Skip to main content
SpringerLink
Log in

Kinetic Processes in Fullerene Solutions

  • Published:
Physics of Particles and Nuclei Aims and scope Submit manuscript

Abstract

In solutions, fullerenes, carbon nanoparticles with size of the order of one nanometer, exhibit a number of interesting properties and kinetic effects. A large part of these effects is connected with the ability of these macromolecules to form aggregates (or clusters), in which the nanoparticles are bound together by dispersion interactions. In this review, we present results of modeling of the kinetics of clusters formation and growth in fullerene C60 solutions of different polarity. The basic approach is the numerical solution of a system of kinetic equations of nucleation theory, applied here for the description of aggregation of fullerenes and accompanying effects. The non-monotonous time dependence of fullerene concentration during dissolution was investigated. A molecular-colloidal solution transition in polar systems is described. In addition, a model description of the critical effect of cluster decomposition after water addition to certain fullerene solutions is presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.
Fig. 9.
Fig. 10.

Similar content being viewed by others

REFERENCES

  1. H. W. Kroto, J. R. Heath, S. C. O’Brien, R. F. Curl, and R. E. Smalley, “C60: Buckminsterfullerene,” Nature 318, 162 (1985).

    Article  ADS  Google Scholar 

  2. A. V. Eletskii and B. M. Smirnov, “Fullerenes,” Phys. Usp. 36 (3), 202–224 (1993).

    Article  ADS  Google Scholar 

  3. R. S. Ruoff, D. S. Tse, R. Malhotra, and D. C. Lorents, “Solubility of C60 in a variety of solvents,” J. Phys. Chem. 97, 3379–3383 (1993).

    Article  Google Scholar 

  4. M. V. Avdeev, V. L. Aksenov, and T. V. Tropin, “Models of cluster formation in solution of fullerenes,” Russ. J. Phys. Chem. A 84, 1273–1283 (2010).

    Article  Google Scholar 

  5. N. O. Mchedlov-Petrossyan, N. N. Kamneva, Y. T. M. Al-Shuuchi, A. I. Marynin, and O. S. Zozulia, “Formation and ageing of the fullerene C60 colloids in polar organic solvents,” J. Mol. Liq. 235, 98–103 (2017).

    Article  Google Scholar 

  6. N. O. Mchedlov-Petrossyan, “Fullerenes in liquid media: An unsettling intrusion into the solution chemistry,” Chem. Rev. 113, 5149–5193 (2013).

    Article  Google Scholar 

  7. T. V. Tropin, M. V. Avdeev, N. Jargalan, M. O. Kuzmenko, and V. L. Aksenov, “Kinetics of cluster growth in fullerene solutions of different polarity,” Mod. Probl. Phys. Liquid Syst. 36, 249–272 (2019).

    Article  Google Scholar 

  8. M. Volmer, Kinetik der Phasenbildung (Steinkopff, Dresden, 1939).

    Google Scholar 

  9. J. W. Gibbs, “On the equilibrium of heterogeneous substances,” Trans. Connect. Acad. Arts Sci. 3, 108–248 (1876).

    MATH  Google Scholar 

  10. J. W. Gibbs, “On the equilibrium of heterogeneous substances,” Trans. Connect. Acad. Arts Sci. 3, 343–524 (1878).

    MATH  Google Scholar 

  11. M. Volmer and A. Weber, “Keimbildung in übersättigten Gebilden,” Z. Phys. Chem. 119U (1) (1926).

  12. L. Farkas, “Keimbildungsgeschwindigkeit in übersättigten Dämpfen,” Z. Phys. Chem. 125U (1) (1927).

  13. R. Kaischew and I. N. Stranski, “Zur kinetischen Ableitung der Keimbildungsgeschwindigkeit,” Z. Phys. Chem. 26 (1), 317–326 (1934).

    Article  MATH  Google Scholar 

  14. R. Kaischew and I. N. Stranski, “Zur Theorie der linearen Kristallisationsgeschwindigkeit,” Z. Phys. Chem. 170 (1), 295–299 (1934).

    Article  MATH  Google Scholar 

  15. R. Becker and W. Döring, “Kinetische Behandlung der Keimbildung in übersättigten Dämpfen,” Ann. Phys. (New York) 416, 719–752 (1935).

    ADS  MATH  Google Scholar 

  16. Ya. B. Zeldovich, “On the theory of new phase formation. Cavitation,” Zh. Eksp. Teor. Fiz. 11 (11–12), 525–538 (1942).

    Google Scholar 

  17. Ya. I. Frenkel, Kinetic Theory of Liquids (New York, 1955).

    MATH  Google Scholar 

  18. D. Turnbull and J. C. Fisher, “Rate of nucleation in condensed systems,” J. Chem. Phys. 17, 71–73 (1949).

    Article  ADS  Google Scholar 

  19. I. S. Gutzow and J. W. P. Schmelzer, The Vitreous State: Thermodynamics, Structure, Rheology, and Crystallization, 2nd ed. (Springer Berlin Heidelberg, 2013).

    Book  Google Scholar 

  20. Nucleation Theory and Applications, Ed. by J. W. P. Schmelzer (Wiley-VCH, 2005).

    Google Scholar 

  21. L. D. Landau and E. M. Lifshitz, Statistical Physics, 3rd ed. (Pergamon Press, Oxford, 1980).

    MATH  Google Scholar 

  22. J. W. P. Schmelzer and A. S. Abyzov, “Crystallization of glass-forming liquids: Thermodynamic driving force,” J. Non. Cryst. Solids 449, 41–49 (2016).

    Article  ADS  Google Scholar 

  23. J. W. P. Schmelzer, G. Ropke, and V. B. Priezzhev, Nucleation Theory and Applications, Ed. by J. W. P. Schmelzer, G. Ropke, and V. B. Priezzhev (JINR, Publ., Dubna, 1999).

    Google Scholar 

  24. V. V. Slezov and J. W. P. Schmelzer, “Kinetics of formation of a phase with an arbitrary stoichiometric composition in a multicomponent solid solution,” Phys. Rev. E 65 (3), 1–13 (2002).

    Article  Google Scholar 

  25. V. V. Slezov and J. W. P. Schmelzer, “Kinetics of formation and growth of a new phase with a definite stoichiometric composition,” J. Phys. Chem. Solids 55, 243–251 (1994).

    Article  ADS  Google Scholar 

  26. V. V. Slezov, Y. J. Tkatch, and J. W. P., Schmelzer, “The kinetics of decomposition of solid solutions,” J. Mater. Sci. 32, 3739–3747 (1997).

    Article  ADS  Google Scholar 

  27. J. Möller, K. I. Jacob, and J. W. P. Schmelzer, “Ostwald ripening in porous viscoelastic materials,” J. Phys. Chem. Solids 59, 1097–1103 (1998).

    Article  ADS  Google Scholar 

  28. D. T. Wu, “Nucleation theory,” in Solid State Physics (New York, NY, 1996), pp. 37–187.

  29. V. V. Slezov, Kinetics of First-Order Phase Transitions (Wiley-VCH, Weinheim, 2009).

    Book  Google Scholar 

  30. V. L. Aksenov, T. V. Tropin, M. V. Avdeev, V. B. Priezzhev, and J. W. P. Schmelzer, “Kinetics of cluster growth in fullerene molecular solutions,” Phys. Part. Nucl. 36, S52–S61 (2005).

    Google Scholar 

  31. J. W. P. Schmelzer and J. Möller, “Evolution of the cluster size-distribution function for Ostwald ripening in viscoelastic media,” Phase Transitions 38, 261–272 (1992).

    Article  Google Scholar 

  32. V. V. Slezov and V. V. Sagalovich, “Diffusive decomposition of solid solutions,” Sov. Phys. Usp. 30, 23–45 (1987).

    Article  ADS  Google Scholar 

  33. I. M. Lifshitz and V. V. Slezov, “Kinetics of diffusive decomposition of supersaturated solid solutions,” Sov. Phys. JETP 35, 331–339 (1959).

    MathSciNet  Google Scholar 

  34. M. V. Korobov and A. L. Smith, “Solubility of fullerenes,” in Fullerenes: Chemistry, Physics and Technology, Ed. by K. M. Kadish and R. S. Ruoff (John Wiley & Sons, 2000), pp. 53–89.

    Google Scholar 

  35. K. N. Semenov, N. A. Charykov, V. A. Keskinov, A. K. Piartman, A. A. Blokhin, and A. A. Kopyrin, “Solubility of light fullerenes in organic solvents,” J. Chem. Eng. Data 55, 13–36 (2010).

    Article  Google Scholar 

  36. V. N. Bezmel’nitsyn, A. V. Eletskii, and M. V. Okun’, “Fullerenes in solutions,” Phys.-Usp. 168, 1195 (1998).

    Google Scholar 

  37. K. A. Affholter, S. J. Henderson, G. D. Wignall, G. J. Bunick, R. E. Haufler, and R. N. Compton, “Structural characterization of C60 and C70 fullerenes by small-angle neutron scattering,” J. Chem. Phys. 99, 9224 (1993).

    Article  ADS  Google Scholar 

  38. N. O. Mchedlov-Petrossyan, “Fullerenes in molecular liquids. Solutions in "good” solvents: Another view,” J. Mol. Liq. 161, 1–12 (2011).

    Article  Google Scholar 

  39. M. V. Avdeev, T. V. Tropin, I. A. Bodnarchuk, S. P. Yaradaikin, L. Rosta, V. L. Aksenov, and L. A. Bulavin, “On structural features of fullerene C60 dissolved in carbon disulfide: Complementary study by small-angle neutron scattering and molecular dynamic simulations,” J. Chem. Phys. 132, 164515 (2010).

    Article  ADS  Google Scholar 

  40. T. V. Tropin, V. B. Priezzhev, M. V. Avdeev, J. W. P. Schmelzer, and V. L. Aksenov, “Fullerene cluster formation in carbon disulfide and toluene,” Fullerenes, Nanotubes, Carbon Nanostruct. 14, 481–488 (2006).

    Article  ADS  Google Scholar 

  41. T. V. Tropin and V. L. Aksenov, “Theoretical study of the effect of decrease of cluster size on dilution of a solution with water,” JETP 128, 274–280 (2019).

    Article  ADS  Google Scholar 

  42. T. V. Tropin, M. V. Avdeev, and V. L. Aksenov, “Modeling of the evolution of cluster-size distribution functions in polar fullerene C60 solutions,” J. Surf. Invest.: X-ray Synchrotron Neutron Tech. 13, 82–86 (2019).

    Article  Google Scholar 

  43. T. Tomiyama, S. Uchiyama, and H. Shinohara, “Solubility and partial specific volumes of C60 and C70,” Chem. Phys. Lett. 264, 143–148 (1997).

    Article  ADS  Google Scholar 

  44. T. V. Tropin, M. V. Avdeev, and V. L. Aksenov, “Small-angle neutron scattering study of C60/CS2 solutions,” Fullerenes, Nanotubes, Carbon Nanostruct. 16, 616–621 (2008).

    Article  ADS  Google Scholar 

  45. T. V. Tropin, M. V. Avdeev, and V. L. Aksenov, “Small-angle neutron scattering data on C60 clusters in weakly polar solutions,” Cryst. Rep 52, 483–486 (2007).

    Article  Google Scholar 

  46. M. V. Avdeev, T. V. Tropin, V. L. Aksenov, L. Rosta, and M. T. Kholmurodov, “Formation of fullerene clusters in carbon disulfide: Data on small-angle neutron scattering and molecular dynamics,” J. Surf. Invest.: X‑ray Synchrotron Neutron Tech. 2, 819–825 (2008).

    Article  Google Scholar 

  47. T. V. Tropin, M. V. Avdeev, V. B. Priezzhev, and V. L. Aksenov, “Nonmonotonic behavior of the concentration in the kinetics of dissolution of fullerenes,” JETP Lett. 83, 399–404 (2006).

    Article  ADS  Google Scholar 

  48. N. P. Yevlampieva, Yu. F. Biryulin, E. Yu. Melenev-skaja, V. N. Zgonnik, and E. I. Rjumtsev, “Aggregation of fullerene C60 in N-methylpyrrolidone,” Colloids Surf. A Physicochem. Eng. Asp. 209, 167–171 (2002).

    Article  Google Scholar 

  49. O. A. Kyzyma, L. A. Bulavin, V. L. Aksenov, T. V. Tropin, M. V. Avdeev, M. V. Korobov, S. V. Snegir, and L. Rosta, “Aggregation in C60/NMP, C60/NMP/Water and C60/NMP/toluene mixtures,” Fullerenes, Nanotubes, Carbon Nanostruct. 16, 610–615 (2008).

    Article  ADS  Google Scholar 

  50. O. A. Kyzyma, M. V. Korobov, M. V. Avdeev, V. M. Garamus, S. V. Snegir, V. I. Petrenko, V. L. Aksenov, and L. A. Bulavin, “Aggregate development in C60/N-methyl-2-pyrrolidone solution and its mixture with water as revealed by extraction and mass spectroscopy,” Chem. Phys. Lett. 493, 103–106 (2010).

    Article  ADS  Google Scholar 

  51. S. V. Snegir, T. V. Tropni, O. A. Kyzyma, M. O. Kuzmenko, V. I. Petrenko, V. M. Garamus, M. V. Korobov, M. V. Avdeev, and L. A. Bulavin, “On a specific state of C60 fullerene in N-methyl-2-pyrrolidone solution: Mass spectrometric study,” Appl. Surf. Sci. 481, 1566–1572 (2019).

    Article  ADS  Google Scholar 

  52. T. V. Tropin, M. V. Avdeev, O. A. Kyzyma, R. A. Yeremin, N. Jargalan, M. V. Korobov, and V. L. Aksenov, “Towards description of kinetics of dissolution and cluster growth in C60/NMP solutions,” Phys. Status Solidi B 248, 2728–2731 (2011).

    Article  ADS  Google Scholar 

  53. T. V. Tropin, N. Jargalan, M. V. Avdeev, O. A. Kyzyma, R. A. Eremin, D. Sangaa, and V. L. Aksenov, “Kinetics of cluster growth in polar solutions of fullerene: Experimental and theoretical study of C60/NMP solution,” J. Mol. Liq. 175, 4–11 (2012).

    Article  Google Scholar 

  54. N. Jargalan, T. V. Tropin, M. V. Avdeev, and V. L. Aksenov, “Investigation and modeling of evolution of C60/NMP solution UV-Vis spectra,” Nanosyst. Phys. Chem. Math. 7, 99–103 (2016).

    Article  Google Scholar 

  55. J. W. P. Schmelzer and I. S. Gutzow, “On the kinetic description of Ostwald ripening in elastic media,” Z. Phys. Chem. 269, 753–767 (1988).

    Google Scholar 

  56. R. Pascova, I. S. Gutzow, and J. W. P. Schmelzer, “A model investigation of the process of phase formation in photochromic glasses,” J. Mater. Sci. 25, 921–931 (1990).

    Article  ADS  Google Scholar 

  57. A. Mrzel, A. Mertelj, A. Omerzu, M. Copic, and D. Mihailovic, “Investigation of encapsulation and solvatochromism of fullerenes in binary solvent mixtures,” J. Phys. Chem. B 103, 11256–11260 (1999).

    Article  Google Scholar 

  58. V. L. Aksenov, M. V. Avdeev, T. V. Tropin, M. V. Korobov, N. V. Kozhemyakina, N. V. Avramenko, and L. Rosta, “Formation of fullerene clusters in the system C60/NMP/water by SANS,” Phys. B Condens. Matter 385–386, 795–797 (2006).

    Google Scholar 

  59. T. V. Tropin, T. O. Kyrey, O. A. Kyzyma, A. V. Feoktistov, M. V. Avdeev, L. A. Bulavin, L. Rosta, and V. L. Aksenov, “Experimental investigation of C60/NMP/toluene solutions by UV-Vis spectroscopy and small-angle neutron scattering,” J. Surf. Invest.: X‑ray Synchrotron Neutron Tech. 7, 1–4 (2013).

    Article  Google Scholar 

  60. V. L. Aksenov, T. V. Tropin, O. A. Kyzyma, M. V. Avdeev, M. V. Korobov, and L. Rosta, “Formation of C60 fullerene clusters in nitrogen-containing solvents,” Phys. Solid State 52, 1059–1062 (2010).

    Article  ADS  Google Scholar 

  61. P. Jain and S. H. Yalkowsky, “Solubilization of poorly soluble compounds using 2-pyrrolidone,” Int. J. Pharm. 342, 1–5 (2007).

    Article  Google Scholar 

  62. R. Sanghvi, R. Narazaki, S. G. Machatha, and S. H. Yalkowsky, “Solubility improvement of drugs using N-methyl pyrrolidone,” Am. Assoc. Pharm. Sci. 9, 366–376 (2008).

    Google Scholar 

  63. R. G. Davey, S. L. M. Schroeder, and J. H. ter Horst, “Nucleation of Organic Crystals—A Molecular Perspective,” Angew. Chem. Int. 52, 2–16 (2013). https://doi.org/10.1002/anie.201204824

    Article  Google Scholar 

  64. R. J. Davey, S. L. M. Schroeder, and J. H. Ter Horst, “Nucleation of organic crystals – A molecular perspective,” Angew. Chem. Int. Ed. 52, 2167–2179 (2013).

    Article  Google Scholar 

  65. T. V. Tropin, M. V. Avdeev, O. A. Kyzyma, and V. L. Aksenov, “Nucleation theory models for describing kinetics of cluster growth in C60/NMP solutions,” Phys. Status Solidi 247, 3022—3025 (2010).

    Article  Google Scholar 

  66. G. E. Norman and V. V. Stegailov, “Stochastic theory of the classical molecular dynamics method,” Math. Mod. Comp. Simul. 5, 305–333 (2013).

    Article  Google Scholar 

  67. G. C. Sosso, J. Chen, S. J. Cox, M. Fitzner, P. Pedevilla, A. Zen, and A. Michaelides, “Crystal nucleation in liquids: Open questions and future challenges in molecular dynamics simulations,” Chem. Rev. 116, 7078–7116 (2016).

    Article  Google Scholar 

  68. A. O. Tipeev, E. D. Zanotto, and J. P. Rino, “Diffusivity, interfacial free energy, and crystal nucleation in a supercooled Lennard-Jones liquid,” J. Phys. Chem. C 122, 28884–28894 (2018).

    Article  Google Scholar 

  69. V. G. Baidakov and A. O. Tipeev, “Molecular dynamics simulation of homogeneous nucleation in a superheated Lennard-Jones crystal,” J. Non-Cryst. Solids 503–504, 302–307 (2019).

    Article  ADS  Google Scholar 

  70. C. Rey, L. J. Gallego, and J. A. Alonso, “Molecular-dynamics study of the structure, binding energy, and melting of small clusters of fullerene molecules using Girifalco’s spherical model,” Phys. Rev. B 49, 8491–8494 (1994).

    Article  ADS  Google Scholar 

  71. C. I. Wang, C. C. Hua, and S. A. Chen, “Dynamic solvation shell and solubility of C60 in organic solvents,” J. Phys. Chem. B 118, 9964–9973 (2014).

    Article  Google Scholar 

  72. T. Malaspina, E. E. Fileti, and R. Rivelino, “Structure and UV-Vis spectrum of C60 fullerene in ethanol: A sequential molecular dynamics/quantum mechanics study,” J. Phys. Chem. B 111, 11935–11939 (2007).

    Article  Google Scholar 

  73. R. Dattani, K. F. Gibson, S. Few, A. J. Borg, P. A. DiMaggio, J. Nelson, S. G. Kazarian, and J. T. Cabral, “Fullerene oxidation and clustering in solution induced by light,” J. Colloid Interface Sci. 446, 24–30 (2015).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Frank Laboratory of Neutron Physics, Joint Institute for Nuclear Research, 141980, Dubna, Russia

    T. V. Tropin & V. L. Aksenov

  2. Institute of Physics, University of Rostock, 18051, Rostock, Germany

    J. W. P. Schmelzer

Authors
  1. T. V. Tropin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. L. Aksenov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. J. W. P. Schmelzer
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. V. Tropin.

Additional information

This article is dedicated to the memory of Vyacheslav Borisovich Priezzhev

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tropin, T.V., Aksenov, V.L. & Schmelzer, J.W. Kinetic Processes in Fullerene Solutions. Phys. Part. Nuclei 52, 315–329 (2021). https://doi.org/10.1134/S1063779621020076

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063779621020076

Search

Navigation