Mobile-phase concentration

FIGURE 2.15 Concentration profiles of Sphenyl-l-pentanol, obtained on Whatman No. 3 chromatography paper with -octane as mobile phase. Concentrations of the analyte solutions in 2-propanol were (a) 0.5, (b) 1.0, (c) 1.5, and (d) 2.0 mol 1" [14,25]. 

Average Retention Times from Isocratic Separations at Five Mobile Phase Concentrations... 

Note that this kinetic equation is rather similar to Equation 10.15. The major difference between Equations 10.15 and 10.19 is that the general rate and the lumped pore models assume that adsorption takes place from the stagnant mobile phase within the pores, while the lumped kinetic model assumes that the mobile phase concentration is the same in the pores and between the particles. 

When the concentration of the injected sample is not infinitesimally small but finite, the migration velocity of a given concentration zone, u, is not constant but is a function of the mobile phase concentration, C [1] ... 

The assumption of linear chromatography fails in most preparative applications. At high concentrations, the molecules of the various components of the feed and the mobile phase compete for the adsorption on an adsorbent surface with finite capacity. The problem of relating the stationary phase concentration of a component to the mobile phase concentration of the entire component in mobile phase is complex. In most cases, however, it suffices to take in consideration only a few other species to calculate the concentration of one of the components in the stationary phase at equilibrium. In order to model nonlinear chromatography, one needs physically realistic model isotherm equations for the adsorption from dilute solutions. 

Equilibrium The physical process (reaction) of adsorption or ion exchange is considered to be so fast relative to diffusion steps that in and near the solid particles, a local equilibrium exists. Then, the so-called adsorption isotherm of the form q = f(Ce) relates the stationary and mobile-phase concentrations at equilibrium. The surface equilibrium relationship between the solute in solution and on the solid surface can be described by simple analytical equations (see Section 4.1.4). The material balance, rate, and equilibrium equations should be solved simultaneously using the appropriate initial and boundary conditions. This system consists of four equations and four unknown parameters (C, q, q, and Ce). 

This assumption conveniently permits multicomponent cases to be treated as composites of single-component cases the behavior of each species can be calculated separately and the results be superimposed on one another. The assumption is quite acceptable for analytical chromatography at low concentrations and low degree of sorbent loading but becomes untenable at high concentrations or in ion exchange with high conversion, because the solute species then affect one another s sorption behavior as they compete for the limited number of available sorption sites. In equilibrium, the stationary-phase concentration of species i then depends on the mobile-phase concentrations of all species present rather than only on that of i ... 

The following conventions as to nomenclature will be adopted. The exchanging sorbable species are numbered 1,2,. . . , n in the sequence of decreasing affinity for the stationary phase. The number of species is n. Stationary- and mobile-phase concentrations t/i and Xi are so normalized that... 

C is the mobile phase concentration in equilibrium with the stationary phase concentration q k is the rate coefficient which is a lumped mass-transfer coefficient... 

In the case of a single-component system, the adsorption isotherm gives the concentration in the stationary phase C (in moles per liter of bead or grams per liter of bead) versus the mobile phase concentration C when equilibrium is reached (in the same units as for C), at a given temperature. 

Comment on the relationship between k and N at the various mobile phase concentrations. Is this similar to the relationship observed in Chapter 9, Experiment 2 ... 

The adsorption isotherm of SDS on a C18 stationary phase was also measured by determining the amount of surfactant adsorbed onto the stationary phase from frontal chromatography experiments ( 5 ). Figure 1 is a log-log plot of surface concentration vs. mobile phase concentration of SDS with a standard mobile phase of n-propanol water (3 97)(vida infra). The maximum concentration of surfactant adsorbed on the stationary phase occurs at the mobile phase concentration of ca. 10 2 M and gives a surface concentration of ca. 

Most separations are performed using columns of resin and an elution procedure. The sample is introduced as a small band at the top of the column from where the various components are moved down the column at a rate depending on their selectivity coefficients. Sorption isotherms are approximately linear in dilute solutions so that elution peaks are symmetrical. Tailing can be expected at high concentrations as the isotherms curve towards the mobile phase concentration axis (p. 77). 

When the analyte mobile phase concentration is small, only a negligible fraction of the HR is in the form of a complex, hence its concentration [H] in the eluent can be considered invariant [3]. Both the pairing ion isotherm and the surface potential are unchanged by the presence of the sample ion [31,33]. In this case [20], analyte retention as a function of the mobile and stationary phase concentrations of the HR can be described, respectively, by the following expressions ... 

Cecchi, T., Pucciarelli, F., and Passamonti, P. Ion interaction chromatography of zwitterions fractional charge approach to model the inflnence of the mobile phase concentration of the ion-interaction reagent. Analyst 2004, 129, 1037-1042. 

FIGURE 8.1 Family of model IPR adsorption isotherms at different mobile phase concentrations of organic modifier. 

FIGURE 8.2 Theoretical dependence of retention factor of a model analyte oppositely charged to the IPR, as a fnnction of the mobile phase concentration of the IPR, at increasing elnent percentages of organic modifier. 

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