Associating copolymers self-assemble during their passage through a liquid chromatography (LC) column, and the elution differs from that of common non-associating polymers. This computational study aims at elucidating the mechanism of their unique and intricate chromatographic behavior. We focused on amphiphilic diblock copolymers in selective solvents, performed the Monte Carlo (MC) simulations of their partitioning between a bulk solvent (mobile phase) and a cylindrical pore (stationary phase), and investigated the concentration dependences of the partition coefficient and of other functions describing the phase behavior. The observed abruptly changing concentration dependences of the effective partition coefficient demonstrate the significant impact of the association of copolymers with their partitioning between the two phases. The performed simulations reveal the intricate interplay of the entropy-driven and the enthalpy-driven processes, elucidate at the molecular level how the self-assembly affects the chromatographic behavior, and provide useful hints for the analysis of experimental elution curves of associating polymers.

Department of Physical and Macromolecular Chemistry Faculty of Science Charles University Hlavova 8 128 43 Prague Czech Republic

School of Materials and Energy Guangdong University of Technology Guangzhou 510006 China

See more in PubMed

Netopilík M., Janata M., Trhlíková O., Berek D. Fast and efficient single step liquid chromatography separation of parent homopolymers from block copolymers. J. Chromatogr. A. 2021;1653:462441. doi: 10.1016/j.chroma.2021.462441. PubMed DOI

Niezen L.E., Staal B.B., Lang C., Pirok B.W., Schoenmakers P.J. Thermal modulation to enhance two-dimensional liquid chromatography separations of polymers. J. Chromatogr. A. 2021;1653:462429. doi: 10.1016/j.chroma.2021.462429. PubMed DOI

Chang T. Chapter 3—Temperature gradient interaction chromatography of polymers. In: Malik M.I., Mays J., Shah M.R., editors. Molecular Characterization of Polymers. Elsevier; Amsterdam, The Netherlands: 2021. pp. 97–128.

Radke W. Polymer separations by liquid interaction chromatography: Principles–prospects–limitations. J. Chromatogr. A. 2014;1335:62–79. doi: 10.1016/j.chroma.2013.12.010. PubMed DOI

Berek D. Size exclusion chromatography—A blessing and a curse of science and technology of synthetic polymers. J. Sep. Sci. 2010;33:315–335. doi: 10.1002/jssc.200900709. PubMed DOI

Chang T. Macromolecular Engineering. John Wiley & Sons, Ltd.; Hoboken, NJ, USA: 2022. Separation of Polymers by Chromatography; pp. 1–40.

Netopilík M., Janata M., Svitáková R., Trhlíková O., Berek D., Macova E., Limpouchová Z., Procházka K. Chromatographic study of the conformational behavior of graft copolymers with a broad distribution of grafting densities in dilute solutions in selective solvents for grafts. J. Liq. Chromatogr. Relat. Technol. 2016;39:50–58. doi: 10.1080/10826076.2015.1126727. DOI

García-Alvarez-Coque M.C., Ruiz-Angel M.J., Peris-García E. Liquid chromatography|Micellar Liquid Chromatography. In: Worsfold P., Poole C., Townshend A., Miró M., editors. Encyclopedia of Analytical Science. 3rd ed. Academic Press; Oxford, UK: 2019. pp. 133–142.

Ibrahim A.E., Elmaaty A.A., El-Sayed H.M. Determination of six drugs used for treatment of common cold by micellar liquid chromatography. Anal. Bioanal. Chem. 2021;413:5051–5065. doi: 10.1007/s00216-021-03469-3. PubMed DOI

Alwera V., Sehlangia S., Alwera S. Enantioseparation of racemic amino alcohols using green micellar liquid chromatography and confirmation of absolute configuration with elution order. Sep. Sci. Technol. 2021;56:2278–2286. doi: 10.1080/01496395.2020.1819826. DOI

Waters L.J., Shokry D.S., Parkes G.M. Predicting human intestinal absorption in the presence of bile salt with micellar liquid chromatography. Biomed. Chromatogr. 2016;30:1618–1624. doi: 10.1002/bmc.3731. PubMed DOI

Pawar R.P., Mishra P., Durgbanshi A., Bose D., Albiol-Chiva J., Peris-Vicente J., García-Ferrer D., Esteve-Romero J. Use of Micellar Liquid Chromatography to Determine Mebendazole in Dairy Products and Breeding Waste from Bovine Animals. Antibiotics. 2020;9:86 PubMed PMC

Stȩpnik K.E. A concise review of applications of micellar liquid chromatography to study biologically active compounds. Biomed. Chromatogr. 2017;31:e3741. doi: 10.1002/bmc.3741. PubMed DOI

Stȩpnik K.E., Malinowska I., Maciejewska M. A new application of micellar liquid chromatography in the determination of free ampicillin concentration in the drug–human serum albumin standard solution in comparison with the adsorption method. Talanta. 2016;153:1–7. doi: 10.1016/j.talanta.2016.02.045. PubMed DOI

Ke J., Dong Y., Luo T., Xie Y. Development of a gradient micellar liquid chromatographic method eluting from micellar mode to high submicellar mode for the rapid separation of free amino acids. Anal. Methods. 2017;9:1762–1770. doi: 10.1039/C6AY03453E. DOI

Elias H.G., Šolc K. Multimerization: Association and aggregation, 14. Distinction between open and closed associations. Die Makromol. Chem. 1975;176:365–371. doi: 10.1002/macp.1975.021760210. DOI

Procházka K., Mandák T., Bednář B., Trněná J., Tuzar Z. Behavior of Reversibly Associating Systems in Size Exclusion Chromatography. Interpretation of Experimental Data Based on Theoretical Model. J. Liq. Chromatogr. 1990;13:1765–1783. doi: 10.1080/01483919008048991. DOI

Procházka K., Mandák T., Kočiřík M., Bednář B., Tuzar Z. Chromatographic behaviour of reversibly associating macromolecules. Part 1.—Theoretical model. J. Chem. Soc. Faraday Trans. 1990;86:1103–1108. doi: 10.1039/FT9908601103. DOI

Grubišic-Gallot Z., Sedláček J., Gallot Y. Study Of Polystyrene-block-poly(methyl methacrylate) Micelles by Size Exclusion Chromatography/Low Angle Laser Light Scattering Anomalous Micellization. J. Liq. Chromatogr. Relat. Technol. 1998;21:2459–2472. doi: 10.1080/10826079808003591. DOI

Desjardins A., Eisenberg A. Colloidal properties of block ionomers. 1. Characterization of reverse micelles of styrene-b-metal methacrylate diblocks by size-exclusion chromatography. Macromolecules. 1991;24:5779–5790. doi: 10.1021/ma00021a009. DOI

Hvidt S., Batsberg W. Characterization and Micellization of a Poloxamer Block Copolymer. Int. J. Polym. Anal. Charact. 2007;12:13–22. doi: 10.1080/10236660601094093. DOI

Nixon S.K., Hvidt S., Booth C. Micellization of block copolymer P94 in aqueous solution. J. Colloid Interface Sci. 2004;280:219–223. doi: 10.1016/j.jcis.2004.07.031. PubMed DOI

Adawy A., Groves M.R. The Use of Size Exclusion Chromatography to Monitor Protein Self-Assembly. Crystals. 2017;7:331. doi: 10.3390/cryst7110331. DOI

Wang X., Lísal M., Procházka K., Limpouchová Z. Computer Study of Chromatographic Separation Process: A Monte Carlo Study of H-Shaped and Linear Homopolymers in Good Solvent. Macromolecules. 2016;49:1093–1102. doi: 10.1021/acs.macromol.5b02327. DOI

Ahn J., Chang T., Wang X., Limpouchová Z., Procházka K. Influence of the Chain Architecture and the Presence of End-Groups or Branching Units Chemically Different from Repeating Structural Units on the Critical Adsorption Point in Liquid Chromatography. Macromolecules. 2017;50:8720–8730. doi: 10.1021/acs.macromol.7b01786. DOI

Wang X., Procházka K., Limpouchová Z. Partitioning of polymers between bulk and porous media: Monte Carlo study of the effect of pore size distribution. J. Colloid Interface Sci. 2020;567:103–112. doi: 10.1016/j.jcis.2020.01.119. PubMed DOI

Ziebarth J.D., Wang Y. Interactions of complex polymers with nanoporous substrate. Soft Matter. 2016;12:5245–5256. doi: 10.1039/C6SM00768F. PubMed DOI

Ziebarth J.D., Gardiner A.A., Wang Y., Jeong Y., Ahn J., Jin Y., Chang T. Comparison of Critical Adsorption Points of Ring Polymers with Linear Polymers. Macromolecules. 2016;49:8780–8788. doi: 10.1021/acs.macromol.6b01925. DOI

Zhu Y., Ziebarth J., Fu C., Wang Y. A Monte Carlo study on LCCC characterization of graft copolymers at the critical condition of side chains. Polymer. 2015;67:47–54. doi: 10.1016/j.polymer.2015.04.067. DOI

Yang X., Zhu Y., Wang Y. Can the individual block in block copolymer be made chromatographically “invisible” at the critical condition of its corresponding homopolymer? Polymer. 2013;54:3730–3736. doi: 10.1016/j.polymer.2013.05.018. DOI

Bleha T., Cifra P. Polymer-Induced Depletion Interaction between Weakly Attractive Plates. Langmuir. 2004;20:764–770. doi: 10.1021/la035401h. PubMed DOI

Škrinárová Z., Bleha T., Cifra P. Concentration Effects in Partitioning of Macromolecules into Pores with Attractive Walls. Macromolecules. 2002;35:8896–8905. doi: 10.1021/ma020808z. DOI

Cifra P., Teraoka I. Confined Polymer Chains in a Θ Solvent: A Model with Polymer–Solvent Interactions. Macromolecules. 2003;36:9638–9646. doi: 10.1021/ma034656z. DOI

Škrinárová Z., Cifra P. Partitioning of Semiflexible Macromolecules into a Slit in Theta Solvent. Macromol. Theory Simul. 2002;11:401–409. doi: 10.1002/1521-3919(20020401)11:4<401::AID-MATS401>3.0.CO;2-I. DOI

Cifra P., Bleha T. Partition Coefficients and the Free Energy of Confinement from Simulations of Nonideal Polymer Systems. Macromolecules. 2001;34:605–613. doi: 10.1021/ma000964a. DOI

Škrinárová Z., Cifra P. Partitioning of Semiflexible Macromolecules into a Slit in Good Solvents. Macromol. Theory Simul. 2001;10:523–531. doi: 10.1002/1521-3919(20010601)10:5<523::AID-MATS523>3.0.CO;2-W. DOI

Wang Y., Teraoka I. Computer Simulation of Semidilute Polymer Solutions in Confined Geometry: Pore as a Microscopic Probe. Macromolecules. 1997;30:8473–8477. doi: 10.1021/ma970741t. DOI

Wang X., Limpouchová Z., Procházka K. Separation of polymers differing in their chain architecture by interaction chromatography: Phase equilibria and conformational behavior of polymers in strongly adsorbing porous media. Polymer. 2019;175:99–106. doi: 10.1016/j.polymer.2019.05.006. DOI

Yan N., Zhu Y., Jiang W. Recent progress in the self-assembly of block copolymers confined in emulsion droplets. Chem. Commun. 2018;54:13183–13195. doi: 10.1039/C8CC05812A. PubMed DOI

Yan N., Liu X., Zhang Y., Sun N., Jiang W., Zhu Y. Confined co-assembly of AB/BC diblock copolymer blends under 3D soft confinement. Soft Matter. 2018;14:4679–4686. doi: 10.1039/C8SM00486B. PubMed DOI

Xu Z., Lin J., Zhang Q., Wang L., Tian X. Theoretical simulations of nanostructures self-assembled from copolymer systems. Polym. Chem. 2016;7:3783–3811. doi: 10.1039/C6PY00535G. DOI

Cui T., Li X., Dong B., Li X., Guo M., Wu L., Li B., Li H. Janus onions of block copolymers via confined self-assembly. Polymer. 2019;174:70–76. doi: 10.1016/j.polymer.2019.04.062. DOI

Horechyy A., Paturej J., Nandan B., Jehnichen D., Göbel M., Reuter U., Sommer J.U., Stamm M. Nanoparticle assembly under block copolymer confinement: The effect of nanoparticle size and confinement strength. J. Colloid Interface Sci. 2020;578:441–451. doi: 10.1016/j.jcis.2020.05.115. PubMed DOI

Bordin J.R., Krott L.B. How Competitive Interactions Affect the Self-Assembly of Confined Janus Dumbbells. J. Phys. Chem. B. 2017;121:4308–4317. doi: 10.1021/acs.jpcb.7b01696. PubMed DOI

Park J.H., Joo Y.L. Formation of interconnected morphologies via nanorod inclusion in the confined assembly of symmetric block copolymers. Phys. Chem. Chem. Phys. 2014;16:8865–8871. doi: 10.1039/C4CP00352G. PubMed DOI

Huang J.H., Wu J.J., Huang X.W. Self-assembly of symmetric rod-coil diblock copolymers in cylindrical nanopore. RSC Adv. 2016;6:100559–100567. doi: 10.1039/C6RA22122J. DOI

Liu M., Chen K., Li W., Wang X. Tunable helical structures formed by ABC triblock copolymers under cylindrical confinement. Phys. Chem. Chem. Phys. 2019;21:26333–26341. doi: 10.1039/C9CP04978A. PubMed DOI

Yu B., Sun P., Chen T., Jin Q., Ding D., Li B., Shi A.C. Confinement-Induced Novel Morphologies of Block Copolymers. Phys. Rev. Lett. 2006;96:138306. doi: 10.1103/PhysRevLett.96.138306. PubMed DOI

Hao J., Wang Z., Wang Z., Yin Y., Jiang R., Li B., Wang Q. Self-Assembly in Block Copolymer Thin Films upon Solvent Evaporation: A Simulation Study. Macromolecules. 2017;50:4384–4396. doi: 10.1021/acs.macromol.7b00200. DOI

Kong W., Li B., Jin Q., Ding D., Shi A.C. Helical Vesicles, Segmented Semivesicles, and Noncircular Bilayer Sheets from Solution-State Self-Assembly of ABC Miktoarm Star Terpolymers. J. Am. Chem. Soc. 2009;131:8503–8512. doi: 10.1021/ja900405r. PubMed DOI

Larson R. Monte Carlo simulations of the phase behavior of surfactant solutions. J. De Phys. II. 1996;6:1441–1463. doi: 10.1051/jp2:1996141. DOI

Kivenson A., Hagan M.F. Mechanisms of Capsid Assembly around a Polymer. Biophys. J. 2010;99:619–628. doi: 10.1016/j.bpj.2010.04.035. PubMed DOI PMC

Jo W.H., Jang S.S. Monte Carlo simulation of the order–disorder transition of a symmetric cyclic diblock copolymer system. J. Chem. Phys. 1999;111:1712–1720. doi: 10.1063/1.479431. DOI

Siepmann J.I., Frenkel D. Configurational bias Monte Carlo: A new sampling scheme for flexible chains. Mol. Phys. 1992;75:59–70. doi: 10.1080/00268979200100061. DOI

Rolińska K., Sikorski A. Adsorption of Linear and Cyclic Multiblock Copolymers from Selective Solvent. A Monte Carlo Study. Macromol. Theory Simul. 2020;29:2000053. doi: 10.1002/mats.202000053. DOI

Hugouvieux V., Axelos M.A.V., Kolb M. Micelle formation, gelation and phase separation of amphiphilic multiblock copolymers. Soft Matter. 2011;7:2580–2591. doi: 10.1039/c0sm01018a. DOI

Kim S.H., Jo W.H. A Monte Carlo simulation for the micellization of ABA- and BAB-type triblock copolymers in a selective solvent. II. Effects of the block composition. J. Chem. Phys. 2002;117:8565–8572. doi: 10.1063/1.1512646. DOI

Kim S.H., Jo W.H. A Monte Carlo Simulation for the Micellization of ABA- and BAB-Type Triblock Copolymers in a Selective Solvent. Macromolecules. 2001;34:7210–7218. doi: 10.1021/ma0105136. DOI

Havránková J., Limpouchová Z., Procházka K. A New Simulation Algorithm with Revised “Association Criteria” for Studying the Association of Heteroarm Star Copolymers. Macromol. Theory Simul. 2005;14:560–568. doi: 10.1002/mats.200500040. DOI

Kuldová J., Košovan P., Limpouchová Z., Procházka K. Computer Study of the Association Behavior of Gradient Copolymers: Analysis of Simulation Results Based on a New Algorithm for Recognition and Classification of Aggregates. Macromol. Theory Simul. 2013;22:61–70. doi: 10.1002/mats.201200055. DOI

Willis J.D., Beardsley T.M., Matsen M.W. Simple and Accurate Calibration of the Flory–Huggins Interaction Parameter. Macromolecules. 2020;53:9973–9982. doi: 10.1021/acs.macromol.0c02115. DOI

Li X., Chiew Y.C. Monte Carlo simulation of Lennard-Jones chains. J. Chem. Phys. 1994;101:2522–2531. doi: 10.1063/1.467691. DOI

Panagiotopoulos A.Z. Direct determination of phase coexistence properties of fluids by Monte Carlo simulation in a new ensemble. Mol. Phys. 1987;61:813–826. doi: 10.1080/00268978700101491. DOI

Wijmans C.M., Linse P. Modeling of Nonionic Micelles. Langmuir. 1995;11:3748–3756. doi: 10.1021/la00010a027. DOI

Uhlík F., Limpouchová Z., Jelínek K., Procházka K. A Monte Carlo study of shells of hydrophobically modified amphiphilic copolymer micelles in polar solvents. J. Chem. Phys. 2003;118:11258–11264. doi: 10.1063/1.1575732. DOI

Šindelka K., Limpouchová Z., Lísal M., Procházka K. The electrostatic co-assembly in non-stoichiometric aqueous mixtures of copolymers composed of one neutral water-soluble and one polyelectrolyte (either positively or negatively charged) block: A dissipative particle dynamics study. Phys. Chem. Chem. Phys. 2016;18:16137–16151. doi: 10.1039/C6CP01047D. PubMed DOI

Procházka K., Šindelka K., Wang X., Limpouchová Z., Lísal M. Self-assembly and co-assembly of block polyelectrolytes in aqueous solutions. Dissipative particle dynamics with explicit electrostatics. Mol. Phys. 2016;114:3077–3092. doi: 10.1080/00268976.2016.1225130. DOI

Casassa E.F. Equilibrium distribution of flexible polymer chains between a macroscopic solution phase and small voids. J. Polym. Sci. Part B Polym. Lett. 1967;5:773–778. doi: 10.1002/pol.1967.110050907. DOI

Bhattacharjee J.K., Kaatze U. Fluctuations Near the Critical Micelle Concentration. I. Premicellar Aggregation, Relaxation Rate, and Isentropic Compressibility. J. Phys. Chem. B. 2013;117:3790–3797. doi: 10.1021/jp4011185. PubMed DOI

Humphrey W., Dalke A., Schulten K. VMD: Visual molecular dynamics. J. Mol. Graph. 1996;14:33–38. doi: 10.1016/0263-7855(96)00018-5. PubMed DOI

Riess G. Micellization of block copolymers. Prog. Polym. Sci. 2003;28:1107–1170. doi: 10.1016/S0079-6700(03)00015-7. DOI

Zhang X., Wang C. Supramolecular amphiphiles. Chem. Soc. Rev. 2011;40:94–101. doi: 10.1039/B919678C. PubMed DOI

Lodge T.P., Bang J., Hanley K.J., Krocak J., Dahlquist S., Sujan B., Ott J. Origins of Anomalous Micellization in Diblock Copolymer Solutions. Langmuir. 2003;19:2103–2109. doi: 10.1021/la0268808. DOI

Mansour O.T., Cattoz B., Beaube M., Montagnon M., Heenan R.K., Schweins R., Appavou M.S., Griffiths P.C. Assembly of small molecule surfactants at highly dynamic air–water interfaces. Soft Matter. 2017;13:8807–8815. doi: 10.1039/C7SM01914A. PubMed DOI

Peng M., Nguyen A.V. Adsorption of ionic surfactants at the air-water interface: The gap between theory and experiment. Adv. Colloid Interface Sci. 2020;275:102052. doi: 10.1016/j.cis.2019.102052. PubMed DOI

Szutkowski K., Kołodziejska Z., Pietralik Z., Zhukov I., Skrzypczak A., Materna K., Kozak M. Clear distinction between CAC and CMC revealed by high-resolution NMR diffusometry for a series of bis-imidazolium gemini surfactants in aqueous solutions. RSC Adv. 2018;8:38470–38482. doi: 10.1039/C8RA07081D. PubMed DOI PMC

Diamant H., Andelman D. Free energy approach to micellization and aggregation: Equilibrium, metastability, and kinetics. Curr. Opin. Colloid Interface Sci. 2016;22:94–98. doi: 10.1016/j.cocis.2016.03.004. DOI

Zhang X., Arce Nunez J.G., Kindt J.T. Derivation of micelle size-dependent free energies of aggregation for octyl phosphocholine from molecular dynamics simulation. Fluid Phase Equilibria. 2019;485:83–93. doi: 10.1016/j.fluid.2018.12.001. DOI

Wang Y., Mattice W.L., Napper D.H. Simulation of the formation of micelles by diblock copolymers under weak segregation. Langmuir. 1993;9:66–70. doi: 10.1021/la00025a017. DOI

Rosenbluth M.N., Rosenbluth A.W. Monte Carlo Calculation of the Average Extension of Molecular Chains. J. Chem. Phys. 1955;23:356–359. doi: 10.1063/1.1741967. DOI

Wang X., Limpouchová Z., Procházka K., Liu Y., Min Y. Phase equilibria and conformational behavior of dendrimers in porous media: Towards chromatographic analysis of dendrimers. J. Colloid Interface Sci. 2022;608:830–839. doi: 10.1016/j.jcis.2021.09.177. PubMed DOI

Somasundaran P., Huang L. Adsorption/aggregation of surfactants and their mixtures at solid–liquid interfaces. Adv. Colloid Interface Sci. 2000;88:179–208. doi: 10.1016/S0001-8686(00)00044-0. PubMed DOI

Chingin K., Yan R., Zhong D., Chen H. Enrichment of Surface-Active Compounds in Bursting Bubble Aerosols. ACS Omega. 2018;3:8709–8717. doi: 10.1021/acsomega.8b01157. PubMed DOI PMC

Viduna D., Limpouchová Z., Procházka K. Monte Carlo simulation of polymer brushes in narrow pores. J. Chem. Phys. 2001;115:7309–7318. doi: 10.1063/1.1405444. DOI

Self-Assembly of Symmetric Copolymers in Slits with Inert and Attractive Walls