ABSTRACT
Application of a linear simulation model (LSM) (Gille, 2002 [82]; Enke et al., 2002 [32]) analyzing the scattering pattern of a VYCOR glass sample with L = L1 ≈ (25-30) nm (see Fig. 8.5). Presupposing fixed chord lengths, it is possible to construct the theoretical behavior of γ(r, L), the function of occupancy Z(r, L) and the set covariance C(r, c) as well. A 33% sample porosity results from the LSM. Sample material: PVG disks (Corning Co.,
Code 7939) with a thickness 0.4 mm were used. The PVG was prepared by phase separation of a subsequent acid leaching. Only after making a sequence of additional assumptions can an estimation
of c be carried out. A specific model that is suitable for describing this sample case must be selected. Thus, the particle volume fraction c, which is of interest here, depends on the order range L, where c = c(L). Chapter 8 discusses several approaches for estimating c(L) from the scattering pattern if certain additional assumptions are fulfilled. Typical examples of this are as follows:
• Approach A: The simplest case is that of a known mean chord length l1 = −1/γ′0(0) of the single particle(s). Thus, for a well-defined L, the particle volume fraction c is defined in terms of the first derivative γ′(0, L) of the sample CF in the origin and the average mean chord length of the particles, where c = 1− lp(L)/l1. If the mean chord length l1 is unknown beforehand, this length parameter can be estimated from the behavior of γ(r, L) in some practical cases.
