Tubes, Topology, and Polymer Entanglement

From disorder to order: A dynamic approach to mesophase formation in soft sphere model

This study explores the dynamics of self-assembly and mesophase formation through molecular dynamics simulations of hexagonal and lamellar systems using a simplified coarse-grained model. We focus on characterizing the order-disorder transitions driven by temperature variations and emphasize the often overlooked disordered regime, which serves as a precursor to periodic mesoscale ordering. Our findings not only underscore the morphological richness of the disordered regime, comparable to that of its periodic counterparts, but also reveal the presence of clustering regimes within isotropic phases, thus corroborating prior experimental and theoretical observations. By employing the dynamic correlation coefficient, this work introduces a novel approach to understanding the fundamental mechanisms of mesophase formation, providing new insights into the complex dynamics of self-assembly.

Elucidating the role of physicochemical interactions on gel rheology

Soft materials are characterized by their intricate interplay of structure, dynamics, and rheological properties. This complexity makes it challenging to accurately predict their response to shear stress. Here, we investigate how the nature of bonds - electrostatic attractions, physical entanglements, physical repulsion, and covalent bonds - affects the linear and nonlinear rheology of gels. Specifically, we determine the critical roles these bonds play in the yield transition and thixotropic recovery of gel properties through a combination of linear oscillatory deformations, serial creep divergence measurements, and time-resolved flow sweeps. Different classes of gels are prepared with nearly identical linear rheology but significantly different yield transitions and nonlinear properties post-yielding. These differences are directly related to the kinetics by which the underlying elastic networks rebuild after flow. Gels which exhibit thixotropic hysteresis are able to fully recover their yield stress over time while non-thixotropic gels possess time-independent yielding metrics. This direct comparison between thixotropy and yielding reveals the intimate relationship between these phenomena and their controlling physical mechanisms within soft, amorphous materials.

Molecular dynamics simulation of the impact of the surface topology of carbon black on the mechanical properties of elastomer nanocomposites

Carbon black has always played a pivotal role in reinforcing elastomers because it remarkably improves the mechanical properties. The reinforcing effect of carbon black is influenced by its grades, which mainly depend on the difference in the structure of the carbon black particles. Despite many traditional experiments on the performance of carbon black composites, there has been less emphasis on reinforcement mechanisms due to the challenges associated with unraveling the intermolecular interactions. In this paper, a coarse grained molecular dynamics simulation was employed to examine the relationship between the morphology of the carbon black particles and the mechanical properties of the elastomer nanocomposites. Specifically, three different morphological carbon black nanoparticle models, including the smooth particle model, rough particle model, and the rough ellipsoid model, were constructed first. We then focused on investigating the changes of the mechanical properties by systematically varying the filling fraction of the carbon black particles, and the strength of the interfacial interaction between the filler and the rubber. The results indicated that the surface roughness and the filler's shape had a significant impact on the mechanical properties of the filled rubber models. The mechanical enhancement effect of the rough ellipsoidal carbon black is around 50-400% higher than that of the smooth carbon black, and the stronger the interfacial interactions, the more pronounced the enhancement. In addition, the rough ellipsoid filled system has low hysteresis, low permanent deformation, and high fatigue resistance. In general, this work explores the strengthening mechanism of carbon black on the elastomer at the molecular level and generates new insight into the design and fabrication of novel reinforcing fillers.

Molecular Dynamics Simulation of Entangled Melts at High Rates: Identifying Entanglement Lockup Mechanism Leading to True Strain Hardening

In the present work, molecular dynamics simulations are carried out based on the bead-spring model to indicate how the entanglement lockup manifests in the late stage of fast Rouse-Weissnberg number (Wi_R >>1) uniaxial melt stretching of entangled polymer melts. At high strains, distinct features show up to reveal the emergence of an increasingly tightened entanglement network. Chain tension can build up, peaking at the middle of the chain, to a level for chain scission, through accumulated interchain interactions, as if there is a tug-of-war ongoing for each load-bearing chain. Thanks to the interchain uncrossability, network junctions form by the pairing of two or more hairpins. It is hypothesized that the interchain entanglement at junctions can lockup through prevailing twist-like interchain couplings as long as Wi_R > 9. In this limit, a significant fraction of chains act like cyclic chains to form a network held by interchain uncrossability, and appreciable chain tension emerges.

Loading and Release of Quercetin from Contact-Drawn Polyvinyl Alcohol Fiber Scaffolds

Polymeric drug releasing systems have numerous applications for the treatment of chronic diseases and traumatic injuries. In this study, a simple, cost-effective, and scalable method for dry spinning of crosslinked polyvinyl alcohol (PVA) fibers is presented. This method utilizes an entangled solution of PVA to form liquid bridges that are drawn into rapidly drying fibers through extensional flow. The fibers are crosslinked by a one-pot reaction in which glyoxal is introduced to the PVA solution prior to contact drawing. Failure analysis of fiber formation is used to understand the interplay of polymer concentration, glyoxal concentration, and crosslinking time to identify appropriate formulations for the production of glyoxal-crosslinked PVA fibers. The small molecule quercetin (an anti-inflammatory plant flavonoid) can be added to the one-pot reaction and is shown to be incorporated into the fibers in a concentration-dependent manner. Upon rehydration in an aqueous medium, the glyoxal-crosslinked PVA fiber scaffolds retain their morphology and slowly degrade, as measured over the course of 10 days. As the scaffolds degrade, they release the loaded quercetin, reaching a cumulative release of 56 ± 6% of the loaded drug after 10 days. The bioactivity of the released quercetin is verified by combining quercetin-loaded fibers with contact-drawn polyethylene oxide-type I collagen (PEO-Col) fibers and monitoring the growth of PC12 cells on the fibers. PC12 cells readily attach to the PEO-Col fibers and display increased nerve growth factor-induced elongation and neurite formation in the presence of quercetin-loaded PVA fibers relative to substrates formed from only PEO-Col fibers or PEO-Col and PVA fibers without quercetin.

Toward More Universal Prediction of Polymer Solution Viscosity for Solvent-Based Recycling

The viscosity of polymer solutions is important for both polymer synthesis and recycling. Polymerization reactions can become hampered by diffusional limitations once a viscosity threshold is reached, and viscous solutions complicate the cleaning steps during the dissolution–precipitation technique. Available experimental data is limited, which is more severe for green solvents, justifying dedicated viscosity data recording and interpretation. In this work, a systematic study is therefore performed on the viscosity of polystyrene solutions, considering different concentrations, temperatures, and conventional and green solvents. The results show that for the shear rate range of 1–1000 s^–1, the solutions with concentrations between 5 and 39 wt % display mainly Newtonian behavior, which is further confirmed by the applicability of the segment-based Eyring-NRTL and Eyring-mNRF models. Moreover, multivariate data analysis successfully predicts the viscosity of polystyrene solutions under different conditions. This approach will facilitate future data recording for other polymer–solvent combinations while minimizing experimental effort.

Formation of Core-Sheath Polymer Fibers by Free Surface Spinning of Aqueous Two-Phase Systems

Core-sheath fibers have numerous applications ranging from composite materials for advanced manufacturing to materials for drug delivery and regenerative medicine. Here, a simple and tunable approach for the generation of core-sheath fibers from immiscible solutions of dextran and polyethylene oxide is described. This approach exploits the entanglement of polymer molecules within the dextran and polyethylene oxide phases for free surface spinning into dry fibers. The mechanism by which these core-sheath fibers are produced after contact with a solid substrate (such as a microneedle) involves complex flows of the phase-separating polymer solutions, giving rise to a liquid-liquid core-sheath flow that is drawn into a liquid bridge. This liquid bridge then elongates into a core-sheath fiber through extensional flow as the contacting substrate is withdrawn. The core-sheath structure of the fibers produced by this approach is confirmed by attenuated total reflection Fourier-transform infrared spectroscopy and confocal microscopy. Tuning of the core diameter is also demonstrated by varying the weight percentage of dextran added to the reservoir from which the fibers are formed.

Tough, Transparent, 3D-Printable, and Self-Healing Poly(ethylene glycol)-Gel (PEGgel)

Polymer gels, such as hydrogels, have been widely used in biomedical applications, flexible electronics, and soft machines. Polymer network design and its contribution to the performance of gels has been extensively studied. In this study, the critical influence of the solvent nature on the mechanical properties and performance of soft polymer gels is demonstrated. A polymer gel platform based on poly(ethylene glycol) (PEG) as solvent is reported (PEGgel). Compared to the corresponding hydrogel or ethylene glycol gel, the PEGgel with physically cross-linked poly(hydroxyethyl methacrylate-co-acrylic acid) demonstrates high stretchability and toughness, rapid self-healing, and long-term stability. Depending on the molecular weight and fraction of PEG, the tensile strength of the PEGgels varies from 0.22 to 41.3 MPa, fracture strain from 12% to 4336%, modulus from 0.08 to 352 MPa, and toughness from 2.89 to 56.23 MJ m^-3 . Finally, rapid self-healing of the PEGgel is demonstrated and a self-healing pneumatic actuator is fabricated by 3D-printing. The enhanced mechanical properties of the PEGgel system may be extended to other polymer networks (both chemically and physically cross-linked). Such a simple 3D-printable, self-healing, and tough soft material holds promise for broad applications in wearable electronics, soft actuators and robotics.

Facile equilibration of well-entangled semiflexible bead-spring polymer melts

The widely used double-bridging hybrid (DBH) method for equilibrating simulated entangled polymer melts [Auhl et al., J. Chem. Phys. 119, 12718-12728 (2003)] loses its effectiveness as chain stiffness increases into the semiflexible regime because the energy barriers associated with double-bridging Monte Carlo moves become prohibitively high. Here we overcome this issue by combining DBH with the use of core-softened pair potentials. This reduces the energy barriers substantially, allowing us to equilibrate melts with N ≃ 40N_e and chain stiffnesses all the way up to the isotropic-nematic transition using simulations of no more than 100 × 10⁶ time steps. For semiflexible chains, our method is several times faster than the standard DBH; we exploit this speedup to develop improved expressions for Kremer-Grest melts' chain-stiffness-dependent Kuhn length ℓ_K and entanglement length N_e.

Combination of Hybrid Particle-Field Molecular Dynamics and Slip-Springs for the Efficient Simulation of Coarse-Grained Polymer Models: Static and Dynamic Properties of Polystyrene Melts

A quantitative prediction of polymer-entangled dynamics based on molecular simulation is a grand challenge in contemporary computational material science. The drastic increase of relaxation time and viscosity in high-molecular-weight polymeric fluids essentially limits the usage of classic molecular dynamics simulation. Here, we demonstrate a systematic coarse-graining approach for modeling entangled polymers under the slip-spring particle-field scheme. Specifically, a frequency-controlled slip-spring model, a hybrid particle-field model, and a coarse-grained model of polystyrene melts are combined into a hybrid simulation technique. Via a rigorous parameterization strategy to determine the parameters in slip-springs from existing experimental or simulation data, we show that the reptation behavior is clearly observed in multiple characteristics of polymer dynamics, mean-square displacements, diffusion coefficients, reorientational relaxation, and Rouse mode analysis, consistent with the predictions of the tube theory. All dynamical properties of the slip-spring particle-field models are in good agreement with classic molecular dynamics models. Our work provides an efficient and practical approach to establish chemical-specific coarse-grained models for predicting polymer-entangled dynamics.

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.

Cavitation, crazing and bond scission in chemically cross-linked polymer nanocomposites

It is very important to understand the molecular mechanism of the fracture behavior of chemically cross-linked polymer nanocomposites (PNCs). Thus, in this work, by employing a coarse-grained molecular dynamics simulation we investigated the effect of the cross-link density and the cross-link distribution on it by calculating the void formation and the chemical bond scission. Considering the fracture energy, the optimal fracture properties of PNCs are realized at the moderate cross-link density which results from the competition between the chain slippage induced voids and the bond scission induced voids. Meanwhile, more bond scission occurs on the chain backbone while a high broken percentage of the cross-link bonds appears between chains because of the higher average stress borne by one cross-linked bead than by one other bead. In addition, the number of voids is quantified which first increases and then decreases with the strain at low cross-link density. However, the number of newly formed voids increases again at high cross-link density. Finally, it decreases because of the low rate of bond scission. Furthermore, the chemical bonds are broken at a similar strain for the uniform cross-link distribution while they are broken at any strain for the nonuniform cross-link distribution. The low number of broken bonds induces the disappearance of the second peak of the number of voids with the strain for the nonuniform cross-link distribution. In summary, this work could provide a clear understanding of the fracture mechanism of the chemically cross-linked PNCs on the molecular level.

Fast Domain Wall Motion Governed by Topology and Œrsted Fields in Cylindrical Magnetic Nanowires

While the usual approach to tailor the behavior of condensed matter and nanosized systems is the choice of material or finite-size or interfacial effects, topology alone may be the key. In the context of the motion of magnetic domain walls (DWs), known to suffer from dynamic instabilities with low mobilities, we report unprecedented velocities >600  m/s for DWs driven by spin-transfer torques in cylindrical nanowires made of a standard ferromagnetic material. The reason is the robust stabilization of a DW type with a specific topology by the Œrsted field associated with the current. This opens the route to the realization of predicted new physics, such as the strong coupling of DWs with spin waves above >600  m/s.

Determining Tube Theory Parameters by Slip-Spring Model Simulations of Entangled Star Polymers in Fixed Networks

Dynamical properties of branched polymer melts are determined by the polymer molecular weights and architectures containing junction points. Relaxation of entangled symmetric star polymers proceeds via arm-retraction and constraint release (CR). In this work, we investigate arm-retraction dynamics in the framework of a single-chain slip-spring model without CR effect where entanglements are treated as binary contacts, conveniently modeled as virtual "slip-links", each involving two neighboring strands. The model systems are analogous to isolated star polymers confined in a permanent network or a melt of very long linear polymers. We find that the distributions of the effective primitive path lengths are Gaussian, from which the entanglement molecular weight N e , a key tube theory parameter, can be extracted. The procured N e value is in good agreement with that obtained from mapping the middle monomer mean-square displacements of entangled linear chains in slip-spring model to the tube model prediction. Furthermore, the mean first-passage (FP) times of destruction of original tube segments by the retracting arm end are collected in simulations and examined quantitatively using a theory recently developed in our group for describing FP problems of one-dimensional Rouse chains with improbable extensions. The asymptotic values of N e as obtained from the static (primitive path length) and dynamical (FP time) analysis are consistent with each other. Additionally, we manage to determine the tube survival function of star arms μ ( t ) , or equivalently arm end-to-end vector relaxation function ϕ ( t ) , through the mean FP time spectrum τ ( s ) of the tube segments after careful consideration of the inner-most entanglements, which shows reasonably good agreement with experimental data on dielectric relaxation.

Direct Assessment of Tube Dilation in Entangled Polymers

A key ingredient within theories focusing on the rheology of entangled polymers is the way how the topological constraints of an entangled chain are lifted by unconstrained segments, i.e., how the constraining tube is dilated. This important question has been addressed by directly measuring the tube diameter d at the scale of the tube by neutron spin echo spectroscopy. The tube diameter d and plateau modulus G_{N}^{0} of highly entangled polyethylene oxide (PEO) chains of volume fraction c that are diluted by low molecular PEO show a concentration dependence d∝c^{a/2} and G_{N}^{0}∝c^{1+a} with an exponent a close to 4/3. This result allows the clear discrimination between different theoretical models that predict 4/3 or other values between 1 and 2 and provides an important ingredient to tube model theories.

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.

Local Chain Segregation and Entanglements in a Confined Polymer Melt

The reptation mechanism, introduced by de Gennes and Edwards, where a polymer diffuses along a fluffy tube, defined by the constraints imposed by its surroundings, convincingly describes the relaxation of long polymers in concentrated solutions and melts. We propose that the scale for the tube diameter is set by local chain segregation, which we study analytically. We show that the concept of local segregation is especially operational for confined geometries, where segregation extends over mesoscopic domains, drastically reducing binary contacts, and provide an estimate of the entanglement length. Our predictions are quantitatively supported by extensive molecular dynamics simulations on systems consisting of long, entangled chains.

Predicting the Flory-Huggins χ Parameter for Polymers with Stiffness Mismatch from Molecular Dynamics Simulations

The Flory–Huggins χ parameter describes the excess free energy of mixing and governs phase behavior for polymer blends and block copolymers. For chemically-distinct nonpolar polymers, the value of χ is dominated by the mismatch in cohesive energy densities of the monomers. For blends of chemically-similar polymers, the entropic portion of χ, arising from non-ideal local packing, becomes more significant. Using polymer field theory, Fredrickson et al. predicted that a difference in backbone stiffness can result in a positive χ for chains consisting of chemically-identical monomers. To quantitatively investigate this phenomenon, we perform molecular dynamic (MD) simulations for bead-spring chains, which differ only in stiffness. From the simulations, we apply a novel thermodynamic integration to extract χ as low as 10-4 per monomer for blends with stiffness mismatch. To compare with experiments, we introduce a standardized effective monomer to map real polymers onto our bead-spring chains. The predicted χ agrees well with experimental values for a wide variety of pairs of chemically-similar polymers.

Disentanglement of Two Single Polymer Chains: Contacts and Knots

Understanding the consequences of the noncrossing constraint is one of the remaining challenges in the physics of walks and polymers. To address this problem, we performed molecular simulations for the separation of only two initially connected, overlapping polymer chains with interactions tuned such that they are nearly random walks. The separation time for a configuration strongly correlates with the number of monomer contacts between both chains. We obtain a broad distribution of separation times with a slowly decaying tail. Knots only play a role for those configurations that contribute to the tail of the distribution. In contrast, when starting from the same initial configuration but allowing for chain crossings, separation is qualitatively faster and the time distribution narrow. The simulation results are rationalized by analytical theory. A theory of contacts based on polymer fractality and criticality is presented, along with the expected effects of knots.

Tube Dynamics Works for Randomly Entangled Rings

The tube model is the cornerstone of molecular theory for polymer rheology. We test its microscopic assumptions by simulating topologically equilibrated ring polymers, whose dynamics is free from end segment relaxation. We show that a closed-form expression derived from the tube model adapted to ring polymers quantitatively predicts the segmental mean squared displacements over the entire range of time scales from local motion to complete equilibration, with a time-independent local friction factor.

Distance measures and evolution of polymer chains in their topological space

Conformational transitions are ubiquitous in biomolecular systems, have significant functional roles and are subject to evolutionary pressures. Here we provide a first theoretical framework for topological transition, i.e. conformational transitions that are associated with changes in molecular topology. For folded linear biomolecules, arrangement of intramolecular contacts is identified as a key topological property, termed as circuit topology. Distance measures are proposed as reaction coordinates to represent progress along a pathway from initial topology to final topology. Certain topological classes are shown to be more accessible from a random topology. We study dynamic stability and pathway degeneracy associated with a topological reaction and found that off-pathways might seriously hamper evolution to desired topologies. Finally we present an algorithm for estimating the number of intermediate topologies visited during a topological reaction. The results of this study are relevant to, among others, structural studies of RNA and proteins, analysis of topologically associated domains in chromosomes, and molecular evolution.