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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., (© 2023 Wiley-VCH GmbH.)

Hierarchical self-assembly offers elegant and energy-efficient bottom-up strategies for the structuring of complex materials. For block copolymers, the last decade witnessed great progress in diversifying the structural complexity of solution-based assemblies into multicompartment micelles. However, a general understanding of what governs multicompartment micelle morphologies and polydispersity, and how to manipulate their hierarchical superstructures using straightforward concepts and readily accessible polymers remains unreached. Here we demonstrate how to create homogeneous multicompartment micelles with unprecedented structural control via the intermediate pre-assembly of subunits. This directed self-assembly leads to a step-wise reduction of the degree of conformational freedom and dynamics and avoids undesirable kinetic obstacles during the structure build-up. It yields a general concept for homogeneous populations of well-defined multicompartment micelles with precisely tunable patchiness, while using simple linear ABC triblock terpolymers. We further demonstrate control over the hierarchical step-growth polymerization of multicompartment micelles into micron-scale segmented supracolloidal polymers as an example of programmable mesoscale colloidal hierarchies via well-defined patchy nanoobjects.

Molecular bottle-brushes are highly branched macromolecules with side chains densely grafted to a long polymer backbone. The brush-like architecture allows focusing of the side-chain tension to the backbone and its amplification from the pico-Newton to nano-Newton range. The backbone tension depends on the overall molecular conformation and the surrounding environment. Here we study the relation between the tension and conformation of the molecular brushes in solutions, melts, and on substrates. In solutions, we find that the backbone tension in dense brushes with side chains attached to every backbone monomer is on the order of f(0)N(3/8) in athermal solvents, f(0)N(1/3) in theta solvents, and f(0) in poor solvents and melts, where N is the degree of polymerization of side chains, f(0) approximately equal k(B)T/b is the maximum tension in side chains, b is the Kuhn length, k(B) is Boltzmann's constant, and T is the absolute temperature. Depending on the side chain length and solvent quality, molecular brushes develop tension on the order of 10-100 pN, which is sufficient to break hydrogen bonds. Significant amplification of tension occurs upon adsorption of brushes onto a substrate. On a strongly attractive substrate, maximum tension in the brush backbone is approximately f(0)N, reaching values on the order of several nano-Newtons, which exceeds the strength of a typical covalent bond. At low grafting density and high spreading parameter, the cross-sectional profile of an adsorbed molecular brush is approximately rectangular with a thickness approximately b (A/S)1/2, where A is the Hamaker constant, and S is the spreading parameter. At a very high spreading parameter (S > A), the brush thickness saturates at monolayer approximately b. At a low spreading parameter, the cross-sectional profile of adsorbed molecular brush has a triangular tent-like shape. In the cross-over between these two opposite cases, covering a wide range of parameter space, the adsorbed molecular brush consists of two layers. Side chains in the lower layer gain surface energy due to the direct interaction with the substrate, while the second layer spreads on the top of the first layer. Scaling theory predicts that this second layer has a triangular cross-section with width R approximately N(3/5) and height h approximately N(2/5). Using self-consistent field theory we calculate the cap profile y(x) = h(1 - x2/R2)2, where x is the transverse distance from the backbone. The predicted cap shape is in excellent agreement with both computer simulation and experiment.

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]

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]

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]

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]

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]

The structure of a brush made of arm-grafted polymerstars is investigatedusing the Scheutjens–Fleer self-consistent field method. Byusing the “probe macromolecule” approach, conditionaldistributions of end- and branching points were obtained, which allowedfor a detailed analysis of intramolecular correlations in the brush.Results strongly support a previously suggested “two population”picture of the star structure: stars in the brush are divided intotwo populations (i) those with weakly extended arms and (ii) thosewith a very strongly stretched grafting arm (stem) and all free armsextended toward the solvent. The stars in the “stretched”population have no arms that fold back toward the grafting surfaceand their free arms form a new sub-brush with effective grafting densitydetermined solely by the total surface loading: molecular mass ofpolymer grafted onto unit area. With increasing grafting density or/andnumber of star arms the fraction of stars in the “stretched”population grows. The degree of backfolding of arms is estimated,the total fraction of backfolded arms is invariably small and decreaseswith increasing grafting density; only stars of the weakly extendedpopulation contribute to backfolding. The free ends within a givenstar are correlated: the ends of different arms are located approximatelyat the same distance from the grafting plane. Comparison of conditionalends distributions at fixed position of the branching points at differentgrafting densities reveals a conformational universality of graftedstars belonging to the weakly stretched population: the shape of theends distribution does not depend on the grafting density but is determinedsolely by the position of the branching point. We also present analyticalarguments showing that this effect is due to universal parabolic self-consistentpotential acting on monomer units in the star brush, this potentialis independent of the grafting density and the number of star arms. [ABSTRACT FROM AUTHOR]