Analyte retention modeling

Figure 4.17 General phenonenaloglcal retention model for a solute that participates in a secondary chemical equilibrium in liquid chromatography. A - solute, X - equilibrant, AX analyte-equilibrant coeplex, Kjq - secondary chemical equilibrium constant, and and are the primary distribution constants for A and AX, respectively, between the mobile and stationary phases.

Yamamoto, A., Hayakawa, K., Matsunaga, A., Mizukami, E., and Miyazaki, M., Retention model of multiple eluent ion chromatography. A priori estimations of analyte capacity factor and peak intensity /. Chromatogr., 627,17,1992. 

A simple extension of the retention model discussed so far is to include the possibility for a specific interaction between the analyte and the pairing ion. By using a similar reasoning as for the electrochemical potential shown above, it is easily shown that the retention factor follows the relation... 

Further research on mixed IL stationary phases will allow for the chroma-tographer to tune the stationary phase composition to provide enhanced control over the separation selectivity and analyte elution order, particularly for complicated analyte mixtures. The development of models that correlate analyte retention with the IL composition will prove useful for multidimensional GC. Micellar GC utilizing IL solvents presents an exciting class of highly selective stationary phases. The development of CSPs will likely mature as more chiral ILs are synthesized and evaluated from the chiral pool. 

Stoichiometric models forged the flrstrationalization of the retention patterns of IPC. AU stoichiometric models are pictorial and do not need sophisticated mathematical descriptions of analyte retention. What is the link between ion-pairing and chromatography ... 

However, it was qnickly realized during the introduction of this technique that an IPR having a hydrophobic region to interact with the stationary phase was prone to adsorb onto the reversed phase chromatographic bed because (1) the fuU impact of the reagent was felt after many void volumes of the column were displaced, (2) if the analyte and the IPR carried the same charge status, analyte retention decreased upon introduction of the IPR in the eluent, and (3) when the presence of IPRs in the eluent was discontinued, the previous eolumn retentive behavior was not restored promptly. The IPR adsorption could be measured and modeled via the adsorption isotherm [6]. 

This ion interaction retention model of IPC emphasized the role played by the electrical double layer in enhancing analyte retention even if retention modeling was only qualitatively attempted. It was soon realized that the analyte transfer through an electrified interface could not be properly described without dealing with electrochemical potentials. An important drawback shared by all stoichiometric models was neglecting the establishment of the stationary phase electrostatic potential. It is important to note that not even the most recent stoichiometric comprehensive models for both classical [17] and neoteric [18] IPRs can give a true description of the retention mechanism because stoichiometric constants are not actually constant in the presence of a stationary phase-bulk eluent electrified interface [19,20], These observations led to the development of non-stoichiometric models of IPC. Since stoichiometric models are not well founded in physical chemistry, in the interest of brevity they will not be described in more depth. 

The retention model by Cecchi and co-workers also quantitatively faced the prediction of the retention behavior of neutral and zwitterionic analytes in IPC. According to the electrostatic models, at odds with clear experimental data [1,50,52,53], the retention of a neutral solute is not dependent on the presence and concentration of a charged IPR in a chromatographic system. Equation 3.23 is very comprehensive if Ze is zero [50], it simplifies since ion-pairing does not occur (C2= C3 = 0). Adsorption competition models the retention patterns of neutral analytes in IPC and the slight retention decreases of neutral analytes with increasing HR concentration may be quantitatively explained [50,53]. 

The model was recently tested to determine whether it was able to model analyte retention in the presence of novel and unusual IPRs (see Chapter 7) such as chaotro-pic salts and ionic liquids. Chaotropes that break the water structure around them and lipophilic ions (classical IPRs and also ionic liquids) that produce cages around their alkyl chains, thereby disturbing the ordinary water structure, are both inclined to hydrophobic ion-pairing since both are scarcely hydrated. This explains the success of the theory, that is predictive in its own right, when neoteric IPRs are used [64]. Recently a stoichiometric model (vide supra) was put forward to describe retention of analytes in the presence of chaotropic IPRs in eluents [18] but its description of the system is not adequate [64]. 

The model, in the absence of IPR, from an algebraic view, demonstrates the well known relationships in RP-HPLC of the influence of the organic modifier or the ionic strength of the eluent on analyte retention. 

The theory is evidence based it can explain (1) the presence of different theoretical curves when k is plotted as a function of the stationary phase concentrations for different IPRs (2) the influence of IPR concentration on the ratio of the retention of two different analytes and (3) the influence of analyte nature on the klk ratio if the experimental conditions are the same. These experimental behaviors cannot be explained by other genuine electrostatic retention models because they arise from complex formation. The present model was the first to take into account at a thermodynamic level these recently definitively demonstrated equilibria in the mobile phase. 

Bidlingmeyer, B.A. Separation of ionic compounds by reversed-phase liquid chromatography an update of ion-pairing techniques. J. Chmmatogr. 1980,18, 525-539. Sarzanini, C. et al.. Retention model for anionic, neutral and cationic analytes in reversed-phase ion interaction chromatography. AnaL Chem. 1996, 68,4494-4500. 

The first effort to use LSERs in IPC relied on a retention equation based on a mixture of stoichiometric and electrostatic models. Several approximations were made [1-3]. First, ion-pairing in the eluent was neglected, but this is at variance with clear qualitative and quantitative experimental results [4-13]. In Chapter 3 (Section 3.1.1), the detrimental consequences of this assumption were clarified and danonstiated that extensive experimental evidence cannot be rationalized if pairing interactions in the eluent are not taken into account. Furthermore, in the modeling of A as a function of the analyte nature, the presence of the IPR in the eluent was assumed not to influence the retention of neutral analytes. This assumption is only occasionally true [14,15] and the extended thermodynamic retention model of IPC suggests the quantitative relationship between neutral analytes retention and IPC concentration in the eluent [16]. 

To deconvolve the silanophilic effect from the electrostatic repulsion, a nonsilica-based stationary phase may be suitable in research work. On a polystyrene-divinylbenzene reversed phase column, an ethylammonium formate RTIL was not able to produce effective ion-pairing interactions with acidic and basic model compounds, and baseline resolution was only obtained in the presence of classical IPRs (tetrabutylammonium and dodecylsulfate ions, respectively). However, the RTIL was able to mimic the methanol role [123,126]. In summary, IL cations reduce positively charged analyte retention since they (1) screen free silanols and (2) electrify the stationary phase with a positive surface charge that is repulsive for cationic analytes. The hydrophobic character of IL anions is responsible for possible analyte retention increases via ion-pairing. 

Equation 10.12 is algebraically correspondent [15] to the final relationship that describes analyte retention under IPC conditions (Equation 3.21). It upgrades the parallel stoichiometric equation of the model by Kazakevich and co-workers [16] that is inherently inadequate because it cannot predict the decrease of retention for analytes similarly charged to the chaotropic reagent and the electrostatic tuning of the retention of the unpaired analyte in the presence of the electrified stationary phase. It also upgrades electrostatic models [17,18] that disregard the role played by the ion-pair complex (final term in Equation 10.12). 

Further development of the mathematical description of the chromatographic process requires the definition of the analyte distribution function y/(c), or essentially the introduction of the retention model (or mechanism). 

Formation of a thick adsorbed layer of acetonitrile on the surface of reversed-phase adsorbent allows the introduction of a two-stage model of the analyte retention process. The first process is the partitioning of the analyte molecules from the bulk eluent into the adsorbed acetonitrile layer, and the second process is the analyte adsorption on the surface of the packing material. 

As it was discussed in Section 2.7, if the model of the analyte behavior in the column is defined, then this model can be applied in the mass-balance equation. The resulting solution of the mass-balance equation is the expression for the analyte retention behavior, and it is only valid in the frame of the selected model. 

Modeling of the retention of aniline (pT a = 4.6) with derived equation (2-83) had shown that with the increase of the temperature at mobile-phase pH = 4, this will lead to the increase of the model basic analyte retention, whereas at pH above 6 with the increase of the column temperature, this will lead to a corresponding decrease in the model basic analyte retention (Figure 2-17). 

Different models of the retention in these complex systems do not allow for accurate prediction of the analyte retention, but they assist in the understanding of the processes governing analyte migration through the column and also help in the selection of starting conditions and intelligent optimization of a particular separation. 

The thick acetonitrile layer adsorbed on the bonded phase surface acts as a pseudo-stationary phase, thus making retention in acetonitrUe/water systems a superposition of two processes partitioning into the acetonitrile layer and adsorption on the surface of the bonded phase. Based on the model described in reference 166, analyte retention could be represented in the following form ... 

Equation (10-1) is based on the assumption of simple additivity of all interactions and a competitive nature of analyte/eluent interactions with the stationary phase. The paradox is that these assumptions are usually acceptable only as a first approximation, and their application in HPLC sometimes allows the description and prediction of the analyte retention versus the variation in elution composition or temperature. For most demanding separations where discrimination of related components is necessary, the accuracy of such prediction is not acceptable. It is obvious from the exponential nature of equation (10-1) that any minor errors in the estimation of interaction energy, or simple underestimation of mutual influence of molecular fragments (neglected in this model), will generate significant deviation from predicted retention factors. 

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]. 

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