Structural properties of charged diblock copolymer solutions

Aqueous micellar solutions of ionic/neutral block copolymers have been studied by light scattering, small angle neutron scattering and small angle X-ray scattering. We made use of a polymer comprised of a short hydrophobic block (polyethylene-propylene) PEP and of a long polyelectrolytic block (polystyrene-sulfonate) PSSNa which has been shown previously to micellize in water. The apparent polydispersity of these micelles is studied in detail, showing the existence of a few large aggregates coexisting with the population of micelles. Solutions of micelles are found to order above some threshold in polymer concentration. The order is liquid-like, as demonstrated by the evolution with concentration of the peak observed in the structure factor (), and the degree of order is found to be identical over a large range of concentrations (up to 20 wt%). Consistent values of the aggregation number of the micelles are found by independent methods. The effect of salt addition on the order is found to be weak. Received: 19 June 1997 / Received in final form: 4 September 1997 / Accepted: 9 October 1997     

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     

Random copolymers at a selective interface: Many chains with excluded volume interactions

We investigate numerically, using the bond-fluctuation model, the adsorption of many random AB-copolymers with excluded volume interactions at the interface between two solvents. We find two regimes, controlled by the total number of polymers. In the first (dilute) regime, the copolymers near the interface extend parallel to it, while in the second regime they extend perpendicular to it. The density at the interface and the density in the bulk depend differently on the total number of copolymers: In the first regime the density at the interface increases more rapidly than in the bulk, whereas the opposite is true in the second regime. Received 4 March 1998 and Received in final form 22 September 1998     

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     

The state space of short-range Ising spin glasses: the density of states

The correlations between the segments of a semidilute polymer solution are found to induce correlations in the positions of small particles added to the solution. Small means a diameter much less than the polymer's correlation length. In the presence of polymer the particles behave as if they attracted each other. It is shown how the polymer's correlation length may be determined from a scattering experiment performed on the spheres. Received: 7 July 1997 / Received in final form: 12 November 1997 / Accepted: 19 November 1997     

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     

Aqueous mixtures of spherical and rodlike (flexible) macroparticles: structure and dynamics of latex spheres in saltfree solutions

This paper resumes light scattering investigations of saltfree aqueous solutions of two component mixtures of charged spheres by extending those measurements to systems in which one component is replaced by essentially stiff rodlike particles. In a second step of investigations these were replaced by linear flexible particles. Fd-virus particles (length l=883 nm) or macromolecules of NaPSS of four different contour lengths have been used as representatives. Mostly the concentration of latex spheres was fixed at 0.02 Vol%. The concentration of the other component was varied over a wide range. Concerning the scattering intensity, the contribution of the latex spheres dominates, in particular in the systems containing NaPSS particles. This simplifies the interpretation of data considerably. A rearrangement of the spheres is observed, depending on the shape of the other sort of particles. These conclusions can be drawn from the shift of measured static structure factor with concentration c. A power law is found for the q-value of the maximum. The exponent depends on the properties of the second component. For the lower molecular weight (MW) samples of NaPSS below a critical concentration, the exponent is smaller than 1/3, decreasing the more the smaller the MW of the samples is. A tentative explanation in terms of charge number of NaPSS particles is given. The short time dynamics has been explored too. From the data a “dynamically determined structure factor” can be derived, that can be compared with the measured static structure factor. Good (fd) and fair (NaPSS) agreement is obtained respectively. Only at small wavenumbers below the maximum of deviations occur which increase with concentration; they are consistent with hydrodynamic interaction. Received 30 July 1998 and Received in final form 14 December 1998     

Identification of flow mechanisms for a soft crystal

We study the behavior under flow of soft spherical micelles forming a fcc phase at high volume fraction. Due to the size (300 ?) of the elementary objects, the structure can be investigated through X-rays and neutron scattering, at rest and under flow in a Couette cell. Using scattering in two perpendicular directions, different mechanisms of flow are identified. At intermediate shear (around 100 s^-1) the system exhibits the so called layer sliding mechanism where two dimensional hexagonal compact planes of spheres align themselves with the Couette cell walls. At lower shear rate, the fcc structure is locally preserved, and the flow is mediated by defects between crystallites. At high shear rate, we observe the melting of the structure and a liquid-like structure factor. Moreover, we were able to use the existence of the layer sliding regime to generate a fcc monocrystal by annealing the satcking faults between the decorrelated planes created by the layer sliding. Received: 7 July 1997 / Received in final form: 16 January 1998 / Accepted: 5 March 1998     

AC field induced two-dimensional aggregation of multilamellar vesicles

The aggregation of 2D colloidal crystals can be performed by applying an AC field to a colloidal dispersion. This technique is used in this work for assembling multilamellar vesicles in suspension. The dynamics of the aggregation is followed by real-time recording of the pictures of the microsphere assembly through a phase contrast microscope. The influence of both the frequency and the amplitude of the alternating field on the dynamical evolution of the concentration of layered particles is discussed with respect to their size. A phenomenological model of double layer induced trapping of the particles is proposed and an electroconvective instability of the fluid surrounding the particles is suggested from the observation of the local dynamics of the particles, in accordance with a very recent argument of Yeh et al. [#!Yeh:97!#]. Received: 4 December 1997 / Revised: 24 March 1998 / Accepted: 4 May 1998     

Collapse of polyelectrolyte brushes: Scaling theory and simulations

We investigate polyelectrolyte brushes using both scaling arguments and molecular dynamics simulations. As a main result, we find a novel collapsed brush phase. In this phase, the height of the brush results from a competition between steric repulsion between ions and monomers and an attractive force due to electrostatic correlations. As a result, the monomer density inside the brush is independent of the grafting density and the polymerization index. For small ionic and monomer radii (or for large Bjerrum length) the brush undergoes a first-order phase transition from the osmotic into the collapsed state. Received 26 September 2000     

One-dimensional optical reflectors based on self-organization of polymeric comb-shaped supramolecules

We demonstrate that complexation of dodecylbenzenesulphonic acid, DBSA, to a diblock copolymer of polystyrene- block-poly(4-vinylpyridine), PS- block-P4VP, leads to polymeric supramolecules PS- block-P4VP(DBSA)y (y = 1.0, 1.5, and 2.0), which self-organize with a particularly large lamellar periodicity in excess of 1000 A. The structures consist of alternating PS and P4VP(DBSA)y layers, where the latter contains smaller internal structure, probably lamellar. The DBSA side chains are bonded to the pyridines by protonation and hydrogen bonding and they effectively plasticize the material. In this way relatively well-developed structures are obtained even without annealing or macroscopic alignment. Transmission and reflectance measurements show that a relatively narrow and incomplete bandgap exists for supramolecules of high molecular weight block copolymer at ca. 460 nm.     

Viscosity at small scales in polymer melts

Flows around small colloidal particles of diameter b, or in thin films, capillaries, etc., cannot always be described in terms of the macroscopic polymer viscosity. We discuss these features for entangled polymer melts, where two distinct regimes can be found: (a) the thin regime where b is smaller than the coil radius R₀, but larger than the diameter of the Edwards tube; (b) the ultrathin regime, where . We consider (i) non adsorbing particles, where slippage may occur between the melt and the solid surface; (ii) “hairy” particles, which carry some bound polymer chains. We obtain scaling predictions for mobilities of spheres, of needles, and of clusters of particles. We also discuss translational and rotational diffusion of needles. Received 19 April 1999     

Kinetics of microphase segregation in one-dimensional symmetric diblock copolymer systems

An analytical one-dimensional model of the microphase separation in symmetric diblock copolymers is developed. Three stages of the process of the microphase segregation of a quenched diblock copolymer system into a lamella structure are predicted. The first stage involves a fast increase of the amplitude of the quasi-periodical lamella structure (with the average wave vector q₀) up to a nearly equilibrium value; the second stage is a slow phase diffusion process which is characterized by increasing coherency of the lamella structure; the third stage is the slow process of the lamella swelling, which is driven by the thermally activated process of the spontaneous deletion of excessive lamellas, the lamella size increasing from the initial value 2π/q ₀ to the equilibrium 2π/q _eq > 2π/q ₀ during the process. The last two stages are described with the specially introduced coarse-grained “amplitude-phase” approximation. It is shown that the relaxation of the gradient of the phase of the lamellar structure is the slowest relaxation process and, thus, can be used as an effective order parameter of the lamellar structure at the later stages of the microphase segregation. Received 10 March 2000 and Received in final form 5 June 2000     

Swelling kinetics of a compressed lamellar phase

We investigate how multilamellar vesicles prepared in a compressed state under flow return to equilibrium. The kinetics is studied by following the temporal evolution of the viscoelasticity after the shear is stopped. It exhibits a two-step relaxation whose slower stage is strongly affected by temperature. According to a simple model, the temperature-dependent permeability of the lamellar phase is deduced from the measurements. We propose to attribute the permeability to handle-like defects, and its temperature dependence to an increase of the defect density when the lamellar-to-sponge phase transition is approached. Received 25 May 2000 and Received in final form 4 August 2000     

Structure and rheology of the defect-gel states of pure and particle-dispersed lyotropic lamellar phases

We present important new results from light-microscopy and rheometry on a moderately concentrated lyotropic smectic, with and without particulate additives. Shear-treatment aligns the phase rapidly, except for a striking network of oily-streak defects, which anneals out much more slowly. If spherical particles several microns in diameter are dispersed in the lamellar medium, part of the defect network persists under shear-treatment, its nodes anchored on the particles. The sample as prepared has substantial storage and loss moduli, both of which decrease steadily under shear-treatment. Adding particles enhances the moduli and retards their decay under shear. The data for the frequency-dependent storage modulus after various durations of shear-treatment can be scaled to collapse onto a single curve. The elasticity and dissipation in these samples thus arises mainly from the defect network, not directly from the smectic elasticity and hydrodynamics. Received 19 April 1999 and Received in final form 20 May 1999     

Structural evidence of charge renormalization in semi-dilute solutions of highly charged polyelectrolytes

We show experimentally that Manning counterion condensation also leads to a renormalization of the charge density at high concentrations of highly charged, flexible, hydrophilic polyelectrolytes. Investigations by small angle neutron and X-ray scattering of semi-dilute solutions of poly(acrylamide-co-sodium-2-acrylamido-2-methylpropane sulfonate) at different charge densities above the condensation threshold, show that the scattering function is invariant with the charge density. Received 16 June 1998     

Amphiphilic block copolymer nanocontainers as bioreactors

Self-assembly of an amphiphilic triblock copolymer carrying polymerizable end-groups is used to prepare nanometer-sized vesicular structures in aqueous solution. The triblock copolymer shells of the vesicles can be regarded as a mimetic of biological membranes although they are 2 to 3 times thicker than a conventional lipid bilayer. Nevertheless, they can serve as a matrix for membrane-spanning proteins. Surprisingly, the proteins remain functional despite the extreme thickness of the membranes and that even after polymerization of the reactive triblock copolymers. This opens a new field to create mechanically stable protein/polymer hybrid membranes. As a representative example we functionalize (polymerized) triblock copolymer vesicles by reconstituting a channel-forming protein from the outer cell wall of Gram-negative bacteria. The protein used (OmpF) acts as a size-selective filter, which allows only for passage of molecules with a molecular weight below 400 g mol^-1. Therefore substrates may still have access to enzymes encapsulated in such protein/polymer hybrid nanocontainers. We demonstrate this using the enzyme β-lactamase which is able to hydrolyze the antibiotic ampicillin. In addition, a transmembrane voltage above a given threshold causes a reversible gating transition of OmpF. This can be used to reversibly activate or deactivate the resulting nanoreactors. Received 22 August 2000     

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     

Salty solutions near a charged modulated interface

Charged monolayers at a liquid-vapor interface may be found in a crystalline state, resulting in a surface density of charge that displays periodic modulations. In this paper we discuss how these modulations affect different thermodynamical and mechanical properties (compared with the equivalent uniform charge density) of a system consisting of the charged monolayer and a bulk solution including a finite concentration of counter-ions and co-ions. It is shown that very accurate results for low and moderate salt concentrations are possible within an expansion in the Fourier modes of the modulations, the Weak Amplitude Perturbation (WAP), if the finite size of the ions are included as a Stern layer. We conclude by discussing the implications and the relevance of these results for both theoretical studies and experiments.     

Electric field light scattering by flexible linear polyelectrolytes in aqueous solution

Electric field light scattering results on aqueous solutions of linear, flexible NaPSS at minimal ionic strength are reported. Samples of molecular weights between 356 kg/mol and 2870 kg/mol were investigated. With increasing field strength the intensity as a function of wavenumber develops a pronounced oscillating behaviour. Besides the well-known first peak a second maximum is observed at the position at which a weak maximum for some samples already occurs at zero field. The overall intensity strongly depends on the frequency of the electric field. The electro-optical effect shows a maximum at 300 kHz. Increasing the particle concentration gives a large increase of the peak maximum, normalized to concentration. If plotted versus scattering angle the relative intensity increase is maximum for samples of medium molecular weight. The results strongly indicate a stretching and alignment of the chains, thus leading to or enlarging the short range order of the chains. Received 9 April 1999 and Received in final form 18 August 1999