Exclusion of Protein from High Polymer Media: I. Derivation of Probability Distribution for the Number of Fiber Centers Within Any Sphere of Radius r

Ogston's (1958) fiber model based on Poisson's distribution function gives the average number of fibers making contact and no contact inside a sphere of radius r. The probability of penetration of spherical particles within a fibrous network was derived from the moment generating function Formula: see text] A is the number of particles that intrude into a sphere of radious r. α(μ) is the probability that a particle, whose center is μ units away from the origin, intrudes into a sphere of radius r. A has a Poisson distribution with a mean value E(A) = 4πνα(μ)μ² dμ. The theoretical derivation of the distribution function of A gives Ogston's fiber model.