Absorption of a Polyelectrolyte Brush into an Oppositely Charged Layer

Polyelectrolyte Cylindrical Brushes in Hairy Gels

We considered dispersions of cylindrical polyelectrolyte (PE) brushes with stiff backbones, and polymer-decorated nanorods with tunable solubility of the brush-forming PE chains that affected thermodynamic stability of the dispersions. We focused on thermo-induced and deionization-induced conformational transition that provokes loss of aggregative dispersion stability of nanorods decorated with weakly ionized polyions. A comparison between theoretical predictions and experiments enabled rationalization and semi-quantitative interpretation of the experimental results.

Mechanisms of Scaffold-Mediated Microcompartment Assembly and Size Control

This article describes a theoretical and computational study of the dynamical assembly of a protein shell around a complex consisting of many cargo molecules and long, flexible scaffold molecules. Our study is motivated by bacterial microcompartments, which are proteinaceous organelles that assemble around a condensed droplet of enzymes and reactants. As in many examples of cytoplasmic liquid-liquid phase separation, condensation of the microcompartment interior cargo is driven by flexible scaffold proteins that have weak multivalent interactions with the cargo. Our results predict that the shell size, amount of encapsulated cargo, and assembly pathways depend sensitively on properties of the scaffold, including its length and valency of scaffold-cargo interactions. Moreover, the ability of self-assembling protein shells to change their size to accommodate scaffold molecules of different lengths depends crucially on whether the spontaneous curvature radius of the protein shell is smaller or larger than a characteristic elastic length scale of the shell. Beyond natural microcompartments, these results have important implications for synthetic biology efforts to target alternative molecules for encapsulation by microcompartments or viral shells. More broadly, the results elucidate how cells exploit coupling between self-assembly and liquid-liquid phase separation to organize their interiors.

Weak polyelectrolyte brushes: re-entrant swelling and self-organization

We have studied the combined influence of pH and ionic strength on the properties of brushes of a weak polyion, poly(acrylic acid), in conditions of grafting density close to the mushroom-brush crossover. By combining atomic force microscopy AFM and quartz crystal microbalance, we show that at low ionic strengths the conformational change of grafted polyions is non-monotonic with increasing pH due to the counterintuitive variation of the ionization degree. Thus, reentrant swelling of the polymer chains is observed with increasing pH. This effect is more important at low polymer grafting densities, when it is accompanied by in-plane heterogeneous distribution at intermediate pH values. In addition, we observed self-assembly on the polymer brush (formation of holes and islands) at pH values below pKa, due to the short-range attractive interaction between uncharged grafted chains. The sensitivity of the ionization of grafted chains to the physicochemical environment was also studied by measuring the interaction force between a silica tip and polymer brushes by atomic force microscopy. The dependence of the ionization of polyions on the presence of the tip points toward important charge regulation effects, in particular at pH values corresponding to partial ionization of the polyion.

Polyelectrolyte brushes in external fields: molecular dynamics simulations and mean-field theory

A mean-field model is developed to predict the layer-thickness of sparse and salt-free polyelectrolyte brushes, exposed to an external electric field, which attracts the polyelectrolytes to the substrate. In molecular dynamics simulations, it is shown that a fraction of polymers collapses entirely to screen the charge of the substrate. The remaining brushes are then treated as field-free brushes at reduced grafting density. The mean-field model may thus be applied to field-free brushes, both in their osmotic and their weak charge regimes. It yields simple, closed equations for the brush height and for the partition of counterions in- and outside the brushes, and accurately reproduces simulation data of the collapse of the brushes during the crossover between both charge regimes.

Electric-field-induced friction reduction and control

Friction is always present when surfaces in contact are set in motion. In this work I describe how a precise, active control of the global friction is possible by adjusting the local molecular conformation of a polyelectrolyte coating via the application of an alternating electric field. The intensity of the applied field determines the degree of interpenetration between polymer brushes in contact, regulating chain stretching while sliding, which is the process at the origin of the global friction. The dynamics of the problem is controlled by the relaxation times of the polyelectrolyte.

Hard versus soft particle electrokinetics of silica colloids

To verify the existence of a gel layer at the surface of silica, dependences of the electrophoretic mobility of fresh and aged colloidal silica particles on the KCl concentration are measured. These dependences, corrected for the relaxation/polarization effect, are fitted by analytical expressions based on the model of hard, soft, and brush surfaces. A bad fit is obtained for both silicas when its surface is considered ideal (hard). Much better fits are achieved with the invariable soft layer model for the fresh silica but especially for the aged silica whose surface is less charged probably as a result of an extension and/or loosening of the layer. A perfect fit is found for aged silica when applying a trivial model of the soft polyelectrolyte layer combined with the scaling model of polyelectrolyte brushes.

Structure formation in films of weakly charged block polyelectrolyte solutions

A mean-field dynamic density functional theory is used to describe a phase diagram of concentrated solutions of weakly charged flexible block polyelectrolytes in a film. Electrostatics is taken into account by applying the local electroneutrality constraint (the Donnan membrane equilibrium approach). In the Donnan limit it is assumed that a salt added to the solution perfectly screens long-range electrostatic interactions. The phase diagram of a solution of a triblock polyelectrolyte in a film as a function of the solvent concentration and the charge of the polyelectrolyte (solvophilic) block is calculated for a given film thickness. The phase behavior of the block polyelectrolyte film arises from the interplay between surface-induced alignment and the electrostatically-driven structure formation. The observed mesoscopic structures (lamellar, perforated lamellar, cylindrical, micellar, and mixed phases) are oriented parallel to the surfaces for the considered case of morphologies unfrustrated by the film thickness. Structures with connections between parallel layers (bicontinuous, etc.) are not formed. As a result of surface-induced ordering, the region of ordered phases in a film is wider than in bulk and the phase boundary between ordered and disordered phases is more diffuse. As in the case of unconfined block polyelectrolyte solution, the solution in a film does not follow the lyotropic sequence of phases of such a block copolymer upon increase in the charge of the polyelectrolyte block. Upon changing the charge of the solvophilic copolymer block, transformations of copolymer morphology take place via change in curvature of polymeric domains. Due to confinement of a polyelectrolyte film, no swelling of solvophilic domains is observed.

Molecular thermodynamics for swelling of a mesoscopic ionomer gel in 1 : 1 salt solutions

For a microphase-separated diblock copolymer ionic gel swollen in salt solution, a molecular-thermodynamic model is based on the self-consistent field theory in the limit of strongly segregated copolymer subchains. The geometry of microdomains is described using the Milner generic wedge construction neglecting the packing frustration. A geometry-dependent generalized analytical solution for the linearized Poisson-Boltzmann equation is obtained. This generalized solution not only reduces to those known previously for planar, cylindrical and spherical geometries, but is also applicable to saddle-like structures. Thermodynamic functions are expressed analytically for gels of lamellar, bicontinuous, cylindrical and spherical morphologies. Molecules are characterized by chain composition, length, rigidity, degree of ionization, and by effective polymer-polymer and polymer-solvent interaction parameters. The model predicts equilibrium solvent uptakes and the equilibrium microdomain spacing for gels swollen in salt solutions. Results are given for details of the gel structure: distribution of mobile ions and polymer segments, and the electric potential across microdomains. Apart from effects obtained by coupling the classical Flory-Rehner theory with Donnan equilibria, viz. increased swelling with polyelectrolyte charge and shrinking of gel upon addition of salt, the model predicts the effects of microphase morphology on swelling.

Diblock polyampholytes grafted onto spherical particles: Monte Carlo simulation and lattice mean-field theory

Spherical brushes composed of diblock polyampholytes (diblock copolymers with oppositely charged blocks) grafted onto solid spherical particles in aqueous solution are investigated by using the primitive model solved with Monte Carlo simulations and by lattice mean-field theory. Polyampholyte chains of two compositions are considered: a copolymer with a long and a short block, A100B10, and a copolymer with two blocks of equal length, A50B50. The B block is end-grafted onto the surface, and its charge is varied, whereas the charge of the A block is fixed. Single-chain properties, radial and lateral spatial distributions of different types, and structure factors are analyzed. The brush structure strongly depends on the charge of the B block. In the limit of an uncharged B block, the chains are stretched and form an extended polyelectrolyte brush. In the other limit with the charges of the blocks compensating each other, the chains are collapsed and form a polyelectrolyte complex surrounding the particles. At intermediate charge conditions, a polyelectrolyte brush and a polyelectrolyte complex coexist and constitute two substructures of the spherical brush. The differences of the brush structures formed by the A100B10 and A50B50 polyampholytes are also analyzed. Finally, a comparison of the predictions of the two theoretical approaches is made.

Microphase separation of weakly charged block polyelectrolyte solutions: Donnan theory for dynamic polymer morphologies

A mean-field dynamic density functional theory for the phase behavior of concentrated weakly charged block polyelectrolyte solutions is developed, using the Donnan membrane equilibrium approach to account for electrostatic interactions. In this limit all long-range electrostatic interactions are canceled and the net charge density in any region on a coarse-grained scale is zero. The phase diagram of a model triblock polyelectrolyte in solution as a function of the charge of the solvophilic block and the solvent concentration is established. Different mesoscopic structures (lamellar, bicontinuous, hexagonal, micellar, and dispersed coexisting phases) are formed depending on the copolymer charge asymmetry. It is found that upon changing the charge of the solvophilic copolymer block the polyelectrolyte solution does not follow the lyotropic sequence of phases of this polymer. Upon increase in the charge of the solvophilic blocks, changes in copolymer morphology take place by means of change in curvature of polymeric domains.