Retention equations

Describe the principle of separation involved in elution chromatography and derive the retention equation ... 

The principles of separation by elution chromatography are considered in Volume 2, Sections 19.1 and 19.2. The derivation of the retention equation is given by equations 19.1-19.8 in Section 19.2.2 of Volume 2. 

Equation 19.8 is the basic retention equation of elution chromatography. It is founded on the assumptions that the distribution isotherm, the plot of q against c at constant temperature, is linear and that equilibrium of the solute between phases is achieved instantaneously throughout the column. 

In some cases, the solution is possible in explicit form allowing direct calculations of the retention data however, for some combinations of gradient functions and retention equations iterative solntion approach is necessary, which can be applied using standard calculation software. An overview of possible solntions of Equation 5.3 for various HPLC modes and gradient profiles was pnblished earlier [4,33]. 

By appropriate choice of the type (or combination) of the organic solvent(s), selective polar dipole-dipole, proton-donor, or proton-acceptor interactions can be either enhanced or suppressed and the selectivity of separation adjusted [42]. Over a limited concentration range of methanol-water and acetonitrile-water mobile phases useful for gradient elution, semiempirical retention equation (Equation 5.7), originally introduced in thin-layer chromatography by Soczewinski and Wachtmeister [43], is used most frequently as the basis for calculations of gradient-elution data [4-11,29,30] ... 

Equation 5.10 applies in systems where the solute retention is very high in the pure nonpolar solvent. If this is not the case, another retention equation was derived [54-56]. 

In NP systems where the retention is controlled by the three-parameter retention equation (Equation 5.11), the elution volumes in normal-phase gradient-elution chromatography can be calculated using [55-57]... 

In mobile phases that are good sample solvents, the retention mechanism of high molecular compounds can be explained on the basis of conventional theory of RPC or NPC gradient elution applying for small molecnles, considering the effect of increasing size of molecules on the values of the constants a, b, ko, and m of the retention equations— Equation 5.7, 5.10, or 5.11. 

FIGURE 5.4 Effect of the gradient dwell volume, V7>. the elution volume, Vj, in reversed-phase chromatography. Solute neburon, retention equation (Equation 5.7) with parameters a=A, m = 4. Linear gradients 2.125% methanol/min (a) from 57.5% to 100% methanol in water in 20min ( i = 50) (b) from 75% to 100% methanol in water in 11.75 min (k = 10). Vg uncorrected calculated from Equation 5.8, Vg + Vg, Vg, added to Vg uncorrected, Vg corrected calculated from Equation 5.21. (A) A conventional analytical C18 column, hold-up volume y ,= ImL flowrate l.OmL/min. (B) A microbore analytical C18 column, hold-up volume y = 0.1mL flow rate 0.1 mL/min. 

The classical FEE retention equation (see Equation 12.11) does not apply to ThEEE since relevant physicochemical parameters—affecting both flow profile and analyte concentration distribution in the channel cross section—are temperature dependent and thus not constant in the channel cross-sectional area. Inside the channel, the flow of solvent carrier follows a distorted, parabolic flow profile because of the changing values of the carrier properties along the channel thickness (density, viscosity, and thermal conductivity). Under these conditions, the concentration profile differs from the exponential profile since the velocity profile is strongly distorted with respect to the parabolic profile. By taking into account these effects, the ThEEE retention equation (see Equation 12.11) becomes ... 

Optically active (+)-(R) methylpropylphenyl phosphine oxide 39 was reduced using the Homer method, and then the produced phosphine was oxidized by adding 1.2 molar equivalent of BTSP at room temperature. (—)-(S) methylpropylphenyl phosphine oxide 40 was obtained with 95% stereospecificity. Since the reduction step is known to proceed with inversion of the configuration at the phosphorus center , oxidation occurs with retention (equation 63). 

It can be clearly seen from equation (9) that the expression for the retention volume of a solute, although generally correct, is grossly over simplified if accurate measurements of retention volumes are required Some of the stationary phase may not be chromatographically available and not all the pore contents have the same composition as the mobile phase and, therefore, being static, can act as a second stationary phase. This situation is akin to the original reverse phase system of Martin and Synge where a dispersive solvent was absorbed Into the pores of support to provide a liquid/liquid system. As a consequence a more accurate form of the retention equation would be,... 

Partitioning of the solutes between the two liquid phases is the only chemical mechanism responsible for solute separation. The retention equation is... 

The retention equation allows us to understand the first major difference between the CCC solute retention and the retention obtained with any other chromatographic technique. Usually, in chromatography, the same solute mixture separated on the same column and using the same mobile phase produces the same chromatogram. If it is not the case, it is a sign of column wearing or problems in the hardware (pump, detector, or injector). 

Inversion or retention Equation 12-5 pictures the reaction of a glycoside (such as a glucose unit at... 

The formation of the alkoxide ligand occurred with 50% retention (R ) and 50% racemization (R). This finding was suggested to occur by a two-step reaction, the first step involving formation of a reactive alkyl peroxide intermediate by a radical process involving racemization, followed by a bimolecular reaction, proceeding with retention (equations 36 and 37). 

A more convenient form of the earlier retention equation is... 

The reaction of 3-ketoacids with allyl carboxylates is also believed to proceed via a palladium enolate intermediate.126 Less than complete stereospecificity is also observed in these reactions (equation 163). Interestingly, the bicyclic lactone substrate employed to ascertain the stereointegrity of this reaction, in addition to being incapable of any syn-anti isomerization, cannot epimerize the starting material by car-boxylate attack at the metal. The observed stereochemical leakage could be due to epimerization of the intermediate allyl complex (equation 164) or reductive elimination of an allylpalladium enolate (retention) (equation 165). 

The palladium-catalyzed reaction of aryl- and vinyl-tin reagents with stereochemically defined allyl chlorides proceeds with overall retention of configuration, indicating that the second step, entailing interaction of the iT-allylpalladium complex and the organotin, proceeds by transmetallation and reductive elimination (attack at Pd, retention) (equations 166 and 167).142145 Comparable results were obtained with cyclic vinyl epoxides and aryltins.143... 

For the density-only retention surface, retention data were collected at 4 different densities (0.1,0.2,0.3 and 0.4 g/mL) at a temperature of 80°C. Data were fit to equation 2 via nonlinear regression, and the resulting retention equations for each solute could be used to calculate the response surface. Although the goodness of fit was difficult to estimate since there was only one degree of freedom (and it is easy for R2 values to exceed 0.999 under these conditions), the good agreement of the predicted and measured retention values at the optimum (vide infra) provided additional support for the accuracy of equation 2. 

The reaction has been carried out on an optically active a-methoxy organolead reagent and shown to proceed with retention (equation II). 

The reaction of organogermylmetal compounds with organic halides is an effective route to form germanium-carbon bonds. The stereochemistry of these reactions was established as predominantly retention (equation 81)129,130 131 - see Section V.C.2. 

The derivation of these different retention equations is important in several respects. First, they allow for calculation of micelle-solute binding constants, parameters which are important in many areas of micellar kinetics or chemistry. There have been several reports in the literature demonstrating this chromatographic approach for determination of micelle - solute binding constants (1,8,104,105). More importantly, they allow for prediction of retention behavior as a function of surfactant concentration (or of pH at constant micelle concentration), provided that the micelle - solute binding constant (or solute ionization constant) is known (which can be determined spectroscopically or from kinetic studies) (1,96,102). Consequently, the theory allows the chromatographer to determine the optimum conditions required for a desired separation. 

One form of the psuedophase retention equation is shown below (14). It relates LC retention (as the capacity factor, k ) to the binding of a solute to cyclodextrin, K., and to the concentration of cyclodextrin in the mobile phase, [CD]. 

The terms in the denominator of the right side of Equation 1 include 0, the phase ratio A, stationary phase adsorption site and K, the association constant of a solute to the stationary phase binding site. The binding constant, K., can be evaluated graphically (by plotting 1/k versus [CD]) or by linear least squares. When complex equilibria are involved, Equation 1 deviates from linearity. In cases where two cyclodextrin molecules bind to a simple solute the correct pseudophase retention equation is (jl) ... 

S-FFF has been compared with analytical ultracentrifugation (AUC) with respect to the fractionation of a 10-component latex standard mixture with narrow particle size distribution, known diameters (67-1220 nm) and concentration [ 127]. With an analytical ultracentrifuge, the particle sizes as well as their quantities could be accurately determined in a single experiment whereas in S-FFF deviations from the ideal retention behavior were found for particles >500 nm resulting in smaller particle size determination in the normal as well as in the programmed operation. It was concluded that, without a modified retention equation which accounts for hydrodynamic lift forces and steric exclusion effects, S-FFF cannot successfully be used for the size characterization of samples in that size range. 

---