TY - JOUR
T1 - Revisiting Bangham's law of adsorption-induced deformation
T2 - Changes of surface energy and surface stress
AU - Gor, Gennady Y.
AU - Bernstein, Noam
N1 - Funding Information:
This research was performed while one of the authors (G. G.) held a National Research Council Research Associateship Award at Naval Research Laboratory. The work of G. G. and N. B. was funded by the Office of Naval Research through the Naval Research Laboratory?s basic research program.
Publisher Copyright:
© the Owner Societies 2016.
PY - 2016/4/14
Y1 - 2016/4/14
N2 - When fluids are adsorbed on a solid surface they induce noticeable stresses, which cause the deformation of the solid. D. H. Bangham and co-authors performed a series of experimental measurements of adsorption-induced strains, and concluded that physisorption causes expansion, which is proportional to the lowering of the surface energy Δγ. This statement is referred to as the Bangham effect or Bangham's law. However, it is known that the quantity that controls the deformation is actually the change in surface stress Δf rather than surface energy Δγ, but this difference has not been considered in the context of adsorption-induced deformation of mesoporous materials. We use the Brunauer-Emmett-Teller (BET) theory to derive both values and show the difference between them. We find the condition when the difference between the two vanishes, and Bangham's law is applicable; it is likely that this condition is satisfied in most cases, and prediction of strain based on Δγ is a good approximation. We show that this is the case for adsorption of argon and water on Vycor glass. Finally, we show that the difference between Δγ and Δf can explain some of the experimental data that contradicts Bangham's law.
AB - When fluids are adsorbed on a solid surface they induce noticeable stresses, which cause the deformation of the solid. D. H. Bangham and co-authors performed a series of experimental measurements of adsorption-induced strains, and concluded that physisorption causes expansion, which is proportional to the lowering of the surface energy Δγ. This statement is referred to as the Bangham effect or Bangham's law. However, it is known that the quantity that controls the deformation is actually the change in surface stress Δf rather than surface energy Δγ, but this difference has not been considered in the context of adsorption-induced deformation of mesoporous materials. We use the Brunauer-Emmett-Teller (BET) theory to derive both values and show the difference between them. We find the condition when the difference between the two vanishes, and Bangham's law is applicable; it is likely that this condition is satisfied in most cases, and prediction of strain based on Δγ is a good approximation. We show that this is the case for adsorption of argon and water on Vycor glass. Finally, we show that the difference between Δγ and Δf can explain some of the experimental data that contradicts Bangham's law.
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U2 - 10.1039/c6cp00051g
DO - 10.1039/c6cp00051g
M3 - Article
AN - SCOPUS:84964000599
SN - 1463-9076
VL - 18
SP - 9788
EP - 9798
JO - Physical Chemistry Chemical Physics
JF - Physical Chemistry Chemical Physics
IS - 14
ER -