Direct multilayer adsorption of vapor in solids with multiscale porosity and hindered adsorbed layers in nanopores

Zdeněk P. Bažant*, Hoang Thai Nguyen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Hindered adsorbed layers completely filling the nanopores must cause signifficant deviations from the classical BET isotherms for multimolecular adsorption of vapor in porous solids. Since the point of transition from free to hindered adsorption moves into wider nanopores adsorption layer exposed to vapor gets reduced by an area reduction factor that decreases with increasing adsorbed volume, and thus also with increasing vapor pressure (or humidity). The area reduction factor does not affect the rates of direct adsorption or condensation from individual vapor/gas molecule, which represent a local process, but imposes a lateral constraint on the total area and volume of the free portion of the adsorption layer that is in direct contact with vapor. Assuming an inverse power law for the dependence of the area reduction factor on the number of molecular layers, one can express the modified isotherm in terms of logarithmic or polylogarithm (aka Jonquière) functions. The power-law exponent is a property that serves as an additional data fitting parameter. For the same initial slope, the modified isotherms deviate from the BET isotherm downwards, and the deviation increases with the exponent. Comparisons with some published isotherms obtained experimentally on cement pastes show that the present modification of the BET theory for hindered adsorption goes in the right direction. Detailed calibration of the theory and an extension for indirect communication of vapor molecules with the molecules adsorbed in nanopores less than a few nm wide will require further research.

Original languageEnglish (US)
JournalUnknown Journal
StatePublished - Dec 28 2018


  • Adsorption isotherm
  • BET theory
  • Capillary condensation theory
  • Evaporation and condensation
  • Free adsorption
  • Hindered adsorption
  • Jonquière functions
  • Polylogarithm
  • Pore size distribution
  • Statistical analysis
  • Variation of adsorption surface

ASJC Scopus subject areas

  • General

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