mriselMagnetic Resonance in SolidsMagnetic Resonance in Solids2072-5981Kazan Federal Universitymrisel-140Research ArticleСтатьиShort-time diffusion behavior of Brownian particles in porous solidsFatkullinN. F.

Kremlevskaya, 18, Kazan 420008

Nail.Fatkullin@kpfu.ruValiullinR.

Linnestraße 5, D-04103 Leipzig

Kazan Federal UniversityRussian FederationUniversity of LeipzigGermany201419042014162SPECIAL ISSUE dedicated to Boris I. Kochelaev's 80th birthday14202 (7 pp.)Copyright © Fatkullin N.F., Valiullin R., 20242024Fatkullin N.F., Valiullin R.Fatkullin N.F., Valiullin R.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.mrsej.ru/jour/article/view/140

The process of self-diffusion of particles confined to porous solids is studied for time intervals corresponding to particle displacements shorter than the characteristic pore size. The solid matrix is modeled as a (random) potential field with an infinitely large potential within the solid which decays to zero at distances of the order of a few particle sizes from the pore walls. Diffusion of particles in the thus created potential field is described by the Smoluchowski diffusion equation. It is shown that, for short diffusion times, the resulting equation for the time-depended diffusivity reproduces that earlier obtained in the literature [Mitra et al., Phys. Rev. Lett. 68, 3555 (1992)], but with the numerical constant differing by factor 2. The conditions under which this discrepancy arises are highlighted and discussed.

diffusionporous solidsshort-time expansionSmoluchowski equationReferencesEinstein A., Ann. Phys.-Berlin 17, 549 (1905).Einstein A., Ann. Phys.-Berlin 17, 549 (1905).Cussler E. L., Diffusion: Mass Transfer in Fluid Systems, 3rd ed. (Cambridge University Press, Cambridge, 2009).Cussler E. L., Diffusion: Mass Transfer in Fluid Systems, 3rd ed. (Cambridge University Press, Cambridge, 2009).Kimmich R., NMR: tomography, diffusometry, relaxometry (Springer-Verlag, Berlin Heidelberg, 1997).Kimmich R., NMR: tomography, diffusometry, relaxometry (Springer-Verlag, Berlin Heidelberg, 1997).Price W. S., NMR Studies of Translational Motion (University Press, Cambridge, 2009).Price W. S., NMR Studies of Translational Motion (University Press, Cambridge, 2009).Callaghan P. T., Translational Dynamics and Magnetic Resonance (Oxford University Press, New York, 2011).Callaghan P. T., Translational Dynamics and Magnetic Resonance (Oxford University Press, New York, 2011).Grebenkov D. S., Rev. Mod. Phys. 79, 1077 (2007).Grebenkov D. S., Rev. Mod. Phys. 79, 1077 (2007).Mitra P. P., Sen P. N., Schwartz L. M., Ledoussal P., Phys. Rev. Lett. 68, 3555 (1992).Mitra P. P., Sen P. N., Schwartz L. M., Ledoussal P., Phys. Rev. Lett. 68, 3555 (1992).Mitra P. P., Sen P. N., Schwartz L. M., Phys. Rev. B 47, 8565 (1993).Mitra P. P., Sen P. N., Schwartz L. M., Phys. Rev. B 47, 8565 (1993).Latour L. L., Mitra P. P., Kleinberg R. L., Sotak C. H., J. Magn. Reson. A 101, 342 (1993).Latour L. L., Mitra P. P., Kleinberg R. L., Sotak C. H., J. Magn. Reson. A 101, 342 (1993).Novikov D. S., Fieremans E., Jensen J. H., Helpern J. A., Nat. Phys. 7, 508 (2011).Novikov D. S., Fieremans E., Jensen J. H., Helpern J. A., Nat. Phys. 7, 508 (2011).Hurlimann M. D., Helmer K. G., Latour L. L., Sotak C. H., J. Magn. Reson. A 111, 169 (1994).Hurlimann M. D., Helmer K. G., Latour L. L., Sotak C. H., J. Magn. Reson. A 111, 169 (1994).Sorland G. H., J. Magn. Reson. 126, 146 (1997).Sorland G. H., J. Magn. Reson. 126, 146 (1997).Gjerdaker L., Sorland G. H., Aksnes D. W., Microporous Mesoporous Mat. 32, 305 (1999).Gjerdaker L., Sorland G. H., Aksnes D. W., Microporous Mesoporous Mat. 32, 305 (1999).Johns M. L., Gladden L. F., J. Colloid Interface Sci. 238, 96 (2001).Johns M. L., Gladden L. F., J. Colloid Interface Sci. 238, 96 (2001).Butler J. P., Mair R. W., Hoffmann D., Hrovat M. I., Rogers R. A., Topulos G. P., Walsworth R. L., Patz S., J. Phys.-Condes. Matter 14, L297 (2002).Butler J. P., Mair R. W., Hoffmann D., Hrovat M. I., Rogers R. A., Topulos G. P., Walsworth R. L., Patz S., J. Phys.-Condes. Matter 14, L297 (2002).Szutkowski K., Klinowski J., Jurga S., Solid State Nucl. Magn. Reson. 22, 394 (2002).Szutkowski K., Klinowski J., Jurga S., Solid State Nucl. Magn. Reson. 22, 394 (2002).Miller G. W., Carl M., Mata J. F., Cates G. D., Mugler J. P., IEEE Trans. Med. Imaging 26, 1456 (2007).Miller G. W., Carl M., Mata J. F., Cates G. D., Mugler J. P., IEEE Trans. Med. Imaging 26, 1456 (2007).Bogdan M., Parnau A., Badea C., Ardelean I., Appl. Magn. Reson. 34, 63 (2008).Bogdan M., Parnau A., Badea C., Ardelean I., Appl. Magn. Reson. 34, 63 (2008).Tyurin V. A., Maklakov A. I., Colloid J. 64, 190 (2002).Tyurin V. A., Maklakov A. I., Colloid J. 64, 190 (2002).Muncaci S., Ardelean I., Appl. Magn. Reson. 44, 837 (2013).Muncaci S., Ardelean I., Appl. Magn. Reson. 44, 837 (2013).Doi M., Edwards S., The Theory of Polymer Dynamics (Oxford University Press, Oxford, 1986).Doi M., Edwards S., The Theory of Polymer Dynamics (Oxford University Press, Oxford, 1986).Chang D. B., Cooper R. L., Young A. C., Martin C. J., Ancker-Johnson B., J. Theor. Biol. 50, 285 (1975).Chang D. B., Cooper R. L., Young A. C., Martin C. J., Ancker-Johnson B., J. Theor. Biol. 50, 285 (1975).Fatkullin N. F., J. Exp. Theor. Phys. 98, 2030 (1990).Fatkullin N. F., J. Exp. Theor. Phys. 98, 2030 (1990).Valiullin R., Skirda V., J. Chem. Phys. 114, 452 (2001).Valiullin R., Skirda V., J. Chem. Phys. 114, 452 (2001).Sen P. N., Concepts Magn. Reson. Part A 23A, 1 (2004).Sen P. N., Concepts Magn. Reson. Part A 23A, 1 (2004).Zielinski L. J., J. Chem. Phys. 121, 352 (2004).Zielinski L. J., J. Chem. Phys. 121, 352 (2004).

The authors declare that there are no conflicts of interest present.