Langmuir, Vol.20, No.16, 6719-6726, 2004
A method for the estimation of pore anisotropy in porous solids
In this work a method for the estimation of pore anisotropy, b, in porous solids is suggested. The methodology is based on the pore size distribution and the surface area distribution, both calculated from trivial N-2 adsorption-desorption isotherms. The materials used for testing the method were six MCM-Al-x solids in which the ordered pore structure (for x = 0) was gradually destroyed by the introduction of Al atoms (x = 5,10, 15,20, 50) into the solids. Additionally, four silicas having random porosity were examined, in which the surface of the parent material SiO2 (pure silica) was gradually functionalized with organosilicate groups of various lengths (equivalent toSi-H, equivalent toSi-CH2OH, equivalent toSi-(CH2)(3)OH) in order to block a variable amount of pores. As pore anisotropy, the ratio b(i) = L-i/D-i is defined where L-i and D-i are the length and the diameter of each group of pores i filled at a particular partial pressure (P-i/P-0). The ratio of the surface area Si over the pore volume Vi, at each particular pressure (P-i/P-0), is then expressed as Si-3/V-i(2) = 16pi(N(i)b(i)) = 167pilambda(i), where N(i)b(i) is the number of pores having anisotropy b(i) which are filled at each pressure (P-i/P-0) and lambda(i) is the total anisotropy of all the pores N-i belonging to the group i of pores. Then plot of lambda(i) vs (P-i/P-0) provides a clear picture of the variation of the total pore anisotropy lambda(i) as the partial pressure (P-i/P-0) increases. For the functionalized silicas there appears a continuous drop of lambda(i) as partial pressure (P-i/P-0) increases, a fact indicating that both Ni and bi are continuously diminished. In contrast, for the MCM-Al-x materials a sudden kink of lambda(i) appears at the partial pressure where the well-defined mesopores are filled up, a fact indicating that at this point Ni and/or bi is large. The kink disappears as the ordered porosity is destroyed by increasing the x doping in MCM-Al-x. The pore anisotropy bi of each group i of pores is then estimated using the expression (S-i(3)/V-i(2)) = 8piN(i)r(i)(Si) and plotting log(lambda(i)) vs log r(i). From those plots, the values of s(i) can be found and therefore the values of b(i) = 0.5r(i)(Si) are next defined. In the MCM-Al-x materials the maximum pore anisotropy b is very high (b(i) similar to 250) for x = 0. Then as mesoporosity is destroyed by increasing x, the maximum b values drop gradually to b similar to 11 (x = 5), b similar to 8 (x = 10), and b similar to 3 (x = 15). For x = 20 and x = 50, the maximum b obtains values equal to unity. The same phenomena, although less profound, are also observed for the functionalized silicas, where the anisotropy b is altered by the process of functionalization, and from b(i) similar to 0.5 for the nonfunctionalized or b(i) similar to 0.9 for the solid functionalized with equivalent toSi-H groups drops to b = 0.3 and b = 0.2 for the solid functionalized with equivalent toSi-(CH2)OH and equivalent toSi-(CH2)(3)OH, respectively. A correlation factor F is suggested in cases where the pore model departs from the cylindrical geometry.