Dynamic cross-correlations between entangled biofilaments as they diffuse.

Entanglement in polymer and biological physics involves a state in which linear interthreaded macromolecules in isotropic liquids diffuse in a spatially anisotropic manner beyond a characteristic mesoscopic time and length scale (tube diameter). The physical reason is that linear macromolecules become transiently localized in directions transverse to their backbone but diffuse with relative ease parallel to it. Within the resulting broad spectrum of relaxation times there is an extended period before the longest relaxation time when filaments occupy a time-averaged cylindrical space of near-constant density. Here we show its implication with experiments based on fluorescence tracking of dilutely labeled macromolecules. The entangled pairs of aqueous F-actin biofilaments diffuse with separation-dependent dynamic cross-correlations that exceed those expected from continuum hydrodynamics up to strikingly large spatial distances of ≈15 µm, which is more than 104 times the size of the solvent water molecules in which they are dissolved, and is more than 50 times the dynamic tube diameter, but is almost equal to the filament length. Modeling this entangled system as a collection of rigid rods, we present a statistical mechanical theory that predicts these long-range dynamic correlations as an emergent consequence of an effective long-range interpolymer repulsion due to the de Gennes correlation hole, which is a combined consequence of chain connectivity and uncrossability. The key physical assumption needed to make theory and experiment agree is that solutions of entangled biofilaments localized in tubes that are effectively dynamically incompressible over the relevant intermediate time and length scales.

Intermolecular structural correlations in model globular and unconcatenated ring polymer liquids.

We employ the field theoretic polymer integral equation theory to construct a segment-level theory for the thermodynamics and pair structure of dense liquids of interpenetrating ring polymers and a simple globule model. The latter is defined by a fractal mass distribution on all internal length scales with an exponent equal to the spatial dimension (dF = ds = 3). In an isochoric ensemble the dimensionless compressibility and pressure is predicted to vary exponentially with macromolecular volume fraction. An intermolecular correlation hole exists down to small length scales. This model appears to be useful for a recently studied experimental soft nanoparticle suspension, and also serves as a reference system for our analysis of ring liquids. Motivated by simulations, a two-fractal exponent ring model is adopted for the intramolecular structure factor. At smaller lengths it describes chain-like macromolecules, while on larger scales it corresponds to a space-filling object in the sense that dF = ds = 3. The crossover between these two regimes is of order the entanglement length of the linear chain analog. Based on a constant compressibility ensemble, the effective volume fraction grows at intermediate values of degree of polymerization (N), and crosses over to a very slow logarithmic growth at large N. A weaker intermolecular correlation hole is predicted. The number of nearest neighbor rings increases dramatically at small N, akin to linear chain melts, but then tends to saturate at large N, in accord with simulations. The tools developed may be relevant for other partially interpenetrating soft objects such as core-shell nanogels or microgels.

Anomalous packing and dynamics of a polymer chain confined in a static porous environment.

Polymers in confined porous environments are ubiquitous throughout biology, physics, materials science, and engineering. Several experiments have suggested that in some porous environments, chain dynamics can become extremely slow. While phenomenological explanations exist, the exact mechanisms for these slow dynamics have not been fully characterized. In this work, we initiate a joint simulation-theory study to investigate chain packing and dynamics in a static porous environment. The main theoretical concept is the free energy of the chain partitioning into several chambers of the porous environment. Both the theoretical results and Langevin dynamics simulations show that chain packing in each of the chambers is predominantly independent of chain length; it is determined by the maximal packing of segments in each chamber. Dynamically, short chains (compared to the chamber size) become trapped in a single chamber and dynamics become extremely slow, characteristic of an Ogston sieving-like behavior. For longer chains, on the other hand, a hierarchy of slow dynamics is observed due to entropic trapping, characterized by sub-diffusive behavior and a temporary plateau in the mean square displacement. Due to the slow nature of the dynamics, the inevitable long-time diffusive behavior of the chains is not captured by our simulations. Theoretically, the slow dynamics are understood in terms of a free energy barrier required to thread the chain from one chamber to the next. There is overall qualitative and quantitative agreement between simulations and theory. This work provides foundations for a better understanding of how chain dynamics are affected by porous environments.

Segment-scale, force-level theory of mesoscopic dynamic localization and entropic elasticity in entangled chain polymer liquids.

We develop a segment-scale, force-based theory for the breakdown of the unentangled Rouse model and subsequent emergence of isotropic mesoscopic localization and entropic elasticity in chain polymer liquids in the absence of ergodicity-restoring anisotropic reptation or activated hopping motion. The theory is formulated in terms of a conformational N-dynamic-order-parameter generalized Langevin equation approach. It is implemented using a universal field-theoretic Gaussian thread model of polymer structure and closed at the level of the chain dynamic second moment matrix. The physical idea is that the isotropic Rouse model fails due to the dynamical emergence, with increasing chain length, of time-persistent intermolecular contacts determined by the combined influence of local uncrossability, long range polymer connectivity, and a self-consistent treatment of chain motion and the dynamic forces that hinder it. For long chain melts, the mesoscopic localization length (identified as the tube diameter) and emergent entropic elasticity predictions are in near quantitative agreement with experiment. Moreover, the onset chain length scales with the semi-dilute crossover concentration with a realistic numerical prefactor. Distinctive novel predictions are made for various off-diagonal correlation functions that quantify the full spatial structure of the dynamically localized polymer conformation. As the local excluded volume constraint and/or intrachain bonding spring are softened to allow chain crossability, the tube diameter is predicted to swell until it reaches the radius-of-gyration at which point mesoscopic localization vanishes in a discontinuous manner. A dynamic phase diagram for such a delocalization transition is constructed, which is qualitatively consistent with simulations and the classical concept of a critical entanglement degree of polymerization.

Microscopic Theory for the Role of Attractive Forces in the Dynamics of Supercooled Liquids.

We formulate a microscopic, no adjustable parameter, theory of activated relaxation in supercooled liquids directly in terms of the repulsive and attractive forces within the framework of pair correlations. Under isochoric conditions, attractive forces can nonperturbatively modify slow dynamics, but at high enough density their influence vanishes. Under isobaric conditions, attractive forces play a minor role. High temperature apparent Arrhenius behavior and density-temperature scaling are predicted. Our results are consistent with recent isochoric simulations and isobaric experiments on a deeply supercooled molecular liquid. The approach can be generalized to treat colloidal gelation and glass melting, and other soft matter slow dynamics problems.

Theory of Transient Localization, Activated Dynamics, and a Macromolecular Glass Transition in Ring Polymer Liquids.

We construct a segmental scale force level theory for the center-of-mass diffusion constant and corresponding relaxation time for globally compact unconcatenated ring polymer solutions and melts (degree of polymerization N). The approach is based on slowly decaying macromolecular scale intermolecular force dynamic correlations as the origin of their unusual dynamics. Unentangled Rouse, weakly caged, and activated regimes are predicted. The barrier of the activated regime scales linearly with N and as a power law of concentration, which drives a kinetic glass transition on the radius-of-gyration scale. The values of N at the two dynamic crossovers (Rouse to weakly caged, weakly caged to activated) are proportional, with nonuniversality entering mainly via macromolecular volume fraction and dimensionless compressibility. Quantitative comparisons with simulation data reveal good agreement. Aspects of intermediate time dynamics are analyzed, and predictions are made for the conditions required to observe a macromolecular glass transition in the laboratory and on the computer.

Correlated two-particle diffusion in dense colloidal suspensions at early times: Theory and comparison to experiment.

The spatially resolved diffusive dynamic cross correlations of a pair of colloids in dense quasi-two-dimensional monolayers of identical particles are studied experimentally and theoretically at early times where motion is Fickian. In very dense systems where strong oscillatory equilibrium packing correlations are present, we find an exponential decay of the dynamic cross correlations on small and intermediate length scales. At large separations where structure becomes random, an apparent power law decay with an exponent of approximately -2.2 is observed. For a moderately dense suspension where local structural correlations are essentially absent, this same apparent power law decay is observed over all probed interparticle separations. A microscopic nonhydrodynamic theory is constructed for the dynamic cross correlations which is based on interparticle frictional effects and effective structural forces. Hydrodynamics enters only via setting the very short-time single-particle self-diffusion constant. No-adjustable-parameter quantitative predictions of the theory for the dynamic cross correlations are in good agreement with experiment over all length scales. The origin of the long-range apparent power law is the influence of the constraint of fixed interparticle separation on the amplitude of the mean square force exerted on the two tagged particles by the surrounding fluid. The theory is extended to study high-packing-fraction 3D hard sphere fluids. The same pattern of an oscillatory exponential form of the dynamic cross correlation function is predicted in the structural regime, but the long-range tail decays faster than in monolayers with an exponent of -3.