation procedures are listed. An empirical approach was used in the early models, followed by the application of thermodynamic considerations, iterative calculation procedures and statistical methods, based on increased computing power now available. Multiple column arrangements, simultaneous temperature and pressure programming, applications of two-dimensional and fast chromatography are summarised.     

The correlation equations describing retention index data on OV-101, OV-275 and PEG 20M.n-alkanes andn-alkynes

Summary The correlation equations between Kovats retention indices ofn-alkenes andn-alkynes, column temperature and number of carbon atoms in molecules of these compounds on OV-101, OV-225 and PEG 20M capillary columns have been calculated. The two variable equationI=A + B · n + C / T give a good fit and are the simplest for practical use.     

Linear compartmental systems. I. kinetic analysis and derivation of their optimized symbolic equations

The study of many biological systems requires the application of a compartmental analysis, together with the use of isotopic tracers, parameter identification and methods to evaluate the mean parameters. For all this, the kinetic equations of the compartmental system as a function of its parameters are needed. In this paper, we present some considerations on the diagrams of connectivity of linear compartmental systems and obtain new properties from the matrix corresponding to the ordinary first-order linear differential equation systems which describe their kinetic behaviour. Using these properties, symbolic equations are obtained in a simplified form. These equations provide the instantaneous amount of substance in any compartment of the system when zero input is injected into one or more of the system compartments, solely as a function of those parameters of compartmental systems which really have an influence on the sought expression. This is unlike what happens in the other symbolic equations obtained in a previous contribution that included all the fractional transfer coefficients involved in the compartmental system, regardless of whether or not they had an influence on the instantaneous amount of substance.     

Mathematical models of solute retention in gas chromatography as sources of thermodynamic data. Part IV. Aliphatic alcohols as the test analytes

This study is the fourth consecutive part belonging to the cycle devoted to an alternative approach to deriving certain thermodynamic magnitudes. The previous three papers were dedicated, respectively, to ketones, aldehydes, and alkylbenzenes. In our present study (similar to the previous ones) the following working procedure is adopted. With the aid of capillary gas chromatography, the retention times are obtained for a wide variety of the aliphatic alcohols. The analyses are carried out isothermally on stationary phases of different polarity and at five different measuring temperatures. These data constitute an experimental basis for further processing with the aid of the specially devised mathematical equations. The fitting parameters of these equations, due to their physicochemical meaning, enable determination of certain thermodynamic data. Nine equations used in this study are the relationships coupling the selected retention data [relative retention (r), non-reduced relative retention (rG), the retention factor (k), or the Kováts retention index (I)] and a variety of the physical magnitudes [the boiling point of the analyte (T(B)), its molar volume (Vm), or its molar refraction (Rm)]. These relationships are tested with respect to their performance to predict the molar enthalpy of vaporization (deltaHvap) of the analytes of interest (i.e., of aliphatic alcohols). Evaluation of the equations' performance is carried out through a comparison of the numerical values generated from this approach with those originating from the other methods, and a very good agreement was found between these two series of the data. The best molar enthalpy vaporization values (deltaHvap) are obtained from the retention data originating from the most polar of the three investigated stationary phases (i.e., DB-Wax). Models V and VIII proved the best performing ones among the nine models tested in this study.     

Separation of potentially therapeutic peptide hormones by liquid chromatography. Optimisation of the composition and pH of the mobile phase

The aim of this work is to optimise the proportion of the organic modifier and the pH of the mobile phase, in order to separate a series of peptide hormones with therapeutic interest in the molecular mass range from 500 to 6000. The composition of the mobile phase was optimised by establishing relationships between retention parameters and either the scale of solvent polarity, or the Kamlet–Taft multiparameter solvent scale of the eluent, using linear solvation energy relationships. Likewise, linear correlations between the chromatographic retention and Reichardt’s E^N_T parameter were obtained. These relationships allowed an important reduction of the experimental retention data needed for developing a given separation. In addition, a model describing the effect of the correctly measured pH of the mobile phase on retention in LC was established and tested for the series of selected peptides using an octadecylsilica column. The proposed equations permit the prediction of the optimum pH and also permit the determination of the acidity constants of the peptides in the hydro-organic mixtures using a minimum number of measurements.     

Correct identification of polychlorinated biphenyls in temperature-programmed GC with ECD detection

A method has been developed for peak identification of PCBs in GC with ECD detection under different temperature programs and isothermal conditions on two commonly used columns (DB-5 and DB-1701). This was achieved by means of accurate calibration of retention times based on the concept of the relative retention index P (i) and retention times of the selected PCB internal standards. The P (i) was calculated from the predicted retention times with the database of the retention parameters (A, B) and the migration equations. Through comparison of the calibrated and experimental retention times of PCBs in technical samples, it was shown that the developed method was effective for correct PCB comprehensive, quantitative, congener-specific (CQCS) analyses.     

New equations describing the combined effect of pH and organic modifier concentration on the retention in reversed-phase liquid chromatography

Six equations that express the combined effect of mobile phase pH and organic modifier content on sample retention in reversed-phase liquid chromatography (RPLC) are developed based on either the adsorption or the partition model for retention. The equations are tested against five retention data sets taken from literature. In the tests two pH scales are used, w(w)pH and s(s)pH. It is shown that a new seven-parameter equation works more satisfactorily, because it exhibits good numerical behavior, gives low values of the sum of squares of residuals and represents the experimental retention surfaces successfully. In addition, the danger of overfitting, which leads to the prediction of physically meaningless retention surfaces, is minimized by using the proposed new seven-parameter equation. Finally, the possibility of obtaining reliable pK values of weak acids or bases chromatographically by means of the derived equations is also considered and discussed.     

Comparative study on the thermodynamic retention models in HPLC

Summary A series of model substances with known solubility parameter were chromatographed and from the temperature dependence of the capacity factor, some of the thermodynamic parameters influencing solute retention were determined. A linear relationship was derived between the enthalpy density and the solute solubility parameter from which a graphical method was introduced for the determination of phase characteristics.Comparing the predicted and measured capacity factor values it has been found that the predicted values are very sensitive to the literature data selected for the computation; however, by using the van der Waals molecular volume in the calculation significantly lower deviation was found from the measured data. Two equations are given for the prediction of selectivity and as the mathematical criteria of the validity of the used thermodynamic models. The results show that the predicted selectivity values are similar to the measured data using given initial parameters in the computation. However, the unreliability of the literature data makes the application of the retention models difficult.Dedicated to Professor J. F. K. Huber on the occasion of his 60th birthday.     

Prediction of gas chromatographic retention indices of linear,branched, and cyclic alkanes from their physicochemical properties

Kováts retention indices for a series of linear, branched, and cyclic alkanes on squalane at any temperature, and on other stationary phases of different polarity at a given temperature, are related to physicochemical properties of the solutes, such as boiling point and molar refraction, by multiple regression analysis. The equations found permit calculation of the Kováts retention index for all alkanes, with standard deviations close to experimental error. The same equations can also be used for calculating the physicochemical parameters they contain.