Polyelectrolytes In Poor Solvents Research Articles

Polyelectrolytes: From Seminal Works to the Influence of the Charge Sequence.

We propose a selected tour of the physics of polyelectrolytes (PE) following the line initiated by de Gennes and coworkers in their seminal 1976 paper. The early works which used uniform charge distributions along the PE backbone achieved tremendous progress and set most milestones in the field. Recently, the focus has shifted to the role of the charge sequence. Revisited topics include PE complexation and polyampholytes (PA). We develop the example of a random PE in poor solvent forming pearl-necklace structures. It is shown that the pearls typically adopt very asymmetric mass and charge distributions. Individual sequences do not necessarily reflect the ensemble statistics and a rich variety of behaviors emerges (specially for PA). Pearl necklaces are dynamic structures and switch between various types of pearl-necklace structures, as described for both PE and PA.

Self-organized polyelectrolyte end-grafted layers under nanoconfinement.

Layers of end-grafted weak polyelectrolytes in poor solvent self-organize into a rich variety of structures (such as micelles, micelles coexisting with nonaggregated chains, stripes and layers with solvent-filled holes) due to the subtle competition among hydrophobic, electrostatic and steric interactions and the chemical acid-based equilibria of the weak polyelectrolyte. In this work, a molecular theory has been used to systematically study how nanoconfinement modulates the competition among these interactions and, therefore, dictates the morphology of the self-assembled layer. Two different types of confinement were considered and compared: (i) soft lateral confinement due to increasing surface coverage in a planar polyelectrolyte brush and (ii) hard vertical confinement due to the interaction of a planar polyelectrolyte brush with an opposing surface, as typically found in AFM-colloidal-tip and surface-force-apparatus experiments. It is shown that increasing the surface coverage (soft lateral confinement) or compressing the layer with an opposing wall (hard vertical confinement) have a similar qualitative effect on the morphology of the system: both types of nanoconfinement increase the stability of morphologies that extend in one or two dimensions (such as the homogeneous brush, holes and stripes) over nonextended aggregates (such as hemispherical micelles). However, vertical confinement can also lead to pillar-like structures that are not observed in the absence of the opposing wall. Interestingly, the pillar structures, which bridge the grafting and opposing surfaces, may coexist with metastable structures collapsed to the grafting surface only. This coexistence may help to understand the hysteresis commonly observed in surface-force experiments.

Conformation of polyelectrolytes in poor solvents: variational approach and quantitative comparison with scaling predictions.

We present the results of variational calculations of a polyelectrolyte solution with low salt in poor solvent conditions for a polymer backbone. By employing the variation method, we quantitatively determined the diagram of the state of the polyelectrolyte in poor solvents as a function of the charge density and the molecular weight. The exact structure and diagram of the polyelectrolyte were compared to the scaling predictions of the necklace model developed by Dobrynin and Rubinstein [Prog. Polym. Sci. 30, 1049-1118 (2005); Dobrynin and Rubinstein, Macromolecules 32, 915-922 (1999); Dobrynin and Rubinstein, Macromolecules 34, 1964-1972 (2001)]. We find that the scaling necklace model may be used as a rather good estimation and analytical approximation of the exact variational model. It is also pointed out that the molecular connection of polymer is crucial for ellipsoid and necklace conformation.

Shapes of strongly absorbed polyelectrolytes in poor solvents

The pearl necklace instability has been predicted to occur for single polyelectrolyte chains immersed in an incompatible (or poor) solvent, but still direct imaging of this chain conformation is not conclusive. We therefore examine how a surface may interact with the polyelectrolyte to, possibly, inhibit this instability. We show from explicit calculations that for strongly absorbed polyelectrolyte chains another conformation of the chain is stable in parts of the diagram of states. We support this calculation with more rigorous numerical, self-consistent mean field calculations which exhibit both elliptical globules and a pseudo pearl necklace structure.

Rayleigh instability of charged aggregates: Role of the dimensionality, ionic strength, and dielectric contrast

We extended a previous analysis of the classical Rayleigh instability of spherical charged droplets in the presence of neutralizing monovalent counterions [M. Deserno, Eur. Phys. J. E 6, 163 (2001)], by generalizing the problem for suspensions of aggregates with D-dimensional symmetry, corresponding for D = 2 to infinite (rodlike) cylindrical charged bundles and for D = 3 to spherical charged droplets. In addition, we include the effects of added monovalent salt and of dielectric contrast between the charged aggregate and the surrounding solvent. The electrostatic energy taking the microion screening into account is estimated using uniform profiles within the framework of the cell model. We verify the robustness of these results by also considering Debye-Hückel-type microion profiles that are obtained by the minimization of a linearized Poisson-Boltzmann free-energy functional. In the case when the microions can enter inside the charged aggregates, we confirm the occurrence of a discontinuous phase change between aggregates of finite size and an infinite aggregate, which takes place at a collapse temperature that depends on their volume fraction phi and on the salt content. Decrease of phi shifts the phase-change temperature toward higher values, while salt addition has an opposite effect. We obtain analytical expressions for the phase-separation line in the asymptotic limit of infinite dilution (phi-->0), showing that the collapse temperature depends logarithmically on phi . As an application for D = 3 we discuss the stability of the pearl-necklace structures of flexible polyelectrolytes in poor solvents. The case D = 2 is applied to the problem of finite bundle sizes of stiff polyelectrolytes that attract each other-via, e.g., multivalent counterions-leading to an effective surface tension.

Dilute Solutions of Strongly Charged Flexible Polyelectrolytes in Poor Solvents: Molecular Dynamics Simulations with Explicit Solvent

The behavior of dilute salt-free solutions of charged flexible polymer molecules in poor solvents is studied using molecular dynamics simulations. The polymer molecule is modeled as a chain of char...

Solvent quality influence on the dielectric properties of polyelectrolyte solutions: A scaling approach

The dielectric properties of polyelectrolytes in solvent of different quality have been measured in an extended frequency range and the dielectric parameters associated with the polarization induced by counterion fluctuation over some peculiar polyion lengths have been evaluated. Following the scaling theory of polyelectrolyte solutions and the recent models developed by Dobrynin and Rubinstein that explicitly take into account the quality of the solvent on the polyion chain conformation, we have reviewed and summarized a set of scaling laws that describe the dielectric behavior of these systems in the dilute and semidilute regime. Moreover, for poorer solvents, where theory of hydrophobic polyelectrolytes predicts, and computer simulation confirms, a particular chain structure consisting of partially collapsed monomers (beads) connected by monomer strings, we derived a scaling law. These predictions are compared with the results obtained from the dielectric parameters (the dielectric increment delta epsilon and the relaxation time tau(ion)) of the "intermediate" frequency relaxation of two partially charged polymers, which possess a carbon-based backbone for which water is a poor solvent and ethylene glycol is a good solvent. By varying the solvent composition (a water-ethylene glycol mixture), we have tuned the quality of the solvent, passing from poor to good condition and have observed the predicted scaling for all the systems investigated. These findings give a further support to the scaling theory of polyelectrolyte solutions and to the necklace model for hydrophobic polyelectrolytes in poor solvents.

Conformations and solution structure of polyelectrolytes in poor solvent

AbstractUsing extensive Molecular Dynamics (MD) simulations we study the behavior of polyelectrolytes in poor solvents, where we take explicitely care of the counterions. The resulting pearl‐necklace structures are subject to strong conformational fluctuations, only leading to small signatures in the form factor, which is a severe obstacle for experimental observations. In addition we study how the necklace collapses as a function of Bjerrum length. At last we demonstrate that the position of the first peak in the inter‐chain structure factor varies with the monomer density close to $ρ^{1/3}_{m}$ for all densities. This is in strong contrast to polyelectrolyte solutions in good solvent.

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.

Self‐Consistent Integral Equation Theory for Semiflexible Polyelectrolytes in Poor Solvent

AbstractSelf‐consistent hybrid MC/PRISM method is presented for calculating properties of polyelectrolytes in semidilute and more concentrated regimes in a poor solvent. The static structure and conformational behavior of salt‐free polyelectrolyte solutions composed of semiflexible polyions and monovalent counterions are studied using the approach which combines the traditional Monte‐Carlo (MC) simulation with the numerical solution of the polymer integral PRISM equation. The MC technique is applied to generate the configurations of a single chain molecule and obtain the averaged intrapolymer correlation function. The PRISM equation is then numerically solved for a given monomer density to obtain the various correlation functions and the medium‐induced intrapolymer potential. This is used in a single chain MC simulation, where the polymer sites interact via the bare Coulomb potential together with the short range attractive potential and a self‐consistently determined medium‐induced potential. The monomer‐monomer pair correlation functions and static structure factors are calculated for a large variety of parameters. Conformational properties such as the radius of gyration and visual images are obtained as a function of attractive short‐range interaction, monomer density, Bjerrum length, and chain stiffness. The MC/PRISM study predicts that there is a range of hydrophobicity and monomer density for which polyion chains can form the toroidal structure in a poor solvent. Nonmonotonic dependence of the chain size on monomer density is predicted over the entire range of parameters. Polyion structure factor peak position as a function of density is described. Two concentration regimes in which the polyion structure factors exhibit physically different peaks were found. Over the entire concentration regime considered polyelectrolyte chains undergo strong compression with Rg ∝ l.Conformation of a polyion chain for lB = 2, ε = 0.18 at ρ* = 0.2 and α = 10°.imageConformation of a polyion chain for lB = 2, ε = 0.18 at ρ* = 0.2 and α = 10°.

Strongly charged flexible polyelectrolytes in poor solvents: Molecular dynamics simulations with explicit solvent

The behavior of salt-free solutions of charged flexible polymer molecules in poor solvents is studied using molecular dynamics simulations. The polymer molecules are modeled as chains of charged spheres, the counterions as charged spheres, and the solvent molecules are incorporated explicitly and modeled as uncharged spheres. The equilibrium static and dynamic properties are studied as a function of solvent quality. In many-chain systems, for slightly poor solvents, no peak is observed in the static structure factor at low semidilute concentrations, but a peak appears at higher concentrations. In this regime, chains form bead–necklace structures, and the counterions are strongly correlated with the polyions. When the solvent quality is decreased further, at nonzero but low polymer concentrations, the solution becomes unstable towards phase separation. The dense phase takes on spherical, cylindrical, or lamellar structures depending on the polymer concentration. The mass and charge density profiles of polyions and counterions in the dense phase are an oscillatory function of distance. The phase separation slows down the diffusion normal to the phase interface by two to three orders of magnitude, but has little effect on the diffusion parallel to the interface. These results are qualitatively different from the behavior observed in simulations where the solvent is treated implicitly via a pairwise-induced attraction between polymer beads.

NMR Spectra of Polyelectrolytes in Poor Solvents Are Consistent with the Pearl Necklace Model of the Chain Molecules

NMR Spectra of Polyelectrolytes in Poor Solvents Are Consistent with the Pearl Necklace Model of the Chain Molecules

Conformations of Bridging Polyelectrolytes in Poor Solvent: Single-Chain Self-Consistent Field Calculations

We report on numerical self-consistent field (SCF) calculations on the single-chain conformation of an electrostatically charged, yet poorly soluble, flexible polymer. We find numerical evidence that a “necklace of beads” conformation is self-organized and speculate that the predicted cascade of conformational transitions can be probed via a single-chain mechanical experiment with an atomic force microscope.

Dynamics of Collapse of Flexible Polyelectrolytes in Poor Solvents

The collapse kinetics of strongly charged polyelectrolytes in poor solvents is investigated by Langevin simulations and scaling arguments. We investigate the role of valence z of counterions, solvent quality, and shape of counterions on the dynamics of collapse. On the basis of the simulations, a number of results are obtained. (1) The rate of collapse, which is measured using the time dependence of the radius of gyration of the chain, increases sharply as z increases from 1 to 4. The collapse is particularly slow for the monovalent case and is observed only when the solvent quality is sufficiently poor. (2) Although the routes to collapse depend on z and the solvent quality a general collapse mechanism emerges. Upon quenching to low temperatures, counterions condense rapidly on a diffusion-limited time scale. At intermediate times metastable pearl-necklace structures form. The clusters merge at longer times with the largest one growing at the expense of smaller ones which is reminiscent of the Lifshitz−S...

Polyelectrolyte gels in poor solvent: Elastic moduli

We study theoretically using scaling arguments the behavior of polyelectrolyte gels in poor solvents. Following the classical picture of Katchalsky, our approach is based on single-chain elasticity but it accounts for the recently proposed pearl necklace structure of polyelectrolytes in poor solvents. The elasticity both of gels at swelling equilibrium and of partially swollen gels is studied when parameters such as the ionic strength or the fraction of charged monomers are varied. Our theory could be useful to interpret recent experiments performed in Strasbourg that show that if identical gel samples are swollen to the same extent at different pH the sample with the highest charge has the lowest shear modulus.

Strongly Charged, Flexible Polyelectrolytes in Poor Solvents: Molecular Dynamics Simulations

We present a set of molecular dynamics (MD) simulations of strongly charged, flexible polyelectrolyte chains under poor solvent conditions in a salt-free solution. Structural properties of the chains and of the solutions are reported. By varying the polymer density and the electrostatic interaction strength, we study the crossover from a dominating electrostatic interaction to the regime of strong screening, where the hydrophobic interactions dominate. During the crossover a multitude of structures is observed. In the limit of low polymer density strongly stretched, necklace like conformations are found. In the opposite limit of high polymer density, which is equivalent to strongly screened electrostatic interactions, we find that the chains are extremely collapsed; however, we observe no agglomeration or phase separation. The investigations show that the density of free charges is one of the relevant parameters that rules the behavior of the system and hence should be used as a parameter to explain exper...

Conformational properties of isolated polyelectrolytes in poor solvents

The conformational behavior of isolated polyelectrolytes in poor solvents is investigated using theory and computer simulation. DiMarzio’s approach for the collapse transition in neutral polymers is extended to uniformly charged polymers [E. A. diMarzio, Macromolecules 17, 969 (1984)]. The theory predicts a discontinuous collapse transition with decreasing solvent quality in highly charged polymers. A discontinuous collapse transition is also observed when the charge fraction is decreased in very poor solvents. Monte Carlo simulations are reported for the collapse transition in a lattice model of polyelectrolytes. Under some conditions the distribution of polymer size is bimodal, consistent with the theory.

Behavior of tethered polyelectrolytes in poor solvents

Using scaling theory and a two-dimensional self-consistent field calculation (SCF), we determine the morphology and phase behavior of charged polymers tethered by one end onto a flat substrate, and immersed in a poor solvent. For degrees of ionization, α, below a critical value, α*, the effects of the poor solvent dominate and the tethered chains collapse into pinned micelles on the planar surface. For values of α>α*, the chains extend to form a laterally uniform layer. This collapsed-to-stretched transformation constitutes a first-order phase transition. The specific routes to this transition are dependent on the relative solvent quality, and are described via the scaling theory. The structure of the layers above and below α* can be visualized through the polymer density profiles, which are obtained from the SCF calculations. The SCF calculations also show agreement with predictions from the scaling analysis.

Cascade of Transitions of Polyelectrolytes in Poor Solvents

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.

Microphase separation in poor‐solvent polyelectrolyte solutions: Phase diagram

AbstractMicrophase separation in solutions of weakly charged polyelectrolytes in poor solvents is studied in the weak segregation limit within the framework of the mean field approximation using a method first developed by Leibler. As a result a complete phase diagram of the solution near the critical point is obtained. The regions of the stability of the disordered, homogeneous phase and of body‐centered cubic (bcc), triangular and lamellar microdomain structures, as well as the phase separation regions are determined. The most striking difference in comparison with the corresponding diagram for block‐copolymer melts is the existence of broad phase separation regions even for monodisperse systems. As the quality of solvent becomes poorer, the triangular microdomain structure remains the most stable among microdomain phases of other symmetry.