Retention data approach

The description of the degree of retention data correlation is more complicated than it appears. For example, the 2D retention maps cannot be characterized by a simple correlation coefficient (Slonecker et al., 1996) since it fails to describe the datasets with apparent clustering (Fig. 12.2f). Several mathematical approaches have been developed to define the data spread in 2D separation space (Gray et al., 2002 Liu et al., 1995 Slonecker et al., 1996), but they are nonintuitive, complex, and use multiple descriptors to define the degree of orthogonality. 

The differential equations (Equation 5.2a or b) can be solved by integration after introducing the actual dependence of k on the time, t (or on the volume of the eluate, V, which has passed through the column) from the start of the gradient until the elution of the band maximum. Freiling [26] and Drake [27] were the first to introduce this approach, which has been used later to derive equations allowing calculations of gradient retention data in various LC modes [2,4-7,28-30]. 

In some cases, the solution is possible in explicit form allowing direct calculations of the retention data however, for some combinations of gradient functions and retention equations iterative solntion approach is necessary, which can be applied using standard calculation software. An overview of possible solntions of Equation 5.3 for various HPLC modes and gradient profiles was pnblished earlier [4,33]. 

Qualitative analysis by gas chromatography (GC) in the classical sense involves the comparison of retention data of an unknown sample with that of a known sample. The alternate approach involves combination and comparison of gas chromatographic data with data from other instrumental and chemical methods. 

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). 

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 ... 

There is an approach in QSRR in which principal components extracted from analysis of large tables of structural descriptors of analytes are regressed against the retention data in a multiple regression, i.e., principal component regression (PCR). Also, the partial least square (PLS) approach with cross-validation 29 finds application in QSRR. Recommendations for reporting the results of PC A have been published 130). 

Ounnar and co-workers [31,32] widely apply in their QSRR studies the approach called correspondence factor analysis (CFA). CFA is mathematically related to PCA, differing in the preprocessing and scaling of the data. Those authors often succeeded in assigning definite physical sense to abstract factors, e.g., they identified the Hammett constants of substituents in meta and para positions of 72 substituted /V-benzylideneanilines (NBA) in determining the first factorial axis resulting from the CFA analysis of retention data of NBA in diverse normal-phase HPLC systems. 

The driving force in chromatography for the. separation of an analyte is the equilibrium between the stationary and the mobile phases. As it was di.scus.sed in Chapter 11 in more detail, the chromatographic equilibrium can be related to the chemical potential of the compound. Unfortunately, the relationship between retention parameters and the quantities related to the chemical structure cannot be solved in. strictly thermodynamic terms. Therefore, the extra-thermodynamic approach is applied to reveal the relationships. During chromatography we do not achieve a proper equilibrium, the separation is still a result of the difference of equilibrium constants for the compounds in the stationaiy and the mobile phases. The.se equilibrium con.stants can be related to measured retention data as was discussed in the previous chapter. So whenever our chromatographic system (the stationary and the mobile phase) can be considered as two immiscible phases the retention data (equilibrium data) will provide a partition coefficient. 

In Eq. 11, Cl and C4 are the already discussed parameters, whereas ca is related to the molecular dipole the higher it is, the stronger is the retention increase on HR addition. A parallel expression can also be obtained from Eq. 7 to model retention data as a function of the stationary-phase concentration of the IIR. A fractional charge approach to the lie of zwitterions was also recently put forward. ... 

An alternative approach to that described above is a direct use of the retention data to calculate the adsorption energy distribution [138-146]. This approach was initiated in 1974 by Rudzinski et al. [138], who showed that the energy distribution function can be expressed as a series, which contains derivatives of the retention volume with respect to the equilibrium pressure. According to this formulation, the retention volume plotted as a function of the adsorption energy is the first-order approximation of the energy distribution. However, first derivative of the retention volume is the second-order approximation of this distribution. This approach was later refined and used to calculate energy distributions for different porous solids [143]. 

The approach is to measure retention times of metal cations on columns containing low-capacity resins with eluents containing perchloric acid or various perchlorate salt.s. The perchlorate anion is used to eliminate any possible complexing of a metal ion by the eluent anion. Retention factors (k) are calculated from the retention data. 

The most commonly followed approach for calculating retention indices in the column, in order to allow retention data comparison between laboratories (with other GCxGC results or with reference IDGC data), is to map the retention scale of the column using reference compounds much as has been described in the previous paragraph for one-dimensional RI or LRI. Since elution in the second column is very fast, its operation can be considered to be isothermal, and then Rl values are more appropriate. 

Type of estimated retention data. Retention times are required when the objective is to help in developing a GCxGC method, and resolution or retention patterns must be estimated for different conditions. A promising possibility consists in predicting, instead of specific retention data, parameters that allow their calculation for different columns and conditions. At the time of writing, only a simplified approach based on a solvation parameter model [32] has been presented [33]. 

Equations (12) and (IS) assume ideal conditions for gradient dution. However, several efiects can contribute errors in each of these approaches, as summarized in Table I. Guidelines are given in Table I and Re. (26) and 30) to minimize and correct for these various effects. Fbrther recommendations for minimizing other errors in the prediction of isocratic retention data from gradient runs are given u. Section n,C... 

Thagradient retention data of Parent and Wetlaufer (25) can also be used to calcuate values of K and Z. Two approaches are possible, as discussed in Section n,C [Eqs. (27) and (28) versus (24) and (25)]. Parente and Wetlaufer (25) report the numerical solution of Eqs. (27) and (28) for individual pairs of gradient runs, where only gradient time is varied. Typical results obtained in this fashion are shown in Table VI. Using the same values of Table Vl, have determined K and Z values by a different prcK dure. Equations (24) and (25) were used to obtain vrlu s of b and ko. The latter were then used as describe eariier to obtain approximate values of kt, k, c, and from which a preliminary value of Z was obtained from Eq. (5). Finally the value of Z was reduced by 0.3 units, and a value of K was calculated from Eq. (18) ... 

These two approaches to deriving K and Z from gradient retention data are equivalent. We prefer our approach because the same computer program used for deriving values of 5 and k, from reversed-phase gradient data can be used in similar fiuhion fbr ion exchange. 

A computer-assisted system for predicting retention of aromatic compounds has been investigated in reversed-phase liquid chromatography. The basic retention descriptions have been derived from the studies on quantitative structure-retention relationships. The system was constructed on a 16-bit microcomputer and then evaluated by comparing the retention data between measured and predicted values. The excellent agreement between both values were observed on an octadecyl-silioa stationsu y phase with acetonitrile and methanol aqueous mobile phase systems. This system has been modified to give us the information for optimal separation conditions in reversed-phase separation mode. The approach could also work well for any other reveraed— phase stationsury phases such as octyl, phenyl and ethyl silicas. 

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