Patrik Forssén

An improved algorithm for solving inverse problems in liquid chromatography

Competitive adsorption isotherms must be measured in order to simulate and optimize modern continuous modes of liquid chromatography, such as simulated moving bed chromatography, in situations where experimental trial-and-error approaches are too complex and expensive. An attractive method for obtaining adsorption isotherms is to solve the inverse problem, i.e., to numerically estimate adsorption isotherm parameters so that the simulated batch separation coincides with actual experimental results. The chromatographic community refers to this as the inverse method and it has many advantages over conventional methods of adsorption isotherm determination. This work examines and proposes improvements to the four basic parts of the algorithm used in the inverse method, i.e., the partial differential equation solver routine, calculation of the Jacobian of the computer-simulated elution profiles with respect to the adsorption isotherm parameters, conversion of experimental detector response into individual concentration contributions and screening between different possible adsorption isotherm models.

Theoretical and experimental study of binary perturbation peaks with focus on peculiar retention behaviour and vanishing peaks in chiral liquid chromatography

The perturbation peak theory was recently developed for acquiring binary isotherm data using the perturbation method (PM) and it was applied for some chiral systems. However, the binary plateaus of these systems were only weakly to moderately nonlinear. In this article the perturbation theory for LC, is developed for both retention times and peak areas and is verified by systematic experiments over the whole range of non-linearity. Attention is focused on non-linear effects that complicate the proper use of the PM method under moderately to strongly non-linear conditions. A serious complication was that the second perturbation peak vanished already at moderate plateau concentrations. A solution to this problem based on a firm theoretical basis and verified experimentally is presented. We also investigated a peculiar retention dependence on the binary plateau concentration, as the retentions of the two perturbation peaks of the binary plateau was compared with the single plateau peak of the more retained enantiomer.

Injection profiles in liquid chromatography. I. A fundamental investigation

This is a fundamental experimental and theoretical investigation on how the injection profile depends on important experimental parameters. The experiments revealed that the injection profile becomes more eroded with increased (i) flow rate, (ii) viscosity of the eluent, (iii) size of the solute, (iv) injection volume and (v) inner diameter of the injection loop capillary. These observations cannot be explained by a 1D-convection-diffusion equation, since it does not account for the effect of the parabolic flow and the radial diffusion on the elution profile. Therefore, the 1D model was expanded into a 2D-convection-diffusion equation with cylindrical coordinates, a model that showed a good agreement with the experimental injection profiles dependence on the experimental parameters. For a deeper understanding of the appearance of the injection profile the 2D model is excellent, but to account for injection profiles of various injection volumes and flow rates in preparative and process-chromatography using computer-optimizations, a more pragmatic approach must be developed. The result will give guidelines about how to reduce the extra-column variance caused by the injection profile. This is important both for preparative and analytical chromatography; in particular for modern analytical systems using short and narrow columns.

Adsorption behaviour of a quinidine carbamate-based chiral stationary phase: Role of the additive

In this study, we incorporate the additive properties into the theoretical model of a general preparative chromatographic system; this is normally not done and this limits a proper process optimization. As a model phase system, we used the adsorption of 9H-fluoren-9-ylmethoxycarbonyl-allylglycine (Fmoc-allylglycine) enantiomers on a quinidine carbamate-based chiral stationary phase (anion exchanger) together with a methanol-glacial acetic acid-ammonium acetate eluent. The inverse method was used to measure the competitive adsorption isotherms of both the Fmoc-allylglycine enantiomers as well as the non-detectable additive acetic acid. It was concluded that this enantioselective preparative system is well described by a non-heterogeneous adsorption model and that the loading capacity is very high. The proposed model is valid over a wide range of additive concentrations, which is important for process optimization.

Determination of adsorption isotherms in supercritical fluid chromatography

In this study we will demonstrate the potential of modern integrated commercial analytical SFC-systems for rapid and reliable acquisition of thermodynamic data. This will be done by transferring the following adsorption isotherm determination methods from liquid chromatography (LC) to supercritical fluid chromatography (SFC): Elution by Characteristic Points (ECP), the Retention Time Method (RTM), the Inverse Method (IM) and the Perturbation Peak (PP) method. In order to transfer these methods to SFC in a reliable, reproducible way we will demonstrate that careful system verification using external sensors of mass flow, temperature and pressure are needed first. The adsorption isotherm data generated by the different methods were analyzed and compared and the adsorption isotherms ability to predict new experimental elution profiles was verified by comparing experiments with simulations. It was found that adsorption isotherm data determined based on elution profiles, i.e., ECP, IM and RTM, were able to accurately predict overloaded experimental elution profiles while the more tedious and time-consuming PP method, based on small injections on concentration plateaus, failed in doing so.

Injection profiles in liquid chromatography II : predicting accurate injection-profiles for computer-assisted preparative optimizations.

In computer assisted optimization of liquid chromatography it has been known for some years that it is important to use experimental injection profiles, instead of rectangular ones, in order to calculate accurate elution bands. However, the incorrectly assumed rectangular profiles are still mostly used especially in numerical optimizations. The reason is that the acquisition of injection profiles, for each injection volume and each flow rate considered in a computer-assisted optimization requires a too large number of experiments. In this article a new function is proposed, which enables highly accurate predictions of the injection profiles and thus more accurate computer optimizations, with a minimum experimental effort. To model the injection profiles for any injection volume at a constant flow rate, as few as two experimental injection profiles are required. If it is desirable to also take the effect of flow rate on the injection profiles into account, then just two additional experiments are required. The overlap between fitted and experimental injection profiles at different flow rates and different injection volumes were excellent, more than 90%, using experimental injection profiles from just four different injection volumes at two different flow rates. Moreover, it was demonstrated that the flow rate has a minor influence on the injection profiles and that the injection volume is the main parameter that needs to be accounted for.

Effects of a strongly adsorbed additive on process performance in chiral preparative chromatography

The shapes of elution profiles are often significantly influenced by the presence of strongly adsorbed additives in the mobile phase. This aspect needs to be considered in quantitative optimization of preparative chromatography. The theoretical study carried out here is based on available thermodynamic information for the enantiomers of three beta-blockers, alprenolol, propranolol, and atenolol, on a teicoplanin chiral stationary phase (Chirobiotic T) using methanol/acetonitrile as the mobile phase and acetic acid/triethylamine as the additive. The properties of this strong additive made it possible to tune the binary elution profiles in any combination of the following apparent band shapes: anti-Langmuir/anti-Langmuir, anti-Langmuir/Langmuir and Langmuir/Langmuir. Optimization of the productivity and yield, when performing repetitive batch injections, was investigated using the equilibrium dispersive model. We show that it is important to consider the invisible additive perturbation peak when defining the cycle time and therefore a model-based optimization needs to take this into account. Furthermore, both productivity and yield could be improved for the two unusual shape combinations in comparison to the traditional Langmuir/Langmuir case.

A systematic investigation of algorithm impact in preparative chromatography with experimental verifications.

Computer-assisted optimization of chromatographic separations requires finding the numerical solution of the Equilibrium-Dispersive (ED) mass balance equation. Furthermore, the competitive adsorption isotherms needed for optimization are often estimated numerically using the inverse method that also solves the ED equations. This means that the accuracy of the estimated adsorption isotherm parameters explicitly depends on the numerical accuracy of the algorithm that is used to solve the ED equations. The fast and commonly used algorithm for this purpose, the Rouchon Finite Difference (RFD) algorithm, has often been reported not to be able to accurately solve the ED equations for all practical preparative experimental conditions, but its limitations has never been completely and systematically investigated. In this study, we thoroughly investigate three different algorithms used to solve the ED equations: the RFD algorithm, the Orthogonal Collocation on Finite Elements (OCFE) method and a Central Difference Method (CDM) algorithm, both for increased theoretical understanding and for real cases of industrial interest. We identified discrepancies between the conventional RFD algorithm and the more accurate OCFE and CDM algorithms for several conditions, such as low efficiency, increasing number of simulated components and components present at different concentrations. Given high enough efficiency, we experimentally demonstrate good prediction of experimental data of a quaternary separation problem using either algorithm, but better prediction using OCFE/CDM for a binary low efficiency separation problem or separations when the compounds have different efficiency. Our conclusion is to use the RFD algorithm with caution when such conditions are present and that the rule of thumb that the number of theoretical plates should be greater than 1000 for application of the RFD algorithm is underestimated in many cases.

A quest for the optimal additive in chiral preparative chromatography

Traditionally, the choice of acid/base additives used in chiral preparative chromatography has not been considered very important. However, it was recently demonstrated that strongly adsorbing additives can result in the most unexpected enantiomer band shapes in modern chiral preparative chromatographic systems. In the present study we demonstrate that, depending on the choice of additive, it is actually possible to obtain the following four binary band-shape compositions when a racemic mixture is injected: (i) anti-Langmuir/anti-Langmuir, (ii) anti-Langmuir/Langmuir, (iii) Langmuir/Langmuir and (iv) Langmuir/anti-Langmuir. Further, we made an advanced numerical investigation, in order to ascertain which one of the four band-shape compositions, is the most favourable one in preparative batch chromatography of a racemic mixture. We found that if the target for purification is either the first eluting enantiomer or both ones, the traditional Langmuir/Langmuir band-shape composition should be chosen. But, if only the second eluting enantiomer is to be purified the optimal situation is the anti-Langmuir/Langmuir band-shape composition. Thus, it was concluded that the best choice of additive depends on which enantiomer is of interest and it is useful to perform a thorough additive screening to find the optimal additive, giving the most advantageous peak shape composition and accordingly the best process performance for a particular separation problem.

Relative importance of column and adsorption parameters on the productivity in preparative liquid chromatography. I: investigation of a chiral separation system.

Starting out from an experimental chiral separation system we have used computer simulations for a systematic investigation on how the maximum productivity depends on changes in column length, packing particle size, column efficiency, back pressure, sample concentration/solubility, selectivity, retention factor of the first eluting component and monolayer saturation capacity. The study was performed by changing these parameters, one at a time, and then calculating the corresponding change in maximum productivity. The three most important parameters for maximum production rate was found to be (i) the selectivity (ii) the retention factor of the first eluting component and (iii) the column length. Surprisingly, the column efficiency and sample concentration/solubility were of minor importance. These findings can be used as rough guidelines for column selection, e.g. a low-efficiency column are more likely perform better, in terms of productivity, than a high-efficiency column that have higher retention factor for the first eluting component.