Stretching necklaces

Polyelectrolytes in poor solvents show a necklace structure where collapsed polymer pearls are linked to stretched strings. In the present paper the elasticity of such chains is studied in detail. Different deformation regimes are addressed. The first is the continuous regime, where many pearls are present. A continuous force extension relation ship is calculated. The main contribution comes from the tension balance and the electrostatic repulsion of consecutive pearls. The main correction term stems from the finite size of the pearls, which monitors their surface energy. For a finite amount of pearls discontinuous stretching is predicted. Finally counterion effects are discussed qualitatively.Comment: to appear in European Phys. Journal E (soft matter

Compression of finite size polymer brushes

We consider edge effects in grafted polymer layers under compression. For a semi-infinite brush, the penetration depth of edge effects $\xi\propto h_0(h_0/h)^{1/2}$ is larger than the natural height $h_0$ and the actual height $h$. For a brush of finite lateral size $S$ (width of a stripe or radius of a disk), the lateral extension $u_S$ of the border chains follows the scaling law $u_S = \xi \phi (S/\xi)$. The scaling function $\phi (x)$ is estimated within the framework of a local Flory theory for stripe-shaped grafting surfaces. For small $x$, $\phi (x)$ decays as a power law in agreement with simple arguments. The effective line tension and the variation with compression height of the force applied on the brush are also calculated.Comment: 6 pages, 7 figures, submitted to PCC

A finite excluded volume bond-fluctuation model: Static properties of dense polymer melts revisited

The classical bond-fluctuation model (BFM) is an efficient lattice Monte Carlo algorithm for coarse-grained polymer chains where each monomer occupies exclusively a certain number of lattice sites. In this paper we propose a generalization of the BFM where we relax this constraint and allow the overlap of monomers subject to a finite energy penalty \overlap. This is done to vary systematically the dimensionless compressibility $g$ of the solution in order to investigate the influence of density fluctuations in dense polymer melts on various s tatic properties at constant overall monomer density. The compressibility is obtained directly from the low-wavevector limit of the static structure fa ctor. We consider, e.g., the intrachain bond-bond correlation function, $P(s)$, of two bonds separated by $s$ monomers along the chain. It is shown that the excluded volume interactions are never fully screened for very long chains. If distances smaller than the thermal blob size are probed ($s \ll g$) the chains are swollen acc ording to the classical Fixman expansion where, e.g., $P(s) \sim g^{-1}s^{-1/2}$. More importantly, the polymers behave on larger distances ($s \gg g$) like swollen chains of incompressible blobs with P(s) \si m g^0s^{-3/2}.Comment: 46 pages, 12 figure

Non-extensivity of the chemical potential of polymer melts

Following Flory's 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 $\delta \mu_c(n) \sim +1/\rho\sqrt{n}$ arises ($\rho$ being the monomer density) for all $\P(N)$ if $n \ll$ 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 $\delta \mu_c(n) \approx (1- 2 n/) / \rho \sqrt{n}$ for $n \ll ^2$, hence, $\delta \mu_c(n) \approx - 1/\rho \sqrt{n}$ if $n$ is similar to the typical length of the bath $$. 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 $K_p \equiv 1 - /p!^p$ to decay as $K_p \approx 1 / \sqrt{}$ for all moments $p$ of the distribution.Comment: 14 pages, 6 figures, submitted to EPJ

Slow plasmon modes in polymeric salt solutions

The dynamics of polymeric salt solutions are presented. The salt consists of chains $\rm A$ and $\rm B$, which are chemically different and interact with a Flory-interaction parameter $\chi$, the $\rm A$ chain ends carry a positive charge whereas the $\rm B$ chain ends are modified by negative charges. The static structure factor shows a peak corresponding to a micro phase separation. At low momentum transfer, the interdiffusion mode is driven by electrostatics and is of the plasmon-type, but with an unusually low frequency, easily accessible by experiments. This is due to the polymer connectivity that introduces high friction and amplifies the charge scattering thus allowing for low charge densities. The interdiffusion mode shows a minimum (critical slowing down) at finite $k$ when the interaction parameter increases we find then a low $k$ frequency quasi-plateau.Comment: accepted in Europhys. Let

Long Range Bond-Bond Correlations in Dense Polymer Solutions

The scaling of the bond-bond correlation function $C(s)$ along linear polymer chains is investigated with respect to the curvilinear distance, $s$, along the flexible chain and the monomer density, $\rho$, via Monte Carlo and molecular dynamics simulations. % Surprisingly, the correlations in dense three dimensional solutions are found to decay with a power law $C(s) \sim s^{-\omega}$ with $\omega=3/2$ and the exponential behavior commonly assumed is clearly ruled out for long chains. % In semidilute solutions, the density dependent scaling of $C(s) \approx g^{-\omega_0} (s/g)^{-\omega}$ with $\omega_0=2-2\nu=0.824$ ($\nu=0.588$ being Flory's exponent) is set by the number of monomers $g(\rho)$ contained in an excluded volume blob of size $\xi$. % Our computational findings compare well with simple scaling arguments and perturbation calculation. The power-law behavior is due to self-interactions of chains on distances $s \gg g$ caused by the connectivity of chains and the incompressibility of the melt. %Comment: 4 pages, 4 figure