Dynamics of probe diffusion in rod solutions

Exploring nanofibrous networks with x-ray photon correlation spectroscopy through a digital twin

We demonstrate a framework of interpreting data from x-ray photon correlation spectroscopy experiments with the aid of numerical simulations to describe nanoscale dynamics in soft matter. This is exemplified with the transport of passive tracer gold nanoparticles in networks of charge-stabilized cellulose nanofibers. The main structure of dynamic modes in reciprocal space could be replicated with a simulated system of confined Brownian motion, a digital twin, allowing for a direct measurement of important effective material properties describing the local environment of the tracers.

Passive and active tracer dynamics in polymer solutions with isotropic-to-nematic phase transition

Macromolecular crowding plays a crucial role in determining the dynamics in a living cell. We adopt Langevin dynamics simulations to investigate the anomalous diffusion dynamics of passive and active particles in a solution of polymer chains with tunable stiffness. The solution's anisotropic feature is modulated by changing both the polymer stiffness and volume fraction, where isotropic-to-nematic phase transition is involved. Our results demonstrate the significant impact of polymer flexibility on the dynamics of both passive and active probes. The distinct diffusion mechanism for an active particle is clarified by the interplay between polymer stiffness, crowdedness and activity. Polymer stiffness leads to a global inhibition effect on passive particle diffusion. The diffusion coefficient exhibits an intriguing non-monotonic variation at increasing polymer stiffness, which is due to the fact that the alignment of polymer chains is beneficial for diffusion along the nematic direction but unfavorable for that in the direction perpendicular to it. In sharp contrast, polymer stiffness plays a dominant role in facilitating active particle diffusion. Self-propulsion of the particle can utilize stiffness-induced elastic interactions more efficiently, which promotes its mobility in both directions. Meanwhile, an active particle might have a stronger ability to take advantage of the polymer alignment, contributing substantially enhanced diffusivity. In addition, the diffusion coefficient of an active particle is subject to a tendency of degeneration against varying volume fraction. This counter-intuitive behavior is due to the contrasting factors that increasing crowdedness induces a lower particle speed but a longer persistent motion time.

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.

Influence of pore morphology on the diffusion of water in triblock copolymer membranes

Understanding the transport properties of water in self-assembled block copolymer morphologies is important for furthering the use of such materials as water-purifying membranes. In this study, we used coarse-grained dissipative particle dynamics simulations to clarify the influence of pore morphology on the self-diffusion of water in linear-triblock-copolymer membranes. We considered representative lamellar, cylindrical, and gyroid morphologies and present results for both the global and local diffusivities of water in the pores. Our results suggest that the diffusivity of water in the confined, polymer-coated pores differs from that in the unconfined bulk. Explicitly, in confinement, the mobility of water is reduced by the hydrodynamic friction arising from the hydrophilic blocks coating the pore walls. We demonstrate that in lamella and cylindrical morphologies, the latter effects can be rendered as a universal function of the pore size relative to the brush height of the hydrophilic blocks.

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.

Perspective: Outstanding theoretical questions in polymer-nanoparticle hybrids

This topical review discusses the theoretical progress made in the field of polymer nanocomposites, i.e., hybrid materials created by mixing (typically inorganic) nanoparticles (NPs) with organic polymers. It primarily focuses on the outstanding issues in this field and is structured around five separate topics: (i) the synthesis of functionalized nanoparticles; (ii) their phase behavior when mixed with a homopolymer matrix and their assembly into well-defined superstructures; (iii) the role of processing on the structures realized by these hybrid materials and the role of the mobilities of the different constituents; (iv) the role of external fields (electric, magnetic) in the active assembly of the NPs; and (v) the engineering properties that result and the factors that control them. While the most is known about topic (ii), we believe that significant progress needs to be made in the other four topics before the practical promise offered by these materials can be realized. This review delineates the most pressing issues on these topics and poses specific questions that we believe need to be addressed in the immediate future.

Diffusion of a Rouse chain in porous media: A mode-coupling-theory study

We use a kinetic mode-coupling theory (MCT) combining with generalized Langevin equation (GLE) to study the diffusion and conformational dynamics of a bead-spring Rouse chain (RC) dissolved in porous media. The media contains fluid particles and immobile matrix ones wherein the latter leads to the lack of translational invariance. The friction kernel ζ(t) used in the GLE can be obtained directly by adopting a simple density-functional approach in which the density correlators calculated by MCT equations of porous media serve as inputs. Due to cage effects generated by surrounding particles, ζ(t) shows a very long tail memory in the high volume fraction of fluid and matrix. It is found that the long-time center-of-mass diffusion constant D_{CM} of the RC decreases with the increment of volume fraction, influencing more strongly by the matrix particles than by the fluid ones. The auto-correlation function (ACF) of the end-to-end distance fluctuation can also be calculated theoretically based on GLE. Of particular interest is that the power-law region of ACF has a nearly fixed length in logarithmic scale when it shifts to longer time range, with increasing the volume fraction of media particles. Moreover, the effect of lack of translational invariance has been investigated by comparing the results between fluid-matrix and pure fluid cases under identical total volume fraction.

Tracer diffusion in a polymer gel: simulations of static and dynamic 3D networks using spherical boundary conditions

We have investigated an alternative to the standard periodic boundary conditions for simulating the diffusion of tracer particles in a polymer gel by performing Brownian dynamics simulations using spherical boundary conditions. The gel network is constructed by randomly distributing tetravalent cross-linking nodes and connecting nearest pairs. The final gel structure is characterised by the radial distribution functions, chain lengths and end-to-end distances, and the pore size distribution. We have looked at the diffusion of tracer particles with a wide range of sizes, diffusing in both static and dynamic networks of two different volume fractions. It is quantitatively shown that the dynamical effect of the network becomes more important in facilitating the diffusional transport for larger particle sizes, and that one obtains a finite diffusion also for particle sizes well above the maximum in the pore size distribution.

Size-Dependent Dynamics of Nanoparticles in Unentangled Polyelectrolyte Solutions

The mobility of polystyrene nanoparticles ranging in diameter from 300 nm to 2 μm was measured in dilute and semidilute solutions of partially hydrolyzed polyacrylamide. In this model system, the ratio of particle to polymer size controls the long-time diffusivity of nanoparticles. The particle dynamics transition from subdiffusive on short time scales to Fickian on long time scales, qualitatively similar to predictions for polymer dynamics using a Rouse model. The diffusivities extracted from the long-time Fickian regime, however, are larger than those predicted by the Stokes-Einstein equation and the bulk zero-shear viscosity and moreover do not collapse according to hydrodynamic models. The size-dependent deviations of the long-time particle diffusivities derive instead from the coupling between the dynamics of the particle and the polymer over the length scale of the particle. Although the long-time diffusivities collapse according to predictions, deviations of the short-time scaling exponents and the crossover time between subdiffusive and Fickian dynamics indicate that the particles are only partially coupled to the relaxation modes of the polymer.

Diffusive dynamics of nanoparticles in arrays of nanoposts

The diffusive dynamics of dilute dispersions of nanoparticles of diameter 200-400 nm were studied in microfabricated arrays of nanoposts using differential dynamic microscopy and single particle tracking. Posts of diameter 500 nm and height 10 μm were spaced by 1.2-10 μm on a square lattice. As the spacing between posts was decreased, the dynamics of the nanoparticles slowed. Moreover, the dynamics at all length scales were best represented by a stretched exponential rather than a simple exponential. Both the relative diffusivity and the stretching exponent decreased linearly with increased confinement and, equivalently, with decreased void volume. The slowing of the overall diffusive dynamics and the broadening distribution of nanoparticle displacements with increased confinement are consistent with the onset of dynamic heterogeneity and the approach to vitrification.

Diffusion of nanoparticles in semidilute and entangled polymer solutions

We studied the diffusion of gold nanoparticles in semidilute and entangled solutions of polystyrene (PS) in toluene using fluctuation correlation spectroscopy (FCS). The polymer concentration was varied from approximately 6c* to 20c*, where c* is the overlap concentration. In our experiments, the particle radius (R approximately 2.5 nm) was much smaller compared to the radius of gyration (Rg approximately 18 nm) of the chain but comparable to the average mesh size (xi) of the fluctuating polymer network. The diffusion coefficient (D) of the particles decreased monotonically with polymer concentration and it can be fitted with a stretched exponential function, D=D0 exp(-microcnu), with the value of the scaling parameter, nu approximately 0.9. At high concentration of the polymer, a clear subdiffusive motion of the particles was observed. The results were compared with the diffusion of free dyes (coumarin 480), which showed normal diffusive behavior for all concentrations.

Equilibrium characteristics of semiflexible polymer solutions near probe particles

We present a numerical analysis of the mean-field theory for the structure of semiflexible polymer solutions near spherical surfaces, and use the framework to study the depletion characteristics of semiflexible polymers near colloids and nanoparticles. Our results suggest that the depletion characteristics depend sensitively on the polymer concentrations, the persistence lengths, and the radius of the particles. Broadly, two categories of features are identified based on the relative ratios of the persistence lengths to the correlation length of the polymer solution. For the limit where the correlation length is larger than the persistence length, the correlation length proves to be the critical length scale governing both the depletion thickness and the curvature effects. In contrast, for the opposite limit, the depletion thickness and the curvature effects are dependent on a length scale determined by an interplay between the persistence length and the correlation length. This leads to nontrivial (numerical) scaling laws governing the concentration and radii dependence of the depletion thicknesses. Our study also highlights the manner by which the preceding features rationalize the parametric dependencies of insertion free energies of small probes in semiflexible polymer solutions.