Creep dynamics of non-entangled miscible polymer blends and block copolymers

The bead-spring model, as a fundamental model of polymer physics, has been widely utilized so far for polymer chains under the strain-controlled conditions. Nevertheless, full analysis of conformational dynamics of the polymer chains during the creep (stress-controlled) process has not been given until recently by Watanabe and Inoue (Rheol. Acta 43: 634–644, 2004a). In this paper, this analysis is extended to disordered block copolymers and miscible polymer blends for which an effect of frictional distribution/heterogeneity manifests. Due to the requirement of constant stress, segments of different blocks of the block copolymers as well as those of different components of the polymer blends exhibit correlated anisotropic change during the creep process. Furthermore, this change contains two stages with a growth of the orientational correlation among the segments, that is, the first segmental stage where the anisotropic change reflects the intrinsic mobility of segments, and the second global stage where the anisotropy approaches the steady-state defined with respect to the specific position of a chain.     

Finitely extensible bead spring chains in time-dependent shear flows

The configurational and rheological properties of bead spring chains in time-dependent shear flows are calculated. The finite extensibility is incorporated through the constraint of constant contour length of the chain. Start-up of shear flow yields a stress overshoot, whereas oscillatory shear flow yields the same frequency dependence of the dynamic moduli as the simple bead spring model. The results show that finite extensibility can lead to non-linear rheological behavior of dilute polymer solutions. The influence of preaveraged hydrodynamic interaction on the obtained results is discussed.     

Primitive chain network simulations for branched polymers

We present simulations of branched polymer dynamics based on a sliplink network model, which also accounts for topological change around branch points, i.e., for branch-point diffusion. It is well-known that, with the exception of stars, branched polymers may show a peculiar rheological behavior due to the exceptionally slow relaxation of the backbone chains bridging branch points. Though Brownian simulations based on sliplinks are powerful tools to study the motion of polymers and to predict rheological properties, none of the existing methods can simulate the relaxation of the bridge chains. The reason for that is lack of a rule for network topology rearrangement around branch points, so that entanglements between bridge chains cannot be renewed. Therefore, we introduce in this paper one possible branch-point mobility rule into our primitive chain network model. For star polymers, diffusion coefficients were calculated and compared with experiments. For both star and H-shaped polymers, diffusion was simulated both with and without the new rule, and the effect on linear viscoelasticity was also determined in one case.     

Monte Carlo simulation of self-avoiding lattice chains subject to oscillatory shear flow in polymer solution

 This paper has introduced a pseudo-potential in bond-fluctuation model to simulate oscillatory shear flow of multiple self-avoiding chains in three dimensions following our previous work under simple shear flow. The oscillatory flow field was reasonably reproduced by lattice Monte Carlo simulation using this pseudo-potential neglecting hydrodynamic interaction. By sampling the configuration distribution functions, the macroscopic viscoelasticity of semi-concentrated polymer solution was determined. Both Newtonian and non-Newtonian regimes were studied. The complex modulus and dynamic viscosity exhibit a reasonable power relation with oscillatory frequency, which is consistent with present theories and experiments. Consequently, lattice Monte Carlo simulation has been extended to model free-draining self-avoiding multi chains subject to oscillatory shear flow and to investigate associated viscoelasticity on the molecular level. Received: 1 October 1999 Accepted: 19 October 1999     

A mesoscopic tube model of polymer/layered silicate nanocomposites

Rheology of isothermal suspensions of completely exfoliated silicate lamellae in polymer melts is investigated. In order to express more faithfully the physics involved in low shear rates and low frequencies, we model the polymer molecules composing the melt as chains whose motion is confined to a tube formed by surrounding chains and lamellae. In the absence of lamellae, the model reduces to the mesoscopic model of reptating chains developed in Eslami and Grmela (Rheol Acta, 2008). If the chains are seen only as FENE-P dumbbells, the model reduces to the model developed in Eslami et al. (J Rheol 51:1189–1222, 2007). Responses to oscillatory, transient, and steady shear flows are calculated and compared with available experimental data. Particular attention is payed to the region of low shear rate and low frequency.     

Constitutive equations for non-affine polymer networks with slippage of chains

A model is derived for isothermal three-dimensional deformation of polymers with finite strains. A polymer fluid is treated as a permanent network of chains bridged by junctions (entanglements). Macro-deformation of the medium induces two motions at the micro-level: (i) sliding of junctions with respect to their reference positions that reflects non-affine deformation of the network, and (ii) slippage of chains with respect to entanglements that is associated with unfolding of back-loops. Constitutive equations are developed by using the laws of thermodynamics. Three important features characterize the model: (i) the symmetry of relations between the elongation of strands and an appropriate configurational tensor, (ii) the strong nonlinearity of the governing equations, and (iii) the account for the volumetric deformation of the network induced by stretching of chains. The governing equations are applied to the numerical analysis of extensional and shear flows. It is demonstrated that the model adequately describes the time-dependent response of polymer melts observed in conventional rheological tests.     

Diffusion mechanism during the swelling hidroxy-methyl cellulose membrane formation

The conduction properties of HMC polymer gel prepared by the phase inversion method were investigated through the diffusion coefficient in order to confirm the conduction mechanism. The solution introduced in the polymer is stored in the pores and then penetrates into the polymer chains. For swelling the polymer network. A model describing the swelling hidroxy-methyl cellulose is presented. The model is used to predict the type liquid–liquid phase separation (instantaneous or delayed) that occurs when HMC-PVPD-Solvent-Water casting solutions are immersed in a gelation bath. The model includes the thermodynamic interactions parameters and the transport parameters. The predictions of the model agree with the experimental observations.     

Molecular simulation guided constitutive modeling on finite strain viscoelasticity of elastomers

Viscoelasticity characterizes the most important mechanical behavior of elastomers. Understanding the viscoelasticity, especially finite strain viscoelasticity, of elastomers is the key for continuation of their dedicated use in industrial applications. In this work, we present a mechanistic and physics-based constitutive model to describe and design the finite strain viscoelastic behavior of elastomers. Mathematically, the viscoelasticity of elastomers has been decomposed into hyperelastic and viscous parts, which are attributed to the nonlinear deformation of the cross-linked polymer network and the diffusion of free chains, respectively. The hyperelastic deformation of a cross-linked polymer network is governed by the cross-linking density, the molecular weight of the polymer strands between cross-linkages, and the amount of entanglements between different chains, which we observe through large scale molecular dynamics (MD) simulations. Moreover, a recently developed non-affine network model (Davidson and Goulbourne, 2013) is confirmed in the current work to be able to capture these key physical mechanisms using MD simulation. The energy dissipation during a loading and unloading process of elastomers is governed by the diffusion of free chains, which can be understood through their reptation dynamics. The viscous stress can be formulated using the classical tube model (Doi and Edwards, 1986); however, it cannot be used to capture the energy dissipation during finite deformation. By considering the tube deformation during this process, as observed from the MD simulations, we propose a modified tube model to account for the finite deformation behavior of free chains. Combing the non-affine network model for hyperelasticity and modified tube model for viscosity, both understood by molecular simulations, we develop a mechanism-based constitutive model for finite strain viscoelasticity of elastomers. All the parameters in the proposed constitutive model have physical meanings, which are signatures of polymer chemistry, physics or dynamics. Therefore, parametric materials design concepts can be easily gleaned from the model, which is also demonstrated in this study. The finite strain viscoelasticity obtained from our simulations agrees qualitatively with experimental data on both un-vulcanized and vulcanized rubbers, which captures the effects of cross-linking density, the molecular weight of the polymer chain and the strain rate.     

The computer simulations of polymer dynamics in porous media

We designed and developed a simple model of polymer chains. Three types of model chains with different internal macromolecular architecture were studied: linear, star-branched with f=3 arms of equal length and rings. The chains consisted of identical united atoms (segments) and were restricted to a simple cubic lattice with the excluded volume interactions only (the athermal system). The macromolecules were confined between two parallel impenetrable walls with a set of irregular obstacles that can be treated as a crude model of porous media. The properties of the model studied were determined by the Monte Carlo simulations. A Metropolis-like sampling algorithm with local changes of chains’ conformation was used. The short- and long-time dynamic properties of the model system were studied. The differences in the mobility of chains and their fragments for different internal polymer architectures were shown and discussed. The possible mechanisms of chain’s motion were discussed.This paper was presented at the 2nd Annual European Rheology Conference (AERC) held on April 21–23, 2005 in Grenoble, France.     

The MSF model: relation of nonlinear parameters to molecular structure of long-chain branched polymer melts

The elongational viscosity data of model PS combs (Hepperle J, Einfluss der Molekularen Struktur auf Rheologische Eigenschaften von Polystyrol- und Polycarbonatschmelzen. Doctoral Thesis, University Erlangen-Nürnberg, 2003) are reconsidered by including the interchain pressure term of Marrucci and Ianniruberto [Macromolecules 37:3934–3942, 2004] in the Molecular Stress Function model [Wagner et al., J Rheol 47(3):779–793, 2003, Wagner et al., J Rheol 49:1317–1327, 2005d]. Two nonlinear model parameters are needed to describe elongational flow, β and . The parameterβ determines the slope of the elongational viscosity after the inception of strain hardening. It is directly related to the molecular structure of the polymer and represents the ratio of the molar mass of the (branched) polymer to the molar mass of the backbone alone. β follows from the hypothesis of Wagner et al. [J Rheol 47(3):779–793, 2003] that side chains are compressed onto the backbone. We consider also the case that side chains are oriented by deformation, but not stretched, and found little difference in the model predictions. The parameter represents the maximum strain energy stored in the polymeric system and determines the steady-state value of the viscosity in extensional flows. The relation of this energy parameter to the molecular structure is discussed. Good correlations between the energy parameter and different coil contraction ratios, as determined either experimentally or calculated theoretically by considering the topology of the macromolecule, are found. The smaller the relative size of the polymer coil, the larger is the energy parameter and the more strain energy can be stored in the polymeric system. Presented at the 3rd Annual European Rheology Conference, AERC2006, Crete, Greece.     

Modelling the curing process in magneto-sensitive polymers: Rate-dependence and shrinkage

This paper deals with a phenomenologically motivated magneto-viscoelastic coupled finite strain framework for simulating the curing process of polymers under the application of a coupled magneto-mechanical load. Magneto-sensitive polymers are prepared by mixing micron-sized ferromagnetic particles in uncured polymers. Application of a magnetic field during the curing process causes the particles to align and form chain-like structures lending an overall anisotropy to the material. The polymer curing is a viscoelastic complex process where a transformation from fluid to solid occurs in the course of time. During curing, volume shrinkage also occurs due to the packing of polymer chains by chemical reactions. Such reactions impart a continuous change of magneto-mechanical properties that can be modelled by an appropriate constitutive relation where the temporal evolution of material parameters is considered. To model the shrinkage during curing, a magnetic-induction-dependent approach is proposed which is based on a multiplicative decomposition of the deformation gradient into a mechanical and a magnetic-induction-dependent volume shrinkage part. The proposed model obeys the relevant laws of thermodynamics. Numerical examples, based on a generalised Mooney–Rivlin energy function, are presented to demonstrate the model capacity in the case of a magneto-viscoelastically coupled load.     

The Monte Carlo dynamics of polymer chains in sandwich brushes

We designed and developed a simple model of polymer chains. The chains consist of identical united atoms (segments) and were restricted to a simple cubic lattice with the excluded volume interactions only (an athermal system).The polymers were confined between two parallel impenetrable walls with one end of each chain was grafted to the wall. A motion of a probe single linear chain in such environment was studied. The properties of the model studied were determined from the Monte Carlo simulations employing a Metropolis-like sampling algorithm with local changes of chains’ conformation. The influence of the system density and the length of chains on the polymer mobility was studied and discussed. We found that the number of chains forming the brush was the major quantity which governed the dynamics of a probe chain, while the length of the chains in the brush also influenced the diffusivity of the probe chain. The diffusion coefficients scaled with the length of a probe chain is stronger than in the Rouse model with the exponent γ?=??1.3.     

Characterizing dynamic load propagation in cohesionless granular packing using force chain

When dynamic load is applied on a granular assembly, the time-dependent dynamic load and initial static load (such as gravity stress) act together on individual particles. In order to better understand how dynamic load triggers the micro-structure's evolution and furtherly the ensemble behavior of a granular assembly, we propose a criterion to recognize the major propagation path of dynamic load in 2D granular materials, called the “dynamic force chain”. Two steps are involved in recognizing dynamic force chains: (1) pick out particles with dynamic load larger than the threshold stress, where the attenuation of dynamic stress with distance is considered; (2) among which quasi-linear arrangement of three or more particles are identified as a force chain. The spatial distribution of dynamic force chains in indentation of granular materials provides a direct measure of dynamic load diffusion. The statistical evolution of dynamic force chains shows strong correlation with the indentation behaviors.     

Computer simulation of polymer brushes under shear

 Recently two different methods were used to simulate the stationary properties of polymer brushes under strong shear: stochastic dynamics of a multi-chain brush model, and self-consistent Brownian dynamics of a one-chain model. The former explicitly describes volume interactions (VI) between polymer segments but does not take into account hydrodynamic interactions (HI) inside the brush. In the latter the self-consistent molecular field method has been chosen to calculate VI, and HI were accounted for using the Brinkman equation. Despite a significant difference between models a collapse of the brush under shear was observed in both studies. In particular, the density profile changes from parabolic to step-like and the free ends of the chains become concentrated in a narrow region at the periphery of the brush. However, when HI are taken into account much higher shear rates are necessary to attain the same brush deformation because the shear flow only slightly penetrates into the brush in contrast to the free-draining case. The inner brush structure is also found to be different for the two models. In the first model all chains are inclined approximately at the same angle when shear is applied. In the second model chains with the free ends found in the inner sublayer of the brush do not feel the flow at all whereas those in the upper sublayer are stretched and inclined by the flow. Received: 24 June 1999 Accepted: 8 February 2000     

Prediction of multiple overshoots in shear stress during fast flows of bidisperse polymer melts

We present a differential constitutive model of stress relaxation in polydisperse linear polymer melts and solutions that contains contributions from reptation, contour-length fluctuations, and chain stretching. The predictions of the model during fast start-up and steady shear flows of polymer melts are in accord with experimental observations. Moreover, in accordance with reported experimental literature (Osaki et al. in J Polym Sci B Polym Phys 38:2043–2050, 2000), the model predicts, for a range of shear rates, two overshoots in shear stress during start-up of steady shear flows of bidisperse polymer melts having components with widely separated molar masses. Two overshoots result only when the stretch or Rouse relaxation time of the higher molar mass component is longer than the terminal relaxation time of the lower molar mass component. The “first overshoot” is the first to appear with increasing shear rate and occurs as a result of the stretching of longer chains. Transient stretching of the short chains is responsible for the early time second overshoot. The model predictions in steady and transitional extensional flows are also remarkable for both monodisperse and bidisperse polymer solutions. The computationally efficient differential model can be used to predict rheology of commercial polydisperse polymer melts and solutions.     

聚合物分子链微结构-力学性能关系的数据驱动模型

聚合物一般由随机分布的大分子链组成,分子链的分布、缠绕、交联等微结构状态显著影响聚合物的力学和物理性能。本文通过数据驱动方法,建立了聚合物分子链微结构-力学性能关系。使用有限元方法建立了两种分子链的随机微结构模型并得到了其力学性能。基于微结构-力学性能关系建立数据集,以聚合物的随机分子链微结构为输入,以聚合物的弹性刚度为响应输出,进行数据驱动模型的训练和验证。得到了精度满意的微结构-力学性能关系的分析结果。结果表明,通过数据驱动方法研究聚合物的弹性刚度问题是可靠的。