Nanoparticle Mobility within Permanently Cross-Linked Polymer Networks

Influence of Number and Strength of Hydrogen Bonds on Fracture Property and Microscopic Mechanisms of Associative Hydrogen-Bonded Polymers via Molecular Dynamics Simulation

A coarse-grained model combining the acceptor-hydrogen-donor 3-body potential is first developed in this work to explore the fracture property and microscopic mechanisms of associative hydrogen-bonded polymers (AHBPs). Next, a triaxial deformation mode is performed to reveal that the fracture toughness of AHBPs initially improves and then is reduced as the number of active groups increases. By characterizing the stress decomposition, the strong hydrogen bond (HB) network improves the maximum stress but reduces the elongation. The destructive process of the HB network is described by quantifying the broken number and reduced energy of HBs. Interestingly, the strength of a single HB first decreases and then rises with strain. The initial decrease is mainly caused by the disruption of strong/moderate HBs, while the following rise is due to the further breakage of weak HBs and partial recovery of strong/moderate HBs. Meanwhile, the formed clusters of HBs due to the self-attraction act as the physical cross-links, whose evolution process is recorded by analyzing their number and size. Following it, the orientation degree and asphericity factor are calculated with strain to reflect the change in chain configuration, which is influenced by the HB network. Subsequently, the nucleation and growth process of voids is quantified. More than 90% of voids are nucleated in the polymer region, while others are in the HB region, which can be proved by the local elastic modulus and snapshots. The growth and coalescence rate of the voids can be suppressed by the strong HB network. Finally, the fracture toughness of AHBPs exhibits a continuous increase with improving strength of HBs due to the strong HB network. In summary, our work presents a clear and novel comprehension of the fracture property of AHBPs at the molecular scale.

Scaling variation in the pinch-off of colloid-polymer mixtures

HYPOTHESIS

The scaling laws of drop pinch-off are known to be affected by drop compositions including dissolved polymers and non-Brownian particles. When the size of the particles is comparable to the characteristic length scale of the polymer network, these particles may interact strongly with the polymer environment, leading to new types of scaling behaviors not reported before.

EXPERIMENTS

Using high-speed imaging, we experimentally studied the time evolution of the neck diameter hmin of drops composed of silica nanoparticles dispersed in PEO solution when extruded from a nozzle.

FINDINGS

After initial Newtonian necking with hmin ∼ t2/3, the subsequent stage may exhibit scaling variation, characterized by either exponential or power-law decay, depending on the nanoparticle volume fraction ϕ. The exponential decay hmin ∼ e-t/τ signifies the coil-stretch transition in typical viscoelastic suspensions. We conducted an analysis of the power-law scenario hmin ∼ tα at high ϕ, categorizing the entire process into three distinct regimes based on the exponents α. The dependences of critical thicknesses at transition points and exponents on polymer concentration offer initial insights into the potential transition from heterogeneous to homogeneous thinning in the mixture. This novel scaling variation bears implications for accurately predicting and controlling droplet fragmentation in industrial applications.

Nanoparticle transport in biomimetic polymer-linked emulsions

The ability of nanoparticles to penetrate and transport through soft tissues is essential to delivering therapeutics to treat diseases or signaling agents for advanced imaging and sensing. Nanoparticle transport in biological systems, however, is challenging to predict and control due to the physicochemical complexity of tissues and biological fluids. Here, we demonstrate that nanoparticles suspended in a novel class of soft matter-polymer-linked emulsions (PLEs)-exhibit characteristics essential for mimicking transport in biological systems, including subdiffusive dynamics, non-Gaussian displacement distributions, and decoupling of dynamics from material viscoelasticity. Using multiple particle tracking, we identify the physical mechanisms underlying this behavior, which we attribute to a coupling of nanoparticle dynamics to fluctuations in the local network of polymer-linked droplets. Our findings demonstrate the potential of PLEs to serve as fully synthetic mimics of biological transport.

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.

How Segmental Dynamics and Mesh Confinement Determine the Selective Diffusivity of Molecules in Cross-Linked Dense Polymer Networks

The diffusion of molecules ("penetrants") of variable size, shape, and chemistry through dense cross-linked polymer networks is a fundamental scientific problem broadly relevant in materials, polymer, physical, and biological chemistry. Relevant applications include separation membranes, barrier materials, drug delivery, and nanofiltration. A major open question is the relationship between transport, thermodynamic state, and penetrant and polymer chemical structure. Here we combine experiment, simulation, and theory to unravel these competing effects on penetrant transport in rubbery and supercooled polymer permanent networks over a wide range of cross-link densities, size ratios, and temperatures. The crucial importance of the coupling of local penetrant hopping to polymer structural relaxation and the secondary importance of mesh confinement effects are established. Network cross-links strongly slow down nm-scale polymer relaxation, which greatly retards the activated penetrant diffusion. The demonstrated good agreement between experiment, simulation, and theory provides strong support for the size ratio (penetrant diameter to the polymer Kuhn length) as a key variable and the usefulness of coarse-grained simulation and theoretical models that average over Angstrom scale structure. The developed theory provides an understanding of the physical processes underlying the behaviors observed in experiment and simulation and suggests new strategies for enhancing selective polymer membrane design.

Stimulus-Responsive Transport Properties of Nanocolloidal Hydrogels

Applications of polymer hydrogels in separation technologies, environmental remediation, and drug delivery require control of hydrogel transport properties that are largely governed by the pore dimensions. Stimulus-responsive change in pore size offers the capability to change gel's transport properties "on demand". Here, we report a nanocolloidal hydrogel that exhibits temperature-controlled increase in pore size and, as a result, enhanced transport of encapsulated species from the gel. The hydrogel was formed by the covalent cross-linking of aldehyde-modified cellulose nanocrystals and chitosan carrying end-grafted poly(N-isopropylacrylamide) (pNIPAm) molecules. Owing to the temperature-mediated coil-to-globule transition of pNIPAm grafts, they acted as a temperature-responsive "gate" in the hydrogel. At elevated temperature, the size of the pores showed up to a 4-fold increase, with no significant changes in volume, in contrast with conventional pNIPAm-derived gels exhibiting a reduction in both pore size and volume in similar conditions. Temperature-mediated transport properties of the gel were explored by studying diffusion of nanoparticles with different dimensions from the gel, leading to the established correlation between the kinetics of diffusion-governed nanoparticle release and the ratio nanoparticle dimensions-to-pore size. The proposed approach to stimulus-responsive control of hydrogel transport properties has many applications, including their use in nanomedicine and tissue engineering.

Dispersion and Diffusion Mechanism of Nanofillers with Different Geometries in Bottlebrush Polymers: Insights from Molecular Dynamics Simulation

The dispersion and diffusion mechanism of nanofillers in polymer nanocomposites (PNCs) are crucial for understanding the properties of PNCs, which is of great significance for the design of novel materials. Herein, we investigate the dispersion and diffusion behavior of two geometries of nanofillers, namely, spherical nanoparticles (SNPs) and nanorods (NRs), in bottlebrush polymers by utilizing coarse-grained molecular dynamics simulations. With the increase of the interaction strength between the nanofiller and polymer (ε_np), both the SNPs and NRs experience a typical "aggregated phase-dispersed phase-bridged phase" state transition in the bottlebrush polymer matrix. We evaluate the validity of the Stokes-Einstein (SE) equation for predicting the diffusion coefficient of nanofillers in bottlebrush polymers. The results demonstrate that the SE predictions are slightly larger than the simulated values for small SNP sizes because the local viscosity that is felt by small SNPs in the densely grafted bottlebrush polymer does not differ much from the macroscopic viscosity. The relative size of the length of the NRs (L) and the radius of gyration (R_g) of the bottlebrush polymer play a key role in the diffusion of NRs. In addition, we characterize the anisotropic diffusion of NRs to analyze their translational and rotational diffusion. The motion of NRs in the direction perpendicular to the end-to-end vector is more hindered, indicating that there is a strong coupling between the rotation of NRs and the motion of the polymer. The NR motion shows stronger anisotropic diffusion at short time scales because of the steric effects generated by side chains of the bottlebrush polymer. In general, our results provide a fundamental understanding of the dispersion of nanofillers and the microscopic mechanism of nanofiller diffusion in bottlebrush polymers.

Dissipative Particle Dynamics Simulation of Nanoparticle Diffusion in a Crosslinked Polymer Network

Dissipative particle dynamics simulation is conducted to investigate the diffusion of a nanoparticle in a crosslinked polymer network based on a bead-spring model. Focusing on cases where the particle is comparable in size to the network mesh, we find from rigid networks that the excluded-volume and hydrodynamic interaction effects associated with solvent beads lead to lubricity, which assists the particle to slip through an opening into the adjacent cell. For flexible networks, the hopping mechanism for particle escape becomes less pronounced with higher network flexibility due to either a smaller spring constant or slacker strands, each consisting of more beads. This behavior could be explained by the larger cell size fluctuation and its slower relaxation, whereby large enough openings temporarily formed are longer-lived, increasing the chance for particle hopping.

Molecular Simulation of Hopping Mechanisms of Nanoparticles in Regular Cross-Linked Polymer Networks

We use coarse-grained simulations to explore the diffusion mechanism of nanoparticles with different sizes at various nanoparticle-polymer interactions in regular cross-linked polymer networks. The long time diffusivities of nanoparticles show a non-monotonic tendency at various nanoparticle-polymer interactions, due to the intermittent hopping of nanoparticles through network cells. The preferred locations of small nanoparticles switch from the cell centers to the corner of cells as they interact with network more strongly, which results in the hopping energy barrier between different cells switching from cell center localization to adsorption on networks. Steric hindrance seriously hampers large nanoparticles from hopping to neighboring network cells, the interactions between nanoparticle and network enhance the network deformability and also affect the hopping of nanoparticles. The multiple constraint mechanisms result in the non-monotonic diffusivities of nanoparticles with different interactions and non-Brownian motions at different time scales. Our work illustrates the hopping mechanisms of nanoparticles in polymer networks from thermodynamic and dynamic points of view.

Relationship between Gel Mesh and Particle Size in Determining Nanoparticle Diffusion in Hydrogel Nanocomposites

The diffusion of poly(ethylene glycol) methyl ether thiol (PEGSH)-functionalized gold nanoparticles (NPs) was measured in polyacrylamide gels with various cross-linking densities. The molecular weight of the PEGSH ligand and particle core size were both varied to yield particles with hydrodynamic diameters ranging from 7 to 21 nm. The gel mesh size was varied from approximately 36 to 60 nm by controlling the cross-linking density of the gel. Because high-molecular-weight ligands are expected to yield more compressible particles, we expected the diffusion constants of the NPs to depend on their hard/soft ratios (where the hard component of the particle consists of the particle core and the soft component of the particle consists of the ligand shell). However, our measurements revealed that NP diffusion coefficients resulted primarily from changes in the overall hydrodynamic diameter and not the ratio of particle core size to ligand size. Across all particles and gels, we found that the diffusion coefficient was well predicted by the confinement ratio calculated from the diameter of the particle and an estimate of the gel mesh size obtained from the elastic blob model and was well described using a hopping model for nanoparticle diffusion. These results suggest that the elastic blob model provides a reasonable estimate of the mesh size that particles "see" as they diffuse through the gel. This work brings new insights into the factors that dictate how NPs move through polymer gels and will inform the development of hydrogel nanocomposites for applications such as drug delivery in heterogeneous, viscoelastic biological materials.

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.

Heterogeneous Dynamics of Polymer Melts Exerted by Chain Loops Anchored on the Substrate: Insights from Molecular Dynamics Simulation

Understanding polymer-substrate interfacial dynamics at the molecular level is crucial for tailoring the properties of polymer ultrathin films (PUFs). Herein, through coarse-grained molecular dynamics simulation, the effect of length (N_loop) and rigidity (K_loop) of loop chains on the dynamics of linear chains is systematically explored, in which the loop chains are adsorbed on a solid substrate and the linear chains are covered on the loop chains. It is found that there is an optimal K_loop, which strongly confines the motion of the linear chains. Meanwhile, compared to increasing the rigidity of the loop chains, increasing the length of the loop chains can more effectively confine the motion of the linear chains. More interestingly, we observe that the mismatch of the length (ΔN) and rigidity (ΔK) between the loop and linear chains leads to dynamic asymmetry (ΔD_c). The relationship between the ΔN, ΔK, and ΔD_c are found to follow the mathematical expression of ΔD_c ∼ (ΔN)^α(ΔK)^β, in which the values of α and β are around 4.58 and 0.83, separately. Remarkably, using the Gaussian process regression model, we construct a master curve of diffusion coefficient on the segmental and chain length scales of the linear chains as a function of N_loop and K_loop, which is further validated by our simulated prediction. In general, this work provides a fundamental understanding of polymer interfacial dynamics at the molecular level, enlightening some rational principles for manipulating the physical properties of PUFs.

Universal description of steric hindrance in flexible polymer gels

In this work, the long-time diffusion of a solute in a chemically crosslinked and flexible hydrogel is computed from a bead-spring model of a polymeric network to assess the effect of steric obstruction. The relative diffusivities obtained for a wide variety of systems can be described by an exponential decay depending on a parameter that differs from that employed for rigid gels. The mathematical expression derived here can approximately predict the diffusivity in flexible gels if steric hindrance is the mechanism ruling diffusion.

Optimizing the heterogeneous network structure to achieve polymer nanocomposites with excellent mechanical properties

Designing and optimizing the polymer network structure at the molecular level to manipulate its mechanical properties are of great scientific significance. Although heterogeneous multi-network structures have been extensively investigated, little effort has been devoted to investigating heterogeneous single-networks with a well-defined interface. Herein, through coarse-grained molecular dynamics simulation, we successfully fabricated a heterogeneous single-network, which was divided into several regions with different crosslink densities. Firstly, we found that there is an optimal crosslink density ratio between high and low crosslink density regions to obtain the best stress-strain behavior. Secondly, the effect of the regularity of the network topology (by changing the distribution of two-phase regions) on mechanical properties was also studied. It was clearly observed that the polymer network showed better elastic response and mechanical properties as the distribution of two-phase regions became uniform. Finally, we investigated the effect of the selective distribution of nanoparticles (NPs) on mechanical properties by introducing NPs into a pre-designed multiphase network. Results showed that the selective distribution of NPs in the high crosslink density region had a more significant effect on the mechanical reinforcement. Generally, our simulated results may provide some guidelines to design polymer network structures to achieve high-performance polymer nanocomposites with excellent mechanical properties.

Tracer Diffusion in Tightly-Meshed Homogeneous Polymer Networks: A Brownian Dynamics Simulation Study

We report Brownian dynamics simulations of tracer diffusion in regularly crosslinked polymer networks in order to elucidate the transport of a tracer particle in polymer networks. The average mesh size of homogeneous polymer networks is varied by assuming different degrees of crosslinking or swelling, and the size of a tracer particle is comparable to the average mesh size. Simulation results show subdiffusion of a tracer particle at intermediate time scales and normal diffusion at long times. In particular, the duration of subdiffusion is significantly prolonged as the average mesh size decreases with increasing degree of crosslinking, for which long-time diffusion occurs via the hopping processes of a tracer particle after undergoing rattling motions within a cage of the network mesh for an extended period of time. On the other hand, the cage dynamics and hopping process are less pronounced as the mesh size decreases with increasing polymer volume fractions. The interpretation is provided in terms of fluctuations in network mesh size: at higher polymer volume fractions, the network fluctuations are large enough to allow for collective, structural changes of network meshes, so that a tracer particle can escape from the cage, whereas, at lower volume fractions, the fluctuations are so small that a tracer particle remains trapped within the cage for a significant period of time before making infrequent jumps out of the cage. This work suggests that fluctuation in mesh size, as well as average mesh size itself, plays an important role in determining the dynamics of molecules and nanoparticles that are embedded in tightly meshed polymer networks.