Tube Concept for Entangled Stiff Fibers Predicts Their Dynamics in Space and Time

Single-walled carbon nanotube reptation dynamics in submicron sized pores from randomly packed mono-sized colloids

Studying the Brownian motion of fibers and semi-flexible filaments in porous media is the key to understanding the transport and mechanical properties in a variety of systems. The motion of semi-flexible filaments in gel-like porous media including polymer networks and cell cytoskeleton has been studied theoretically and experimentally, whereas the motion of these materials in packed-colloid porous media, advanced foams, and rock-like systems has not been thoroughly studied. Here we use video microscopy to directly visualize the reptation and transport of intrinsically fluorescent, semiflexible, semiconducting single-walled carbon nanotubes (SWCNTs) in the sub-micron pores of packed colloids as fixed obstacles of packed-colloid porous media. By visualizing the filament motion and Brownian diffusion at different locations in the pore structures, we study how the properties of the environment, like the pore shape and pore structure of the porous media, affect SWCNT mobility. These results show that the porous media structure controls SWCNT reorientation during Brownian diffusion. In packed-colloid pores, SWCNTs diffuse along straight pores and bend across pores; conversely, in gel pores, SWCNTs consistently diffuse into curved pores, displaying a faster parallel motion. In both gel and packed-colloid porous media, SWCNT finite stiffness enhances SWCNT rotational diffusion and prevents jamming, allowing for inter-pore diffusion.

How macromolecules softness affects diffusion under crowding

Diffusion in a macromolecularly crowded environment is essential for many intracellular processes, from metabolism and catalysis to gene transcription and translation. So far, theoretical and experimental work has focused on anomalous subdiffusion, and the effects of interactions, shapes, and composition, while the compactness or softness of macromolecules has received less attention. Herein, we use Brownian dynamics simulations to study how the softness of crowders affects macromolecular diffusion. We find that in most cases, soft crowders slow down the diffusion less effectively than hard crowders like Ficoll. For instance, at a 30% occupied volume fraction, the diffusion in Ficoll70 is about 20% slower than in soft crowders of the same size. However, our simulations indicate that elongated macromolecules, such as double-stranded DNA pieces, can diffuse comparably or even faster in hard crowders. We relate these effects to the volume excluded by soft and hard crowders to different tracers. Our results show that the softness and shape of macromolecules are crucial factors determining diffusion under crowding, relevant to diverse intracellular environments.

Two-dimensional Brownian motion of anisotropic dimers

We study the two-dimensional motion of colloidal dimers by single-particle tracking and compare the experimental observations obtained by bright-field microscopy to theoretical predictions for anisotropic diffusion. The comparison is based on the mean-square displacements in the laboratory and particle frame as well as generalizations of the self-intermediate scattering functions, which provide insights into the rotational dynamics of the dimer. The diffusional anisotropy leads to a measurable translational-rotational coupling that becomes most prominent by aligning the coordinate system with the initial orientation of the particles. In particular, we find a splitting of the time-dependent diffusion coefficients parallel and perpendicular to the long axis of the dimer which decays over the orientational relaxation time. Deviations of the self-intermediate scattering functions from pure exponential relaxation are small but can be resolved experimentally. The theoretical predictions and experimental results agree quantitatively.

Crowding-Enhanced Diffusion: An Exact Theory for Highly Entangled Self-Propelled Stiff Filaments

We study a strongly interacting crowded system of self-propelled stiff filaments by event-driven Brownian dynamics simulations and an analytical theory to elucidate the intricate interplay of crowding and self-propulsion. We find a remarkable increase of the effective diffusivity upon increasing the filament number density by more than one order of magnitude. This counterintuitive "crowded is faster" behavior can be rationalized by extending the concept of a confining tube pioneered by Doi and Edwards for highly entangled, crowded, passive to active systems. We predict a scaling theory for the effective diffusivity as a function of the Péclet number and the filament number density. Subsequently, we show that an exact expression derived for a single self-propelled filament with motility parameters as input can predict the nontrivial spatiotemporal dynamics over the entire range of length and timescales. In particular, our theory captures short-time diffusion, directed swimming motion at intermediate times, and the transition to complete orientational relaxation at long times.

Elastic behavior of a semiflexible polymer in 3D subject to compression and stretching forces

We elucidate the elastic behavior of a wormlike chain in 3D under compression and provide exact solutions for the experimentally accessible force-extension relation in terms of generalized spheroidal wave functions. In striking contrast to the classical Euler buckling instability, the force-extension relation of a clamped semiflexible polymer exhibits a smooth crossover from an almost stretched to a buckled configuration. In particular, the associated susceptibility, which measures the strength of the response of the polymer to the applied force, displays a prominent peak in the vicinity of the critical Euler buckling force. For increasing persistence length, the force-extension relation and the susceptibility of semiflexible polymers approach the behavior of a classical rod, whereas thermal fluctuations permit more flexible polymers to resist the applied force. Furthermore, we find that semiflexible polymers confined to 2D can oppose the applied force more strongly than in 3D.

Bimodal probability density characterizes the elastic behavior of a semiflexible polymer in 2D under compression

We explore the elastic behavior of a wormlike chain under compression in terms of exact solutions for the associated probability densities. Strikingly, the probability density for the end-to-end distance projected along the applied force exhibits a bimodal shape in the vicinity of the critical Euler buckling force of an elastic rod, reminiscent of the smeared discontinuous phase transition of a finite system. These two modes reflect the almost stretched and the S-shaped configuration of a clamped polymer induced by the compression. Moreover, we find a bimodal shape of the probability density for the transverse fluctuations of the free end of a cantilevered polymer as fingerprint of its semiflexibility. In contrast to clamped polymers, free polymers display a circularly symmetric probability density and their distributions are identical for compression and stretching forces.

Disentangling entanglements in biopolymer solutions

Reptation theory has been highly successful in explaining the unusual material properties of entangled polymer solutions. It reduces the complex many-body dynamics to a single-polymer description, where each polymer is envisaged to be confined to a tube through which it moves in a snake-like fashion. For flexible polymers, reptation theory has been amply confirmed by both experiments and simulations. In contrast, for semiflexible polymers, experimental and numerical tests are either limited to the onset of reptation, or were performed for tracer polymers in a fixed, static matrix. Here, we report Brownian dynamics simulations of entangled solutions of semiflexible polymers, which show that curvilinear motion along a tube (reptation) is no longer the dominant mode of dynamics. Instead, we find that polymers disentangle due to correlated constraint release, which leads to equilibration of internal bending modes before polymers diffuse the full tube length. The physical mechanism underlying terminal stress relaxation is rotational diffusion mediated by disentanglement rather than curvilinear motion along a tube.

Dynamically crowded solutions of infinitely thin Brownian needles

We study the dynamics of solutions of infinitely thin needles up to densities deep in the semidilute regime by Brownian dynamics simulations. For high densities, these solutions become strongly entangled and the motion of a needle is essentially restricted to a one-dimensional sliding in a confining tube composed of neighboring needles. From the density-dependent behavior of the orientational and translational diffusion, we extract the long-time transport coefficients and the geometry of the confining tube. The sliding motion within the tube becomes visible in the non-Gaussian parameter of the translational motion as an extended plateau at intermediate times and in the intermediate scattering function as an algebraic decay. This transient dynamic arrest is also corroborated by the local exponent of the mean-square displacements perpendicular to the needle axis. Moreover, the probability distribution of the displacements perpendicular to the needle becomes strongly non-Gaussian; rather, it displays an exponential distribution for large displacements. On the other hand, based on the analysis of higher-order correlations of the orientation we find that the rotational motion becomes diffusive again for strong confinement. At coarse-grained time and length scales, the spatiotemporal dynamics of the needle for the high entanglement is captured by a single freely diffusing phantom needle with long-time transport coefficients obtained from the needle in solution. The time-dependent dynamics of the phantom needle is also assessed analytically in terms of spheroidal wave functions. The dynamic behavior of the needle in solution is found to be identical to needle Lorentz systems, where a tracer needle explores a quenched disordered array of other needles.

Onset of static and dynamic universality among molecular models of polymers

A quantitatively accurate prediction of properties for entangled polymers is a long-standing challenge that must be addressed to enable efficient development of these materials. The complex nature of polymers is the fundamental origin of this challenge. Specifically, the chemistry, structure, and dynamics at the atomistic scale affect properties at the meso and macro scales. Therefore, quantitative predictions must start from atomistic molecular dynamics (AMD) simulations. Combined use of atomistic and coarse-grained (CG) models is a promising approach to estimate long-timescale behavior of entangled polymers. However, a systematic coarse-graining is still to be done for bridging the gap of length and time scales while retaining atomistic characteristics. Here we examine the gaps among models, using a generic mapping scheme based on power laws that are closely related to universality in polymer structure and dynamics. The scheme reveals the characteristic length and time for the onset of universality between the vastly different scales of an atomistic model of polyethylene and the bead-spring Kremer-Grest (KG) model. The mapping between CG model of polystyrene and the KG model demonstrates the fast onset of universality, and polymer dynamics up to the subsecond time scale are observed. Thus, quantitatively traceable timescales of polymer MD simulations can be significantly increased.

Intermediate scattering function of an anisotropic Brownian circle swimmer

Microswimmers exhibit noisy circular motion due to asymmetric propulsion mechanisms, their chiral body shape, or by hydrodynamic couplings in the vicinity of surfaces. Here, we employ the Brownian circle swimmer model and characterize theoretically the dynamics in terms of the directly measurable intermediate scattering function. We derive the associated Fokker-Planck equation for the conditional probabilities and provide an exact solution in terms of generalizations of the Mathieu functions. Different spatiotemporal regimes are identified reflecting the bare translational diffusion at large wavenumbers, the persistent circular motion at intermediate wavenumbers and an enhanced effective diffusion at small wavenumbers. In particular, the circular motion of the particle manifests itself in characteristic oscillations at a plateau of the intermediate scattering function for wavenumbers probing the radius.

Exact solution for the force-extension relation of a semiflexible polymer under compression

Exact solutions for the elastic and thermodynamic properties for the wormlike chain model are elaborated in terms of Mathieu functions. The smearing of the classical Euler buckling instability for clamped polymers is analyzed for the force-extension relation. Interestingly, at strong compression forces the thermal fluctuations lead to larger elongations than for the elastic rod. The susceptibility defined as the derivative of the force-extension relation displays a prominent maximum at a force that approaches the critical Euler buckling force as the persistence length is increased. We also evaluate the excess entropy and heat capacity induced by the compression and find that they vary nonmonotonically with the load. These findings are corroborated by pseudo-Brownian simulations.