%0 Book Section %1 statphys23_0083 %A Beckrich, P. %A Johner, A. %A Semenov, A.N. %A Obukhov, S.P. %A Wittmer, J.P. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K correlations long polymer range statphys23 topic-7 %T Correlations in Dense Polymer Solutions %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=83 %X It is generally believed that correlations in dense polymer solutions (semi-dilute solutions or molten polymer) are short range. This assumption dates back to Flory. Here we discuss long range correlations coming from two effects generally overlooked in standard theories: i)The impact of overall incompressibility on single chain conformations. ii)Non local effects that correct for the spurious contribution of cyclic conformations in the Mean-Field.\\ i) Intrachain properties We obtain algebraic bond/bond orientation correlations decaying along the chain as $1/s^d/2$. This is in formal analogy with the long-time tail of the velocity auto-corelation function. Systematic deviations of the single chain structure factor from the Debye function describing Gaussian conformations are also obtained. For an infinite chain these take the simple form $\delta1S_1(q) = q^332 c$ independent of both the bare interaction and statistical segment which hence survives renormalization. The effects are enhanced in two dimensions where the topological constraints also become relevant to statics (strict and weak excluded volume systems belong to different universality classes). Agreement with numerical simulations is achieved without free parameter\\ ii)Collective properties We show that the usual local Hamiltonian describing density/density correlations leads to inconsistencies. To restore consistency a non-local Hamiltonian has to be introduced which leads to the non-analytical correction $\delta1S(q) = q^364 c$ which is also universal. The deeper reason for the effect is that the local Hamiltonian does not distinguish between open and cyclic conformations. Our treatment amounts to subtract the contribution of cycles to the Mean-Field free energy. We predict long range repulsion between embeded colloids (decaying as $1/r^2d$ or $1/h^d-1$ at closer separations) cut at the chain radius. Long range correlations also contribute a chain length dependent term to the surface tension.

@incollection{statphys23_0083, abstract = {It is generally believed that correlations in dense polymer solutions (semi-dilute solutions or molten polymer) are short range. This assumption dates back to Flory. Here we discuss long range correlations coming from two effects generally overlooked in standard theories: i)The impact of overall incompressibility on single chain conformations. ii)Non local effects that correct for the spurious contribution of cyclic conformations in the Mean-Field.\\ {\bf i) Intrachain properties} We obtain algebraic bond/bond orientation correlations decaying along the chain as $1/s^{d/2}$. This is in formal analogy with the long-time tail of the velocity auto-corelation function. Systematic deviations of the single chain structure factor from the Debye function describing Gaussian conformations are also obtained. For an infinite chain these take the simple form $\delta\frac{1}{S_1(q)} = \frac{q^3}{32 c}$ independent of both the bare interaction and statistical segment which hence survives renormalization. The effects are enhanced in two dimensions where the topological constraints also become relevant to statics (strict and weak excluded volume systems belong to different universality classes). Agreement with numerical simulations is achieved without free parameter\\ {\bf ii)Collective properties} We show that the usual local Hamiltonian describing density/density correlations leads to inconsistencies. To restore consistency a non-local Hamiltonian has to be introduced which leads to the non-analytical correction $\delta\frac{1}{S(q)} = \frac{q^3}{64 c}$ which is also universal. The deeper reason for the effect is that the local Hamiltonian does not distinguish between open and cyclic conformations. Our treatment amounts to subtract the contribution of cycles to the Mean-Field free energy. We predict long range repulsion between embeded colloids (decaying as $1/r^{2d}$ or $1/h^{d-1}$ at closer separations) cut at the chain radius. Long range correlations also contribute a chain length dependent term to the surface tension.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Beckrich, P. and Johner, A. and Semenov, A.N. and Obukhov, S.P. and Wittmer, J.P.}, biburl = {https://www.bibsonomy.org/bibtex/206ca3d5d463a2b314ca7742ec41d0d15/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {cc3c93416cba6718c9791cdd140e494c}, intrahash = {06ca3d5d463a2b314ca7742ec41d0d15}, keywords = {correlations long polymer range statphys23 topic-7}, month = {9-13 July}, timestamp = {2007-06-20T10:16:11.000+0200}, title = {Correlations in Dense Polymer Solutions}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=83}, year = 2007 }