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.

gollark: The resistor behaves ohmically and the current through both things is the same.

gollark: IIRC, if we assume the LED is an ideal diode, it'll just always have a 2V potential difference across it (if there's more than 2V in the circuit and also it is the right way round oops).

gollark: Well, that would actually have been right if you used the right units then added 2, possibly.

gollark: Not just... multiply... them?

gollark: I'm pretty sure you'd have to work out what voltage across the resistor would give you 20mA through it, then add 2 to it for the LED.

References

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" (PDF), Phys. Rep. (Review), 461 (1): 1–36, Bibcode:2008PhR...461....1M, doi:10.1016/j.physrep.2008.02.001
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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[NMRC_(SRS)-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

[NMRC_Review_(MWS)-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

[NMRC_Review_(PF)-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