Retention modeling stoichiometric models

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 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 obtain a simple interpretation of the experimental findings in IIC, theoretical chromatographers first adopted a stoichiometric strategy that pioneered this separation mode. Unfortunately, the reaction schemes of stoichiometric models in both the mobile phase (ion pair model) and stationary phase (dynamic ion exchange model) lack a firm foundation in physical chemistry because they are not able to account for the stationary-phase modification that results from the addition of the HR to the eluent, and they fail to properly describe experimental results, as pointed out by Bidlingmeyer et al. " Key insights on these retention models were also provided by... 

Research activities on emissions for fluid bed coal combustors are also more and more concerned with the reduction of NO emissions by means of staged (sub-stoichiometric) combustion. However, and NO emissions are found to be strongly interrelated in general emissions increase with a lower primary air ratio (26), while NO emissions increase with a higher sorbent hold-up and a lower sorbent fractional sulfation (27). So it is also necessary to incorporate the oxygen influence in such a sulfur retention model. 

Drager, R. R. and Regnier, F. E., Application of the stoichiometric displacement model of retention to anion-exchange chromatography of nucleic acids,... 

The general solution of this equation was obtained and applied for a special case where/(c) is defined according to the stoichiometric model of protein retention as ... 

A stoichiometric model can conveniently be invoked to explain the ion-exchange retention process [43 6]. As discussed in detail in these cited papers on ion-exchange theory, useful information about the involved ion-exchange process can be deduced from plots of log k vs. the log of the counterion concentration [X], which commonly show linear dependencies according to the stoichiometric displacement model (Equation 1.1)... 

Influence of Acid Additives on Retention Characteristics of 2-Methoxy-2-(1-Naphthyl)Propionic Acid on a 0-9-(tert-ButylcarbamoyOQuinine CSP as Assessed by the Characteristic Parameters of the Stoichiometric Displacement Model (Slopes and Interc ... 

According to this theoretical treatment, the slope of the plots of In k versus the solvent concentration, [3]m, can be employed to derive the contact area associated with the peptide-nonpolar ligand interaction. The retention and elution of a peptide in RPC can then be treated as a series of microequilibriums between the different components of the system, as represented by eq 6. The stoichiometric solvent displacement model addresses a set of considerations analogous to that of the preferential interaction model, but from a different empirical perspective. Thus, the affinity of the organic solvent for the free peptide P, in the mobile phase can be represented as follows ... 

This influence of the valence and activity coefficients of the displacer salt on the retention behavior of polypeptides and proteins can be anticipated from theoretical treatments of the ion-exchange chromatographic separation of proteins. According to the nonmechanistic stoichiometric model of protein retention behavior in HP-IEX80,82-85 the influence of a divalent cation salt such as CaCl2 on the retention behavior of a protein in HP-IEC can be evaluated in terms of the following relationships ... 

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 ... 

Cantwell and co-workers submitted the second genuine electrostatic model the theory is reviewed in Reference 29 and described as a surface adsorption, diffuse layer ion exchange double layer model. The description of the electrical double layer adopted the Stem-Gouy-Chapman (SGC) version of the theory [30]. The role of the diffuse part of the double layer in enhancing retention was emphasized by assigning a stoichiometric constant for the exchange of the solute ion between the bulk of the mobile phase and the diffuse layer. However, the impact of the diffuse layer on organic ion retention was danonstrated to be residual [19],... 

Starting from this idea, Cecchi and co-workers snbmitted an extended thermodynamic theoretical treatment of the retention behavior that covers and comprehends both stoichiometric and gennine electrostatic models bnt surpasses them [20,26,27,50-64]. The subject is not difficnlt and a tutorial description is given below. More detailed and comprehensive descriptions of the model can be found elsewhere [20,63],... 

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]. 

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). 

The basic principles of ion exchange have been discussed by Walton [78]. However, this discussion was mainly limited to the case of small inorganic ions. For the separation of biomolecules, e stoichiometric displacement model (SDM, next subsection) is of particular interest. This model is based on the assumption that ion exchange is the only mechanism of retention of the components studied and that the ion-exchange process can be modeled as a stoichiometric "reaction" described by the mass action principle. 

General theories for the retention of small ions are based on either stoichiometric or electrostatic double layer models [159,160,329,428,441,443,444]. Stoichiometric models provide a simple picture of the retention process with reasonable predictive... 

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