Binary mixed homopolymer brushes grafted on nanorod particles: A self-consistent field theory study

Surface Orthogonal Patterning and Bidirectional Self-Assembly of Nanoparticles Tethered by V-Shaped Diblock Copolymers

We investigated the surface orthogonal patterning and bidirectional self-assembly of binary hairy nanoparticles (NPs) constructed by uniformly tethering a single NP with multiple V-shaped AB diblock copolymers using Brownian dynamics simulations in a poor solvent. At low concentration, the chain collapse and microphase separation of binary polymer brushes can lead to the patterning of the NP surface into A- and B-type orthogonal patches with various numbers of domains (valency), n = 1-6, that adopt spherical, linear, triangular, tetrahedral, square pyramidal, and pentagonal pyramidal configurations. There is a linear relationship between the valency and the average ratio of NP diameter to the polymers' unperturbed root-mean-square end-to-end distance for the corresponding valency. The linear slope depends on the grafting density and is independent of the interaction parameters between polymers. At high concentration, the orthogonal patch NPs serve as building blocks and exhibit directional attractions by overlapping the same type of domains, resulting in self-assembly into a series of fascinating architectures depending on the valency and polymer length. Notably, the 2-valent orthogonal patch NPs have the bidirectional bonding ability to form the two-dimensional (2D) square NP arrays by two distinct pathways. Simultaneously patching A and B blocks enables the one-step formation of 2D square arrays via bidirectional growth, whereas step-by-step patching causes the directional formation of 1D chains followed by 2D square arrays. Moreover, the gap between NPs in the 2D square arrays is related to the polymer length but independent of the NP diameter. These 2D square NP arrays are of significant value in practical applications such as integrated circuit manufacturing and nanotechnology.

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 versus 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.

Patterning of Polymer-Functionalized Nanoparticles with Varied Surface Mobilities of Polymers

The polymers can be either dynamically tethered to or permanently grafted to the nanoparticle to produce polymer-functionalized nanoparticles. The surface mobility of polymer ligands with one end anchored to the nanoparticle can affect the surface pattern, but the effect remains unclear. Here, we addressed the influence of lateral polymer mobility on surface patterns by performing self-consistent field theory calculations on a modeled polymer-functionalized nanoparticle consisting of immobile and mobile brushes. The results show that except for the radius of nanoparticles and grafting density, the fraction of mobile brushes substantially influences the surface patterning of polymer-functionalized nanoparticles, including striped patterns and patchy patterns with various patches. The number of patches on a nanoparticle increases as the fraction of mobile brushes decreases, favored by the entropy of immobile brushes. Critically, we found that broken symmetry usually occurs in patchy nanoparticles, associated with the balance of enthalpic and entropic effects. The present work provides a fundamental understanding of the dependence of surface patterning on lateral polymer mobility. The work could also guide the preparation of diversified nanopatterns, especially for the asymmetric patchy nanoparticles, enabling the fundamental investigation of the interaction between polymer-functionalized nanoparticles.

Mixed Polymer Brushes for "Smart" Surfaces

Mixed polymer brushes (MPBs) are composed of two or more disparate polymers covalently tethered to a substrate. The resulting phase segregated morphologies have been extensively studied as responsive "smart" materials, as they can be reversible tuned and switched by external stimuli. Both computational and experimental work has attempted to establish an understanding of the resulting nanostructures that vary as a function of many factors. This contribution highlights state-of-the-art MPBs studies, covering synthetic approaches, phase behavior, responsiveness to external stimuli as well as novel applications of MPBs. Current limitations are recognized and possible directions for future studies are identified.

Predicting the effect of chain-length mismatch on phase separation in noble metal nanoparticle monolayers with chemically mismatched ligands

Nanoparticles (NPs) protected with a ligand monolayer hold promise for a wide variety of applications, from photonics and catalysis to drug delivery and biosensing. Monolayers that include a mixture of ligand types can have multiple chemical functionalities and may also self-assemble into advantageous patterns. Previous work has shown that both chemical and length mismatches among these surface ligands influence phase separation. In this work, we examine the interplay between these driving forces, first by using our previously-developed configurationally-biased Monte Carlo (CBMC) algorithm to predict, then by using our matrix assisted laser desorption/ionization mass spectrometry (MALDI-MS) technique to experimentally probe, the surface morphologies of a series of two-ligand mixtures on the surfaces of ultrasmall silver NPs. Specifically, we examine three such mixtures, each of which has the same chemical mismatch (consisting of a hydrophobic alkanethiol and a hydrophilic mercapto-alcohol), but varying degrees of chain-length mismatch. This delicate balance between chemical and length mismatches provides a challenging test for our CBMC prediction algorithm. Even so, the simulations are able to quantitatively predict the MALDI-MS results for all three ligand mixtures, while also providing atomic-scale details from the equilibrated ligand structures, such as patch sizes and co-crystallization patterns. The resulting monolayer morphologies range from randomly-mixed to Janus-like, demonstrating that chain-length modifications are an effective way to tune monolayer morphology without needing to alter chemical functionalities.

Fluctuation Effects on the Brush Structure of Mixed Brush Nanoparticles in Solution

A potentially attractive way to control nanoparticle assembly is to graft one or more polymers on the nanoparticle, to control the nanoparticle-nanoparticle interactions. When two immiscible polymers are grafted on the nanoparticle, they can microphase separate to form domains at the nanoparticle surface. Here, we computationally investigate the phase behavior of such binary mixed brush nanoparticles in solution, across a large and experimentally relevant parameter space. Specifically, we calculate the mean-field phase diagram, assuming uniform grafting of the two polymers, as a function of the nanoparticle size relative to the length of the grafted chains, the grafting density, the enthalpic repulsion between the grafted chains, and the solvent quality. We find a variety of phases including a Janus phase and phases with varying numbers of striped domains. Using a nonuniform, random distribution of grafting sites on the nanoparticle instead of the uniform distribution leads to the development of defects in the mixed brush structures. Introducing fluctuations as well leads to increasingly defective structures for the striped phases. However, we find that the simple Janus phase is preserved in all calculations, even with the introduction of nonuniform grafting and fluctuations. We conclude that the formation of the Janus phase is more realistic experimentally than is the formation of defect-free multivalent mixed brush nanoparticles.

Extremely asymmetric phase diagram of homopolymer-monotethered nanoparticles: Competition between chain conformational entropy and particle steric interaction

The phase behaviors of homopolymer-monotethered nanoparticles (HMNs) in melt are investigated via a theoretical method combining self-consistent field theory for polymers and density functional theory for hard spheres. An extremely asymmetric phase diagram is observed: (i) microphases are only possible for the volume fraction of the tethered polymer f_A > 0.35; (ii) in addition to lamellar phase, the system can only self-assemble into various morphologies with a polymer-rich matrix, including gyroid phase, cylindrical phase, and spherical phase. In the frame of this theory, the critical point for HMNs' microphase separation is significantly lower than that of linear diblock copolymers. Furthermore, the characteristic length of microphase-separated structures of HMNs is much smaller than that of linear diblock copolymers with the same molecular weight. Our calculation results on morphologies and characteristic length agree well with recent simulations and experimental observations.

Surface-Initiated Controlled Radical Polymerization: State-of-the-Art, Opportunities, and Challenges in Surface and Interface Engineering with Polymer Brushes

The generation of polymer brushes by surface-initiated controlled radical polymerization (SI-CRP) techniques has become a powerful approach to tailor the chemical and physical properties of interfaces and has given rise to great advances in surface and interface engineering. Polymer brushes are defined as thin polymer films in which the individual polymer chains are tethered by one chain end to a solid interface. Significant advances have been made over the past years in the field of polymer brushes. This includes novel developments in SI-CRP, as well as the emergence of novel applications such as catalysis, electronics, nanomaterial synthesis and biosensing. Additionally, polymer brushes prepared via SI-CRP have been utilized to modify the surface of novel substrates such as natural fibers, polymer nanofibers, mesoporous materials, graphene, viruses and protein nanoparticles. The last years have also seen exciting advances in the chemical and physical characterization of polymer brushes, as well as an ever increasing set of computational and simulation tools that allow understanding and predictions of these surface-grafted polymer architectures. The aim of this contribution is to provide a comprehensive review that critically assesses recent advances in the field and highlights the opportunities and challenges for future work.

Opportunities for dual RDRP agents in synthesizing novel polymeric materials

Dual RDRP agents provide access to new polymeric materials by combining ATRP, NMP, and RAFT polymerization without end group transformations.

Theoretical and Experimental Investigation of Microphase Separation in Mixed Thiol Monolayers on Silver Nanoparticles

Silver nanoparticles with mixed ligand self-assembled monolayers were synthesized from dodecanethiol and another ligand from a homologous series of alkanethiols (butanethiol, pentanethiol, heptanethiol, octanethiol, nonanethiol, decanethiol, undecanethiol, or dodecanethiol[D25]). These were hypothesized to exhibit ligand phase separation that increases with degree of physical mismatch between the ligands based on the difference in the number of carbons in the two ligands. Dodecanethiol/dodecanethiol[D25] was expected to exhibit minimal phase separation as the ligands have only isotopic differences, while dodecanethiol/butanethiol was hypothesized to exhibit the most phase separation due to the difference in chain length. Phase separation of all other ligand mixtures was expected to fall between these two extremes. Matrix-assisted laser desorption ionization (MALDI) mass spectroscopy provided a value for ligand phase separation by comparison with a binomial (random) model and subsequent calculation of the sum-of-squares error (SSR). These nanoparticle systems were also modeled using the Scheutjens and Fleer self-consistent mean-field theory (SCFT), which determined the most thermodynamically favorable arrangement of ligands on the surface. From MALDI, it was found that dodecanethiol/dodecanethiol[D25] formed a well-mixed monolayer with SSR = 0.002, and dodecanethiol/butanethiol formed a microphase separated monolayer with SSR = 0.164; in intermediate dodecanethiol/alkanethiol mixtures, SSR increased with increasing ligand length difference as expected. For comparison with experiment, an effective SSR value was calculated from SCFT simulations. The SSR values obtained by experiment and theory show good agreement and provide strong support for the validity of SCFT predictions of monolayer structure. These approaches represent robust methods of characterization for ligand phase separation on silver nanoparticles.

Hierarchical Superstructures Assembled by Binary Hairy Nanoparticles

Hierarchical superstructures assembled by binary mixed homopolymer-grafted nanoparticles are investigated by using a self-consistent field theory (SCFT). Our results demonstrate that grafting mixed homopolymer brushes provides an effective way to program the spatial lattice arrangement of the nanoparticles. For the polymer-grafted nanoparticles with specific interaction parameter and total grafting density, the unusual non-close-packed simple cubic (SC) crystal lattice is obtained at small spherical core/polymer size ratios (R/([Formula: see text]) < 1). As the size ratio increases to [Formula: see text] > 1, the nanoparticle arrangement transforms into a body-centered cubic (BCC) crystal lattice. Meanwhile, some unconventional microphases are formed in the polymer matrix, such as the tetragonal cylinder and simple cubic sphere phases. Furthermore, the two-dimensional (2D) model calculations reveal that the binary hairy nanoparticles prefer to arrange into the lattice in a way they can maintain the free energy-minimizing morphology as an isolated particle. Our findings suggest a possible strategy to design hierarchical nanomaterials composed of unique inorganic/organic hybrid superstructures.

Molecular dynamics simulations of cylindrical polyelectrolyte brushes in monovalent and multivalent salt solutions

Molecular dynamics simulations are applied to investigate the cylindrical polyelectrolyte brushes in monovalent and multivalent salt solutions. By varying the salt valence and concentration, the brush thickness, shape factor of grafted chains, and distributions of monomers and ions in the solutions are studied. The simulation results show that the single osmotic pressure effect in the brush leads to changes in conformation in the presence of monovalent salt, while the ion exchange effect induces the collapse of the brushes in the multivalent salt solutions. Furthermore, the snapshots combined with the distributions of the end-monomers and the mean bond angles demonstrate a nonuniform stretching picture of the grafted chains, which is different with the chains tethered on the planar surface. The charge ratios between the ions trapped in the brush and the monomers are also calculated to elucidate the details of ion exchange process.

Ripple structures of mixed homopolymer brushes grafted on cylindrical surfaces: controlling the orientation of the pattern by attuning the substrate curvatures

We employed the strong segregation theory (SST) to study the phase structures of mixed homopolymer brushes grafted on cylindrical surfaces. We considered a simplified case in which two incompatible homopolymers have the same chain length and grafting density. Under these conditions, micro-phase separation in the brush may result in either ripple or helix structures. By comparing the free energy of the possible candidate structures, we found that the helix structure is never the most stable one, while the stability of the perpendicular and parallel ripple structures are sensitive to the curvature of the grafting substrate. It was found that the morphology orientation of the mixed homopolymer brushes can be controlled by attuning the geometry of the substrates.

Synthesis of mixed poly(ε-caprolactone)/polystyrene brushes from Y-initiator-functionalized silica particles by surface-initiated ring-opening polymerization and nitroxide-mediated radical polymerization

This article reports the synthesis of mixed brushes by ring-opening polymerization of ε-caprolactone and nitroxide-mediated radical polymerization of styrene from Y-initiator-functionalized silica particles.