Skip to main content
Log in

Local NMR Relaxation of Dendrimers in the Presence of Hydrodynamic Interactions

  • Original Paper
  • Published:
Applied Magnetic Resonance Aims and scope Submit manuscript

Abstract

We study the role of hydrodynamic interactions for the relaxation of segments’ orientations in dendrimers. The dynamics is considered in the Zimm framework. It is shown that inclusion of correlations between segments’ orientations plays a major role for the segments’ mobility, which reveals itself in the nuclear magnetic resonance relaxation functions. The enhancement of the reorientation dynamics of segments due to the hydrodynamic interactions is more significant for the inner segments. This effect is clearly pronounced in the reduced spectral density \(\omega J(\omega )\), maximum of which shifts to higher frequencies when the hydrodynamic interactions are taken into account.

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

Access this article

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

Similar content being viewed by others

References

  1. A.W. Bosman, H.M. Janssen, E.W. Meijer, Chem. Rev. 99(7), 1665 (1999)

    Article  Google Scholar 

  2. S.M. Grayson, J.M.J. Frechet, Chem. Rev. 101(12), 3819 (2001)

    Article  Google Scholar 

  3. C.C. Lee, J.A. MacKay, J.M.J. Fréchet, F.C. Szoka, Nat. Biotechnol. 23(12), 1517 (2005)

    Article  Google Scholar 

  4. E.R. Gillies, J.M.J. Frechet, Drug Discov. Today 10(1), 35 (2005)

    Article  Google Scholar 

  5. H.J. Hsu, J. Bugno, S.R. Lee, S. Hong, WIREs Nanomed. Nanobiotechnol. 9, e1409 (2017). doi:10.1002/wnan.1409

    Article  Google Scholar 

  6. D. Astruc, F. Chardac, Chem. Rev. 101(9), 2991 (2001)

    Article  Google Scholar 

  7. A.M. Caminade, Chem. Soc. Rev. 45, 5174 (2016)

    Article  Google Scholar 

  8. H. Wang, G.P. Simon, C. Hawker, C. Tiu, Mater. Res. Innov. 6(4), 160 (2002)

    Article  Google Scholar 

  9. E. Hajizadeh, B.D. Todd, P.J. Daivis, J. Chem. Phys. 141(19), 194905 (2014)

    Article  Google Scholar 

  10. E. Wiener, M. Brechbiel, H. Brothers, R.L. Magin, O. Gansow, D. Tomalia, P. Lauterbur, Magn. Reson. Med. 31(1), 1 (1994)

    Article  Google Scholar 

  11. W. Sun, J. Li, M. Shen, X. Shi, in Dendrimer-Based Nanodevices as Contrast Agents for MR Imaging Applications, ed. by D. Zhifei. Advances in Nanotheranostics I, Springer Series in Biomaterials Science and Engineering, vol 6 (Springer, Heidelberg, 2016), pp. 249–270. doi:10.1007/978-3-662-48544-6_8

  12. A. Kumar, P. Biswas, Phys. Chem. Chem. Phys. 15(46), 20294 (2013)

    Article  Google Scholar 

  13. D.A. Markelov, M. Dolgushev, Y.Y. Gotlib, A. Blumen, J. Chem. Phys. 140, 244904 (2014)

    Article  ADS  Google Scholar 

  14. J. Grimm, M. Dolgushev, Phys. Chem. Chem. Phys. 18(28), 19050 (2016)

    Article  Google Scholar 

  15. D.A. Markelov, S.G. Falkovich, I.M. Neelov, M.Y. Ilyash, V.V. Matveev, E. Lähderanta, P. Ingman, A.A. Darinskii, Phys. Chem. Chem. Phys. 17(5), 3214 (2015)

    Article  Google Scholar 

  16. O.V. Shavykin, I.M. Neelov, A.A. Darinskii, Phys. Chem. Chem. Phys. 18(35), 24307 (2016)

    Article  Google Scholar 

  17. D.A. Markelov, A.N. Shishkin, V.V. Matveev, A.V. Penkova, E. Lähderanta, V.I. Chizhik, Macromolecules 49(23), 9247 (2016)

    Article  ADS  Google Scholar 

  18. L.F. Pinto, J. Correa, M. Martin-Pastor, R. Riguera, E. Fernandez-Megia, J. Am. Chem. Soc. 135(5), 1972 (2013)

    Article  Google Scholar 

  19. L.F. Pinto, R. Riguera, E. Fernandez-Megia, J. Am. Chem. Soc. 135(31), 11513 (2013)

    Article  Google Scholar 

  20. M. Hofmann, C. Gainaru, B. Cetinkaya, R. Valiullin, N. Fatkullin, E.A. Rössler, Macromolecules 48(20), 7521 (2015)

    Article  ADS  Google Scholar 

  21. F. Mohamed, M. Hofmann, B. Pötzschner, N. Fatkullin, E.A. Rössler, Macromolecules 48(10), 3294 (2015)

    Article  Google Scholar 

  22. D.A. Markelov, M. Dolgushev, E. Lähderanta, Annu. Rep. NMR Spectrosc. 91, 1 (2017)

    Article  Google Scholar 

  23. M. Chai, Y. Niu, W.J. Youngs, P.L. Rinaldi, J. Am. Chem. Soc. 123(20), 4670 (2001)

    Article  Google Scholar 

  24. A. Sagidullin, V.D. Skirda, E.A. Tatarinova, A.M. Muzafarov, M.A. Krykin, A.N. Ozerin, B. Fritzinger, U. Scheler, Appl. Magn. Reson. 25, 129 (2003)

    Article  Google Scholar 

  25. C. Malveau, W.E. Baille, X.X. Zhu, W.T. Ford, J. Polym. Sci. Part B Polym. Phys. 41, 2969 (2003)

    Article  ADS  Google Scholar 

  26. D.A. Markelov, V.V. Matveev, P. Ingman, M.N. Nikolaeva, E. Lähderanta, V.A. Shevelev, N.I. Boiko, J. Phys. Chem. B 114(12), 4159 (2010)

    Article  Google Scholar 

  27. D.A. Markelov, V.V. Matveev, P. Ingman, M.N. Nikolaeva, A.V. Penkova, E. Lähderanta, N.I. Boiko, V.I. Chizhik, Sci. Rep. 6, 24270 (2016)

    Article  ADS  Google Scholar 

  28. M. Dolgushev, A. Blumen, J. Chem. Phys. 131, 044905 (2009)

    Article  ADS  Google Scholar 

  29. M. Bixon, R. Zwanzig, J. Chem. Phys. 68(4), 1896 (1978)

    Article  ADS  Google Scholar 

  30. Y.Y. Gotlib, Y.Y. Svetlov, Polym. Sci. USSR 21, 1682 (1980)

    Article  Google Scholar 

  31. M. Guenza, A. Perico, Macromolecules 25(22), 5942 (1992)

    Article  ADS  Google Scholar 

  32. R.G. Winkler, P. Reineker, L. Harnau, J. Chem. Phys. 101(9), 8119 (1994)

    Article  ADS  Google Scholar 

  33. R. La Ferla, J. Chem. Phys. 106(2), 688 (1997)

    Article  ADS  Google Scholar 

  34. C. von Ferber, A. Blumen, J. Chem. Phys. 116(19), 8616 (2002)

    Article  ADS  Google Scholar 

  35. M. Doi, S.F. Edwards, The Theory of Polymer Dynamics (Clarendon Press, Oxford, 1988)

  36. M.L. Mansfield, W.H. Stockmayer, Macromolecules 13(6), 1713 (1980)

    Article  ADS  Google Scholar 

  37. M. Dolgushev, A. Blumen, Macromolecules 42, 5378 (2009)

    Article  ADS  Google Scholar 

  38. N. Biggs, Algebraic Graph Theory (Cambridge University Press, Cambridge, 1993)

  39. F. Fürstenberg, M. Dolgushev, A. Blumen, J. Chem. Phys. 136, 154904 (2012)

    Article  ADS  Google Scholar 

  40. B.H. Zimm, J. Chem. Phys. 24(2), 269 (1956)

    Article  ADS  MathSciNet  Google Scholar 

  41. I. Teraoka, Polymer Solutions (Wiley Online Library, New York, 2002)

  42. K. Osaki, Macromolecules 5(2), 141 (1972)

    Article  ADS  MathSciNet  Google Scholar 

  43. K. Osaki, J.L. Schrag, J.D. Ferry, Macromolecules 5(2), 144 (1972)

    Article  ADS  Google Scholar 

  44. P. Biswas, R. Kant, A. Blumen, J. Chem. Phys. 114(5), 2430 (2001)

    Article  ADS  Google Scholar 

  45. A. Kumar, P. Biswas, Macromolecules 43(17), 7378 (2010)

    Article  ADS  Google Scholar 

  46. M. Galiceanu, J. Chem. Phys. 140(3), 034901 (2014)

    Article  ADS  Google Scholar 

  47. M. Galiceanu, A. Jurjiu, J. Chem. Phys. 145(10), 104901 (2016)

    Article  ADS  Google Scholar 

  48. Z.Y. Chen, C. Cai, Macromolecules 32, 5423 (1999)

    Article  ADS  Google Scholar 

  49. T. Khazanovich, Polym. Sci. USSR 4(4), 727 (1963)

    Article  Google Scholar 

  50. A. Perico, M. Guenza, J. Chem. Phys. 83, 3103 (1985)

    Article  ADS  Google Scholar 

  51. A. Abragam, The Principles of Nuclear Magnetism (Oxford University Press, Oxford, 1961)

  52. R. Kimmich, N. Fatkullin, vol. 170. Advances in Polymer Science (Springer, Berlin, Heidelberg, 2004), p. 1

  53. R. Kimmich, NMR: Tomography, Diffusometry, Relaxometry (Springer Science & Business Media, Berlin, 2012)

  54. V.I. Chizhik, Y.S. Chernyshev, A.V. Donets, V.V. Frolov, A.V. Komolkin, M.G. Shelyapina, Magnetic Resonance and its Applications (Springer, Cham, 2014)

  55. Yu.Ya. Gotlib, D.A. Markelov, Polym. Sci. Ser. A 49(10), 1137 (2007)

    Article  Google Scholar 

  56. D.A. Markelov, S.V. Lyulin, Y.Y. Gotlib, A.V. Lyulin, V.V. Matveev, E. Lahderanta, A.A. Darinskii, J. Chem. Phys. 130(4), 044907 (2009)

    Article  ADS  Google Scholar 

  57. D.A. Markelov, Y.Y. Gotlib, A.A. Darinskii, A.V. Lyulin, S.V. Lyulin, Polym. Sci. Ser. A 51(3), 331 (2009)

    Article  Google Scholar 

  58. S.V. Lyulin, A.A. Darinskii, A.V. Lyulin, M. Michels, Macromolecules 37(12), 4676 (2004)

    Article  ADS  Google Scholar 

  59. C. Cai, Z.Y. Chen, Macromolecules 30, 5104 (1997)

    Article  ADS  Google Scholar 

  60. Yu.Ya. Gotlib, D.A. Markelov, Polym. Sci. Ser. A 44(12), 1341 (2002)

    Google Scholar 

Download references

Acknowledgements

M.D. acknowledges the support through Grant No. GRK 1642/1 of the Deutsche Forschungsgemeinschaft. D.A.M. acknowledges the Russian Foundation for Basic Research (project no. 14-03-00926) and the Government of the Russian Federation (project no. 074-U01).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Maxim Dolgushev.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dolgushev, M., Schnell, S. & Markelov, D.A. Local NMR Relaxation of Dendrimers in the Presence of Hydrodynamic Interactions. Appl Magn Reson 48, 657–671 (2017). https://doi.org/10.1007/s00723-017-0897-6

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00723-017-0897-6

Navigation