Mesopore Diffusion Within Porous Silicon

  • Jörg Kärger
  • Rustem Valiullin
Living reference work entry

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In applications such as sensing and drug delivery, the performance of mesoporous silicon (PSi) may be controlled by the rate of diffusive propagation of the confined molecules. The pulsed field gradient technique of nuclear magnetic resonance provides the most direct access to molecular diffusion. The different factors determining the diffusivities in PSi are the focus of this updated review. In particular, diffusivities in liquid state are shown to be most strongly affected by mesoscale disorder. Atomistic disorder is shown to control surface diffusion in applications in which PSi is brought into contact with gas phases at low vapor pressures. Correlations between the compositions of phases coexisting within the pore space, namely, liquid and gaseous, and liquid and solid ones, respectively, are briefly discussed.


Diffusion Pulsed field gradient NMR Confinements Phase state-transport correlations 


  1. Acquaroli LN, Urteaga R, Berli CLA, Koropecki RR (2011) Capillary filling in nanostructured porous silicon. Langmuir 27(5):2067–2072CrossRefGoogle Scholar
  2. Ala-Nissila T, Ferrando R, Ying SC (2002) Collective and single particle diffusion on surfaces. Adv Phys 51(3):949–1078CrossRefGoogle Scholar
  3. Anglin EJ, Schwartz MP, Ng VP, Perelman LA, Sailor MJ (2004) Engineering the chemistry and nanostructure of porous silicon fabry-perot films for loading and release of a steroid. Langmuir 20(25):11264–11269CrossRefGoogle Scholar
  4. Barthelemy P, Ghulinyan M, Gaburro Z, Toninelli C, Pavesi L, Wiersma DS (2007) Optical switching by capillary condensation. Nat Photonics 1(3):172–175CrossRefGoogle Scholar
  5. Berezhkovskii AM, Pustovoit MA, Bezrukov SM (2007) Diffusion in a tube of varying cross section: numerical study of reduction to effective one-dimensional description. J Chem Phys 126(13):134705–134706CrossRefGoogle Scholar
  6. Burada PS, Hanggi P, Marchesoni F, Schmid G, Talkner P (2009) Diffusion in confined geometries. ChemPhysChem 10(1):45–54CrossRefGoogle Scholar
  7. Carslaw HS, Jaeger JC (1946) Conduction of heat in solids. Clarendon, OxfordGoogle Scholar
  8. Cerclier CV, Ndao M, Busselez R, Lefort R, Grelet E, Huber P, Kityk AV, Noirez L, Schonhals A, Morineau D (2012) Structure and phase behavior of a discotic columnar liquid crystal confined in nanochannels. J Phys Chem C 116(35):18990–18998CrossRefGoogle Scholar
  9. Chung HH, Chan CK, Khire TS, Marsh GA, Clark A, Waugh RE, JL MG (2014) Highly permeable silicon membranes for shear free chemotaxis and rapid cell labelling. Lab Chip 14(14):2456–2468CrossRefGoogle Scholar
  10. Cussler EL (2009) Diffusion: mass transfer in fluid systems, 3rd edn. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  11. de Smet L, Zuilhof H, EJR S, Wittstock G, Duerdin MS, Lie LH, Houlton A, Horrocks BR (2002) Diffusion in porous silicon: effects on the reactivity of alkenes and electrochemistry of alkylated porous silicon. Electrochim Acta 47(16):2653–2663CrossRefGoogle Scholar
  12. Desai TA, Hansford D, Ferrari M (1999) Characterization of micromachined silicon membranes for immunoisolation and bioseparation applications. J Membr Sci 159(1–2):221–231CrossRefGoogle Scholar
  13. Dvoyashkin M, Khokhlov A, Valiullin R, Kärger J (2008) Freezing of fluids in disordered mesopores. J Chem Phys 129(15):154702–154706CrossRefGoogle Scholar
  14. Dvoyashkin M, Khokhlov A, Naumov S, Valiullin R (2009) Pulsed field gradient NMR study of surface diffusion in mesoporous adsorbents. Microporous Mesoporous Mater 125(1–2):58–62CrossRefGoogle Scholar
  15. Gaburro Z, Daldosso N, Pavesi L, Faglia G, Baratto C, Sberveglieri G (2001) Monitoring penetration of ethanol in a porous silicon microcavity by photoluminescence interferometry. Appl Phys Lett 78(23):3744–3746CrossRefGoogle Scholar
  16. Gomer R (1990) Diffusion of adsorbates on metal-surfaces. Rep Prog Phys 53(7):917–1002CrossRefGoogle Scholar
  17. Gruener S, Huber P (2008) Knudsen diffusion in silicon nanochannels. Phys Rev Lett 100(6):064502–064504CrossRefGoogle Scholar
  18. Guegan R, Morineau D, Loverdo C, Beziel W, Guendouz M (2006) Evidence of anisotropic quenched disorder effects on a smectic liquid crystal confined in porous silicon. Phys Rev E 73(1):011706–011707CrossRefGoogle Scholar
  19. Hofmann T, Wallacher D, Mayorova M, Zorn R, Frick B, Huber P (2012) Molecular dynamics of n-hexane: a quasi-elastic neutron scattering study on the bulk and spatially nanochannel-confined liquid. J Chem Phys 136(12):124505CrossRefGoogle Scholar
  20. Huber P (2015) Soft matter in hard confinement: phase transitions, thermodynamics, structure, texture, diffusion and flow in nanoporous media. J Phys Condens Matter 27:103102CrossRefGoogle Scholar
  21. Ileri N, Stroeve P, Palazoglu A, Faller R, Zaidi SH, Nguyen HT, Britten JA, Letant SE, Tringe JW (2012) Fabrication of functional silicon-based nanoporous membranes. J Micro-Nanolithogr MEMS MOEMS 11(1):013012CrossRefGoogle Scholar
  22. Jackson CL, McKenna GB (1990) The melting behavior of organic materials confined in porous solids. J Chem Phys 93(12):9002–9011CrossRefGoogle Scholar
  23. Jobic H, Theodorou DN (2007) Quasi-elastic neutron scattering and molecular dynamics simulation as complementary techniques for studying diffusion in zeolites. Microporous Mesoporous Mater 102(1–3):21–50CrossRefGoogle Scholar
  24. Kärger J, Ruthven DM (2016) Diffusion in nanoporous materials- fundamental principles, insights and challenges. New J Chem 40:4027–4048CrossRefGoogle Scholar
  25. Kärger J, Valiullin R (2013) Mass transfer in mesoporous materials: the benefit of microscopic diffusion measurement. Chem Soc Rev 42(9):4172–4197CrossRefGoogle Scholar
  26. Kärger J, Ruthven DM, Theodorou D (2012) Diffusion in zeolites and other nanoporous materials. Wiley, WeinheimCrossRefGoogle Scholar
  27. Kavalenka MN, Striemer CC, Fang DZ, Gaborski TR, JL MG, Fauchet PM (2012) Ballistic and non-ballistic gas flow through ultrathin nanopores. Nanotechnology 23(14):145706CrossRefGoogle Scholar
  28. Kondrashova D, Dvoyashkin M, Valiullin R (2011) Structural characterization of porous solids by simultaneously monitoring the low-temperature phase equilibria and diffusion of intrapore fluids using nuclear magnetic resonance. New J Phys 13(1):015008CrossRefGoogle Scholar
  29. Kondrashova D, Lauerer A, Mehlhorn D, Jobic H, Feldhoff A, Thommes M, Chakraborty D, Gommes C, Zecevic J, de Jongh P, Bunde A, Kärger J, Valiullin R (2017) Scale-dependent diffusion anisotropy in nanoporous silicon. Sci Rep 7: 40207.CrossRefGoogle Scholar
  30. Kovalev D, Fujii M (2005) Silicon nanocrystals: photosensitizers for oxygen molecules. Adv Mater 17(21):2531–2544CrossRefGoogle Scholar
  31. Kusmin A, Gruener S, Henschel A, de Souza N, Allgaier J, Richter D, Huber P (2010) Polymer dynamics in nanochannels of porous silicon: a neutron spin echo study. Macromolecules 43(19):8162–8169CrossRefGoogle Scholar
  32. Lauerer A, Zeigermann P, Lenzner J, Chmelik C, Thommes M, Valiullin R, Kärger J (2015) Micro imaging of liquid-vapor phase transition in nano-channels. Microporous Mesoporous Mater 214:143–148CrossRefGoogle Scholar
  33. Lehmann V, Stengl R, Luigart A (2000) On the morphology and the electrochemical formation mechanism of mesoporous silicon. Mater Sci Eng B 69:11–22CrossRefGoogle Scholar
  34. Li MD, Hu M, Liu QL, Ma SY, Sun P (2013) Microstructure characterization and NO2-sensing properties of porous silicon with intermediate pore size. Appl Surf Sci 268:188–194CrossRefGoogle Scholar
  35. Lysenko V, Vitiello J, Remaki B, Barbier D (2004) Gas permeability of porous silicon nanostructures. Phys Rev E 70(1):017301CrossRefGoogle Scholar
  36. Mares JW, Weiss SM (2011) Diffusion dynamics of small molecules from mesoporous silicon films by real-time optical interferometry. Appl Optics 50(27):5329–5337CrossRefGoogle Scholar
  37. Naumov S, Khokhlov A, Valiullin R, Kärger J, Monson PA (2008a) Understanding capillary condensation and hysteresis in porous silicon: network effects within independent pores. Phys Rev E 78(6):060601–060604CrossRefGoogle Scholar
  38. Naumov S, Valiullin R, Monson PA, Kärger J (2008b) Probing memory effects in confined fluids via diffusion measurements. Langmuir 24(13):6429–6432CrossRefGoogle Scholar
  39. Naumov S, Valiullin R, Kärger J, Monson PA (2009) Understanding adsorption and desorption processes in mesoporous materials with independent disordered channels. Phys Rev E 80(3):031607CrossRefGoogle Scholar
  40. Petersen EE (1958) Diffusion in a pore of varying cross section. AICHE J 4(3):343–345CrossRefGoogle Scholar
  41. Pollard WG, Present RD (1948) On gaseous self-diffusion in long capillary tubes. Phys Rev 73(7):762–774CrossRefGoogle Scholar
  42. Prestidge CA, Barnes TJ, Lau CH, Barnett C, Loni A, Canham L (2007) Mesoporous silicon: a platform for the delivery of therapeutics. Expert Opin Drug Deliv 4(2):101–110CrossRefGoogle Scholar
  43. Puibasset J, Porion P, Grosman A, Rolley E (2016) Structure and permeability of porous silicon investigated by self-diffusion NMR measurements of ethanol and heptane. Oil Gas Sci Techn 71(4):54CrossRefGoogle Scholar
  44. Renisch S, Schuster R, Wintterlin J, Ertl G (1999) Dynamics of adatom motion under the influence of mutual interactions: O/Ru(0001). Phys Rev Lett 82(19):3839–3842CrossRefGoogle Scholar
  45. Schechter I, Benchorin M, Kux A (1995) Gas-sensing properties of porous silicon. Anal Chem 67(20):3727–3732CrossRefGoogle Scholar
  46. Valiullin R, Khokhlov A (2006) Orientational ordering of linear n-alkanes in silicon nanotubes. Phys Rev E 73(5):051604–051605CrossRefGoogle Scholar
  47. Valiullin R, Kortunov P, Kärger J, Timoshenko V (2004) Concentration-dependent self-diffusion of liquids in nanopores: a nuclear magnetic resonance study. J Chem Phys 120(24):11804–11814CrossRefGoogle Scholar
  48. Valiullin R, Kortunov P, Kärger J, Timoshenko V (2005a) Surface self-diffusion of organic molecules adsorbed in porous silicon. J Phys Chem B 109:5746–5752CrossRefGoogle Scholar
  49. Valiullin R, Kortunov P, Kärger J, Timoshenko V (2005b) Concentration-dependent self-diffusion of adsorbates in mesoporous materials. Magn Reson Imaging 23:209–213CrossRefGoogle Scholar
  50. Valiullin R, Kärger J, Gläser R (2009) Correlating phase behaviour and diffusion in mesopores: perspectives revealed by pulsed field gradient NMR. Phys Chem Chem Phys 11(16):2833–2853CrossRefGoogle Scholar
  51. Velleman L, Shearer CJ, Ellis AV, Losic D, Voelcker NH, Shapter JG (2010) Fabrication of self-supporting porous silicon membranes and tuning transport properties by surface functionalization. Nanoscale 2(9):1756–1761CrossRefGoogle Scholar
  52. Wallacher D, Kunzner N, Kovalev D, Knorr N, Knorr K (2004) Capillary condensation in linear mesopores of different shape. Phys Rev Lett 92(19):195704CrossRefGoogle Scholar
  53. Wu CC, Sailor MJ (2013) Selective functionalization of the internal and the external surfaces of mesoporous silicon by liquid masking. ACS Nano 7(4):3158–3167CrossRefGoogle Scholar
  54. Zhao Y, Gaur G, Retterer ST, Labinis PE, Weiss SM (2016) Flow-through porous silicon membranes for real time label-free biosensing. Anal Chem 88(22):10940–10948CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of LeipzigLeipzigGermany
  2. 2.Felix Bloch Institute for Solid State PhysicsUniversity of LeipzigLeipzigGermany

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