Physics: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 [math]\displaystyle{ \Delta v }[/math] with pore diameter between [math]\displaystyle{ x }[/math] and [math]\displaystyle{ x + \Delta\,x }[/math] may be obtained from the increase in melted liquid volume for an increase of temperature between [math]\displaystyle{ T }[/math] and [math]\displaystyle{ T + \Delta T }[/math] by:[1]
[math]\displaystyle{ \frac{dv}{dx} = \frac{dv}{d\,T} \frac{k_{GT}}{x^2} }[/math]
Where: [math]\displaystyle{ k_{GT} }[/math] is the Gibbs–Thomson coefficient for the liquid in the pores.
References
- ↑ 1.0 1.1 1.2 Strange, J.H.; Rahman, M.; Smith, E.G. (Nov 1993), "Characterization of Porous Solids by NMR", Phys. Rev. Lett. 71 (21): 3589–3591, doi:10.1103/PhysRevLett.71.3589, PMID 10055015, Bibcode: 1993PhRvL..71.3589S
- ↑ Mitchell, J.; Webber, J. Beau W.; Strange, J.H. (2008), "Nuclear Magnetic Resonance Cryoporometry", Phys. Rep. 461 (1): 1–36, doi:10.1016/j.physrep.2008.02.001, Bibcode: 2008PhR...461....1M, http://kar.kent.ac.uk/13467/6/NMRcryov10c_BibTexRefs_figs_ed.pdf
- ↑ 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
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