Chord-length and free-path distribution functions for many-body systems

Journal Article · Thu Apr 15 04:00:00 EDT 1993 · Journal of Chemical Physics; (United States)

DOI:https://doi.org/10.1063/1.464812· OSTI ID:6708315

Lu, B ^[1]; Torquato, S ^[2]

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1. Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, North Carolina 27695-7910 (United States)
2. Princeton Materials Institute and Department of Civil Engineering and Operations Research, Princeton University, Princeton, New Jersey 08544 (United States)

We study fundamental morphological descriptors of disordered media (e.g., heterogeneous materials, liquids, and amorphous solids): [ital the] [ital chord]-[ital length] [ital distribution] [ital function] [ital p]([ital z]) and the [ital free]-[ital path] [ital distribution] [ital function] [ital p]([ital z],[ital a]). For concreteness, we will speak in the language of heterogeneous materials composed of two different materials or phases.'' The probability density function [ital p]([ital z]) describes the distribution of chord lengths in the sample and is of great interest in stereology. For example, the first moment of [ital p]([ital z]) is the mean intercept length'' or mean chord length.'' The chord-length distribution function is of importance in transport phenomena and problems involving discrete free paths'' of point particles (e.g., Knudsen diffusion and radiative transport). The free-path distribution function [ital p]([ital z],[ital a]) takes into account the finite size of a simple particle of radius [ital a] undergoing discrete free-path motion in the heterogeneous material and we show that it is actually the chord-length distribution function for the system in which the pore space'' is the space available to a finite-sized particle of radius [ital a]. Thus it is shown that [ital p]([ital z])=[ital p]([ital z],0). We demonstrate that the functions [ital p]([ital z]) and [ital p]([ital z],[ital a]) are related to another fundamentally important morphological descriptor of disordered media, namely, the so-called lineal-path function [ital L]([ital z]) studied by us in previous work [Phys. Rev. A [bold 45], 922 (1992)]. The lineal path function gives the probability of finding a line segment of length [ital z] wholly in one of the phases'' when randomly thrown into the sample.

• DOE Contract Number: FG02-92ER14275
• OSTI ID: 6708315
• Journal Information: Journal of Chemical Physics; (United States), Journal Name: Journal of Chemical Physics; (United States) Vol. 98:8; ISSN JCPSA6; ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

661300 -- Other Aspects of Physical Science-- (1992-)
665000* -- Physics of Condensed Matter-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
AMORPHOUS STATE
COMPOSITE MATERIALS
CRYSTAL STRUCTURE
DISPERSIONS
DISTRIBUTION FUNCTIONS
FLUID FLOW
FLUIDS
FUNCTIONS
GAS FLOW
KNUDSEN FLOW
LIQUIDS
MANY-BODY PROBLEM
MATERIALS
MEAN FREE PATH
MICROSTRUCTURE
PHASE STUDIES
POROUS MATERIALS
PROBABILITY
RANDOMNESS
SOLIDS
SUSPENSIONS