Pore properties, power laws and Benford's Law

Margellou, Antigoni; Pomonis, P.J.

doi:10.1016/j.jssc.2023.123866

Cited by 1 publication

(5 citation statements)

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“…The experimental data to be used in the present study are taken from some recent investigations referring to power laws of pores in solids [24][25][26][27][28]34]. They represent twelve (12) kinds of porous materials that belong to five (5) different classes, and are shown in Table 1.…”

Section: Experimental Datamentioning

confidence: 99%

“…(ii) One ( 1) mesoporous soil sample with pore diameters in the mm scale. The data were read from Figure 5 in a paper by Wang et al [37] and estimated as explained in ref [34]. The determination of differential pore diameters D i and pore numbers N i encountered in this porous soil took place using Mercury Intrusion Porosimetry (MIP) and the Pressure Plate Test (PPT) [37].…”

Section: Experimental Datamentioning

confidence: 99%

“…The four typical differential pore properties, namely specific pore volumes V i (cm 3 •g −1 ), specific surface areas S i (cm 2 •g −1 ), specific pore lengths L i (cm•g −1 ), and specific pore numbers N i , that correspond to specific pore anisotropies i = L i /D i (g −1 ) (e.g., N i ≡ B i ), because the method of their estimation for cylindrical pores (for details please see either of refs [24][25][26]34]), are actually each the differential of the previous property in relation to pore diameter D i ≈ V i /S i (cm), as shown next.…”

Section: Cumulative and Differential Power Lawsmentioning

confidence: 99%

“…In ref. [34], we estimated the values of those four typical pore properties, namely j= V i , S i , L i , and B i , for 206 different porous materials belonging to 17 dissimilar groups, namely mixed oxides, spinels, various silicas, and aluminophosphates; metalo-aluminophoshates, pillared clays, beta zeolites, and MSU, SBA, and MCM materials; as well as various organized mesoporous silicates doped with metal cations.…”

Section: Cumulative and Differential Power Lawsmentioning

confidence: 99%

“…The points for each of those 17 sub-sets are indicated by different-colored points; for details, see ref. [34].…”

Section: Cumulative and Differential Power Lawsmentioning

confidence: 99%

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Exchangeable Quantities and Power Laws: Τhe Case of Pores in Solids

Margellou,

Pomonis

2024

Foundations

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In this work we suggest that the common cause for the development of various power laws is the existence of a suitable exchangeable quantity between the agents of a set. Examples of such exchangeable quantities, leading to eponymous power laws, include money (Pareto’s Law), scientific knowledge (Lotka’s Law), people (Auerbach’s Law), and written or verbal information (Zipf’s Law), as well as less common cases like bullets during deadly conflicts, recognition in social networks, heat between the atmosphere and sea-ice floes, and, finally, mass of water vapors between pores in solids. This last case is examined closely in the present article based on extensive experimental data. It is shown that the transferred mass between pores, which eventually grow towards a power law distribution, may be expressed using different parameters, either transferred surface area, or transferred volume, or transferred pore length or transferred pore anisotropy. These distinctions lead to different power laws of variable strength as reflected by the corresponding exponent. The exponents depend quantitatively on the spread of frequency distribution of the examined parameter and tend to zero as the spread of distribution tends to a single order of magnitude. A comparison between the energy and the entropy of different kinds of pore distributions reveals that these two statistical parameters are linearly related, implying that the system poise at a critical state and the exchangeable quantities are the most convenient operations helping to keep this balance.

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