Evapoporometry

Evapoporometry is a method used to determine pore-size in synthetic membranes. Based on the kelvin equation, this technique is most accurate for determination of pore diameters between 4 nm to 150 nm.^[1][2][3]

Theory

Evapoporometry uses modified forms of the kelvin equation to relate the evaporation of a volatile liquid (usually 2-propanol) from a membrane to the average diameter of the pores in that membrane.^[1] The first modified equation used in this technique is:

$ln{p'A \over p^{\circ}A} = -{4yV_\text{A} \over RTd}$

Where $p'A$ is the instantaneous vapor pressure of the volatile liquid, $p^{\circ}A$ is the normal vapor pressure, $y$ is the surface tension, $V_\text{A}$ is the liquid molar volume, $R$ is the gas constant, $T$ is the absolute temperature, and $d$ is the pore diameter.^[1] Since these pressures can be expressed as mole fractions, the equation is further modified to relate these mole fractions to evaporation rate in the following equation:

Where $X_\text{A0}$ and $X^{\circ}_\text{A0}$ are mole fractions, $W_\text{A}$ is the evaporation rate during pore draining, $W^{\circ}_\text{A}$ is the evaporation rate of the initial liquid film over the membrane, $d_\text{c}$ is the diameter of the testing cell, and $k_\text{x}$ is a constant.^[1]

An example schematic of an evapoporometry curve for a synthetic polymeric membrane.

Method

Evapoporometry has the significant advantage of requiring only a lab scale, 2-propanol, and a cell in which to contain the sample and 2-propanol.^[1][3]The sample is immersed for some time in 2-propanol prior to measurement to ensure saturation of pores, and is then placed into the cell and immersed again in 2-propanol, after which the change in mass due to evaporation is measured over the course of three to seven hours. This data is input into modified kelvin equations to yield both an average pore diameter as well as a pore-size distribution for the sample. This distribution is easily determined, as evaporation from small pores will only occur after 2-propanol in larger pores has completely evaporated.^[1]

See also

• Synthetic membrane
• Porosimetry

References

1. Krantz, William B.; Greenberg, Alan R.; Kujundzic, Elmira; Yeo, Adrian; Hosseini, Seyed S. (July 2013). "Evapoporometry: A novel technique for determining the pore-size distribution of membranes". Journal of Membrane Science 438: 153–166. doi:10.1016/j.memsci.2013.03.045.
2. Takei, T.; Chikazawa, M.; Kanazawa, T. (December 1997). "Validity of the Kelvin equation in estimation of small pore size by nitrogen adsorption". Colloid & Polymer Science 275 (12): 1156–1161. doi:10.1007/s003960050196.
3. Merriman, Lauren; Moix, Alex; Beitle, Robert; Hestekin, Jamie (October 2014). "Carbon dioxide gas delivery to thin-film aqueous systems via hollow fiber membranes". Chemical Engineering Journal 253: 165–173. doi:10.1016/j.cej.2014.04.075.