Universal Relation for Effective Interaction between Polymer-Grafted Nanoparticles

Characterizing the shear response of polymer-grafted nanoparticles

Grafting polymer chains to the surface of nanoparticles overcomes the challenge of nanoparticle dispersion within nanocomposites and establishes high-volume fractions that are found to enable enhanced material mechanical properties. This study utilizes coarse-grained molecular dynamics simulations to quantify how the shear modulus of polymer-grafted nanoparticle (PGN) systems in their glassy state depends on parameters such as strain rate, nanoparticle size, grafting density, and chain length. The results are interpreted through further analysis of the dynamics of chain conformations and volume fraction arguments. The volume fraction of nanoparticles is found to be the most influential variable in deciding the shear modulus of PGN systems. A simple rule of mixture is utilized to express the monotonic dependence of shear modulus on the volume fraction of nanoparticles. Due to the reinforcing effect of nanoparticles, shortening the grafted chains results in a higher shear modulus in PGNs, which is not seen in linear systems. These results offer timely insight into calibrating molecular design parameters for achieving the desired mechanical properties in PGNs.

Nanoparticles insertion and dimerization in polymer brushes

Molecular dynamics simulations are conducted to systematically investigate the insertion of spherical nanoparticles (NPs) in polymer brushes as a function of their size, strength of their interaction with the polymers, polymer grafting density, and polymer chain length. For attractive interactions between the NPs and the polymers, the depth of NPs' penetration in the brush results from a competition between the enthalpic gain due to the favorable polymer-NP interaction and the effect of osmotic pressure resulting from displaced polymers by the NP's volume. A large number of simulations show that the average depth of the NPs increases by increasing the strength of the interaction strength. However, it decreases by increasing the NPs' diameter or increasing the polymer grafting density. While the NPs' effect on the polymer density is local, their effect on their conformations is long-ranged and extends laterally over length scales larger than the NP's size. This effect is manifested by the emergence of laterally damped oscillations in the normal component of the chains' radius of gyration. Interestingly, we found that for high enough interaction strength, two NPs dimerize in the polymer brush. The dimer is parallel to the substrate if the NPs' depth in the brush is shallow. However, the dimer is perpendicular to the substrate if the NPs' are deep in the brush. These results imply that polymer brushes can be used as a tool to localize and self-assemble NPs in polymer brushes.

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).

Charge shielding effects of PEG bound to NH2-terminated PAMAM dendrimers - an experimental approach

Cationic poly(amido amine) (PAMAM) dendrimers exhibit great potential for use in drug delivery, but their high charge density leads to an inherent cytotoxicity. To increase biocompatibility, many studies have attached poly(ethylene glycol) (PEG) chains to the dendrimer surface. It is unclear how these tethered PEG chains influence the physicochemical properties of the dendrimer. Here, we develop a fluorescence-based assay utilizing anionic biological tissue to quantify the electrostatic binding affinity of a library of PEG-PAMAM conjugates with various PEG chain lengths and grafting densities. We find that covalently bound PEG chains reduce the electrostatic binding affinity more significantly than what can be achieved through covalent bonds only. Contrary to previous thought, this reduction is not explained by the steric hindrance effects of PEG chains, suggesting that other, non-covalent interactions between PEG and PAMAM are present. Using acetylated PAMAM conjugates, we convert electrostatic binding affinity to the number of charged amines accessible to the physiological environment. These data, coupled with ¹H-NMR, allows us to study more closely the non-covalent interactions between PEG and PAMAM. We find that increasing PEG chain length increases the number of non-covalent interactions. Additionally, at low grafting densities, increasing the number of PEG chains on the PAMAM surface also increases the non-covalent interactions. At higher grafting densities, however, PEG chains sterically repel one another, forcing chains to elongate away from the surface and reducing the number of interactions between PAMAM and individual PEG chains. The data presented here provides a framework for a more precise mechanistic understanding of how the length and density of tethered PEG chains on PAMAM dendrimers influence drug delivery properties.

Thermoformable and transparent one-component nanocomposites based on surface grafted cellulose nanofiber

One-component nanocomposites based on poly(methyl methacrylate)(PMMA) and polystyrene (PS) grafted cellulose nanofiber (CNF) with high polymer graft percentage were fabricated. At relative ambient conditions, less active vinyl monomer, MMA, and styrene were grafted from CNF via surface-initiated Cu(0)-mediated reversible deactivation radical polymerizations (RDRP), and PMMA/PS grafted CNFs could reach a graft percentage as high as 7550 % and 3530 %, respectively. The one-component composite films were manufactured by simple hot-pressing subsequentially. Optical transparency, thermal stability, and glass transition temperature of one-component nanocomposites were enhanced dramatically in contrast with the bicomponent nanocomposite. The uniform fracture surface confirmed the uniform dispersity by morphological observation. Mechanical tests indicated that break elongation and tensile strength ascended notably, and tensile modulus slightly descended as the graft percentage increased for PS and PMMA grafted CNF one-component composite. It was concluded that for glassy graft chains, obtaining one-component nanocomposites with high enough graft chain length was essential to achieve moderated mechanical performance without compromising optical properties and thermal manufacturing ability.

Realizability of iso-g2 processes via effective pair interactions

An outstanding problem in statistical mechanics is the determination of whether prescribed functional forms of the pair correlation function g2( r) [or equivalently, structure factor S( k)] at some number density ρ can be achieved by many-body systems in d-dimensional Euclidean space. The Zhang–Torquato conjecture states that any realizable set of pair statistics, whether from a nonequilibrium or equilibrium system, can be achieved by equilibrium systems involving up to two-body interactions. To further test this conjecture, we study the realizability problem of the nonequilibrium iso- g2 process, i.e., the determination of density-dependent effective potentials that yield equilibrium states in which g2 remains invariant for a positive range of densities. Using a precise inverse algorithm that determines effective potentials that match hypothesized functional forms of g2( r) for all r and S( k) for all k, we show that the unit-step function g2, which is the zero-density limit of the hard-sphere potential, is remarkably realizable up to the packing fraction ϕ = 0.49 for d = 1. For d = 2 and 3, it is realizable up to the maximum “terminal” packing fraction ϕ c = 1/2 d, at which the systems are hyperuniform, implying that the explicitly known necessary conditions for realizability are sufficient up through ϕ c. For ϕ near but below ϕ c, the large- r behaviors of the effective potentials are given exactly by the functional forms exp[ − κ( ϕ) r] for d = 1, r−1/2 exp[ − κ( ϕ) r] for d = 2, and r−1 exp[ − κ( ϕ) r] (Yukawa form) for d = 3, where κ−1( ϕ) is a screening length, and for ϕ = ϕ c, the potentials at large r are given by the pure Coulomb forms in the respective dimensions as predicted by Torquato and Stillinger [Phys. Rev. E 68, 041113 (2003)]. We also find that the effective potential for the pair statistics of the 3D “ghost” random sequential addition at the maximum packing fraction ϕ c = 1/8 is much shorter ranged than that for the 3D unit-step function g2 at ϕ c; thus, it does not constrain the realizability of the unit-step function g2. Our inverse methodology yields effective potentials for realizable targets, and, as expected, it does not reach convergence for a target that is known to be non-realizable, despite the fact that it satisfies all known explicit necessary conditions. Our findings demonstrate that exploring the iso- g2 process via our inverse methodology is an effective and robust means to tackle the realizability problem and is expected to facilitate the design of novel nanoparticle systems with density-dependent effective potentials, including exotic hyperuniform states of matter.

Free energy cost to assemble superlattices of polymer-grafted nanoparticles

Mesoparticles consisting of a hard core and a soft corona like polymer-grafted nanoparticles (PGNPs) can assemble into various superlattice structures, in which each mesoparticle assumes the shape of the corresponding Wigner-Seitz (or Voronoi) cell. Conventional wisdom often perceives the stability of these superlattices in a mean-field view of surface area minimization or corona entropy maximization, which lacks molecular interpretation. We develop a simulation method to calculate the free energy cost to deform spherical PGNPs into Wigner-Seitz polyhedra, which are then relaxed in a certain crystalline superlattice. With this method, we successfully quantify the free energy differences between model BCC, FCC and A15 systems of PGNPs and identify BCC as the most stable structure in most cases. Analysis of polymer configurations in the corona, whose boundary is blurred by chain interpenetration, shows that the radial distribution of grafted chains and the corresponding entropy are almost identical between BCC and FCC, suggesting that the higher stability of the BCC structure cannot be explained by the mean-field description of the corona shape.

Polymer-Grafted Nanoparticles (PGNs) with Adjustable Graft-Density and Interparticle Hydrogen Bonding Interaction

Polymer-grafted nanoparticles (PGNs) receive great attention because they possess the advantages of both the grafted polymer and inorganic cores, and thus demonstrate superior optical, electronic, and mechanical properties. Thus, PGNs with tailorable interparticle interactions are indispensable for the formation of a superlattice with a defined and ordered structure. In this work, the synthesis of PGNs is reported which can form interparticle hydrogen-bonding to enhance the formation of well-defined 2D nanoparticle arrays. Various polymers, including poly(4-vinyl pyridine) (P4VP), poly(dimethyl aminoethyl acrylate) (PDMAEMA), and poly(4-acetoxy styrene) (PAcS), are attached to silica cores by a "grafting from" in a mini emulsion-like synthesis approach. SiO₂ -PAcS brushes are deprotected by hydrazinolysis and converted into poly(4-vinyl phenol) (PVP), containing hydroxyl groups as potential hydrogen-bonding donor sites. Understanding and controlling interparticle interactions by varying grafting density in the range of 10^-2 -10^-3 chain nm^-2 , and the formation of interparticle hydrogen bonding relevant for self-assembly of PGNs and potential formation of PGN superlattice structures are the motivations for this study.

Internal Microstructure Dictates Interactions of Polymer-grafted Nanoparticles in Solution

Understanding the effects of polymer brush architecture on particle interactions in solution is requisite to enable the development of functional materials based on self-assembled polymer-grafted nanoparticles (GNPs). Static and dynamic light scattering of polystyrene-grafted silica particle solutions in toluene reveals that the pair interaction potential, inferred from the second virial coefficient, A 2, is strongly affected by the grafting density, σ, and degree of polymerization, N, of tethered chains. In the limit of intermediate σ (∼0.3 to 0.6 nm-2) and high N, A 2 is positive and increases with N. This confirms the good solvent conditions and can be qualitatively rationalized on the basis of a pair interaction potential derived for grafted (brush) particles. In contrast, for high σ > 0.6 nm-2 and low N, A 2 displays an unexpected reversal to negative values, thus indicating poor solvent conditions. These findings are rationalized by means of a simple analysis based on a coarse-grained brush potential, which balances the attractive core-core interactions and the excluded volume interactions imparted by the polymer grafts. The results suggest that the steric crowding of polymer ligands in dense GNP systems may fundamentally alter the interactions between brush particles in solution and highlight the crucial role of architecture (internal microstructure) on the behavior of hybrid materials. The effect of grafting density also illustrates the opportunity to tailor the physical properties of hybrid materials by altering geometry (or architecture) rather than a variation of the chemical composition.