Polyelectrolyte brush in a cylindrical pore: A Poisson-Boltzmann theory.

The conformation of a polyelectrolyte (PE) brush grafted to the inner surface of a long cylindrical mesopore was described within analytical Poisson-Boltzmann strong stretching approximation. The internal structure of the PE brush, including brush thickness and radial density profile of monomer units, and radial distribution of electrostatic potential were analyzed as functions of the pore radius, degree of polymerization, and grafting density of the brush-forming PE chains as well as ionic strength of the solution. It is demonstrated that narrowing of the pore leads to a non-monotonous variation of the brush thickness, which passes through a maximum when the brush thickness becomes equal to the pore radius.

Polyelectrolyte Brushes with Protein-Like Nanocolloids.

Electrostatic interaction of ampholytic nanocolloidal particles (NPs), which mimic globular proteins, with polyelectrolyte brushes is analyzed within mean-field Poisson-Boltzmann approximation. In accordance with experimental findings, the theory predicts that an electrostatic driving force for the particle uptake by the brush may emerge when the net charge of the particle in the buffer and the charge of the brush are of the same sign. The origin of this driving force is change in the ionization state of weak cationic and anionic groups on the NP surface provoked by interaction with the brush.

[Tuberculosis infection in patients with inflammatory bowel diseases. Clinacal cases].

In most cases Tuberculosis (TB) affects the lungs, but 10-15% of patients have extrapulmonary TB localisations, that is difficult to diagnose. TB is more spread among patients having the human immunodeficiency virus and among those who receive immunosuppressive therapy, specifically in patients with inflammatory bowel disease requiring long-term treatment with immunosuppressants and/or biologics. The symptoms of intestinal TB are nonspecific and may include chronic diarrhea, weight loss, fever and ascites.

Interaction of Polyanionic and Polycationic Brushes with Globular Proteins and Protein-like Nanocolloids.

A large number of experimental studies have demonstrated that globular proteins can be absorbed from the solution by both polycationic and polyanionic brushes when the net charge of protein globules is of the same or of the opposite sign with respect to that of brush-forming polyelectrolyte chains. Here, we overview the results of experimental studies on interactions between globular proteins and polycationic or polyanionic brushes, and present a self-consistent field theoretical model that allows us to account for the asymmetry of interactions of protein-like nanocolloid particles comprising weak (pH-sensitive) cationic and anionic groups with a positively or negatively charged polyelectrolyte brush. The position-dependent insertion free energy and the net charge of the particle are calculated.

Surface-Immobilized Interpolyelectrolyte Complexes Formed by Polyelectrolyte Brushes.

A scaling theory of interaction and complex formation between planar polyelectrolyte (PE) brush and oppositely charged mobile linear PEs is developed. Counterion release is found to be the main driving force for the complexation. An interpolyelectrolyte coacervate complex (IPEC) between the brush and oppositely charged mobile PEs is formed at moderate grafting density and low salt concentration.

Cylindrical brushes with ionized side chains: Scaling theory revisited.

We revisit the classic scaling model of a cylindrical polyelectrolyte (PE) brush focusing on molecular brushes with stiff backbones and dispersions of polymer-decorated nanorods. Based on the blob representation we demonstrate that similarly to the case of planar PE brushes, separation of intra- and intermolecular repulsions between charges leads to novel scaling regimes for cylindrical PE brushes in salt-added solution and a sharper decrease in its thickness salt concentration dependence. These theoretical predictions may inspire further comprehensive experimental research and computer simulations of synthetic and biopolyelectrolyte cylindrical brushes.

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.

Polyelectrolyte Brush Interacting with Ampholytic Nanoparticles as Coarse-Grained Models of Globular Proteins: Poisson-Boltzmann Theory.

The self-consistent field Poisson-Boltzmann framework is applied to analyze equilibrium partitioning of ampholytic nanoparticles (NPs) between buffer solution and polyelectrolyte (PE) polyanionic brush. We demonstrate that depending on pH and salt concentration in the buffer solution, interactions between ionizable (acidic and basic) groups on the NP surface and electrostatic field created by PE brush may either lead to the spontaneous uptake of NPs or create an electrostatic potential barrier, preventing the penetration of NPs inside PE brush. The capability of PE brush to absorb or repel NPs is determined by the shape of the insertion free energy that is calculated as a function of NP distance from the grafting surface.

Selective Colloid Transport across Planar Polymer Brushes.

Polymer brushes are attractive as surface coatings for a wide range of applications, from fundamental research to everyday life, and also play important roles in biological systems. How colloids (e.g.

Bovine Serum Albumin Interaction with Polyanionic and Polycationic Brushes: The Case Theoretical Study.

We apply a coarse-grained self-consistent field Poisson-Boltzmann framework to study interaction between Bovine Serum Albumin (BSA) and a planar polyelectropyte brush. Both cases of negatively (polyanionic) and positively (polycationic) charged brushes are considered. Our theoretical model accounts for (1) re-ionization free energy of the amino acid residues upon protein insertion into the brush; (2) osmotic force repelling the protein globule from the brush; (3) hydrophobic interactions between non-polar areas on the globule surface and the brush-forming chains.

Hairy Gels: A Computational Study.

We present results of MD and MC simulations of the equilibrium properties of swelling gels with comb-like or bottlebrush subchains and compare them to scaling-theory predictions. In accordance with theory, the simulation results demonstrate that swelling coefficient of the gel increases as a function of the polymerization degree of the main chains and exhibits a very weak maximum (or is virtually constant) as a function of the polymerization degree and grafting density of side chains. The bulk osmotic modulus passes through a shallow minimum as the polymerization degree of the side chains increases.

Theoretical advances in molecular bottlebrushes and comblike (co)polymers: solutions, gels, and self-assembly.

We present an overview of state-of-the-art theory of (i) conformational properties of molecular bottlebrushes in solution, (ii) self-assembly of di- and triblock copolymers comprising comb-shaped and bottlebrush blocks in solutions and melts, and (iii) cross-linked and self-assembled gels with bottlebrush subchains. We demonstrate how theoretical models enable quantitative prediction and interpretation of experimental results and provide rational guidance for design of new materials with physical properties tunable by architecture of constituent bottlebrush blocks.

Colloidal particles interacting with a polymer brush: a self-consistent field theory.

The interaction of colloidal particles with a planar polymer brush immersed in a solvent of variable thermodynamic quality is studied by a numerical self-consistent field method combined with analytical mean-field theory. The effect of embedded particle on the distribution of polymer density in the brush is analyzed and the particle insertion free energy profiles are calculated for variable size and shape of the particles and sets of polymer-particle and polymer-solvent interaction parameters. In particular, both cases of repulsive and attractive interactions between particles and brush-forming chains are considered.

Injectable bottlebrush hydrogels with tissue-mimetic mechanical properties.

Injectable hydrogels are desired in many biomedical applications due to their minimally invasive deployment to the body and their ability to introduce drugs. However, current injectables suffer from mechanical mismatch with tissue, fragility, water expulsion, and high viscosity. To address these issues, we design brush-like macromolecules that concurrently provide softness, firmness, strength, fluidity, and swellability.

Bottlebrush polymer gels: architectural control over swelling and osmotic bulk modulus.

Swelling behaviour and bulk moduli of polymer gels comprising of crosslinked bottlebrush subchains enable fine tuning by varying polymerization degrees of the main and side chains of the bottlebrush strands as well as their grafting densities. By using scaling approach we predict power law dependences of structural and elastic properties of swollen bottlebrush gels on the set of relevant architectural parameters and construct phase diagrams consisting of regions corresponding to different power law asymptotics for these dependences. In particular, our theory predict that bulk elastic modulus of the gel exhibits non-monotonous dependence on the degree of polymerization of side chains of the bottlebrush strands.

Polymer Brush in a Nanopore: Effects of Solvent Strength and Macromolecular Architecture Studied by Self-Consistent Field and Scaling Theory.

To study conformational transition occuring upon inferior solvent strength in a brush formed by linear or dendritically branched macromolecules tethered to the inner surface of cylindrical or planar (slit-like) pore, a self-consistent field analytical approach is employed. Variations in the internal brush structure as a function of variable solvent strength and pore radius, and the onset of formation of a hollow channel in the pore center are analysed. The predictions of analytical theory are supported and complemented by numerical modelling by a self-consistent field Scheutjens-Fleer method.

Micelles Formed by an Copolymer with Bottlebrush Blocks: Scaling Theory.

We present a scaling theory describing the equilibrium properties of spherical micelles formed by a diblock copolymer with bottlebrush blocks in a selective solvent. The theory predicts a number of new thermodynamic regimes inherent for copolymers with relatively short main chains (long side chains) in the bottlebrush blocks. These regimes with a novel set of scaling exponents for the micelle properties are characterized by limiting extension of the main chains of the core or/and corona-forming blocks and do not exist for micelles of conventional linear block copolymers.

Self-Assembly of Bottlebrush Block Copolymers in Selective Solvent: Micellar Structures.

Block copolymers comprising chemically different bottlebrush blocks can self-assemble in selective solvents giving rise to micellar-like solution nanostructures. The self-consistent field theoretical approach is used for predicting relation between architectural parameters of both bottlebrush blocks (polymerization degrees of the main and side chains, density of grafting of the side chains to the backbone) and structural properties of micelles as well as critical micelle concentration (CMC). As predicted by the theory, replacement of linear blocks by bottlebrush ones with the same degrees of polymerization results in a decrease in the micellar core size (in aggregation number) and extension of the corona, whereas the CMC increases.

Proteins and Polyampholytes Interacting with Polyelectrolyte Brushes and Microgels: The Charge Reversal Concept Revised.

Weak polyampholytes and globular proteins among them can be efficiently absorbed from solutions by polyelectrolyte brushes or microgels even if the net charge of the polyampholyte is of the same sign as that of the brush/microgel. We use a mean-field approach for calculating the free energy of insertion of a probe polyampholyte molecule into a polyelectrolyte brush/microgel. We anticipate that the insertion of the polyampholyte into similarly charged brush/microgel may be thermodynamically favorable due to the gain in the cumulative re-ionization free energy of the pH-sensitive acidic and basic residues.

Brushes and lamellar mesophases of comb-shaped (co)polymers: a self-consistent field theory.

Theory describing equilibrium structural properties of solvent-free brushes formed by comblike polymers tethered by end segment of backbone to planar surface is developed using strong-stretching self-consistent field (SS-SCF) analytical approach and supported by numerical self-consistent field calculations based on the Scheutjens-Fleer (SF-SCF) method. The explicit dependence of self-consistent molecular potential on architectural parameters of comblike polymers is analyzed. It is demonstrated that distribution of local tension in backbones of long comblike polymers approaches that for linear chains.

Electroresponsive Polyelectrolyte Brushes Studied by Self-Consistent Field Theory.

End-grafting of polyelectrolyte chains to conducting substrates offers an opportunity to fabricate electro-responsive surfaces capable of changing their physical/chemical properties (adhesion, wettability) in response to applied electrical voltage. We use a self-consistent field numerical approach to compare the equilibrium properties of tethered strong and weak (pH-sensitive) polyelectrolytes to applied electrical field in both salt-free and salt-containing solutions. We demonstrate that both strong and weak polyelectrolyte brushes exhibit segregation of polyions in two populations if the surface is oppositely charged with respect to the brush.

Morphological Transitions in Patchy Nanoparticles.

Nanoparticles (NPs) decorated with topographically or chemically distinct surface patches are an emerging class of colloidal building blocks of functional hierarchical materials. Surface segregation of polymer ligands into pinned micelles offers a strategy for the generation of patchy NPs with controlled spatial distribution and number of patches. The thermodynamic nature of this approach poses a question about the stability of multiple patches on the NP surface, as the lowest energy state is expected for NPs carrying a single patch.

Non-linear elasticity effects and stratification in brushes of branched polyelectrolytes.

Brushes formed by arm-tethered starlike polyelectrolytes may exhibit internal segregation into weakly and strongly extended populations (stratified two-layer structure) when strong ionic intermolecular repulsions induce stretching of the tethers up to the limit of their extensibility. We propose an approximate Poisson-Boltzmann theory for analysis of the structure of the stratified brush and compare it with results of numerical self-consistent field modeling. Both analytical and numerical models point to the formation of a narrow cloud of counterions (internal double electrical layer) localized inside a stratified brush at the boundary between the layers.

Theory of Microphase Segregation in the Melts of Copolymers with Dendritically Branched, Bottlebrush, or Cycled Blocks.

Theory of microphase segregation in the melt of diblock copolymers comprising two strongly incompatible blocks of similar or different topologies is developed. The spectrum of considered architectures include copolymers with arbitrary combinations of bottlebrush-like, dendritic, cycled blocks, and so on. Our theory provides quantitative predictions of how the morphology of the microphase segregated structures can be controlled not only by the volume fractions of the incompatible blocks, but also by their architecture.

Helicoidal Patterning of Gold Nanorods by Phase Separation in Mixed Polymer Brushes.

The spatial distribution of polymer ligands on the surface of nanoparticles (NPs) is of great importance because it determines their interactions with each other and with the surrounding environment. Phase separation in mixtures of polymer brushes has been studied for spherical NPs; however, the role of local surface curvature of nonspherical NPs in the surface phase separation of end-grafted polymer ligands remains an open question. Here, we examined phase separation in mixed monolayers of incompatible polystyrene and poly(ethylene glycol) brushes end-capping the surface of gold nanorods in a good solvent.