# Do Pores Exist?--Foundational Issues in Pore Structural Characterisation
## The Problem of the Definition of a 'Pore'
### The Pore Size Distribution  
As can be seen from Figure 3, the PNM extraction process naturally leads to the association of characteristic dimensions with features of the void space, and the potential to have distributions of these dimensions. This is useful because the raw forms of the holistic, 3D statistical reconstructions of porous media obtained from scattering, or 3D imaging, are not very directly informative, except in a vague, subjective way. In order to understand differences in behavior arising for the same physical process but within different porous media, it is necessary to compare the void spaces of the latter in some objective way. This requires the abstraction of statistical descriptors that can meaningfully characterise important aspects of the void space. Here,'meaningfully characterise' means adequately describing an identifiable entity that can form an independent part of a causal chain for the phenomenon of interest, such that, if it were missing, the phenomenon would not occur as before. Then, for example, a comparison of the frequencies of such entities (e.g., volumes of pores of particular sizes) allows for meaningful distinctions to be made between different porous media. While it is known that pore size distributions (typically weighted by volume or number) obtained from image analysis and more indirect methods, like mercury porosimetry, are often very different, this was previously attributed to various known phenomena such that mercury porosimetry can only probe externally accessible porosity (and, therefore, misses out isolated, disconnected voids), and the size distribution is skewed towards smaller pores by the so-called pore-shielding, or pore-shadowing, effect, which are not issues for imaging methods [74]. However, recently, attention has been drawn to the more fundamental issue that there are actually two distinctive forms that the distribution of frequencies of pores can take for fully-interconnected void spaces, and mercury porosimetry and image analysis are each archetypal examples of the methods that lead to these two different forms [75]. The image analysis methods discussed above (as in Figure 3) are based on partitioning the void space up into individual elements with clear boundaries, leading to a discrete distribution of pore sizes. In contrast, more indirect pore structure characterisation methods, such as mercury porosimetry, gas sorption and thermoporometry, obtain a continuous spectrum of pore sizes. The difference between discrete and continuous pore size distributions is shown schematically in Figure 4. Many of the indirect methods for obtaining a continuous PSD involve the utilisation of a physical phase transition (e.g., gas sorption) or fluid-fluid displacement process (e.g., mercury porosimetry) wherein a meniscus between phases advances into the porous medium gradually as the relevant control variable (e.g., vapour or hydrostatic pressure) is changed [1; 2; 3; 4; 5]. This meniscus marks the boundary of pores of sizes accessible by the value of the control value reached, and the volume of the phase behind it indicates the volume of those pores. Since the meniscus can advance incrementally as the control variable is changed, the PSD thereby obtained is a continuous spectrum of sizes, particularly if the void space geometry intruded is, say, of conical form (or an analogue), as shown in Figure 4. In one of the conical arms of the structure in the '3D pore size map' in Figure 4, there are no clear partitions between 'pores' of different size consisting of thin cross-sectional slices of the cone. In contrast, the partitions between individual pore bodies and necks in the extracted PNM shown at the bottom of Figure 3 are relatively much less ambiguous, although they are not completely unambiguous since they are still somewhat extraction algorithm-dependent, as mentioned above. The existence of the two possible, distinguishable forms for the PSD begs the question of which is the 'correct' PSD.