Presenting theoretical arguments and numerical results we demonstrate long-range intrachain correlations in concentrated solutions and melts of long flexible polymers which cause a systematic swelling of short chain segments. They can be traced back to the incompressibility of the melt leading to an effective repulsion u(s) ≈ s/ρR 3 (s) ≈ c e / √ s when connecting two segments together where s denotes the curvilinear length of a segment, R(s) its typical size, c e ≈ 1/ρb 3 e the "swelling coefficient", b e the effective bond length and ρ the monomer density. The relative deviation of the segmental size distribution from the ideal Gaussian chain behavior is found to be proportional to u(s). The analysis of different moments of this distribution allows for a precise determination of the effective bond length b e and the swelling coefficient c e of asymptotically long chains. At striking variance to the short-range decay suggested by Flory's ideality hypothesis the bond-bond correlation function of two bonds separated by s monomers along the chain is found to decay algebraically as 1/s 3/2 . Effects of finite chain length are considered briefly. PACS numbers: 61.25.Hq,64.60.Ak,05.40.Fb * Electronic address: jwittmer@ics.u-strasbg.fr † URL: http://www-ics.u-strasbg.fr/~etsp/welcome.php 1 I. FLORY'S IDEALITY HYPOTHESIS REVISITEDA cornerstone of polymer physics. Polymer melts are dense disordered systems consisting of macromolecular chains [1]. Theories that predict properties of chains in a melt or concentrated solutions generally start from the "Flory ideality hypothesis" formulated already in the 1940s by Flory [2,3,4]. This cornerstone of polymer physics states that chain conformations correspond to "ideal" random walks on length scales much larger than the monomer diameter [1,4,5,6]. The commonly accepted justification of this mean-field result is that intrachain and interchain excluded volume forces compensate each other if many chains strongly overlap which is the case for three-dimensional melts [5]. Since these systems are essentially incompressible, density fluctuations are known to be small. Hence, all correlations are supposed to be short-ranged as has been systematically discussed first by Edwards who developed the essential statistical mechanical tools [6,7,8,9, 10] also used in this paper.One immediate consequence of Flory's hypothesis is that the mean-squared size of chain segments of curvilinear length s = m − n (with 1 ≤ n < m < N) should scale as R Both equations are expected to hold as long as the moment is not too high for a given segment length and the finite-extensibility of the polymer strand remains irrelevant [6].Deviations caused by the segmental correlation hole effect. Recently, Flory's hypothesis has been challenged both theoretically [11,12,13,14,15] and numerically for threedimensional solutions [16,17,18,19,20] and ultrathin films [21,22]. These studies suggest 2 that intra-and interchain excluded volume forces do not fully compensate each other on intermediate length scales, l...

We present a theoretical description of polymer adsorption from solution which is based on a mean field approximation but which goes beyond the standard ground state dominance approximation. The properties of the adsorbed polymer chains are described by two coupled order parameters. This allows a description of the chains in terms of tails and loops. When the bulk solution is dilute, the adsorbed polymer layer has a double layer structure with an inner layer dominated by loops and an outer layer dominated by tails. Explicit asymptotic forms are found for the monomer concentration profile and for the crossover distance between the loops and tail regions. The precise concentration profile is obtained by a numerical solution of two coupled differential equations. One of the surprising results is that the total polymer adsorbed amount has a nonmonotonic variation with molecular weight and decreases for large values of the molecular weight. The concentration profiles are also determined when the bulk solution is semidilute or concentrated. At any bulk concentration, the monomer concentration has a nonmonotonic variation with the distance to the adsorbing wall and shows a minimum at a finite distance. This depletion effect can be significant in the vicinity of the crossover between dilute and semidilute solutions. All the results are in agreement with the existing numerical solutions of the complete mean field theory of polymer adsorption. Excluded volume correlations are taken into account by constructing scaling laws for polymers in a good solvent both in dilute and in semidilute solutions.

Two models of dense two-dimensional (2d) polymers are considered: (1) when chain intersections in 2d are totally forbidden, and (2) when they are allowed to some extent. It is shown that both polymer chain statistics and dynamics are entirely different for the two models. In the first case studied by Duplantier in 1986 polymer chains are essentially segregated and are characterized by non-classical gamma exponents. The contact line between segregated chains is fractal which leads to an unusual demixing behavior in 2d blends. In the second case (crossings are allowed) polymer coils are overlapping and show mean-field statistics with logarithmic corrections. The correlation function of concentration fluctuations in this system is predicted to exhibit a universal long range power tail (1/r4) which is due to non-mean-field effects. The dynamical behavior of the two models is even more drastically different: The first model is characterized by a relatively fast dynamics with conformational relaxation time tN is proportional to N(15/8) (i.e. tN is slightly shorter than the Rouse time is proportional to N2). On the other hand an exponentially slow dynamics is predicted for model 2 (with 3d entanglements).