Theory Of Nonlinear Chromatography Research Articles

Precision and accuracy of the gas—solid adsorption isotherms derived by the elution-by-characteristic-points method

The influence of the fluctuations of the experimental parameters of the reproducibility of the overloaded band profiles used to determine the isotherms by the elution-by-characteristic-points (ECP) method was investigated using two new tools. A parameter measuring the difference between two similar curves, such as overloaded elution profiles or adsorption isotherms, was defined. The band profiles measured were compared with those calculated from the derived isotherm, using models from the theory of non-linear chromatography. The agreement between both profiles was defined as a distance lower than twice the average distance between two profiles measured on the same day on the same column. The degree of validity of the various assumptions made in the ECP method was assessed.

Quantitative extraction of thymine-thymine dimer from a large excess of thymine by preparative liquid chromatography

Extremely small amounts of thymine-thymine dimer can be extracted from thymine solutions using overloaded elution and shaving a narrow fraction at the front of the overloaded, later eluting thymine band. A two- or three-step procedure, involving the concentration and reinjection of the collected fraction, permits the preparation of solutions in which the ratio of the concentrations of the dimer and the monomer is close to unity compared with less than 1:25 000 in the original samples.The theory of non-linear chromatography and the semi-ideal model permits the accurate prediction of the location of the trace component band and the determination of the appropriate time to start and stop collection of the enriched fraction.

Nonlinear chromatography Recent theoretical and experimental results

The theory of nonlinear chromatography has been advanced by the incorporation of recent results obtained by the theory of partial differential equations. The system of equations of the ideal model has been solved analytically in the case of a single component for which the equilibrium isotherm between the mobile and the stationary phases is given by a Langmuir equation. A series of computer programs has been written which permits the calculation of numerical solutions of the semi-ideal model. The properties of the solutions obtained are described and discussed for a one-component system (profile of high concentration bands of a pure compound eluted by a pure solvent), several two-component systems (elution of a pure compound band by a binary mobile phase, separation of a binary mixture eluted by a pure mobile phase), and three-component systems (separation of a binary mixture eluted by a binary solvent, displacement and separation of a binary mixture). Experimental results are reported which validate the conclusions derived from the numerical integration of the model. The conclusions of the work apply to all high-performance chromatographic procedures, i.e., to those where the kinetics of mass transfer are fast enough for the mobile and stationary phases always to be near equilibrium. More specifically, the contribution from the kinetics of the retention mechanism to the mass transfer resistance must itself be negligible. This clearly excludes affinity chromatography.

Comparison between experimental and theoretical band profiles in nonlinear liquid chromatography with a pure mobile phase

The experimental profiles obtained for large size samples in normal- and reversed-phase liquid chromatography are compared to the profiles predicted by the theory of nonlinear chromatography. When the sorption isotherms of the analytes are determined accurately, the agreement between the experimental and the theoretical profiles is quantitative in all cases. When the solvent is a mixture of a strong and a weak solvent, and if a nonselective detector is used, both the competitive adsorption isotherms of the analyte and the strong solvent should be taken into account. Then a two-component model of nonlinear chromatography must be used, and the system peaks are predicted. If a nonselective detector is used, however, which gives no response for the solvent (i.e., no system peak is detected), and the strong solvent is less strongly adsorbed than the solute studied, the elution profile of a large concentration band can be predicted with a one-compound model, knowing the adsorption isotherm of the solute from the solution. The conditions under which a single-component model can be used to predict with good or excellent agreement the profiles of large concentration bands of analyte eluted with a binary mobile phase are investigated.

Contribution to the Theory of Nonlinear Chromatography

Abstract A new approach to the theory of nonlinear chromatography is presented. It applies to isotherms which are not too nonlinear, in which case it is shown that the center of gravity of the peak moves at a relative velocity equal to 1/√2 of the velocity of peak maximum. Equations relating peak retention time, asymmetry, and peak shape in terms of the nonlinearity constant β, plate number N, and base capacity ratio k o are derived. The derived equations are checked by comparing them with the exact answers obtained from the numerical solution of the differential equations of the plate model applied to the nonlinear isotherm. The deviations are found to be small. It is also demonstrated that for slightly nonlinear isotherms, the resulting peak shapes are asymmetric Poisson distributions with asymmetries which can be calculated from the above-mentioned parameters.