Self-consistent integral equation theory for solutions of finite extensible semiflexible polyelectrolyte chains

Electrostatic correlations and the polyelectrolyte self energy

We address the effects of chain connectivity on electrostaticfluctuations in polyelectrolyte solutions using a field-theoretic, renormalizedGaussian fluctuation (RGF) theory. As in simple electrolyte solutions [Z.-G. Wang,Phys. Rev. E 81, 021501 (2010)], the RGF provides a unified theory forelectrostatic fluctuations, accounting for both dielectric and charge correlationeffects in terms of the self-energy. Unlike simple ions, the polyelectrolyte self energydepends intimately on the chain conformation, and our theory naturally provides aself-consistent determination of the response of intramolecular chain structure topolyelectrolyte and salt concentrations. The effects of the chain-conformation on theself-energy and thermodynamics are especially pronounced for flexiblepolyelectrolytes at low polymer and salt concentrations, where application of thewrong chain structure can lead to a drastic misestimation of the electrostaticcorrelations. By capturing the expected scaling behavior of chain size from dilute tosemi-dilute regimes, our theory provides improved estimates of the self energy at lowpolymer concentrations and correctly predicts the eventual N-independenceof the critical temperature and concentration of salt-free solutions of flexiblepolyelectrolytes. We show that the self energy can be interpreted in terms of aninfinite-dilution energy μ_m,0^el and a finite concentrationcorrelation correction μ^corr which tends to cancel out the formerwith increasing concentration.

Softening of the stiffness of bottle-brush polymers by mutual interaction

We study bottle-brush macromolecules in a good solvent by small-angle neutron scattering (SANS), static light scattering (SLS), and dynamic light scattering (DLS). These polymers consist of a linear backbone to which long side chains are chemically grafted. The backbone contains about 1600 monomer units (weight average) and every second monomer unit carries side chains with approximately 60 monomer units. The SLS and SANS data extrapolated to infinite dilution lead to the form factor of the polymer that can be described in terms of a wormlike chain with a contour length of 380 nm and a persistence length of 17.5 nm. An analysis of the DLS data confirms these model parameters. The scattering intensities taken at finite concentration can be modeled using the polymer reference interaction site model. It reveals a softening of the bottle-brush polymers caused by their mutual interaction. We demonstrate that the persistence decreases from 17.5 nm down to 5 nm upon increasing the concentration from dilute solution to the highest concentration (40.59 gl) under consideration. The observed softening of the chains is comparable to the theoretically predicted decrease of the electrostatic persistence length of linear polyelectrolyte chains at finite concentrations.

Theoretical aspects and computer simulations of flexible charged oligomers in salt-free solutions

The structural and thermodynamic properties of a model solution containing flexible charged oligomers and an equivalent number of counterions were studied by means of the canonical Monte Carlo simulation and integral equation theory. The oligomers were represented as freely jointed chains of charged hard spheres. In accordance with the primitive model of electrolyte solutions, the counterions were modeled as charged hard spheres and the solvent as a dielectric continuum. Simulations were performed for a set of model parameters, independently varying the chain length and concentration of the oligomers. Structural properties in the form of pair distribution functions were calculated as functions of model parameters. In addition, thermodynamic properties such as the excess energy of solution and the excess chemical potential of counterions were obtained. These properties were correlated with the conformational averages of oligomers as reflected in the end-to-end distances and radii of gyration obtained from the simulations. The relation with the experimental data for heats of dilution and for the activity coefficient is discussed. Finally, theories based on Wertheim's integral equation approach (product reactant Ornstein-Zernike approach) [J. Stat. Phys. 42, 477 (1986)] in the so-called polymer mean spherical and polymer hypernetted chain approximations were tested against the new and existing computer simulations. For the values of parameters examined in this study, the integral equation theory yields semiquantitative agreement with computer simulations.

Electrostatic effects in DNA stretching

The response of a semiflexible polyelectrolyte chain to stretching in the regimes of moderate and weak screening is studied theoretically, with a special focus on DNA experiments. By using the nonlinear Poisson-Boltzmann description of electrostatic self-interactions of the chain, we explicitly demonstrate the applicability of the concept of effective charge to certain aspects of the problem. This charge can be extracted from the far-field asymptotic behavior of the electrostatic potential of the fully aligned chain. Surprisingly, in terms of the effective charge, the electrostatically renormalized persistence length can be formally described by the classical Odijk-Skolnick-Fixman formula, whose domain of applicability is normally limited to the linearized Debye-Hückel (DH) approximation. However, the short-scale behavior of the chain in the nonlinear regime deviates from the of DH-based result, even upon charge renormalization. This difference is revealed in the calculated stretching curves for strongly charged DNA. These results are in good agreement with recent experiments. In the limit of weak screening we predict the elastic response to have a distinctive two-stage character, with a peculiar intermediate "unstretchable" regime.

Strong and weak adsorptions of polyelectrolyte chains onto oppositely charged spheres

We investigate the complexation of long thin polyelectrolyte (PE) chains with oppositely charged spheres. In the limit of strong adsorption, when strongly charged PE chains adapt a definite wrapped conformation on the sphere surface, we analytically solve the linear Poisson-Boltzmann equation and calculate the electrostatic potential and the energy of the complex. We discuss some biological applications of the obtained results. For weak adsorption, when a flexible weakly charged PE chain is localized next to the sphere in solution, we solve the Edwards equation for PE conformations in the Hulthen potential, which is used as an approximation for the screened Debye-Huckel potential of the sphere. We predict the critical conditions for PE adsorption. We find that the critical sphere charge density exhibits a distinctively different dependence on the Debye screening length than for PE adsorption onto a flat surface. We compare our findings with experimental measurements on complexation of various PEs with oppositely charged colloidal particles. We also present some numerical results of the coupled Poisson-Boltzmann and self-consistent field equation for PE adsorption in an assembly of oppositely charged spheres.

Entropy- or enthalpy-driven collapse of strongly charged polymer chains in a one-component charged fluid of counterions or coions

We applied a simulation method [T. Sumi and H. Sekino, J. Chem. Phys. 122, 194910 (2005)] to an infinitely dilute polyelectrolyte immersed in one-component charged fluids in order to investigate salt effects on its collapse. In this model system, the degree of freedom of the counterion (or the coion) is considered using a density-functional theory for polymer-solvent admixtures, while the oppositely charged ions are treated as a structureless background having the opposite charge. Results obtained by these simulations show that not only the counterion but also the coion makes the polymer chain collapsed. The effects by the coion are stronger than that by the counterion. Temperature variation of the gyration radius of the polymer chain immersed in the counterion is opposite to that in the coion: while the radius of gyration decreases as the temperature decreases in the case of the counterion, it decreases as the temperature increases in the case of the coion. From these results we conclude that the former is interpreted as an enthalpy-driven collapse caused by the screening effects of the counterion, whereas the latter is interpreted as an entropy-driven one due to the translational entropy of the coion.

Monte Carlo simulation and self-consistent integral equation theory for polymers in quenched random media

The conformational properties and static structure of freely jointed hard-sphere chains in matrices composed of stationary hard spheres are studied using Monte Carlo simulations and integral equation theory. The simulations show that the chain size is a nonmonotonic function of the matrix density when the matrix spheres are the same size as the monomers. When the matrix spheres are of the order of the chain size the chain size decreases monotonically with increasing matrix volume fraction. The simulations are used to test the replica-symmetric polymer reference interaction site model (RSP) integral equation theory. When the simulation results for the intramolecular correlation functions are input into the theory, the agreement between theoretical predictions and simulation results for the pair-correlation functions is quantitative only at the highest fluid volume fractions and for small matrix sphere sizes. The RSP theory is also implemented in a self-consistent fashion, i.e., the intramolecular and intermolecular correlation functions are calculated self-consistently by combining a field theory with the integral equations. The theory captures qualitative trends observed in the simulations, such as the nonmonotonic dependence of the chain size on media fraction.

Integral equation theory of random copolymer melts: Self-consistent treatment of intramolecular and intermolecular correlations

A self-consistent integral equation theory is presented for the conformational properties and spinodal lines of random copolymer melts. The theory combines field-theoretic methods with the polymer reference interaction site model (PRISM) theory. The many-chain problem is replaced by a single chain where the sites interact via a bare plus a self-consistently determined medium-induced potential, and the conformational properties are obtained using a variational method. The theoretical prediction for the spinodal line is qualitatively similar to that of non-self-consistent PRISM theory. The theory predicts macroscopic phase separation for all values of the monomer correlation strength, lambda. The inverse spinodal temperature is a nonmonotonic function of lambda with a maximum at lambda(max). For large values of lambda( approximately 1), the values of spinodal temperatures are almost identical to those of non-self-consistent PRISM theory. For low values of lambda, however, the theory predicts higher values for spinodal temperatures than non-self-consistent PRISM theory. The theory predicts significant changes in the mean-square end-to-end distance as the temperature is decreased.

Variational theory for a single polyelectrolyte chain revisited

We reconsider the electrostatic contribution to the persistence length, le, of a single, infinitely long-charged polymer in the presence of screening. A Gaussian variational method is employed, taking le as the only variational parameter. For weakly charged and flexible chains, crumpling occurs at small length scales because conformational fluctuations overcome electrostatic repulsion. The electrostatic persistence length depends on the square of the screening length, le approximately kappa(-2), as first argued by Khokhlov and Khachaturian by applying the Odijk-Skolnick-Fixman (OSF) theory to a string of crumpled blobs. We compare our approach to previous theoretical works (including variational formulations) and show that the result le approximately kappa(-2), found by several authors comes from the improper use of a cutoff at small length scales. For highly charged and stiff chains, crumpling does not occur; here we recover the OSF result and validate the perturbative calculation for slightly bent rods.