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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. The theoretical model predicts that if the numbers of cationic and anionic ionizable groups of the protein are approximately equal, then the interaction patterns for both cationic and anionic brushes at equal offset on the "wrong side" from the isoelectric point (IEP), i.e., when the particle and the brush charge are of the same sign, are similar. An essential asymmetry in interactions of particles with polycationic and polyanionic brushes is predicted when fractions of cationic and anionic groups differ significantly. That is, at a pH above IEP, the anionic brush better absorbs negatively charged particles with a larger fraction of ionizable cationic groups and vice versa. [ABSTRACT FROM AUTHOR]

The morphology of superstructures formed by bottlebrush block copolymers in the melt can be tuned by changing the side chain length or/and their grafting density at constant volume fractions of the blocks. This feature enables fabrication of microphase separated bulk structures and mesoporous materials thereof with spherical or cylindrical domains (precursors of the mesopores), with high porosity unattainable for materials produced from conventional linear block copolymers. These paradigms are proven by DPD simulations that allow constructing morphological phase diagrams of the melt of block copolymers comprising one linear and one bottlebrush block and comparing the simulation results to the predictions of the mean field analytical theory. While the binodal lines separating the stability regions of spherical and cylindrical domains predicted by the theory perfectly match the simulation results, the simulation indicates appearance of a gyroid phase around the theoretical binodal separating the stability ranges of cylinders and lamellae. The results of our work provide guidelines for macromolecular design of novel composite and mesoporous materials with a wide spectrum of potential applications. [ABSTRACT FROM AUTHOR]

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., functional nanoparticles, proteins, viruses) bind and move across polymer brushes is an important yet under‐studied problem. A mean‐field theoretical approach is presented to analyze the binding and transport of colloids in planar polymer brushes. The theory explicitly considers the effect of solvent strength on brush conformation and of colloid‐polymer affinity on colloid binding and transport. The position‐dependent free energy of the colloid insertion into the polymer brush which controls the rate of colloid transport across the brush is derived. It is shown how the properties of the brush can be adjusted for brushes to be highly selective, effectively serving as tuneable gates with respect to colloid size and affinity to the brush‐forming polymer. The most important parameter regime simultaneously allowing for high brush permeability and selectivity corresponds to a condition when the repulsive and attractive contributions to the colloid insertion free energy nearly cancel. This theory should be useful to design sensing and purification devices with enhanced selectivity and to better understand mechanisms underpinning the functions of biological polymer brushes. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. We demonstrate that calculated position-dependent insertion free energy exhibits different patterns, corresponding to either thermodynamically favourable BSA absorption in the brush or thermodynamically or kinetically hindered absorption (expulsion) depending on the p H and ionic strength of the solution. The theory predicts that due to the re-ionization of BSA within the brush, a polyanionic brush can efficiently absorb BSA over a wider p H range on the "wrong side" of the isoelectric point (IEP) compared to a polycationic brush. The results of our theoretical analysis correlate with available experimental data and thus validate the developed model for prediction of the interaction patterns for various globular proteins with polyelectrolyte brushes. [ABSTRACT FROM AUTHOR]

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. This minimum is attributed to the onset of overlap of side chains belonging to different bottlebrush strands in the swollen gel. [ABSTRACT FROM AUTHOR]

We present a mean-field theory for the solution properties of polyelectrolyte molecular brushes, comprising multiple ionically charged side chains tethered to the main chain (backbone). The power-law dependences for local and large-scale conformational properties, i.e., the brush thickness, extension of spacers between the grafts, and end-to-end distance for the main chain macromolecule, are derived as a function of architectural parameters (the lengths of the main chain and of the grafts, grafting density). We demonstrate that at high grafting density or/and a large fraction of charged monomer units in the grafts, the localization of counterions in the intra-molecular volume occurs and we specify the onset of this transition. We prove that such localization of the counterions is accompanied by full extension of the main chain of the polyelectrolyte molecular brush in salt-free solution. This stretching of the main chain is relaxed upon an increase in the salt concentration. The dependence of the macromolecular dimensions of the polyelectrolyte molecular brush on the salt concentration is derived, and multiple power-law exponents valid in different salt concentration ranges are predicted. [ABSTRACT FROM AUTHOR]

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. It is demonstrated that for large particles the insertion free energy is dominated by repulsive (osmotic) contribution and is approximately proportional to the particle volume in accordance with earlier theoretical predictions [Halperin et al., Macromolecules, 2011, 44, 3622]. For the particles of smaller size or/and large shape asymmetry the adsorption or depletion of a polymer from the particle surface essentially contributes to the insertion free energy balance. As a result, depending on the set of polymer–solvent and polymer–particle interaction parameters and brush grafting density the insertion free energy profile may exhibit complex patterns, i.e., from a pure repulsive effective potential barrier to an attractive well. The results of our study allow for predicting equilibrium partitioning and controlling diffusive transport of (bio)nanocolloids across (bio)polymer brushes of arbitrary geometry including polymer-modified membranes or nanopores. [ABSTRACT FROM AUTHOR]

Author(s): Rachelle M. Choueiri [1]; Elizabeth Galati [1]; Hlose Thrien-Aubin [1]; Anna Klinkova [1]; Egor M. Larin [1]; Ana Querejeta-Fernndez [1]; Lili Han [2, 3]; Huolin L. Xin [2]; Oleg [...]

The parabolic approximation for self‐consistent molecular potential is widely used for theoretical analysis of conformational and thermodynamic properties of polymer brushes formed by linear or branched macromolecules. The architecture‐dependent parameter of the potential (topological coefficient) can be calculated for arbitrary branched polymer architecture from the condition of elastic stress balance in all the branching points. However, the calculation routine for the topological coefficient does not allow unambiguously identifying the range of applicability and the accuracy of the parabolic approximation. Here the limits of applicability of parabolic approximation are explored by means of numerical self‐consistent field method for brushes formed by Y‐shaped and comb‐like polymers. It is demonstrated that violation of the potential parabolic shape can be evidenced by appearance of multimodal distribution of the end monomer unit in the longest elastic path of the macromolecule. The asymmetry of branching of Y‐shaped polymers does not disturb the parabolic shape of the potential as long as the degree of polymerization of the root segment remains sufficiently large. The same applies to comb‐shape polymers with sufficiently long main chain and large number of branching points. For short comb‐like polymers multiple modes in the distribution of the end monomer unit of the main chain are observed and related to deviation from the parabolic shape of the potential. [ABSTRACT FROM AUTHOR]

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. The star-to-comblike transition in solvent-free lamellas which occurs upon increase of backbone length of graft-polymer is analyzed. [ABSTRACT FROM AUTHOR]

The self-consistent field theory of brushes of neutral water-soluble polymers described by two-state models is formulated in terms of the effective Flory interaction parameter χ[sub eff](T,[lowercase_phi_synonym]) that depends on both temperature, T, and the monomer volume fraction, [lowercase_phi_synonym]. The concentration profiles, distribution of free ends and compression force profiles are obtained in the presence and in the absence of a vertical phase separation. A vertical phase separation within the layer leads to a distinctive compression force profile and a minimum in the plot of the moments of the concentration profile versus the grafting density. The analysis is applied explicitly to the Karalstrom model. The relevance to brushes of Poly(N-isopropylacrylamide)(PNIPAM) is discussed. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Using two orthogonal external stimuli, programmable staged surface patterning and self‐assembly of inorganic nanoparticles (NPs) was achieved. For gold NPs capped with end‐grafted poly(styrene‐block‐(4‐vinylbenzoic acid)), P(St‐block‐4VBA), block copolymer ligands, surface‐pinned micelles (patches) formed from NP‐adjacent PSt blocks under reduced solvency conditions (Stimulus 1); solvated NP‐remote P(4VBA) blocks stabilized the NPs against aggregation. Subsequent self‐assembly of patchy NPs was triggered by crosslinking the P(4VBA) blocks with copper(II) ions (Stimulus 2). Block copolymer ligand design has a strong effect on NP self‐assembly. Small, well‐defined clusters assembled from NPs functionalized with ligands with a short P(4VBA) block, while NPs tethered with ligands with a long P(4VBA) block formed large irregularly shaped assemblies. This approach is promising for high‐yield fabrication of colloidal molecules and their assemblies with structural and functional complexity. [ABSTRACT FROM AUTHOR]

Chiral packing of ligands on the surface of nanoparticles (NPs) is of fundamental and practical importance, as it determines how NPs interact with each other and with the molecular world. Herein, for gold nanorods (NRs) capped with end‐grafted nonchiral polymer ligands, we show a new mechanism of chiral surface patterning. Under poor solvency conditions, a smooth polymer layer segregates into helicoidally organized surface‐pinned micelles (patches). The helicoidal morphology is dictated by the polymer grafting density and the ratio of the polymer ligand length to nanorod radius. Outside this specific parameter space, a range of polymer surface structures was observed, including random, shish‐kebab, and hybrid patches, as well as a smooth polymer layer. We characterize polymer surface morphology by theoretical and experimental state diagrams. The helicoidally organized polymer patches on the NR surface can be used as a template for the helicoidal organization of other NPs, masked synthesis on the NR surface, as well as the exploration of new NP self‐assembly modes. Gold nanorods, end‐grafted with achiral polymer ligands, show a new mechanism of chiral surface patterning giving a helicoidal morphology. This morphology is dictated by the relationship between the polymer grafting density and the ratio of the polymer length to the nanorod radius. [ABSTRACT FROM AUTHOR]

Investigates the interaction between surfaces coated with triblock copolymers. Creation of polymer-coated colloidal systems with additional minima in the interaction; Use of the systems for optical switches; Formation of stable crystal structures; Impact of morphological changes on surface interactions.

A scaling theory of adsorption of polyampholyte chains at charged spherical particles from dilute low salt solutions is developed. The expressions for the surface coverage and the thickness of adsorbed layer are derived as functions of bulk polymer concentration, particle size, and surface charge density.

The equilibrium structure of an interpolyelectrolyte complex (IPEC) coacervate consisting of weakly charged flexible polyanions and polycations with equal degree of ionization is considered. We study effects of salt concentration cs and solvent quality defined by second virial coefficient v on polymer density, surface tension, salt absorption, and correlations of charges and monomer units in equilibrium IPEC. Five different scaling regimes of IPEC are revealed, and a salt-solvent quality (cs-v) diagram of coacervate states is constructed. Boundaries between different regimes correspond to crossovers between low/high salt concentrations and poor/Θ-/good solvent conditions. Derived scaling laws for coacervate physical properties in each of regimes are in agreement with analysis based on the random phase approximation (RPA). This study summarizes and complements current theoretical comprehension of symmetrical IPEC of weakly charged polyions. [ABSTRACT FROM AUTHOR]

We present a theory of conformational transition triggered by inferior solvent strength in brushes formed by dendritically branched macromolecules tethered to planar, concave, or convex cylindrical and spherical surfaces. In the regime of linear elasticity for brush-forming dendrons, an analytical strong stretching self-consistent field (SS-SCF) approach provides brush conformational properties as a function of solvent strength. A boxlike model is applied to describe the collapse transition in brushes formed by macromolecules with arbitrary treelike topology, including hyperbranched polymers. We demonstrate that an increase in the degree of branching, that is, an increase in the number of generations or/and functionality of branching points in tethered macromolecules, makes the swelling-to-collapse transition less sharp. A decrease in surface curvature has a similar effect. The numerical Scheutjens-Fleer self-consistent field approach is used to analyze the collapse transition in dendron brushes in the nonlinear stretching regime. It is demonstrated that inferior solvent strength suppresses stratification that is exhibited under good solvent conditions by densely grafted dendron brushes. [ABSTRACT FROM AUTHOR]

We present a theory describing structural properties of brushes formed by cycled macromolecules tethered to planar surface. Diverse architectures of macromolecules that differ with respect to position and number of subchains in macrocycle are considered. We use the self-consistent field analytical approach based on strong stretching approximation and assumption of Gaussian elasticity of brush-forming molecules. Predictions of the analytical theory are systematically compared to the results of numerical SF-SCF modeling. Similarity of the effects of cyclization and branching on large-scale properties of polymer brush is demonstrated. It is also predicted that weaker interpenetration of sliding brushes formed by cyclic macromolecules might enhance their performance as lubricants. [ABSTRACT FROM AUTHOR]

Grand canonical Monte Carlo (MC) simulations are performed to analyse conformations of projection domains in a neurofilament (NF) brush composed of three types of tails (L, M, and H) at different concentrations of added salt. The NF is modelled as a rigid, uniformly charged cylinder (backbone), surrounded by tethered, flexible polyampholytic chains with charge distributions and stoichiometry similar to those in natural NFs. We calculate the equilibrium trajectory for each projection; that is, the average distance of the amino acid residue from the surface of the backbone as a function of its ranking number. These trajectories demonstrate the tendency for projections to fold back and adopt loop-like conformations at moderate solution salinities. We also perform extended analysis of MC data to identify metastable states of the system, and demonstrate representative snapshots of tail conformations in major metastable states. [ABSTRACT FROM AUTHOR]

We develop a scaling model relating the friction forces between two polyelectrolyte brushes sliding over each other to the separation between grafted surfaces, number of monomers and charges per chain, grafting density of chains, and solvent quality. We demonstrate that the lateral force between brushes increases upon compression, but to a lesser extent than the normal force. The shear stress at larger separations is due to solvent slip layer friction. The thickness of this slip layer sharply decreases at distances on the order of undeformed brush thickness. The corresponding effective viscosity of the layer sharply increases from the solvent viscosity to a much higher value, but this increase is smaller than the jump of the normal force resulting in the drop of the friction coefficient. At stronger compression we predict the second sharp increase of the shear stress corresponding to interpenetration of the chains from the opposite brushes. In this regime the velocity-dependent friction coefficient between two partially interpenetrating polyelectrolyte brushes does not depend on the distance between substrates because both normal and shear forces are reciprocally proportional to the plate separation. Although lateral forces between polyelectrolyte brushes are larger than between bare surfaces, the enhancement of normal forces between opposing polyelectrolyte brushes with respect to normal forces between bare charged surfaces is much stronger resulting in lower friction coefficient. The model quantitatively demonstrates how polyelectrolyte brushes provide more effective lubrication than bare charged surfaces or neutral brushes. [ABSTRACT FROM AUTHOR]

The self-assembly of synthetic diblockcopolymers has been extensivelystudied experimentally and theoretically. In contrast, self-assemblyof polypeptide diblock copolymers has so far been mostly studied experimentally.We discovered that the theory developed for synthetic diblock copolymerdoes not fully explain the self-assembly of elastin-like polypeptidediblock copolymers, leading us to generalize the theory to make itapplicable for these polypeptides. We demonstrated that elastin-likepolypeptide diblocks self-assemble into weak micelles with dense coresand almost unstretched coronas, a state not previously observed forsynthetic diblock copolymers. Weak micelles form if the surface tensionat the core–corona interface is low compared to that expectedof a micelle with a dense core. The predictions of the theory of weakmicelles for the critical micelle temperature, hydrodynamic radius,and aggregation number of elastin-like polypeptide diblocks are inreasonable agreement with the experimentally measured values. Theunique and unprecedented control of amphiphilicity in these recombinantpeptide polymers reveals a new micellar state that has not been previouslyobserved in synthetic diblock copolymer systems. [ABSTRACT FROM AUTHOR]

A planar polymer brush of arm-grafted polymer stars subjected to external deformation is studied theoretically We propose a simple mean-field model of the star brush that takes into account segregation of the brush-forming stars in two populations: (i) those with weakly extended arms and (ii) those with a very strongly stretched grafting arm (stem) and all free arms extended towards brush periphery. The polymer density profile in the brush is assumed to have a 'two-step' shape. Stars in the extended population are assumed to be equally stretched, the position of extended stars' branching points sets the boundary between two parts of the brush. We show that the theory quantitatively accurately describes earlier numerical results obtained with Scheutjens-Fleer numerical self-consistent field (SF-SCF) approach for free (non-deformed) star brush. We study compression of a star brush by an impenetrable plane by using two complementary models, the SF- SCF approach and the developed mean-field theory, and demonstrate a very good quantitative agreement between the two models. It is shown than depending on the grafting density of the stars, compression could affect the two-population brush structure in opposite ways. In sparsely grafted brushes the fraction of stars in the stretched population increases while in densely grafted brushes it decreases with deformation. [ABSTRACT FROM AUTHOR]

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. Scaling arguments are used to study microphase segregation under poor solvent conditions leading to formation of a laterally and longitudinally patterned structure in planar and cylindrical pores, respectively, and the effects of confinement on "octopus-like" clusters in the pores of different geometries. [ABSTRACT FROM AUTHOR]