Temperature-Dependent Suppression of Polymer Diffusion in Polymer Nanocomposites

Temperature-mediated diffusion of nanoparticles in semidilute polymer solutions

The temperature is often a critical factor affecting the diffusion of nanoparticles in complex physiological media, but its specific effects are still to be fully understood. Here, we constructed a temperature-regulated model of semidilute polymer solution and experimentally investigated the temperature-mediated diffusion of nanoparticles using the particle tracking method. By examining the ensemble-averaged mean square displacements (MSDs), we found that the MSD grows gradually as the temperature increases while the transition time from sublinear to linear stage in MSD decreases. Meanwhile, the temperature-dependent measured diffusivity of the nanoparticles shows an exponential growth. We revealed that these temperature-mediated changes are determined by the composite effect of the macroscale property of polymer solution and the microscale dynamics of polymer chain as well as nanoparticles. Furthermore, the measured non-Gaussian displacement probability distributions were found to exhibit non-Gaussian fat tails, and the tailed distribution is enhanced as the temperature increases. The non-Gaussianity was calculated and found to vary in the same trend with the tailed distribution, suggesting the occurrence of hopping events. This temperature-mediated non-Gaussian feature validates the recent theory of thermally induced activated hopping. Our results highlight the temperature-mediated changes in diffusive transport of nanoparticles in polymer solutions and may provide the possible strategy to improve drug delivery in physiological media.

When does a macromolecule transition from a polymer chain to a nanoparticle?

Frequently, the defining characteristic of a nanoparticle is simply its size, where objects that are 1-100 nm are characterized as nanoparticles. However, synthetic and biological macromolecules, in particular high molecular weight chains, can satisfy this size requirement without providing the same phenomena as one would expect from a nanoparticle. At the same time, soft polymer nanoparticles are important in a broad range of fields, including understanding protein folding, drug delivery, vitrimers, catalysis and nanomedicine. Moreover, the recent flourish of all polymer nanocomposites has led to the synthesis of soft all-polymer nanoparticles, which emerge from internal crosslinking of a macromolecule. Thus, there exists a transition of an internally crosslinked macromolecule from a polymer chain to a nanoparticle as the amount of internal crosslinks increases, where the polymer chain exhibits different behavior than the nanoparticle. Yet, this transition is not well understood. In this work, we seek to address this knowledge gap and determine the transition of a macromolecule from a polymer chain to a nanoparticle as internal crosslinking increases. In this work, small angle neutron scattering (SANS) offers insight into the structure of polystyrene and poly(ethyl hexyl methacrylate) nanostructures in dilute solutions, with crosslinking densities that vary from 0.1 to 10.7%. Analyses of the SANS data provides structural characteristics to classify a nanostructure as chain-like or particle-like and identify a crosslinking dependent transition between the two morphologies. It was found that for both types of polymeric nanostructures, a crosslinking density of 0.81% (∼ a crosslink for every 1 in 125 monomers) or higher exhibit clear particle-like behavior. Lower crosslinking density nanostructures showed amounts of collapse similar to that of a star polymer (0.1% XL) or a random walk polymer chain (0.4% XL). Thus, the transition of an internally crosslinked macromolecule from a polymer chain to a nanoparticle is not an abrupt transition but occurs via the gradual contraction of the chain with incorporated crosslinks.

Collective Nanoparticle Dynamics Associated with Bridging Network Formation in Model Polymer Nanocomposites

The addition of nanoparticles (NPs) to polymers is a powerful method to improve the mechanical and other properties of macromolecular materials. Such hybrid polymer-particle systems are also rich in fundamental soft matter physics. Among several factors contributing to mechanical reinforcement, a polymer-mediated NP network is considered to be the most important in polymer nanocomposites (PNCs). Here, we present an integrated experimental-theoretical study of the collective NP dynamics in model PNCs using X-ray photon correlation spectroscopy and microscopic statistical mechanics theory. Silica NPs dispersed in unentangled or entangled poly(2-vinylpyridine) matrices over a range of NP loadings are used. Static collective structure factors of the NP subsystems at temperatures above the bulk glass transition temperature reveal the formation of a network-like microstructure via polymer-mediated bridges at high NP loadings above the percolation threshold. The NP collective relaxation times are up to 3 orders of magnitude longer than the self-diffusion limit of isolated NPs and display a rich dependence with observation wavevector and NP loading. A mode-coupling theory dynamical analysis that incorporates the static polymer-mediated bridging structure and collective motions of NPs is performed. It captures well both the observed scattering wavevector and NP loading dependences of the collective NP dynamics in the unentangled polymer matrix, with modest quantitative deviations emerging for the entangled PNC samples. Additionally, we identify an unusual and weak temperature dependence of collective NP dynamics, in qualitative contrast with the mechanical response. Hence, the present study has revealed key aspects of the collective motions of NPs connected by polymer bridges in contact with a viscous adsorbing polymer medium and identifies some outstanding remaining challenges for the theoretical understanding of these complex soft materials.

Polymer-Infiltrated Nanoparticle Films Using Capillarity-Based Techniques: Toward Multifunctional Coatings and Membranes

Polymer-infiltrated nanoparticle films (PINFs) are a new class of nanocomposites that offer synergistic properties and functionality derived from unusually high fractions of nanomaterials. Recently, two versatile techniques,capillary rise infiltration (CaRI) and solvent-driven infiltration of polymer (SIP), have been introduced that exploit capillary forces in films of densely packed nanoparticles. In CaRI, a highly loaded PINF is produced by thermally induced wicking of polymer melt into the nanoparticle packing pores. In SIP, exposure of a polymer-nanoparticle bilayer to solvent vapor atmosphere induces capillary condensation of solvent in the pores of nanoparticle packing, leading to infiltration of polymer into the solvent-filled pores. CaRI/SIP PINFs show superior properties compared with polymer nanocomposite films made using traditional methods, including superb mechanical properties, thermal stability, heat transfer, and optical properties. This review discusses fundamental aspects of the infiltration process and highlights potential applications in separations, structural coatings, and polymer upcycling-a process to convert polymer wastes into useful chemicals.

A novel shift in the glass transition temperature of polymer nanocomposites: a molecular dynamics simulation study

The effect of the loading of nanoparticles on the glass transition temperature, Tg, of polymer nanocomposites is studied by using molecular dynamics simulations. Tg is estimated from the variation of system volume with temperature and the temperature-dependent diffusion of the polymer described by the Vogel-Fulcher-Tammann law. The estimated values of Tg from the two methods are consistent with each other. Results show that Tg can be regulated by changing the volume fraction of nanoparticles, fNP. A novel shift in Tg is observed, that is, Tg increases with fNP at fNP < , while it decreases with increasing fNP at fNP > . The basic mechanism behind the novel shift in Tg is the competition between the attraction of nanoparticles towards polymer chains and the fast diffusion of nanoparticles. The increase in Tg at low fNP is due to the attraction of nanoparticles, whereas the decrease in Tg at high fNP is attributed to the fast diffusion of nanoparticles. The diffusion of the polymer above Tg is also investigated. The diffusion of the polymer decreases with increasing fNP below and increases with fNP above , in agreement with the variation of Tg.

Theory of polymer diffusion in polymer-nanoparticle mixtures: effect of nanoparticle concentration and polymer length

The dynamics of polymer-nanoparticle (NP) mixtures, which involves multiple scales and system-specific variables, has posed a long-standing challenge on its theoretical description. In this paper, we construct a microscopic theory for polymer diffusion in mixtures based on a combination of the generalized Langevin equation, mode-coupling approach, and polymer physics ideas. The parameter-free theory has an explicit expression and remains tractable on a pair correlation level with system-specific equilibrium structures as input. Taking a minimal polymer-NP mixture as an example, our theory correctly captures the dependence of polymer diffusion on NP concentration and average interparticle distance. Importantly, the polymer diffusion exhibits a power law decay as the polymer length increases at dense NPs and/or a long chain, which marks the emergence of entanglement-like motion. The work provides a first-principles theoretical foundation to investigate dynamic problems in diverse polymer nanocomposites.

Diffusion in a biased washboard potential revisited

The celebrated Sutherland-Einstein relation for systems at thermal equilibrium states that spread of trajectories of Brownian particles is an increasing function of temperature. Here, we scrutinize the diffusion of underdamped Brownian motion in a biased periodic potential and analyze regimes in which a diffusion coefficient decreases with increasing temperature within a finite temperature window. Comprehensive numerical simulations of the corresponding Langevin equation performed with unprecedented resolution allow us to construct a phase diagram for the occurrence of the nonmonotonic temperature dependence of the diffusion coefficient. We discuss the relation of the later effect with the phenomenon of giant diffusion.

Diffusivity and glass transition of polymer chains in polymer nanocomposites

The diffusivity and glass transition of polymer chains in polymer nanocomposites are studied by using dynamic Monte Carlo simulation. Nanoparticles are modeled as immobile and distributed in a cubic lattice in the system. The diffusion coefficient D of polymer chains is reduced, while the glass transition temperature Tg is increased by nanoparticles. Our results show that the effect of nanoparticles can be summarized as D = D0[1 - exp(-α·ID/2Rg)] and Tg = Tg,0[1 - exp(-α·ID/2Rg)]-1, with D0 and Tg,0 being the diffusion coefficient and the glass transition temperature in the absence of nanoparticles, Rg the radius of gyration of polymer chains, and ID the surface spacing between nearest-neighbor nanoparticles. The parameter α that governs the dynamics of polymer chains decreases with increasing nanoparticles' size or decreasing the temperature. Our results also show that smaller nanoparticles exert a stronger influence on the polymer dynamics at the same concentration of nanoparticles, whereas larger nanoparticles show a stronger effect at the same ID.

Nanoscale Particle Motion Reveals Polymer Mobility Gradient in Nanocomposites

Polymer mobility near nanoparticle surfaces has been extensively discussed; however, direct experimental observation in the nanocomposite melts has been a difficult task. Here, by taking advantage of large dynamical asymmetry between the miscible matrix and surface-bound polymers, we highlighted their interphases and studied the resulting effect on the nanoparticle relaxation using X-ray photon correlation spectroscopy. The local mobility gradient is signified by an unprecedented increase in the relaxation time at length scales on the order of polymer radius of gyration. The effect is accompanied by a transition from simple diffusive to subdiffusive behavior in accord with viscous and entangled dynamics of polymers in the matrix and in the interphase, respectively. Our results demonstrate that the nanoparticle-induced polymer mobility changes in the interphases of nanocomposite melts can be extracted from the length-scale-dependent slow particle motion.

Modeling of Entangled Polymer Diffusion in Melts and Nanocomposites: A Review

This review concerns modeling studies of the fundamental problem of entangled (reptational) homopolymer diffusion in melts and nanocomposite materials in comparison to experiments. In polymer melts, the developed united atom and multibead spring models predict an exponent of the molecular weight dependence to the polymer diffusion very similar to experiments and the tube reptation model. There are rather unexplored parameters that can influence polymer diffusion such as polymer semiflexibility or polydispersity, leading to a different exponent. Models with soft potentials or slip-springs can estimate accurately the tube model predictions in polymer melts enabling us to reach larger length scales and simulate well entangled polymers. However, in polymer nanocomposites, reptational polymer diffusion is more complicated due to nanoparticle fillers size, loading, geometry and polymer-nanoparticle interactions.

Effect of Crosslinker Length and Architecture on the Thermomechanical Properties of CNT-Loaded Elastomeric Polymer Matrix Composites

An evolving understanding of elastomeric polymer nanocomposites continues to expand commercial, defense, and industrial products and applications. This work explores the thermomechanical properties of elastomeric nanocomposites prepared from bisphenol A diglycidyl ether and three amine-terminated poly(propylene oxides) (Jeffamines). The Jeffamines investigated include difunctional crosslinkers with molecular weights of 2000 and 4000 g mol^-1 and a trifunctional crosslinker with a molecular weight of 3000 g mol^-1 . Additionally, carbon nanotubes (CNTs) are added, up to 1.25 wt%, to each thermoset. The findings indicate that the T _g and storage modulus of the polymer nanocomposites can be controlled independently within narrow concentration windows, and that effects observed following CNT incorporation are dependent on the crosslinker molecular weight. Finally, the impact of crosslinker length and architecture as well as CNT addition on the molecular weight between crosslink points in the glassy and rubbery states are discussed.

Effects of polymer-nanoparticle interactions on the viscosity of unentangled polymers under extreme nanoconfinement during capillary rise infiltration

We explore the effect of confinement and polymer-nanoparticle interactions on the viscosity of unentangled polymers undergoing capillary rise infiltration (CaRI) in dense packings of nanoparticles. In CaRI, a polymer is thermally induced to wick into the dense packings of nanoparticles, leading to the formation of polymer-infiltrated nanoparticle films, a new class of thin film nanocomposites with extremely high concentrations of nanoparticles. To understand the effect of this extreme nanoconfinement, as well as polymer-nanoparticle interactions on the polymer viscosity in CaRI films, we use two polymers that are known to have very different interactions with SiO2 nanoparticles. Using in situ spectroscopic ellipsometry, we monitor the polymer infiltration process, from which we infer the polymer viscosity based on the Lucas-Washburn model. Our results suggest that physical confinement increases the viscosity by approximately two orders of magnitude. Furthermore, confinement also increases the glass transition temperature of both polymers. Thus, under extreme nanoconfinement, the physical confinement has a more significant impact than the polymer-nanoparticle interactions on the viscosity of unentangled polymers, measured through infiltration dynamics, as well as the glass transition temperature. These findings will provide fundamental frameworks for designing processes to enable the fabrication of CaRI nanocomposite films with a wide range of nanoparticles and polymers.

Nanoscale Particle Motion in Attractive Polymer Nanocomposites

Using x-ray photon correlation spectroscopy, we examined the slow nanoscale motion of silica nanoparticles individually dispersed in an entangled poly (ethylene oxide) melt at particle volume fractions up to 42%. The nanoparticles, therefore, serve as both fillers for the resulting attractive polymer nanocomposites and probes for the network dynamics therein. The results show that the particle relaxation closely follows the mechanical reinforcement in the nanocomposites only at the intermediate concentrations below the critical value for the chain confinement. Quite unexpectedly, the relaxation time of the particles does not further slow down at higher volume fractions-when all chains are practically on the nanoparticle interface-and decouples from the elastic modulus of the nanocomposites that further increases orders of magnitude.

Brownian ratchets: How stronger thermal noise can reduce diffusion

We study diffusion properties of an inertial Brownian motor moving on a ratchet substrate, i.e., a periodic structure with broken reflection symmetry. The motor is driven by an unbiased time-periodic symmetric force that takes the system out of thermal equilibrium. For selected parameter sets, the system is in a non-chaotic regime in which we can identify a non-monotonic dependence of the diffusion coefficient on temperature: for low temperature, it initially increases as the temperature grows, passes through its local maximum, next starts to diminish reaching its local minimum, and finally it monotonically increases in accordance with the Einstein linear relation. Particularly interesting is the temperature interval in which diffusion is suppressed by the thermal noise, and we explain this effect in terms of transition rates of a three-state stochastic model.

Squishy nanotraps: hybrid cellulose nanocrystal-zirconium metallogels for controlled trapping of biomacromolecules

A brick-and-mortar-like ultrasoft nanocomposite metallogel is formed by crosslinking cellulose nanocrystals (CNC) with ammonium zirconium carbonate (AZC) to trap and reconfigure dextran, a model biomacromolecule.

A study on the diffusivity of polymers in crowded environments with periodically distributed nanoparticles

Two novel diffusion behaviors of polymers at low temperature: a minimum at an intermediate inter-particle distance and oscillation with polymer length.