Primitive Chain Network Simulations for Double Peaks in Shear Stress under Fast Flows of Bidisperse Entangled Polymers.

A few experiments have reported that the time development of shear stress under fast-startup shear deformations exhibits double peaks before reaching a steady state for bimodal blends of entangled linear polymers under specific conditions. To understand this phenomenon, multi-chain slip-link simulations, based on the primitive chain network model, were conducted on the literature data of a bimodal polystyrene solution. Owing to reasonable agreement between their data and our simulation results, the stress was decomposed into contributions from long- and short-chain components and decoupled into segment number, stretch, and orientation. The analysis revealed that the first and second peaks correspond to the short-chain orientation and the long-chain stretch, respectively. The results also implied that the peak positions are not affected by the mixing of short and long chains, although the intensity of the second peak depends on mixing conditions in a complicated manner.

Increase in rod diffusivity emerges even in Markovian nature.

Rod-shaped particles embedded in certain matrices have been reported to exhibit an increase in their center of mass diffusivity upon increasing the matrix density. This increase has been considered to be caused by a kinetic constraint in analogy with tube models. We investigate a mobile rodlike particle in a sea of immobile point obstacles using a kinetic Monte Carlo scheme equipped with a Markovian process, that generates gaslike collision statistics, so that such kinetic constraints do essentially not exist. Even in such a system, provided the particle's aspect ratio exceeds a threshold value of about 24, the unusual increase in the rod diffusivity emerges. This result implies that the kinetic constraint is not a necessary condition for the increase in the diffusivity.

Fluctuating diffusivity emerges even in binary gas mixtures.

Diffusivity in some soft matter and biological systems changes with time, called the fluctuating diffusivity. In this work, we propose a novel origin for fluctuating diffusivity based on stochastic simulations of binary gas mixtures. In this system, the fraction of one component is significantly small, and the mass of the minor component molecule is different from that of the major component. The minor component exhibits fluctuating diffusivity when its mass is sufficiently smaller than that of the major component. We elucidate that this fluctuating diffusivity is caused by the time scale separation between the relaxation of the velocity direction and the speed of the minor component molecule.

Brownian simulations for tetra-gel-type phantom networks composed of prepolymers with bidisperse arm length.

We studied the effect of arm length contrast of prepolymers on the mechanical properties of tetra-branched networks via Brownian dynamics simulations. We employed a bead-spring model without the excluded volume interactions, and we did not consider the solvent explicitly. Each examined 4-arm star branch prepolymer has uneven arm lengths to attain two-against-two (2a2) or one-against-three (1a3) configurations. The arm length contrast was varied from 38-2 to 20-20 for 2a2, and from 5-25 to 65-5 for 1a3, with the fixed total bead number of 81, including the single bead located at the branch point for prepolymers. We distributed 400 molecules in the simulation box with periodic boundary conditions, and the bead number density was fixed at 4. We created polymer networks by cross-end-coupling of equilibrated tetra-branched prepolymers. To mimic the experiments of tetra gels, we discriminated the molecules into two types and allowed the reaction only between different types of molecules at their end beads. The final conversion ratio was more than 99%, at which unreacted dangling ends are negligible. We found that the fraction of double linkage, in which two of the four arms connect a pair of branch points, increases from 3% to 15% by increasing the arm length contrast. We stretched the resultant tetra-type networks to obtain the ratio of mechanically effective strands. We found that the ratio is 96% for the monodisperse system, decreasing to 90% for high arm length contrast. We introduced bond scission according to the bond stretching to observe the network fracture under sufficiently slow elongation. The fracture behavior was not correlated with the fraction of double linkage because the scission occurs at single linkages.

Effects of Slip-Spring Parameters and Rouse Bead Density on Polymer Dynamics in Multichain Slip-Spring Simulations.

The multichain slip-spring (MCSS) model is one of the coarse-grained models of polymers developed in the niche between bead-spring models and tube type descriptions. In this model, polymers are represented by Rouse chains connected by virtual springs that temporally connect the chains, hop along the chain, and are constructed and annihilated at the chain ends. Earlier studies have shown that MCSS simulations can nicely reproduce entangled and unentangled polymer dynamics. However, the model parameters have been chosen arbitrarily, and their effects have not been reported. In this study, for the first time, we systematically investigated the effects of model parameters: fugacity of virtual springs, its intensity, and the Rouse bead density. We validated the employed simulation code by confirming that the statistics of the system follow the theoretical setup. Namely, the virtual spring density is correctly controlled, and polymer chains exhibit ideal chain statistics irrespective of the chosen parameter values. For diffusion and linear viscoelasticity, simulation results obtained for different parameters can be superposed with each other by conversion factors for the bead number per chain and units of length, time, and modulus. These conversion factors follow scaling laws concerning the number of Rouse segments between two consecutive anchoring points of virtual springs along the polymer chain. Besides, diffusion and viscoelasticity excellently agree with literature data for the standard bead-spring simulation. These results imply that the coarse-graining level for the MCSS model can be arbitrarily chosen and controlled by model parameters.

Analysis of Elongational Viscosity of Entangled Poly (Propylene Carbonate) Melts by Primitive Chain Network Simulations.

It has been established that the elongational rheology of polymers depends on their chemistry. However, the analysis of experimental data has been reported for only a few polymers. In this study, we analyzed the elongational viscosity of poly (propylene carbonate) (PPC) melts in terms of monomeric friction via primitive chain network simulations. By incorporating a small polydispersity of materials, the linear viscoelastic response was semi-quantitatively reproduced. Owing to this agreement, we determined units of time and modulus to carry out elongational simulations. The simulation with constant monomeric friction overestimated elongational viscosity, whereas it nicely captured the experimental data if friction decreased with increasing segment orientation. To see the effect of chemistry, we also conducted the simulation for a polystyrene (PS) melt, which has a similar entanglement number per chain and a polydispersity index. The results imply that PPC and PS behave similarly in terms of the reduction of friction under fast deformations.

Quantitative bridging between full-atomistic and bead-spring models for polybutadiene and poly(butadiene-styrene) copolymers.

Despite lots of attempts on the bridging between full-atomistic and coarse-grained models for polymers, a practical methodology has not been established yet. One of the problems is computation costs for the determination of spatial and temporal conversion parameters, which are ideally obtained for the long chain limit. In this study, we propose a practical, yet quantitative, bridging method utilizing the simulation results for rather short chains. We performed full-atomistic simulations for polybutadiene and some poly(butadiene-styrene) copolymers in the melt state by varying the number of repeating units as 20, 30, and 40. We attempted to construct corresponding coarse-grained models for such systems. We employed the Kremer-Grest type bead-spring chains with bending rigidity. The stiffness parameter of coarse-grained models and the spatial conversion factor between the full-atomistic and coarse-grained models were obtained according to the conformational statistics of polymer chains. Although such a bridging strategy is similar to the earlier studies, we incorporated the molecular weight dependence of the conformational statistics for the first time. By introducing several empirical functions of the conformational statistics for the molecular weight dependence, we attained a rigorous bridging for the conformational statistics. We confirmed that the structural distribution functions of the coarse-grained systems are entirely consistent with the target full-atomistic ones. Owing to the structural conversion parameters thus obtained, we constructed the coarse-grained models that corresponded to the polymers consisting of 200 repeating units and traced the segmental diffusion. The full-atomistic simulations were also performed from the initial configurations created from the equilibrated coarse-grained models via the back-mapping scheme. From the comparison of the mean-square-displacement of the segments positioned at the middle of the chain, we obtained the temporal conversion factors.

DNA-Chitosan Hydrogels: Formation, Properties, and Functionalization with Catalytic Nanoparticles.

DNA-chitosan (DNA-CS) hydrogels were prepared on the basis of interpolyelectrolyte complexes (IPEC) in a co-assembled regime by in situ charging of the polysaccharide in a DNA solution. In contrast to poorly controlled coacervates formed upon mixing of DNA and CS solutions, stable DNA-CS IPEC hydrogels are formed at near-stoichiometric ratios of DNA and chitosan ionogenic groups. Structure, stability, and ion absorption properties of such hydrogels depended strongly on the ratio between cationic (CS) and anionic (DNA) counterparts in hydrogels. Abundant amino- and nitrogen-containing aromatic groups of co-assembled DNA and CS make their hydrogel an efficient, multitarget absorbent toward metal ions. Such strong affinity of both DNA and CS to Au3+ cation was used to entrap Au3+ ions into the DNA-CS hydrogels. Subsequent reduction of Au3+ ion inside hydrogels resulted in the formation of ∼2-3 nm size Au nanoparticles on DNA-CS scaffolds. Metallized hydrogels demonstrated catalytic activity in reduction of various nitroaromatics that depended on the ratio between CS and DNA in the hydrogel.

Complex Network Representation of the Structure-Mechanical Property Relationships in Elastomers with Heterogeneous Connectivity.

The complicated structure-property relationships of materials have recently been described using a methodology of data science that is recognized as the fourth paradigm in materials science. In network polymers or elastomers, the manner of connection of the polymer chains among the crosslinking points has a significant effect on the material properties. In this study, we quantitatively evaluate the structural heterogeneity of elastomers at the mesoscopic scale based on complex network, one of the methods used in data science, to describe the elastic properties. It was determined that a unified parameter with topological and spatial information universally describes some parameters related to the stresses. This approach enables us to uncover the role of individual crosslinking points for the stresses, even in complicated structures. Based on the data science, we anticipate that the structure-property relationships of heterogeneous materials can be interpretatively represented using this type of "white box" approach.

Short-time dynamics of a tracer in an ideal gas.

A small tagged particle immersed in a fluid exhibits Brownian motion and diffuses on a long timescale. Meanwhile, on a short timescale, the dynamics of the tagged particle cannot be simply described by the usual generalized Langevin equation with Gaussian noise, since the number of collisions between the tagged particle and fluid particles is rather small. On such a timescale, we should explicitly consider individual collision events between the tagged particle and the surrounding fluid particles. In this study we analyze the short-time dynamics of a tagged particle in an ideal gas, where we do not have static or hydrodynamic correlations between fluid particles. We perform event-driven hard-sphere simulations and show that the short-time dynamics of the tagged particle is correlated even under such an idealized situation. Namely, the velocity autocorrelation function becomes negative when the tagged particle is relatively light and the fluid density is relatively high. This result can be attributed to the dynamical correlation between collision events. To investigate the physical mechanism which causes the dynamical correlation, we analyze the correlation between successive collision events. We find that the tagged particle can collide with the same ideal-gas particle several times and such collisions cause a strong dynamical correlation for the velocity.

Primitive chain network simulations for the interrupted shear response of entangled polymeric liquids.

The non-linear viscoelastic response under interrupted shear flows is one of the interesting characteristics of entangled polymers. In particular, the stress overshoot in the resumed shear has been discussed concerning the recovery of the entanglement network in some studies. In this study, we performed multichain slip-link simulations to observe the molecular structure of an entangled polymer melt. After confirming the reasonable reproducibility of our simulation with the literature data, we analyzed the molecular characteristics following the decoupling approximation. We reasonably found that the segment orientation dominates the stress overshoot even under the resumed shear with minor contributions from the segment stretch and entanglement density. We defined the mitigation function for the recovery of the stress overshoot as a function of the rest time and compared it with the relaxation of the molecular quantities after the initial shear. As a result, we have found that the mitigation of the stress overshoot coincides with the relaxation of entanglement density.

Primitive chain network simulations for H-polymers under fast shear.

Branchpoint Withdrawal (BPW) has been recognized as one of the important molecular mechanisms for the description of the dynamics of entangled branched polymers under fast flows. However, the relation to the other known molecular mechanisms has not been fully elucidated yet. In this study we performed primitive chain network (i.e., multi-chain slip-link) Brownian simulations for a melt of a well-characterized monodisperse polystyrene H-polymer, for which the linear viscoelasticity and shear viscosity growth curves at several shear rates are available in the literature. After confirming the consistency of the simulations with the rheological data, we used the simulations to analyze the molecular motion in detail. The results reveal that molecular tumbling occurs in branched polymers just as in linear ones, and that it is accelerated by BPW. Furthermore, BPW not only mitigates backbone stretch, as expected, but also arm stretch. However, because the transient startup viscosity is anyhow dominated by chain stretch dynamics rather than by molecular tumbling, our results rationalize the fact that pom-pom theories successfully ignore tumbling in shear flows.

Retardation of the reaction kinetics of polymers due to entanglement in the post-gel stage in multi-chain slip-spring simulations.

Although the reaction kinetics of network formation of polymers has been extensively investigated, the role of entanglement between polymers has not been fully elucidated yet. In this study, we discuss the effect of entanglement via multi-chain slip-spring simulations, in which Rouse chains are dispersed in space and connected by slip-springs that mimic the entanglement. For stoichiometric conditions for the systems containing pre-polymers and cross-linkers, the simulations without slip-springs exhibited reaction kinetics that is consistent with the earlier mean-field theory. Meanwhile, the inclusion of slip-springs in the system retards the reaction in the post-gel stage after the percolation of the system. According to the analysis of the network structure, the reaction in the post-gel stage is dominated by the tethered chains. The entanglement indirectly retards the reaction kinetics through the suppression of tethered chain dynamics.

Contraction of Entangled Polymers After Large Step Shear Deformations in Slip-Link Simulations.

Although the tube framework has achieved remarkable success to describe entangled polymer dynamics, the chain motion assumed in tube theories is still a matter of discussion. Recently, Xu et al. [ACS Macro Lett. 2018, 7, 190⁻195] performed a molecular dynamics simulation for entangled bead-spring chains under a step uniaxial deformation and reported that the relaxation of gyration radii cannot be reproduced by the elaborated single-chain tube model called GLaMM. On the basis of this result, they criticized the tube framework, in which it is assumed that the chain contraction occurs after the deformation before the orientational relaxation. In the present study, as a test of their argument, two different slip-link simulations developed by Doi and Takimoto and by Masubuchi et al. were performed and compared to the results of Xu et al. In spite of the modeling being based on the tube framework, the slip-link simulations excellently reproduced the bead-spring simulation result. Besides, the chain contraction was observed in the simulations as with the tube picture. The obtained results imply that the bead-spring results are within the scope of the tube framework whereas the failure of the GLaMM model is possibly due to the homogeneous assumption along the chain for the fluctuations induced by convective constraint release.

Comparison among multi-chain models for entangled polymer dynamics.

Although lots of coarse-grained models have been proposed to trace the long-term behaviors of entangled polymers, compatibility among the different models has not been frequently discussed. In this study, some dynamical and static quantities, such as diffusion, relaxation modulus, chain dimension, and entanglement density, were examined for the multi-chain slip-link model (primitive chain network model) and the multi-chain slip-spring model, and the results were compared with those reported for the standard bead-spring model. For the diffusion, three models are compatible with scale-conversion parameters for units of length, time and bead (segment) number (or the molecular weight). The relaxation modulus is also compatible given that the model dependence can be accommodated by the entanglement density and the additional scale-conversion for the unit of modulus. The chain dimension is reasonably coincident with small deviations due to the weak non-Gaussianity of the models. Apart from these plausible compatibilities, significant discrepancies have been found for the inter-chain cross-correlations in the relaxation modulus.

Coil-globule transitions drive discontinuous volume conserving deformation in locally restrained gels.

The equilibrium volume of a thermoresponsive polymer gel changes dramatically across a temperature due to the coil-globule transitions of the polymers. When cofacially oriented nanosheets are embedded in such a gel, the composite gel deforms at the temperature, without changing the volume, and the response time is considerably shorter. We here theoretically predict that the deformation of the composite gel results from the fact that the nanosheets restrain the deformation of some polymers, while other polymers deform relatively freely. The unrestrained polymers collapse due to the coil-globule transitions and this generates the solvent flows to the restrained regions. The response time of this process is rather fast because solvent molecules travel only by the distance of the size of a nanosheet, instead of permeating out to the external solution. This concept may provide insight in the physics of composite gels and the design of thermoresponsive gels of fast response.

Orientational cross correlations between entangled branch polymers in primitive chain network simulations.

Although it has not been frequently discussed, contributions of the orientational cross-correlation (OCC) between entangled polymers are not negligible in the relaxation modulus. In the present study, OCC contributions were investigated for 4- and 6-arm star-branched and H-branched polymers by means of multi-chain slip-link simulations. Owing to the molecular-level description of the simulation, the segment orientation was traced separately for each molecule as well as each subchain composing the molecules. Then, the OCC was calculated between different molecules and different subchains. The results revealed that the amount of OCC between different molecules is virtually identical to that of linear polymers regardless of the branching structure. The OCC between constituent subchains of the same molecule is significantly smaller than the OCC between different molecules, although its intensity and time-dependent behavior depend on the branching structure as well as the molecular weight. These results lend support to the single-chain models given that the OCC effects are embedded into the stress-optical coefficient, which is independent of the branching structure.

Shear induced formation of lubrication layers of negative normal stress gels.

Many biopolymer gels generate negative normal stress, with which the polymer networks shrink in the normal of applied shear. Here we theoretically predict the sliding velocity of such a gel on a solid surface when a constant shear stress is applied to the gel. Our theory predicts that the negative normal stress drives the flow of the solvent in the gel and this produces a solvent layer between the gel and the surface. The sliding velocity of the gel is proportional to the thickness of the solvent layer and is a cubic function of the applied shear stress. With constant applied normal and shear stresses, the thickness of the solvent layer is a non-monotonic function of time with a maximum because the solvent flow from the gel to the solvent layer is dominant in the short time scale and the solvent flow from the solvent layer to the outside is dominant in a longer time scale. The maximum layer thickness depends on the ratio of the time scales of the solvent flow in the gel and in the solvent layer.

Primitive chain network simulations of probe rheology.

Probe rheology experiments, in which the dynamics of a small amount of probe chains dissolved in immobile matrix chains is discussed, have been performed for the development of molecular theories for entangled polymer dynamics. Although probe chain dynamics in probe rheology is considered hypothetically as single chain dynamics in fixed tube-shaped confinement, it has not been fully elucidated. For instance, the end-to-end relaxation of probe chains is slower than that for monodisperse melts, unlike the conventional molecular theories. In this study, the viscoelastic and dielectric relaxations of probe chains were calculated by primitive chain network simulations. The simulations semi-quantitatively reproduced the dielectric relaxation, which reflects the effect of constraint release on the end-to-end relaxation. Fair agreement was also obtained for the viscoelastic relaxation time. However, the viscoelastic relaxation intensity was underestimated, possibly due to some flaws in the model for the inter-chain cross-correlations between probe and matrix chains.

Onset of static and dynamic universality among molecular models of polymers.

A quantitatively accurate prediction of properties for entangled polymers is a long-standing challenge that must be addressed to enable efficient development of these materials. The complex nature of polymers is the fundamental origin of this challenge. Specifically, the chemistry, structure, and dynamics at the atomistic scale affect properties at the meso and macro scales. Therefore, quantitative predictions must start from atomistic molecular dynamics (AMD) simulations. Combined use of atomistic and coarse-grained (CG) models is a promising approach to estimate long-timescale behavior of entangled polymers. However, a systematic coarse-graining is still to be done for bridging the gap of length and time scales while retaining atomistic characteristics. Here we examine the gaps among models, using a generic mapping scheme based on power laws that are closely related to universality in polymer structure and dynamics. The scheme reveals the characteristic length and time for the onset of universality between the vastly different scales of an atomistic model of polyethylene and the bead-spring Kremer-Grest (KG) model. The mapping between CG model of polystyrene and the KG model demonstrates the fast onset of universality, and polymer dynamics up to the subsecond time scale are observed. Thus, quantitatively traceable timescales of polymer MD simulations can be significantly increased.