Structure of Polyelectrolytes in Poor Solvent

We present simulations on charged polymers in poor solvent. First we investigate in detail the dilute concentration range with and without imposed extension constraints. The resulting necklace polymer conformations are analyzed in detail. We find strong fluctuations in the number of pearls and their sizes leading only to small signatures in the form factor and the force-extension relation. The scaling of the peak in the structure factor with the monomer density shows a pertinent different behavior from good solvent chains.Comment: 7 pages, 5 figures. submitted to EP

Pearlnecklacelike chain conformation of hydrophobic polyelectrolyte: a SANS study of partially sulfonated polystyrene in water

The form factor of partially sulfonated polystyrene PSSNa (degree of sulfonation f =1, 0.72, 0.64 and 0.36), at polymer concentration 0.17M and 0.34M, without or with added salt (0 M, 0.34M, & 0.68M), is measured by Small Angle Neutron Scattering using the Zero Average Contrast method. The total scattering function is also measured, allowing extracting the distinct interchain function and an apparent structure factor. The main result is the behavior of the form factor which shows contributions of spherical entities as well as extended chain parts. This is striking for 0.64, while for f = 0.36 the sphere contribution is more dominant. The conformation does not depend on polymer concentration. When salt is added, the sphere sizes do not vary, but the contribution attributed to the stretched parts does vary very much like for fully sulfonated PSSNa. Discussion of the interchain contribution establishes that chains are interpenetrated for f= 0.64, and at the overlap limit for f=0.36. The pearl necklace model appears very suitable. Comparisons are made with analytical calculation and simulation data. While the roles of Rayleigh transition, heterogeneous architecture, and strong hydrophobicity of non sulfonated PS monomers remain to discuss, data give an accurate 3 d image of the pearl necklace

Linear lambda terms as invariants of rooted trivalent maps

The main aim of the article is to give a simple and conceptual account for the correspondence (originally described by Bodini, Gardy, and Jacquot) between $\alpha$-equivalence classes of closed linear lambda terms and isomorphism classes of rooted trivalent maps on compact oriented surfaces without boundary, as an instance of a more general correspondence between linear lambda terms with a context of free variables and rooted trivalent maps with a boundary of free edges. We begin by recalling a familiar diagrammatic representation for linear lambda terms, while at the same time explaining how such diagrams may be read formally as a notation for endomorphisms of a reflexive object in a symmetric monoidal closed (bi)category. From there, the "easy" direction of the correspondence is a simple forgetful operation which erases annotations on the diagram of a linear lambda term to produce a rooted trivalent map. The other direction views linear lambda terms as complete invariants of their underlying rooted trivalent maps, reconstructing the missing information through a Tutte-style topological recurrence on maps with free edges. As an application in combinatorics, we use this analysis to enumerate bridgeless rooted trivalent maps as linear lambda terms containing no closed proper subterms, and conclude by giving a natural reformulation of the Four Color Theorem as a statement about typing in lambda calculus.Comment: accepted author manuscript, posted six months after publicatio

Single chain properties of polyelectrolytes in poor solvent

Using molecular dynamics simulations we study the behavior of a dilute solution of strongly charged polyelectrolytes in poor solvents, where we take counterions explicitly into account. We focus on the chain conformational properties under conditions where chain-chain interactions can be neglected, but the counterion concentration remains finite. We investigate the conformations with regard to the parameters chain length, Coulomb interaction strength, and solvent quality, and explore in which regime the competition between short range hydrophobic interactions and long range Coulomb interactions leads to pearl-necklace like structures. We observe that large number and size fluctuations in the pearls and strings lead to only small direct signatures in experimental observables like the single chain form factor. Furthermore we do not observe the predicted first order collapse of the necklace into a globular structure when counterion condensation sets in. We will also show that the pearl-necklace regime is rather small for strongly charged polyelectrolytes at finite densities. Even small changes in the charge fraction of the chain can have a large impact on the conformation due to the delicate interplay between counterion distribution and chain conformation.Comment: 20 pages, 27 figures, needs jpc.sty (included), to appear in Jour. Phys. Chem

Intermediate State in Type-I Superconductors

Intermediate state in type-I superconductors is one of the oldest challenges of superconductivity put forward by Gorter and Casimir, Pearls, F. London, and Landau back in the 1930s. In this chapter, we review the main properties of this state and principal theoretical approaches to interpret them. Recent experimental and theoretical achievements in this field are discussed in more details

Early Stages of Homopolymer Collapse

Interest in the protein folding problem has motivated a wide range of theoretical and experimental studies of the kinetics of the collapse of flexible homopolymers. In this Paper a phenomenological model is proposed for the kinetics of the early stages of homopolymer collapse following a quench from temperatures above to below the theta temperature. In the first stage, nascent droplets of the dense phase are formed, with little effect on the configurations of the bridges that join them. The droplets then grow by accreting monomers from the bridges, thus causing the bridges to stretch. During these two stages the overall dimensions of the chain decrease only weakly. Further growth of the droplets is accomplished by the shortening of the bridges, which causes the shrinking of the overall dimensions of the chain. The characteristic times of the three stages respectively scale as the zeroth, 1/5 and 6/5 power of the the degree of polymerization of the chain.Comment: 11 pages, 3 figure

End-effects of strongly charged polyelectrolytes - a molecular dynamics study

We investigate end-effects in the ion distribution around strongly charged, flexible polyelectrolytes with a quenched charge distribution by molecular dynamics simulations of dilute polyelectrolyte solutions. We take the counterions explicitly into account and calculate the full Coulomb interaction via an Ewald summation method. We find that the free counterions of the solution are distributed in such a way that a fraction of the chain charges is effectively neutralized. This in turn leads to an effective charge distribution which is similar to those found for weakly charged titrating polyelectrolytes that have an annealed charge distribution. The delicate interplay between the electrostatic interactions, the chain conformation and the counterion distribution is studied in detail as a function of different system parameters such as the chain length Nm, the charge fraction f, the charged particle density rho, the ionic strength and the solvent quality. Comparisons are made with predictions from a scaling theory.Comment: 20 pages, 10 figures. J. Chem. Phys, to appear June 200

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

Pearling instability of nanoscale fluid flow confined to a chemical channel

We investigate the flow of a nano-scale incompressible ridge of low-volatility liquid along a "chemical channel": a long, straight, and completely wetting stripe embedded in a planar substrate, and sandwiched between two extended less wetting solid regions. Molecular dynamics simulations, a simple long-wavelength approximation, and a full stability analysis based on the Stokes equations are used, and give qualitatively consistent results. While thin liquid ridges are stable both statically and during flow, a (linear) pearling instability develops if the thickness of the ridge exceeds half of the width of the channel. In the flowing case periodic bulges propagate along the channel and subsequently merge due to nonlinear effects. However, the ridge does not break up even when the flow is unstable, and the qualitative behavior is unchanged even when the fluid can spill over onto a partially wetting exterior solid region.Comment: 17 pages, 12 figures, submitted to Physics of Fluids, fixed equation numbering after Eq. (17