Radial distribution function of rod-like polyelectrolytes

We study the effect of electrostatic interactions on the distribution function of the end-to-end distance of a single polyelectrolyte chain in the rod-like limit. The extent to which the radial distribution function of a polyelectrolyte is reproduced by that of a wormlike chain with an adjusted effective persistence length is investigated. Strong evidence is found for a universal scaling formula connecting the effective persistence length of a polyelectrolyte with the strength of the electrostatic interaction and the Debye screening length. Received 4 March 2002 and Received in final form 1 July 2002 RID="a" ID="a"e-mail: jrudnick@physics.ucla.edu     

The electrostatic persistence length of polymers beyond the OSF limit

We use large-scale Monte Carlo simulations to test scaling theories for the electrostatic persistence length l _e of isolated, uniformly charged polymers with Debye-Hückel intrachain interactions in the limit where the screening length κ^-1 exceeds the intrinsic persistence length of the chains. Our simulations cover a significantly larger part of the parameter space than previous studies. We observe no significant deviations from the prediction l _e∝κ^-2 by Khokhlov and Khachaturian which is based on applying the Odijk-Skolnick-Fixman theories of electrostatic bending rigidity and electrostatically excluded volume to the stretched de Gennes-Pincus-Velasco-Brochard polyelectrolyte blob chain. A linear or sublinear dependence of the persistence length on the screening length can be ruled out. We show that previous results pointing into this direction are due to a combination of excluded-volume and finite chain length effects. The paper emphasizes the role of scaling arguments in the development of useful representations for experimental and simulation data. Received 12 February 2002     

Drift of a polymer chain in a porous medium --A Monte Carlo study

We investigate the drift of an end-labeled telehelic polymer chain in a frozen disordered medium under the action of a constant force applied to the one end of the macromolecule by means of an off-lattice bead spring Monte Carlo model. The length of the polymers N is varied in the range 8 < N < 128, and the obstacle concentration in the medium C is varied from zero up to the percolation threshold C≈ 0.75. For field intensities below a C-dependent critical field strength B _c, where jamming effects become dominant, we find that the conformational properties of the drifting chains can be interpreted as described by a scaling theory based on Pincus blobs. The variation of drag velocity with C in this interval of field intensities is qualitatively described by the law of Mackie-Meares. The threshold field intensity B _c itself is found to decrease linearly with C. Received 20 August 2001 and Received in final form 19 November 2001     

Polymer chain in a quenched random medium: slow dynamics and ergodicity breaking

The Langevin dynamics of a self-interacting chain embedded in a quenched random medium is investigated by making use of the generating functional method and one-loop (Hartree) approximation. We have shown how this intrinsic disorder causes different dynamical regimes. Namely, within the Rouse characteristic time interval the anomalous diffusion shows up. The corresponding subdiffusional dynamical exponents have been explicitly calculated and thoroughly discussed. For the larger time interval the disorder drives the center of mass of the chain to a trap or frozen state provided that the Harris parameter, (Δ/b ^d)N ^{2 - νd}≥1, where Δ is a disorder strength, b is a Kuhnian segment length, N is a chain length and ν is the Flory exponent. We have derived the general equation for the non-ergodicity function f (p) which characterizes the amplitude of frozen Rouse modes with an index p = 2πj/N. The numerical solution of this equation has been implemented and shown that the different Rouse modes freeze up at the same critical disorder strength Δ _c ∼ N ^{- γ} where the exponent γ ≈ 0.25 and does not depend from the solvent quality. Received 17 December 2002 Published online 23 May 2003 RID="a" ID="a"e-mail: vilgis@mpip-mainz.mpg.de     

Dynamical properties of the slithering-snake algorithm: A numerical test of the activated-reptation hypothesis

Correlations in the motion of reptating polymers in a melt are investigated by means of Monte Carlo simulations of the three-dimensional slithering-snake version of the bond-fluctuation model. Surprisingly, the slithering-snake dynamics becomes inconsistent with classical reptation predictions at high chain overlap (created either by chain length N or by the volume fraction φ of occupied lattice sites), where the relaxation times increase much faster than expected. This is due to the anomalous curvilinear diffusion in a finite time window whose upper bound (N) is set by the density of chain ends φ/N. Density fluctuations created by passing chain ends allow a reference polymer to break out of the local cage of immobile obstacles created by neighboring chains. The dynamics of dense solutions of “snakes” at t ≪ is identical to that of a benchmark system where all chains but one are frozen. We demonstrate that the subdiffusive dynamical regime is caused by the slow creeping of a chain out of its correlation hole. Our results are in good qualitative agreement with the activated-reptation scheme proposed recently by Semenov and Rubinstein (Eur. Phys. J. B, 1 (1998) 87). Additionally, we briefly comment on the relevance of local relaxation pathways within a slithering-snake scheme. Our preliminary results suggest that a judicious choice of the ratio of local to slithering-snake moves is crucial to equilibrate a melt of long chains efficiently. Received: 18 December 2002 / Accepted: 3 April 2003 / Published online: 12 May 2003 RID="a" ID="a"e-mail: jwittmer@dpm.univ-lyon1.fr RID="b" ID="b"Current address: University of Illinois at Urbana-Champaign.     

Stretching DNA: Role of electrostatic interactions

The effect of electrostatic interactions on the stretching of DNA is investigated using a simple worm like chain model. In the limit of small force there are large conformational fluctuations which are treated using a self-consistent variational approach. For small values of the external force f, we find the extension scales as where is the Debye screening length. In the limit of large force the electrostatic effects can be accounted for within the semiflexible chain model of DNA by assuming that only small excursions from rod-like conformations are possible. In this regime the extension approaches the contour length as where f is the magnitude of the external force. The theory is used to analyze experiments that have measured the extension of double-stranded DNA subject to tension at various salt concentrations. The theory reproduces nearly quantitatively the elastic response of DNA at small and large values of f and for all concentration of the monovalent counterions. The limitations of the theory are also pointed out. Received 13 October 1998 and Received in final form 9 June 1999     

Structure of gels and aggregates of disk-like colloids

The static structure factor (S(q)) of dispersions and gels of disk-like mineral colloids (Laponite) was investigated using time- and ensemble-averaged light scattering. The evolution of S(q) in time after increasing the ionic strength of well-dispersed Laponite suspensions shows that Laponite aggregates and forms fractal clusters. The structure of the aggregates does not depend on the ionic strength, but the rate of growth increases very strongly with the ionic strength. At concentrations below about 3 g/l (0.12% v/v) the aggregates sediment while at higher concentrations space-filling gels are formed. The gels are homogeneous on length scales larger than the correlation length which decreases strongly with decreasing ionic strength and increasing concentration. However, the local structure is the same, independent of the concentration and the ionic strength. Received 6 August 2000 and Received in final form 16 March 2001     

Variational theory for a single polyelectrolyte chain

Variational methods are applied to a single polyelectrolyte chain. The polymer is modeled as a Gaussian chain with screened electrostatic repulsion between all monomers. As a variational Hamiltonian, the most general Gaussian kernel, including the possibility of a classical or mean polymer path, is employed. The resulting self-consistent equations are systematically solved both for large and small monomer-monomer separations along the chain. In the absence of screening, the polymer is stretched on average. It is described by a straight classical path with Gaussian fluctuations around it. If the electrostatic repulsion is screened, the polymer is isotropically swollen for large separations, and for small separations the polymer correlation function is calculated as an analytic expansion in terms of the monomer-monomer separation along the chain. The electrostatic persistence length and the electrostatic blobsize are inferred from the crossover between distinct scaling ranges. We perform a global analysis of the scaling behavior as a function of the screening length and electrostatic interaction strength , where is the Bjerrum length and A is the distance of charges along the polymer chain. We find three different scaling regimes. i) A Gaussian-persistent regime with Gaussian behavior at small, persistent behavior at intermediate, and isotropically swollen behavior at large length scales. This regime occurs for weakly charged polymers and only for intermediate values of the screening length. The electrostatic persistence length is defined as the crossover length between the persistent and the asymptotically swollen behavior and is given by and thus disagrees with previous (restricted) variational treatments which predict a linear dependence on the screening length .ii) A Gaussian regime with Gaussian behavior at small and isotropically swollen behavior at large length scales. This regime occurs for weakly charged polymers and/or strong screening, and the electrostatic repulsion between monomers only leads to subfluent corrections to Gaussian scaling at small separations. The concept of a persistence length is without meaning in this regime. iii) A persistent regime , where the chain resembles a stretched rod on intermediate and small scales. Here the persistence length is given by the original Odijk prediction, , if the overstretching of the chain is avoided. We also investigate the effects of a finite polymer length and of an additional excluded-volume interaction, which modify the resultant scaling behavior. Applications to experiments and computer simulations are discussed. Received 24 December 1997     

Topological and geometrical entanglement in a model of circular DNA undergoing denaturation

The linking number (topological entanglement) and the writhe (geometrical entanglement) of a model of circular double stranded DNA undergoing a thermal denaturation transition are investigated by Monte Carlo simulations. By allowing the linking number to fluctuate freely in equilibrium we see that the linking probability undergoes an abrupt variation (first-order) at the denaturation transition, and stays close to 1 in the whole native phase. The average linking number is almost zero in the denatured phase and grows as the square root of the chain length, N, in the native phase. The writhe of the two strands grows as in both phases. Received 8 May 2002 Published online 13 August 2002     

Spherical polyelectrolyte block copolymer micelles: Structural change in presence of monovalent salt

Spherical polyelectrolyte block copolymer micelles were investigated as a function of added NaCl salt concentration using Small-Angle Neutron Scattering (SANS) and Light Scattering (LS). The micelles are formed by the self-association of charged-neutral copolymers made of a long deuterated polyelectrolyte moiety (NaPSS_d)₂₅₁ and a short hydrophobic moiety (PEP)₅₂. In presence of salt, the core shape and the aggregation number of the micelles are not affected. The hydrodynamic radius of the micelle is found to be identical to the radius of the whole micelle deduced from neutron scattering and thus the hydrodynamic radius is a valid measure of the corona thickness. At the lowest salt concentrations investigated the thickness of the corona, R_s, remains essentially constant and a contraction is observed above an added-salt concentration c_s of 2×10^-2 M where this crossover concentration corresponds to the average ionic strength of the free counterions in the corona. The contraction takes place while maintaining a rod-like behavior of the chains at short scale and obeys to: R_s c_s^-0.18. The exponent 0.18 suggests an electrostatic persistence length proportional to the Debye screening length.     

Equilibrium charge distribution on annealed polyelectrolytes

Monte Carlo simulations are used to study the non-uniform equilibrium charge distribution along a single annealed polyelectrolyte chain under θ solvent conditions and with added salt. Within a range of the order of the Debye length charge accumulates at chain ends while a slight charge depletion appears in the central part of the chain. The simulation results are compared with theoretical predictions recently given by Castelnovo et al. In the parameter range where the theory can be applied we find almost perfect quantitative agreement. Received 7 March 2002 and Received in final form 28 May 2002     

Oppositely charged polyelectrolytes grafted onto planar surface: Mean-field lattice theory

Equilibrium structures of planar polyelectrolyte brushes formed by grafted chains carrying charges of opposite sign are examined by employing mean-field lattice theory. Two brushes of different architecture are considered: one formed by grafted diblock copolymers with oppositely charged blocks and the other being a mixed brush composed of oppositely charged homopolymers. The systems display nontrivial intrinsically inhomogeneous brush structures originating from the chain connectivity and the electrostatic interaction among the segments. In addition, a coexistence of stretched and coiled chains inside the brush is observed. The influence of the charges of the blocks, the relative length of the oppositely charged blocks, and the ionic strength of the solution on the brush inhomogeneity and structural differences between the two types of brushes are discussed. Received 14 March 2001 and Received in final form 18 June 2001     

Counterion distribution in a spherical charged sparse brush

The counterion distribution within a spherical polyelectrolyte sparse brush was measured by small-angle X-ray scattering using contrast variation with different counterions by means of ion dialysis. The brush was made by self-association of charged diblock copolymers. Thanks to the contrast variation method, we were able to separate the signal due to the monomers and the signal due to the counterions. At a small length scale, it is demonstrated that the system behaves as independent charged rods whose counterion distribution follows the Poisson-Boltzmann model. Received 14 February 2001 and Received in final form 2 May 2001     

Adsorption of hydrophobic polyelectrolytes onto oppositely charged surfaces

We present a scaling theory for the adsorption of a weakly charged polyelectrolyte chain in a poor solvent onto an oppositely charged surface. Depending on the fraction of charged monomers and on the solvent quality for uncharged monomers, the globule in the bulk of the solution has either a spherical conformation or a necklace structure. At sufficiently high surface charge density, a chain in the globular conformation adsorbs in a flat pancake conformation due to the Coulombic attraction to the oppositely charged surface. Different adsorption regimes are predicted depending on two screening lengths (the Debye screening length monitored by the salt concentration and the Gouy-Chapman length monitored by the surface charge density), on the degree of ionization of the polymer and on the solvent strength. At low bulk ionic strength, an increase in the surface charge density may induce a transition from an adsorbed necklace structure to a uniform pancake due to the enhanced screening of the intra-chain Coulombic repulsion by the counterions localized near the surface. Received 12 April 2001     

Weak violation of universality for polyelectrolyte chains: Variational theory and simulations

A variational approach is considered to calculate the free energy and the conformational properties of a polyelectrolyte chain in d dimensions. We consider in detail the case of pure Coulombic interactions between the monomers, when screening is not present, in order to compute the end-to-end distance and the asymptotic properties of the chain as a function of the polymer chain length N. We find R≃N ^ν(log N)^γ, where ν = and λ is the exponent which characterizes the long-range interaction U∝ 1/r ^λ. The exponent γ is shown to be non-universal, depending on the strength of the Coulomb interaction. We check our findings by a direct numerical minimization of the variational energy for chains of increasing size 2⁴ < N < 2¹⁵. The electrostatic blob picture, expected for small enough values of the interaction strength, is quantitatively described by the variational approach. We perform a Monte Carlo simulation for chains of length 2⁴ < N < 2¹⁰. The non-universal behavior of the exponent γ previously derived within the variational method is also confirmed by the simulation results. Non-universal behavior is found for a polyelectrolyte chain in d = 3 dimension. Particular attention is devoted to the homopolymer chain problem, when short-range contact interactions are present. Received 8 August 2000 and Received in final form 19 December 2000     

Adsorption of a semiflexible wormlike chain

Adsorption of ideal polymers with stiff backbone onto a flat surface is considered theoretically. Both scaling approach and quantitative theory are developed. We predict a self-similar monomer concentration profile c(x) ∼ x ^-4/3 near the surface (when the distance to the surface x is much smaller than the chain persistence length l /2). The typical conformation of a weakly adsorbed chain can be viewed as a sequence of alternating flat (2-dimensional) trains of wormlike short loops (flat blobs) and coil-like (3-dimensional) loops forming a triple-layer structure: contact layer (x < Δ) of adsorbed fragments virtually laid on the surface, proximal layer (Δ < x < l) of flat blobs, and more dilute distal corona layer (x > l). Here Δ defines the range of monomer/surface attraction, Δ ≪ l. The adsorption transition is continuous. However, its relative width is small (T ^* is the adsorption temperature, ΔT is the relevant temperature interval): ∼ , i.e. a discontinuous transition in the limit Δ/l↦ 0. Received 10 October 2002 and Received in final form 22 November 2002 RID="a" ID="a"Permanent address: Physics Department, Moscow State University, Moscow 119992, Russia. e-mail: semenov@polly.phys.msu.ru     

Mobility in thin polymer films ranging from local segmental motion, Rouse modes to whole chain motion: A coupling model consideration

Large increases of mobility of local segmental relaxation observed in polymer films as the film thickness is decreased, as evidenced by decreases of the glass temperature, are not found for relaxation mechanisms that have longer length scales including the Rouse relaxation modes and the diffusion of entire polymer chains. We show that the coupling model predictions, when extended to consider polymer thin films, are consistent with a large increase of the mobility of the local segmental motions and the lack of such a change for the Rouse modes and the diffusion of entire polymer chains. There are two effects that can reduce the coupling parameter of the local segmental relaxation in thin films. One is the chain orientation that is induced parallel to the surface when the film thickness h becomes smaller than the end-to-end distance of the chains and the other is a finite-size effect when h is no longer large compared to the cooperative length scale. Extremely thin ( ≈ 1.5 nm) films obtained by intercalating a polymer into layered silicates have thickness significantly less than the cooperative length scale near the bulk polymer glass transition temperature. As a result, the coupling parameter of the local segmental relaxation in such thin films is reduced almost to zero. With this plausible assumption, we show the coupling model can explain quantitatively the large decrease of the local segmental relaxation time found experimentally. Received 1 August 2001 and Received in final form 1 December 2001     

Polyelectrolyte chains in poor solvent. A variational description of necklace formation

We study the properties of polyelectrolyte chains under different solvent conditions, using a variational technique. The free energy and the conformational properties of a polyelectrolyte chain are studied by minimizing the free energy F_N, depending on N(N - 1)/2 trial probabilities that characterize the conformation of the chain. The Gaussian approximation is considered for a ring of length 2⁴ < N < 2⁸ and for an open chain of length 50 < N < 200 in poor- and theta-solvent conditions, including a Coulomb repulsion between the monomers. In theta-solvent conditions the blob size is measured and found in agreement with scaling theory, including charge depletion effects, expected for the case of an open chain. In poor-solvent conditions, a globule instability, driven by electrostatic repulsion, is observed. We notice also inhomogeneous behavior of the monomer-monomer correlation function, reminiscence of necklace formation in poor-solvent polyelectrolyte solutions. A global phase diagram in terms of solvent quality and inverse Bjerrum length is presented. Received 7 June 2001 and Received in final form 17 October 2001     

On the organization of self-assembled actin networks in giant vesicles

We studied the formation of actin scaffolds in giant vesicles of dimyristoylphosphatidylcholine (DMPC). Polymerization of actin was induced at low ionic strength through ionophore-mediated influx of Mg²⁺ (2 mM). The spatial organization of the filamentous actin was visualized by confocal and epifluorescence microscopy as a function of the filaments length and membrane composition, by including various amounts of cholesterol or lipids with neutral and positively charged polyethyleneglycol headgroups (PEG lipopolymers). In vesicles of pure DMPC, the newly polymerized actin adsorbs to the membrane and forms a thin shell. In the presence of 2.5 mol% lipopolymers or of cholesterol at a molar fraction x = 0.37, formation of a thin adsorbed film is impeded. A fuzzy cortex is predominantly formed in vesicles of diameter d smaller than the filament persistence length ( d ⩽ 15μm) while for larger vesicles a homogeneous network formation is favoured in the bulk of the vesicle. The fuzzy-cortex formation is interpreted as a consequence of the reduction of the bending energy if the actin filaments accumulate close to the vesicle wall. Received: 17 January 2002 / Accepted: 21 March 2003 / Published online: 24 April 2003 RID="a" ID="a"e-mail: Laurent_Limozin@ph.tum.de     

Flexible linear polyelectrolytes in multivalent salt solutions: Solubility conditions

Single- and double-stranded DNA and many biological and synthetic polyelectrolytes undergo two structural transitions upon increasing the concentration of multivalent salt or molecules. First, the expanded-stretched chains in low monovalent salt solutions collapse into nearly neutral compact structures when the density of multivalent salt approaches that of the monomers. With further addition of multivalent salt the chains redissolve acquiring expanded-coiled conformations. We study the redissolution transition using a two-state model (F.J. Solis, M. Olvera de la Cruz, J. Chem. Phys. 112, 2030 (2000)). The redissolution occurs when there is a high degree of screening of the electrostatic interactions between monomers, thus reducing the energy of the expanded state. The transition is determined by the chemical potential of the multivalent ions in the solution, μ and the inverse screening length, κ. The transition point also depends on the charge distribution along the chain but is nearly independent of the molecular weight and degree of flexibility of the polyelectrolytes. We generate a diagram of μversusκ² where we find two regions of expanded conformations, one with charged chains and the other with overcharged (inverted charge) chains, separated by a collapsed nearly neutral conformation region. The collapse and redissolution transitions occur when the trajectory of the properties of the salt crosses the boundaries between these regions. We find that in most cases the redissolution occurs within the same expanded branch from which the chain precipitates. Received 15 May 2000 and Received in final form 28 June 2000