Bingchang Lin

Study of the representation of competitive isotherms and of the intersection between adsorption isotherms

Abstract Theoretical investigations of the separation of the components of a mixture by preparative liquid chromatography require a knowledge of the competitive equilibrium isotherms of the components of the mixture between the two phases of the chromatographic system. In many instances the set of competitive Langmuir equations provide a satisfactory model. When the competitive isotherms of the two components of a binary mixture intersect each other, however, the Langmuir model becomes unsuitable. This model postulates constant selectivity for the equilibrium between the two phases of a chromatographic system. A modified Langmuir model is proposed, using the ratio between two second-degree polynomials. This model is supported by general results from statistical mechanics. It accounts well for some experimental data that could not be explained in terms of the Langmuir isotherm.

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.

Influence of calculation errors in the numerical simulation of chromatographic elution band profiles using an ideal or semi-ideal model

Abstract The theoretical models of chromatography, whether they assume or not quasi-equilibrium between the phases of the chromatographic system, lead to a set of partial differential equations that cannot be integrated but must be solved by numerical calculations. This procedure leads to computational errors. An analysis of the origin and importance of these errors is presented. A comparison is made between the errors introduced by different calculation procedures (mainly the characteristic and the Lax-Wendroff methods). The concentration dependence of the artificial diffusion introduced by the characteristic algorithm is discussed.

Numerical Simulation of Chromatographic Band Profiles at Large Concentrations: Length of Space Increment and Height Equivalent to a Theoretical Plate

Abstract It is shown that the numerical integration of the system of partial differential equations accounting for the idea model of chromatography provides the band profiles observed with a column of finite efficiency if the space length increment of the integration is chosen equal to the column HETP for a zero sample size and the time increment is then chosen so that the Courant number is 2.

Study of the influence of axial dispersion on the band profile in nonlinear chromatography using the Lax-Wendroff method

Abstract A comparison is made between the results obtained with the Lax-Wendroff and the characteristic algorithms for the integration of the system of partial differential equations of chromatography. The influence of the diffusion coefficient on the elution profiles is determined in the linear and the nonlinear cases by using two different sets of boundary conditions, and the results are compared. A new phenomenon is predicted in the nonlinear case, which has no equivalent in the linear case; the regressive behavior of the retention time of the band maximum when the diffusion coefficient increases from values near 0 to very high values. On the other hand, it is observed that the elution profiles predicted by the Lax-Wendroff method are relatively independent of the values of the space and time increment chosen for the calculation, the opposite of what has been reported with the characteristic algorithm. This will provide a suitable procedure for the numerical calculation of solutions of kinetic models.

Shock layer analysis for a single-component in preparative elution chromatography

The onset of the nonlinear behavior of band profiles in elution chromatography is investigated by studying the profile of the shock layer caused by a finite mass transfer resistance in the absence of axial dispersion for a single component. A closed-form analytical expression of the shock layer is obtained for a parabolic isotherm. This solution depends on a dimensionless number which may be used to characterize the degree of nonlinear behavior of the band profiles and to select the model most appropriate for their accurate description. The profiles resulting from this solution are compared with those obtained by numerical calculations under different conditions to assess the influence of the assumptions made. The differences observed illustrate the sensitivity of the elution profiles to small changes in the equilibrium isotherm.

Perturbation analysis of the influence of the isotherm coupling factor on the resolution between two compounds in chromatography

Abstract The influence of the coupling factor between the adsorption isotherms of the two components of a binary mixture on the elution profiles of their bands in liquid chromatography, on their retention times and on the resolution between these bands is discussed using a perturbation approach.