We develop a scaling model for the dilute solution conformation of a uniformly charged polymer in a poor solvent. We find that there is a range of temperatures and charge densities for which the polymer has a necklace-like shape with compact beads joined by narrow strings. The free energy of a polyelectrolyte in this conformation is lower than in a cylindrical globule because the length of the necklace is larger than that of a cylinder and is proportional to the total charge on the chain. With changing charge on the chain or temperature, the polyelectrolyte undergoes a cascade of abrupt transitions between necklaces with different numbers of beads.

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Non-classical behaviour, brought about by a confinement that imposes spatial constraints on molecules, is opening avenues to novel applications. For example, carbon nanotubes, which show rapid and selective transport of small molecules across the nanotubes, have significant potential as biological or chemical separation materials for organic solvents or gaseous molecules. With polymers, when the dimensions of a confining volume are much less than the radius of gyration, a quantitative understanding of perturbations to chain dynamics due to geometric constraints remains a challenge and, with the development of nanofabrication processes, the dynamics of confined polymers have significant technological implications. Here, we describe a weak molecular-weight-dependent mobility of polymers confined within nanoscopic cylindrical pores having diameters smaller than the dimension of the chains in the bulk. On the basis of the chain configuration along the pore axis, the measured mobility of polymers in the confined geometry is much higher than the mobility of the unconfined chain. With the emergence of nanofabrication processes based on polymer flow, the unexpected enhancement in flow and reduction in intermolecular entanglements are of significant importance in the design and execution of processing strategies.

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The scaling of the bond-bond correlation function P1(s) along linear polymer chains is investigated with respect to the curvilinear distance, s, along the flexible chain and the monomer density, ρ, via Monte Carlo and molecular dynamics simulations. Surprisingly, the correlations in dense three dimensional solutions are found to decay with a power law P1(s) ∼ s −ω with ω = 3/2 and the exponential behavior commonly assumed is clearly ruled out for long chains. In semidilute solutions, the density dependent scaling of P1(s) ≈ g −ω 0 (s/g) −ω with ω0 = 2 − 2ν = 0.824 (ν = 0.588 being Flory's exponent) is set by the number of monomers g(ρ) contained in an excluded volume blob of size ξ. Our computational findings compare well with simple scaling arguments and perturbation calculation. The power-law behavior is due to self-interactions of chains caused by the chain connectivity and the incompressibility of the melt. This study suggests a careful reexamination of the operational definitions used for the experimental determination of the persistence length.PACS numbers: 05.40. Fb, 05.10.Ln, 61.25.Hq In this Letter we study the correlations of the directions of bonds along polymer chains in semidilute solutions and melts [1,2,3]. We focus on flexible monodisperse chains of N monomers (cf. Fig. 1) under good solvent conditions in three dimensions (d = 3) where both the bond length l and the excluded volume screening length ξ [2, 4] are always much smaller than the chain end-to-end distance R e . In principle, once the bond-bond correlations are computed all other conformational single chain properties can be derived. Importantly, being the (second) derivative of the spatial distances along the chains, they allow us to probe directly -without trivial ideal contributions -the non-gaussian corrections proposed recently [5]. As we shall see, these corrections are crucial to make the description of dense polymer systems, first proposed by Flory [3] and later corroborated by Edwards [2, 4], fully self-consistent.The bond-bond correlation function P 1 (s) is generally believed to decrease exponentially [3]. This belief is based on the few simple single chain models which have been solved rigorously [3,6] and on the assumption that all long range interactions are negligible on distances larger than ξ due to the screening mechanism described by Edwards [2,4]. Hence, only correlations along the backbone of the chains are expected to matter and it is then straightforward to work out that an exponential cut-off is inevitable due to the multiplicative loss of any information transferred recursively along the chain [3].We demonstrate here that this assumption is in fact incorrect and that unexpected long range correlations remain. They are responsible for a scale free power law regime with P 1 (s) = c a (ρ)s −ω for g(ρ) ≪ s ≪ N (g(ρ) being the number of monomers per blob at monomer density ρ) characterized by an exponent ω > 1 and a density dependent amplitude. Our simulation results are pre- sented first and discussed together wi...