Diffusion of Nanoparticles with Activated Hopping in Crowded Polymer Solutions

Navigating the future: Microfluidics charting new routes in drug delivery

Microfluidics has emerged as a transformative force in the field of drug delivery, offering innovative avenues to produce a diverse range of nano drug delivery systems. Thanks to its precise manipulation of small fluid volumes and its exceptional command over the physicochemical characteristics of nanoparticles, this technology is notably able to enhance the pharmacokinetics of drugs. It has initiated a revolutionary phase in the domain of drug delivery, presenting a multitude of compelling advantages when it comes to developing nanocarriers tailored for the delivery of poorly soluble medications. These advantages represent a substantial departure from conventional drug delivery methodologies, marking a paradigm shift in pharmaceutical research and development. Furthermore, microfluidic platformsmay be strategically devised to facilitate targeted drug delivery with the objective of enhancing the localized bioavailability of pharmaceutical substances. In this paper, we have comprehensively investigated a range of significant microfluidic techniques used in the production of nanoscale drug delivery systems. This comprehensive review can serve as a valuable reference and offer insightful guidance for the development and optimization of numerous microfluidics-fabricated nanocarriers.

Nonspecific membrane-matrix interactions influence diffusivity of lipid vesicles in hydrogels

The diffusion of extracellular vesicles and liposomes in vivo is affected by different tissue environmental conditions and is of great interest in the development of liposome-based therapeutics and drug-delivery systems. Here, we use a bottom-up biomimetic approach to better isolate and study steric and electrostatic interactions and their influence on the diffusivity of synthetic large unilamellar vesicles in hydrogel environments. Single-particle tracking of these extracellular vesicle-like particles in agarose hydrogels as an extracellular matrix model shows that membrane deformability and surface charge affect the hydrogel pore spaces that vesicles have access to, which determines overall diffusivity. Moreover, we show that passivation of vesicles with PEGylated lipids, as often used in drug-delivery systems, enhances diffusivity, but that this effect cannot be fully explained with electrostatic interactions alone. Finally, we compare our experimental findings with existing computational and theoretical work in the field to help explain the nonspecific interactions between diffusing particles and gel matrix environments.

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.

Triggering Gaussian-to-Exponential Transition of Displacement Distribution in Polymer Nanocomposites via Adsorption-Induced Trapping

In many disordered systems, the diffusion of classical particles is described by a displacement distribution P(x, t) that displays exponential tails instead of Gaussian statistics expected for Brownian motion. However, the experimental demonstration of control of this behavior by increasing the disorder strength has remained challenging. In this work, we explore the Gaussian-to-exponential transition by using diffusion of poly(ethylene glycol) (PEG) in attractive nanoparticle-polymer mixtures and controlling the volume fraction of the nanoparticles. In this work, we find "knobs", namely nanoparticle concentration and interaction, which enable the change in the shape of P(x,t) in a well-defined way. The Gaussian-to-exponential transition is consistent with a modified large deviation approach for a continuous time random walk and also with Monte Carlo simulations involving a microscopic model of polymer trapping via reversible adsorption to the nanoparticle surface. Our work bears significance in unraveling the fundamental physics behind the exponential decay of the displacement distribution at the tails, which is commonly observed in soft materials and nanomaterials.

Single-Particle Tracking in Poly(Ethylene Glycol) Diacrylate: Probe Size Effect on the Diffusion Behaviors of Nanoparticles in Unentangled Polymer Solutions

A thorough understanding of the relevant factors governing the transport of nanoparticles in poly(ethylene glycol) diacrylate (PEGDA) is crucial for many applications utilizing this polymer. Here, single-particle tracking (SPT) was used to systematically investigate the role of the probe size (3-200 nm) on the diffusion behaviors of individual fluorescent nanoparticles in semidilute and unentangled PEGDA solutions. The quantitative assessment of the SPT data via the recorded single-particle trajectories and diffusion coefficients (D) not only showed that the observed probe dynamics in PEGDA were temporally and spatially heterogeneous, but more importantly that the measured D were observed to be significantly reduced (vs in solvent) and strongly size-dependent. We explained these results based on a modified multiscale model for particle diffusion, built upon well-established hydrodynamics and obstruction theories. We furthermore showed that the presence of steric interactions and probe confinement effects in highly crowded, unentangled PEGDA microstructures can lead to deviations in the single-particle displacements from the expected Gaussian behavior, as revealed by the van Hove displacement distributions and the associated non-Gaussian parameters. This study has demonstrated the power of SPT methods in offering an advanced characterization of the transport characteristics in complex polymer structures, overcoming challenges posed by traditional characterization techniques.

Microfluidics for nano-drug delivery systems: From fundamentals to industrialization

In recent years, owing to the miniaturization of the fluidic environment, microfluidic technology offers unique opportunities for the implementation of nano drug delivery systems (NDDSs) production processes. Compared with traditional methods, microfluidics improves the controllability and uniformity of NDDSs. The fast mixing and laminar flow properties achieved in the microchannels can tune the physicochemical properties of NDDSs, including particle size, distribution and morphology, resulting in narrow particle size distribution and high drug-loading capacity. The success of lipid nanoparticles encapsulated mRNA vaccines against coronavirus disease 2019 by microfluidics also confirmed its feasibility for scaling up the preparation of NDDSs via parallelization or numbering-up. In this review, we provide a comprehensive summary of microfluidics-based NDDSs, including the fundamentals of microfluidics, microfluidic synthesis of NDDSs, and their industrialization. The challenges of microfluidics-based NDDSs in the current status and the prospects for future development are also discussed. We believe that this review will provide good guidance for microfluidics-based NDDSs.

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.

Non-Gaussian Diffusion Near Surfaces

We study the diffusion of particles confined close to a single wall and in double-wall planar channel geometries where the local diffusivities depend on the distance to the boundaries. Displacement parallel to the walls is Brownian as characterized by its variance, but it is non-Gaussian having a nonzero fourth cumulant. Establishing a link with Taylor dispersion, we calculate the fourth cumulant and the tails of the displacement distribution for general diffusivity tensors along with potentials generated by either the walls or externally, for instance, gravity. Experimental and numerical studies of the motion of a colloid in the direction parallel to the wall give measured fourth cumulants which are correctly predicted by our theory. Interestingly, contrary to models of Brownian-yet-non-Gaussian diffusion, the tails of the displacement distribution are shown to be Gaussian rather than exponential. All together, our results provide additional tests and constraints for the inference of force maps and local transport properties near surfaces.

Electro-optical Study of the Anomalous Rotational Diffusion in Polymer Solutions

Brownian diffusion of spherical nanoparticles is usually exploited to ascertain the rheological properties of complex media. However, the behavior of the tracer particles is affected by a number of phenomena linked to the interplay between the dynamics of the particles and polymer coils. For this reason, the characteristic lengths of the dispersed entities, depletion phenomena, and the presence of sticking conditions have been observed to affect the translational diffusion of the probes. On the other hand, the retardation effect of the host fluid on the rotational diffusion of nonspherical particles is less understood. We explore the possibility of studying this phenomenon by analyzing the electro-orientation of the particles in different scenarios in which we vary the ratio between the particle and polymer characteristic size, and the geometry of the particles, including both elongated and oblate shapes. We find that the Stokes-Einstein relation only applies if the radius of gyration of the polymer is much shorter than the particle size and when some repulsive interaction between both is present.

Hopping Behavior Mediates the Anomalous Confined Diffusion of Nanoparticles in Porous Hydrogels

Diffusion is an essential means of mass transport in porous materials such as hydrogels, which are appealing in various biomedical applications. Herein, we investigate the diffusive motion of nanoparticles (NPs) in porous hydrogels to provide a microscopic view of confined diffusion. Based on the mean square displacement from particle tracking experiments, we elucidate the anomalous diffusion dynamics of the embedded NPs and reveal the heterogeneous pore structures in hydrogels. The results demonstrate that diffusive NPs can intermittently escape from single pores through void connective pathways and exhibit non-Gaussian displacement probability distribution. We simulate this scenario using the Monte Carlo method and clarify the existence of hopping events in porous diffusion. The resultant anomalous diffusion can be fully depicted by combining the hopping mechanism and the hydrodynamic effect. Our results highlight the hopping behavior through the connective pathways and establish a hybrid model to predict NP transport in porous environments.

Heterogeneous Nanostructures Cause Anomalous Diffusion in Lipid Monolayers

The diffusion and mobility in biomembranes are crucial for various cell functions; however, the mechanisms involved in such processes remain ambiguous due to the complex membrane structures. Herein, we investigate how the heterogeneous nanostructures cause anomalous diffusion in dipalmitoylphosphatidylcholine (DPPC) monolayers. By identifying the existence of condensed nanodomains and clarifying their impact, our findings renew the understanding of the hydrodynamic description and the statistical feature of the diffusion in the monolayers. We find a universal characteristic of the multistage mean square displacement (MSD) with an intermediate crossover, signifying two membrane viscosities at different scales: the short-time scale describes the local fluidity and is independent of the nominal DPPC density, and the long-time scale represents the global continuous phase taking into account nanodomains and increases with DPPC density. The constant short-time viscosity reflects a dynamic equilibrium between the continuous fluid phase and the condensed nanodomains in the molecular scale. Notably, we observe an "anomalous yet Brownian" phenomenon exhibiting an unusual double-peaked displacement probability distribution (DPD), which is attributed to the net dipolar repulsive force from the heterogeneous nanodomains around the microdomains. The findings provide physical insights into the transport of membrane inclusions that underpin various biological functions and drug deliveries.

A prediction model for nanoparticle diffusion behavior in fibrous materials considering steric and hydrodynamic resistances

Precise prediction of the hindered diffusion behavior of electroneutral particles in fibrous media plays a critical role in the development of drugs, polymer membranes, and porous electrodes. However, the random microstructure and unknown coupling relationship of multiple resistance mechanisms lead to the lack of a universal prediction model. In this work, a dual-resistance model is proposed by reconstructed pore-scale simulations, which presents the coexistence of steric and hydrodynamic resistances in the multiplication form. The simulation results show that the relationship between steric resistance and structural parameters (porosity, fiber radius, and particle radius) is exponential, while that for hydrodynamic resistance is polynomial. The dominant diffusion resistance is found to change from hydrodynamic to steric resistance with a decrease in porosity. The fluorescent polystyrene microsphere diffusivity in a series of SiO₂ fibrous media is determined by single-particle tracking experiments, quantitatively confirming the dual-resistance model. The present model can be used for rapid diffusivity prediction and fibrous membrane and drug design.

Impact of Chain Conformation on Structural Heterogeneity in Polymer Network

Polymer networks generally consist of an ensemble of single chains. However, understanding how chain conformation affects the structure and properties of polymer networks remains a challenge for optimizing their functionality. Here, we present the fabrication and comparative study of a polymer network composed of collapsed self-entangled chains (intrachain entangled network) and a standard polymer network in which random-coil chains are entangled with each other (interchain entangled network). For poly(methyl methacrylate) thin films composed of these networks, we coupled solvent vapor swelling and single-molecule tracking techniques to examine the anomalies in the dynamics of a small-molecular probe included in the system. We demonstrate that when compared to the interchain entangled network the intrachain one exhibits a more substantial structural heterogeneity, particularly under highly crowded conditions. This network also exhibits physical compactness, which keeps the heterogeneous network structure frozen over time and impedes network plasticization through solvent uptake by the film.

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.

Molecular diffusion in ternary poly(vinyl alcohol) solutions

The diffusion kinetics of a molecular probe—rhodamine B—in ternary aqueous solutions containing poly(vinyl alcohol), glycerol, and surfactants was investigated using fluorescence correlation spectroscopy and dynamic light scattering. We show that the diffusion characteristics of rhodamine B in such complex systems is determined by a synergistic effect of molecular crowding and intermolecular interactions between chemical species. The presence of glycerol has no noticeable impact on rhodamine B diffusion at low concentration, but significantly slows down the diffusion of rhodamine B above 3.9% (w/v) due to a dominating steric inhibition effect. Furthermore, introducing surfactants (cationic/nonionic/anionic) to the system results in a decreased diffusion coefficient of the molecular probe. In solutions containing nonionic surfactant, this can be explained by an increased crowding effect. For ternary poly(vinyl alcohol) solutions containing cationic or anionic surfactant, surfactant—polymer and surfactant—rhodamine B interactions alongside the crowding effect of the molecules slow down the overall diffusivity of rhodamine B. The results advance our insight of molecular migration in a broad range of industrial complex formulations that incorporate multiple compounds, and highlight the importance of selecting the appropriate additives and surfactants in formulated products.

Local Confinement Controls Diffusive Nanoparticle Dynamics in Semidilute Polyelectrolyte Solutions

We investigate the mobility of polystyrene particles ranging from 100 to 790 nm in diameter in dilute and semidilute sodium polystyrene sulfonate (NaPSS) solutions using fluorescence microscopy. We tune the polymer conformations by varying the ionic strength of the solution. The nanoparticle mean-squared displacements evolve linearly with time at all time scales, indicating Fickian diffusive dynamics. In solutions of high ionic strength, chains adopt a random walk conformation and particle dynamics couple to the bulk zero-shear rate viscosity, according to the Stokes-Einstein picture. In solutions of low ionic strength, however, particle dynamics nonmonotonically deviate from bulk predictions as polymer concentration increases and are not accurately predicted by the available models. These nonmonotonic dynamics directly correlate with the non-Gaussianity in distributions of particle displacements, suggesting the emergence of a local confining length scale as polyelectrolyte concentration increases.

Large Deviations for Continuous Time Random Walks

Recently observation of random walks in complex environments like the cell and other glassy systems revealed that the spreading of particles, at its tails, follows a spatial exponential decay instead of the canonical Gaussian. We use the widely applicable continuous time random walk model and obtain the large deviation description of the propagator. Under mild conditions that the microscopic jump lengths distribution is decaying exponentially or faster i.e., Lévy like power law distributed jump lengths are excluded, and that the distribution of the waiting times is analytical for short waiting times, the spreading of particles follows an exponential decay at large distances, with a logarithmic correction. Here we show how anti-bunching of jump events reduces the effect, while bunching and intermittency enhances it. We employ exact solutions of the continuous time random walk model to test the large deviation theory.