Dynamics of Adsorbed Star‐Branched Polymer Chains: A Computer Simulation Study

The simple cubic‐lattice model of polymer chains was used to study the dynamic properties of adsorbed, branched polymers. The model star‐branched chains consisted of f = 3 arms of equal lengths. The chain was modeled with excluded volume, that is, in good solvent conditions. The only interaction assumed was a contact potential between polymer segments and an impenetrable surface. This potential was varied to cover both weak and strong adsorption regimes. The classical Metropolis sampling algorithm was used for models of star‐branched polymers in order to calculate the dynamic properties of adsorbed chains. It was shown that long‐time dynamics (diffusion constant) and short‐time dynamics (the longest relaxation time) were different for weak and strong adsorption. The diffusion of weakly adsorbed chains was found to be qualitatively the same as for free nonadsorbed chains, whereas strongly adsorbed chains behaved like two‐dimensional polymers. The time‐dependent properties of structural elements such as tails, loops, and trains were also determined.

The mean lifetimes of tails, loops, and trains versus the bead number for the chain with N = 799 beads for the case of the weak adsorption ε_a = −0.3.     

Computer simulation of relaxation phenomena in star‐branched polymers. Temperature dependence

Dynamic Monte Carlo simulations of simple models of star‐branched polymers were conducted. A model star macromolecule consisted of f = 3 arms of equal length with a total number of polymer segments up to 800. The chain was confined to a simple cubic lattice with simple nearest neighbor attractive interactions. The relaxation phenomena were studied by means of autocorrelation functions in wide ranges of temperatures. Short‐time‐scale dynamic processes in the entire star‐branched chain were examined. It was found that under good solvent conditions the longest relaxation time of the end‐to‐center vector decreases with decreasing temperature. For low temperatures (below the Θ‐point) where the chain is collapsed, the dependence of the relaxation time on the temperature is opposite.     

Temperature induced structural evolution of a fluorene‐thiophene copolymer on rubbed surfaces

The thermal alignment of the liquid crystalline fluorene‐thiophene copolymer (F8T2) on rubbed polyimide surfaces is investigated by ex‐situ and in‐situ X‐ray scattering experiments. The ex‐situ characterization allows an assignment of the observed diffraction peaks to distances between polymer backbones (1.6 nm), distances between the flexible side groups of the polymer chains (0.43 nm), and intramolecular distances of adjacent ring units (0.5 nm). The in‐situ characterization allows a temperature dependent observation of the polymer chain alignment. A gradual alignment process of the polymer backbones is observed for temperatures up to 563 K. Decreasing temperature after the polymer chain alignment is accompanied by a glass transition of the side chains at 380 K. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47:1599–1604, 2009     

Miscibility behavior and single chain properties in polymer blends: a bond fluctuation model study

Computer simulation studies on the miscibility behavior and single chain properties in binary polymer blends are reviewed. We consider blends of various architectures in order to identify important architectural parameters on a coarse grained level and study their qualitative consequences for the miscibility behavior. The phase diagram, the relation between the exchange chemical potential and the composition, and the intermolecular pair correlation functions for symmetric blends of linear chains, blends of cyclic polymers, blends with an asymmetry in cohesive energies, blends with different chain lengths, blends with distinct monomer shapes, and blends with a stiffness disparity between the components are discussed. For strictly symmetric blends the Flory‐Huggins theory becomes quantitatively correct in the long chain length limit, when the χ parameter is identified via the intermolecular pair correlation function. For small chain lengths composition fluctuations are important. They manifest themselves in 3D Ising behavior at the critical point and an upward parabolic curvature of the χ parameter from small‐angle neutron scattering close to the critical point. The ratio between the mean field estimate and the true critical temperature decreases like √χ/(ρb³) for long chain lengths. The chain conformations in the minority phase of a symmetric blend shrink as to reduce the number of energeticaly unfavorable interactions. Scaling arguments, detailed self‐consistent field calculations and Monte Carlo simulations of chains with up to 512 effective segments agree that the conformational changes decrease around the critical point like 1/√N. Other mechanisms for a composition dependence of the single chain conformations in asymmetric blends are discussed. If the constituents of the blends have non‐additive monomer shapes, one has a large positive chain‐length‐independent entropic contribution to the χ parameter. In this case the blend phase separates upon heating at a lower critical solution temperature. Upon increasing the chain length the critical temperature approaches a finite value from above. For blends with a stiffness disparity an entropic contribution of the χ parameter of the order 10^–3 is measured with high accuracy. Also the enthalpic contribution increases, because a back folding of the stiffer component is suppressed and the stiffer chains possess more intermolecular contacts. Two aspects of the single chain dynamics in blends are discussed: (a) The dynamics of short non‐entangled chains in a binary blend are studied via dynamic Monte Carlo simulations. There is hardly any coupling between the chain dynamics and the thermodynamic state of the mixture. Above the critical temperatures both the translational diffusion and the relaxation of the chain conformations are independent of the temperature. (b) Irreversible reactions of a small fraction of reactive polymers at a strongly segregated interface in a symmetric binary polymer blend are investigated. End‐functionalized homopolymers of different species react at the interface instantaneously and irreversibly to form diblock copolymers. The initial reaction rate for small reactant concentrations is time dependent and larger than expected from theory. At later times there is a depletion of the reactive chains at the interface and the reaction is determined by the flux of the chains to the interface. Pertinent off‐lattice simulations and analytical theories are briefly discussed.     

Phase diagram and entropic interaction parameter of athermal all‐polymer nanocomposites

An entropic model is introduced for the prediction of the χ interaction parameter and phase diagram of athermal all‐polymer nanocomposites (chemically identical polymer‐nanoparticle/linear‐polymer blends). According to this model, dilution of contact (hard sphere‐like) nanoparticle/nanoparticle interactions upon mixing plays a key role in explaining the miscibility behavior of athermal all‐polymer nanocomposites in the presence of unfavorable chain expansion (or contraction) effects. The new model is valid both for the cases of chain stretching and chain contraction and provides an appropriate capture of entropy changes accompanying the mixing of chemically identical nanoparticles and polymers. A good agreement was found between predicted χ interaction parameter (χ_cal = ?2.3 × 10^?3) and reported small angle neutron scattering (SANS) experimental data ( ～ ?2 × 10^?3) for 211 kDa cross‐linked poly(styrene) (PS)‐nanoparticles dissolved in 473 kDa deuterated linear‐PS. In addition, the miscibility boundary calculated from the model for PS‐nanoparticle/linear‐PS nanocomposites (?₁ = 0.02) compared very favorably to that experimentally found. For this system, the spinodal line in the polymer radius of gyration (R_g) versus nanoparticle radius (a) phase diagram was found to follow the simple scaling law: , being the polymer radius of gyration at which the second derivative of the free energy of mixing vanishes. Finally, the model has been employed for the prediction of the entropic χ interaction parameter, the miscibility behavior, and the melting point depression of athermal poly(ethylene) (PE)‐nanoparticle/linear‐PE nanocomposites using recent chain dimension data from Monte Carlo (MC) simulations, where chain stretching or chain contraction effects were observed depending on nanoparticle size. Copyright © 2007 John Wiley & Sons, Ltd.     

Ordered nanostructures at two different length scales mediated by temperature: A triphenylene‐containing mesogen‐jacketed liquid crystalline polymer with a long spacer

A mesogen‐jacketed liquid crystalline polymer (MJLCP) containing triphenylene (Tp) moieties in the side chains with 12 methylene units as spacers (denoted as PP12V) was synthesized. Its liquid crystalline (LC) phase behavior was studied with a combination of solution ¹H NMR, solid‐state NMR, gel permeation chromatography, thermogravimetric analysis, polarized light microscopy, differential scanning calorimetry, and one‐ and two‐dimensional wide‐angle X‐ray diffraction. By simply varying the temperature, two ordered nanostructures at sub‐10‐nm length scales originating from two LC building blocks were obtained in one polymer. The low‐temperature phase of the polymer is a hexagonal columnar phase (Φ_H, a = 2.06 nm) self‐organized by Tp discotic mesogens. The high‐temperature phase is a nematic columnar phase with a larger dimension (a′ = 4.07 nm) developed by the rod‐like supramolecular mesogen—the MJLCP chain as a whole. A re‐entrant isotropic phase is found in the medium temperature range. Partially homeotropic alignment of the polymer can be achieved when treated with an electric field, with the polymer in the Φ_H phase developed by the Tp moieties. The incorporation of Tp moieties through relatively long spacers (12 methylene units) disrupts the ordered packing of the MJLCP at low temperatures, which is the first case for main‐chain/side‐chain combined LC polymers with MJLCPs as the main‐chain LC building block to the best of our knowledge. The relationship of the molecular structure and the novel phase behavior of PP12V has implications in the design of LC polymers containing nanobuilding blocks toward constructing ordered nanostructures at different length scales. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 295–304     

Collapse of Cylindrical Brushes with 2‐Isopropyloxazoline Side Chains Close to the Phase Boundary

A high‐molar‐mass cylindrical brush polymer with a main chain degree of polymerization of P_w = 1047 is synthesized by free‐radical polymerization of a poly‐2‐isopropyloxazoline macromonomer with P_n = 28. The polymerization is conducted above the lower phase transition temperature of the macromonomer, i.e., in the phase‐separated regime, which provides a sufficiently concentrated macromonomer phase mandatory to obtain high‐molar‐mass cylindrical brushes. Upon heating to the phase transition temperature, the hydrodynamic radius is observed to shrink from 34 to 27 nm. Further increase in temperature resulted in aggregated chains which were observed to coexist with single chains until eventually only aggregates of μm size were detectable.

     

A Novel μ2‐(H2O)‐Bridged Double‐Chain Coordination Polymer [Cd(pc)(phen)(H2O)]n with Rhombic Grids (H2pc = pamoic acid,phen = 1,10‐phenanthroline)

A novel coordination polymer [Cd(pc)(phen)(H₂O)]_n (H₂pc = pamoic acid, phen = 1,10‐phenanthroline) has been synthesized under hydrothermal conditions. Single crystal X‐ray diffraction analysis reveals that the compound crystallizes in triclinic space group P1. All the Cd^II atoms in the compound are hexacoordinate and are linked by pamoicate ligands to form a one‐dimensional zigzag chain. Furthermore, two adjacent zigzag chains are connected by the μ₂‐(H₂O) molecules to form a double‐chain with rhombic grids. There exist intermolecular C–H ··· π contacts, π–π stacking and hydrogen‐bonding interactions. Compound 1 displays strong fluorescent emission in the solid state at room temperature.     

Thermoreversible gelation with hydrogen‐bonded zipper‐like crosslink junctions

Thermoreversible gelation of polymer chains bearing hydrogen‐bonding functional groups is studied by off‐lattice Monte Carlo simulation with semiflexible bead‐and‐spring model chains. To see the formation of zipper‐like sequential crosslink junctions (domino effect), we introduce stabilization energy ?Δε between the nearest neighboring hydrogen‐bonded beads along a chain in addition to the ordinary pairwise hydrogen‐bond energy ?ε. It is found that the condition nθ/ = 2 is fulfilled at the sol/gel transition point, where is the average zipper length, θ the zipper content per chain, and n the total number of beads on a chain. It is also shown that, at low temperature, zipper growth dominates the nucleation of new zippers, and as a result, there is another transition from a three‐dimensional network to a pairwisely bound state (network/pair transition). © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 3331–3336, 2005     

Mean-square radius of gyration of polymer chains

The calculations of the mean-square radius of gyration for more than thirty sorts of polymer chains are reviewed on the basis of a unified approach. A general expression of the mean-square radius of gyration was developed for polymer chains with side groups and/or heteroatoms. It consists of two parts. The first part is the mean-square radius of gyration of a model chain, in which every side group, R, was considered to be located in the centroid of the substituent flanking the related skeletal atom, and the second one is the total contribution of the square radius of gyration of every substituent around its centroid. Numerical calculations showed that the logarithmic relationship between the mean-square radius of gyration and the degree of polymerization becomes linear when x is greater than 100, and the dependence of the mean-square radius of gyration on the molecular weight can be expressed by the general formula 〈S²〉 = aM^b, which was supported by a number of experimental measurements. A comparison of our expression for the mean-square radius of gyration with that reported by Flory was made. The difference is obvious in the range of lower molecular weight, and gradually declines with increasing degree of polymerization.     

Aggregation behavior of polystyrene‐b‐poly(ethylene/butylene)‐b‐polystyrene triblock copolymer in N‐methylpyrrolidone

Solution property of hydrogenated polystyrene‐b‐poly(ethylene/butylene)‐b‐polystyrene triblock copolymer (SEBS copolymer) was studied by using static light scattering and dynamic light scattering for cyclohexane and N‐methylpyrrolidone (NMP) solutions. From the values of dimensionless parameters ρ, defined as the ratio of radius of gyration 〈S²〉^1/2 to hydrodynamic radius R_H, and solubility parameters, SEBS copolymer proved to exist as single chain close to random coil in nonpolar cyclohexane, whereas aggregate into the core‐shell micelle consisting of poly(ethylene/butylene) (PEB) core surrounded by PS shell in polar NMP. The core‐shell micelle formed in NMP is composed of 65 polymer chains, having three times larger average chain density (d = 0.12 g cm^?3) than a single polymer chain (d = 0.04 g cm^?3) in cyclohexane. The comparison with the aggregation behaviors in other solvents demonstrated that the aggregate compactness of the copolymer depended largely on solvent polarity, resulting in formation of the highly dense PEB core (R_c = 4.5 nm) and the thick PS shell (ΔR = 22.9 nm) in high‐polar NMP. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 588–594, 2010     

Aggregation of Poly(γ‐benzyl L‐glutamate)s Followed by Time‐Resolved Emission Anisotropy

Syntheses of poly(γ‐benzyl L ‐glutamate)s (PBLGs) labeled with various fluorophores (tryptophan, dansyl, and anthracene) having different molecular weights are reported. Association of PBLG chains was studied by time‐resolved emission anisotropy in the solvents supporting the aggregation process (1,4‐dioxane and tetrahydrofuran) and in N,N‐dimethylformamide, where the aggregates were not formed. The influence of molecular weight and polymer concentration on PBLG association was studied as well. The limiting emission anisotropy (r_∞) and rotational correlation times (ϕ) were determined. The chain relaxation dynamics were compared with the fluorescence lifetimes of the fluorophores and spectroscopically suitable labels were selected. Tryptophan was found to be an inconvenient fluorophore for the association study of PBLGs because of its short excited‐state lifetime. Dansyl and anthracene fluorophores, however, proved to be suitable labels for the chain dynamics study of PBLGs in solution. The mobilities of PBLG chains in 1,4‐dioxane were slower than those in tetrahydrofuran and N,N‐dimethylformamide because of PBLG association in this solvent.     

NMR investigation of effect of dissolved salts on the thermoresponsive behavior of oligo(ethylene glycol)‐methacrylate‐based polymers

The synthesis of thermo‐ and ionic‐responsive copolymers based on polyethylene glycol methyl ether methacrylate (OEGMA) and 2,2,2‐trifluoroethyl acrylate (TFEA) via reversible addition‐fragmentation chain transfer polymerization is described. Reactivity ratios for the copolymerization of OEGMA and TFEA are r_OEGMA = 2.46 and r_TFEA = 0.22, indicating that OEGMA is incorporated more rapidly than TFEA monomers. The copolymers are thermosensitive and exhibit volume phase transitions (lower critical solution behavior) at temperature, which depend on copolymer composition and the presence of added salts in the aqueous solutions. It was found that the copolymers exhibited LCST transitions at temperatures below 353 K only in salt solutions. ¹H NMR measurements indicated that motion of the protons located in and near the hydrophobic main chain are more sensitive to temperature than protons in the hydrophilic OEGMA side chains. The hydrophilic side chains remain largely hydrated; however, the presence of two distinct conformations of the terminal groups of the side chains was confirmed. The influence of OEGMA side chain length, copolymer composition, and salt type on aggregation behavior and dynamics was examined in detail. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 2375–2385     

A MONTE CARLO STUDY OF THE GLASS TRANSITION OF POLYMETHYLENE*

By this Monte Carlo simulation we studied the glass transition of polymethylene using themodified bond-fluctuation model combined with considering the rotational-isomeric state model. Theconfigurational properties in the polymethylene (PM) melts, such as the mean length, the mean energy perbond and the mean square radius of gyration were monitored. We found that the chains cannot be in theequilibrium states after a very long time when the temperature of the dense PM chains decreases to 120 K. Asthe melt vitrifies, these quantities gradually become independent of temperature in a narrow range. The glasstransition temperature T_g depends upon the chain length of PM chains, and extrapolation to (CH_2)_∞givesT_g~∞=212 K. The dynamics in the PM melts was also studied. It was found that the diffusion coefficients canbe described by the Vogel-Fulcher law and the Vogel-Fulcher temperature T_0 is 124 K. This method may beused to investigate the glass transition of other real polymer chains.     

Polymer Polydispersity Effect on Depletion Interaction between Colloidal Particles

The effect of polymer polydispersity on the polymer‐induced interaction between colloidal particles due to non‐adsorbing ideal chains is investigated. An analytical theory is developed for the polymer‐segment density between two plates and in the space surrounding two spheres by extending a recently proposed superposition approximation to include polymer polydispersity. Monte Carlo computer simulations were made to test the validity of the analytical theory. The polymer densities predicted by the superposition approximation are in reasonable agreement with simulation results for the polydisperse case. The simulations show that depletion leads to a size fractionation of the polymers. It is shown that size polydispersity has a small effect on the interaction between two parallel plates but a more significant effect on the interaction between two spheres. The range of the potential increases and the contact potential drops with increasing polydispersity.

Polymer‐segment density as a function of y for three values of x, as indicated, in the space surrounding two colloidal spheres with radius R = R_g0 and h = 0.48R_g0. Symbols are the MC results: polydisperse polymer (○; z = 1) and monodisperse polymer (•) samples. Curves are the predictions of the product‐function approximation for monodisperse polymer (solid lines) and polydisperse polymer (z = 1, dashed lines).     

Variable temperature 19F solid‐state NMR study of the effect of electrostatic interactions on thermally‐stimulated molecular motions in perfluorosulfonate ionomers

This study uses variable temperature ¹⁹F solid‐state nuclear magnetic resonance (SSNMR) spectroscopy to determine the influence of electrostatic interactions on the T₁, T_1ρ, and T₂ values of Nafion®. Because of a “homogenizing” of the T₁'s as a result of spin diffusion, it was not possible to resolve from the T₁ experiments the relative motions of the side‐ and main‐chain. The initial increase in T_1ρ as a function of increasing temperature has been attributed to backbone rotations that increase with increasing temperature. The maxima observed in the T_1ρ plots suggest a change in the dominant relaxation mechanism at that temperature. The similarity in relaxation behavior of the side‐ and main‐chains suggests that the motions are dynamically coupled, because of the fact that the side‐chain is directly attached to the main‐chain. Two T_1ρ values were observed for the main‐chain at high temperatures, which has been attributed to a thermally activated ion‐hopping process. The results of T₂ studies show that correlated motions of the side‐ and main‐chain exist at low temperatures. However, at elevated temperatures the T₂ values for the side‐chain increase rapidly while remaining relatively constant for the main‐chain, indicating an onset of mobility of the side‐chains. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2177–2186, 2007     

Disruptions in the crystallinity of poly(lauryl methacrylate) due to adsorption on silica

The effects of adsorption of poly(lauryl methacrylate) (PLMA), a side‐chain crystalline polymer, on silica were investigated. Fourier transform infrared spectroscopy and differential scanning calorimetry (DSC) measurements were made on both bulk and adsorbed PLMA. The reversible heat flow rates were observed as a function of temperature and the degree of crystallinity of the samples determined based on the broad melting transitions of the side chains in the surface samples. It was found that adsorption caused a disruption of the side‐chain crystallinity primarily in the tightly bound layer of the polymer, but did not significantly affect its glass transition temperature. A change in the packing of the hydrophobic side chains, as a result of adsorption, was also observed for the tightly adsorbed polymer. These results indicated that PLMA side chains in proximity to the silica surface have different properties from those in bulk PLMA. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 89–96     

Phase behavior of a single polyethylene chain confined between two adsorption walls

The phase behavior of a single polyethylene chain confined between two adsorption walls is investigated by using molecular dynamics simulations. In the free space, it is confirmed in our calculation that the isolated polymer chain exhibits a disordered coil state at high temperatures, and collapses into a condensed state at low temperatures, that is, the coil‐to‐globule transition, and the finite chain length effects are considered since the critical region depends on chain lengths. When the chain is confined between two attractive walls, however, the equilibrium properties not only depend on the chain length but also depend on the adsorption energy and the confinement. Mainly, we focus on the influence of polymer chain length, confinement, and adsorption interaction on the equilibrium thermodynamic properties of the polyethylene chains. Chain lengths of N = 40, 80, and 120 beads, distances between the two walls of D = 10, 20, 30, 50, and 90 Å, and adsorption energies of w = 1.5, 2.5, 3.5, 6.5, and 8.5 kcal/mol are considered here. By considering the confinement–adsorption interactions, some new folding structures are found, that is, the hairpin structure for short chain of N = 40 beads, and the enhanced hairpin or crystal like structures for long chains of N = 80 and 120 beads. The results obtained in our simulations may provide some insights into the phase behaviors of confined polymers, which can not be obtained by previous studies without considering confinement–adsorption interactions. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 370–387, 2008     

Model phase diagrams of binary nematic mixtures. A comparative study between linear and crosslinked polymers

Model calculations of phase diagrams of side chain liquid crystal polymers (SCLCP) and low molecular weight liquid crystals (LMWLC) are presented. The polymer is assumed to have grafted side chain units characterized by a nematic‐isotropic transition temperature T_{NI 2}, and the LMWLC presents also a similar transition at a temperature T_{NI 1} . The model calculations can accommodate for the cases where the latter two temperatures are comparable or widely different. For the sake of illustration, the case T_{NI 1} = 60°C and T_{NI 2} = 80°C is adopted here. The main point of interest here is to perform a comparative study of the equilibrium phase diagrams of SCLCP made either of linear free chains or crosslinked chains forming a single network. To our knowledge this is the first comparative study of the phase behavior of binary nematic mixtures involving linear and crosslinked polymer matrices which permits to clearly identify the effects of crosslinks present in the polymer matrix. The crosslinks attribute elasticity to the polymer constituent which induces important distortions in the phase diagram. To highlight these distortions, examples of hypothetical binary nematic mixtures are chosen involving both linear and crosslinked polymers with side chain mesogen units. The quadrupole interaction parameter between the two nematogens is related to individual parameters via a geometric average ν²₁₂ = κν₁₁ν₂₂ with a coupling parameter κ. Different values of this parameter are considered and the impact of coupling strength on the phase diagram is discussed for crosslinked and linear polymers.     

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

Self‐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 R_g ∝ lequation/tex2gif-stack-1.gif.

Conformation of a polyion chain for l_B = 2, ε = 0.18 at ρ* = 0.2 and α = 10°.