Relations between kinetic parameters of different column models for liquid chromatography applying core-shell particles

References

• Guiochon, G.; Lin, B. Modeling for Preparative Chromatography; Academic Press: New York, USA, 2003.
   Google Scholar
• Guiochon, G.; Felinger, A.; Shirazi, D. G.; Katti, A. M. Fundamentals of Preparative and Nonlinear Chromatography; 2nd ed.; Elsevier Academic Press: New York, USA, 2006.
   Google Scholar
• Li, P.; Xiu, G.; Rodrigues, A. E. Modeling Separation of Proteins by Inert Core Adsorbent in a Batch Adsorber. Chem. Eng. Sci. 2003, 58, 3361–3371. DOI: 10.1016/S0009-2509(03)00217-3.
   Web of Science ®Google Scholar
• Kaczmarski, K.; Guiochon, G. Modeling of the Mass-transfer Kinetics in Chromatographic Columns Packed with Shell and Pellicular Particles. Anal. Chem. 2007, 79, 4648–4656. DOI: 10.1021/ac070209w.
   PubMed Web of Science ®Google Scholar
• Horvath, C. G.; Preiss, B. A.; Lipsky, S. R. Fast Liquid Chromatography: An Investigation of Operating Parameters and the Separation of Nucleotides on Pellicular Ion Exchangers. Anal. Chem. 1967, 39, 1422–1428. DOI: 10.1021/ac60256a003.
   PubMed Web of Science ®Google Scholar
• Guiochon, G.; Gritti, F. Shell Particles, Trials, Tribulations and Triumphs. J. Chromatogr. A. 2011, 1218, 1915–1938. DOI: 10.1016/j.chroma.2011.01.080.
   PubMed Web of Science ®Google Scholar
• Kaczmarsk, K. On the Optimization of the Solid Core Radius of Superficially Porous Particles for Finite Adsorption Rate. J. Chromatogr. A. 2011, 1218, 951–958. DOI: 10.1016/j.chroma.2010.12.093.
   PubMed Web of Science ®Google Scholar
• Felinger, A.; Guiochon, G. Comparison of the Kinetic Models of Linear Chromatography. J. Chromatogr. Suppl. 2004, 60, S175–S180.
   Google Scholar
• Broeckhoven, K.; Cabooter, D.; Desmet, G. Kinetic Performance Comparison of Fully and Superficially Porous Particles with Sizes Ranging between 2.7 μm and 5 μm : Intrinsic Evaluation and Application to a Pharmaceutical Test Compound. J. Pharm. Anal. 2013, 3, 313–323. DOI: 10.1016/j.jpha.2012.12.006.
   Google Scholar
• Cavazzini, A.; Gritti, F.; Kaczmarski, K.; Marchetti, N.; Guiochon, G. Mass-transfer Kinetics in a Shell Packing Material for Chromatography. Anal. Chem. 2007, 79, 5972–5979. DOI: 10.1021/ac070571a.
   PubMed Web of Science ®Google Scholar
• Gu, T.; Liu, M.; Cheng, K.-S. C.; Ramaswamy, S.; Wang, C. A General Rate Model Approach for the Optimization of the Core Radius Fraction for Multicomponent Isocratic Elution in Preparative Nonlinear Liquid Chromatography Using Cored Beads. Chem. Eng. Sci. 2011, 66, 3531–3539. DOI: 10.1016/j.ces.2011.04.021.
   Web of Science ®Google Scholar
• Kahsay, G.; Broeckhoven, K.; Adams, E.; Desmet, G.; Cabooter, D. Kinetic Performance Comparison of Fully and Superficially Porous Particles with a Particle Size of 5 μm: Intrinsic Evaluation and Application to the Impurity Analysis of Griseofulvin. Talanta. 2014, 122, 122–129. DOI: 10.1016/j.talanta.2014.01.050.
   Google Scholar
• Lambert, N.; Kiss, I.; Felinger, A . Mass-transfer Properties of Insulin on Core-shell and Fully Porous Stationary Phases. J. Chromatogr. A. 2014, 1366, 84–91. DOI: 10.1016/j.chroma.2014.09.025.
   PubMed Web of Science ®Google Scholar
• Li, P.; Xiu, G.; Rodrigues, A. E. Analytical Breakthrough Curves for Inert Core Adsorbent with Sorption Kinetics. AIChE J. 2003, 49, 2974–2979. DOI: 10.1002/aic.690491127.
   Web of Science ®Google Scholar
• Li, P.; Xiu, G.; Rodrigues, A. E. Modeling Break Through and Elution Curves in Fixed Bed of Inert Core Adsorbents: Analytical and Approximate Solutions. Chem. Eng. Sci. 2004, 59, 3091–3103. DOI: 10.1016/j.ces.2004.04.034.
   Web of Science ®Google Scholar
• Li, P.; Yu, J.; Xiu, G.; Rodrigues, A. E. A Strategy for Tailored Design of Efficient and Low-pressure Drop Packed Column Chromatography. AIChE J. 2010, 56, 3091–3098. DOI: 10.1002/aic.12218.
   Web of Science ®Google Scholar
• Li, P.; Xiu, G.; Rodrigues, A. E. Modeling Diffusion and Reaction for Inert-Core Catalyst in Batch and Fixed Bed Reactors. Can. J. Chem. Eng. 2019, 97, 217-225. DOI: 10.1002/cjce.23189.
   Google Scholar
• Gengling, Y.; Zhide, H. Universal Theoretical Moment Expression for Elution and Formal Chromatography of Pellicular Ion Exchange Resins. React. Funct. Polym. 1996, 31, 25–29. DOI: 10.1016/1381-5148(96)00037-5.
   Web of Science ®Google Scholar
• Zhou, X.; Sun, Y.; Liu, Z. Superporous Pellicular Agarose-glass Composite Particle for Protein Adsorption. Biochem. Eng. J. 2007, 34, 99–106. DOI: 10.1016/j.bej.2006.09.018.
   Web of Science ®Google Scholar
• Javeed, S.; Qamar, S.; Ashraf, W.; Seidel-Morgenstern, A.; Warnecke, G. Analysis and Numerical Investigation of Two Dynamic Models for Liquid Chromatography. Chem. Eng. Sci. 2013, 90, 17–31. DOI: 10.1016/j.ces.2012.12.014.
   Web of Science ®Google Scholar
• Qamar, S.; Abbasi, J. N.; Javeed, S.; Shah, M.; Khan, F. U.; Seidel-Morgenstern, A. Analytical Solutions and Moment Analysis of Chromatographic Models for Rectangular Pulse Injections. J. Chromatogr. A. 2013, 1315, 92–106. DOI: 10.1016/j.chroma.2013.09.031.
   PubMed Web of Science ®Google Scholar
• Qamar, S.; Abbasi, J. N.; Javeed, S.; Seidel-Morgenstern, A. Analytical Solutions and Moment Analysis of General Rate Model for Linear Liquid Chromatography. Chem. Eng. Sci. 2014, 107, 192–205. DOI: 10.1016/j.ces.2013.12.019.
   Web of Science ®Google Scholar
• Qamar, S.; Abbasi, J. N.; Mehwish, A.; Seidel-Morgenstern, A. Linear General Rate Model of Chromatography for Core-shell Particles: Analytical Solutions and Moment Analysis. Chem. Eng. Sci. 2015, 137, 352–363. DOI: 10.1016/j.ces.2015.06.053.
   Web of Science ®Google Scholar
• Durbin, F. Numerical Inversion of Laplace Transforms: An Efficient Improvement to Dubner and Abate’s Method. Comput. J. 1974, 17, 371–376. DOI: 10.1093/comjnl/17.4.371.
   Web of Science ®Google Scholar
• Rice, R. G.; Do, D. D. Applied Mathematics and Modeling for Chemical Engineers; Wiley-Interscience: New York, USA, 1995.
   Google Scholar
• Dorota, A.; Kaczmarski, K.; Wojciech, P.; Seidel-Morgenstern, A. Concentration Dependence of Lumped Mass Transfer Coefficients Linear versus Non-linear Chromatography and Isocratic versus Gradient Operation. J. Chromatogr. A. 2003, 1006, 61–76. DOI: 10.1016/S0021-9673(03)00948-8.
   PubMed Web of Science ®Google Scholar
• Kubin, M. Beitrag Zur Theorie Der Chromatographie. Collect. Czech. Chem. Commun. 1965, 30, 1104–1118. DOI: 10.1135/cccc19651104.
   Web of Science ®Google Scholar
• Kubin, M. Beitrag Zur Theorie Der Chromatographie II. Einfluss Der Diffusion Ausserhalb Und Der Adsorption Innerhalb Des Sorbens-Korns. Collect. Czech. Chem. Commun. 1965, 30, 2900–2907. DOI: 10.1135/cccc19652900.
   Google Scholar
• Kucera, E. Contribution to the Theory of Chromatography: Linear Non-equilibrium Elution Chromatography. J. Chromatogr. A. 1965, 19, 237–248. DOI: 10.1016/S0021-9673(01)99457-9.
   PubMed Web of Science ®Google Scholar
• Li, P.; Yu, J.; Xiu, G.; Rodrigues, A. E. Perturbation Chromatography with Inert Core Adsorbent: Moment Solution for Two-component Nonlinear Isotherm Adsorption. Chem. Eng. Sci. 2011, 66, 4555–4560. DOI: 10.1016/j.ces.2011.06.016.
   Web of Science ®Google Scholar
• Miyabe, K.; Guiochon, G. Influence of the Modification Conditions of Alkyl Bonded Ligands on the Characteristics of Reversed-phase Liquid Chromatography. J. Chromatogr. A. 2000, 903, 1–12. DOI: 10.1016/S0021-9673(00)00891-8.
   PubMed Web of Science ®Google Scholar
• Miyabe, K.; Guiochon, G. Measurement of the Parameters of the Mass Transfer Kinetics in High Performance Liquid Chromatography. J. Sep. Sci. 2003, 26, 155–173. DOI: 10.1002/jssc.200390024.
   Web of Science ®Google Scholar
• Miyabe, K. Surface Diffusion in Reversed-phase Liquid Chromatography Using Silica Gel Stationary Phases of Different C1 and C18 Ligand Densities. J. Chromatogr. A. 2007, 1167, 161–170. DOI: 10.1016/j.chroma.2007.08.045.
   PubMed Web of Science ®Google Scholar
• Miyabe, K. Moment Analysis of Chromatographic Behavior in Reversed-phase Liquid Chromatography. J. Sep. Sci. 2009, 32, 757–770. DOI: 10.1002/jssc.200800607.
   PubMed Web of Science ®Google Scholar
• Ruthven, D. M. Principles of Adsorption and Adsorption Processes; Wiley-Interscience: New York, USA, 1984.
   Google Scholar
• Schneider, P.; Smith, J. M. Adsorption Rate Constants from Chromatography. AIChE J. 1968, 14, 762–771. DOI: 10.1002/aic.690140516.
   Web of Science ®Google Scholar
• Suzuki, M. Notes on Determining the Moments of the Impulse Response of the Basic Transformed Equations. J. Chem. Eng. Japan. 1974, 6, 540–543. DOI: 10.1252/jcej.6.540.
   Google Scholar
• Wolff, H.-J.; Radeke, K.-H.; Gelbin, D. Heat and Mass Transfer in Packed beds-IV Use of Weighted Moments to Determine Axial Dispersion Coefficient. Chem. Eng. Sci. 1979, 34, 101–107. DOI: 10.1016/0009-2509(79)85181-7.
   Web of Science ®Google Scholar
• Wolff, H.-J.; Radeke, K.-H.; Gelbin, D. Weighted Moments and the Pore-diffusion Model. Chem. Eng. Sci. 1980, 35, 1481–1485. DOI: 10.1016/0009-2509(80)85152-9.
   Web of Science ®Google Scholar
• Qamar, S.; Sattar, F. A.; Abbasi, J. N.; Seidel-Morgenstern, A. Numerical Simulation of Nonlinear Chromatography with Core-shell Particles Applying the General Rate Model. Chem. Eng. Sci. 2016, 147, 54–64. DOI: 10.1016/j.ces.2016.03.027.
   Web of Science ®Google Scholar
• Van der Laan, T. Letter to the Editors on Notes on the Diffusion Type Model for the Longitudinal Mixing in Flow. Chem. Eng. Sci. 1958, 7, 187–191.
   Web of Science ®Google Scholar
• Papoulis, A. Probability, Random Variables, and Stochastic Processes, 2nd ed.; McGraw-Hill: New York, USA, 1984; p. 146.
   Google Scholar