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 ${\displaystyle \Delta v}$ with pore diameter between ${\displaystyle x}$ and ${\displaystyle x+\Delta \,x}$ may be obtained from the increase in melted liquid volume for an increase of temperature between ${\displaystyle T}$ and ${\displaystyle T+\Delta T}$ by:[1]

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

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

References

1. 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
2. Mitchell, J.; Webber, J. Beau W.; Strange, J.H. (2008), "Nuclear Magnetic Resonance Cryoporometry" (PDF), Phys. Rep. (Review), 461 (1): 1–36, Bibcode:2008PhR...461....1M, doi:10.1016/j.physrep.2008.02.001
3. Petrov, Oleg V.; Furo, Istvan (February 2009), "NMR cryoporometry: Principles, applications, and potential", Prog. Nucl. Mag. Res. Sp., 54 (2): 97–122, doi:10.1016/j.pnmrs.2008.06.001