Pore Size Distribution and Chord Length Distribution of Porous VYCOR Glass (PVG)

Abstract

A porous VYCOR-glass of porosity c ≈ 30% was analyzed by use of nitrogen adsorption (NA), mercury intrusion (MI) and small-angle scattering (SAS). The distribution density of the pore diameter was determined from the SAS experiment, based on the stereological information for a fixed order range L = 40 nm. A pore can be described by use of two random variables, which depend on each other: The pore diameter d and the chord length l. In a first step, an assumption free data evaluation method yields the second derivative of the SAS correlation function γ″(r). Then, based on the intimate connection between γ″(r) with random chord lengths, an interpretation of the first two mean γ″ peaks was performed. These peaks reflect the chord length distributions of pore and wall. The problem of the allocation of the peaks has been solved based on the information of the NA and MI experiments. The transformation of the distribution densities of the pore diameters V M(d) (obtained by MI a experiment) and V N(d) (obtained by a MI experiment) into chord length distribution densities A M(l) and A N(l) have allowed the clear interpretation of γ″(r). It was possible to separate the chord distributions of the pores from those of the walls. The first γ″(r) peak reflects the chord length distribution density Φ(l) of the pores (first moment l¯ = 10.6 nm) and the second one that of the walls f(m) (first moment m¯ = 21 nm). It follows c ≈ 30%. The average mean chord length is d¯ lm ≈ 15 nm. The second moment of Φ(l) is 108 nm2. Finally, from the separated function Φ(l), the diameter distribution density of the pores V SAS(d) has been obtained. V SAS(d) was calculated, neither assuming a defined mathematical function type of the distribution nor a certain shape or dimension of the pore. The first and second moments of V SAS(d) are 7 nm and 74 nm2. From comparing the three distribution densities V SAS(d), V M(d) and V N(d) it can be concluded that the assumption of cylindrical pores is fulfilled. While the chord length distribution density of the walls is a highly symmetrical function, which can be approximated by a Gauss term, the pores have an unsymmetrical chord distribution density with the PVG.