Strange–Rahman–Smith equation

The Strange–Rahman–Smith equation is used in the cryoporometry method of measuring porosity. NMR cryoporometry ^[1]^[2]^[3] is a recent technique for measuring total porosity and pore size distributions. NMRC is based on two equations: the Gibbs–Thomson equation, which maps the melting point depression to pore size, and the Strange–Rahman–Smith equation, ^[1] which maps the melted signal amplitude at a particular temperature to pore volume.

Equation

If the pores of the porous material are filled with a liquid, then the incremental volume of the pores $\Delta v$ with pore diameter between $x$ and $x+\Delta \,x$ may be obtained from the increase in melted liquid volume for an increase of temperature between $T$ and $T+\Delta T$ by:^[1]

${\frac {dv}{dx}}={\frac {dv}{d\,T}}{\frac {k_{GT}}{x^{2}}}$

Where: $k_{GT}$ is the Gibbs–Thomson coefficient for the liquid in the pores.

References

1 2 3 Strange, J.H.; Rahman, M.; Smith, E.G. (Nov 1993), "Characterization of Porous Solids by NMR", Phys. Rev. Lett., 71 (21): 3589–3591, Bibcode:1993PhRvL..71.3589S, doi:10.1103/PhysRevLett.71.3589, PMID 10055015
↑ Mitchell, J.; Webber, J. Beau W.; Strange, J.H. (2008), "Nuclear Magnetic Resonance Cryoporometry", Phys. Rep. (Review), 461: 1–36, Bibcode:2008PhR...461....1M, doi:10.1016/j.physrep.2008.02.001
↑ SE-10044 Stockholm Sweden. [Furo Istvan Royal Inst TechnolDiv Phys Chem Dept Chem SE-10044 Stockholm Sweden. Royal Inst Chem SE-10044 Stockholm Sweden. [Furo Istvan] Royal Inst Technol Technol Ind NMR Ctr Dept Chem SE-10044 Stockholm Sweden. Div Phys Chem Dept Chem SE-10044 Stockholm Sweden. Royal Inst], "NMR cryoporometry: Principles, applications, and potential"

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[NMRC_(SRS)-1] 1 2 3 Strange, J.H.; Rahman, M.; Smith, E.G. (Nov 1993), "Characterization of Porous Solids by NMR", Phys. Rev. Lett., 71 (21): 3589–3591, Bibcode:1993PhRvL..71.3589S, doi:10.1103/PhysRevLett.71.3589, PMID 10055015

[NMRC_Review_(MWS)-2] Mitchell, J.; Webber, J. Beau W.; Strange, J.H. (2008), "Nuclear Magnetic Resonance Cryoporometry", Phys. Rep. (Review), 461: 1–36, Bibcode:2008PhR...461....1M, doi:10.1016/j.physrep.2008.02.001

[NMRC_Review_(PF)-3] SE-10044 Stockholm Sweden. [Furo Istvan Royal Inst TechnolDiv Phys Chem Dept Chem SE-10044 Stockholm Sweden. Royal Inst Chem SE-10044 Stockholm Sweden. [Furo Istvan] Royal Inst Technol Technol Ind NMR Ctr Dept Chem SE-10044 Stockholm Sweden. Div Phys Chem Dept Chem SE-10044 Stockholm Sweden. Royal Inst], "NMR cryoporometry: Principles, applications, and potential"