Self-assembly of amphiphilic polyelectrolytes in trivalent salt solution.

Multivalent salt plays important roles in polyelectrolyte (PE) systems. Some special effects, such as ion mediated electrostatic correlation and reentrant condensation can be induced in the presence of multivalent salt. In this work, the self-assembly behaviors of diblock PEs in trivalent salt solutions are mainly investigated by molecular dynamics (MD) simulations, and partial results are qualitatively verified by experiments. The electrostatic correlation between PE chains and trivalent counterions is first enhanced with the increase of salt concentration, and then the large complexes of co-ions and trivalent counterions reduce the correlation at the excessive salt regime. Therefore, the electrostatic correlation mediated by trivalent ions shows a non-monotonic dependence on salt content. It should be noted that one-dimensional chain-like and two-dimensional planar network supra-micellar structures are obtained at different concentrations of PEs. It is the strong electrostatic correlation mediated by trivalent counterions that leads to the cross-linking of micelles, and homogeneous spherical micelles rather than anisotropic micelles are used as building blocks. Both of these supra-micellar structures predicted by simulations are qualitatively confirmed by experiments, and a micron sized long polymer chain and planar networks of inter-connected micelles are demonstrated in transmission electron microscopy (TEM) images. Reentrant behavior of the assembled micelles is demonstrated at a lower polymer concentration. The transitions from a dispersed micellar phase to a fully phase separated phase (where all the copolymer chains aggregate into one micelle to precipitate out of the solution) and to the re-dissolution of micelles are displayed with an increase in trivalent salt. The non-monotonic dependence of electrostatic correlation on the salt content is well displayed by the four states of the assembled micelles: (i) dispersed micelles, (ii) a single micelle comprising of all copolymer chains, (iii) micellar complex, and (iv) re-dispersed micelles. Our analysis may provide guidance for cross-linking of isotropic micelles into superstructures.

Self-assembled morphologies of polyelectrolyte-grafted nanoparticles directed by oppositely charged polymer matrices.

Self-assembled structure of polymer grafted nanoparticles is an interesting and growing subject in the field of hybrid electronics and high energy density materials. In light of this, the self-assembled morphologies of polyelectrolyte (PE) sparsely grafted nanoparticles tuned by oppositely charged matrix chains are studied using molecular dynamics simulations. Our focus is to elucidate the effect of matrix chain polymerization on modulating the stretching properties of tethered PE layers, on the self-assembled structuring of nanoparticles. Through varying the matrix chain length and stiffness as well as electrostatic interaction strength, rich phase behaviors of PE coated nanoparticles are predicted, including spherical micelle-like structures being preferred with short matrix chains and percolating network morphologies favored with long matrix chains, which is more pronounced with an enhanced matrix chain rigidness. To pinpoint the mechanisms of self-assembled structure formation, the thickness of grafted layers, the gyration radius of tethered chains, and pair correlation functions between nanoparticles are analyzed carefully. Additionally, electrostatic correlations, manifested as the bridging via matrix chains, are examined by identifying three states of matrix PE chains. Our simulation results may be useful for designing smart polymer nanocomposites based on PE coated nanoparticles.

Self-assembly of polyelectrolyte diblock copolymers within mixtures of monovalent and multivalent counterions.

In this study, the self-assembly behavior of polyelectrolyte (PE) diblock copolymers in solutions containing mixtures of monovalent and multivalent counterions was investigated using molecular dynamics simulation. The properties of the assembled micelles and counterion condensations at different charge fractions of multivalent ions have been discussed. The bridging effect of multivalent ions induces the electrostatic correlations of the PE chains, leading to the fusion of large micelles and the formation of bulky aggregates. Notably, lamellar and well-organized face-centered cubic (FCC) arrangements of the assembled micelles were observed in the mixture of monovalent and trivalent ions. At large fractions of multivalent ions, cylindrical and lamellar precipitates composed of the assembled micelles were formed owing to the inter-connecting coronas. The mixtures of monovalent and multivalent counterions allow the regulation of the electrostatic interactions and tuning of the properties in assembled micelles.

Morphologies of a polyelectrolyte brush grafted onto a cubic colloid in the presence of trivalent ions.

We study the morphologies of a polyelectrolyte brush grafted onto a surface of cubic geometry under good solvent conditions in the presence of trivalent counterions, using molecular dynamics simulations. The electrostatic correlation effect and excluded volume effect on the morphologies are studied through varying the charge fraction and grafting density, respectively. Combining snapshots of surface morphologies, brush height, distribution profiles of polymer monomers, and monomer-monomer/counterion pair correlation functions, it is clearly shown that the electrostatic correlation effect, represented by the trivalent-counterion-mediated bridging effect, can induce lateral microphase separation of the cubic polyelectrolyte brush, resulting in the formation of pinned patches. These structures then lead to multi-scale ordering in the brush system and, thereby, a non-monotonic dependence of the brush height, corresponding to a collapse-to-swell transition, on the grafting density. Our simulation results demonstrate that, with the sequence of surface morphologies responsive to adjusting external parameters, the cubic polyelectrolyte brush can serve as a candidate system for the manufacturing of smart stimuli-responsive materials.

Self-assembly of polyelectrolyte diblock copolymers at monovalent and multivalent counterions.

In this work, the self-assembly behaviors of diblock copolymers consisting of one hydrophobic block and one ionizable polyelectrolyte (PE) block in the presence of monovalent and multivalent counterions are systematically discussed through molecular dynamics simulation. Copolymers are molded as bead-spring chains and the ions are explicitly considered. First, the self-assembled structures of symmetrical block copolymers at different charge fractions are analyzed in detail. Spherical hydrophobic cores are favored by all of the micelles. The effect of counterion valence is much more noticeable at high values of charge fraction. When the PE blocks are fully charged, the presence of multivalent counterions preferably provokes the formation of macroscopic structures. A precipitant spherical micelle is generated in the presence of divalent counterions. Special shapes of coronas are created in the presence of trivalent ions, and a remarkable one dimensional macroscopic cylindrical aggregation of micelles forms; the whole assembly is not typical core-shell micelles, but rather a cylinder with alternating spherical micelles arranged perpendicular to the cylinder axis. The self-assemblies with different lengths of fully charged PE blocks are also discussed. Surprisingly, in the presence of divalent counterions, two dimensional in-plane macroscopic aggregation of micelles is realized when the proportion of PE blocks is larger than 1/2; the self-assembled spherical micelles locate approximately in the same plane to form an inter-linked network. One dimensional aggregation of micelles in the presence of trivalent counterions is maintained with an increased proportion of the PE block. Owing to the dominant intra- and inter-condensation of divalent and trivalent counterions, respectively, two and one dimensional macroscopic aggregation of the micelles is achieved. Our findings indicate that varying the counterion valence is a powerful mechanism to tune the properties of self-assemblies, and the bridging effect introduced by multivalent counterions is the key parameter for the aggregation of the micelles.

Surface morphologies of spherical polyelectrolyte brushes induced by trivalent salt ions.

The surface morphologies of spherical polyelectrolyte brushes in salt solutions with opposite trivalent ions are studied using molecular dynamics (MD) simulations. The impact of salt concentration, grafting density, and charge fraction on brush morphologies is investigated systematically. A variety of surface patterns are predicted and the phase diagrams are presented. Both lateral and radial microphase separated structures in the brushes are observed upon varying the salt concentration. With low grafting density the spherical brush is separated into several patches, the number of which decreases with the addition of salt. At high grafting density, the polymer brush changes its morphology from an extended micelle to a 'carpet + brush' to the collapsed state upon increasing the salt concentration. Especially, the 'carpet + brush' structure consists of a core formed by partially collapsed brush chains and a corona formed by other stretched chains. The inter-chain 'bridging' interactions mediated by trivalent ions and the curvature effect play important roles in determining the chain conformations and brush structures.

Sphere-forming diblock copolymers in slit confinement: A dynamic density functional theory study.

With mean-field dynamic density functional theory, we study the morphologies of sphere-forming diblock copolymers confined between two homogeneous surfaces. The effects of the film thickness and the surface field strength on the phase behavior of sphere-forming copolymer film are investigated. The morphologies deviating from the bulk sphere-forming structure are revealed, including cylinders oriented perpendicular to the surface, cylinders oriented parallel to the surface, perforated lamellae and lamellae by varying the film thickness, and surface field strength. We also construct the phase diagram of surface reconstruction, in which some interesting phase transitions are presented. Besides, we compare the present phase diagram with the relevant phase diagram of cylinder-forming block copolymer film.

Effect of polydispersity on the depletion interaction in nonadsorbing polymer solutions.

The effect of polymer polydispersity on the depletion interaction between two plates immersed in a nonadsorbing polymer solution is studied by self-consistent-field theory. The depletion potential is calculated numerically for the Schulz molecular weight distribution. The results show that as the two plates approach the polymers with different chain lengths are excluded from the gap gradually for conformational entropy penalty, and the range of the depletion potential increases and the depth of the potential decreases with increasing polydispersity. For the case of two large spheres the Derjaguin approximation is used to study the effect of polydispersity. The result shows that the polydispersity has little effect on the contact potential. However, it induces more broad interaction than the monodisperse polymers.

Depletion interaction between two colloidal particles in a nonadsorbing polymer solution.

The depletion effect between two spherical colloidal particles in nonadsorbing polymer solutions is investigated using the self-consistent field theory. The density distributions of polymer segments, the depleted amount and depletion potential are calculated numerically in bispherical coordinates. The effects of chain length, bulk concentration, and solvency are also investigated. In the dilute regime the depleted amount and the depletion potential decrease as the two spherical particles approach to each other. The depth of interaction increases and the width of interaction varies slightly with increasing bulk concentrations. In the semidilute regime, with increasing bulk concentrations the width of interaction decreases and the depth of interaction increases. No distinct repulsive potential is observed in semidilute regime. However, at high concentration the depleted amount exhibits a barrier. The width and the depth of depletion potential increase with increasing the chain length and the solvency. The contact potential is proportional to the polymer concentration and almost independent on the solvency. In addition, the effect of depletion interaction on colloidal stability is analyzed.