Hydration and swelling: a theoretical investigation on the cooperativity effect of H-bonding interactions between p-hydroxy hydroxymethyl calix[4]/[5]arene and H2O by many-body interaction and density functional reactivity theory


In order to explore the nature of the hydration and swelling of superabsorbent resin, a theoretical investigation into the cooperativity effect of the H-bonding interactions in the hydrates of four model compounds that can be regarded as the units of hydroquinone formaldehyde resin (HFR) (i.e., O-hydroxymethyl-1,4-dihydroxybenzene, methylene di-O-hydroxymethyl-1,4-dihydroxybenzene, p-hydroxy hydroxymethyl calix[4]arene and p-hydroxy hydroxymethyl calix[5]arene) was carried out by many-body interaction and density functional reactivity theory. The HFR···H2O···H2O complexes, in which the H2O···H2O moieties are bound with both the hydroxyl groups of HFR, are the most stable. For the HFR(H2O)n clusters, the interaction energy per building block is increased as the number of the size n increases, indicating the cooperativity effect. Therefore, a deduction is given that the cooperativity effects of the H-bonding interactions play an important role in the process of the hydration and swelling of HFR, and the swelling behavior is mainly attributed to the cooperativity effects which arised from the interactions between the H2O molecules. The origin of the cooperativity effect was examined employing several information-theoretic quantities in the density functional reactivity theory. The degree of swelling of HFR was quantitated using a measure of volume.

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  1. 1.

    Chen X, Pao W, Thornton S, Small J (2016) Unsaturated hydro-mechanical–chemical constitutive coupled model based on mixture coupling theory: hydration swelling and chemical osmosis. Int J Eng Sci 104:97–109

    CAS  Google Scholar 

  2. 2.

    Chen X (2013) Constitutive unsaturated hydro-mechanical model based on modified mixture theory with consideration of hydration swelling. Int J Solids Struct 50:3266–3273

    Google Scholar 

  3. 3.

    Wojtasz J, Carlstedt J, Fyhrc P, Kocherbitov V (2016) Hydration and swelling of amorphous cross-linked starch microspheres. Carbohydr Polym 135:225–233

    CAS  PubMed  Google Scholar 

  4. 4.

    Michot LJ, Ferrage E, Delville J-RM (2016) Influence of layer charge, hydration state and cation nature on the collective dynamics of interlayer water in synthetic swelling clay minerals. Appl Clay Sci 119:375–384

    CAS  Google Scholar 

  5. 5.

    Rahromostaqim M, Sahimi M (2018) Molecular dynamics simulation of hydration and swelling of mixed-layer clays. J Phys Chem C 122:14631–14639

    CAS  Google Scholar 

  6. 6.

    Rahromostaqim M, Sahimi M (2019) Molecular dynamics simulation of hydration and swelling of mixed-layer clays in the presence of carbon dioxide. J Phys Chem C 123:4243–4255

    CAS  Google Scholar 

  7. 7.

    Verger L, Natu V, Ghidiu M, Barsoum MW (2019) Effect of cationic exchange on the hydration and swelling behavior of Ti3C2Tz Mxenes. J Phys Chem C 123:20044–20050

    CAS  Google Scholar 

  8. 8.

    Zeng SZ, Jin NZ, Zhang HL, Hai B, Chen XH, Shi JL (2014) High-modulus all-carbon ladder polymer of hydroquinone and formaldehyde that bridges the gap between single-strand polymers and graphene nanoribbons. RSC Adv 4:18676–18682

    CAS  Google Scholar 

  9. 9.

    Wang YJ, Assaad E, Ispas-Szabo P, Mateescu MA, Zhu XX (2011) NMR imaging of chitosan and carboxymethyl starch tablets: swelling and hydration of the polyelectrolyte complex. Int J Pharm 419:215–221

    CAS  PubMed  Google Scholar 

  10. 10.

    Ruan W, Lian Y, Zhen T, Huang L, Qiao J (2006) pH-response superabsorbant hydrogel synthesized by ultraviolet photopolymerization. J Appl Polym Sci 103:1847–1852

    Google Scholar 

  11. 11.

    Ruan W, Qiao J, Huang Y, Niu A (2005) Superabsorbent resin of acrylic acid/ammonium acrylate copolymers synthesized by ultraviolet photopolymerization. J Appl Polym Sci 95:546–555

    CAS  Google Scholar 

  12. 12.

    Sawut A, Yimit M, Sun W, Nurulla I (2014) Photopolymerisation and characterization of maleylatedcellulose-g-poly(acrylic acid) superabsorbent polymer. Carbohydr Polym 101:231–239

    CAS  PubMed  Google Scholar 

  13. 13.

    Han M, Yin X, Wu H, Hou Z, Song C, Li X, Zhang L, Cheng L (2016) Ti3C2 MXenes with modified surface for high-performance electromagnetic absorption and shielding in the X-band. ACS Appl Mater Interfaces 8:21011–21019

    CAS  PubMed  Google Scholar 

  14. 14.

    Shahzad F, Alhabeb M, Hatter CB, Anasori B, Man Hong S, Koo CM, Gogotsi Y (2016) Electromagnetic interference shielding with 2D transition metal carbides (MXenes). Science 353:1137–1140

    CAS  PubMed  Google Scholar 

  15. 15.

    Anasori B, Lukatskaya MR, Gogotsi Y (2017) 2D metal carbides and nitrides (MXenes) for energy storage. Nat Rev Mater 2:16098

    CAS  Google Scholar 

  16. 16.

    Pang J, Mendes RG, Bachmatiuk A, Zhao L, Ta HQ, Gemming T, Liu H, Liu Z, Rummeli MH (2019) Applications of 2D MXenes in energy conversion and storage systems. Chem Soc Rev 48:72–133

    CAS  PubMed  Google Scholar 

  17. 17.

    Song Y, Iyi N, Hoshide T, Ozawa TC, Ebina Y, Ma R, Yamamoto S, Miyamoto N, Sasaki T (2018) Massive hydration-driven swelling of layered perovskite niobate crystals in aqueous solutions of organo-ammonium bases. Dalton Trans 47:3022–3028

    CAS  PubMed  Google Scholar 

  18. 18.

    Meleshyn A, Bunnenberg C (2005) Swelling of Na/Mg-montmorillonites and hydration of interlayer cations: a Monte Carlo study. J Chem Phys 123:074706

    PubMed  Google Scholar 

  19. 19.

    Xu J, Camara M, Liu J, Peng L, Zhang R, Ding T (2017) Molecular dynamics study of the swelling patterns of Na/Cs-, Na/Mg montmorillonites and hydration of interlayer cations. Mol Simul 43:575–589

    CAS  Google Scholar 

  20. 20.

    Meng S, Li W, Yin X, Xie J (2013) A comprehensive theoretical study of the hydrogen bonding interactions and microscopic solvation structures of a pyridyl-urea-based hydrogelator in aqueous solution. Comput Theor Chem 1006:76–84

    CAS  Google Scholar 

  21. 21.

    Jezierska A, Panek JJ (2019) Cooperativity of hydrogen bonding network in microsolvated biotin, the ligand of avidin class proteins. J Mol Model 25:361

    CAS  PubMed  Google Scholar 

  22. 22.

    DeChancie J, Houk KN (2007) The origins of femtomolar protein−ligand binding: hydrogen-bond cooperativity and desolvation energetics in the biotin−(strept)avidin binding site. J Am Chem Soc 129:5419–5429

    CAS  PubMed  PubMed Central  Google Scholar 

  23. 23.

    Lei Y, Li H, Zhang R, Han S (2007) Theoretical study of cooperativity in biotin. J Phys Chem B 111:14370–14377

    CAS  PubMed  Google Scholar 

  24. 24.

    Wiehemeier L, Cors M, Wrede O, Oberdisse J, Hellweg T, Kottke T (2019) Swelling behaviour of core-shell microgels in H2O, analysed by temperature-dependent FTIR spectroscopy. Phys Chem Chem Phys 21:572–580

    CAS  PubMed  Google Scholar 

  25. 25.

    Pradhan SM, M.Asce KSK, M.Asce DRK (2015) Evolution of molecular interactions in the interlayer of Na-montmorillonite swelling clay with increasing hydration. Int J Geomech 15:04014073

    Google Scholar 

  26. 26.

    Derbali I, Emilie-Laure Zins EL, Mohammad Esmaïl Alikhani ME (2019) What is the hydrophobic interaction contribution to the stabilization of micro-hydrated complexes of trimethylamine oxide (TMAO)? A joint DFT-D, QTAIM, and MESP study. J Mol Model 25:363

    PubMed  Google Scholar 

  27. 27.

    Mahadevi AS, Sastry GN (2016) Cooperativity in noncovalent interactions. Chem Rev 116:2775–2825

    CAS  PubMed  Google Scholar 

  28. 28.

    Vijay D, Sastry GN (2010) The cooperativity of cation-π and π-π interactions. Chem Phys Lett 485:235–242

    CAS  Google Scholar 

  29. 29.

    Mignon P, Loverix S, Steyaert J, Geerlings P (2005) Influence of the π-π interaction on the hydrogen bonding capacity of stacked DNA/RNA bases. Nucleic Acids Res 33:1779–1789

    CAS  PubMed  PubMed Central  Google Scholar 

  30. 30.

    Hesselmann A, Jansen G, Schutz M (2006) Interaction energy contributions of H-bonded and stacked structures of the AT and GC DNA base pairs from the combined density functional theory and intermolecular perturbation theory approach. J Am Chem Soc 128:11730–11731

    CAS  PubMed  Google Scholar 

  31. 31.

    Leist R, Frey JA, Ottiger P, Frey HM, Leutwyler S, Bachorz RA, Klopper W (2007) Nucleobase-fluorobenzene interactions: hydrogen bonding wins over π-stacking. Angew Chem Int Ed 46:7449–7452

    CAS  Google Scholar 

  32. 32.

    Hruby SL, Shanks BH (2009) Acid–base cooperativity in condensation reactions with functionalized mesoporous silica catalysts. J Catal 263:181–188

    CAS  Google Scholar 

  33. 33.

    Varfolomeev MA, Abaidullina DI, Gainutdinova AZ, Solomonov BN (2010) FTIR study of H-bonds cooperativity in complexes of 1,2-dihydroxybenzene with proton acceptors in aprotic solvents: influence of the intramolecular hydrogen bond. Spectrochim Acta Part A 77:965–972

    Google Scholar 

  34. 34.

    Garcia-Raso A, Albertí FM, Fiol JJ, Tasada A, Barceló-Oliver M, Molins E, Escudero D, Frontera A, Quiñonero D, Deyà PM (2007) Anion-π interactions in bisadenine derivatives: a combined crystallographic and theoretical study. Inorg Chem 46:10724–10735

    CAS  PubMed  Google Scholar 

  35. 35.

    Alkorta I, Blanco F, Deyà PM, Elguero J, Estarellas C, Frontera A, Quiñonero D (2010) Cooperativity in multiple unusual weak bonds. Theor Chim Acta 126:1–14

    CAS  Google Scholar 

  36. 36.

    Hunter CA, Anderson HL (2009) What is cooperativity? Angew Chem Int Ed Eng 48:7488–7499

    CAS  Google Scholar 

  37. 37.

    Ferguson A, Liu Z, Chan HS (2009) Desolvation barrier effects are a likely contributor to the remarkable diversity in the folding rates of small proteins. J Mol Biol 389:619–636

    CAS  PubMed  Google Scholar 

  38. 38.

    Madeiraa PP, Bessaa A, Loureiro JA, Álvares-Ribeiroc L, Rodrigues AE, Zaslavsky BY (2015) Cooperativity between various types of polar solute–solvent interactions in aqueous media. J Chromatogr A 1408:108–117

    Google Scholar 

  39. 39.

    Zaitseva KV, Varfolomeev MA, Novikov VB, Solomonov BN (2011) Enthalpy of cooperative hydrogen bonding in complexes of tertiary amines with aliphatic alcohols: calorimetric study. J Chem Thermodynamics 43:1083–1090

    CAS  Google Scholar 

  40. 40.

    Zaitseva KV, Varfolomeev MA, Solomonov BN (2012) Thermodynamic functions of hydrogen bonding of amines in methanol derived from solution calorimetry data and headspace analysis. Thermochim Acta 535:8–16

    CAS  Google Scholar 

  41. 41.

    Rong C, Zhao D, Yu D, Liu S (2018) Quantification and origin of cooperativity: insights from density functional reactivity theory. Phys Chem Chem Phys 20:17990–17998

    CAS  PubMed  Google Scholar 

  42. 42.

    Liu SB, Rong CY, Lu T (2014) Information conservation principle determines electrophilicity, nucleophilicity, and regioselectivity. J Phys Chem A 118:3698–3704

    CAS  PubMed  Google Scholar 

  43. 43.

    Zhou XY, Rong CY, Lu T, Zhou PP, Liu SB (2016) Information functional theory: electronic properties as functionals of information for atoms and molecules. J Phys Chem A 120:3634–3642

    CAS  PubMed  Google Scholar 

  44. 44.

    Liu SB (2015) Quantifying reactivity for electrophilic aromatic substitution reactions with Hirshfeld charge. J Phys Chem A 119:3107–3111

    CAS  PubMed  Google Scholar 

  45. 45.

    Rong CY, Lu T, Ayers PW, Chattaraj PK, Liu SB (2015) Scaling properties of information-theoretic quantities in density functional reactivity theory. Phys Chem Chem Phys 17:4977–4988

    CAS  PubMed  Google Scholar 

  46. 46.

    Wu WJ, Wu ZM, Rong CY, Lu T, Huang Y, Liu SB (2015) Computational study of chemical reactivity using information-theoretic quantities from density functional reactivity theory for electrophilic aromatic substitution reactions. J Phys Chem A 119:8216–8224

    CAS  PubMed  Google Scholar 

  47. 47.

    Wu ZM, Rong CY, Lu T, Ayers PW, Liu SB (2015) Density functional reactivity theory study of SN2 reactions from the information-theoretic perspective. Phys Chem Chem Phys 17:27052–27061

    CAS  PubMed  Google Scholar 

  48. 48.

    Tsyurupa MP, Davankov VA (2006) Porous structure of hypercrosslinked polystyrene: state-of-the-art mini-review. React Funct Polym 66:768–779

    CAS  Google Scholar 

  49. 49.

    Tan L, Tan B (2017) Hypercrosslinked porous polymer materials: design, synthesis, and applications. Chem Soc Rev 46:3322–3356

    CAS  PubMed  Google Scholar 

  50. 50.

    Gutsche CD (1983) Calixarenes. Acc Chem Res 16:161–170

    CAS  Google Scholar 

  51. 51.

    Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Scalmani G, Barone V, Mennucci B, Petersson GA, Nakatsuji H, Caricato M, Li X, Hratchian HP, Izmaylov AF, Bloino J, Zheng G, Sonnenberg JL, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Vreven T, Montgomery JA, Jr, Peralta JE, Ogliaro F, Bearpark M, Heyd JJ, Brothers E, Kudin KN, Staroverov VN, Kobayashi R, Normand J, Raghavachari K, Rendell A, Burant JC, Iyengar SS, Tomasi J, Cossi M, Rega N, Millam JM, Klene M, Knox JE, Cross JB, Bakken V, Adamo C, Jaramillo J, Gomperts R, Stratmann RE, Yazyev O, Austin AJ, Cammi R, Pomelli C, Ochterski JW, Martin RL, Morokuma K, Zakrzewski VG, Voth GA, Salvador P, Dannenberg JJ, Dapprich S, Daniels AD, Farkas O, Foresman JB, Ortiz JV, Cioslowski J, Fox DJ (2009) Gaussian 09, Inc.. USA: Wallingford CT

  52. 52.

    Duijineveldt FB, Duijineveldt-van de Rijdt JCMV, Lenthe JHV (1994) State of the art in counterpoise theory. Chem Rev 94:1873–1885

    Google Scholar 

  53. 53.

    Boys SF, Bernardi F (1970) The calculation of small molecular interactions by the difference of separate total energies. Some procedures with reduced errors. Mol Phys 19:553–566

    CAS  Google Scholar 

  54. 54.

    Lu T, Chen F (2012) Multiwfn: a multifunctional wavefunction analyzer. J Comput Chem 33:580–592

    PubMed  Google Scholar 

  55. 55.

    Hajipour AR, Karimzadeh M, Jalilvand S, Farrokhpour H, Chermahini AN (2014) A complete scheme of tautomerism on diacetyl monoxime in the gas and solution phases. A comparative DFT study between B3LYP and M06-2X functionals. Comp Theor Chem 1045:10–21

    CAS  Google Scholar 

  56. 56.

    Kumar PP, Kalinichev AG, Kirkpatrick RJ (2006) Hydration, swelling, interlayer structure, and hydrogen bonding in organolayered double hydroxides: insights from molecular dynamics simulation of citrate-intercalated hydrotalcite. J Phys Chem B 110:3841–3844

    CAS  Google Scholar 

  57. 57.

    Jain KK (2008) Drug delivery systems. In: Walker JM (ed) Methods in molecular biology. Humana Press, Totowa, pp 220–224

    Google Scholar 

  58. 58.

    Jiang L, Bai P, Ren F, Wang J, Liu B, Li Y (2020) Theoretical evaluation to improve the performance of composite wax powder: cooperativity effects involving the strong Na+···π/σ and weak hydrogen-bonding interactions in the complex of graphene oxide with Na+ and CH4. Mol Phys118, In press, https://doi.org/10.1080/00268976.2019.1612106

  59. 59.

    Escudero D, Frontera A, Quiñnero D, Deyà PM (2008) Interplay between cation-π and hydrogen bonding interactions. Chem Phys Lett 456:257–261

    CAS  Google Scholar 

  60. 60.

    Rong C, Zhao D, Zhou T, Liu S, Yu D, Liu S (2019) Homogeneous molecular systems are positively cooperative but charged molecular systems are negatively cooperative. J Phys Chem Lett 10:1716–1721

    CAS  PubMed  Google Scholar 

  61. 61.

    Zhou T, Liu S, Yu D, Zhao D, Rong C, Liu S (2019) On the negative cooperativity of argon clusters containing one lithium cation or fluorine anion. Chem Phys Lett 716:192–198

    CAS  Google Scholar 

  62. 62.

    Bulat FA, Toro-Labbé A, Brinck T, Murray JS, Politzer P (2010) Quantitative analysis of molecular surfaces: areas, volumes, electrostatic potentials and average local ionization energies. J Mol Model 16:1679–1691

    CAS  PubMed  Google Scholar 

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The authors are very grateful to Professor Chun-ying Rong (Hunan Normal University) and Professor Shu-bin Liu (University of North Carolina) for their help in the calculations of the information-theoretic quantities. The authors are grateful for the financial support from the Shanxi Province Natural Science Foundation of China (No. 201801D121067).

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Correspondence to Fu-de Ren.

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We allow the journal to review all the data, and we confirm the validity of results. There is none of the financial relationships. This work was not published previously, and it is not submitted to more than one journal. It is also not split up into several parts to submit. No data have been fabricated or manipulated.

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Optimized structures of eight binary systems and the numerical values of the interaction energies per building block and the change of four information-theoretic quantities (ΔSS: Shannon entropy; ΔIF: Fisher information; ΔSGBP: Ghosh-Berkowitz-Parr entropy; ΔIG:information gain) per building block in HFR(H2O)15 are collected in Supplementary data.


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Gong, H., Ren, F., Zhao, L. et al. Hydration and swelling: a theoretical investigation on the cooperativity effect of H-bonding interactions between p-hydroxy hydroxymethyl calix[4]/[5]arene and H2O by many-body interaction and density functional reactivity theory. J Mol Model 26, 190 (2020). https://doi.org/10.1007/s00894-020-04442-0

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  • Hydration and swelling
  • Cooperativity effect
  • Hydroquinone formaldehyde resin
  • Density functional reactivity theory