Rheology and Microscopic Topology of Entangled Polymeric Liquids

Topological tuning of DNA mobility in entangled solutions of supercoiled plasmids

Ring polymers in dense solutions are among the most intriguing problems in polymer physics. Because of its natural occurrence in circular form, DNA has been extensively used as a proxy to study the fundamental physics of ring polymers in different topological states. Yet, torsionally constrained-such as supercoiled-topologies have been largely neglected so far. The applicability of existing theoretical models to dense supercoiled DNA is thus unknown. Here, we address this gap by coupling large-scale molecular dynamics simulations with differential dynamic microscopy of entangled supercoiled DNA plasmids. We find that, unexpectedly, larger supercoiling increases the size of entangled plasmids and concomitantly induces an enhancement in DNA mobility. These findings are reconciled as due to supercoiling-driven asymmetric and double-folded plasmid conformations that reduce interplasmid entanglements and threadings. Our results suggest a way to topologically tune DNA mobility via supercoiling, thus enabling topological control over the (micro)rheology of DNA-based complex fluids.

Comparing equilibration schemes of high-molecular-weight polymer melts with topological indicators

Recent theoretical studies have demonstrated that the behaviour of molecular knots is a sensitive indicator of polymer structure. Here, we use knots to verify the ability of two state-of-the-art algorithms-configuration assembly and hierarchical backmapping-to equilibrate high-molecular-weight (MW) polymer melts. Specifically, we consider melts with MWs equivalent to several tens of entanglement lengths and various chain flexibilities, generated with both strategies. We compare their unknotting probability, unknotting length, knot spectra, and knot length distributions. The excellent agreement between the two independent methods with respect to knotting properties provides an additional strong validation of their ability to equilibrate dense high-MW polymeric liquids. By demonstrating this consistency of knotting behaviour, our study opens the way for studying topological properties of polymer melts beyond time and length scales accessible to brute-force molecular dynamics simulations.

Thermodynamically consistent incorporation of entanglement spatial fluctuations in the slip-link model

We evaluate the thermodynamic consistency of the anisotropic mobile slip-link model for entangled flexible polymers. The level of description is that of a single chain, whose interactions with other chains are coarse grained to discrete entanglements. The dynamics of the model consist of the motion of entanglements through space and of the chain through the entanglements, as well as the creation and destruction of entanglements, which are implemented in a mean-field way. Entanglements are modeled as discrete slip links, whose spatial positions are confined by quadratic potentials. The confinement potentials move with the macroscopic velocity field, hence the entanglements fluctuate around purely affine motion. We allow for anisotropy of these fluctuations, described by a set of shape tensors. By casting the model in the form of the general equation for the nonequilibrium reversible-irreversible coupling from nonequilibrium thermodynamics, we show that (i) since the confinement potentials contribute to the chain free energy, they must also contribute to the stress tensor, (ii) these stress contributions are of two kinds: one related to the virtual springs connecting the slip links to the centers of the confinement potentials and the other related to the shape tensors, and (iii) these two kinds of stress contributions cancel each other if the confinement potentials become anisotropic in flow, according to a lower-convected evolution of the confinement strength or, equivalently, an upper-convected evolution of the shape tensors of the entanglement spatial fluctuations. In previous publications, we have shown that this cancellation is necessary for the model to obey the stress-optical rule and the Green-Kubo relation, and simultaneously to agree with plateau modulus predictions of multichain models and simulations.

Crowded solutions of single-chain nanoparticles under shear flow

Single-chain nanoparticles (SCNPs) are ultrasoft objects obtained through purely intramolecular cross-linking of single polymer chains. By means of computer simulations with implemented hydrodynamic interactions, we investigate for the first time the effect of the shear flow on the structural and dynamic properties of SCNPs in semidilute and concentrated solutions. We characterize the dependence of several conformational and dynamic observables on the shear rate and the concentration, obtaining a set of power-law scaling laws. The concentration has a very different effect on the shear rate dependence of the former observables in SCNPs than in simple linear chains. Whereas for the latter the scaling behaviour is marginally dependent on the concentration, two clearly different scaling regimes are found for the SCNPs below and above the overlap concentration. At fixed shear rate SCNPs and linear chains also respond very differently to crowding. Whereas, at moderate and high Weissenberg numbers the linear chains swell, the SCNPs exhibit a complex non-monotonic behaviour. We suggest that these findings are inherently related to the topological interactions preventing concatenation of the SCNPs, which lead to less interpenetration than for linear chains, and to the limitation to stretching imposed by the permanent cross-links in the SCNPs, which itself limits the ways to spatially arrange in the shear flow.

Dynamical Entanglement and Cooperative Dynamics in Entangled Solutions of Ring and Linear Polymers

Understanding how entanglements affect the behavior of polymeric complex fluids is an open challenge in many fields. To elucidate the nature and consequence of entanglements in dense polymer solutions, we propose a novel method: a "dynamical entanglement analysis" (DEA) to extract spatiotemporal entanglement structures from the pairwise displacement correlation of entangled chains. By applying this method to large-scale molecular dynamics simulations of linear and unknotted, nonconcatenated ring polymers, we find a strong and unexpected cooperative dynamics: the footprint of mutual entrainment between entangled chains. We show that DEA is a powerful and sensitive probe that reveals previously unnoticed and architecture-dependent spatiotemporal structures of dynamical entanglement in polymeric solutions. We also propose a mean-field approximation of our analysis that provides previously under-appreciated physical insights into the dynamics of generic entangled polymers. We envisage DEA will be useful to analyze the dynamical evolution of entanglements in generic polymeric systems such as blends and composites.

In-Situ Rheological Studies of Cationic Lignin Polymerization in an Acidic Aqueous System

The chemistry of lignin polymerization was studied in the past. Insights into the rheological behavior of the lignin polymerization system would provide crucial information required for tailoring lignin polymers with desired properties. The in-situ rheological attributes of lignin polymerization with a cationic monomer, [2-(methacryloyloxy)ethyl] trimethylammonium chloride (METAC), were studied in detail in this work. The influences of process conditions, e.g., temperature, component concentrations, and shear rates, on the viscosity variations of the reaction systems during the polymerization were studied in detail. Temperature, METAC/lignin molar ratio, and shear rate increases led to the enhanced viscosity of the reaction medium and lignin polymer with a higher degree of polymerization. The extended reaction time enhanced the viscosity attributing to the larger molecular weight of the lignin polymer. Additionally, the size of particles in the reaction system dropped as reaction time was extended. The lignin polymer with a larger molecular weight and Rg behaved mainly as a viscose (tan δ > 1 or G″ > G') material, while the lignin polymer generated with smaller molecular weight and shorter Rg demonstrated strong elastic characteristics with a tan (δ) lower than unity over the frequency range of 0.1-10 rad/s.

Novel Mode of Noncrystallographic Branching in the Initial Stages of Polymer Fibril Growth

Spherulites are the most ubiquitous of polycrystalline microstructure of polymers; they develop under a wide range of conditions by the subsequent branching of crystalline lamella that results in an overall spherical shape. Despite significant efforts over decades, the mechanisms behind branching remain unclear. Molecular dynamics simulations in polyethylene reveal the molecular-level origin of noncrystallographic branching and the initial formation of fibrils. We find that the growth of crystalline lamella by reeling in and folding of polymer chains causes surprisingly large local deformation which, in turn, aligns the chains in the neighboring undercooled liquid. Thus, subsidiary grains nucleate with preferred orientations resulting in fibril growth with branching at small angles, consistent with those observed experimentally.

Efficient equilibration of confined and free-standing films of highly entangled polymer melts

Equilibration of polymer melts containing highly entangled long polymer chains in confinement or with free surfaces is a challenge for computer simulations. We approach this problem by first studying polymer melts based on the soft-sphere coarse-grained model confined between two walls with periodic boundary conditions in two directions parallel to the walls. Then, we insert the microscopic details of the underlying bead-spring model. Tuning the strength of the wall potential, the monomer density of confined polymer melts in equilibrium is kept at the bulk density even near the walls. In a weak confining regime, we observe the same conformational properties of chains as in the bulk melt showing that our confined polymer melts have reached their equilibrated state. Our methodology provides an efficient way of equilibrating large polymer films with different thicknesses and is not confined to a specific underlying microscopic model. Switching off the wall potential in the direction perpendicular to the walls enables to study free-standing highly entangled polymer films or polymer films with one supporting substrate.

Glass Transition of Disentangled and Entangled Polymer Melts: Single-Chain-Nanoparticles Approach

We study the effect of entanglements on the glass transition of high molecular weight polymers, by the comparison of single-chain nanoparticles (SCNPs) and equilibrated melts of high-molecular weight polystyrene of identical molecular weight. SCNPs were prepared by electrospraying technique and characterized using scanning electron microscopy and atomic force microscopy techniques. Differential scanning calorimetry, Brillouin light spectroscopy, and rheological experiments around the glass transition were compared. In parallel, entangled and disentangled polymer melts were also compared under cooling from molecular dynamics simulations based on a bead-spring polymer model. While experiments suggest a small decrease in the glass transition temperature of films of nanoparticles in comparison to entangled melts, simulations do not observe any significant difference, despite rather different chain conformations.

Prediction of crossover in the molecular weight dependence of polyethylene viscosity using a polymer free volume theory

Based upon the Doolittle concept that viscosity and free volume are inversely related, we used the Boltzmann equation along with a polymer free volume theory to calculate the viscosity (η) of polyethylene with three different molecular structures - linear, ring and four-arm symmetrical star - over a molecular weight (M) range of 420-14 000 g mol-1. Free volume parameters were estimated using the Polymer Reference Interaction Site Model (PRISM) and generic van der Waals (GvdW) equation. The polymer free volume theory was able to describe the crossovers in the molecular weight dependence of the viscosity of the aforementioned molecular structures. In particular, the crossover for the linear structure was predicted at about 3000 g mole-1 with η ∼ M1.5 in the unentangled regime and η ∼ M3.3 in the entangled regime that agree reasonably well with experiment. The predictions for the other two structures also agree with the available simulation data. We also demonstrated that the accuracy of the viscosity prediction was sensitive to the difference between two free volume parameters (i.e., (φ+ - F)). Here, F signifies the probability of a bead finding free volume greater than the critical free volume while the fraction of such beads (φ+) can be used to calculate the activation energy. The theory also reproduced the temperature dependence of η for the linear structure at different M, giving apparent activation energy (Eappa) values in the range of 5.30-7.70 kcal mole-1 that are in good agreement with experimental values of 5.50-6.75 kcal mole-1. This work demonstrates for the first time that viscosity of polymer melts can be determined from the polymer free volume theory.

Incident Velocity Induced Nonmonotonic Aging of Vapor-Deposited Polymer Glasses

Physical vapor deposition can produce remarkably stable glassy materials. However, a mechanistic understanding of the interplay between control parameters during such nonequilibrium processing (e.g., deposition rate, substrate temperature, incident velocity, etc.) remains an unresolved challenge to date. In this study, we report on the discovery of a dual role of incident molecules' mass-center velocity in controlling the stability of vapor-deposited glasses through atomistic modeling. On one hand, larger velocities would impose the surface atoms into a higher effective temperature environment and facilitate the relaxation as the sample approaches the glass transition temperature. On the other hand, larger velocities would meanwhile cause faster cooling rates for the deposited molecules and destabilize the sample. The competition between the two factors results in a remarkable nonmonotonic variation of the sample's stability where an optimal velocity can be quantitatively resolved. Implications of our findings for better controlling molecular-level mechanisms in glassy materials are discussed.

Dynamics of poly[n]catenane melts

Inspired by advances in the chemical synthesis of interlocking polymer architectures, extensive molecular dynamics simulations have been conducted to study the dynamical properties of poly[n]catenanes-polymers composed entirely of interlocking rings-in the melt state. Both the degree of polymerization (number of links) and the number of beads per ring are systematically varied, and the results are compared to linear and ring polymers. A simple Rouse-like model is presented, and its analytical solution suggests a decomposition of the dynamics into "ring-like" and "linear-like" regimes at short and long times, respectively. In agreement with this picture, multiple sub-diffusive regimes are observed in the monomer mean-squared-displacements even though interchain entanglement is not prevalent in the system. However, the Rouse-type model does not account for the topological effects of the mechanical bonds, which significantly alter the dynamics at intermediate length scales both within the rings and at the chain segment scales. The stress relaxation in the system is extremely rapid and may be conveniently separated into ring-like and linear-like contributions, again in agreement with the Rouse picture. However, the viscosity has a non-monotonic dependence on the ring size for long chains, which disagrees strongly with theoretical predictions. This unexpected observation cannot be explained in terms of chain disentanglement and is inconsistent with other measures of polymer relaxation. Possible mechanisms for this behavior are proposed and implications for materials design are discussed.

Threading-Induced Dynamical Transition in Tadpole-Shaped Polymers

The relationship between polymer topology and bulk rheology remains a key question in soft matter physics. Architecture-specific constraints (or threadings) are thought to control the dynamics of ring polymers in ring-linear blends, which thus affects the viscosity to range between that of the pure rings and a value larger, but still comparable to, that of the pure linear melt. Here we consider qualitatively different systems of linear and ring polymers, fused together in "chimeric" architectures. The simplest example of this family is a "tadpole"-shaped polymer, a single ring fused to the end of a single linear chain. We show that polymers with this architecture display a threading-induced dynamical transition that substantially slows chain relaxation. Our findings shed light on how threadings control dynamics and may inform design principles for chimeric polymers with topologically tunable bulk rheological properties.

Unified Analytic Expressions for the Entanglement Length, Tube Diameter, and Plateau Modulus of Polymer Melts

By combining molecular dynamics simulations and topological analyses with scaling arguments, we obtain analytic expressions that quantitatively predict the entanglement length N_{e}, the plateau modulus G, and the tube diameter a in melts that span the entire range of chain stiffnesses for which systems remain isotropic. Our expressions resolve conflicts between previous scaling predictions for the loosely entangled [Lin-Noolandi, Gℓ_{K}^{3}/k_{B}T∼(ℓ_{K}/p)^{3}], semiflexible [Edwards-de Gennes: Gℓ_{K}^{3}/k_{B}T∼(ℓ_{K}/p)^{2}], and tightly entangled [Morse, Gℓ_{K}^{3}/k_{B}T∼(ℓ_{K}/p)^{1+ϵ}] regimes, where ℓ_{K} and p are, respectively, the Kuhn and packing lengths. We also find that maximal entanglement (minimal N_{e}) coincides with the onset of local nematic order.

Single particles as resonators for thermomechanical analysis

Thermal methods are indispensable for the characterization of most materials. However, the existing methods require bulk amounts for analysis and give an averaged response of a material. This can be especially challenging in a biomedical setting, where only very limited amounts of material are initially available. Nano- and microelectromechanical systems (NEMS/MEMS) offer the possibility of conducting thermal analysis on small amounts of materials in the nano-microgram range, but cleanroom fabricated resonators are required. Here, we report the use of single drug and collagen particles as micro mechanical resonators, thereby eliminating the need for cleanroom fabrication. Furthermore, the proposed method reveals additional thermal transitions that are undetected by standard thermal methods and provide the possibility of understanding fundamental changes in the mechanical properties of the materials during thermal cycling. This method is applicable to a variety of different materials and opens the door to fundamental mechanistic insights.

Packing structure of semiflexible rings

Unraveling the packing structure of dense assemblies of semiflexible rings is not only fundamental for the dynamical description of polymer rings, but also key to understand biopackaging, such as observed in circular DNA of viruses or genome folding. Here we use X-ray tomography to study the geometrical and topological features of disordered packings of rubber bands in a cylindrical container. Assemblies of short bands assume a liquid-like disordered structure, with short-range orientational order, and reveal only minor influence of the container. In the case of longer bands, the confinement causes folded configurations and the bands interpenetrate and entangle. Most of the systems are found to display a threading network which percolates the system. Surprisingly, for long bands whose diameter is more than twice the diameter of the container, we found that all bands interpenetrate each other, in a complex fully entangled structure.

Performance of Coarse Graining in Estimating Polymer Properties: Comparison with the Atomistic Model

Combining atomistic and coarse-grained (CG) models is a promising approach for quantitative prediction of polymer properties. However, the gaps between the length and time scales of atomistic and CG models still need to be bridged. Here, the scale gaps of the atomistic model of polyethylene melts, the bead–spring Kremer–Grest model, and dissipative particle dynamics with the slip-spring model were investigated. A single set of spatial and temporal scaling factors was determined between the atomistic model and each CG model. The results of the CG models were rescaled using the set of scaling factors and compared with those of the atomistic model. For each polymer property, a threshold value indicating the onset of static or dynamic universality of polymers was obtained. The scaling factors also revealed the computational efficiency of each CG model with respect to the atomistic model. The performance of the CG models of polymers was systematically evaluated in terms of both the accuracy and computational efficiency.

Research Progress on the Collaborative Drag Reduction Effect of Polymers and Surfactants

Polymer additives and surfactants as drag reduction agents have been widely used in the field of fluid drag reduction. Polymer additives can reduce drag effectively with only a small amount, but they degrade easily. Surfactants have an anti-degradation ability. This paper categorizes the mechanism of drag reducing agents and the influencing factors of drag reduction characteristics. The factors affecting the degradation of polymer additives and the anti-degradation properties of surfactants are discussed. A mixture of polymer additive and surfactant has the characteristics of high shear resistance, a lower critical micelle concentration (CMC), and a good drag reduction effect at higher Reynolds numbers. Therefore, this paper focuses more on a drag reducing agent mixed with a polymer and a surfactant, including the mechanism model, drag reduction characteristics, and anti-degradation ability.

Topological Linking Drives Anomalous Thickening of Ring Polymers in Weak Extensional Flows

Molecular dynamics simulations confirm recent extensional flow experiments showing ring polymer melts exhibit strong extension-rate thickening of the viscosity at Weissenberg numbers Wi≪1. Thickening coincides with the extreme elongation of a minority population of rings that grows with Wi. The large susceptibility of some rings to extend is due to a flow-driven formation of topological links that connect multiple rings into supramolecular chains. Links form spontaneously with a longer delay at lower Wi and are pulled tight and stabilized by the flow. Once linked, these composite objects experience larger drag forces than individual rings, driving their strong elongation. The fraction of linked rings depends nonmonotonically on Wi, increasing to a maximum when Wi∼1 before rapidly decreasing when the strain rate approaches 1/τ_{e}.

Investigating the effect of grafting density on the surface properties for sequence-determined fluoropolymer films

Six sequence-determined fluoropolymers were synthesized and their surface properties were affected by their grafting densities. The reason can be attributed to the assembled structure of the perfluoroalkyl chains at the surface.

Brush-Like Polymers and Entanglements: From Linear Chains to Filaments

Dynamics of melts and solutions of high molecular weight polymers and biopolymers is controlled by topological constraints (entanglements) imposing a sliding chain motion along an effective confining tube. For linear chains, the tube size is determined by universal packing number P_e, the number of polymer strands within a confining tube that is required for chains to entangle. Here we show that in melts of brush-like (graft) polymers, consisting of linear chain backbones with grafted side chains, P_e is not a universal number and depends on the molecular architecture. In particular, we use coarse-grained molecular dynamics simulations to demonstrate that the packing number is a nonmonotonic function of the ratio R_nsc/R_ng of the size of the side chains R_nsc to that of the backbone spacer between neighboring grafting points R_ng. This parameter characterizes the degree of mutual interpenetration between side chains of the same macromolecule. We show that P_e of brush-like polymers first decreases with increasing side chain grafting density in the dilute side chain regime (R_nsc < R_ng), then begins to increase in the regime of overlapping side chains (R_nsc > R_ng), approaching the value for linear chains in the limit of densely grafted side chains. This dependence of the packing number reflects a crossover from chain-like entanglements in systems with loosely grafted side chains (comb-like polymers) to entanglements between flexible filaments (bottlebrush-like polymers). Our simulation results are in agreement with the experimental data for the dependence of a plateau modulus on the molecular architecture of graft poly(n-butyl acrylates) and poly(norbornene)-graft-poly(lactide) melts.

Polymer dynamics under confinement

We review recent neutron scattering work and related results from simulation and complementary techniques focusing on the microscopic dynamics of polymers under confinement. Confinement is either realized in model porous materials or in polymer nanocomposites (PNC). The dynamics of such confined polymers is affected on the local segmental level, the level of entanglements as well as on global levels: (i) at the segmental level the interaction with the surface is of key importance. At locally repulsive surfaces compared to the bulk the segmental dynamics is not altered. Attractive surfaces slow down the segmental dynamics in their neighborhood but do not give rise to dead, glassy layers. (ii) Confinement generally has little effect on the inter-chain entanglements: both for weakly as well as for marginally confined polymers the reptation tube size is not changed. Only for strongly confined polymers disentanglement takes place. Similarly, in PNC at higher NP loading disentanglement phenomena are observed; in addition, at very high loading a transition from polymer caused topological constraints to purely geometrical constraints is observed. (iii) On the more global scale NSE experiments revealed important information on the nature of the interphase between adsorbed layer and bulk polymer. (iv) Polymer grafts at NP mutually confine each other, an effect that is most pronounced for one component NP. (v) Global diffusion of entangled polymers both in weakly and strongly attractive PNC is governed by the ratio of bottle-neck to chain size that characterizes the 'entropic barrier' for global diffusion.

Clustering of Entanglement Points in Highly Strained Polymer Melts

Polymer melts undergoing large deformation by elongation are studied by molecular dynamics simulations of bead-spring chains in melts. By applying a primitive path analysis to strongly deformed polymer melts, the role of topological constraints in highly entangled polymer melts is investigated and quantified. We show that the overall, large scale conformations of the primitive paths (PPs) of stretched chains follow affine deformation while the number and the distribution of entanglement points along the PPs do not. Right after deformation, PPs of chains retract in both directions parallel and perpendicular to the elongation. Upon further relaxation we observe a long-lived clustering of entanglement points. Together with the delayed relaxation time this leads to a metastable inhomogeneous distribution of topological constraints in the melts.