Grafted polymer chains suppress nanoparticle diffusion in athermal polymer melts

Role of Ligand Shell Density in the Diffusive Behavior of Nanoparticles in Hydrogels

The diffusion coefficients of poly(ethylene glycol) methyl ether thiol (PEGSH)-functionalized gold nanoparticles (NPs) with different effective grafting densities were measured in polyacrylamide hydrogels. The NP core size was held constant, and the NPs were functionalized with mixtures of short oligomeric ligands (254 Da PEGSH) and longer (either 1 or 2 kDa PEGSH) ligands. The ratio of short and long ligands was varied such that the grafting density of the high-molecular-weight (MW) ligand ranged from approximately 1 to 100 high-MW ligands/NP. The diffusion coefficients of the NPs were then measured in gels with varying average mesh sizes. The measured diffusion coefficients decreased with higher MW ligand density. Interestingly, the diffusion coefficients for NPs with high effective grafting densities were well-predicted by their hydrodynamic diameters, but the diffusion coefficients for NPs with low effective grafting densities were higher than expected from their hydrodynamic diameters. These results suggest that crowding in the NP ligand shell influences the mechanism of diffusion, with lower grafting densities allowing ligand chain relaxations that facilitate movement through the gel. This work brings new insights into the factors that dictate how NPs move through hydrogels and will inform the development of models for applications such as drug delivery in complex viscoelastic biological materials.

Facile Entropy-Driven Segregation of Imprinted Polymer-Grafted Nanoparticle Brush Blends by Solvent Vapor Annealing Soft Lithography

Polymer-grafted nanoparticles (PGNPs) have attracted extensive research interest due to their potential for enhancing mechanical and electrical properties of both bulk polymer composite materials, as well as thin polymer films incorporating these nanoparticles (NPs). In previous studies, we have shown that an entropic driving force serves to organize low-molecular-mass PGNPs in imprinted blend films of PGNPs with low-molecular-mass homopolymers. In this work, we developed a novel solvent vapor annealing soft lithography (SVA-SL) method to overcome the technical difficulties in processing the high-molecular-mass PGNP blends due to the intrinsically sluggish melt annealing kinetics found in the phase separation of these blend PGNP materials. In particular, we utilized SVA-SL to create nanopatterns in blends of PGNPs having relatively high-molecular-mass-grafted layers but with cores of NPs having greatly different sizes. The minimization of the entropic free energy in the present system corresponded to larger PGNPs partitioning almost exclusively into the "mesa" regions of the imprinted PGNP blend films, as quantified by the estimation of the partition coefficient, K_p. The use of the SVA-SL processing method is important because it allows facile imprint patterning of PGNP materials and large-scale organization of the PGNPs even when the grafted chain lengths are long enough for the chains to be highly entangled, allowing enhanced thermo-mechanical property enhancements of the resulting films and a corresponding extended range of potential nanotech applications.

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.

Universal Polymeric-to-Colloidal Transition in Melts of Hairy Nanoparticles

Two different classes of hairy self-suspended nanoparticles in the melt state, polymer-grafted nanoparticles (GNPs) and star polymers, are shown to display universal dynamic behavior across a broad range of parameter space. Linear viscoelastic measurements on well-characterized silica-poly(methyl acrylate) GNPs with a fixed core radius (R_core) and grafting density (or number of arms f) but varying arm degree of polymerization (N_arm) show two distinctly different regimes of response. The colloidal Regime I with a small N_arm (large core volume fraction) is characterized by predominant low-frequency solidlike colloidal plateau and ultraslow relaxation, while the polymeric Regime II with a large N_arm (small core volume fractions) has a response dominated by the starlike relaxation of partially interpenetrated arms. The transition between the two regimes is marked by a crossover where both polymeric and colloidal modes are discerned albeit without a distinct colloidal plateau. Similarly, polybutadiene multiarm stars also exhibit the colloidal response of Regime I at very large f and small N_arm. The star arm retraction model and a simple scaling model of nanoparticle escape from the cage of neighbors by overcoming a hopping potential barrier due to their elastic deformation quantitatively describe the linear response of the polymeric and colloidal regimes, respectively, in all these cases. The dynamic behavior of hairy nanoparticles of different chemistry and molecular characteristics, investigated here and reported in the literature, can be mapped onto a universal dynamic diagram of f/[R_core³/ν₀)^1/4] as a function of (N_armν₀f)/(R_core³), where ν₀ is the monomeric volume. In this diagram, the two regimes are separated by a line where the hopping potential ΔU_hop is equal to the thermal energy, k_BT. ΔU_hop can be expressed as a function of the overcrowding parameter x (i.e., the ratio of f to the maximum number of unperturbed chains with N_arm that can fill the volume occupied by the polymeric corona); hence, this crossing is shown to occur when x = 1. For x > 1, we have colloidal Regime I with an overcrowded volume, stretched arms, and ΔU_hop > k_BT, while polymeric Regime II is linked to x < 1. This single-material parameter x can provide the needed design principle to tailor the dynamics of this class of soft materials across a wide range of applications from membranes for gas separation to energy storage.

Detecting bound polymer layers in attractive polymer-nanoparticle hybrids

When polymer-nanoparticle (NP) attractions are sufficiently strong, a bound polymer layer with a distinct dynamic signature spontaneously forms at the NP interface. A similar phenomenon occurs near a fixed attractive substrate for thin polymer films. While our previous simulations fixed the NPs to examine the dilute limit, here, we allow the NP to move. Our goal is to investigate how NP mobility affects the signature of the bound layer. For small NPs that are relatively mobile, the bound layer is slaved to the motion of the NP, and the signature of the bound layer relaxation in the intermediate scattering function essentially disappears. The slow relaxation of the bound layer can be recovered when the scattering function is measured in the NP reference frame, but this process would be challenging to implement in experimental systems with multiple NPs. Instead, we use the counterintuitive result that the NP mass affects its mobility in the nanoscale limit, along with the more expected result that the bound layer increases the effective NP mass, to suggest that the signature of the bound polymer manifests as a change in NP diffusivity. These findings allow us to rationalize and quantitatively understand the results of recent experiments focused on measuring NP diffusivity with either physically adsorbed or chemically end-grafted chains.

Grafted Nanoparticle Surface Wetting during Phase Separation in Polymer Nanocomposite Films

Wetting of polymer-grafted nanoparticles (NPs) in a polymer nanocomposite (PNC) film is driven by a difference in surface energy between components as well as bulk thermodynamics, namely, the value of the interaction parameter, χ. The interplay between these contributions is investigated in a PNC containing 25 wt % polymethyl methacrylate (PMMA)-grafted silica NPs (PMMA-NPs) in poly(styrene-ran-acrylonitrile) (SAN) upon annealing above the lower critical solution temperature (LCST, 160 °C). Atomic force microscopy (AFM) studies show that the areal density of particles increases rapidly and then approaches 80% of that expected for random close-packed hard spheres. A slightly greater areal density is observed at 190 °C compared to 170 °C. The PMMA-NPs are also shown to prevent dewetting of PNC films under conditions where the analogous polymer blend is unstable. Transmission electron microscopy (TEM) imaging shows that PMMA-NPs symmetrically wet both interfaces and form columns that span the free surface and substrate interface. Using grazing-incidence Rutherford backscattering spectrometry (GI-RBS), the PMMA-NP surface excess (Z*) initially increases rapidly with time and then approaches a constant value at longer times. Consistent with the areal density, Z* is slightly greater at deeper quench depths, which is attributed to the more unfavorable interactions between the PMMA brush and SAN segments. The Z* values at early times are used to determine the PMMA-NP diffusion coefficients, which are significantly larger than theoretical predictions. These studies provide insights into the interplay between wetting and phase separation in PNCs and can be utilized in nanotechnology applications where surface-dependent properties, such as wettability, durability, and friction, are important.

Dynamic Mixing Behaviors of Ionically Tethered Polymer Canopy of Nanoscale Hybrid Materials in Fluids of Varying Physical and Chemical Properties

An emerging area of sustainable energy and environmental research is focused on the development of novel electrolytes that can increase the solubility of target species and improve subsequent reaction performance. Electrolytes with chemical and structural tunability have allowed for significant advancements in flow batteries and CO₂ conversion integrated with CO₂ capture. Liquid-like nanoparticle organic hybrid materials (NOHMs) are nanoscale fluids that are composed of inorganic nanocores and an ionically tethered polymeric canopy. NOHMs have been shown to exhibit enhanced conductivity making them promising for electrolyte applications, though they are often challenged by high viscosity in the neat state. In this study, a series of binary mixtures of NOHM-I-HPE with five different secondary fluids, water, chloroform, toluene, acetonitrile, and ethyl acetate, were prepared to reduce the fluid viscosity and investigate the effects of secondary fluid properties (e.g., hydrogen bonding ability, polarity, and molar volume) on their transport behaviors, including viscosity and diffusivity. Our results revealed that the molecular ratio of secondary fluid to the ether groups of Jeffamine M2070 (λ_SF) was able to describe the effect that secondary fluid has on transport properties. Our findings also suggest that in solution, the Jeffamine M2070 molecules exist in different nanoscale environments, where some are more strongly associated with the nanoparticle surface than others, and the conformation of the polymer canopy was dependent on the secondary fluid. This understanding of the polymer conformation in NOHMs can allow for the better design of an electrolyte capable of capturing and releasing small gaseous or ionic species.

Effects of Tethered Polymers on Dynamics of Nanoparticles in Unentangled Polymer Melts

Polymer-tethered nanoparticles (NPs) are commonly added to a polymer matrix to improve material properties. Critical to the fabrication and processing of such composites is the mobility of the tethered NPs. Here we study the motion of tethered-NPs in unentangled polymer melts using molecular dynamics simulations, which offer a precise control of the grafted chain length N _g and the number z of grafted chains per particle. As N _g increases, there is a crossover from particle-dominated to tethered-chain-dominated terminal diffusion of NPs with the same z. The mean squared displacement of loosely tethered NPs in the case of tethered-chain dominated terminal diffusion exhibits two sub-diffusive regimes at intermediate time scales for small z. The first one at shorter time scales arises from the dynamical coupling of the particle and matrix chains, while the one at longer time scales is due to the participation of the particle in the dynamics of the tethered chains. The friction of loosely grafted chains in unentangled melts scales linearly with the total number of monomers in the chains, as the frictions of individual monomers are additive in the absence of hydrodynamic coupling. As more chains are grafted to a particle, hydrodynamic interactions between grafted chains emerge. As a result, there is a non-draining layer of hydrodynamically coupled chain segments surrounding the bare particle. Outside the non-draining layer is a free-draining layer of grafted chain segments with no hydrodynamic coupling. The boundary of the two layers is the stick surface where the shear stress due to the relative melt flow is balanced by the friction between grafted and melt chains in the interpenetration layer. The stick surface is located further away from the bare surface of the particle with higher grafting density.

Mobility of Polymer-Tethered Nanoparticles in Unentangled Polymer Melts

A scaling theory is developed for the motion of a polymer-tethered nanoparticle (NP) in an unentangled polymer melt. We identify two types of scaling regimes depending on the NP diameter d and the size of a grafted polymer chain (tail) R tail . In one type of regimes, the tethered NP motion is dominated by the bare NP, as the friction coefficient of the tails is lower than that of the less mobile particle. The time dependence of the mean square displacement (MSD) of the tethered NP ⟨Δr 2(t)⟩ in the particle-dominated regime can be approximated by ⟨Δr 2(t)⟩ bare for the bare NP. In the other type of regimes, the tethered NP motion is dominated by the tails when the friction coefficient of the tails surpasses that of the particle at times longer than the crossover time τ ∗. In a tail-dominated regime, the MSD ⟨Δr 2(t)⟩ ≈ ⟨Δr 2(t)⟩ bare only for t < τ ∗. ⟨Δr 2(t)⟩ of a single-tail NP for t > τ ∗ is approximated as the MSD ⟨Δr 2(t)⟩ tail of monomers in a free tail, whereas ⟨Δr 2(t)⟩ of a multi-tail NP for t > τ ∗ is approximated as the MSD ⟨Δr 2(t)⟩ star of the branch point of a star polymer. The time dependence of ⟨Δr 2(t)⟩ in a tail-dominated regime exhibits two qualitatively different sub-diffusive regimes. The first sub-diffusive regime for t < τ ∗ arises from the dynamical coupling between the particle and the melt chains. The second sub-diffusive regime for t > τ ∗ occurs as the particle participates in the dynamics of the tails. For NPs with loosely grafted chains, there is a Gaussian brush region surrounding the NP, where the chain strands in Gaussian conformations undergo Rouse dynamics with no hydrodynamic coupling. The crossover time τ ∗ for loosely grafted multi-tail NPs in a tail-dominated regime decreases as the number of tails increases. For NPs with densely grafted chains, the tails are hydrodynamically coupled to each other. The hydrodynamic radii for the diffusion of densely grafted multi-tail NPs are approximated by the sum of the particle and tail sizes.

Nanoparticle-polymer interfacial layer properties tune fragility and dynamic heterogeneity of athermal polymer nanocomposite films

Enthalpic interactions at the interface between nanoparticles and matrix polymers are known to influence various properties of the resultant polymer nanocomposites (PNC). For athermal PNCs, consisting of grafted nanoparticles embedded in chemically identical polymers, the role and extent of the interface layer (IL) interactions in determining the properties of the nanocomposites are not very clear. Here, we demonstrate the influence of the interfacial layer dynamics on the fragility and dynamical heterogeneity (DH) of athermal and glassy PNCs. The IL properties are altered by changing the grafted to matrix polymer size ratio, f, which in turn changes the extent of matrix chain penetration into the grafted layer, λ. The fragility of PNCs is found to increase monotonically with increasing entropic compatibility, characterised by increasing λ. Contrary to observations in most polymers and glass formers, we observe an anti-correlation between the dependence on IL dynamics of fragility and DH, quantified by the experimentally estimated Kohlrausch-Watts-Williams parameter and the non-Gaussian parameter obtained from simulations.

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.

Dynamics of Nanoparticles in Entangled Polymer Solutions

The mean square displacement ⟨r²⟩ of nanoparticle probes dispersed in simple isotropic liquids and in polymer solutions is interrogated using fluorescence correlation spectroscopy and single-particle tracking (SPT) experiments. Probe dynamics in different regimes of particle diameter (d), relative to characteristic polymer length scales, including the correlation length (ξ), the entanglement mesh size (a), and the radius of gyration (R_g), are investigated. In simple fluids and for polymer solutions in which d ≫ R_g, long-time particle dynamics obey random-walk statistics ⟨r²⟩:t, with the bulk zero-shear viscosity of the polymer solution determining the frictional resistance to particle motion. In contrast, in polymer solutions with d < R_g, polymer molecules in solution exert noncontinuum resistances to particle motion and nanoparticle probes appear to interact hydrodynamically only with a local fluid medium with effective drag comparable to that of a solution of polymer chain segments with sizes similar to those of the nanoparticle probes. Under these conditions, the nanoparticles exhibit orders of magnitude faster dynamics than those expected from continuum predictions based on the Stokes-Einstein relation. SPT measurements further show that when d > a, nanoparticle dynamics transition from diffusive to subdiffusive on long timescales, reminiscent of particle transport in a field with obstructions. This last finding is in stark contrast to the nanoparticle dynamics observed in entangled polymer melts, where X-ray photon correlation spectroscopy measurements reveal faster but hyperdiffusive dynamics. We analyze these results with the help of the hopping model for particle dynamics in polymers proposed by Cai et al. and, on that basis, discuss the physical origins of the local drag experienced by the nanoparticles in entangled polymer solutions.

Translational and rotational dynamics of an ultra-thin nanorod probe particle in linear polymer melts

Translational and rotational dynamics of a single rigid ultra-thin nanorod probe particle in linear polymer melts are investigated using coarse-grained molecular dynamics (CG-MD) simulations.

Altering surface fluctuations by blending tethered and untethered chains

"Partially tethering" a thin film of a polymer melt by covalently attaching to the substrate a fraction of the chains in an unentangled melt dramatically increases the relaxation time of the surface height fluctuations. This phenomenon is observed even when the film thickness, h, is 20 times the unperturbed chain radius, R_g,tethered, of the tethered chains, indicating that partial tethering is more influential than any physical attraction with the substrate. Furthermore, a partially tethered layer of a low average molecular weight of 5k showed much slower surface fluctuations than did a reference layer of pure untethered chains of much greater molecular weight (48k), so the partial tethering effect is stronger than the effects of entanglement and increase in glass transition temperature, T_g, with molecular weight. Partial tethering offers a means of tailoring these fluctuations which influence wetting, adhesion, and tribology of the surface.