Retention modeling electrostatic models

Ng, K.L., Pauli, B., Haddad, P.R., and Tanaka, K., Retention modeling of electrostatic and adsorption effects of aliphatic and aromatic carboxylic acids in ion-exclusion chromatography, /. Chromatogr. A, 850, 17, 1999. 

As noted, the retention of a polypeptide or protein with HP-IEX sorbents primarily arises from electrostatic interactions between the ionized surface of the polypeptide or protein and the charged surface of the HPLC sorbent. Various theoretical models based on empirical relationships or thermodynamic considerations have been used to describe polypeptide and protein retention, and the involvement of the different ions, in HP-IEC under isocratic and gradient elution conditions (cf. Refs.6,19 33 40,78-90). Over a limited range of ionic strength conditions, the following empirical dependencies derived from the stoichiometric retention model can be used to describe the isocratic and gradient elution relationships between the capacity factor In and the corresponding salt concentration [C,] or the median capacity factor In k ex, and the median salt concentration [C,] of a polypeptide or protein solute, namely,... 

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 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. 

Bartha, A. and Stahlbeig, J. Electrostatic retention model of reversed-phase ion-pair chromatography. J. Chmmatogr. A. 1994, 668, 255-284. 

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]. 

J. Stahlberg, Electrostatic retention model for ion-exchange chromatography, Anal. Chem. 66 (1994), 440-449. 

Figure 2 A schematic representation of the electrostatic potential as a function of the distance from the surface according to the Stern-Gouy-Chapman model. (Reprinted with permission from Stahiberg J (1999) Retention models for ions in chromatography (review). Journal of Chromatography A 855 3 Elsevier.)...

Several theoretical models, such as the ion-pair model [342,360,361,363,380], the dyneuaic ion-exchange model [342,362,363,375] and the electrostatic model [342,369,381-386] have been proposed to describe retention in reversed-phase IPC. The electrostatic model is the most versatile and enjoys the most support but is mathematically complex euid not very intuitive. The ion-pair model emd dynamic ion-exchange model are easier to manipulate and more instructive but are restricted to a narrow range of experimental conditions for trtilch they might reasonably be applied. The ion-pair model assumes that an ion pair is formed in the mobile phase prior to the sorption of the ion-pair complex into the stationary phase. The solute capacity factor is governed by the equilibrium constants for ion-pair formation in the mobile phase, extraction of the ion-pair complex into the stationary phase, and the dissociation of th p ion-pair complex in the... 

Figure 7.28b shows that membrane retention is very systematically increased for almost all of the weak bases. This is a general pattern for bases with any of the negatively charged membrane models, and is probably best explained by the increased electrostatic attractions between the drugs and the membranes. Still, all retentions are below 50%, due to the offsetting sink condition created in the acceptor wells. 

For acids, the membrane retention actually increases in the case of egg lecithin, compared to soy lecithin. This may be due to decreased repulsions between the negatively charged sample and negatively charged phospholipid, allowing H-bond-ing and hydrophobic forces to more fully realize in the less negatively charged egg lecithin membranes. The neutral molecules display about the same transport properties in soy and egg lecithin, in line with the absence of direct electrostatic effects. These differences between egg and soy lecithins make soy lecithin the preferred basis for further model development. 

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