pore size determination by k0 method

modified Gas Translation (GT)-model

\( P_i = \frac{k_{0,i}}{\sqrt{M_iRT}} \exp (-\frac{E_{P,i}}{RT}) \) (1)

where
\( k_{0,i} = k_{0}(d_p - d_{i})^3 \), \( k_0 = \frac{\sqrt{2 \pi} N_p}{6 \tau L A_m} \)

\(P_i\):permeance of i-th component \(\rm{[mol/(m^2 \ s \ Pa)]}\) \(E_{p,i}\):activation energy of permeation for the i-th component \(\rm{[J/ \ mol]}\)

\(R\):gas constant \(\rm{[J \ mol^{-1} \ K^{-1}]}\) \(T\):absolute temperature \(\rm{[K]}\) \(k_{0,i}\):permeation constant for the i-th component [-]

\(d_p\):pore diameter \(\rm{[m]}\) \(d_i\):diameter of the i-th component \(\rm{[m]}\) \(k_0\):structural constant \(\rm{[m^3]}\) \(N_p\):number of pores [-]

\(\tau\):tortuosity [-] \(L\):membrane thickness \(\rm{[m]}\) \(A_m\):membrane area \(\rm{[m^2]}\) \(M_i\):Molecular weight of i-th component \(\rm{[kg \ mol^{-1}]}\)

The gas permeation rate, \(P_i\), is analyzed based on the modified Gas Translation model represented by Eq.(1) to obtain a constant \(k_{0,i}\) and activation energy \(E_{p,i}\).
Pore sizes, \(d_0\), of membranes are obtained by regressing each \(k_{0,i}\) to Eq.(2)

\(\ \sqrt[3]{k_{0,i}} = \sqrt[3]{k_0} d_0 - \sqrt[3]{k_0} d_i\) (2)

Reference

1) Kanezashi M, Sasaki T,Tawarayama H, Nagasawa N, Yoshioka T, Ito K, Tsuru T. Experimental and Theoretical Study on Small Gas Permeation Properties through Amorphous Silica Membranes Fabricated at Different Temperatures. J PHYS CHEM C. 2014;118:20326–20331.
2) Yoshioka T, Kanezashi M, Tsuru T. Micropore size estimation on gas separation membranes: a study in experimental and molecular dynamics. AIChE J. 2013;59:2179–2194.

How to use this web

1. Please select "Model type"

2. Please select "Gas type" and "Molecular size"

3. Please input Experimental temperature \(\rm{[K]}\) and permeance \(\rm{[mol/(m^2 \ s \ Pa)]}\)

4. Please click the button

Model type Activated permeation model type GT-model type

Gas type
Molecular weight,\(M_i\) [g/mol]
Molecular size,\(d_i\) [nm]
Type of Molecular size

Calculate Activation energy and Stuructre parameter

Experimental temperature [K]	Permeance [mol/(m2 s Pa)]	Permeance [mol/(m2 s Pa)]	Permeance [mol/(m2 s Pa)]	Permeance [mol/(m2 s Pa)]	Permeance [mol/(m2 s Pa)]	Permeance [mol/(m2 s Pa)]	Permeance [mol/(m2 s Pa)]	Permeance [mol/(m2 s Pa)]











Activation energy,\(E_{p,i}\) [J/mol]
permeation constant,\(k_{0,i}\) [-]
R2[-]
download of calculation data
Which gas species do you use to determine the pore size by k0 method?
	No select

pore size