Polymer brushes on flat and curved surfaces: How computer simulations can help to test theories and to interpret experiments

Dynamics of Droplets Moving on Lubricated Polymer Brushes

Understanding the dynamics of drops on polymer-coated surfaces is crucial for optimizing applications such as self-cleaning materials or microfluidic devices. While the static and dynamic properties of deposited drops have been well characterized, a microscopic understanding of the underlying dynamics is missing. In particular, it is unclear how drop dynamics depends on the amount of uncross-linked chains in the brush, because experimental techniques fail to quantify those. Here we use coarse-grained simulations to study droplets moving on a lubricated polymer brush substrate under the influence of an external body force. The simulation model is based on the many body dissipative particle dynamics (MDPD) method and designed to mimic a system of water droplets on poly(dimethylsiloxane) (PDMS) brushes with chemically identical PDMS lubricant. In agreement with experiments, we find a sublinear power law dependence between the external force F and the droplet velocity v, F ∝ vα with α < 1; however, the exponents differ (α ∼ 0.6-0.7 in simulations versus α ∼ 0.25 in experiments). With increasing velocity, the droplets elongate and the receding contact angle decreases, whereas the advancing contact angle remains roughly constant. Analyzing the flow profiles inside the droplet reveals that the droplets do not slide but roll, with vanishing slip at the substrate surface. Surprisingly, adding lubricant has very little effect on the effective friction force between the droplet and the substrate, even though it has a pronounced effect on the size and structure of the wetting ridge, especially above the cloaking transition.

Polymer Brushes on Nanoparticles for Controlling the Interaction with Protein-Rich Physiological Media

The interaction of nanoparticles (NPs) with biological environments triggers the formation of a protein corona (PC), which significantly influences their behavior in vivo. This review explores the evolving understanding of PC formation, focusing on the opportunity for decreasing or suppressing protein-NP interactions by macromolecular engineering of NP shells. The functionalization of NPs with a dense, hydrated polymer brush shell is a powerful strategy for imparting stealth properties in order to elude recognition by the immune system. While poly(ethylene glycol) (PEG) has been extensively used for this purpose, concerns regarding its stability and immunogenicity have prompted the exploration of alternative polymers. The stealth properties of brush shells can be enhanced by tailoring functionalities and structural parameters, including the molar mass, grafting density, and polymer topology. Determining correlations between these parameters and biopassivity has enabled us to obtain polymer-grafted NPs with high colloidal stability and prolonged circulation time in biological media.

Theory and simulation of ligand functionalized nanoparticles - a pedagogical overview

Synthesizing reconfigurable nanoscale synthons with predictive control over shape, size, and interparticle interactions is a holy grail of bottom-up self-assembly. Grand challenges in their rational design, however, lie in both the large space of experimental synthetic parameters and proper understanding of the molecular mechanisms governing their formation. As such, computational and theoretical tools for predicting and modeling building block interactions have grown to become integral in modern day self-assembly research. In this review, we provide an in-depth discussion of the current state-of-the-art strategies available for modeling ligand functionalized nanoparticles. We focus on the critical role of how ligand interactions and surface distributions impact the emergent, pre-programmed behaviors between neighboring particles. To help build insights into the underlying physics, we first define an "ideal" limit - the short ligand, "hard" sphere approximation - and discuss all experimental handles through the lens of perturbations about this reference point. Finally, we identify theories that are capable of bridging interparticle interactions to nanoscale self-assembly and conclude by discussing exciting new directions for this field.

Surface-Initiated Polymerization with an Initiator Gradient: A Monte Carlo Simulation

Due to the difficulty of accurately characterizing properties such as the molecular weight (Mn) and grafting density (σ) of gradient brushes (GBs), these properties are traditionally assumed to be uniform in space to simplify analysis. Applying a stochastic reaction model (SRM) developed for heterogeneous polymerizations, we explored surface-initiated polymerizations (SIPs) with initiator gradients in lattice Monte Carlo simulations to examine this assumption. An initial exploration of SIPs with 'homogeneously' distributed initiators revealed that increasing σ slows down the polymerization process, resulting in polymers with lower molecular weight and larger dispersity (Đ) for a given reaction time. In SIPs with an initiator gradient, we observed that the properties of the polymers are position-dependent, with lower Mn and larger Đ in regions of higher σ, indicating the non-uniform properties of polymers in GBs. The results reveal a significant deviation in the scaling behavior of brush height with σ compared to experimental data and theoretical predictions, and this deviation is attributed to the non-uniform Mn and Đ.

Colloidal adsorption in planar polymeric brushes

The design of nano-functionalised membranes or channels, able to effectively adsorb pollutants in aqueous solutions, is a topic that is gaining a great deal of attention in the materials science community. With this work we explore, through a combination of scaling theories and molecular dynamics simulations, the adsorption of spherical non-deformable colloidal nanoparticles within planar polymeric brushes. Our strategy is twofold: first, we generalise the Alexander-de Gennes theory for planar homopolymeric brushes to the case of diblock copolymer brushes, then we map the adsorbing homopolymeric brushes onto a diblock copolymer system, where the adsorbed colloids and all interacting monomers are considered monomers in bad solvent and we apply the generalised scaling theory to this effective diblock copolymer. This allows the prediction of the average conformation of the grafted substrate, i.e. its average height, as a function of the amount of loaded particles, as well as the introduction of a continuous mapping between a homopolymeric brush, the fraction of loaded particles and the average height of the adsorbing substrate.

Confined Dynamics in Spherical Polymer Brushes

We investigate the dynamics of polymers grafted to spherical nanoparticles in solution using hybrid molecular dynamics simulations with a coarse-grained solvent modeled via the multiparticle collision dynamics algorithm. The mean-square displacements of monomers near the surface of the nanoparticle exhibit a plateau on intermediate time scales, indicating confined dynamics reminiscent of those reported in neutron spin-echo experiments. The confined dynamics vanish beyond a specific radial distance from the nanoparticle surface that depends on the polymer grafting density. We show that this dynamical confinement transition follows theoretical predictions for the critical distance associated with the structural transition from confined to semidilute brush regimes. These findings suggest the existence of a hitherto unreported dynamic length scale connected with theoretically predicted static fluctuations in spherical polymer brushes and provide new insights into recent experimental observations.

Self-Assembly of Symmetric Copolymers in Slits with Inert and Attractive Walls

Although the behavior of the confined semi-dilute solutions of self-assembling copolymers represents an important topic of basic and applied research, it has eluded the interest of scientists. Extensive series of dissipative particle dynamics simulations have been performed on semi-dilute solutions of A5B5 chains in a selective solvent for A in slits using a DL-MESO simulation package. Simulations of corresponding bulk systems were performed for comparison. This study shows that the associates in the semi-dilute bulk solutions are partly structurally organized. Mild steric constraints in slits with non-attractive walls hardly affect the size of the associates, but they promote their structural arrangement in layers parallel to the slit walls. Attractive walls noticeably affect the association process. In slits with mildly attractive walls, the adsorption competes with the association process. At elevated concentrations, the associates start to form in wide slits when the walls are sparsely covered by separated associates, and the association process prevents the full coverage of the surface. In slits with strongly attractive walls, adsorption is the dominant behavior. The associates form in wide slits at elevated concentrations only after the walls are completely and continuously covered by the adsorbed chains.

Antidurotaxis Droplet Motion onto Gradient Brush Substrates

Durotaxis motion is a spectacular phenomenon manifesting itself by the autonomous motion of a nano-object between parts of a substrate with different stiffness. This motion usually takes place along a stiffness gradient from softer to stiffer parts of the substrate. Here, we propose a new design of a polymer brush substrate that demonstrates antidurotaxis droplet motion, that is, droplet motion from stiffer to softer parts of the substrate. By carrying out extensive molecular dynamics simulation of a coarse-grained model, we find that antidurotaxis is solely controlled by the gradient in the grafting density of the brush and is favorable for fluids with a strong attraction to the substrate (low surface energy). The driving force of the antidurotaxial motion is the minimization of the droplet-substrate interfacial energy, which is attributed to the penetration of the droplet into the brush. Thus, we anticipate that the proposed substrate design offers a new understanding and possibilities in the area of autonomous motion of droplets for applications in microfluidics, energy conservation, and biology.

Molecular Dynamics Simulations of Ideal Living Polymerization: Terminal Model and Kinetic Aspects

Living polymerization is an important synthetic approach to achieving precise control of synthesized polymers, which is crucial for their applications. The molecular weight distribution (MWD) prescribes the macroscopic properties of polymers and hence is a key feature to characterize polymerization. In this work, we present a systematic molecular dynamics simulation study of ideal living polymerization in bulk and surface-initiated systems based on a terminal stochastic reaction model. The evolution of polymer dispersity and MWD along with the polymerization process is examined. We demonstrate that MWD is generally well captured by the Schulz-Zimm distribution for bulk and surface-initiated systems with low grafting densities. However, as the grafting density in the surface-initiated case increases, heterogeneity in chain growth emerges due to the kinetic trapping of reactive sites, which causes the starving of short chains and the thriving of minority long chains such that a shoulder region shows up in MWD. This effect can be enhanced by kinetic compressing induced by polymerization. In addition, the interplay of bonding reaction kinetics and other kinetic properties (e.g., mass transfer and polymer relaxation) is further explored, alongside the influences of bonding probability and reactant concentration. We expect that this investigation will aid in our understanding of typical kinetic aspects of living polymerization.

Janus Ligand-Tethered Nanoparticles at Liquid-Liquid Interfaces

We investigate the structural properties of Janus ligand-tethered nanoparticles at liquid-liquid interfaces using coarse-grained molecular dynamics simulations. The effect of interactions between different chains and liquids is discussed. We consider the Janus particles with symmetrical interactions with the liquids which correspond to supplementary wettability and particles with uncorrelated interactions. Simulation results indicate that the Janus hairy particles trapped in the interface region have different configurations characterized by the vertical displacement distance, the orientation of the Janus line relative to the interface, and the particle shape. The Janus hairy particles present abundant morphologies, including dumbbell-like and typical core-shell, at the interface. The shape of adsorbed particles is analyzed in detail. The simulation data are compared with those predicted by a simple phenomenological approach. This work can promote the applications of Janus hairy particles in nanotechnology.

Globular Proteins and Where to Find Them within a Polymer Brush-A Case Study

Protein adsorption by polymerized surfaces is an interdisciplinary topic that has been approached in many ways, leading to a plethora of theoretical, numerical and experimental insight. There is a wide variety of models trying to accurately capture the essence of adsorption and its effect on the conformations of proteins and polymers. However, atomistic simulations are case-specific and computationally demanding. Here, we explore universal aspects of the dynamics of protein adsorption through a coarse-grained (CG) model, that allows us to explore the effects of various design parameters. To this end, we adopt the hydrophobic-polar (HP) model for proteins, place them uniformly at the upper bound of a CG polymer brush whose multibead-spring chains are tethered to a solid implicit wall. We find that the most crucial factor affecting the adsorption efficiency appears to be the polymer grafting density, while the size of the protein and its hydrophobicity ratio come also into play. We discuss the roles of ligands and attractive tethering surfaces to the primary adsorption as well as secondary and ternary adsorption in the presence of attractive (towards the hydrophilic part of the protein) beads along varying spots of the backbone of the polymer chains. The percentage and rate of adsorption, density profiles and the shapes of the proteins, alongside with the respective potential of mean force are recorded to compare the various scenarios during protein adsorption.

Concave polymer brushes inwardly grafted in spherical cavities

The structure and scaling properties of inwardly curved polymer brushes, tethered under good solvent conditions to the inner surface of spherical shells such as membranes and vesicles, are studied by extensive molecular dynamics simulations and compared with earlier scaling and self-consistent field theory predictions for different molecular weights of the polymer chains N and grafting densities σ_g in the case of strong surface curvature, R^-1. We examine the variation of the critical radius R*(σ_g), separating the regimes of weak concave brushes and compressed brushes, predicted earlier by Manghi et al. [Eur. Phys. J. E 5, 519-530 (2001)], as well as various structural properties such as the radial monomer- and chain-end density profiles, orientation of bonds, and brush thickness. The impact of chain stiffness, κ, on concave brush conformations is briefly considered as well. Eventually, we present the radial profiles of the local pressure normal, P_N, and tangential, P_T, to the grafting surface, and the surface tension γ(σ_g), for soft and rigid brushes, and find a new scaling relationship P_N(R)∝σ_g ⁴, independent of the degree of chain stiffness.

Hybrid Nanoparticles at Fluid-Fluid Interfaces: Insight from Theory and Simulation

Hybrid nanoparticles that combine special properties of their different parts have numerous applications in electronics, optics, catalysis, medicine, and many others. Of the currently produced particles, Janus particles and ligand-tethered (hairy) particles are of particular interest both from a practical and purely cognitive point of view. Understanding their behavior at fluid interfaces is important to many fields because particle-laden interfaces are ubiquitous in nature and industry. We provide a review of the literature, focusing on theoretical studies of hybrid particles at fluid-fluid interfaces. Our goal is to give a link between simple phenomenological models and advanced molecular simulations. We analyze the adsorption of individual Janus particles and hairy particles at the interfaces. Then, their interfacial assembly is also discussed. The simple equations for the attachment energy of various Janus particles are presented. We discuss how such parameters as the particle size, the particle shape, the relative sizes of different patches, and the amphiphilicity affect particle adsorption. This is essential for taking advantage of the particle capacity to stabilize interfaces. Representative examples of molecular simulations were presented. We show that the simple models surprisingly well reproduce experimental and simulation data. In the case of hairy particles, we concentrate on the effects of reconfiguration of the polymer brushes at the interface. This review is expected to provide a general perspective on the subject and may be helpful to many researchers and technologists working with particle-laden layers.

Polymer brushes for friction control: Contributions of molecular simulations

When polymer chains are grafted to solid surfaces at sufficiently high density, they form brushes that can modify the surface properties. In particular, polymer brushes are increasingly being used to reduce friction in water-lubricated systems close to the very low levels found in natural systems, such as synovial joints. New types of polymer brush are continually being developed to improve with lower friction and adhesion, as well as higher load-bearing capacities. To complement experimental studies, molecular simulations are increasingly being used to help to understand how polymer brushes reduce friction. In this paper, we review how molecular simulations of polymer brush friction have progressed from very simple coarse-grained models toward more detailed models that can capture the effects of brush topology and chemistry as well as electrostatic interactions for polyelectrolyte brushes. We pay particular attention to studies that have attempted to match experimental friction data of polymer brush bilayers to results obtained using molecular simulations. We also critically look at the remaining challenges and key limitations to overcome and propose future modifications that could potentially improve agreement with experimental studies, thus enabling molecular simulations to be used predictively to modify the brush structure for optimal friction reduction.

Morphology of Polymer Brushes in the Presence of Attractive Nanoparticles: Effects of Temperature

We study the role of temperature on the structure of pure polymer brushes and their mixture with attractive nanoparticles in flat and cylindrical geometries. It has previously been established that the addition of such nanoparticles causes the polymer brush to collapse and the intensity of the collapse depends on the attraction strength, the nanoparticle diameter, and the grafting density. In this work, we carry out molecular dynamics simulation under good solvent conditions to show how the collapse transition is affected by the temperature, for both plane grafted and inside-cylinder grafted brushes. We first examine the pure brush morphology and verify that the brush height is insensitive to temperature changes in both planar and cylindrical geometries, as expected for a polymer brush in a good solvent. On the other hand, for both system geometries, the brush structure in the presence of attractive nanoparticles is quite responsive to temperature changes. Generally speaking, for a given nanoparticle concentration, increasing the temperature causes the brush height to increase. A brush which contracts when nanoparticles are added eventually swells beyond its pure brush height as the system temperature is increased. The combination of two easily controlled external parameters, namely, concentration of nanoparticles in solution and temperature, allows for sensitive and reversible adjustment of the polymer brush height, a feature which could be exploited in designing smart polymer devices.

Elucidating Interfacial Chain Conformation of Superhydrophilic Polymer Brushes by Vibrational Sum Frequency Generation Spectroscopy

Surface-tethered macromolecules (polymer brushes) are a potent means to modify surfaces with stimuli-responsive properties while avoiding delamination problems. This vibrational sum frequency generation spectroscopy study describes how the conformation of hydrophilic polymer brushes changes in response to environmental conditions, that is, changes in humidity (in air) and upon exposure to liquid water. Three hydrophilic brushes were prepared on silicon oxide surfaces by surface-initiated reversible deactivation radical polymerization of cationic (quaternary ammonium), anionic (sulfonate), and zwitterionic (containing both) monomers. The average tilt angle of methyl groups was analyzed and used to deduce the chain conformations of the polymer brushes. In air, the brush films absorb water and swell with increasing humidity. This is accompanied by the rotation of interfacial polymer chains. The degree of water uptake and chain conformation vary with the nature of the charged hydrophilic moieties. The hydrophilic polymer brush surfaces appear to remain relatively dry except in near-condensation conditions. In water, the quaternary ammonium groups of cationic and zwitterionic brushes are aligned nearly parallel to the surface. The anionic brush chains appear to assume nearly random conformations in water.

Surface Coassembly of Binary Mixed Polymer Brushes and Linear Block Copolymer Chains

Binary mixed polymer brushes (BMPBs) are two different homopolymer chains that are covalently anchored to the solid surfaces at high grafting densities. One feature of the BMPBs is the unique ability to make surface phase separation under external stimuli. In this research, we demonstrate that different surface nanostructures can be fabricated by surface coassembly of BMPBs and free block copolymer (BCP) chains. Polystyrene/poly(2-(dimethylamino)ethyl methacrylate) (PS/PDMAEMA) BMPBs on silica particles (PS-PDMAEMA-SiO₂) are synthesized by a two-step "grafting to" approach. PDMAEMA-b-PS block copolymer (BCP) chains and PS-PDMAEMA-SiO₂ make surface self-assembly and a variety of surface nanostructures are formed in methanol. The grafting densities of PS and PDMAEMA brushes, solvent, and the BCP structures all exert significant influences on the surface morphology. With an increase in PDMAEMA grafting density, the surface structures change from perforated layers, to rods, and to spherical surface micelles (s-micelles). The PS grafting density also exerts an effect on the formation of the surface nanostructures. At low PS grafting density, sparsely distributed s-micelles are produced, and at high density, densely distributed s-micelles are observed. Based on transmission electron microscopy and scanning electron microscopy results, a surface phase diagram is constructed, which provides a guide to the surface morphology control.

Molecular Theory: A Tool for Predicting the Outcome of Self-Assembly of Polymers, Nanoparticles, Amphiphiles, and Other Soft Materials

The supramolecular organization of soft materials, such as colloids, polymers, and amphiphiles, results from a subtle balance of weak intermolecular interactions and entropic forces. This competition can drive the self-organization of soft materials at the nano-/mesoscale. Modeling soft-matter self-assembly requires, therefore, considering a complex interplay of forces at the relevant length scales without sacrificing the molecular details that define the chemical identity of the system. This mini-review focuses on the application of a tool known as molecular theory to study self-assembly in different types of soft materials. This tool is based on extremizing an approximate free energy functional of the system, and, therefore, it provides a direct, computationally affordable estimation of the stability of different self-assembled morphologies. Moreover, the molecular theory explicitly incorporates structural details of the chemical species in the system, accounts for their conformational degrees of freedom, and explicitly includes their chemical equilibria. This mini-review introduces the general ideas behind the theoretical formalism and discusses its advantages and limitations compared with other theoretical tools commonly used to study self-assembled soft materials. Recent application examples are discussed: the self-patterning of polyelectrolyte brushes on planar and curved surfaces, the formation of nanoparticle (NP) superlattices, and the self-organization of amphiphiles into micelles of different shapes. Finally, prospective methodological improvements and extensions (also relevant for related theoretical tools) are analyzed.

Exact results and the effect of monomer-monomer bond type for a grafted ideal chain

We determine the equilibrium chain end probability density [Formula: see text] for a one-dimensional ideal chain of N monomers grafted to a planar surface. This distribution is also the distribution function of a three-dimensional chain where the tangential dimensions y, z are integrated out of the distribution. With a small modification of the analysis of Erukhimovich, Johner, and Joanny for free chains near a wall, we are able to obtain exact results for [Formula: see text] for any monomer number N though with the restriction that the monomer-monomer bonds lengths are exponentially distributed. In particular, we obtain exact values for [Formula: see text] and its derivative [Formula: see text] at the surface for any N and the full profile [Formula: see text] for selected values of N. To determine the effect of the bond distribution, we find [Formula: see text] numerically for Gaussian and uniformly distributed one-dimensional bonds and compare with the exact results for exponential bonds. We suggest several ways to quantify the effect of bond type based both on [Formula: see text] near the surface and in the scaling region [Formula: see text]. We then extract the large N limit of [Formula: see text] and show that it is similar to the chain end probability for continuous chains but shifted toward smaller x. We show the amount of shift is a measure of the magnitude of the correction to the continuous chain [Formula: see text]. We derive the value of the shift for exponential bonds and show that the value is different for other bond types. We argue the shift can be interpreted as an effective surface behind the actual surface.

Shape Transformations and Self-Assembly of Hairy Particles under Confinement

Molecular dynamics simulations are used to investigate the behavior of polymer-tethered nanoparticles between two inert or attractive walls. The confinement in pores creates new possibilities for controlling the shape transformation of individual hairy particles and their self-organization. We introduce a minimalistic model of the system; only chain-wall interactions are assumed to be attractive, while the others are softly repulsive. We show how the shape of isolated particles can be controlled by changing the wall separation and the strength of the interaction with the surfaces. For attractive walls, we found two types of structures, “bridges” and “mounds”. The first structures are similar to flanged spools in which the chains are connected with both walls and form bridges between them. We observed various bridges, symmetrical and asymmetrical spools, hourglasses, and pillars. The bridge-like structures can be “nano-oscillators” in which the cores jump from one wall to the other. We also study the self-assembly of a dense fluid of hairy particles in slit-like pores and analyze how the system morphology depends on interactions with the surfaces and the wall separation. The hairy particles form layers parallel to the walls. Different ordered structures, resembling two-dimensional crystalline lattices, are reported. We demonstrate that hairy particles are a versatile soft component forming a variety of structures in the slits.

Heat flow through a liquid-vapor interface in a nano-channel: the effect of end-grafting polymers on a wall

Heat transfer through a liquid-vapor interface is a complex phenomenon and crucially relevant in heat-removal and cryogenic applications. The physical coupling among confining walls, liquid and vapor phases is very important for controlling or improving cooling rates or condensation efficiency. Surface modification is a promising route, which has been explored to taylor the heat transfer through confined two-phase systems. We use coarse-grained molecular-dynamics simulations to study the heat transfer through a nano-confined liquid-vapor interface as a function of fluid filling. We set up a stationary heat flow through a liquid-vapor interface, stabilized with the liquid in contact with a colder wall and a vapor in contact with a hotter wall. For these physical conditions, we perform extensive simulations by progressively increasing the number of fluid particles, i.e. the channel filling, and measure the fluid distribution in the channel, density, pressure and temperature profiles We also compare the heat flux behavior between a bare-surfaces nano-channel and others where the hot surface was coated with end-grafted polymers, with different wetting affinities and bending properties. We take extreme cases of polymer properties to obtain a general picture of the polymer effect on the heat transfer, as compared with the bare surfaces. We find that walls covered by end-grafted solvophylic polymers change the heat flux by a factor of 6, as compared with bare walls, if the liquid phase is in contact with the polymers. Once the liquid wets the coated wall, the improve on heat flux is smaller and dominated by the grafting density. We also find that for a wall coated with stiff polymers, the jump in heat flux takes place at a significantly lower channel filling, when the polymers' free ends interact with the liquid surface. Interestingly, the morphology of the polymers induces a 'liquid bridge' between the liquid phase and the hot wall, through which heat is transported with high (liquid-like) thermal conductivity.

Diffusion of polymer-grafted nanoparticles with dynamical fluctuations in unentangled polymer melts

The dynamics of polymer-grafted nanoparticles (PGNPs) in melts of unentangled linear chains were investigated by means of coarse-grained molecular dynamics simulations. The results demonstrated that the graft monomers closer to the particle surface relax more slowly than those farther away due to the constraint of the grafted surface and the confinement of the neighboring chains. Such heterogeneous relaxations of the surrounding environment would perturb the particle motion, making them fluctuating around their centers before they can diffuse through the melt. During such intermediate-time stage, the dynamics is subdiffusive while the distribution of particle displacements is Gaussian, which can be described by the popular fractional Brownian motion model. For the long-time Fickian diffusion, we found that the diffusivity D decreases with increasing grafting density Σ_g, grafted chain length N_g, and matrix chain length N_m. This is due to the fact that the diffusivity is controlled by the viscous drag of an effective core, consisting of the NP and the non-draining layer of graft segments, and that of the free-draining graft layer outside the "core". With increasing Σ_g, the PGNPs become harder with greater effective size and thinner free draining layer, resulting in a reduction in D. At extremely high Σ_g, the diffusivity can even be estimated by the diameter-renormalized Stokes-Einstein (SE) relation. With increasing N_g, both the effective core size and the thickness of the free-draining layer increase, leading to a reduction in diffusivity by D ∼ N-γg with 0.5 < γ < 1. Increasing N_m would lead to the enlargement of the effective core size but meanwhile result in the reduction of the free-draining layer thickness due to autophobic dewetting. The counteraction between these two opposite effects leads to only a slight reduction in the diffusivity, significantly different from the typical SE behavior where D ∼ N_m^-1. These findings bear significance in unraveling the fundamental physics of the anomalous dynamics of PGNPs in various polymers, including biological and synthetic.

Molecular Dynamics Characterization of Radiosensitizing Coated Gold Nanoparticles in Aqueous Environment

Functionalized metal nanoparticles (NPs) have been proposed as promising radiosensitizing agents for more efficient radiotherapy treatment using photons and ion beams. Radiosensitizing properties of NPs may depend on many different parameters (such as size, composition, and density) of the metal core, the organic coatings, and the molecular environment. A systematic exploration of each of these parameters on the atomistic level remains a formidable and costly experimental task, but it can be addressed by means of advanced computational modeling. This paper describes a detailed computational procedure for construction and atomistic-level characterization of radiosensitizing metal NPs in explicit molecular media. The procedure is general and is extensible to many different combinations of the core, coating, and environment. As an illustrative and experimentally relevant case study, we consider nanometer-sized gold NPs coated with thiol-poly(ethylene glycol)-amine molecules of different length and surface density and solvated in water at ambient conditions. The radial distribution of different atoms in the coatings as well as distribution and structural properties of water around the coated NPs are analyzed and linked to radiosensitizing properties of the NPs. It is revealed that the structure of the coating layer on the solvated NPs depends strongly on the surface density of ligands. At surface densities below ∼3 molecules/nm² the coating represents a mixture of different conformation states, whereas elongated "brush"-like structures are formed at higher densities of ligands. The water content in denser coatings is significantly lower at distances from 1 nm up to 3 nm from the gold surface depending on the length of ligand molecules. Such dense and thick coatings may suppress the production of hydroxyl radicals by low-energy electrons emitted from the metal NPs and thus diminish their radiosensitizing properties. The presented computational framework provides precise information for a quantitative atomistic-level description of the structural properties of coated metal NPs in biologically relevant environments and so may form a basis for future developments to achieve a more realistic description of irradiation-driven chemistry effects in the vicinity of coated metal NPs.

Helical self-assembly of a mucin segment suggests an evolutionary origin for von Willebrand factor tubules

Extracellular proteins with mechanical functions often require specialized assembly processes to form covalent oligomers. Progress in tissue bioengineering and repair will benefit from an understanding of how to harness and manipulate these processes. Here, we show that a particular supramolecular assembly mode was pre-encoded in the ancient domain organization common to gel-forming mucins and von Willebrand factor, glycoproteins that are deceptively different due to their divergence for distinct mechanical tasks. This finding highlights symmetry principles and building blocks retooled in nature to construct polymers with wide-ranging properties. These building blocks and knowledge of their self-assembly can be used to design new polymeric structures.

The glycoprotein von Willebrand factor (VWF) contributes to hemostasis by stanching injuries in blood vessel walls. A distinctive feature of VWF is its assembly into long, helical tubules in endothelial cells prior to secretion. When VWF is released into the bloodstream, these tubules unfurl to release linear polymers that bind subendothelial collagen at wound sites, recruit platelets, and initiate the clotting cascade. VWF evolved from gel-forming mucins, the polymeric glycoproteins that coat and protect exposed epithelia. Despite the divergent function of VWF in blood vessel repair, sequence conservation and shared domain organization imply that VWF retained key aspects of the mucin bioassembly mechanism. Here, we show using cryo-electron microscopy that the ability to form tubules, a property hitherto thought to have arisen as a VWF adaptation to the vasculature, is a feature of the amino-terminal region of mucin. This segment of the human intestinal gel-forming mucin (MUC2) was found to self-assemble into tubules with a striking resemblance to those of VWF itself. To facilitate a comparison, we determined the residue-resolution structure of tubules formed by the homologous segment of VWF. The structures of the MUC2 and VWF tubules revealed the flexible joints and the intermolecular interactions required for tubule formation. Steric constraints in full-length MUC2 suggest that linear filaments, a previously observed supramolecular assembly form, are more likely than tubules to be the physiological mucin storage intermediate. Nevertheless, MUC2 tubules indicate a possible evolutionary origin for VWF tubules and elucidate design principles present in mucins and VWF.

Adsorption of Polymer-Tethered Particles on Solid Surfaces

We explore the behavior of polymer-tethered particles on solid surfaces using coarse-grained molecular dynamics simulations. Segment–segment, segment–core, and core–core interactions are assumed to be purely repulsive, while the segment–substrate interactions are attractive. We analyze changes in the internal structure of single hairy particles on the surfaces with the increasing strength of the segment–substrate interactions. For this purpose, we calculate the density profiles along the x, y, z axes and the mass dipole moments. The adsorbed hairy particles are found to be symmetrical in a plane parallel to the substrate but strongly asymmetric in the vertical direction. On stronger adsorbents, the particle canopies become flattened and the cores lie closer to the wall. We consider the adsorption of hairy nanoparticles dispersed in systems of different initial particle densities. We show how the strength of segment–substrate interactions affects the structure of the adsorbed phase, the particle–wall potential of the average force, the excess adsorption isotherms, and the real adsorption isotherms.

Polymerization and Structure of Opposing Polymer Brushes Studied by Computer Simulations

A model of the polymerization process during the formation of a pair of polymer brushes was designed and investigated. The obtained system consisted of two impenetrable parallel surfaces with the same number of chains grafted on both surfaces. Coarse-grained chains embedded in nodes of a face-centered cubic lattice with excluded volume interactions were obtained by a ‘grafted from’ procedure. The structure of synthesized macromolecular systems was also studied. Monte Carlo simulations using the dynamic lattice liquid model were employed using dedicated parallel machine ARUZ in a large size and time scale. The parameters of the polymerization process were found to be crucial for the proper structure of the brush. It was found that for high grafting densities, chains were increasingly compressed, and there is surprisingly little interpenetration of chains from opposite surfaces. It was predicted and confirmed that in a polydisperse sample, the longer chains have unique configurations consisting of a stretched stem and a coiled crown.

The structure of polymer brushes: the transition from dilute to dense systems: a computer simulation study

Monodisperse polymer brushes were studied by means of Monte Carlo simulations. A coarse-grained model of a polymer brush was designed and the Cooperative Motion Algorithm was employed to model the polymerization process 'grafted from' and to study the structure of a brush immersed in a good solvent. The structure of brushes was determined as a function of the chain length and the grafting density. The influence of these parameters on the scaling properties of the brush was presented and discussed. A thorough analysis of the distribution of concentrations of the polymer segments and the distribution of chain free ends was also carried out. The analysis of the depth of penetration of the low molecular weight solvent into the brush area showed that the main factor determining the penetration is the grafting density. Good agreement between the simulation results and theoretical predictions is observed, especially for longer chains and higher grafting density. The origin of small quantitative differences between the simulation and theoretical results is discussed.

Using Dissipative Particle Dynamics to Model Effects of Chemical Reactions Occurring within Hydrogels

Computational models that reveal the structural response of polymer gels to changing, dissolved reactive chemical species would provide useful information about dynamically evolving environments. However, it remains challenging to devise one computational approach that can capture all the interconnected chemical events and responsive structural changes involved in this multi-stage, multi-component process. Here, we augment the dissipative particle dynamics (DPD) method to simulate the reaction of a gel with diffusing, dissolved chemicals to form kinetically stable complexes, which in turn cause concentration-dependent deformation of the gel. Using this model, we also examine how the addition of new chemical stimuli and subsequent reactions cause the gel to exhibit additional concentration-dependent structural changes. Through these DPD simulations, we show that the gel forms multiple latent states (not just the “on/off”) that indicate changes in the chemical composition of the fluidic environment. Hence, the gel can actuate a range of motion within the system, not just movements corresponding to the equilibrated swollen or collapsed states. Moreover, the system can be used as a sensor, since the structure of the layer effectively indicates the presence of chemical stimuli.

Rheological properties of polymer chains at a copper oxide surface: Impact of the chain length, surface coverage, and grafted polymer shape

We employ a recently derived semirealistic set of coarse-grained interactions to simulate polymer brushes of cis-1,4-polybutadiene grafted on a cuprous-oxide surface within the framework of dissipative particle dynamics. We consider two types of brushes, I and Y, that differ in the way they are connected to the surface. Our model explores the impact of free polymer chain length, grafting density of the brush, and imposed shear rate on the structural and dynamic properties of complex metal oxide polymer interfaces.

Dynamics of Opposing Polymer Brushes: A Computer Simulation Study

Opposing polymer brush systems were synthesized and investigated by molecular modeling. Chains were restricted to a face-centered cubic lattice with the excluded volume interactions only. The system was confined between two parallel impenetrable walls, with the same number of chains grafted to each surface. The dynamic properties of such systems were studied by Monte Carlo simulations based on the dynamic lattice liquid model and using a highly efficient parallel machine ARUZ, which enabled the study of large systems and long timescales. The influence of the surface density and mean polymer length on the system dynamic was discussed. The self-diffusion coefficient of the solvent depended strongly on the degree of polymerization and on the polymer concentration. It was also shown that it is possible to capture changes in solvent mobility that can be attributed to the regions of different polymer densities.

Adsorption on Ligand-Tethered Nanoparticles

We use coarse-grained molecular dynamics simulations to study adsorption on ligand-tethered particles. Nanoparticles with attached flexible and stiff ligands are considered. We discuss how the excess adsorption isotherm, the thickness of the polymer corona, and its morphology depend on the number of ligands, their length, the size of the core, and the interaction parameters. We investigate the adsorption-induced structural transitions of polymer coatings. The behavior of systems involving curved and flat "brushes" is compared.

Densely Packed Tethered Polymer Nanoislands: A Simulation Study

COordinated Responsive Arrays of Surface-Linked polymer islands (CORALS) allow for the creation of molecular surfaces with novel and switchable properties. Critical components of CORALs are the uniformly distributed islands of densely grafted polymer chains (nanoislands) separated by regions of bare surface. The grafting footprint and separation distances of nanoislands are comparable to that of the constituent polymer chains themselves. Herein, we characterize the structural features of the nanoislands and semiflexible polymers within to better understand this critical constituent of CORALs. We observe different characteristics of grafted semiflexible polymers depending on the polymer island’s size and distance from the center of the island. Specifically, the characteristics of the chains at the island periphery are similar to isolated tethered polymer chains (full flexible chains), while chains in the center of the island experience the neighbor effect such as chains in the classic polymer brush. Chains close to the edge of the islands exhibit unique structural features between these two regimes. These results can be used in the rational design of CORALs with specific interfacial characteristics and predictable responses to external stimuli. It is hoped that this the discussion of the different morphologies of the polymers as a function of distance from the edge of the polymer will find applications in a wide variety of systems.

Physics of the Nuclear Pore Complex: Theory, Modeling and Experiment

The hallmark of eukaryotic cells is the nucleus that contains the genome, enclosed by a physical barrier known as the nuclear envelope (NE). On the one hand, this compartmentalization endows the eukaryotic cells with high regulatory complexity and flexibility. On the other hand, it poses a tremendous logistic and energetic problem of transporting millions of molecules per second across the nuclear envelope, to facilitate their biological function in all compartments of the cell. Therefore, eukaryotes have evolved a molecular "nanomachine" known as the Nuclear Pore Complex (NPC). Embedded in the nuclear envelope, NPCs control and regulate all the bi-directional transport between the cell nucleus and the cytoplasm. NPCs combine high molecular specificity of transport with high throughput and speed, and are highly robust with respect to molecular noise and structural perturbations. Remarkably, the functional mechanisms of NPC transport are highly conserved among eukaryotes, from yeast to humans, despite significant differences in the molecular components among various species. The NPC is the largest macromolecular complex in the cell. Yet, despite its significant complexity, it has become clear that its principles of operation can be largely understood based on fundamental physical concepts, as have emerged from a combination of experimental methods of molecular cell biology, biophysics, nanoscience and theoretical and computational modeling. Indeed, many aspects of NPC function can be recapitulated in artificial mimics with a drastically reduced complexity compared to biological pores. We review the current physical understanding of the NPC architecture and function, with the focus on the critical analysis of experimental studies in cells and artificial NPC mimics through the lens of theoretical and computational models. We also discuss the connections between the emerging concepts of NPC operation and other areas of biophysics and bionanotechnology.

Programmable site-specific functionalization of DNA origami with polynucleotide brushes

Combining surface-initiated, TdT (terminal deoxynucleotidyl transferase) catalyzed enzymatic polymerization (SI-TcEP) with precisely engineered DNA origami nanostructures (DONs) presents an innovative pathway for the generation of stable, polynucleotide brush-functionalized origami nanostructures. We demonstrate that SI-TcEP can site-specifically pattern DONs with brushes containing both natural and non-natural nucleotides. The brush functionalization can be precisely controlled in terms of the location of initiation sites on the origami core and the brush height and composition. Coarse-grained simulations predict the conformation of the brush-functionalized DONs that agree well with the experimentally observed morphologies. We find that polynucleotide brush-functionalization increases the nuclease resistance of DONs significantly, and that this stability can be spatially programmed through the site-specific growth of polynucleotide brushes. The ability to site-specifically decorate DONs with brushes of natural and non-natural nucleotides provides access to a large range of functionalized DON architectures that would allow for further supramolecular assembly, and for potential applications in smart nanoscale delivery systems.

Effects of cosolvent partitioning on conformational transitions and tethered chain flexibility in spherical polymer brushes

In this work, based on the framework of preferential adsorption concept and analytical self-consistent field (SCF) theory, a model is proposed to investigate the reentrant transition experimentally observed from the thermoresponsive spherical brush in a series of aqueous alcohol solutions. The interaction between monomers is incorporated into the model. Conformational transitions of the spherical brush are quantitatively correlated to the physical parameters, including the number of adsorbed cosolvents which facilitates the solvent quality, the number of cosolvent bridges which drives the brush collapse, as well as their partition coefficients between the brush and the bulk solution. An analytical formula for the number of Kuhn segments per tethered chain is obtained based on the analytical SCF theory, which elucidates the flexibility of tethered chains in the intricate system of multicomponents involving the conformational transitions. Under the experimental conditions associated with the cosolvent-brush interaction, the variation of the monomer chemical potential with the monomer concentration indicates that the monomer distribution of the spherical brush remains continuous. The analysis based on the SFC theory also reveals that the distribution of adsorbed cosolvents is a positive parabola while the distribution of cosolvent bridges appears to be an exponential decay function, implying that the intervening space between tethered chains, rather than the number of adsorbed cosolvents, plays a crucial role in forming the cosolvent bridge. We demonstrate that the model formulated for the reentrant transition under weaker cosolvent-brush interactions provides guidelines for the one under stronger nanoparticle-brush interactions.

Advanced Materials for Energy-Water Systems: The Central Role of Water/Solid Interfaces in Adsorption, Reactivity, and Transport

The structure, chemistry, and charge of interfaces between materials and aqueous fluids play a central role in determining properties and performance of numerous water systems. Sensors, membranes, sorbents, and heterogeneous catalysts almost uniformly rely on specific interactions between their surfaces and components dissolved or suspended in the water-and often the water molecules themselves-to detect and mitigate contaminants. Deleterious processes in these systems such as fouling, scaling (inorganic deposits), and corrosion are also governed by interfacial phenomena. Despite the importance of these interfaces, much remains to be learned about their multiscale interactions. Developing a deeper understanding of the molecular- and mesoscale phenomena at water/solid interfaces will be essential to driving innovation to address grand challenges in supplying sufficient fit-for-purpose water in the future. In this Review, we examine the current state of knowledge surrounding adsorption, reactivity, and transport in several key classes of water/solid interfaces, drawing on a synergistic combination of theory, simulation, and experiments, and provide an outlook for prioritizing strategic research directions.

Tailoring Antifouling Properties of Nanocarriers via Entropic Collision of Polymer Grafting

Polymer graftings (PGs) are widely employed in antifouling surfaces and drug delivery systems to regulate the interaction with a foreign environment. Through molecular dynamics simulations and scaling theory analysis, we investigate the physical antifouling properties of PGs via their collision behaviors. Compared with mushroom-like PGs with low grafting density, we find brush-like PGs with high grafting density could generate large deformation-induced entropic repulsive force during a collision, revealing a microscopic mechanism for the hop motions of polymer-grafted nanoparticles for drug delivery observed in experiment. In addition, the collision elasticity of PGs is found to decay with the collision velocity by a power law, i.e., a concise dynamic scaling despite the complex process involved, which is beyond expectation. These results elucidate the dynamic interacting mechanism of PGs, which are of immediate interest for a fundamental understanding of the antifouling performance of PGs and the rational design of PG-coated nanoparticles in nanomedicine for drug delivery.

Liquid and Droplet Transport in Brush-Coated Cylindrical Nanochannels: Brush-Assisted Droplet Formation

We study, by coarse-grained molecular dynamics simulations, equilibrium and flow properties of a liquid in cylindrical nanochannels, coated with polymer brushes. The parameters of the interaction potential model confer a chemical incompatibility between brush monomers and liquid particles. First, we study cylindrical channels whose radii are larger than the brush height and a continuous column of liquid forms at the center of the channel. These results are contrasted to the limiting case in which the radius of the cylinder is comparable to the brush height. In this second case, the grafted polymers interact across the channel and "close" it. We observe a train of droplets as the stable liquid morphology. The droplet size is comparable to the cylinder radius. By applying a constant body force onto the liquid, we induce a Poiseuille-like flow and investigate the morphology and flow rate as a function of driving force. Upon increasing the driving force, we encounter a nonequilibrium transition from a closed channel with slowly moving droplets to a flowing liquid thread at the center. The switching between these two states is reversible.