Retention theory

Chromatographic methods are classified according to the nature of the mobile and stationary phases used. The terms gas chromatography (GC) and Uquid chromatography (LC) refer to the nature of the mobile phase. 

Schematic illustration of elution chromatography. Three solutes are separating depending on the affinity to stationary phase at different times. 

Chromatogram obtained by elution chromatography of a mixture of three solutes. The retention time tR is the time taken by a solute to pass through the column. tM is the mobile-phase holdup and is measured as the retention time of a non-sorbed solute, is the adjusted retention time, the total time spent by the solute in the stationary phase. 

The R can also be defined as the fraction of the total number of molecules that are in the mobile phase at equilibrium and is given by  

Following the same nomenclature as in adsorption (since the fundamental phenomena for chromatography) is the same as adsorption, if Cs is the concentration of solute in stationary phase and C is the concentration in the mobile phase. Then the distribution coefficient between the two phases K = CsjC can be given by  

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Existing SEC retention theories have been independently developed for each of the molecular-shape models shown in Figure 1. The deep hollow cyclin-drical pore in the figure (A, B, and C) illustrates the SEC exclusion effect on three types of solute molecules, hard-sphere, rigid-rod, and random-coil, respectively. The individual theories and their bases of commonality are now reviewed briefly. 

More rigorous treatments of retention theory start from conservation of mass over a differential length of column 5,6). They require the same assumptions as the simpler analysis presented here and lead to the same result, equation 19.8. 

Retention theory from the work of Lanin and Nikitin [55] (Equation 1.6) was adapted to describe the dependency of retention factors k) as a function of the mobile phase composition [53]. The concentration of the polar modifier is, besides the type, the primary variable for the optimization of the separation and can be described by competitive adsorption reactions of solute (i.e., sorbate) and polar modifier for which the following relationship can be applied (Equation 1.6)... 

This equation has three important consequences for the retention theory of ions ... 

In conclusion, it is easier to develop useful theories for the retention caused by the Coulombic interaction than for the other types of intermolecular interactions. Furthermore, the strength of the Coulombic interaction implies that it usually determines the physico-chemical properties of ions. Theories based on the solution of the P-B equation with appropriate boundary conditions are, therefore, a good starting point for the retention theories of ionic solutes. 

Drawbacks of the asymmetrical design associated with the non-uniform flow velocities are being reduced with innovative channel designs and continued theoretical development [249]. Due to the different generation of the cross-flow, the theoretical description of the flows acting in A-Fl-FFF and thus the whole retention theory is more difficult. Instead of the simple Eq. (54) for S-Fl-FFF, the following relationship is obtained for the cross-flow velocity U in the x-direction ... 

Kesner et al. [36] indicated a discrepancy between the theoretical retention and experimental values for some proteins in a channel with flexible membrane walls. These deviations were probably caused by the flexible membrane walls as such effects were not observed for a channel with rigid walls [256]. Nevertheless, the experimental data of Kesner et al. [36] was in reasonable agreement with the El-FFF theory [87,263] with respect to both retention and dispersion. Deviations were attributed to an electrical field gradient in the vicinity of the membrane interface [263]. Calculation of the dependence of K on 1/E from literature data on electrophoretic mobilities and diffusion coefficients confirmed the validity of the retention theory in El-FFF. 

As hydrodynamic lift forces are as yet only very poorly understood [79], they cannot yet be incorporated into a closed retention theory. However, early studies suggest that the retention ratio R in steric-FFF can be expressed by a quite simple relationship [294] ... 

The retention theory for focusing-FFF was developed for focusing-S-FFF but can be transferred to other focusing mechanisms [72,73]. Janca and Chmelik developed this theory for several shapes of fractionation channels [74] and found that it is advantageous to form axially asymmetrical velocity profiles in channels with modulated cross-sectional permeability [83]. 

The numerous reasons which can account for various deviations from the ideal FFF retention theory were discussed in the corresponding sections. Here, additional problems are treated which can complicate FFF measurements and significantly distort the results obtained. General requirements for a successful FFF measurement include precise flow control and flow rate precise temperature measurement precise determination of t0 and tr correct relaxation procedure control of sample overloading and integrity and control of mixed normal and steric retention effects as well as wall adsorption control. Some of these complications cannot be avoided so one must correct for these effects, usually in a sem-iempirical and partially very complicated fashion. 

Detailed discussion of normal-phase chromatography process, mechanism, and retention theories, as well as types and properties of used stationary phases, is given in Chapter 5. 

Remarkable number of different names was introduced to these methods. The technique has been called soap chromatography [113], solventgenerated ion-exchange [114], ion-interaction [115], and ion-pair [116]. Researchers introduced a similar number of different theories for the description of the effect of ionic mobile-phase additives on the retention of charged analytes essentially, each specific name for this technique corresponds to its own distinct retention theory. Melander and Horvath [116] divided existing theories into two main groups stoichiometric [113,114,117-119] and nonsto-ichiometric [120-133]. 

In addition to molecular weight, thermal FFF is used to measure transport coefficients. For example, the measurement of thermodiffusion coefficients is important for obtaining compositional information on polymer blends and copolymers (see the entry Thermal FFF of Polymers and Particles). Thermal FFF is also used in fundamental studies of thermodiffusion because it is a relatively fast and accurate method for obtaining the Soret coefficient, which is used to quantify the concentration of material in a temperature gradient. However, the accuracy of Soret and thermodiffusion coefficients obtained from thermal FFF experiments depends on properly accounting for several factors that involve temperature. In order to understand the effect of temperature on transport coefficients, as well as the effect on thermal FFF calibration equations, a brief outline of retention theory is given next. 

As a concluding remark, it has to be emphasized that every acceptable retention theory must be consistent with fundamental physics, as well as describe experimental findings. The complex multiplicity of phenomena involved in an IIC system requires a complex description of the thermodynamics solutes have undergone this description is epistemologically acceptable if the model is... 

The FFF retention theory for quadrupole magnetic FFF (QMgFFF) is developed in an analogous way to that of the other FFF techniques. The magnetic force on a single particle due to its interaction with the magnetic field is given by... 

Hoyos, M. Martin, M. Retention theory of sedimentation field-flow fractionation at finite concentration. Anal. Chem. 

The study of the interfacial phenomena between the channel wall and the colloidal suspension under study in sedimentation field-flow fractionation (SdFFF) is of great significance in investigating the resolution of the SdFFF separation method and its accuracy in determining particles physicochemical quantities. The particle-wall interactions in SdFFF affect the exponential transversal distribution of the analyte and the parabolic flow profile, leading to deviations from the classical retention theory, thus influencing the accuracy of analyte quantities measured by SdFFF. Among the various particle-wall interactions, our discussion focuses on the van der Waals attractive and electrostatic repulsion forces, which play dominant roles in SdFFF surface phenomena. 

Martin, M. Deviations to classical retention theory of field-flow fractionation. J. Chromatogr. A, 1999, 831, 73-87. 

The applicability of the additive retention theory to capillary chromatography with modified adsorbents was demonstrated for the first time in paper [125]. This work used experimental data [126] on n-hep-tane retention on an alkaline treated glass capillary column, the walls of which were coated with squalane, as reported by Bruner and Carton [126]. The dependence of retention volume on the liquid phase content was shown to be linear, being in complete agreement with additive absorption-adsorption theory. 

Purnell (30) surveyed numerous gas chromatographic approaches to the study of complex equilibria and developed generalized retention theories for each kind. His classification system, which is summarized in Table 12.6, greatly simpUfies the approach to complexation reactions. 

Retention theory provides the estimate of time the solute is retained in the column (tp). A part of this time Im is required by the solute simply to pass through the mobile phase from inlet to outlet and is measured as the retention time of a non-sorbed solute as shown in Figure 9.2. The adjusted retention time time t p represents the extra retention due to repeated partitioning or distribution of the solute between... 

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