Statistics of linear polymer chains in the self-avoiding walks model

摘要

A strict statistics of self avoiding random walks in d-dimensional discreteud(lattice) and continuous space is proposed. Asymptotic analytical expressionsudfor the distribution and distribution density of corresponding randomudvalues characterizing a conformational state of polymer chain have beenudobtained and their quantitative estimation has been given. It is shown thatudconformation of polymer chain possesses a structure of spherical or, moreudcommonly, of elliptical shell diffusely blurred both outside and inside theudpolymer coil, which nucleus is statistically void and has a radius of aboutudhalf of Flory radius. Statistics of self-avoiding walks describes completelyudan effect of excluded volume and meets the terms of Flory method inudPietronero’s concepti.