Molar Free Energy Of Solution Research Articles

Interpreting the gas chromatographic retention of n-alkanes

Non-linear regressions were applied to n-alkanes retention data for the determination of gas hold-up in a preceding paper. It was found that at temperatures over 100°C the reduced partial molar free energy of solution, Δ G/ RT, tends to be negligible for the solute methane in poly(dimethylsiloxane) stationary phases. A consequence of interest can be inferred from this fact. The C–H bonds from terminal methyl groups of n-alkane solute molecules should not contribute significantly to Δ G/ RT in these conditions. The analysis of data confirms that, within the chromatographic experimental error, the contributions of n-alkane end C–H bonds are also negligible in this temperature range. Consequently, the regression parameter that contains the phase ratio of the column only includes the gas hold-up as the accompanying factor.

Revision of a theoretical expression for gas-liquid chromatographic retention.

In this communication, we revise some aspects of the [ideal gas/Van der Waals fluid] partition, derived in an earlier publication. The general character of the conclusions concerning the dependence of the partial molar free energy of solution, deltaGs(n), on the chain length, n, of linear solute molecules is shown through the relationship with more general partition formulations. Simultaneously, the correction of an error in the expression of the retention time dependence on the phase ratio of the chromatographic column, beta, is carried out. The misleading source of this error was redundant accounting in the solute translational contribution to deltaGs(n).

Consistency of gas hold-up determinations

The retention of methane on poly(dimethylsiloxane) capillary columns was studied focusing its relation with the gas hold-up time t M, which was derived from the retention of n-alkanes. The [ideal gas/Van der Waals fluid] partition equation was applied in order to provide the mathematical expression for the retention factor of the n-alkanes as a function of the carbon number n. In this context the partial molar free energy of solution is a non-linear function of the chain length Δ G s( n) ( n≥5). The resultant retention factor k of methane, determined from its retention time and the calculated t M, approaches an almost constant value when the temperature is increased beyond 100°C. This value of k has the order of the reciprocal column phase ratio 1/ β. Precisely, this is the theoretically expected limit of a non-interacting solute or inert marker.

Evaluation of the effect of the cyanopropyl radical on the interaction of the methylene group with silicone stationary phases

Values of the solute-polymer interaction parameter of n-alkanes and polar substances between 90C and 200°C were obtained on two packed columns (OV-101 and OV-105). Experiments carried out with a capillary column confirmed that with non-polar solute-polymer systems the values of both the specific retention volumes and the thermodynamic parameters derived from them are equivalent to those obtained with packed columns. The results showed that n-alkanes mix better with OV-101 and polar substances are better solvents of OV- 105. The differences are small, however. Partial molar enthalpies and free energies of solution and mixing were calculated. The contribution of the methylene group of the n-alkanes to the thermodynamic parameters of solution was evaluated. The effect of cyanopropyl group substitution on the contribution of the methylene group to the partial molar free energy of solution of n-alkanes was found to be roughly linear with the cyanoalkyl group content, decreasing as the polarity of the polymer increases. The solubility parameter of the stationary phase increases only slightly when a 5% substitution of cyanopropyl groups is introduced in the polymer.

Thermodynamic characteristics of solute-solvent interactions in liquid organic salt solvents, studied by gas chromatography

A number of thermodynamic constants were measured for five McReynolds selectivity probes and a series of aromatic selectivity probes on thirteen tetra-n-butylammonium salts and eleven 4-toluenesulfonate salts to elucidate the nature of intermolecular interactions of solute—liquid organic salts by gas chromatography (GC). The molar free energy of solution for a methylene group was used to determine dispersive contributions of individual cations and anions to retention. The partial molar, mole fraction, and molal free energy of solution and partial mole fraction enthalpy and entropy of solution were determined to estimate the contribution of various intermolecular forces to retention and to compare the magnitude of these interactions to those of non-ionic, polar phases. Weak dispersive interactions increasing with the size of the cation, strong orientation interactions of a relatively constant nature, and proton acceptor interactions that varied greatly and correlated with the properties of the anion were observed for the liquid organic salts. The magnitude of the orientation and proton acceptor interactions in several cases were much larger than equivalent interactions for polar, non-ionic phases. The infinite dilution activity coefficient and partial molar excess free energy of solution were determined for the five McReynolds probes on the tetra-n-butylammonium salts. With the exception of butanol the range of values observed were similar to literature values for polar, non-ionic GC phases.

Influence of concurrent retention mechanisms on the determination of stationary phase selectivity in gas chromatography

Two methods are used to establish the influence of concurrent retention mechanisms on the accuracy of McReynolds phase constants for the stationary phases squalane, OV-225, Carbowax 20M, OV-275, ethylammonium nitrate, n-propylammonium nitrate, n-butylammonium thiocyanate, sec.-butylammonium thiocyanate, and di-n-propylammonium thiocyanate. Phase loading studies of the net retention volume per gram of packing as a function of the percent liquid loading were used to indicate, qualitatively, those cases for which adsorption at the liquid and support interfaces made a significant contribution to the retention mechanism of test solutes and the n-alkane retention index markers. It is shown that for some cases accurate phase constants can be calculated from the gas—liquid partition coefficient of the test probes and n-alkanes obtained by extrapolation to infinite phase volume of plots of VN/VL against 1/VL (VN = net retention volume and VL = volume of liquid phase). This approach was successful for obtaining gas-liquid partition coefficients for all polar probes but not always for the n-alkane retention index markers. The n-alkanes were retained predominantly by interfacial adsorption on OV-275, ethylammonium nitrate, and n-propylammonium nitrate. In these cases accurate McReynolds phase constants can not be determined by any method that relies on measurements based on the partitioning of the n-alkanes. Alternatively, the relative selectivity of all phases evaluated can be determined from the partial molar free energy of solution for the McReynolds test probes. Infinite dilution activity coefficients and the partial molar free energy of solution for a methylene group are used to help establish the nature of solution interactions between the n-alkanes, McReynolds test probes, and the phases studied.

Thermodynamic characteristics of solute—solvent interactions in liquid organic salt solvents, studied by gas chromatography

A number of thermodynamic constants were measured for five McReynolds selectivity probes and a series of aromatic selectivity probes on thirteen tetra- n-butylammonium salts and eleven 4-toluenesulfonate salts to elucidate the nature of intermolecular interactions of solute—liquid organic salts by gas chromatography (GC). The molar free energy of solution for a methylene group was used to determine dispersive contributions of individual cations and anions to retention. The partial molar, mole fraction, and molal free energy of solution and partial mole fraction enthalpy and entropy of solution were determined to estimate the contribution of various intermolecular forces to retention and to compare the magnitude of these interactions to those of non-ionic, polar phases. Weak dispersive interactions increasing with the size of the cation, strong orientation interactions of a relatively constant nature, and proton acceptor interactions that varied greatly and correlated with the properties of the anion were observed for the liquid organic salts. The magnitude of the orientation and proton acceptor interactions in several cases were much larger than equivalent interactions for polar, non-ionic phases. The infinite dilution activity coefficient and partial molar excess free energy of solution were determined for the five McReynolds probes on the tetra- n-butylammonium salts. With the exception of butanol the range of values observed were similar to literature values for polar, non-ionic GC phases.

Influence of concurrent retention mechanisms on the determination of stationary phase selectivity in gas chromatography

Two methods are used to establish the influence of concurrent retention mechanisms on the accuracy of McReynolds phase constants for the stationary phases squalane, OV-225, Carbowax 20M, OV-275, ethylammonium nitrate, n-propylammonium nitrate, n-butylammonium thiocyanate, sec.-butylammonium thiocyanate, and di- n-propylammonium thiocyanate. Phase loading studies of the net retention volume per gram of packing as a function of the percent liquid loading were used to indicate, qualitatively, those cases for which adsorption at the liquid and support interfaces made a significant contribution to the retention mechanism of test solutes and the n-alkane retention index markers. It is shown that for some cases accurate phase constants can be calculated from the gas—liquid partition coefficient of the test probes and n-alkanes obtained by extrapolation to infinite phase volume of plots of V N/ V L against 1/ V L ( V N = net retention volume and V L = volume of liquid phase). This approach was successful for obtaining gas-liquid partition coefficients for all polar probes but not always for the n-alkane retention index markers. The n-alkanes were retained predominantly by interfacial adsorption on OV-275, ethylammonium nitrate, and n-propylammonium nitrate. In these cases accurate McReynolds phase constants can not be determined by any method that relies on measurements based on the partitioning of the n-alkanes. Alternatively, the relative selectivity of all phases evaluated can be determined from the partial molar free energy of solution for the McReynolds test probes. Infinite dilution activity coefficients and the partial molar free energy of solution for a methylene group are used to help establish the nature of solution interactions between the n-alkanes, McReynolds test probes, and the phases studied.

Thermally stable, highly fluorinated stationary phases for gas chromatography

The chromatographic properties of three highly fluorinated stationary phases namely Fomblin YR [a poly(perfluoroalkyl) ether], PPF-20 [a poly(perfluorphenylene) ether], and Fluorad FC-430 [a fluoroalkyl ester], are compared with those of conventional phases. The importance of phase structure, coating solvent, and surface chemistry of the support for the preparation of efficient and stable column packings is outlined. The retention of solutes of different structures is shown to occur by a combination of gas—liquid partitioning and interfacial adsorption. The relative importance of partitioning compared to adsorption is influence by the degree of fluorination and the measurement temperature. From accurately determined gas—liquid partition coefficients, corrected McReynolds phase constants and partial molar free energies of solution for a methylene group (Δ G) were determined for the highly fluorinated phases. In the case of Fomblin YR, the very low value for Δ G(CH 2) compared to conventional phases provides a quantitative indication of the weak intermolecular forces operating in the chromatographic system. Higher values for PPF-20 indicate stronger dispersive interactions for the perfluroaromatic phase compared to the perfluoroalkyl phases.

Apparatus to measure vapor pressure, differential vapor pressure liquid molar volume, and compressibility of liquids and solutions to the critical point. Vapor pressures, molar volumes and compressibilities of benzene and perdeuterated benzene at elevated temperatures

An apparatus designed to measure vapor pressure differences between two similar liquids, such as isotopic isomers, or between a solution and its reference solvent at temperatures and pressures extending to the critical point is described. Vapor-phase volume is minimized and pressure is transmitted to the transducer through the liquid, thereby avoiding several experimental difficulties. Liquid can be injected into the heated part of the system by volumetrically calibrated screw injectors, thus permitting measurements of liquid molar volume, compressibility, and expansivity. The addition of a high-pressure circulating pump and injection valve allows the apparatus to be employed as a continuous dilution differential vapor pressure apparatus for determining partial molar free energies of solution. In the second part of the paper data on the vapor pressure, molar volume, compressibility, and expansivity and their isotope effects for C/sub 6/H/sub 6/ and C/sub 6/D/sub 6/ from room temperature to near the critical temperature are reported.

Comparison of the retention indices and differential molar free energies of solution for thiolic and carboxylic esters on gas-chromatographic columns with various polarities

1. There is no full analogy between the gas-chromatographic behavior of thiolic and carboxylic esters. 2. The retention indices of 24 thiolic esters were determined on columns of Apiezon M, silicone OV-17, Triton X-305, and polyethylene glycol 1000 at 130°C. 3. Equations are proposed for the dependence of the retention indices on the number of carbon atoms in the n-alkyl chain on four stationary phases for the homologous series of n-alkyl thioacetates. The equations can be used for the identification of n-alkyl thioacetates in mixtures of sulfur-containing compounds.

Effect of KF and NA3PO4 on the change in differential molar free energy of sorption of polar substances during analysis in glass capillary columns with polyethylene glycol

1. The change in the energy contribution of the functional groups OH, NH2, NH, SH, Br, and C =O in a series of octane derivatives was studied by chromatography in glass capillary columns with polyethylene gly-col-40M after treatment with KF and Na3PO4. 2. The increase which we observed in the energy contributions of the functional groups which are hydrogen donors when analyzed on PEG in the presence of KF is attributed to their ability to form a hydrogen bond with the salt, the anion acting as a base. 3. We studied the effect of KF and Na3PO4 on the change in the energy contributions of the aromatic compounds toluene, nitrobenzene, and pyridine, compared to that of benzene. In the energy of sorption of pyridine, as well as a tertiary amine, it is probable that electrostatic interaction with the salts' metal ions makes a contribution. 4. In the analysis of n-alkanes on PEG, the differential molar free energy of solution due to the methylene group (ΔGCH2) in unchanged in the presence of KF and Na3PO4.

Determination of the energy of intermolecular interactions in gas chromatography from retention indices

The nature of the coefficients in the linear dependence of a partial molar free energy of solution on a retention index value for all substances analyzed on a stationary phase has been ascertained. A simple procedure for estimating the difference of intermolecular interaction energies after replacement of n-alkyl radicals with isoalkyl or unsaturated radicals in aliphatic sulphides and disulphides has been evaluated. Variations of intermolecular interaction energies of the functional group in metameric thiatridecanes with the displacement of the S atom into the carbon chain have been determined.

Universal system for liquid stationary phase classification on the basis of thermodynamical data

Equations modifying Rohrschneider's relationship between ΔI and thermodynamical characteristics values are derived. Polarity in chromatography is discussed as a possibility of stationary phases or absorbents to enter into intermolecular interactions and is determined on the basis of the partial molar free energies of solution (ΔG) of six test substances. A simple method for the calculation of stationary phase polarity in terms of ΔG from retention indices and McReynolds constants is given. Equations are presented for the calculation of stationary phase selectivity utilizing ΔG data tabulated for selected test substances. The thermodynamical basis of selecting a reference phase for a unified system expressing the selectivity of stationary phases which can also be applied for adsorbents is suggested. The energy equivalent to an index unit, ΔGi.u., is discussed.

The relationship between the connectivity indices and the thermodynamic parameters describing the interaction of fatty acid methyl esters with polar and nonpolar stationary phases

The relationships between the connectivity indices — easily calculated from the molecular structure of the compounds — and the partial molar free energies of solution are investigated for the methyl esters of 39 saturated (normal and branched) mono- and polyunsaturated higher fatty acids on a nonpolar (SE-30) and polar (SILAR 5CP) phase. The prediction of the ΔG values seems possible for any compound assuming that data for standard compounds are available. The relationship may be generally useful for the thermodynamic evaluation of nonspecific interactions of compounds with the stationary phases.

Gas chromatographic characteristics of sulfur-containing compounds 3. n-alkyl isoalkyl sulfides

1. Indices of retention have been determined for 39 n-alkyl isoalkyl sulfides from eight different homologous series, using four different types of stationary phase and working at 130°C. 2. An equation relating the sulfide retention index with the number of carbon atoms in the n-alkyl chain has been developed for each homologous series. 3. The iso radical makes a definite and characteristic contribution to the retention index in each homologous series studied here. 4. The contribution of each of seven isoalkyl radicals to the differential molar free energy of solution in Apiezon M has been determined. 5. Boiling points of the various sulfides have been calculated through the proposed equation, the standard deviation between calculated and measured values being 2.3°C.

Characterization of the selectivity of stationary phases from the partial molar free energies of solution of standards

A thermodynamic description is proposed to express the polarity of stationary phases in terms of the partial molar free energies of solution obtained for standards. This expression is an absolute value for any stationary phase and does not need squalane as the phase with “zero polarity”. Equations are given to express the contributions of dispersive interaction and of the sum of inductive, orientative and specific interactions to the partial molar free energies of solution for any substance in any phase.

Thermodynamic evaluation of the interaction of fatty acid methyl esters with polar and non-polar stationary phases, based on their retention indices

Kovatś retention indices are used to determine the partial molar free energies of solution of 39 methyl esters of saturated (normal and branched), mono- and poly-unsaturated higher fatty acids in the non-polar phase Se-30 and the polar phase SILAR 5CP. Contributions of double bonds as a function of their number and position in the acid chain to the partial molar free energies of solution (ΔG) are evaluated quantitatively. Linear equations are suggested for the calculation of ΔG of any compounds from their retention indices measured in columns with SE-30 and SILAR 5CP.

Dependence of solution thermodynamic functions on the character of the hetero-atom in sulfur- and oxygen-containing compounds

1. Substitution of an oxygen atom by a sulfur in aliphatic and cyclic ethers and aromatic heterocycles brings about a uniform increase in the energy of dispersive interaction, this being the thermodynamic basis for analogies in the GC behavior of S- and O-containing compounds. 2. A simple method for calculating differences of differential molar free energies of solution δ(ΔG)ij from retention indices has been proposed and used to give a quantitative description of the differences in GC behavior of the compounds under discussion here.

Thermodynamic estimate of polarity of stationary phases in gas chromatography

1. A method was proposed for making a thermodynamic estimate of the polarity of stationary liquid phases in gas chromatography based on the values of the differential molar free energies of solution of standard compounds. 2. An equation is given for calculating the energy of the dispersion and the sum of the orientation, induction, and specific interactions of the chromatographed compound with a stationary liquid phase.