Regression against Temperature of Gas–Liquid Chromatography Retention Factors. Van’t Hoff Analysis

Abstract

The present work deals with the precise experimental determination of the gas–liquid chromatography (GLC) retention factors (k) in a sufficiently large temperature range to allow the calculation of the thermodynamic quantities associated with the sorption process. Once isothermal retention factors of three homologous series members of the type H-(CH2) n -Y (Y = CH3, OH, CN) were measured over a temperature range of about 110 K on a low-polar PDMS (HP-1) capillary column and checked for accuracy and precision by “arc plot” representation, the data were analyzed by applying different forms of the van’t Hoff relationship. We compared the linear versus nonlinear van’t Hoff plots representing situations characterized by Δsolv C p ° = 0, Δsolv C p °≠ 0 = constant, and Δsolv C p ° = f(T), respectively (Δsolv C p ° represents the difference in isobaric heat capacity associated with movement of the analyte between the mobile and the stationary phase). The “logarithmic” and “quadratic” nonlinear van ‘t Hoff equations were shown to be more appropriate than the linear van‘t Hoff equation for determining enthalpy and entropy of solvation. Special attention was devoted to the fitting performance and extrapolation capability of models with nonzero Δsolv C p °. By several metrics, the quadratic model exhibits better behavior in extrapolations yielding reasonable accuracy for retention time and/or enthalpy of solvation predictions at temperatures located below the experimental range.

Estimating Vapor Pressure Data from Gas–Liquid Chromatography Retention Times: Analysis of Multiple Reference Approaches, Review of Prior Applications, and Outlook

“…The present study is a continuation of the series of papers − in which we have focused our efforts on a better understanding of indirect gas–liquid chromatography (GLC) based strategies for estimating the vapor pressure of liquid compounds using chromatographic retention times (RT) and on identifying an efficient way of optimizing the operating conditions. In Part 1, we analyzed a method for determining the supercooled vapor pressures based on relative retention times with single reference standards (denoted the GLC-RT1S method).…”

“…Generally, the GLC-RT y S method is based on some previously known principles of chromatography, derived from an ideal thermodynamic equilibrium relationship. Accordingly, the retention process in GLC consists of the distribution of an analyte i between the stationary phase and the mobile phase and is characterized by an equilibrium distribution constant K i defined as the ratio between concentrations of the analyte in the liquid ( C i l ) and the gas ( C i g ) phases at a given temperature. ,, where k i is the retention factor, Δ solv G i o ( T ) is the standard Gibbs energy of solvation, t i is solute retention time, t 0 is the hold-up time (i.e., the retention time of an unretained analyte), β is the phase ratio, that is, the ratio of mobile phase volume to stationary phase volume in the column (β = d C /4 d F ; here, d C is the column diameter and d F is the film thickness).…”

“…In principle, the GLC-RT y S method can be broken into two separate stages: in the first routine, the temperature dependence of ln k i of both test ( i = x ) and reference standard ( i = s) compounds is determined by using a form of the van’t Hoff relationship where the f ( T ) function operating on the right-hand side of the equation reflects the situations when Δ solv C p o = 0, Δ solv C p o ≠ 0 = const., and Δ solv C p o = f ( T ), respectively (Δ solv C p o represents the difference in isobaric heat capacity associated with movement of the analyte between the mobile and the stationary phase). Accordingly, three variants of eq can be globally recognized, namely linear ( f ( T ) = 0, Model A), or nonlinear (Δ solv C p o ≠ 0 = const., f ( T ) = ln T , Model B, and Δ solv C p o ≠ const., f ( T ) = 1/ T 2 , Model C) van’t Hoff plots . Note that the c i X coefficients in eq can be interpreted in terms of thermodynamic properties (see Table in ref ), while the superscripts X at coefficients c i denote the method (A, B, or C).…”

“…Accordingly, three variants of eq can be globally recognized, namely linear ( f ( T ) = 0, Model A), or nonlinear (Δ solv C p o ≠ 0 = const., f ( T ) = ln T , Model B, and Δ solv C p o ≠ const., f ( T ) = 1/ T 2 , Model C) van’t Hoff plots . Note that the c i X coefficients in eq can be interpreted in terms of thermodynamic properties (see Table in ref ), while the superscripts X at coefficients c i denote the method (A, B, or C). The implications of this step of choosing an appropriate functional form for the regression can be great when extrapolation is considered …”

“…Note that the c i X coefficients in eq can be interpreted in terms of thermodynamic properties (see Table in ref ), while the superscripts X at coefficients c i denote the method (A, B, or C). The implications of this step of choosing an appropriate functional form for the regression can be great when extrapolation is considered …”