Retention data modeling

The competition model and solvent interaction model were at one time heatedly debated but current thinking maintains that under defined r iitions the two theories are equivalent, however, it is impossible to distinguish between then on the basis of experimental retention data alone [231,249]. Based on the measurement of solute and solvent activity coefficients it was concluded that both models operate alternately. At higher solvent B concentrations, the competition effect diminishes, since under these conditions the solute molecule can enter the Interfacial layer without displacing solvent molecules. The competition model, in its expanded form, is more general, and can be used to derive the principal results of the solvent interaction model as a special case. In essence, it seems that the end result is the same, only the tenet that surface adsorption or solvent association are the dominant retention interactions remain at variance. 

In ion-pair chromatography, a great number of parameters influence the retention of a charged solute e.g., the type of solute, the type and the concentration of the pairing ion, the type and the concentration of the buffer, the mobile phase composition, etc. This makes ion-pair chromatography a versatile technique at the same time as it appears to be complicated and difficult to control. From the discussion above, it is clear that a few simple basic principles often can be used to understand the retention behavior when the experimental conditions are varied. In practical work, it may be desirable to make predictions of retentions from a limited set of retention data and without going into the more complicated theoretical models. For this purpose, an approximate equation was derived that considers most of the parameters in a simple and practically useful way. For the derivation of this simple version of the model and for a guide to its use and applicability, we refer to Ref. [8]. Here, we will only state the final equation and show one simple example of its use. 

Cluster analysis (numerical toxonomic aggregation) is applied to arrange phases according to their chromatographic behaviour. A set of retention data for 16 monofimctional benzenes, 110 difunctional benzenes and 15 trifunctional benzenes was subjected to analysis. Three groups of stationary phases can be distinguished polar, non-polar, and polyfluorinated. A linear relationship between the retention data of two stationary phases of the same class can be worked out. This linear relationship fits the model... 

Infrared spectra of individual fractions were determined by means of a Beckman IR-5 spectrophotometer equipped with a 5 X KBr lens-type beam condenser. Infrared spectra of selected reference compounds were obtained from samples which had been purified by chromatography. On the basis of identity of infrared spectra and retention data with those of authentic reference compounds, most of the peaks shown in Figures 1 and 2 were identified (15,16). To obtain information about minor components not detectable in the infrared spectra, mass spectra were obtained as components of an irradiated odor concentrate were eluted from a 10-foot, J/g-inch 5% Carbowax 20M column programmed from 20° to 160°C. at 1° per minute. These spectra were obtained on a modified model 14 Bendix Time-of-Flight mass spectrometer. Electron energy was set at 70 e.v., and spectra were scanned from m/e 14-200 in 6 seconds. 

A disadvantage of simple interpretive methods is that the model to which the retention data (or other data) are fit must be fairly accurate. In other words, an interpretive approach may fail if one or more sample components exhibits anomalous retention. Although rare in SFC, such retention behavior is observed occasionally and is difficult to predict intuitively. Note, however, that by anomalous retention we do not mean behavior that is merely unusual, e.g., retention that decreases smoothly with increasing density (at constant temperature). Retention that varies in a regular (continuous) manner, even if unusual, can usually be modeled with a high degree of accuracy (vide infra). 

Table VI gives the results for the multiple regression of the retention data. Values for each coefficient in equation 9 are given for each solute, as well as parameters describing the quality of the fit to the experimental data. As can be seen in Table VI, the fit was exceptional. Interestingly, when the regression was repeated without the interaction term, the fit was not as good, with R2 values less than 0.988. Similar losses in correlation were also observed if the squared-density term was omitted from the model equation. Equation 9 thus appears to be the best model from among those that could be predicted from the relationships in equations 2 and 3.

Solute retention as a function of temperature at constant pressure is seen to be dependent on the partial molar enthalpy of solute transfer between the mobile and stationary phases, the neat capacity of the supercritical fluid mobile phase and the volume expansivity of the fluid. The model was compared to chromatographic retention data for solutes in n-pentane and CO2 as the fluid mobile phase and was seen to fit the data well. 

Retention data that after a possible delay in concentration show a sharp decline followed by a long tail would be modeled by is 2 and h(t > h > h+. The condition h- > h+ ensures that the drift of the random walk (or diffusion) is away from the reflecting barrier. Figure 9.9 illustrates the probability profiles in the distribution and elimination compartments when m = 20, is = 15, h+ = 0.1,... 

A most important contribution to the above means of identification is the Kovats retention index system [28]. The Kovats retention index of a compound is 100 times the number of carbon atoms in a hypothetical n-alkane that would display in the given system the same retention as the compound in question. Hence, the retention index system essentially is also based on the regularities between the retention data and number of carbon atoms in homologous compounds. The concept of the Kovats retention index system is illustrated by the model in Fig. 3.7, which shows a plot of log A) values for homologous compounds of the type CH3(CH2) X and for n-alkanes against carbon number. It is apparent that the retention index of, e.g., C2H5X is 560, i.e., 7(C2HSX) = 200 +... 

Second, previous tests of the displacement model have focused mainly on its ability to correlate and predict retention data in terms of derived correlational equations. Such correlations are based on various free energy relationships, and it is often found that comparisons of this kind can be insensitive to differences in the underlying physical model. That is, correlations of experimental retention data with theory may appear acceptable, in spite of marked deficiencies of the model. In some cases (e.g.. Ref. 12, sorption versus displacement models), radically different models can even yield the same or similar correlational equations. Here we will further test the proposed model for LSC retention in the following ways (1) application of the model to a wide range of LSC systems, involving major variations in solute, solvent, and adsorbent (2) examination of the various free energy terms that individually contribute to overall retention. 

Fig. 21. Experimental and calculated isotherms for various LSC binary-solvent mobile phases /AB and silica as adsorbent. Solid curves are calculated from present model using parameters of Table I (based on retention data only) points are experimental uptake values from Scott and Kucera (4) and Snyder and Poppe (12). (a) CHCt/hexane (b) benzene/ hexane (c) toluene/hexane (d) ethyl acetate/hexane (e) isopropanol/hexane.

On balance, the plots of Fig. 21 suggest that calculated values of 0b from the present approach are reasonably close to actual isotherm values. Thus, these isotherm data can be regarded as supporting the present displacement model (and related equations), or at the least, not disproving the model. Whether the present approach can be extended to predict isotherm data with an acceptable accuracy for other purposes (e.g., preparative separations with column overload) remains to be seen. This will require careful studies of the same adsorbent sample, measuring both solvent isotherm data and appropriate solute retention values, with use of the solute retention data to derive solvent parameters for calculations of 6b ... 

In the past, several theoretical models were proposed for the description of the reversed-phase retention process. Some theories based on the detailed consideration of the analyte retention mechanism give a realistic physicochemical description of the chromatographic system, but are practically inapplicable for routine computer-assisted optimization or prediction due to then-complexity [9,10]. Others allow retention optimization and prediction within a narrow range of conditions and require extensive experimental data for the retention of model compounds at specified conditions [11]. 

In spite of widespread applications, the exact mechanism of retention in reversed-phase chromatography is still controversial. Various theoretical models of retention for RPC were suggested, such as the model using the Hildebrand solubility parameter theory [32,51-53], or the model supported by the concept of molecular connectivity [54], models based on the solvophobic theory [55,56) or on the molecular statistical theory [57j. Unfortunately, sophisticated models introduce a number of physicochemical constants, which are often not known or are difficult and time-consuming to determine, so that such models are not very suitable for rapid prediction of retention data. 

Finally, structure-based predictive software is commercially available (such as CHROMDREAM, CHROMSWORD or ELUEX) for mobile phase optimisation in RPC. This software incorporates some features of the expert system, as it predicts the retention on the basis of the molecular structures of all sample components (which should be known) and the known behaviour of model compounds on various HPLC columns. No initial experimental runs are necessary as the retention data are calculated from the additive contributions of the individual structural elements to the retention, contained in the software databa.se and consequently optimum composition of the mobile phase is suggested. Such predictions are necessarily only approximate, do not take into account stereochemical and intramolecular interaction effects, and predicted separation conditions can be used rather as the recommendation for the initial experimental run in the subsequent optimisation procedure. 

HPLC retention data for QSRR analysis are usually obtained by measuring log at several eluent compositions (isocratic conditions) and then extrapolating the dependence of log on a binary eluent composition to a fixed mobile phase composition, common for all the analytes studied, based on the Soczewinski-Snyder model ... 

In recent years, three-dimensional quantitative structure biological activity relationship methods known as comparative molecular field analysis (CoMFA) has been applied to construct a 3D-QSRR model for prediction of retention data. The CoMFA 3D-QSRR model is obtained by systematically sampling the steric and electrostatic fields surrounding a set of analyte molecules. Next, the differences in these fields are correlated to the corresponding differences in retention. The CoMFA model was successfully applied to HPLC retention data of polycyclic aromatic hydrocarbons [60]. 

Predictions of retention data from structural descriptors by means of neural networks (NN) seem to be very attractive and convenient. By now the predictions provided by NN are of similar reliability as to those obtained from regression models 186,89]. 

The extent of the nonequilibrium region, segment BC of Fig. 1, is dependent on both the polymer-solute system (34) and experimental parameters (13, 33). As the thickness of the polymer film or the flow rate of carrier gas increases, the maximum of the retention diagram shifts towards higher temperatures (13). Equilibrium retention data can, however, be obtained by extrapolation of retention vdumes to zero flow rate. Braun and Guillet (35) have developed a model of the chromatc rq>hic behavior of polymers near Tg which reproduces most features observed experimentally. The effects of the magnitude and temperature depandence of the difihision... 

If one assumes the dynamic ion-exchange model, then equation (3.26) is obtained, which is identical in form to equation (3.24), demonstrating that retention data alone cannot distinguish these two models of retention and that more detailed studies are necessary (Horvath et al., 1977b). 

When Eq. 4 is used to obtain the surface potential that has to be substituted into Eq. 6, we obtain the following expression (a parallel expression can also be obtained from Eq. 7 to model retention data as a function of the stationary-phase concentration of the HR) ... 

---