STATISTICS OF LINEAR POLYMER CHAINS IN THE SELF-AVOIDING WALKS MODEL
Author(s): Yu.G.Medvedevskikh (The Department of the L.V. Pisarzhevsky Institute of Physical Chemistry of the National Academy of Sciences of Ukraine, 3a Naukova Str., 79053 Lviv, Ukraine)
A strict statistics of self avoiding random walks in $d$-dimensional discrete (lattice) and continuous space is proposed. Asymptotic analytical expressions for the distribution and distribution density of corresponding random values characterizing a conformational state of polymer chain have been obtained and their quantitative estimation has been given. It is shown that conformation of polymer chain possesses a structure of spherical or, more commonly, of elliptical shell diffusely blurred both outside and inside the polymer coil, which nucleus is statistically void and has a radius of about half of Flory radius. Statistics of self-avoiding walks describes completely an effect of excluded volume and meets the terms of Flory method in Pietronero's concepti.
Key words: Flory method, statistics, self-intersection, polymer chain,
random walks, lattice, fatigue function, conformation
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