M. Olvera de la Cruz

PRECIPITATION OF HIGHLY CHARGED POLYELECTROLYTE SOLUTIONS IN THE PRESENCE OF MULTIVALENT SALTS

Solutions of highly charged polyelectrolyte chains are described by a model that introduces ion condensation as a random charge along the polymer. The degree of condensation is obtained by solving the Poisson–Boltzmann equation with cylindrical geometry. Short range electrostatic attractions between the monomers via the condensed counterions of high enough valency lead to reversible chain precipitation. The range of polymer concentration over which salt‐free solutions are unstable is determined, as well as the miscibility of the chains when salt is added. Redissolution at high salt concentration is due to a screening of the short range electrostatic attractions. Precipitation of chains in mixtures of movalent and multivalent salts is also studied. We find the range of salt concentration where chains precipitate. The model explains the experimental results on the precipitation of sodium and lanthanum polystyrene sulfonate solutions in presence of multivalent salts [LaCl3 and Th(NO3)4].

Ion condensation in salt‐free dilute polyelectrolyte solutions

We study ion condensation in salt‐free dilute solutions of polyelectrolyte chains of different fractal geometries, from random walks to rigid rods. In finite size chains with a discrete charge distribution, ion condensation is only observed in multiple chain systems. A thermodynamic analysis of ion condensation with linearized interactions among the condensed counterions and the monomers leads to rigid rod lowest free energy conformations, regardless of the values of the valency of the monomers (zm), the negative value of the ratio of the valency of the counterions to the valency of the monomers (Pz), and the ratio of the Bjerrum length (lB) to the distance between charges along the polyion (b). As z2mPzlB/b increases, however, the fraction of condensed counterions increases and the polyion concentration at which ion condensation appears decreases. Above this critical polyion concentration, ion condensation is observed even when lB/b<1/z2mPz. When correlations are included, representing the tendency of th...

Concentration fluctuation effects on disorder-order transitions in block copolymer melts

We study transitions to periodic structures in block copolymers melts, including concentration fluctuations self‐consistently in the analysis. Phase diagrams are constructed for diblock and triblock copolymers of finite molecular weight. The concentration fluctuations increase the stability of the isotropic state, and induce a shift in k*, the wave vector of maximum scattered intensity, to lower values as the transition is approached. We calculate the shift in k* near the transition, and obtain the anisotropic scattering function in the ordered state.

Charge induced pattern formation on surfaces: Segregation in cylindrical micelles of cationic-anionic peptide-amphiphiles

Micelles, vesicles, and films composed of two species of incompatible heterogeneous molecules exhibit full internal segregation of the component species. This macroscopic segregation can be inhibited by oppositely charging the two different molecular species. The degree of compatibility achieved by the charges leads to either fully homogenous mixtures or to local segregation and the possible formation of regular patterns. We investigate the induction of periodic surface patterns by the presence of opposite charges in flat films and cylindrical micelles. In the strong segregation limit the incompatibility between species can be described by a line tension parameter gamma. The size of the patterns formed is of the order of a characteristic size L approximately (gamma/sigma(2))(1/2), where sigma is the surface charge density. The pattern symmetry on flat surfaces is function only of the fraction of area covered by the components, f: lamellar for 0.34<f<0.66 and hexagonal otherwise. In cationic and anionic mixtures aggregated into cylindrical micelles the symmetry and size of the surface charged domains depends also on the radius R of the cylinder. For large radii the patterns are similar to those in the plane, but for small radii only lamellar patterns are formed. At high salt concentration the surface domain size jumps discontinuously to an infinite value, resulting in macroscopic phase segregation.

Concentration fluctuations in polymer blend thermodynamics

Monomer concentration fluctuations in high molecular weight polymer blends are investigated. The fluctuations reduce the value of the χ interaction term in the Flory–Huggins free energy by a factor of (1‐6/π2) and add a concentration and molecular weight contribution which decreases phase stability for off‐critical compositions. Except at the critical point, the spinodal values are smaller than those predicted from a Flory–Huggins‐type free energy. For an incompressible blend with components of equal size N, the corrections to the spinodal were found to vary as ‖1−2φ0‖4/3N−1/3, where φ0 is the mean concentration.

Polyelectrolytes in the presence of multivalent ions: Gelation versus segregation

We analyze solutions of strongly charged chains bridged by linkers such as multivalent ions. The gelation induced by the strong short range electrostatic attractions is dramatically suppressed by the long range electrostatic correlations due to the charge along the non-cross-linked monomers and ions. A modified Debye-Hückel approach of cross-linked clusters of charged chains is used to determine the mean field gelation transition self-consistently. Highly dilute polyelectrolyte solutions tend to segregate macroscopically. Semidilute solutions can form gels if the Bjerrum length l(B) and the distance between neighboring charged monomers along the chain b are both greater than the ion size a.

Theory of microphase separation in block copolymer solutions

Microphase separation in semidilute solutions of block copolymers in nonselective good solvent is analyzed. The swelling due to the presence of solvent is taken into account. The solvent effects on the thermodynamics in the disordered region and in the ordered region in the weak segregation limit are discussed. It is found that the concentration of block copolymer at the microphase separation transition scales as N−0.62 in good solvents and as N−1/2 in Φ solvents. In the asymptotic semidilute regime in good solvents, the coexistence curve at the microphase separation transition is negligible, and the transition scales as (χ’AB φ1.61N)t ∼constant, where the constant is determined by the relative composition of the blocks in the block copolymer and χAB is proportional to the usual Flory interaction parameter.

Phase transitions in random copolymers

Ideal random AB copolymers with degree of polymerization N are mixtures of N+1 types of chains with different compositions (fractions fi of A monomers). Conditions for single phase and multiphase equilibria are studied using Flory–Huggins free energy of mixing with χ representing the A–B interaction parameter. The spinodal for one phase instability is given by χs=[2f(1−f)]−1 for all N, where f is the average A fraction in the system. The transition from one to two phases is continuous at χ=χs when f=0.5 and discontinuous at χ≤χs when f≠0.5. Three, four, and more phases become stable at larger values of χ. Our numerical solution suggests that the stability range for multiple phases approaches Δχ≊0.15 at large (but finite) N. Macroscopically and microscopically phase separated states are investigated with the Landau approach of Fredrickson, Milner and Leibler. The Landau method gives reasonable but inexact results for two macroscopic phases when the random copolymer has compositional symmetry (f=0.5). A dis...

Association in electrolyte solutions: Rodlike polyelectrolytes in multivalent salts

We describe a new approach to determine the degree of association between ionic components in complex electrolyte solutions. We use the electrostatic contribution to the free energy that arises from the exact separation into long and short ranged parts of the correlation functions in a dilute electrolyte solution to determine the effective charge of the various ionic components. We describe the short-ranged direct correlations between different ionic components with delta functions whose strength give the direct association between them. The association is determined self-consistently by minimizing the resulting free energy, which contains long and short range correlations contributions. Association between like charges is mediated by direct association between opposite charges. We analyze rodlike polyelectrolyes in monovalent and/or multivalent salts. We find a broad minimum in the absolute value of effective rod charge at long distances as a function of monovalent salt concentration. This minimum is due to the association of the salt ions among themselves. We also determine the number of multivalent and monovalent ions associated to the rods. The degree of association is a function of the smallest length scale, which determines the electrostatic potential between ionic species at contact.

Random phase approximation for complex charged systems: Application to copolyelectrolytes (polyampholytes)

We study binary polyelectrolytes in the melt state and in concentrated solutions using the random phase approximation (RPA). We compute the thermodynamics and electrostatics of chemically linked polyelectrolytes chains into block copolymer molecules (copolyelectrolytes). Polyelectrolytes blends and copolyelectrolytes in the presence of free ions have Debye–Huckel‐type effective monomer–monomer interactions, even when the polymer chains are not charged. Copolyelectrolyte of chemically linked chains of opposite charge in the absence of counterions, have ion–ion effective interactions characteristic of a dielectric medium, contrary to the case of polyelectrolyte blends where these effective interactions are Debye–Huckel type, even on the absence of free ions. The dielectric constant in such a diblock copolymer melt is proportional to the square of the degree of polymerization Np. In the reference state (without interactions) RPA assumes random walk statistics, which are nearly unperturbed in the dielectric; ...