Effects of Chain Stiffness on Conformational and Dynamical Properties of Individual Ring Polymers in Shear Flow

Supercoiled ring polymers under shear flow

We apply monomer-resolved computer simulations of supercoiled ring polymers under shear, taking full account of the hydrodynamic interactions, accompanied, in parallel, by simulations in which these are switched off. The combination of bending and torsional rigidities inherent in these polymers, in conjunction with hydrodynamics, has a profound impact on their flow properties. In contrast to their flexible counterparts, which dramatically deform and inflate under shear [Liebetreu et al., Commun. Mater. 2020, 1, 4], supercoiled rings undergo only weak changes in their overall shape and they display both a reduced propensity to tumbling (at fixed Weissenberg number) and a much stronger orientational resistance with respect to their flexible counterparts. In the presence of hydrodynamic interactions, the coupling of the polymer to solvent flow is capable of bringing about a topological transformation of writhe to twist at strong shear upon conservation of the overall linking number.

Production and Application of Polymer Foams Employing Supercritical Carbon Dioxide

Polymeric foams have characteristics that make them attractive for different applications. However, some foaming methods rely on chemicals that are not environmentally friendly. One of the possibilities to tackle the environmental issue is to utilize supercritical carbon dioxide ScCO2 since it is a “green” solvent, thus facilitating a sustainable method of producing foams. ScCO2 is nontoxic, chemically inert, and soluble in molten plastic. It can act as a plasticizer, decreasing the viscosity of polymers according to temperature and pressure. Most foam processes can benefit from ScCO2 since the methods rely on nucleation, growth, and expansion mechanisms. Process considerations such as pretreatment, temperature, pressure, pressure drop, and diffusion time are relevant parameters for foaming. Other variables such as additives, fillers, and chain extenders also play a role in the foaming process. This review highlights the morphology, performance, and features of the foam produced with ScCO2, considering relevant aspects of replacing or introducing a novel foam. Recent findings related to foaming assisted by ScCO2 and how processing parameters influence the foam product are addressed. In addition, we discuss possible applications where foams have significant benefits. This review shows the recent progress and possibilities of ScCO2 in processing polymer foams.

Rheology of a Nanopolymer Synthesized through Directional Assembly of DNA Nanochambers, for Magnetic Applications

We present a numerical study of the effects of monomer shape and magnetic nature of colloids on the behavior of a single magnetic filament subjected to the simultaneous action of shear flow and a stationary external magnetic field perpendicular to the flow. We find that based on the magnetic nature of monomers, magnetic filaments exhibit a completely different phenomenology. Applying an external magnetic field strongly inhibits tumbling only for filaments with ferromagnetic monomers. Filament orientation with respect to the flow direction is in this case independent of monomer shape. In contrast, reorientational dynamics in filaments with superparamagnetic monomers are not inhibited by applied magnetic fields, but enhanced. We find that the filaments with spherical, superparamagnetic monomers, depending on the flow and external magnetic field strength, assume semipersistent, collapsed, coiled conformations, and their characteristic time of tumbling is a function of field strength. However, external magnetic fields do not affect the characteristic time of tumbling for filaments with cubic, superparamagnetic monomers, but increase how often tumbling occurs.

How Polytetrafluoroethylene Lubricates Iron: An Atomistic View by Reactive Molecular Dynamics

The tribochemistry and transfer film formation at the metal/polymer interface plays an essential role in surface protection, wear reduction, and lubrication. Although the topic has been studied for decades, challenges persist in clarifying the nanoscale mechanism and dynamic evolution of tribochemical reactions. To investigate the tribochemistry between iron and polytetrafluoroethylene (PTFE) in ambient and cryogenic environments, we have trained and expanded a ReaxFF reactive force field to describe iron-oxygen-water-PTFE systems (C/H/O/F/Fe). Using ReaxFF molecular dynamics simulations, we find that mechanical shearing of single asperity induced the degradation of PTFE molecules and radicals, showing subsequent oxidation and hydroxylation reactions of the radicals initiated by C-C bond cleavage, in agreement with previous experimental observations. Furthermore, we studied mechanisms of interfacial tribochemical reactions and formation of transfer films. We found that tribochemical wear and Fe-C and Fe-F bonding networks are important mechanisms for anchoring molecular chains to form a transfer film on the iron countersurface. Hydroxyl groups can dehydrogenate to form short and strong chelation bonds with the Fe₂O₃ countersurface. A friction-induced oriented molecular layer plays a key role in reducing friction, which is responsible for the excellent lubrication property. By varying temperatures in the range of 10-300 K, we found a nonmonotonic change in friction with a maxima at 100 K. At cryogenic temperatures, the molecular mobility was obviously suppressed, while the chain rigidity was enhanced, resulting in the less oriented interface and brittle-like shear interface, which is responsible for nonmonotonic friction. This work elucidates mechanisms of tribochemical reactions and transfer film formation between iron and PTFE at the atomistic level, facilitating design and development of self-lubricating materials, especially under harsh conditions.

Compression and Stretching of Confined Linear and Ring Polymers by Applying Force

We use Langevin dynamics to study the deformations of linear and ring polymers in different confinements by applying compression and stretching forces on their two sides. Our results show that the compression deformations are the results of an interplay among of polymer rigidity, degree of confinement, and force applied. When the applied force is beyond the threshold required for the buckling transition, the semiflexible chain under the strong confinement firstly buckles; then comes helical deformation. However, under the same force loading, the semiflexible chain under the weaker confinement exhibits buckling instability and shrinks from the folded ends/sides until it becomes three-folded structures. This happens because the strong confinement not only strongly reduces the buckling wavelength, but also increases the critical buckling force threshold. For the weakly confined polymers, in compression process, the flexible linear polymer collapses into condensed states under a small external force, whereas the ring polymer only shows slight shrinkage, due to the excluded volume interactions of two strands in the crowded states. These results are essential for understanding the deformations of the ring biomacromolecules and polymer chains in mechanical compression or driven transport.

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.

Self-Assembly Supramolecular Systems Based on Guanidinium Salts Modified Hyperbranched Polyamidoamine and Cationic Acrylamide Copolymers

Herein, novel hyperbranched polyamidoamine guanidinium salts (GS-h-PAMAM) and two cationic acrylamide copolymers P(AM-DAC-ABSM) and P(AM-DAC-AMTU) were successfully prepared. Then, self-assembly supramolecular systems were synthesized by directly mixing GS-h-PAMAM with copolymers in aqueous solution, and the mechanism of the self-assembly process was speculated. FT-IR, NMR, and SEM were used for structural confirmation. Furthermore, the excellent solution properties revealed that the supramolecular systems had potential application in clay hydration inhibitors. More importantly, utilizing functionalized hyperbranched polyamidoamine in the synthesis self-assembly supramolecular systems was an effective strategy for expanding their application fields and developing new functional materials, providing a powerful reference for the next study.

Understanding conformational and dynamical evolution of semiflexible polymers in shear flow

A clear description of the conformational and dynamical evolution of polymer chains in shear flow is the fundamental basis of microfluidic separations and macroscopic rheological behaviors. We employ graph theory analysis to analyze the local deformation and dynamics of linear polymer chains with different rigidities in shear flow based on the simulation trajectories that record the instantaneous conformations and dynamics. Our results show that all semiflexible chains experience quasi-periodic tumbling motions when the shear strain overwhelms the U-shape (or S-shape) deformation energy barrier. More interestingly, the contact map provides solid evidence for the asymmetric deformation in the whole tumbling motion. In the stretching process: at small and intermediate shear strength, flexible polymers show a quasi-affine deformation while semiflexible ones are initially unfolded from the center of the chains, then both of them follow the extension with half dumbbell- or dumbbell-like ends; at high shear strength, all polymer chains present only a dumbbell-like extension. In the collapse process, all chains prefer to initiate the folding from chain ends. This finding can facilitate our understanding on how semiflexible polymer chains relax and dissipate the stress in shear flow.

Ring polymer dynamics and tumbling-stretch transitions in planar mixed flows

The properties of dilute polymer solutions are governed by the conformational dynamics of individual polymers which can be perturbed in the presence of an applied flow. Much of our understanding of dilute solutions comes from studying how flows manipulate the molecular features of polymer chains out of equilibrium, primarily focusing on linear polymer chains. Recently there has been an emerging interest in the dynamics of nonlinear architectures, particularly ring polymers, which exhibit surprising out-of-equilibrium dynamics in dilute solutions. In particular, it has been observed that hydrodynamics can couple to topology in planar elongational and shear flows, driving molecular expansion in the nonflow direction that is not observed for linear chains. In this paper, we extend our understanding of dilute ring polymer dynamics to mixed flows, which represent flow profiles intermediate between simple shear or planar elongation. We map the conformational behaviors at a number of flow geometries and strengths, demonstrating transitions between coiled, tumbling, and stretched regimes. Indeed, these observations are consistent with how linear chains respond to mixed flows. For both linear and ring polymers, we observe a marked first-order-like transition between tumbling and stretched polymers that we attribute to a dynamic energy barrier between the two states. This manifests as bimodal extension distributions in a narrow range of flow strengths and geometries, with the primary difference between rings and linear chains being the presence of molecular expansion in the vorticity direction.

The Persistence Length of Semiflexible Polymers in Lattice Monte Carlo Simulations

While applying computer simulations to study semiflexible polymers, it is a primary task to determine the persistence length that characterizes the chain stiffness. One frequently asked question concerns the relationship between persistence length and the bending constant of applied bending potential. In this paper, theoretical persistence lengths of polymers with two different bending potentials were analyzed and examined by using lattice Monte Carlo simulations. We found that the persistence length was consistent with theoretical predictions only in bond fluctuation model with cosine squared angle potential. The reason for this is that the theoretical persistence length is calculated according to a continuous bond angle, which is discrete in lattice simulations. In lattice simulations, the theoretical persistence length is larger than that in continuous simulations.

Individual circular polyelectrolytes under shear flow

Individual circular polyelectrolytes in simple shear flow are studied by means of mesoscale hydrodynamic simulations, revealing the complex coupling effects of shear rate, electrostatic interaction, and circular architecture on their conformational and dynamical properties. Shear flow deforms the polyelectrolyte and strips condensed counterions from its backbone. A decrease in condensed counterions alters electrostatic interactions among charged particles, affecting shear-induced polymer deformation and orientation. Circular architecture determines the features of deformation and orientation. At weak electrostatic interaction strengths, the polyelectrolyte changes its shape from an oblate ring at small shear rates to a prolate ring at large shear rates, whereas strong electrostatic interaction strengths are associated with a transition from a prolate coil to a prolate ring. Circular polyelectrolytes exhibit tumbling and tank-treading motions in the range of large shear rates. Further study reveals a similarity between the roles of intramolecular electrostatic repulsion and chain rigidity in shear-induced dynamics.

Star Block-Copolymers in Shear Flow

Star block-copolymers (SBCs) have been demonstrated to constitute self-assembling building blocks with specific softness, functionalization, shape, and flexibility. In this work, we study the behavior of an isolated SBC under a shear flow by means of particle-based multiscale simulations. We systematically analyze the conformational properties of low-functionality stars, as well as the formation of attractive patches on their corona as a function of the shear rate. We cover a wide range of system parameters, including functionality, amphiphilicity, and solvent quality. It is shown that SBCs display a richer structural and dynamical behavior than athermal star polymers in a shear flow [ Ripoll Phys. Rev. Lett. , 2006 , 96 , 188302 ], and, therefore, they are also interesting candidates to tune the viscoelastic properties of complex fluids. We identify three factors of patch reorganization under shear that lead to patch numbers and orientations depending on the shear rate, namely, free arms joining existing patches, fusion of medium-sized patches into bigger ones, and fission of large patches into two smaller ones under high shear rates. Because the conformation of single SBC is expected to be preserved in low-density bulk phases, the presented results are a first step in understanding and predicting the rheological properties of semidilute suspensions of this kind of polymers.

Structural Mechanism for Viscosity of Semiflexible Polymer Melts in Shear Flow

The viscosities of semiflexible polymers with different chain stiffnesses in shear flow are studied via nonequilibrium molecular dynamics techniques. The simulation reproduces the experimentally observed results, giving a complete picture of viscosity as chain stiffness increases. Analysis of flow-induced changes in chain conformation and local structure indicates two distinct mechanisms behind a variety of viscosity curves. For polymers of small stiffnesses, it is related to flow-induced changes in chain conformation and, for those of large stiffnesses, to flow-induced instabilities of nematic structures. The four-region flow curve is confirmed for polymers of contour length close to persistence length and understood by combining the two structural mechanisms. Thus, these findings clarify the microscopic structures indicated by the macroscopic viscosity.

Cyclic polymers revealing topology effects upon self-assemblies, dynamics and responses

A variety of single- and multicyclic polymers having programmed chemical structures with guaranteed purity have now become obtainable owing to a number of synthetic breakthroughs achieved in recent years. Accordingly, a broadening range of studies has been undertaken to gain updated insights on fundamental polymer properties of cyclic polymers in either solution or bulk, in either static or dynamic states, and in self-assemblies, leading to unusual properties and functions of polymer materials based on their cyclic topologies. In this article, we review recent studies aiming to achieve distinctive properties and functions by cyclic polymers unattainable by their linear or branched counterparts. We focus, in particular, on selected examples of unprecedented topology effects of cyclic polymers upon self-assemblies, dynamics and responses, to highlight current progress in Topological Polymer Chemistry.

Effects of excluded volume and hydrodynamic interaction on the deformation, orientation and motion of ring polymers in shear flow

A ring polymer is a classical model to explore the behaviors of biomacromolecules. Compared with its linear counterpart in shear flow, the ring polymer should be more sensitive to excluded volume and hydrodynamic interaction attributed to the absence of chain ends. We carried out multiparticle collision dynamics combined with molecular dynamics simulation to study the effects of excluded volume and hydrodynamic interaction on the behaviors of ring polymers in shear flow. The results show that in the absence of the strong excluded volume interaction, the ring polymer prefers a two-strand linear conformation with high deformation and orientation in the flow-gradient plane, and the tank-treading motion is nearly negligible. Ring polymers without excluded volume show no significant difference from linear polymers in the scaling exponents for the deformation, orientation and tumbling motion. We also observed that the hydrodynamic interaction could efficiently slow down the relaxation of ring polymers while the scaling exponents against the Weissenberg number have rarely been affected.

Shear thinning behavior of linear polymer melts under shear flow via nonequilibrium molecular dynamics

The properties of both untangled and entangled linear polymer melts under shear flow are studied by nonequilibrium molecular dynamics simulations. The results reveal that the dependence of shear viscosity η on shear rate γ, expressed by n ~ γ(-n), exhibits three distinct regimes. The first is the well-known Newtonian regime, namely, η independent of shear rate at small shear rates γ < τ0(-1) (where τ0 is the longest polymer relaxation time at equilibrium). In the non-Newtonian regime (γ > τ0(-1)) the shear dependence of viscosity exhibits a crossover at a critical shear rate γc dividing this regime into two different regimes, shear thinning regime I (ST-I) and II (ST-II), respectively. In the ST-I regime (τ0(-1) < γ < γc), the exponent n increases with increasing chain length N, while in the ST-II regime (γ > γc) a universal power law n ~ γ(-0.37) is found for considered chain lengths. Furthermore, the longer the polymer chain is, the smaller the shear viscosity for a given shear rate in the ST-II regime. The simulation also shows that a characteristic chain length, below which γc will be equal to τ0(-1), lies in the interval 30 < N < 50. For all considered chain lengths in the ST-II regime, we also find that the first and second normal stress differences N1 and N2 follow power laws of N1 ~ γ(2/3) and N2 ~ γ(0.82), respectively; the orientation resistance parameter mG follows the relation mG ~ γ(0.75) and the tumbling frequency ftb follows ftb ~ γ(0.75). These results imply that the effects of entanglement on the shear dependences of these properties may be negligible in the ST-II regime. These findings may shed some light on the nature of shear thinning in flexible linear polymer melts.

Gaussian semiflexible rings under angular and dihedral restrictions

Semiflexible polymer rings whose bonds obey both angular and dihedral restrictions [M. Dolgushev and A. Blumen, J. Chem. Phys. 138, 204902 (2013)], are treated under exact closure constraints. This allows us to obtain semianalytic results for their dynamics, based on sets of Langevin equations. The dihedral restrictions clearly manifest themselves in the behavior of the mean-square monomer displacement. The determination of the equilibrium ring conformations shows that the dihedral constraints influence the ring curvature, leading to compact folded structures. The method for imposing such constraints in Gaussian systems is very general and it allows to account for heterogeneous (site-dependent) restrictions. We show it by considering rings in which one site differs from the others.

Dynamics of a semiflexible polymer or polymer ring in shear flow

Polymers exposed to shear flow exhibit a remarkably rich tumbling dynamics. While rigid rods rotate on Jeffery orbits, a flexible polymer stretches and coils up during tumbling. Theoretical results show that in both of these asymptotic regimes the corresponding tumbling frequency f(c) in a linear shear flow of strength γ scales as a power law Wi(2/3) in the Weissenberg number Wi = γτ, where τ is a characteristic time of the polymer's relaxational dynamics. For a flexible polymer these theoretical results are well confirmed by a large body of experimental single molecule studies. However, for the intermediate semiflexible regime, especially relevant for cytoskeletal filaments like F-actin and microtubules, the situation is less clear. While recent experiments on single F-actin filaments are still interpreted within the classical Wi(2/3) scaling law, theoretical results indicated deviations from it. Here we perform extensive Brownian dynamics simulations to explore the tumbling dynamics of semiflexible polymers over a broad range of shear strength and the polymer's persistence length l(p). We find that the Weissenberg number alone does not suffice to fully characterize the tumbling dynamics, and the classical scaling law breaks down. Instead, both the polymer's stiffness and the shear rate are relevant control parameters. Based on our Brownian dynamics simulations we postulate that in the parameter range most relevant for cytoskeletal filaments there is a distinct scaling behavior with f(c) τ* = Wi(3/4)f(c)(x) with Wi = γτ* and the scaling variable x = (l(p)/L)(Wi)(-1/3); here τ* is the time the polymer's center of mass requires to diffuse its own contour length L. Comparing these results with experimental data on F-actin we find that the Wi(3/4) scaling law agrees quantitatively significantly better with the data than the classical Wi(2/3) law. Finally, we extend our results to single ring polymers in shear flow, and find similar results as for linear polymers with slightly different power laws.

Mechanochemistry of Topological Complex Polymer Systems

Although existing since the concept of macromolecules, polymer mechanochemistry is a burgeoning field which attracts great scientific interest in its ability to bias conventional reaction pathways and its potential to fabricate mechanoresponsive materials. We review here the effect of topology on the mechanical degradation of polymer chains and the activation of mechanophores in polymer backbones. The chapter focuses on both experimental and theoretical work carried out in the past 70 years. After a general introduction (Sect. 1), where the concept, the history, and the application of polymer mechanochemistry are briefly described, flow fields to study polymer mechanochemistry are discussed (Sect. 2), results of mechanochemistry study are presented for linear polymers (Sect. 3), cyclic polymers (Sect. 4), graft polymers (Sect. 5), star-shaped polymers (Sect. 6), hyperbranched polymers and dendrimers (Sect. 7), and systems with dynamic topology (Sect. 8). Here we focus on (1) experimental results involving the topological effect on the coil-to-stretch transition and the fracture of the polymer chains, (2) the underlying mechanisms and the key factor that determines the mechanical stability of the macromolecules, (3) theoretical models that relate to the experimental observations, and (4) rational design of mechanophores in complex topology to achieve multiple activations according to the existing results observed in chain degradation.