Dynamics Of Flexible Polymer Chains Research Articles

Non-monotonic dependence of polymer chain dynamics on active crowder size.

Configuration dynamics of flexible polymer chains is of ubiquitous importance in many biological processes. Here, we investigate a polymer chain immersed in a bath of size-changed active particles in two dimensional space using Langevin dynamics simulations. Particular attention is paid to how the radius of gyration Rg of the polymer chain depends on the size σc of active crowders. We find that Rg shows nontrivial non-monotonic dependence on σc: The chain first swells upon increasing σc, reaching a fully expanded state with maximum Rg, and then, Rg decreases until the chain collapses to a compact coil state if the crowder is large enough. Interestingly, the chain may oscillate between a collapse state and a stretched state at moderate crowder size. Analysis shows that it is the competition between two effects of active particles, one stretching the chain from inside due to persistence motion and the other compressing the chain from outside, that leads to the non-monotonic dependence. Besides, the diffusion of the polymer chain also shows nontrivial non-monotonic dependence on σc. Our results demonstrate the important interplay between particle activity and size associated with polymer configurations in active crowding environments.

Light Scattering Study of Internal Dynamics of Hyperbranched Polymers with Controlled Branching Patterns and Low Polydispersities in Dilute Solutions

Internal dynamics of flexible polymer chains is one of the most important fundamental problems in polymer physics. Although numerous efforts have been devoted to the understanding of internal dynamics for linear polymers, little attention was paid to branched systems. This work aims to elucidate how the branching effect quantitatively influences the internal motions of long-subchain hyperbranched polymers in dilute solution. By light scattering study of four hyperbranched polystyrene samples with controlled branching patterns and low polydispersities (Mw/Mn < 1.40 and Mw ∼ 107 g/mol), we quantified and analyzed the asymptotic behavior of the reduced first cumulant [Γ* = Γ(q)/(q3kBT/η0)], the value of Γ* at high q-regime [the approximate values of Γ*(∞)], the scattering vector (q) dependence of linewidth [Γ(q)], the number of relaxation modes in Γ(q)-distribution curves, the characteristic relaxation time (τ1) of the first internal mode, and the q-dependent relative strength of internal motions. Our results reveal: (i) Γ*(∞) is not sensitive to the branching density, but more related to the fractal dimension of a given system; (ii) the asymptotic power law in the intermediate qRh regime (1.5 < qRh < 3.0), compared to Γ*(∞), is a better indicator, which could reflect the structural details of different branched systems; (iii) the branching effect could lead to the suppression of overall internal motions, but the introduction of moderate branching could enhance the contribution of some energetically favorable internal modes in linewidth distribution; (iv) by comparing the experimentally determined and theoretically calculated τ1, the result provides direct experimental evidence supporting that the classical theory is not applicable to hyperbranched polymer systems. The present work not only helps clarify some long-standing controversial issues existed in previous studies, but also provides useful experimental data for further theoretical calculations of internal dynamics for branched systems.

Kinetics of polymer looping with macromolecular crowding: effects of volume fraction and crowder size.

The looping of polymers such as DNA is a fundamental process in the molecular biology of living cells, whose interior is characterised by a high degree of molecular crowding. We here investigate in detail the looping dynamics of flexible polymer chains in the presence of different degrees of crowding. From the analysis of the looping-unlooping rates and the looping probabilities of the chain ends we show that the presence of small crowders typically slows down the chain dynamics but larger crowders may in fact facilitate the looping. We rationalise these non-trivial and often counterintuitive effects of the crowder size on the looping kinetics in terms of an effective solution viscosity and standard excluded volume. It is shown that for small crowders the effect of an increased viscosity dominates, while for big crowders we argue that confinement effects (caging) prevail. The tradeoff between both trends can thus result in the impediment or facilitation of polymer looping, depending on the crowder size. We also examine how the crowding volume fraction, chain length, and the attraction strength of the contact groups of the polymer chain affect the looping kinetics and hairpin formation dynamics. Our results are relevant for DNA looping in the absence and presence of protein mediation, DNA hairpin formation, RNA folding, and the folding of polypeptide chains under biologically relevant high-crowding conditions.

Do bending and torsional potentials affect the unraveling dynamics of flexible polymer chains in extensional or shear flows?

We compare the flow-induced unraveling of a bead-spring model chain in which each stiff spring corresponds to a single Kuhn step to that of an atomistic representation of the backbone of the same polymer chain with realistic bending and torsional potentials. In our earlier work [Jain, S. and Larson, R.G. 2008. Effect of bending and torsional potentials on high-frequency viscoelasticity of dilute polymer solutions. Macromolecules 41(10), 3692–3700], we showed that in the linear viscoelastic regime, bending and torsional potentials suppress fast local diffusive modes. Now, in strong shear and extensional flows, we observe that bending and torsional potentials have only a slight effect on unraveling dynamics. However, in shear flow, we find that for relatively short coarse-grained chains having less than 20 or so Kuhn steps—representing polymers with fewer than around 150 backbone bonds—coarse-graining introduces periodic peaks in the probability distribution of steady-state stretch. We believe this occurs at high shear because of the dominance of a discrete set of stretch values each of which corresponds to an integral number of bonds that are nearly fully aligned between back-folds that are created during the chain's tumbling orbit. Even this difference between coarse-grained and realistic fine-grained chains disappears for more typical long chain lengths.

Dynamics of polymers in a particle-based mesoscopic solvent

We study the dynamics of flexible polymer chains in solution by combining multiparticle-collision dynamics (MPCD), a mesoscale simulation method, and molecular-dynamics simulations. Polymers with and without excluded-volume interactions are considered. With an appropriate choice of the collision time step for the MPCD solvent, hydrodynamic interactions build up properly. For the center-of-mass diffusion coefficient, scaling with respect to polymer length is found to hold already for rather short chains. The center-of-mass velocity autocorrelation function displays a long-time tail which decays algebraically as (Dt)(-3/2) as a function of time t, where D is the diffusion coefficient. The analysis of the intramolecular dynamics in terms of Rouse modes yields excellent agreement between simulation data and results of the Zimm model for the mode-number dependence of the mode-amplitude correlation functions.

Studies on Dynamic Heterogeneity in Miscible Polymer Blends and Dynamics of Flexible Polymers

This paper presents our three studies: (1) dynamic heterogeneity in miscible polymer blends, (2) dielectric study on the dynamics of flexible polymer chains in melts and solutions, and (3) stress relaxation of entangled polymer systems in biaxial extension. In the study of (1), we investigated the segmental and global dynamics mainly in miscible polyisoprene (PI) / poly(vinyl ethylene) (PVE) blends. Specifically, we estimated the characteristic sizes of the segmental motion. Furthermore, in order to see the effect of the concentration fluctuation (CF) on the segmental dynamics, we compared the dielectric relaxation spectra of the segmental motion between PI/PVE blend and PI-PVE diblock copolymer based on the fact that the CF amplitude is suppressed in the diblock copolymer system. In the second study, dipole inverted type-A polymers are used to investigate the detailed chain dynamics. In the third study, we determined the damping function in biaxial extensional deformation for polystyrene melts and compared with Doi-Edwards theory.

Dynamics of Flexible Polymer Chains in Elongational Flow

This paper focuses on the recent developments achieved in our group in the field of flexible polymer chain dynamics in elongational flow. Stress-induced orientation and deformation in flowing polymer solution is being surveyed in a wide variety of manifestations. Two types of flow fields have been investigated: the opposite-jet flow with a stagnation point, and the abrupt contraction flow with open flowlines. Emphasis has been placed on the latter geometry due to its widespread occurrence. Degradation experiments performed with dilute PS solutions in abrupt contraction flow demonstrate a distinct propensity for midchain scission, a feature apparently consistent with highly extended chains. On the other hand, the critical strain-rate for chain fracture (ἐf) determined under the same experimental conditions scales with M-1. The inverse relationship with polymer MW is characteristic of partly uncoiled chains but not of highly extended chains, for which a stronger MW dependence (ἐf) ∝ M-2 is expected. The 'yo-yo' model, which could rationalize these findings, is refuted by fluorescence depolarisation measurements which indicated that central orientation is more progressive than the average segmental orientation. For the first time, polarization-modulated birefringence was used to determine the state of local chain orientation in abrupt contraction flow. Axisymmetric contraction flow is complicated by the large variations in local molecular orientation along different streamlines. To account for this effect, a numerical inverse Abel transform has been devised to compute local birefringence (Δn) from experimental retardation (δ). Results show a steep decrease in birefringence with axial distance. Birefringence profiles determined in a direction perpendicular to the flow show a maximum, not at the centre, but in the vicinity of the orifice walls. This observation is in accord with flow simulation results which indicated the presence of extreme strain rates near re-entrant corners. Molecular extension ratios calculated with the Kuhn-Grün theory gives a qualitative description of polymer uncoiling up to about one third of the chain contour length at the approach of capillary entrance. A notable departure from the affine deformation model is, however, observed with multiple birefringence saturation levels changing with flow rate conditions. This behaviour could be explained by the presence of transient molecular conformations. Efforts are underway to visualize these metastable states by single chain fluorescence video microscopy using UHMW polystyrene randomly grafted with anthracene chromophores.

Dynamics of rigid and flexible polymer chains in confined geometries III. Wall-bead hydrodynamic interaction

As a continuation of the previous paper, dynamics of rigid and flexible polymer chains in viscous medium was reexamined in order to include the interaction of boundary and polymer chains. As models for rigid and flexible chains, rigid and linear elastic dumbbells were considered, which are essentially composed of two beads of frictional sources. The orientation distribution function was obtained by including anisotropic diffusivities of the bead due to the presence of the walls, and Theological properties were predicted to give us the dependence on an additional parameter, ego,h relative size of bead to the gap width, as expected. Dynamics of flexible polymer chains showed a similar dependence on the relative size of bead, but exhibited no dependence on the shear rate as the case of no boundaries.