Hydration of Spherical PEO-Grafted Gold Nanoparticles: Curvature and Grafting Density Effect

polyGraft 1.0: A program for molecular structure and topology generation of polymer-grafted hybrid nanostructures

Polymer-grafted hybrid materials have been ubiquitously employed in various engineering applications. The design of these hybrid materials with superior performances requires a molecularly detailed understanding of the structure and dynamics of the polymer brushes and their interactions with the grafting substrate. Molecular dynamics (MD) simulations are very well suited for the study of these materials which can provide molecular insights into the effects of polymer composition and length, grafting density, substrate composition and curvatures, and nanoconfinement. However, few existing tools are available to generate such systems, which would otherwise reduce the barrier of preparation for such systems to enable high throughput simulations. Here polyGraft, a general, flexible, and easy to use Python program, is introduced for automated generation of molecular structure and topology of polymer grafted hybrid materials for MD simulations purposes, ranging from polymer brushes grafted to hard substrates, to densely grafted bottlebrush polymers. polyGraft is openly accessible on GitHub (https://github.com/nanogchen/polyGraft).

Approaches and Perspective of Coarse-Grained Modeling and Simulation for Polymer-Nanoparticle Hybrid Systems

Molecular modeling and simulations have emerged as effective and indispensable tools to characterize polymeric systems. They provide fundamental and essential insights to design a product of the required properties and to improve the understanding of a phenomenon at the molecular level for a particular system. The polymer-nanoparticle hybrids are materials with outstanding properties and correspondingly large applications whose study has benefited from this new paradigm. However, despite the significant expansion of modern day computational powers, investigation of the long time and large length scale phenomenon in polymeric and polymer-nanoparticle systems is still a challenging task to complete through all-atom molecular dynamics (AA-MD) simulations. To circumvent this problem, a variety of coarse-grained (CG) models have been proposed, ranging from the generic CG models for qualitative properties predictions to more realistic chemically specific CG models for quantitative properties predictions. These CG models have already delivered some success stories in the study of several spatial and temporal evolutions of many processes. Some of these studies were beyond the feasibility of traditional atomistic resolution models due to either the size or the time constraints. This review captures the different types of popular CG approaches that are utilized in the investigation of the microscopic behavior of polymer-nanoparticle hybrid systems. The rationale of this article is to furnish an overview of the popular CG approaches and their applications, to review several important and most recent developments, and to delineate the perspectives on future directions in the field.

Physisorption of Poly(ethylene glycol) on Inorganic Nanoparticles

Poly(ethylene glycol) (PEG) is the most widely used polymer to decorate inorganic nanoparticles (NPs) by the "grafting-to" method for antifouling properties. PEG also shows diverse supramolecular interactions with nanoparticle surfaces and polar molecules, suggesting that the physisorption between PEG chains and NPs cannot be ignored in the "grafting-to" process. However, the effect of physisorption of PEG to NPs on the process of chemisorption has been rarely studied. Herein, we report that unfunctionalized PEG is physically adsorbed on various NPs by polyvalent supramolecular interactions, adopting "loop-and-train-tail" conformations. We investigated the effect of molecular weight of PEG and ligands of the NPs on the conformation of PEG chains by experimental methods and simulation. It is demonstrated that the physisorption of PEG on NPs can facilitate the chemisorption in the initial stages but delays it in the later stages during the "grafting-to" process. This work provides a deeper understanding of the conformation of physisorbed PEG on NPs and the relationship between physisorption and chemisorption.

Distinct thermoresponsive behaviour of oligo- and poly-ethylene glycol protected gold nanoparticles in concentrated salt solutions

In this work, the methoxy terminated oligo- and polyethylene glycol of different chain lengths (EGn, n = 7, 18, 45 and 136) is grafted on AuNP surfaces under conditions where they attain maximum grafting densities. These EGn-AuNPs gain stability relative to the pristine c-AuNPs in aqueous solutions and in a wide temperature interval and they form stable suspensions in solutions of high NaCl concentrations. To show the thermoresponsive properties of these EGn-AuNPs, temperature titration experiments are carried out in the presence of increasing amounts of salts. The concentrations of NaCl are chosen by checking the stability of EGn-AuNPs at room temperature and choosing the highest concentrations that allow them to form stable suspensions. The analysis of the temperature titration experiments monitored by UV-visible spectroscopy and dynamic light scattering allows us to establish the existence of transitions from individual to assembled nanoparticles, the reversibility of the temperature transitions and hysteretic behaviour in these systems. While EG7-AuNPs only show reversible temperature transitions in the presence of 5 mM NaCl, EG18-AuNPs do up to 1 M NaCl, becoming only partially reversible in 2 M NaCl. The titrations of EG45-AuNPs in 3 and 5 M NaCl show irreversible temperature transitions. Finally, EG136-AuNPs present a complex and interesting behaviour with two temperature transitions, the first one showing hysteresis and the second being reversible.

The Martini Model in Materials Science

The Martini model, a coarse-grained force field initially developed with biomolecular simulations in mind, has found an increasing number of applications in the field of soft materials science. The model's underlying building block principle does not pose restrictions on its application beyond biomolecular systems. Here, the main applications to date of the Martini model in materials science are highlighted, and a perspective for the future developments in this field is given, particularly in light of recent developments such as the new version of the model, Martini 3.

Spherical Micelles with Nonspherical Cores: Effect of Chain Packing on the Micellar Shape

Self-assembly of amphiphilic polymers into micelles is an archetypical example of a "self-confined" system due to the formation of micellar cores with dimensions of a few nanometers. In this work, we investigate the chain packing and resulting shape of C n -PEOx micelles with semicrystalline cores using small/wide-angle X-ray scattering (SAXS/WAXS), contrast-variation small-angle neutron scattering (SANS), and nuclear magnetic resonance spectroscopy (NMR). Interestingly, the n-alkyl chains adopt a rotator-like conformation and pack into prolate ellipses (axial ratio ϵ ≈ 0.5) in the "crystalline" region and abruptly arrange into a more spheroidal shape (ϵ ≈ 0.7) above the melting point. We attribute the distorted spherical shape above the melting point to thermal fluctuations and intrinsic rigidity of the n-alkyl blocks. We also find evidence for a thin dehydrated PEO layer (≤1 nm) close to the micellar core. The results provide substantial insight into the interplay between crystallinity and molecular packing in confinement and the resulting overall micellar shape.

Flow-Induced Formation of Thin PEO Fibers in Water and Their Stability After the Strain Release

Recently, we have shown that a tensile stress applied to chains of poly(ethylene oxide) (PEO) in water reduces the solubility and leads to phase separation of PEO chains from water with the formation of a two-phase region. In this work, we further elucidate the generic mechanism behind strain-induced phase transitions in aqueous PEO solutions with concentrations of 50-60 wt % by performing all-atom molecular dynamics simulations. In particular, we study the stability of oriented PEO fibers after removing stretching forces. We found that the size of the PEO bundle increased with time, which is associated with the dissolution of PEO chains on the fiber surface due to the reformation of hydrogen bonds between the outer PEO molecules and water. For precise characterization of the fibers, the scattering patterns (small- and wide-angle X-ray spectra) for configurations taken at different relaxation times are calculated. The tendency of the oligomer chains to be peeled off from the surface of the bundle eventually might lead to a complete dissolution of the PEO fiber. We conclude that either entanglement constraints or a quick drying process are necessary to conserve the fiber structure in a quiescent state. The scattering results show that external strain induced a liquid-liquid phase separation first. On long time scales, this can be a precursor for crystallization of the fiber.

Influence of the Architecture of Soft Polymer-Functionalized Polymer Nanoparticles on Their Dynamics in Suspension

The behavior of nanogels in suspension can be dramatically affected by the grafting of a canopy of end-tethered polymer chains. The architecture of the interfacial layer, defined by the grafting density and length of the polymer chains, is a crucial parameter in defining the conformation and influencing the dynamics of the grafted chains. However, the influence of this architecture when the core substrate is itself soft and mobile is complex; the dynamics of the core influences the dynamics of the tethered chains, and, conversely, the dynamics of the tethered chains can influence the dynamics of the core. Here, poly(styrene) (PS) particles were functionalized with poly(methyl acrylate) (PMA) chains and swollen in a common solvent. NMR relaxation reveals that the confinement influences the mobility of the grafted chain more prominently for densely grafted short chains. The correlation time associated with the relaxation of the PMA increased by more than 20% when the grafting density increased for short chains, but for less than 10% for long chains. This phenomenon is likely due to the steric hindrance created by the close proximity to the rigid core and of the neighboring chains. More interestingly, a thick layer of a densely grafted PMA canopy efficiently increases the local mobility of the PS cores, with a reduction of the correlation time of more than 30%. These results suggest an interplay between the dynamics of the core and the dynamics of the canopy.

Hydrodynamic Radius of Polymer-Coated Nanoparticles Measured by Taylor Dispersion: A Mathematical Model

This theoretical work addresses the characterization of polymer-coated nanoparticles via the analysis of Taylor dispersion experiments. Our focus is on determining the apparent hydrodynamic radius and the related accuracy bias, which results from polydispersity and optical-absorption-weighted averages. To that end, we construct a statistical model addressing joint distributions of particle core size and ligand surface density, which determine the hydrodynamic radius and optical absorption of such nanoparticles. Our model predicts that a polymer shell that is thick compared with the core radius results in a smaller bias than a thin shell, and the bias may become even negative when ligand surface density is sufficiently high.

Optimizing PEGylation of TiO2 Nanocrystals through a Combined Experimental and Computational Study

PEGylation of metal oxide nanoparticles is the common approach to improve their biocompatibility and in vivo circulation time. In this work, we present a combined experimental and theoretical study to determine the operating condition that guarantee very high grafting densities, which are desirable in any biomedical application. Moreover, we present an insightful conformational analysis spanning different coverage regimes and increasing polymer chain lengths. Based on 13C NMR measurements and molecular dynamics simulations, we show that classical and popular models of polymer conformation on surfaces fail in determining the mushroom-to-brush transition point and prove that it actually takes place only at rather high grafting density values.

Stabilizing Colloidal Particles against Salting-out by Shortening Surface Grafts

A dramatic improvement is reported in the stability of colloidal particles when stabilizing surface grafts are systematically shortened from small polymers to single monomers. The colloidal dispersions consist of fluorinated latex particles, exhibiting a weak van der Waals attraction, with grafted steric layers of poly(ethylene glycol) (PEG) of different chain lengths. Using an effective salting-out electrolyte, Na₂CO₃, particle aggregates are detected above a threshold salt concentration that is independent of the particle concentration. The results are interpreted in terms of a sudden onset of nondispersibility of single particles, triggered by the solvent not completely wetting particle surfaces. By decreasing the PEG chain length, the threshold salt concentration is found to increase sharply. For grafts with just a single ethylene glycol group, dispersions remain stable up to exceedingly high concentrations of Na₂CO₃. However, on removal of the surface coverage altogether, the classical stability behavior of charge-stabilized dispersions is recovered. The behavior can be captured by a simple model that incorporates effective polymer-solvent interactions in the presence of an electrolyte.

Interplay between ligand mobility and nanoparticle geometry during cellular uptake of PEGylated liposomes and bicelles

We explore the cellular uptake process of PEGylated liposomes and bicelles by investigating their membrane wrapping process using large-scale molecular dynamics simulations. We find that due to the mobility of ligands on the liposome/bicelle, the membrane wrapping process of a PEGylated liposome/bicelle can be divided into two stages, whose transition is determined by a critical wrapping fraction fc; it is reached when all the ligands are exhausted and bound to receptors within the cell membrane. Before this critical scenario is approached, the grafted polyethylene glycol (PEG) polymers aggregate together within the membrane-wrapped region of the liposome/bicelle, driven by ligand-receptor binding. For wrapping fractions f > fc, membrane wrapping cannot proceed unless a compressive membrane tension is provided. By systematically varying the membrane tension and PEG molar ratio, we establish phase diagrams about wrapping states for both PEGylated liposomes and bicelles. According to these diagrams, we find that the absolute value of the compressive membrane tension required by a fully wrapped PEGylated bicelle is smaller than that of the PEGylated liposome, indicating that the PEGylated bicelle is easily internalized by cells. Further theoretical analysis reveals that compared to a liposome, the flatter surface at the top of a bicelle makes it energetically more favored beyond the critical wrapping fraction fc. Our simulations confirm that the interplay between ligand mobility and NP geometry can significantly change the understanding about the influence of NP geometry on the membrane wrapping process. It can help us to better understand the cellular uptake process of the PEGylated liposome/bicelle and to improve the design of lipid-like NPs for drug delivery.

Hydration of diblock copolymer micelles: Effects of hydrophobicity and co-solvent

Diblock polymer micelles dispersed in an aqueous environment are being actively investigated for various applications, but there is only a qualitative understanding of the effect of the chemical structure on the micelle hydration and water dynamics as these properties are difficult to assess experimentally. Using all-atom molecular dynamics simulations, we investigate aqueous solutions of three comparable in size diblock copolymer micelles with core-forming blocks of different hydrophobicity: polybutadiene (PB), polycaprolactone (PCL), and polytetrahydrofuran (pTHF) with the same hydrophilic block, polyethylene oxide (PEO). We found that core-block hydrophobicity and ability to form hydrogen bonds with water strongly affect the water dynamics near the core: water molecules spend considerably less time in contact with the PB block than with PCL and pTHF blocks. We obtained polymer and solvent volume fraction profiles and determined that the interfacial width systematically increases with a decrease of core block hydrophobicity with water penetration into the core being negligible for PB-PEO and PCL-PEO micelles, while for pTHF-PEO micelles the interface is more diffuse and there is a noticeable penetration of water (17% by volume). For PCL-PEO micelles, which are commonly used in biomedical applications, we also investigated tetrahydrofuran (THF) penetration into the micelles from mixed THF:water solution at early stages of micelle dissolution. We found an inhomogeneous solvent distribution with a maximum of THF volume fraction in the interfacial core-corona region and partial exclusion from the PEO corona, which slows down micelle dissolution. These results can have important implications for micelle stability and use in biomedical applications.

Quantitative Measure of the Size Dispersity in Ultrasmall Fluorescent Organic-Inorganic Hybrid Core-Shell Silica Nanoparticles by Small-angle X-ray Scattering

Small-angle X-ray scattering (SAXS) was performed on dispersions of ultrasmall (d < 10 nm) fluorescent organic-inorganic hybrid core-shell silica nanoparticles synthesized in aqueous solutions (C' dots) by using an oscillating flow cell to overcome beam induced particle degradation. Form factor analysis and fitting was used to determine the size and size dispersity of the internal silica core containing covalently encapsulated fluorophores. The structure of the organic poly(ethylene glycol) (PEG) shell was modelled as a monodisperse corona containing concentrated and semi-dilute regimes of decaying density and as a simple polydisperse shell to determine the bounds of dispersity in the overall hybrid particle. C' dots containing single growth step silica cores have dispersities of 0.19-0.21; growth of additional silica shells onto the core produces a thin, dense silica layer, and increases the dispersity to 0.22-0.23. Comparison to FCS and DLS measures of size shows good agreement with SAXS measured and modelled sizes and size dispersities. Finally, comparison of a set of same sized and purified particles demonstrates that SAXS is sensitive to the skewness of the gel permeation chromatography elugrams of the original as-made materials. These and other insights provided by quantitative SAXS assessments may become useful for generation of robust nanoparticle design criteria necessary for their successful and safe use, for example in nanomedicine and oncology applications.