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     

Electrophoresis of a charge-inverted macroion complex: Molecular-dynamics study

We have performed molecular-dynamics simulations to study the effect of an external electric field on a macroion in the solution of multivalent Z : 1 salt. To obtain plausible hydrodynamics of the medium, we explicitly make the simulation of many neutral particles along with ions. In a weak electric field, the macroion drifts together with the strongly adsorbed multivalent counterions along the electric field, in the direction proving inversion of the charge sign. The reversed mobility of the macroion is insensitive to the external field, and increases with salt ionic strength. The reversed mobility takes a maximal value at intermediate counterion valence. The motion of the macroion complex does not induce any flow of the neutral solvent away from the macroion, which reveals screening of hydrodynamic interactions at short distances in electrolyte solutions. A very large electric field, comparable to the macroion unscreened field, disrupts charge inversion by stripping the adsorbed counterions off the macroion. Received 5 December 2001 and Received in final form 10 April 2002     

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     

Ordering of urchin-like charged copolymer micelles: Electrostatic, packing and polyelectrolyte correlations

We report the results of small-angle neutron scattering (SANS) studies on aqueous solutions of spherical polyelectrolyte micelles formed by association of charged-neutral diblock copolymers. The neutral moieties are found to self-assemble into small dense spheres (cores of the micelles) whose sizes are independent of the polymer concentration c. In the dilute regime, c<c ^*, where c^* is the overlap concentration of the micelles, the conformation of the charged groups, which form the corona of the micelles, is found to be extended. A liquid-like order is observed over a wide concentration range spanning from the dilute regime to the concentrated regime. For c>c ^*, polyelectrolyte correlations appear at smaller spatial scales and coexist with the liquid-like order. These results suggest that for dense brushes, above c^*, the rod-like statistics of the charged chains begin to disappear due to contraction of corona arms or by interpenetration of coronae. For less dense brushes, the charged chains are found to be extended up to concentrations far above c^*, before the progressive development of polyelectrolyte correlations. Received 8 October 1999     

Shrinking of anionic polyacrylate coils induced by Ca2+, Sr2+ and Ba2+: A combined light scattering and ASAXS study

Anionic polyacrylate chains (NaPA) form precipitates if alkaline earth cations are added in stoichiometric amounts. Accordingly, precipitation thresholds were established for three different alkaline earth cations Ca²⁺, Sr²⁺ and Ba²⁺. Close to the precipitation threshold, the NaPA chains significantly decrease in size. This shrinking process was followed by means of combined static and dynamic light scattering. Intermediates were generated by varying the ratio [MCl₂]/[NaPA] with M denoting the respective alkaline earth cation. All experiments were performed at an inert salt level of 0.01M NaCl. Similar coil-to-sphere transitions could be observed with all three alkaline earth cations Ca²⁺, Sr²⁺ and Ba²⁺. Based on these findings, supplementary conventional and anomalous small-angle X-ray scattering experiments using selected intermediates close to the precipitation threshold of SrPA were performed. The distribution of Sr counterions around the polyacrylate chains in aqueous solution provided the desired scattering contrast. Energy-dependent scattering experiments enabled successful separation of the pure-resonant terms, which solely stem from the counterions. The Sr²⁺ scattering roughly reflects the monomer distribution of the polyacrylate chains. Different ratios of the concentrations of [ SrCl₂]/[NaPA] revealed dramatic changes in the scattering curves. The scattering curve at the lowest ratio indicated an almost coil-like behaviour, while at the higher ratios the scattering curves supported the model of highly contracted polymer chains. Most of X-ray scattering experiments on intermediate states revealed compact structural elements which were significantly smaller than the respective overall size of the NaPA particles.     

Simple model for attraction between like-charged polyions

We present a simple model for the possible mechanism of appearance of attraction between like charged polyions inside a polyelectrolyte solution. The attraction is found to be short ranged, and exists only in the presence of multivalent counterions. It is produced by the correlations in layers of condensed counterions surrounding each polyion and is only weakly temperature dependent. We find the attraction to be maximum at zero temperature and dimish as the temperature is raised. The attraction is only possible if the number of condensed counterions exceeds the threshold, , where is the valence of counterions and Z is the polyion charge. Received 10 March 1999 and Received in final form 20 April 1999     

A small-angle X-ray scattering study of the isotropic and nematic phases of V2O5 suspensions

We report small-angle X-ray scattering experiments performed in both the isotropic and nematic phases of aqueous V₂O₅ suspensions. We show that the scattering in the isotropic phase can be well described in the whole accessible q-range by only considering the form factor of non-interacting ribbons. We investigate the influence of concentration and pH on the dimensions of V₂O₅ ribbons and show that these parameters do not have any significant effect, as long as the system stays well within the chemical stability domain of the ribbons. We then show that nematic single domains display an anisotropic small-angle scattering pattern, even at scattering vectors small compared to that at which a characteristic correlation peak is observed. This feature is expected for a nematic phase, but was rarely observed. We finally try to describe this scattering within the framework of theories developed for the structure factor of a nematic polymer, and we reach the conclusion that chain ends are certainly important to understand this pattern. Received 21 July 1999 and Received in final form 17 December 1999     

Adsorption of anionic polyelectrolytes to dioctadecyldimethylammonium bromide monolayers

Monolayers of dioctadecyldimethylammonium bromide (DODA) at the air/water interface were used as model for charged surfaces to study the adsorption of anionic polyelectrolytes. After spreading on a pure water surface the monolayers were compressed and subsequently transferred onto a polyelectrolyte solution employing the Fromherz technique. The polyelectrolyte adsorption was monitored by recording the changes in surface pressure at constant area. For poly(styrene sulfonate) and carboxymethylcellulose the plot of the surface pressure as function of time gave curves which indicate a direct correlation between the adsorbed amount and surface pressure as well as a solely diffusion controlled process. In the case of rigid rod-like poly(p-phenylene sulfonate)s the situation is more complicated. Plotting the surface pressure as function of time results in a curve with sigmoidal shape, characterized by an induction period. The induction period can be explained by a domain formation, which can be treated like a crystallization process. Employing the Avrami expression developed for polymer crystallization, the change in the surface pressure upon adsorption of rigid rod-like poly(p-phenylene sulfonate)s can be described. Received 1st July 2000 and Received in final form 7 December 2000     

Small-angle X-ray scattering from salt-free solutions of star-branched polyelectrolytes

The dispersion state of sodium-sulphonated polystyrene ( NaPSS) star-branched polyelectrolytes was investigated in salt-free aqueous solutions, by use of the small-angle X-ray scattering technique. With respect to polystyrene (PS) star-branched polymers of identical functionality, the ordering phenomenon occurring in the neighborhood of the overlap concentration c^* is reinforced and observed in a larger range of concentrations. Moreover, the degree of order is no longer maximum at c^* and is improved as the concentration decreases. The dispersion state is then mainly controlled by the electrostatic interaction. A crystalline order should therefore be achieved with stars of lower functionality, provided the electrostatic interaction is added to the osmotic repulsion. On the other hand, unusual scattering patterns are measured for aqueous solutions of NaPSS star polyelectrolytes. Indeed, a diffuse scattering is revealed at high angles, in addition to the regular diffraction rings related to preferred interstar distances. It is similar to the broad scattering peak produced by semidilute solutions of NaPSS linear polyelectrolytes and associated to the electrostatic correlation hole within the isotropic model. In the dilute regime (c < c ^*), it is just an intramolecular characteristic and represents the electrostatic repulsion between arms belonging to the same star. In the semidilute regime (c > c ^*), it also reflects the electrostatic repulsion between arms of distinct stars. So, as the concentration increases, it is mainly caused by the interpenetration of NaPSS stars. Such an observation is in agreement with the composite structure earlier proposed by Daoud and Cotton for star semidilute solutions. For c > c ^*, NaPSS star aqueous solutions can therefore be pictured as effective stars immersed in a matrix formed by the overlap of the arm ends. With respect to the dilute regime, the effective stars are smaller; the higher the concentration the smaller the size. Received 14 May 1999 and Received in final form 15 March 2000     

Non-monotonic swelling of a macroion due to correlation-induced charge inversion

It is known that a large, charged body immersed in a solution of multivalent counterions may undergo charge inversion as the counterions adsorb to its surface. We use the theory of charge inversion to examine the case of a deformable, porous macroion which may adsorb multivalent ions into its bulk to form a three-dimensional strongly-correlated liquid. This adsorption may lead to non-monotonic changes in the size of the macroion as multivalent ions are added to the solution. The macroion first shrinks as its bare charge is screened and then reswells as the adsorbed ions invert the sign of the net charge. We derive a value for the outward pressure experienced by such a macroion as a function of the ion concentration in solution. We find that for small deviations in the concentration of multivalent ions away from the neutral point (where the net charge of the body is zero), the swollen size grows parabolically with the logarithm of the ratio of multivalent ion concentration to the concentration at the neutral point.     

Counterion condensation in ionic micelles as studied by a combined use of SANS and SAXS

We report a combined use of small-angle neutron scattering (SANS) and small-angle X-ray scattering (SAXS) to the study of counterion condensation in ionic micelles. Small-angle neutron and X-ray scattering measurements have been carried out on two surfactants cetyltrimethylammonium bromide (CTABr) and cetyltrimethylammonium chloride (CTACl), which are similar but having different counterions. SANS measurements show that CTABr surfactant forms much larger micelles than CTACl. This is explained in terms of higher condensation of Br⁻ counterions than Cl⁻ counterions. SAXS data on these systems suggest that the Br⁻ counterions are condensed around the micelles over smaller thickness than those of Cl⁻ counterions.     

High temperature phase transitions in the crystal [4]of p-trimethylammoniumbenzenesulfonate zwitterion

Crystals of p-trimethylammoniumbenzenesulfonate (ZWT) have been obtained from the thermally induced soli d-state reaction of methyl p-dimethylaminobenzenesulfonate (MSE) or by recrystallization in aqueous solution. The characterization of four crystalline phases has been performed by calorimetric, birefringence, X-ray and Raman scattering studies. An unknown phase transition at room temperature yielding a new crystallographic phase has been found by calorimetric measurements. ZWT crystalline samples obtained from the solid state reaction are disordered as compared to ZWT single crystals obtained by growing from aqueous solution. This disorder is related to different arrangements of the phenyl ring orientations. Received 21 October 1998 and Received in final form 14 April 1999     

Macroions in salty water with multivalent ions: giant inversion of charge

Screening of a strongly charged macroion by oppositely charged colloidal particles, micelles, or short polyelectrolytes is considered. Because of strong lateral repulsion such multivalent counterions form a strongly correlated liquid at the surface of the macroion. This liquid provides correlation-induced attraction of multivalent counterions to the macroion surface. As a result even a moderate concentration of multivalent counterions in the solution inverts the sign of the net macroion charge. We show that at high concentration of monovalent salt the absolute value of inverted charge can be larger than the bare one. This giant inversion of charge can be observed in electrophoresis.     

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     

Ionic distribution and polymer conformation, near phase separation, in sodium polyacrylate/divalent cations mixtures: small angle X-ray and neutron scattering

Anomalous small angle X-ray scattering experiments show that before demixion in sodium polyacrylate/cobalt and sodium polyacrylate/calcium mixtures all the divalent counterions are in the close vicinity of the polyacrylate chain. The present results are consistent with previous UV/VIS spectroscopy, which have shown that all cobalt ions are chemically associated with acrylate groups. The chemical association dehydrates the acrylate monomers. However, the hydrophobicity of the complexed monomers is not strong enough to induce a collapse of the polymer chain at small spatial scale before the demixion. Indeed, the scattered intensity (X-ray and neutron scattering) decreases with the scattering vector q as q^-x with for q > 0.1 nm ^-1 which indicates that the local conformation of the chain is Gaussian. Received 21 January 1999     

Molecular dynamics simulation analysis of small-angle neutron scattering by a solution of stearic acid in benzene

Data of small-angle neutron scattering by a diluted solution of stearic acid in deuterated benzene have been analyzed using the results of molecular dynamics simulation. The molecular dynamics simulation approach has been used to calculate the time-averaged distribution of the neutron scattering length density at the interface between the acid molecule and the solvent. It has been shown that the organization of the solvent at the interface with the acid molecule leads to a modulation of the neutron scattering length density and makes a significant contribution to the scattering. This contribution should be taken into account when interpreting the experimental small-angle neutron scattering curves for both the considered system and its analogues.     

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.     

Effects of ionic strength and charge annealing in star-branched polyelectrolytes

We have developed a scaling theory that describes the conformations of weak star-branched polyelectrolytes in dilute solutions. The dependences of the overall star size on the number of branches and on the ionic strength of the solution (tuned by the addition of low molecular weight salt) are analyzed. The intrinsic structure of the polyelectrolyte stars in salt-free and salt-added solutions is discussed in terms of concentration and elastic blobs. In contrast to neutral stars, the swollen corona of the polyelectrolyte star consists of blobs which are not closely packed. We have shown that the size of star polyelectrolytes is less sensitive to the variation in the ionic strength than the size of linear polyelectrolytes. The effects of the ionization-recombination balance in the star polyelectrolyte were taken into account. For polyelectrolytes with small ionization constant, the size of the star depends nonmonotonically on the number of branches and on the ionic strength of the solution due to recombination of counterions with charged monomers. Received: 10 November 1997 / Revised: 16 February 1998 / Accepted: 1st April 1998     

Scattering properties of salt-free wormlike micellar solutions

Static and dynamic light scattering and conductivity experiments were carried out on salt-free aqueous micellar solutions of cetyltrimethylammonium n-hexane sulfonate (CTAC_6SO_3) and cetyltrimethylammonium n-heptane sulfonate (CTAC_7SO_3) as a function of surfactant concentration. This study confirms the analogy between the behavior in the semi-dilute regime of elongated micellar systems and “classical” polyelectrolyte solutions. Time-resolved scattering experiments performed after a variation of concentration from about twice the overlap volume fraction to less than half of it revealed the existence of a structural relaxation with a characteristic time of several hours. Received 21 December 1999     

Effect of counterions on the swelling of spherical polyelectrolyte brushes

We investigate the swelling of colloidal spherical polyelectrolyte brushes in the presence of different counterions. The colloidal particles consist of a solid poly(styrene) core of ca. 100 nm diameter onto which linear polyelectrolyte chains are chemically grafted. Two types of polyelectrolyte chains have been used here: The cationic polyelectrolyte poly(2-(acryloyl)ethyltrimethylammonium chloride)) (PATAC) and the anionic poly(styrenesulfonate) (PSS). Both systems are dispersed in water and the degree of swelling of the surface layer is studied by dynamic light scattering. Adding more and more salt leads to a strong shrinking of the surface layer as expected for polyelectrolyte brushes. It is shown that data obtained at low ionic strength can be collapsed on suitable master curves for monovalent and divalent counterions, respectively. For some ions, however, high salt concentrations may lead to a re-swelling of the brush layer in case of the cationic systems. This points to specific interactions of the counterions with the PATAC chains. This strong specific interaction between the counterions and the attached polyelectrolyte may even lead to flocculation of the particles at intermediate salt concentration. Surprisingly, for iodide and magnesium counterions the solubility increases again if the salt concentration is raised to 1 mol/l. Hence, specific interaction leads to salting-out effects as well as to salting-in effects for these colloidal particles. All specific effects seen at high concentrations of added salt can be explained by the increase of the reduced excluded-volume parameter which is due to the adsorption of salt ions.