Morphology optimization of ordered chromatography stationary phases: a workflow designed by machine learning and computational fluid dynamics

Abstract

Chromatography is a significant separation and analysis method widely used in analytical chemistry and biochemistry. A chromatographic system contains a mobile phase and a stationary phase, where the commonly utilized stationary phase is constructed by randomly packed particles. It has been verified by experiments that the usage of ordered structure for the stationary phase, would improve separation performance. However, due to the long time required for experiments and simulation procedures, there were only a few types of ordered structures evaluated for the chromatography system. This work is to investigate the correlation between column separation performance and ordered morphologies, for figuring out ordered structures with optimal chromatographic performance. Machine learning (ML) technology was applied in this work for finding optimal structures. This method was firstly employed for packing quality analysis of around 25000 experiments of pre-packed columns manufactured for a period of over 10 years. The capability of the ML model was validated to offer predictions of column performance with mean absolute percentage error (MAPE) equal to around 10% for reduced height equivalent to a theoretical plate (ℎ) and 7% for peak asymmetry (Aₛ).Also, the model quantitatively indicated that column backbones were the most influential factor for pre-packed column quality. This work proved the capability of ML to evaluate and predict column performance. To generate large amounts of ordered structures, an algorithm was developed in two-dimensional (2D) chromatography. 2D morphologies were considered as a combination of discrete elements, where each element can be defined as a portion of the mobile phase or the stationary phase. Then these discrete elements were transformed into numbers 0 and 1 (corresponding to the mobile phase and stationary phase) in the matrix, in which case they can be controlled and altered easily. The total number of possible topologies as well as the demand for computing resources increase exponentially. Thus three types of constraints (principal pathway, symmetry constraint, and porosity constraint) were implemented into the algorithm to reduce the number of generated topologies. The reduction capability of constraints was evaluated and 97% of possible topologies were reduced. These constraints served as a strong method to reduce the time and required computing resources to examine the possible ordered morphologies. The column separation performance was investigated by computational fluid dynamic (CFD) simulations. A large amount of 2D ordered pillar arrays and some discrete unit cells generated by algorithm and constraints were simulated. Based on the simulations of discrete unit cells, it was proven that the chromatographic performance was strongly affected by the homogeneity velocity profiles within the chromatography system. Structures, such as square and hexagon pillar arrays, having homogenous fluid profiles tended to provide high separation efficiency. In such case, pore-throat ratio, a commonly used parameter in stratigraphy analysis, was proposed for the homogeneity analysis of chromatographic bed due to the strong correlation with column performance and easiness in the determination by experiments. The practicality of pore-throat ratio was proven by the analysis of 2-dimensional (2D) pillar arrays and 3-dimensional (3D) triply periodic minimum surface (TPMS) monoliths. ML methods were then applied to the data set of 2D pillar arrays. The accuracy of the ML model was validated for the prediction of van Deemter curves (smaller than 10% MAPE in general). For seeking the optimal morphologies of 2D pillar arrays, a reinforcement learning system was developed. The particle shape, particle size, and particle radial stretching were selected as the design freedom parameters of optimal pillar arrays. Six example morphologies were suggested by the reinforcement learning system, whose performances were all verified by CFD simulations. The CFD model was further developed with film diffusion, pore diffusion, and adsorption/desorption models considered, to investigate the solute behavior in the porous stationary phase. Considering pore diffusion and adsorption/desorption equilibrium, a comprehensive version of governing equations for different conditions is established with a definition of effective Peclet number. For different model conditions, the corresponding effective Peclet number can be written as a combination of three parts, the original Peclet number Pₑ, the length scale of solid phase and fluid phase (L/Lₛ)² and the system coefficient yₐ. With the definition of yₐ, , the model considering pore diffusion can also be utilized for simulations of pore diffusion and adsorption isotherms. Based on the simulations, it is confirmed that the optimized structures, suggested by machine learning, still maintain the performance superiority for the beds with the porous stationary phase. Overall, this work demonstrates, for the first time, the seeking process of optimal morphologies in chromatography by CFD simulations and ML. The 2D morphologies suggested by the ML tool were validated to have high purification performance. This method is required to be further developed for the 3D morphologies and porous stationary systems in the future. Nevertheless, the presented approach proves that it is possible to search optimal structures of chromatography columns by CFD modeling and ML. It is expected in the future, the purification performance of chromatography will be further enhanced with optimized ordered structures found by ML.