The distribution of counterions around synthetic rod-like polyelectrolytes in solution

An investigation of the radial distribution of the counterions of a synthetic rodlike polyelectrolyte in aqueous solution is presented. The cationic polyelectrolyte used here has a poly(p-phenylene) backbone. For typical molecular weights the macroion comprises approximately one persistence length (ca. 20 nm) and effects of finite stiffness may be disregarded. Each repeating unit bears four charges which leads to a charge parameter of ξ = 6.65. The distribution of the iodide counterions around this highly charged macroion is studied by small-angle X-ray scattering (SAXS) in dilute aqueous solution. These investigations are supplemented by measurements using anomalous small-angle X-ray scattering (ASAXS) that furnishes additional information about the contrast of the macroion. Data taken at high scattering angles give indication for contributions caused by the longitudinal fluctuations of the counterions. After correction for this effect the experimental results are compared to intensities calculated by use of the Poisson-Boltzmann (PB)-cell model. It is found that the PB-cell model describes the corrected data at intermediate and high scattering angles. Deviations at low scattering angle are attributed to the mutual interaction of the rod-like polyelectrolyte that can be described in terms of an effective structure factor. Data taken at lowest scattering angles point to a weak attraction between the rod-like macroions. Received: 27 July 2001 and Received in final form 27 March 2002     

Curved polymer and polyelectrolyte brushes beyond the Daoud-Cotton model

We revise the classical Daoud-Cotton (DC) model to describe conformations of polymer and polyelectrolyte chains end-grafted to convex spherical and cylindrical surfaces. In the framework of the DC model, local stretching of chains in the brush does not depend on the degree of polymerization of grafted chains, and the polymer density profile follows a single-exponent power law. This model, however, does not correspond to a minimum in free energy of the curved brush. The nonlocal (NL) approximation exploited in the present paper implies the minimization of the overall free energy of the brush and predicts that the polymer density profile does not follow a single-exponent power law. In the limit of large surface curvature the NL approximation provides the same scaling laws for brush thickness and free energy as the local DC model. Numerical prefactors are however different. Extra extension of chains in the brush interior region leads to larger equilibrium brush thickness and lower free energy per chain. A significant difference between outcomes of the two models is found for brushes formed by ionic polymers, particularly for weakly dissociating (p H-sensitive) polyelectrolytes at low solution salinity.     

Molecular Dynamics simulation of a polymer chain translocating through a nanoscopic pore

The detection of linear polymers translocating through a nanoscopic pore is a promising idea for the development of new DNA analysis techniques. However, the physics of constrained macromolecules and the fluid that surrounds them at the nanoscopic scale is still not well understood. In fact, many theoretical models of polymer translocation neglect both excluded-volume and hydrodynamic effects. We use Molecular Dynamics simulations with explicit solvent to study the impact of hydrodynamic interactions on the translocation time of a polymer. The translocation time τ that we examine is the unbiased (no charge on the chain and no driving force) escape time of a polymer that is initially placed halfway through a pore perforated in a monolayer wall. In particular, we look at the effect of increasing the pore radius when only a small number of fluid particles can be located in the pore as the polymer undergoes translocation, and we compare our results to the theoretical predictions of Chuang et al. (Phys. Rev. E 65, 011802 (2001)). We observe that the scaling of the translocation time varies from τ ∼ N ^11/5 to τ ∼ N ^9/5 as the pore size increases (N is the number of monomers that goes up to 31 monomers). However, the scaling of the polymer relaxation time remains consistent with the 9/5 power law for all pore radii.     

Polymer brushes near the crystallization density

In this paper, polymer brushes are studied via molecular-dynamics simulations at very high grafting densities, where the crossover between the brush regime and the polymer-crystal regime is taking place. This crossover is directly observed with the structure factor and pair-correlation function. With increasing grafting density, this crystallization is progressing from the core layer of the brush towards the surface layer. The same process is analyzed using the lateral fluctuations of the monomers as a signature of their diminishing mobility. Additionally, bond forces and the chain excess free energy indicate a transition from the brush regime to the overstretched regime, which is in agreement with predictions of a modified self-consistent field theory.     

The absence of physical aging effects on the relaxation of rubbing-induced birefringence in polystyrene

We found, through extensive experimental studies, that the physical aging effects are absent in the relaxation of rubbing-induced birefringence (RIB) in polystyrene (PS), and the relaxation involves very small length scale. A phenomenological model based on individual birefringence elements is proposed for the RIB relaxation. The relaxation times (RTs) of the elements are found to be independent of the thermal or stress history of the samples, either before or after the formation of the birefringence. The RTs are also independent of the molecular weight, rubbing conditions, and film thickness, while the RTs distribution function does depend on the molecular weight and rubbing conditions. The model provides quantitative interpretations that agree very well with all the reported experimental results, and sheds important light on the novel behaviors of the RIB relaxation. The absence of physical aging effects is probably due to the combined effects of small length scale of the RIB relaxation, and the accelerated aging speed in the near surface region in which the RIB concentrates.     

The effects of thermal annealing on the relaxation of rubbing-induced birefringence in polystyrene

We have conducted a systematic study on the effects of post rubbing annealing on the relaxation of rubbing-induced birefringence of polystyrene. It is found that annealing at T₀ only affects the relaxation up to T₀ + T_Lag, where T_Lag is proportional to the logarithm of the annealing time t_A. A theoretical model based on the distribution of relaxation times due to the individual birefringence elements is proposed. To remove its contribution to the net birefringence each element must overcome an energy barrier E = (317 + 1.17ξ)×10³ J/mol, and therefore must have a characteristic relaxation time τ which depends on temperature T and a barrier height which ranges from 340.4 kJ/mol to 445.7 kJ/mol. The relaxation of birefringence is expressed by the equation NB(T, t) = N(ξ)e^-t/τ(T,ξ)dξ, in which both the relaxation time τ(T,ξ) and the distribution function N(ξ) can be extracted from experimental data. The predictions of the model agree well with all the experimental results presented in this work. The differences and similarities of the relaxation of birefringence with respect to the physical aging of quenched PS are discussed. In particular, similarities in terms of the general temperature lag phenomena are noted.     

Complexation and distribution of counterions in a grafted polyelectrolyte layer

The complexation and the distribution of various cations, bound to a poly(styrene sulfonate) brush, have been investigated using infra-red spectroscopy and neutron reflectivity. Small counterions (like tetremethylammonium) are distributed throughout the brush in such a way that a local electroneutrality is ensured. They also exchange readily with other bulk small cations. On the other hand, model polycations are irreversibly trapped to the brush despite a relative small number of ionic bonds involved in the complexation. These complexed polycations are localized at the outer border of the brush, forming a macromolecular barrier. However, this spatial segregation does not allow the buildup of polyelectrolyte multilayers. Cationic surfactants are associated stoichiometrically with the brush sulfonates but unlike small counterions, this complexation is “irreversible” and induces a restructuring of the polymer interface. Received 22 August 2000     

Glass transition of the two distinct single-chain particles of poly(N-isopropylacrylamide)

Two distinct single-chain particles of poly(N-isopropylacrylamide) (PNIPAM) in the state of loose coil and compact globule, have been prepared successfully below and above the lower critical solution temperature (LCST) in extreme dilute aqueous solution by the freeze-drying method, respectively. During the preparation of the compact globular single-chain sample, the surfactant of sodium n-dodecyl sulfate (SDS) was added into the system to prevent aggregation of globular single chains formed at a temperature above the LCST. After all the coil has been transformed into the compact globular particle, the SDS molecules were removed by dialysis. The glass transition temperature (T_g) of the two single-chain samples has been measured by differential scanning calorimetery (DSC) in comparison with that of bulk polymer. It was found that the T_g of the single-chain sample in compact-globule state was very near to that of the bulk polymer, whereas the T_g of the single-chain sample in loose-coil state was approximately 6 K lower than that of the bulk polymer. After treating the sample with repeated DSC cycles, the T_g of the single-chain sample in loose-coil state rose up successively near to that of the bulk polymer. These results have been explained in terms of the effect of entanglement on the mobility of the polymer segments in the two distinct single-chain samples.     

Monte Carlo simulations of star-branched polyelectrolyte micelles

The concentration profiles of monomers and counterions in star-branched polyelectrolyte micelles are calculated through Monte Carlo simulations, using the freely jointed chain model. We have investigated the onset of different regimes corresponding to the spherical and Manning condensation of counterions as a function of the strength of the Coulomb coupling. The Monte Carlo results are in fair agreement with the predictions of Self-Consistent-Field analytical models. We have simulated a real system of diblock copolymer micelles of (sodium-polystyrene-sulfonate)(NaPSS)-(polyethylene-propylene)(PEP) with f = 54 hydrophilic branches of N = 251 monomers at room temperature in salt-free solution. The calculated form factor compares nicely with our neutron scattering data. Received 18 July 2002 and Received in final form 11 October 2002 RID="a" ID="a"e-mail: roger@drecam.saclay.cea.fr     

Electrostatic image effects for counterions between charged planar walls

We study the effect of dielectric inhomogeneities on the interaction between two planparallel charged surfaces with oppositely charged mobile charges in between. The dielectric constant between the surfaces is assumed to be different from the dielectric constant of the two semiinfinite regions bounded by the surfaces, giving rise to electrostatic image interactions. We show that on the weak-coupling level the image charge effects are generally small, making their mark only in the second-order fluctuation term. However, in the strong-coupling limit, the image effects are large and fundamental. They modify the interactions between the two surfaces in an essential way. Our calculations are particularly useful in the regime of parameters where computer simulations would be difficult and extremely time consuming due to the complicated nature of the long-range image potentials.     

Tethered polyelectrolytes under the action of an electrical field

For a polyelectrolyte undergoing electrophoretic motion, it is predicted (D. Long, J.L. Viovy, A. Ajdari, Phys. Rev. Lett. 76, 3858 (1996); D. Long, A. Ajdari, Electrophoresis 17, 1161 (1996)) that the mechanical force necessary to stall the molecule is substantially smaller than the sum of electrical forces applied on all monomers. In fact, it should be proportional to its hydrodynamic friction coefficient and therefore to the size of its conformation. In our work we examine this prediction using coarse-grained molecular-dynamics simulations in which we explicitly include the polymer, the solvent, the counterions and salt. The electrophoretic mobility of polyelectrolytes is evaluated, the mechanical force necessary to keep the molecules tethered is measured and the resulting anisotropic polymer conformations are observed and quantified. Our results corroborate Long et al.'s prediction.     

Collapse of spherical polyelectrolyte brushes in the presence of multivalent counterions

We consider the interaction of multivalent counterions with spherical polyelectrolyte brushes (SPB). The SPB result if linear polyelectrolyte (PE) chains (contour length: 60 nm) are densely grafted to colloidal spheres of 116 nm in diameter. Dispersed in water, the surface layer consisting of chains of the strong PE poly(styrene sulfonic acid) (PSS) will swell. We demonstrate that successive addition of trivalent ions (La3+) leads to a collapse in which the surface layer is shrinking drastically. All findings are discussed on the base of a theoretical mean-field approach using the Donnan equilibrium. The ion exchange and a strong binding of trivalent ions by PE chains is followed up by a drop in the osmotic pressure inside the brush. This reduction is the driving force for the collapse. The strong ion-chain correlation is discussed with results obtained from molecular dynamics simulations.     

Correlation in a Gaussian chain with the ends fixed

We consider an ideal chain whose ends are fixed without fluctuation at different points, possibly by optical tweezers. We derive a two-point probability distribution of a corresponding random walk and explicitly calculate the scattering function. We find that the contour plot of the resulting function shows a kind of normal butterfly pattern, contaminated by wavy texture. These results are compared with some representative previous models.     

Conformation of poly(L-lysine)-graft-poly(ethylene glycol) molecular brushes in aqueous solution studied by small-angle neutron scattering

Small-angle neutron scattering (SANS) has been employed for the analysis of conformations of poly(L-lysine)-graft-poly(ethylene glycol) (PLL-g -PEG) molecular bottle brushes in aqueous solutions. The degree of polymerisation of the PEG chains was systematically varied in order to unravel dependence of the conformational properties of the bottle brushes on the molecular weight of the grafted chains. The grafting density was kept constant and high enough to ensure strong overlap of the PEG chains. The scattering spectra were fitted on the basis of the model of an effective worm-like chain with the account of average radial distribution and local fluctuations of the PEG density in the bottle brush. The results of the fits indicate that molecular brushes retain weakly bent configuration on the length scale of the order of (or larger than) the brush thickness. This finding is in agreement with earlier simulation and recent theoretical results.     

Scattering properties of gradient heteropolymers obtained by “living” free-radical copolymerization

An original, quantitative, theory of “living” radical copolymerization has been developed proceeding from the current concepts of its kinetics and mechanism. This theory enables one to calculate both the dependence of monomers' conversion on time and any statistical characteristics of the chemical structures of the copolymers formed. Expressions have been derived describing the angular dependence of the scattering amplitude of the copolymerization products. The results of quantitative calculations of these characteristics have been also presented to exemplify the potentialities of the theory. Received 13 February 2001 and Received in final form 4 February 2002     

Observation of Hydration--Drying Effect on Clotrimazole--Carbopol System

The possibility to use the polyacrylic acid （carbopol） as polymeric matrix for the clotrimazole is analysed. The hydration-drying effect on the polymeric matrix is observed by Raman spectroscopy. Similar observations are obtained on the clotrimazole included in the polymeric matrix. No modifications of the properties of the clotrimazole and of the polymeric matrix are observed under the repeated action of water.     

A non-Gaussian model in polymeric network

We investigate a finite chain approximation, the non-Gaussian Tsallis distribution, to the polymeric network, which gives an improvement to the Gaussian model. This distribution presents some necessary characteristics, like a cutoff to the maximum chain length and a continuous limit to the Gaussian one for a large number of monomers. It also presents a simple quadratic structure that allows to generalize the Gaussian properties such as exact-moments calculation and Wick theorem. We obtain the free-energy density in its full tensorial structure.     

Characterization of magnetic colloids by means of magnetooptics

A new, efficient method for the characterization of magnetic colloids based on the Faraday effect is proposed. According to the main principles of this technique, it is possible to detect the stray magnetic field of the colloidal particles induced inside the magnetooptical layer. The magnetic properties of individual particles can be determined providing measurements in a wide range of magnetic fields. The magnetization curves of capped colloids and paramagnetic colloids were measured by means of the proposed approach. The registration of the magnetooptical signals from each colloidal particle in an ensemble permits the use of this technique for testing the magnetic monodispersity of colloidal suspensions.     

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.