Templated porous materials equations

Statistical thermodynamic theories such as atomistic density functional theory (DFT) for the computation of adsorption isotherms in simple pore geometries such as slits [15] or cylindrical capillaries [16] This category also includes integral equation methods for porous matrices [17] and templated porous materials [18],... 

A adsorption model for a templated porous material may be posed in terms of seven replica Ornstein-Zernicke (ROZ) integral equations [58-60] that relate the direct and total correlation functions, c, (r) and hij (r), respectively, of the matrix-adsorbate system... 

Once the correlation functions have been solved, adsorption isotherms can be obtained from the Fourier transform of the direct correlation function Cc(r) [55]. The ROZ integral equation approach is noteworthy in that it yields model adsorption isotherms for disordered porous materials that have irregular pore geometries without resort to molecular simulation. In contrast, most other disordered structural models of porous solids implement GCMC or other simulation techniques to compute the adsorption isothem. However, no method has yet been demonstrated for determining the pore structure of model disordered or templated structures from experimental isotherm measurements using integral equation theory. 

According to Wenzel s equation, obviously, high roughness can enhance the hydrophilicity of a native hydrophilic surface. In our study, such porous film is much rougher than relatively flat surface obtained without using template, so this model can explain why our as-synthesized films show superhydrophilicity with a CA about 5°. After modification with a lower surface free energy material, the air can be trapped in such ordered pore array, and hence a composite surface composed of air and pore array is formed. The measurements show that the surface is superhydrophobic with water CA of 154°. In this case, the Cassie equation is applicable. Based on a simplified model, as schematically illustrated in Fig. 6, the relationship... 

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