Diffusion of Nanoparticles in Semidilute Polymer Solutions: Effect of Different Length Scales

The Influence of Local Constraints on Solvent Motion in Polymer Materials

The influence of obstacles in the form of polymer chains on the diffusion of a low-molecular-weight solvent was the subject of this research. Studies were performed by computer simulations. A Monte Carlo model-the Dynamic Lattice Liquid algorithm-based on the idea of cooperative movements was used. The tested materials were polymer networks with an ideal structure (with a uniform mesh size) and real, irregular networks (with a non-uniform mesh size) obtained numerically by copolymerization. The diffusion of the solvent was analyzed in systems with a polymer concentration that did not exceed 16%. The influence of the polymer concentration and macromolecular architecture structure on the mobility and character of the motion of the solvent was discussed. The influence of irregular network morphology on solvent dynamics appeared to be significantly stronger than that of regular networks and star-like polymers.

Dynamics of Single-Chain Nanoparticles under Crowding: A Neutron Spin Echo Study

We present a neutron spin echo (NSE) investigation to examine the impact of macromolecular crowding on the dynamics of single-chain nanoparticles (SCNPs), serving as synthetic models for biomacromolecules with flexibility and internal degrees of freedom, such as intrinsically disordered proteins (IDPs). In particular, we studied the dynamics of a medium-size poly(methyl methacrylate) (PMMA)-based SCNP (33 kDa) in solutions with low- (10 kDa) and high- (100 kDa) molecular weight analogous deuterated PMMA linear crowders. The dynamic structure factors of the SCNPs in dilute solution show certain degrees of freedom, yet the analysis in terms of the Zimm model reveals high internal friction that effectively stiffens the chain-a phenomenon also observed for IDPs. Under crowding conditions, the internal dynamics remains essentially unchanged, but the center-of-mass diffusion slows down. The effective viscosity felt by the SCNPs at the timescales probed by NSE is lower than the macroscopic viscosity of the crowder solution, and it does not depend significantly on the molecular weight.

From Nature-Sourced Polysaccharide Particles to Advanced Functional Materials

Polysaccharides constitute over 90% of the carbohydrate mass in nature, which makes them a promising feedstock for manufacturing sustainable materials. Polysaccharide particles (PSPs) are used as effective scavengers, carriers of chemical and biological cargos, and building blocks for the fabrication of macroscopic materials. The biocompatibility and degradability of PSPs are advantageous for their uses as biomaterials with more environmental friendliness. This review highlights the progresses in PSP applications as advanced functional materials, by describing PSP extraction, preparation, and surface functionalization with a variety of functional groups, polymers, nanoparticles, and biologically active species. This review also outlines the fabrication of PSP-derived macroscopic materials, as well as their applications in soft robotics, sensing, scavenging, water harvesting, drug delivery, and bioengineering. The paper is concluded with an outlook providing perspectives in the development and applications of PSP-derived materials.

Universal scaling of the diffusivity of dendrimers in a semidilute solution of linear polymers

The static and dynamic properties of dendrimers in semidilute solutions of linear chains of comparable size are investigated using Brownian dynamics simulations. The radius of gyration and diffusivity of a wide variety of low generation dendrimers and linear chains in solution follow universal scaling laws independent of their topology. Analysis of the shape functions and internal density of dendrimers shows that they are more spherical than linear chains and have a dense core. At intermediate times, dendrimers become subdiffusive, with an exponent higher than that previously reported for nanoparticles in semidilute polymer solutions. The long-time diffusivity of dendrimers does not follow theoretical predictions for nanoparticles. We propose a new scaling law for the long-time diffusion coefficients of dendrimers which accounts for the fact that, unlike nanoparticles, dendrimers shrink with an increase in background solution concentration. Analysis of the properties of a special case of a higher functionality dendrimer shows a transition from polymer-like to nanoparticle-like behaviour.

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.

Diffusion of gold nanoparticles in porous silica monoliths determined by dynamic light scattering

HYPOTHESIS

The applicability of the dynamic light scattering method for the determination of particle diffusivity under confinement without applying refractive index matching was not adequately explored so far. The confinement effect on particle diffusion in a porous material which is relevant for particle chromatography has also not yet been fully characterized.

EXPERIMENTS

Dynamic light scattering experiments were performed for unimodal dispersions of 11-mercaptoundecanoic acid-capped gold nanoparticles. Diffusion coefficients of gold nanoparticles in porous silica monoliths were determined without limiting refractive index matching fluids. Comparative experiments were also performed with the same nanoparticles and porous silica monolith but applying refractive index matching.

FINDINGS

Two distinct diffusivities could be determined inside the porous silica monolith, both smaller than that in free media, showing a slowing-down of the diffusion processes of nanoparticles under confinement. While the larger diffusivity can be related to the slightly slowed-down diffusion of particles in the bulk of the pores and in the necks connecting individual pores, the smaller diffusivity might be related to the diffusion of particles near the pore walls. It shows that the dynamic light scattering method with a heterodyne detection scheme can be used as a reliable and competitive tool for determining particle diffusion under confinement.

Diffusion 19F-NMR of Nanofluorides: In Situ Quantification of Colloidal Diameters and Protein Corona Formation in Solution

The NMR-detectability of elements of organic ligands that stabilize colloidal inorganic nanocrystals (NCs) allow the study of their diffusion characteristics in solutions. Nevertheless, these measurements are sensitive to dynamic ligand exchange and often lead to overestimation of diffusion coefficients of dispersed colloids. Here, we present an approach for the quantitative assessment of the diffusion properties of colloidal NCs based on the NMR signals of the elements of their inorganic cores. Benefiting from the robust ¹⁹F-NMR signals of the fluorides in the core of colloidal CaF₂ and SrF₂, we show the immunity of ¹⁹F-diffusion NMR to dynamic ligand exchange and, thus, the ability to quantify, with high accuracy, the colloidal diameters of different types of nanofluorides in situ. With the demonstrated ability to characterize the formation of protein corona at the surface of nanofluorides, we envision that this study can be extended to additional formulations and applications.

Crowding and confinement act in concert to slow DNA diffusion within cell-sized droplets

Dynamics of biological macromolecules, such as DNA, in crowded and confined environments are critical to understanding cellular processes such as transcription, infection, and replication. However, the combined effects of cellular confinement and crowding on macromolecular dynamics remain poorly understood. Here, we use differential dynamic microscopy to investigate the diffusion of large DNA molecules confined in cell-sized droplets and crowded by dextran polymers. We show that confined and crowded DNA molecules exhibit universal anomalous subdiffusion with scaling that is insensitive to the degree of confinement and crowding. However, effective DNA diffusion coefficients Deff decrease up to 2 orders of magnitude as droplet size decreases—an effect that is enhanced by increased crowding. We mathematically model the coupling of crowding and confinement by combining polymer scaling theories with confinement-induced depletion effects. The generality and tunability of our system and models render them applicable to elucidating wide-ranging crowded and confined systems.

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DNA diffusion measured in cell-sized droplets with differential dynamic microscopy

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Combination of crowding and confinement leads to subdiffusion and slowing

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Diffusion coefficients of DNA decrease strongly with decreasing droplet size

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Polymer scaling theories and depletion effects predict observed dynamics

Confinement anisotropy drives polar organization of two DNA molecules interacting in a nanoscale cavity

There is growing appreciation for the role phase transition based phenomena play in biological systems. In particular, self-avoiding polymer chains are predicted to undergo a unique confinement dependent demixing transition as the anisotropy of the confined space is increased. This phenomenon may be relevant for understanding how interactions between multiple dsDNA molecules can induce self-organized structure in prokaryotes. While recent in vivo experiments and Monte Carlo simulations have delivered essential insights into this phenomenon and its relation to bacteria, there are fundamental questions remaining concerning how segregated polymer states arise, the role of confinement anisotropy and the nature of the dynamics in the segregated states. To address these questions, we introduce an artificial nanofluidic model to quantify the interactions of multiple dsDNA molecules in cavities with controlled anisotropy. We find that two dsDNA molecules of equal size confined in an elliptical cavity will spontaneously demix and orient along the cavity poles as cavity eccentricity is increased; the two chains will then swap pole positions with a frequency that decreases with increasing cavity eccentricity. In addition, we explore a system consisting of a large dsDNA molecule and a plasmid molecule. We find that the plasmid is excluded from the larger molecule and will exhibit a preference for the ellipse poles, giving rise to a non-uniform spatial distribution in the cavity that may help explain the non-uniform plasmid distribution observed during in vivo imaging of high-copy number plasmids in bacteria.

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.

Transport of a self-propelled tracer through a hairy cylindrical channel: interplay of stickiness and activity

Active transport of biomolecules assisted by motor proteins is imperative for the proper functioning of cellular activities. Inspired by the diffusion of active agents in crowded cellular channels, we computationally investigate the transport of an active tracer through a polymer grafted cylindrical channel by varying the activity of the tracer and stickiness of the tracer to the polymers. Our results reveal that the passive tracer exhibits profound subdiffusion with increasing stickiness by exploring deep into the grafted polymeric zone, while purely repulsive one prefers to diffuse through the pore-like space created along the cylindrical axis of the channel. In contrast, the active tracer shows faster dynamics and intermediate superdiffusion even though the tracer preferentially stays close to the dense polymeric region. This observation is further supported by the sharp peaks in the density profile of the probability of radial displacement of the tracer. We discover that the activity plays an important role in deciding the pathway that the tracer takes through the narrow channel. Interestingly, increasing the activity washes out the effect of stickiness. Adding to this, van-Hove functions manifest that the active tracer dynamics deviates from Gaussianity, and the degree of deviation grows with the activity. Our work has direct implications on how effective transportation and delivery of cargo can be achieved through a confined medium where activity, interactions, and crowding are interplaying. Looking ahead, these factors will be crucial for understanding the mechanism of artificial self-powered machines navigating through the cellular channels and performing in vivo challenging tasks.

Effects of Macromolecular Crowding on Nanoparticle Diffusion: New Insights from Mössbauer Spectroscopy

In this work, we used Mössbauer spectroscopy as a new approach for experimental quantification of the self-diffusion coefficient (D_Mössbauer) and hydrodynamic (HD) size of iron-containing nanoparticles (NPs) in complex crowded solutions, mimicking cell cytoplasm. As a probe, we used 9 nm cobalt ferrite NPs (CFNs) dispersed in solutions of bovine serum albumin (BSA) with a volume fraction (φ_BSA) of 0-0.2. Our results show that the broadening of Mössbauer spectra is highly sensitive to the diffusion of CFNs, while when φ_BSA = 0.2, the CFN-normalized diffusivity is reduced by 86% compared to that of a protein-free solution. CFN colloids were also studied by dynamic light scattering (DLS). Comparison of the experimental data shows that DLS significantly underestimates the diffusion coefficient of CFNs and, consequently, overestimates the HD size of CFNs at φ_BSA > 0, which cannot be attributed to the formation of the BSA monolayer on the surface of CFNs.

Non-magnetic shell coating of magnetic nanoparticles as key factor of toxicity for cancer cells in a low frequency alternating magnetic field

This work is devoted to studying the effects of non-magnetic shell coating on nanoparticles in a low frequency alternating magnetic field (LF AMF) on tumor cells in vitro. Two types of iron oxide nanoparticles with the same magnetic core with and without silica shells were synthesized. Nanoparticles with silica shells significantly decreased the viability of PC3 cancer cells in a low frequency alternating magnetic field according to the cytotoxicity test, unlike uncoated nanoparticles. We showed that cell death results from the intracellular membrane integrity failure, and the calcium ions concentration increase with the subsequent necrosis. Transmission electron microscopy images showed that the uncoated silica nanoparticles are primarily found in an aggregated form in cells. We believe that uncoated nanoparticles lose their colloidal stability in an acidic endosomal environment after internalization into the cell due to surface etching and the formation of aggregates. As a result, they encounter high endosomal macromolecular viscosity and become unable to rotate efficiently. We assume that effective rotation of nanoparticles causes cell death. In turn, silica shell coating increases nanoparticles stability, preventing aggregation in endosomes. Thus, we propose that the colloidal stability of magnetic nanoparticles inside cells is one of the key factors for effective magneto-mechanical actuation.

One-photon excited photoluminescence of gold nanospheres and its application in prostate specific antigen detection via fluorescence correlation spectroscopy (FCS)

Gold nanoparticles are known to exhibit appealing intrinsic plasmon-modulated photoluminescence (PL) properties which can be explored in various fluorescence-based sensing applications. In this paper, we evaluate the PL of different-sized gold nanospheres (AuNSs) under one-photon excitation (1PE) and develop a sensitive homogeneous immunoassay for the detection of prostate specific antigen (PSA) in colloidal suspension via fluorescence correlation spectroscopy (FCS). The 1PE PL of AuNSs of three different sizes are evaluated in solution phase under excitation at 405 nm via steady-state fluorescence spectroscopy measurements, while FCS analysis emphasizes the feasibility of using 1PE PL properties to monitor their diffusion behavior. Fluorescence lifetime imaging microscopy (FLIM) assays coupled with PL spectral profile analysis performed on single-particles-like structures conform the plasmonic origin of the detected PL and validate their potential of synthesized AuNSs as fluorescent probes in bioimaging and bioassays. Finally, to the best of our knowledge, we provide the first demonstration of the successful use of the 1PE PL of the synthesized AuNSs as probes for the FCS-based one-step label-free sensitive optical detection of PSA biomarker. The approach consisting in monitoring the diffusion of the AuNSs-oligomers induced by the interaction of anti-PSA-conjugated AuNSs with PSA molecules is successfully validated for the detection of PSA levels as low as 4.4 ng/ml in solution. Considering that the development of rapid, efficient and label-free biosensing methods is of continuous interest nowadays, we are confident that our results may have a strong impact on medicine towards more efficient, sensitive and reliable diagnosis.

Fast nanoparticle rotational and translational diffusion in synovial fluid and hyaluronic acid solutions

Nanoparticles are under investigation as diagnostic and therapeutic agents for joint diseases, such as osteoarthritis. However, there is incomplete understanding of nanoparticle diffusion in synovial fluid, the fluid inside the joint, which consists of a mixture of the polyelectrolyte hyaluronic acid, proteins, and other components. Here, we show that rotational and translational diffusion of polymer-coated nanoparticles in quiescent synovial fluid and in hyaluronic acid solutions is well described by the Stokes-Einstein relationship, albeit with an effective medium viscosity that is much smaller than the macroscopic low shear viscosity of the fluid. This effective medium viscosity is well described by an equation for the viscosity of dilute polymer chains, where the additional viscous dissipation arises because of the presence of the polymer segments. These results shed light on the diffusive behavior of polymer-coated inorganic nanoparticles in complex and crowded biological environments, such as in the joint.

Liquid-Liquid Phase Separation of Peptide/Oligonucleotide Complexes in Crowded Macromolecular Media

The membraneless organelles (MLOs) and coacervates of oppositely charged polyelectrolytes are both formed by liquid-liquid phase separation. To reveal how the crowded cell interior regulates the MLOs, we chose the coacervates formed by peptide S5 and single-stranded oligonucleotide (ss-oligo) at 1:1 charge ratio and investigated the phase separation processes in polyacrylamide (PAM) and poly(ethylene oxide) (PEO) media at varying concentrations. Results show that the droplet formation unit is the neutral primary complex, instead of individual S5 or ss-oligo. Therefore, the coacervation process can be described by the classic theory of nucleation and growth. The dynamic scaling relationships show that S5/ss-oligo coacervation undergoes in sequence the heterogeneous nucleation, diffusion-limited growth, and Brownian motion coalescence with time. The inert crowders generate multiple effects, including accelerating the growth of droplets, weakening the electrostatic attraction, and slowing down or even trapping the droplets in the crowder network. The overall effect is that both the size and size distribution of the droplets decrease with increasing crowder concentration, and the effect of PEO is stronger than that of PAM. Our study provides a further step toward a deeper understanding of the kinetics of MLOs in crowded living cells.

Scale-dependent particle diffusivity and apparent viscosity in polymer solutions as probed by dynamic magnetic nanorheology

In several upcoming rheological approaches, including methods of micro- and nanorheology, the measurement geometry is of critical impact on the interpretation of the results. The relative size of the probe objects employed (as compared to the intrinsic length scales of the sample to be investigated) becomes of crucial importance, and there is increasing interest to investigate the dynamic processes and mobility in nanostructured materials. A combination of different rheological approaches based on the rotation of magnetically blocked nanoprobes is used to systematically investigate the size-dependent diffusion behavior in aqueous poly(ethylene glycol) (PEG) solutions with special attention paid to the relation of probe size to characteristic length scales within the polymer solutions. We employ two types of probe particles: nickel rods of hydrodynamic length L_h between 200 nm and 650 nm, and cobalt ferrite spheres with diameter d_h between 13 nm and 23 nm, and examine the influence of particle size and shape on the nanorheological information obtained in model polymer solutions based on two related, dynamic-magnetic approaches. The results confirm that as long as the investigated solutions are not entangled, and the particles are much larger than the macromolecular correlation length, a good accordance between macroscopic and nanoscopic results, whereas a strong size-dependent response is observed in cases where the particles are of similar size or smaller than the radius of gyration R_g or the correlation length ξ of the polymer solution.

Observation of intensity dependent phase-separation in photoreactive monomer-nanoparticle formulations under non-uniform visible light irradiation

We report observations of photopolymerization driven phase-separation in a mixture of a photo-reactive monomer and inorganic nanoparticles. The mixture is irradiated with visible light possessing a periodic intensity profile that elicits photopolymerization along the depth of the mixture, establishing a competition between photo-crosslinking and thermodynamically favorable phase-separating behavior inherent to the system. In situ Raman spectroscopy was used to monitor the polymerization reaction and morphology evolution, and reveals a key correlation between irradiation intensity and composite morphology extending the entire depth of the mixture, i.e. unhindered phase-separation at low irradiation intensity and arrested phase-separation at high irradiation intensity. 3D Raman volume mapping and energy dispersive X-ray mapping confirm that the intensity-dependent irradiation process dictates the extent of phase separation, enabling single-parameter control over phase evolution and subsequent composite morphology. These observations can potentially enable a single-step route to develop polymer-inorganic composite materials with tunable morphologies.

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.

Anomalous Diffusion Inside Soft Colloidal Suspensions Investigated by Variable Length Scale Fluorescence Correlation Spectroscopy

The diffusion of molecules and particles inside the aqueous suspension of soft colloids (polymer microgels) is investigated using variable length scale fluorescence correlation spectroscopy (VLS-FCS). Carbopol 940 is chosen as the model matrix system, and two factors affecting diffusion are investigated: the spatial hindrance and the diffusant-matrix interaction. By studying diffusion of molecules and particles with different sizes inside the suspension, VLS-FCS reveals the restricted motion at a short length scale, that is, in the gaps between the microgels, and normal diffusion at a larger length scale. The information on the gap's length scale is also accessed. On the other hand, by tuning the pH value, the diffusant-matrix electrostatic attraction is adjusted and the results expose a short-time fast diffusion of probe molecules inside the gaps and a long-time restricted diffusion because of trapping inside the microgels. It is proved that VLS-FCS is a powerful method, investigating anomalous diffusion at different length scales and it is a promising approach to investigate diffusion in complex soft matter systems.

A comparative study of semi-flexible linear and ring polymer conformational change in an anisotropic environment

We adopt a Langevin-dynamics based simulation to systematically study the conformational change of a semi-flexible probed polymer in a rod crowding environment. Two topologically different probed polymer types, linear and ring polymers, are specifically considered. Our results unravel the significance of the interplay of probed polymer's semi-flexibility and crowding anisotropy. Firstly, both ring and linear polymers show a non-trivial dimensional change including nonmonotonicity and collapse-swelling crossover as their stiffness increases. Secondly, we modulate rod crowder length to investigate the anisotropic effect. We reveal that the formation of an ordered parallel arrangement of the environment can effectively lead to a remarkable stretching effect on the probed polymer. The coupling between the crowding anisotropy-induced stretching and the polymer stiffness can account for the unusual swelling behavior. Lastly, nonmonotonic swelling and shape change of the ring polymer are analyzed. We find out that the ring polymer is subject to most pronounced swelling at robust stiffness. Moreover, the maximum prolate shape is also observed at the same robust location.

Unexpected entanglement dynamics in semidilute blends of supercoiled and ring DNA

Blends of polymers of different topologies, such as ring and supercoiled, naturally occur in biology and often exhibit emergent viscoelastic properties coveted in industry. However, due to their complexity, along with the difficulty of producing polymers of different topologies, the dynamics of topological polymer blends remains poorly understood. We address this void by using both passive and active microrheology to characterize the linear and nonlinear rheological properties of blends of relaxed circular and supercoiled DNA. We characterize the dynamics as we vary the concentration from below the overlap concentration c* to above (0.5c* to 2c*). Surprisingly, despite working at the dilute-semidilute crossover, entanglement dynamics, such as elastic plateaus and multiple relaxation modes, emerge. Finally, blends exhibit an unexpected sustained elastic response to nonlinear strains not previously observed even in well-entangled linear polymer solutions.

Diffusion of nanoparticles within a semidilute polyelectrolyte solution

We studied the diffusion of charged gold nanoparticles within a semidilute solution of weakly charged polyelectrolyte, polyacrylic acid (PAA) of high molecular weight (M_w = 10⁶ g mol^-1) by using fluorescence correlation spectroscopy (FCS). Nanoparticle size (d) was varied between 5 nm to 40 nm and PAA volume fraction (φ) in water ranged from about 8φ* to 33φ*, where φ* is the overlap volume fraction. The reduced diffusion coefficient - defined as -D/D_o, where D is the diffusion coefficient in PAA solution and D_o is that in neat water - has a weak dependence on the particle size. D follows a power law of the form ∼φ^-0.5, which can be explained by a mean-field hydrodynamic theory in porous medium. Additional, rheology measurements showed a zero shear rate viscosity and shear thinning, which are typical of high molecular weight polyelectrolytes.

Quantifying the protein-protein association rate in polymer solutions: crowding-induced diffusion and energy modifications

A theoretical framework is developed to study protein-protein association in polymer solutions under diffusion-limited conditions. Starting from the basal association rate, two fundamental aspects concerning macromolecular crowding are particularly taken into account. One is the effect of microviscosity on protein diffusion. The length-scale dependent relations of translational and rotational diffusion coefficients are incorporated. Another is relevant to the crowding-induced effective interaction between the pair of proteins. The resultant energy modifications to the basal association rate are properly introduced, following an instructive classification with increasing crowder size: repulsive interaction dominant, repulsive and attractive interactions competitive, and attractive interaction prevailing. With specific energy modification terms, we are able to investigate the deviations of the association rate from the Stokes-Einstein (SE) behavior (i.e., the linear relationship with respect to the reciprocal of macroviscosity) in a quantitative manner. Our theory is applied to study the association of TEM1-β-lactamase (TEM) and the β-lactamase inhibitor protein (BLIP) in polyethylene glycol (PEG) solutions, with varying concentration and polymerization. We explicitly evaluate the relative association rate constant as a function of the solution macroviscosity. The theoretical results demonstrate very good agreement with the experimental data. Moreover, the complicated non-trivial deviations, either positive (slower than SE) or negative (faster than SE), are systematically rationalized. The precise role of energy modifications and the microviscosity effect on diffusion, in particular on rotational diffusion, are clearly unraveled.

Unusual crowding-induced chain looping kinetics in hard-sphere fluids: a contrastive study with polymer solutions

A theoretical framework is developed to investigate the looping kinetics of a chain in hard-sphere (HS) fluids, based on a generalized Smoluchowski diffusion-reaction equation. A contrastive study with polymer solutions is performed. The crowding-associated effective viscosity and collapse effects are properly taken into account, which obey different scaling relations in HS and polymer fluids. We examine the dependence of the looping time on both concentration and size of crowders, demonstrating unusual and distinct discrepancies in the two crowded media. Firstly, in the solution of large polymers, the looping rate grows monotonically with polymer concentration. On the other hand, in the solution of large HSs, a caging regime can be observed, where the looping time tends to the value in the absence of crowders. Secondly, polymers in moderate size generally impede chain looping due to the enhanced viscosity. However, in HS fluids, the looping time exhibits a rather complicated variation with increasing HS size. We show a possible mechanism where in the case of small crowders with a relatively strong compaction in the probed chain, the looping kinetics can be facilitated. As the crowder size increases, the collapse effect is reduced and looping is dominated by viscosity-induced inhibition. Simultaneously, our theory rationalizes another possibility of the mechanism observed by recent simulation work. We conclude that the looping kinetics in specific systems actually should be governed by the critical competition between the two crowding factors. By giving reasonable measurements of effective viscosity and collapse, our theoretical framework can provide a unified strategy to analyze crowding effects on the looping rate in a systematic manner.

Nanoparticle Diffusion within Dilute and Semidilute Xanthan Solutions

We measured the translation diffusion coefficient ( D) of nanoparticles within dilute and semidilute solutions of a semiflexible polymer, xanthan. Our results showed that for particle diameters ( d) of 5 and 10 nm, the obstruction theory can explain the concentration ( c) dependence of D in the dilute regime. Diffusion in semidilute solutions is better explained by additionally considering the modified Darcy flow with the hydrodynamic screening length varying according to κ ≈ c^-0.76_. The depletion effect is operative for larger particles ( d = 30 nm) within semidilute solutions. We used a scaling relation for the depletion layer thickness δ ≈ ξ^ν, where ξ is the static correlation length and the exponent ν ≈ 0.42 that can explain our data. This is in contrast with a flat surface, where the exponent is expected to be 1. Our results showed that in the situation, when the polymer network relaxation is much slower compared to the diffusive time-scale of particles, no single theory is capable to describe the concentration and size dependence of particle mobility.

Study of active Brownian particle diffusion in polymer solutions

The diffusion behavior of an active Brownian particle (ABP) in polymer solutions is studied using Langevin dynamics simulations. We find that the long time diffusion coefficient D can show a non-monotonic dependence on the particle size R if the active force Fa is large enough, wherein a bigger particle would diffuse faster than a smaller one which is quite counterintuitive. By analyzing the short time dynamics in comparison to the passive one, we find that such non-trivial dependence results from the competition between persistent motion of the ABP and the length-scale dependent effective viscosity that the particle experiences in the polymer solution. We have also introduced an effective viscosity ηeff experienced by the ABP phenomenologically. Such an active ηeff is found to be larger than a passive one and strongly depends on R and Fa. In addition, we find that the dependence of D on propelling force Fa presents a good power-law scaling at a fixed R and the scaling factor changes non-monotonically with R. Such results demonstrate that the active process plays rather subtle roles in the diffusion of nano-particles in complex solutions.

Influence of polymer flexibility on nanoparticle dynamics in semidilute solutions

The hierarchical structure and dynamics of polymer solutions control the transport of nanoparticles (NPs) through them. Here, we perform multi-particle collision dynamics simulations of solutions of semiflexible polymer chains with tunable persistence length lp to investigate the effect of chain stiffness on NP transport. The NPs exhibit two distinct dynamical regimes - subdiffusion on short time scales and diffusion on long time scales. The long-time NP diffusivities are compared with predictions from the Stokes-Einstein relation (SER), mode-coupling theory (MCT), and a recent polymer coupling theory (PCT). Increasing deviations from the SER as the polymer chains become more rigid (i.e. as lp increases) indicate that the NP motions become decoupled from the bulk viscosity of the polymer solution. Likewise, polymer stiffness leads to deviations from PCT, which was developed for fully flexible chains. Independent of lp, however, the long-time diffusion behavior is well-described by MCT, particularly at high polymer concentration. We also observed that the short-time subdiffusive dynamics are strongly dependent on polymer flexibility. As lp is increased, the NP dynamics become more subdiffusive and decouple from the dynamics of the polymer chain center-of-mass. We posit that these effects are due to differences in the segmental mobility of the semiflexible chains.

Activity–crowding coupling effect on the diffusion dynamics of a self-propelled particle in polymer solutions

The anomalous diffusion dynamics of an active particle in polymer solutions is studied based on a Langevin Brownian dynamics simulation.

Comparative study of the crowding-induced collapse effect in hard-sphere, flexible polymer and rod-like polymer systems

A systematic Langevin simulation is performed to study the crowding-induced collapse effect on a probed chain in three typical systems: hard sphere (HS), flexible polymer and rod-like polymer.

Understanding chain looping kinetics in polymer solutions: crowding effects of microviscosity and collapse

A theoretical framework based on a generalized Langevin equation with fractional Gaussian noise is presented to describe the looping kinetics of chains in polymer solutions. Particular attention is paid to quantitatively revealing crowding effects on the loop formation rate in terms of microviscosity and collapse. By the aid of empirical relations for these two crowding associated physical quantities, we explicitly investigate the relationship between the looping rate and polymer concentration, the degree of polymerization, and system parameters. According to our analysis, the dependence of the looping rate on the crowder volume fraction exhibits three typical regimes: monotonic decreasing, a non-monotonic trend and monotonic increasing. We reveal that these non-trivial behaviors can be attributed to the competition between the two opposing factors of viscosity-associated inhibition and collapse-induced facilitation of loop formation. We apply our theory to analyze the kinetics of single-stranded DNA hairpin base pairing in polyethylene glycol solutions. The theoretical results can reproduce the experimental data on the closing rate of hairpins quantitatively to a certain degree with reasonable fitting parameters. The unexpected increase of the closing rate upon the addition of increasing amounts of polymer is well rationalised. Such good agreements clearly demonstrate the validity of our theory, appropriately addressing the very role of crowding effects in the relevant kinetics.

Diffusion of small particles in polymer films

The motion of small probe molecules in a two-dimensional system containing frozen polymer chains was studied by means of Monte Carlo simulations. The model macromolecules were coarse-grained and restricted to vertices of a triangular lattice. The cooperative motion algorithm was used to generate representative configurations of macromolecular systems of different polymer concentrations. The remaining unoccupied lattice sites of the system were filled with small molecules. The structure of the polymer film, especially near the percolation threshold, was determined. The dynamic lattice liquid algorithm was then employed for studies of the dynamics of small objects in the polymer matrix. The influence of chain length and polymer concentration on the mobility and the character of motion of small molecules were studied. Short- and long-time dynamic behaviors of solvent molecules were also described. Conditions of anomalous diffusions' appearance in such systems are discussed. The influence of the structure of the matrix of obstacles on the molecular transport was discussed.

On the parallelism between the mechanisms behind chromatography and drug delivery: the role of interactions with a stationary phase

A huge number of studies and work in the drug delivery literature are focused on understanding and modeling transport phenomena, the pivotal point for a good device design. The rationalization of all phenomena involved is fundamental, but several concerns arise leaving many issues unsolved. In order to change the point of view we decided to focus our attention on the parallelisms between two fields that seem to be very far from each other: chromatography and drug release. Taking advantages of the studies conducted by many researchers using chromatographic columns we decided to explain all the phenomena involved in drug delivery considering sodium ibuprofen (IP) molecules as analytes and hydrogel as a stationary phase. In particular, we considered not only diffusion, but also drug-polymer interactions as adsorption on the stationary phase and drug-drug interactions as aggregation of analytes. The hydrogel investigated is a promising formulation made of agarose and carbomer 974p (AC) loaded with IP, a non-steroidal common anti-inflammatory drug. The self-diffusion coefficient of IP in AC formulations was measured by using an innovative method based on a magic angle spinning NMR spectroscopic technique to produce high resolution (liquid-like) spectra. This method (HR-MAS NMR) is used in combination with pulsed field gradient spin echo (PGSE) liquid-state techniques. The model predictions satisfactorily match with the experimental data obtained in water and the gel environment, indicating that the model presented here, despite its simplicity, is able to describe the key phenomena governing the device behavior and could be used to rationalize the experimental activity.

Nanoscale Rheology and Anisotropic Diffusion Using Single Gold Nanorod Probes

The complex rotational and translational Brownian motion of anisotropic particles depends on their shape and the viscoelasticity of their surroundings. Because of their strong optical scattering and chemical versatility, gold nanorods would seem to provide the ultimate probes of rheology at the nanoscale, but the suitably accurate orientational tracking required to compute rheology has not been demonstrated. Here we image single gold nanorods with a laser-illuminated dark-field microscope and use optical polarization to determine their three-dimensional orientation to better than one degree. We convert the rotational diffusion of single nanorods in viscoelastic polyethylene glycol solutions to rheology and obtain excellent agreement with bulk measurements. Extensions of earlier models of anisotropic translational diffusion to three dimensions and viscoelastic fluids give excellent agreement with the observed motion of single nanorods. We find that nanorod tracking provides a uniquely capable approach to microrheology and provides a powerful tool for probing nanoscale dynamics and structure in a range of soft materials.

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.