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تسجيل مستخدم جديدNon-extensivity of the chemical potential of polymer melts
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Following Florys ideality hypothesis the chemical potential of a test chain of length $n$ immersed into a dense solution of chemically identical polymers of length distribution P(N) is extensive in $n$. We argue that an additional contribution $delta mu_c(n) sim +1/rhosqrt{n}$ arises ($rho$ being the monomer density) for all $P(N)$ if $n ll <N>$ which can be traced back to the overall incompressibility of the solution leading to a long-range repulsion between monomers. Focusing on Flory distributed melts we obtain $delta mu_c(n) approx (1- 2 n/<N>) / rho sqrt{n}$ for $n ll <N>^2$, hence, $delta mu_c(n) approx - 1/rho sqrt{n}$ if $n$ is similar to the typical length of the bath $<N>$. Similar results are obtained for monodisperse solutions. Our perturbation calculations are checked numerically by analyzing the annealed length distribution P(N) of linear equilibrium polymers generated by Monte Carlo simulation of the bond-fluctuation model. As predicted we find, e.g., the non-exponentiality parameter $K_p equiv 1 - <N^>/p!<N>^p$ to decay as $K_p approx 1 / sqrt{<N>}$ for all moments $p$ of the distribution.
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