Search

Primitive chain network simulations for randomly cross-linked slip-link networks were performed. For the percolated networks, the stress-strain relationship was compared to the theories by Ball et al. [Polymer, 22, 1010 (1981)] and Rubinstein and Panyukov [Macromolecules, 35, 6670 (2002)]. The simulation results were reasonably reproduced by both theories, given that the contributions from cross-links and slip-links were used as fitting parameters. However, these parameters were model dependent. Besides, the theories cannot describe the simulation results if the parameters were determined from the number of active links involved in the percolated networks. These results reveal that the fitting of experimental data to the theories does not provide a fraction of entanglements in the system unless the network only consists of Gaussian strands and it correctly reaches the state of free-energy minimum., Comment: 20 pages, 6 figures

The poly(lactic acid) (PLA)-tricalcium phosphate (TCP) composite attracts much attention as a material for a bone fixation device because both have bioabsorbability. However, the applications of the composite bone fixation device are limited to low-loaded regions because of lower strengths. In this study, PLA and TCP/PLA composite cylindrical billets were extruded to improve their strengths, with the aim of clarifying the molecular orientation behavior of the PLA and TCP/PLA billets in extrusion. First, the effect of the orientation behavior in the PLA billets on the extrusion ratio (ER) was calculated. Next, the TCP/PLA billets were analyzed. The molecular orientation obtained by extrusion was investigated by a combination of the finite element method and the chain network model. Consequently, the orientation function of the extruded billet was found to increase with the ER. Furthermore, the orientation function of the TCP/PLA billet was higher than that of the PLA billet, which may be due to the change in the yield stress and n value of the billet by TCP addition. The orientation distribution in the radius direction of the extruded PLA billet showed that the orientation function at the surface region was larger than that at the center region. This orientation distribution might be because the movement distance of the surface region during extrusion was longer than that in the center region. The surface region in the billet was drawn by the difference of those movement distances and might be orientated. The workability of the PLA and TCP/PLA billets was also investigated using pressure during extrusion. The results showed that the extrusion pressure increased with the TCP content and ER. Therefore, extrusion workability decreased with the TCP content and the ER.

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., ファイル公開：2021/07/28

Poly(lactic acid) (PLA) has attracted much attention for use in bone fixation devices, which are used for fracture treatment, because it degrades to nontoxic lactic acid through nonenzymatic hydrolytic degradation. However, the application of such device is limited to relatively low-load regions, because mechanical properties of PLA is poor than that of metal materials. The process of drawing PLA fibers has attracted much attention as an approach for improving the mechanical properties of PLA bone fixation devices. The mechanical properties and molecular orientation of drawn PLA fibers and films have been investigated. However, the optimization of drawing conditions in bulk processes in relation to bone fixation devices is difficult because a large number of potential drawing conditions exist. The purpose of this study was to analytically clarify molecular orientation behavior in drawn PLA billets. The molecular orientation obtained by extrusion in PLA billets was investigated using a combination of the finite element method (FEM) and a chain network model. As a result of the FEM, first principal plastic strain was generated, mainly in the tapered components during extrusion; this strain was in the axial direction of the rod. Radius strain distributions showed that strain in the center region was almost uniform, whereas strain peaked near the surface. The orientation function increased with extrusion ratio (ER), and the peak orientation function in the surface region increased with taper angle. Thus, the magnitude and distribution of the orientation function in extruded PLA billets may be controllable by ER and taper angle, respectively.

Inspired by inorganic oligomers and their polymerization, we herein develop a heterogeneous inorganic polymerization tactic that can be used to prepare a muscle-like hybrid hydrogel by inducing the polymerization of calcium phosphate oligomers (CPO) onto a polyvinyl alcohol (PVA) molecular chain network. In this heterogeneous process, the CPO units bond with PVA molecules via assistance from sodium alginate (SA), and then gradually polymerize along the organic chains to form ultrafine hydroxyapatite nanolines with a diameter of ∼1 nm. Because of the well integration of organic and inorganic phases from the heterogeneous polymerization, the hierarchical structured hydrogel can exhibit ultratough mechanical properties of ∼17.84 MPa in strength and ∼8.97 kJ m-2 in fracture energy, which exceed natural muscles and almost synthetic hydrogels. Moreover, the damaged hydrogel can be repaired readily by adding the precursors of CPO, PVA, and SA, which can induce in situ re-polymerization. The hydrogel also exhibits muscle-like rotational motion under aqueous conditions, which can be developed into a water-driven biomimetic motor. This study indicates that inorganic polymerization can achieve a novel organic-inorganic integration rather than conventional organic-inorganic composition, and it provides a novel tactic for design and manufacture of advanced materials.

The frequency dependence modeling of viscoelastic (VE) materials faces the challenge of high modeling accuracy over a wide frequency range and double-objective optimization in model paramet...

Nanosized gel particles, so-called nanogels, have attracted substantial interest in different application fields, thanks to their controllable and three-dimensional physical structure, good mechanical properties and potential biocompatibility. Literature reports many technologies for their preparation and design, however a recurrent limitation remains in their broad size distributions as well as in the poor size control. Therefore, the monodisperse and size-controlled nanogels preparation by simple process –like emulsification– is a real challenge still in abeyance to date. In this study we propose an original low energy emulsification approach for the production of monodisperse nanogels, for which the size can be finely controlled in the range 30 to 200 nm. The principle lies in the fabrication of a direct nano-emulsion containing both oil (medium chain triglycerides) and a bi-functional acrylate monomer. The nanogels are thus formed in situ upon UV irradiation of the droplet suspension. Advantage of such modification of the oil nano-carriers are the potential modulation of the release of encapsulated drugs, as a function of the density and/or properties of the polymer chain network entrapped in the oil nano-droplets. This hypothesis was confirmed using a model of hydrophobic drug –ketoprofen– entrapped into the nanogels particles, along with the study of the release profile, carried out in function of the nature of the monomers, density of polymer chains, and different formulation parameters.

Due to the slow relaxation nature of polymers, attempts for the development of multi-scale simulations have been made towards the optimization of material processing concerning the molecular characteristics. However, transferability among the utilized models has not been frequently discussed. In this study, a few multi-chain simulations for entangled polymers were compared for the viscosity growth curve under fast shear flows. The multi-chain slip-spring (MCSS) simulations and the multi-chain slip-link simulations (also known as primitive chain network (PCN) simulations) were performed, and the results were compared to the data reported by Cao and Likhtman for the bead-spring model proposed by Kremer and Grest. The conversion parameters for the unit of time and stress were determined from the comparison for the linear viscoelasticity, for which the tree models are essentially transferrable. The obtained viscosity growth curve for the MCSS simulations was in good agreement with that reported for the bead-spring simulations, including the viscosity overshoot. For the PCN simulations, the magnitude of viscosity overshoot was underestimated, whereas the steady state viscosity was reasonably captured. The results demonstrate that the multi-scale strategy by the examined models would work in a certain extent.

Submerged in a solvent-containing environment and subject to applied forces, a nonaffine molecular chain network absorbs the solvent and deforms, forming an elastomeric gel. The Helmholtz free energy of the gel is separated into the contribution due to stretching the nonaffine molecular chain network and that due to mixing the polymer and the solvent. The effect of the nonaffine movement of the molecular chain on the deformation behavior of the gel is discussed.

In this paper, a physically-based constitutive model, considering the crystallization micro-mechanism at the chain-scale, is formulated within the framework of continuum thermodynamics. The stretch-induced formation of crystallized segments in the molecular chain is regarded as an irreversible thermodynamic process accompanied with energy dissipation. The microsphere-based strategy is employed to realize the transition from chain-scale to macro-scale, and to account for the crystallization anisotropy induced by the preferred network orientation. The two antagonist phenomena, i.e. the crystallization-induced softening and stiffening, are well reproduced by controlling the spatial orientation and form of the crystallized segments at the chain-scale. The micro-macro constitutive model, fully tridimensional, is implemented into a finite element program and a quantitative evaluation of the model is performed by comparisons with a few illustrative experiments. A fairly well agreement of the model is shown with tensile experiments under stretching/recovery, in terms of stress-stretch curves and crystallization kinetics, at different stretch levels and temperatures. To illustrate further the capability of the model, numerical simulations are compared to experimental non-homogeneous tensile response in terms of local crystallization/orientation fields of a specimen containing cracks.

New experiments show that tensile stress vanishes shortly after preyield deformation of polymer glasses while tensile stress after postyield deformation stays high and relaxes on much longer time scales, thus hinting at a specific molecular origin of stress in ductile cold drawing: chain tension rather than intersegmental interactions. Molecular dynamics simulation based on a coarse-grained model for polystyrene confirms the conclusion that the chain network plays an essential role, causing the glassy state to yield and to respond with a high level of intrachain retractive stress. This identification sheds light on the future development regarding an improved theoretical account for molecular mechanics of polymer glasses and the molecular design of stronger polymeric materials to enhance their mechanical performance.

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.

To clarify the essential deformation characteristics of silica-filled rubber, we construct the finite element homogenization models of silica-filled rubber with newly proposed nonaffine molecular chain network model of rubber. These models can reflect the generation of complicated inter-fillers connecting phases where the characteristics of rubber are intricately changed depending on the volume fraction of silica coupling agent and relative size of particles and their location. The results obtained clarified the essential physical enhancement mechanisms of deformation resistance and hysteresis loss for rubber filled with silica with different distribution patterns under diffrent rate of deformation. The volume fraction of coupling agent essentially affects the deformation behavior of silica filled rubber which suggests the high controlability of the material characteristics of silica filled rubber as compared with carbon black filled rubber.

It has been well established that the entangled molecular network facilitates the formation of shish-kebabs under flow field, however, the entangled network, usually formed by long chains, tends to disentangle due to molecular relaxation. In the present work, a small amount of lightly cross-linked polyethylene (LCPE), which can be considered as stable molecular chain networks, was added to short-chain polyethylene and then injection-molded using a modified injection molding technology-oscillation shear injection molding (OSIM), which can exert a successive shear field on the melt in the mold cavity during packing stage. The hierarchic structure of the OSIM samples was characterized through differential scanning calorimetry (DSC), wide-angle X-ray diffraction (WAXD) and scanning electron microscopy (SEM). It was found that the oscillation flow field promoted the formation of interlinked shish-kebabs in the intermediate layer of OSIM samples, while there are still typical spherulites in the core layer of OS...

For entangled linear monodisperse polymers, uniaxial elongational flow behavior was examined with the primitive chain network (PCN) simulation, which was originally formulated for a network of Gaus...

In this paper, the polymer chain packing and primitive path (PP) network of uncrosslinked and crosslinked cis-polyisoprene (PI) polymer are analyzed upon employing coarse-grained molecular dynamics simulation. The crosslinking effect is found to enhance intra-chain packing of PI polymers, while weakening their inter-chain packing. Surprisingly, these effects cancel each other in the global packing behavior of this polymeric system. We systematically study the effects of molecular weight (MW) and crosslink density on the PP. Both the PP contour length and number of entanglements per chain, 〈 Z 〉 , are found to increase linearly with MW for uncrosslinked cis-PI. The corresponding entanglement molecular length N e of cis-PI is estimated to be 76 ± 1, in good agreement with experimental results. The polymer end-to-end distance, the PP contour length as well as 〈 Z 〉 of crosslinked PI are reduced by higher intra-chain packing density, compared with uncrosslinked PI, if the crosslinkers are ignored in the PP analysis. At the same time, the tube diameter of crosslinked PI is enlarged by the sparse inter-chain packing. By dividing the crosslinked cis-PI chain network into subchains through crosslinked or crosslinker beads, the PP networks of these partial systems are treated as well. We obtain scaling laws between MW/crosslinking density and 〈 Z 〉 for crosslinked PI polymers. The simulation results indicate that the random walk assumption, often encountered during the analysis of PPs, can only be applied to the entanglement-dominated (low crosslink density) polymers. For crosslink-dominated (high crosslink density) polymers, whose subchains have a molecular length below 100, this assumption would imply a greatly overestimated entanglement density; we thus avoid the assumption in our analysis. To our best knowledge, this is the first work to uncover the PP of crosslinked polymers.

The 2D extended homogenization model based on molecular chain network theory is employed to investigate the micro-to macroscopic mechanical behavior of polymer with randomly distributed voids under macroscopic compaction. A parametric study is performed to quantify the effect of the volume fraction of voids and the macroscopic stress triaxiality of loading conditions on the compaction behavior of porous polymer. The results suggest that the onset of localized shear band at the ligament between voids leads to the macroscopic yield of porous polymer. Furthermore, the microscopic localized shear deformation behavior is promoted in the polymer with high-volume fraction of voids under high macroscopic stress triaxiality loading condition, which results in the early appearance of the macroscopic yield. After the macroscopic yield, a remarkable strain hardening is shown in the macroscopic response of porous polymer under high macroscopic stress triaxiality loading condition, which is due to the onset and propagation of a large number of shear bands at the ligaments between voids. On the other hand, microscopic buckling develops at the narrowest ligament in the polymer with high-volume fraction of voids under high macroscopic stress triaxiality loading condition, which leads to the relative low macroscopic deformation resistance. Furthermore, to develop the macroscopic constitutive model of polymer with high-volume fraction of voids under high macroscopic stress triaxiality loading condition, a modified Gurson model is proposed which takes account of microscopic buckling and gives a good agreement with the unit cell computational results.

Prediction of relaxation behavior of polymeric materials from molecular architecture attracts industrial interests and scientific challenges. In this study a coarse-grained molecular model called primitive chain network model is developed. The model is capable for quantitative prediction of linear and non-linear viscoelasticity of entangled polymers. Also it is indicated that the simulation for cross-linked network is fair, though quantitative test is demanded.

The mechanical properties of polymers are strongly influenced by meso-scale (10-9~10-3 m) structure such as entanglement, molecular weight distribution, orientation, etc. It is important to understand the relationship between the mechanical properties of polymeric material and meso-scale structure. Some studies related to the relationship have been made. However detail of the relationship is still unclear. Especially, the studies emphasize on entanglement and branch are few. This study aims to clear the role of entanglement and branch for mechanical properties by simulating the meso-scale structure using 3D network models. In the models, there are two structures considered. One of them has no branch, and, others have branch. Large strain deformation of network models is evolved via improved molecular dynamics analysis.

We invistigate the characteristic deformation behavior of rubber with carbon black filler. The deformation behaviors of plane strain rubber unit cell contained fillers under combined monotonic and cyclic straining are investigated by computational simulation with the nonaffine molecular chain network model. The results reveal the substantial enhancement of resistance to the macroscopic deformation, which is caused by the remarkable orientation hardening due to the highly localized deformation in the rubber. The disentanglement of molecular chain during the deformation of rubber results the magnification of the hysteresis of the macroscopic stress-strain relations under cyclic straining. Furthermore, we discussed an additional strengthening and hysteresis loss caused by the increase of the volume fraction of filler, the heterogeneity of the distribution of filler and the heterogeneity of initial average number of segments of modecular chains.

The purpose of the present article is to provide a perspective of constitutive equations for glassy polymers developed using the molecular chain network theory. The results of experimental observations of the deformation behavior of glassy polymers at macro- and microscale are indicated, and an accommodation of the characteristic feature of deformation behavior into the molecular chain network theories is discussed. The related computational simulations of neck formation and its propagation under plane strain and three-dimensional conditions are illustrated. The results clarified the three-dimensional characteristic feature of neck propagation behavior under isothermal condition and the effect of deformation-induced heat and pre-drawing on the plane strain neck propagation behavior.

The purpose of the present article is to provide a perspective for computational predictions related to plastic instabilities such as bulge, neck and shear band formation and their propagation in polymeric materials under a variety of deformation conditions. Constitutive models of polymeric materials are developed for glassy polymers and phenomenological models, which duplicate the experimentally observed characteristic behavior of polymeric materials, and physical models, which are developed by using the molecular chain network theory, are discussed. Since the instabilities propagate under almost steady state conditions without significant change in force, the special attention should be given to the computational simulations, which is briefly discussed. Instability behaviors such as the onset of bulge, neck and shear band and their propagation are presented with illustrative examples of computational simulations.

The purpose of the present article is to provide a perspective of constitutive equations for glassy polymers developed using the molecular chain network theory. The experimental observations of the deformation behavior of glassy polymers at macro- and micro-scale are indicated, and an accommodation of the characteristic feature of deformation behavior into the molecular chain network theories is discussed. The related computational simulations such as neck and shear band formation, and their propagations in plane strain conditions with thermomechanically coupled conditions are illustrated using examples.

This Letter reports elastic-driven internal yielding in strained ductile polymer glasses. After cold drawing of two different polymer glasses to neck at room temperature, we show that the samples display considerable retractive stress when warmed up above the storage temperature but still considerably below their glass transition temperatures. We conclude that the elastic yielding arises from the distortion of backbones leading to intra-segmental tension in the chain network.

We propose a model of an unstable chain network to study the pattern formation of cross-linked polymer blends in the thermodynamically unstable state. When the instability is triggered by a small number of point triggers, target patterns emerge. As time proceeds each concentric ring separates into several parts, but the overall image of the target pattern is maintained. Such patterns are frozen-in.

スルホン酸型カチオン交換基を有する多孔性橋かけポリマーを架橋度及び孔構造を制御して合成した. 孔構造は, ポリマー内の全空孔に対するマクロボア (ここでは固定孔と呼ぶ) の割合を固定孔率φihとし定量化を行った. 合成したカチオン交換体を用いてイオン交換反応を行ったところ, カチオン交換体の物理構造の違いによって交換特性は大きく異なった. φihが大きく, かつ高分子相の高分子鎖密度及び架橋密度が大きい場合, 極端に遅いイオン交換反応が生じることが明らかとなった. Nd3+とPr3+のイオン交換では, φih=0.94のポリマーを用いると, 交換時間が60分経過後の交換率は0.622であり約4割のイオンが未交換であった. これは, 堅く柔軟性のない高分子鎖によって, イオン交換場の一部に非常に安定な交換場が形成されるためと推定した.

An evolving internal stress variable is introduced as the macroscopic manifestation of the molecular chain network resistance to deform affinely instantaneously. The inelastic response is obtained by the corotational rate equation of evolution for the internal stress, with respect to a properly defined constitutive spin

Polymeric materials with dispersed solid particles are often used as functional materials. Hence their dynamics is worth being investigated. However, effective simulation methods of particle suspensions in polymeric matrices do not seem available. In this study a novel simulation method is proposed, which extends the primitive chain network model for entangled polymers. The model represents the liquid as a 3‐dimensional sliplink network, and the solid particles floating in the liquid as cross‐linked domains with elastic and viscous contrast from the matrix. The interaction between the liquid and the solid is a repulsive potential similar to that of incompatible polymer blends, while a no‐slip boundary condition at the solid surface is controlled by the hooking and unhooking dynamics of the polymer chain ends with the crosslinked network of the suspended particles. Shear flow simulations were here limited to the linear regime, with shear rates smaller than the inverse longest relaxation time of the matrix. With the appropriate set of parameters, earlier results for the intrinsic viscosity and the Huggins coefficient are reproduced.

Damping functions of entangled polymers for shear, uniaxial, biaxial, and planar deformations, as well as normal stress ratios for shear deformations, were obtained from Brownian simulations making use of the primitive chain network model. To investigate the effect of the force balance over the entanglements and of the convective constraint release mechanism, comparisons with predictions of earlier theories and with experimental data in the literature were performed. It was found that the obtained damping functions are close to the three-chain theory [Marrucci, Greco, and Ianniruberto, Macromol Symp, 158, 57 (2000)] suggesting that the force balance is a dominant correction over the basic Doi-Edwards theory as compared with the effect of convective constraint release. Furthermore, the predicted normal stress ratio in shear, i.e., a quantity very sensitive to the different assumptions, is in good agreement with experiments, suggesting that the combination of force balance, convective constraint release, and other relaxation modes, as accounted for through the primitive chain network model, is quite acceptable.

The primitive‐chain network model for Brownian simulation of entangled polymers is extended so as to include the case of polymer blends. Predictions for the phase diagram and for the linear viscoelastic response appear consistent with earlier works.

The micro- to macroscopic deformation behavior of the polymer under macroscopically uniform tension and shearing, and surface deformation of the plane strain polymer block under compression were investigated by means of computational simulation with the nonafflne molecular chain network model with slightly heterogeneous distribution of the molecular chain, in other words, the distribution of the initial strength of the polymer. The results clarified the onset of microscopic shear bands emanating from the slightly weak points and their evolution, interaction and percolation. The interaction of weak points and the evolution of surface undulation under compression have been demonstrated.