Review on the Brownian Dynamics Simulation of Bead-Rod-Spring Models Encountered in Computational Rheology

Kinetic theory is a mathematical framework intended to relate directly the most relevant characteristics of the molecular structure to the rheological behavior of the bulk system. In other words, kinetic theory is a micro-to-macro approach for solving the flow of complex fluids that circumvents the use of closure relations and offers a better physical description of the phenomena involved in the flow processes. Cornerstone models in kinetic theory employ beads, rods and springs for mimicking the molecular structure of the complex fluid. The generalized bead-rod-spring chain includes the most basic models in kinetic theory: the freely jointed bead-spring chain and the freely-jointed bead-rod chain. Configuration of simple coarse-grained models can be represented by an equivalent Fokker-Planck (FP) diffusion equation, which describes the evolution of the configuration distribution function in the physical and configurational spaces. FP equation can be a complex mathematical object, given its multidimensionality, and solving it explicitly can become a difficult task. Even more, in some cases, obtaining an equivalent FP equation is not possible given the complexity of the coarse-grained molecular model. Brownian dynamics can be employed as an alternative extensive numerical method for approaching the configuration distribution function of a given kinetic-theory model that avoid obtaining and/or resolving explicitly an equivalent FP equation. The validity of this discrete approach is based on the mathematical equivalence between a continuous diffusion equation and a stochastic differential equation as demonstrated by Itô in the 1940s. This paper presents a review of the fundamental issues in the BD simulation of the linear viscoelastic behavior of bead-rod-spring coarse grained models in dilute solution. In the first part of this work, the BD numerical technique is introduced. An overview of the mathematical framework of the BD and a review of the scope of applications are presented. Subsequently, the links between the rheology of complex fluids, the kinetic theory and the BD technique are established at the light of the stochastic nature of the bead-rod-spring models. Finally, the pertinence of the present state-of-the-art review is explained in terms of the increasing interest for the stochastic micro-to-macro approaches for solving complex fluids problems. In the second part of this paper, a detailed description of the BD algorithm used for simulating a small-amplitude oscillatory deformation test is given. Dynamic properties are employed throughout this work to characterise the linear viscoelastic behavior of bead-rod-spring models in dilute solution. In the third and fourth part of this article, an extensive discussion about the main issues of a BD simulation in linear viscoelasticity of diluted suspensions is tackled at the light of the classical multi-bead-spring chain model and the multi-bead-rod chain model, respectively. Kinematic formulations, integration schemes and expressions to calculate the stress tensor are revised for several classical models: Rouse and Zimm theories in the case of multi-bead-spring chains, and Kramers chain and semi-flexible filaments in the case of multi-bead-rod chains. The implemented BD technique is, on the one hand, validated in front of the analytical or exact numerical solutions known of the equivalent FP equations for those classic kinetic theory models; and, on the other hand, is control-set thanks to the analysis of the main numerical issues involved in a BD simulation. Finally, the review paper is closed by some concluding remarks

Forced assembly by multilayer coextrusion to create oriented graphene reinforced polymer nanocomposites

A potential advantage of platelet-like nanofillers as nanocomposite reinforcements is the possibility of achieving two-dimensional stiffening through planar orientation of the platelets. The ability to achieve improved properties through in-plane orientation of the platelets is a challenge and, here, we present the first results of using forced assembly to orient graphene nanoplatelets in poly(methyl methacrylate)/ polystyrene (PMMA/PS) and PMMA/PMMA multilayer films produced through multilayer coextrusion. The films exhibited a multilayer structure made of alternating layers of polymer and polymer containing graphene as evidenced by electron microscopy. Significant single layer reinforcement of 118% at a concentration of 2 wt % graphene was achieveddhigher than previously reported reinforcement for randomly dispersed graphene. The large reinforcement is attributed to the planar orientation of the graphene in the individual polymer layers. Anisotropy of the stiffening was also observed and attributed to imperfect planar orientation of the graphene lateral to the extrusion flow

Coalescence modeling and experimental validation of sintering of thermoplastic polyamide fibers

In order to study the coalescence mechanisms of thermoplastic polymer powders, a 2D mathematical model has been established based on Frenkel, Eshelby and Pokluda’s model. Sintering experiments have been carried out by using two polyamide fibers that can be considered as infinite cylinders with its length much larger than the diameter. 2D mathematical model has been validated through comparison with results of sintering experiments as well as Constrained Natural Element Method (C-NEM) coalescence simulation. This consistence shows that the proposed coalescence model and experimental results can provide a reference for the numerical simulation of sintering process

Simulation du procédé de fabrication directe de pièces thermoplastiques par fusion laser de poudre

Le procédé de fabrication directe de pièces thermoplastiques est un procédé innovant qui permet de créer sans outillage, à partir d'une modélisation géométrique numérique, des pièces de géométrie complexe en quelques heures. La fabrication dite additive est réalisée par étalement successif de couches de poudre thermoplastique de quelques dizaines de micromètres, dont une partie est fondue sous rayonnement laser et refroidie lentement afin de permettre la densification de la poudre par diffusion de l'air emprisonné. La résistance mécanique finale du matériau dépend fortement de cette densification. Un grand nombre de paramètres procédé et matériau influencent les mécanismes physiques mis en jeu qui sont contrôlés par la thermique du procédé. La clé de la maîtrise de ce procédé réside dans la parfaite maîtrise de la thermique du lit de poudre. Cette étude a pour objectif de modéliser le procédé de fabrication directe de pièces thermoplastiques haute température de type PEEK. Dans un premier temps, une simulation microscopique de la fusion laser d'un lit de poudre préchauffé et de la coalescence des grains est développée à l'aide de la méthode C-NEM implémentée sur le logiciel Matlab. Les cycles thermiques, la densification et le soudage des grains sont étudiés en fonction des paramètres matériau et procédé. Dans un second temps, l'étude de la thermique d'une couche de poudre à l'état liquide refroidie par apport d'une nouvelle couche de poudre par-dessus est menée à l'aide d'un logiciel éléments finis commercial. L'objectif est de définir les conditions d'étalement permettant au polymère fondu de rester à l'état liquide.Direct manufacturing technology using Selective Laser Sintering of thermoplastic powder allows obtaining final parts in a short time, with a high degree of geometry flexibility and evolution. Parts are built layer by layer, a specific area of each layer is melted by the laser radiation and the whole part is cooled down slowly to induce a good densification, permitting the gas diffusion through the melted material. The mechanical properties of parts made by this process highly depend on the final polymer density. A lot of process and material parameters control the parts properties. The key of the process master lies in its perfect thermal control. The aim of this work is to model the selective laser sintering process for high temperature polymers like PEEK at two scales. Firstly, a microscopic simulation of the melting and the grain coalescence of preheated polymer powder bed is performed using the C-NEM method implemented on Matlab. This tool allows to study the material thermal cycles, the powder densification and the welding quality of grains for different material and process parameters. Then, the thermal study of the additional powder layer spreading on the melted layer is performed on a commercial finite element software. This study aims to determine the good spreading conditions allowing the melted material not to decrease below its crystallization temperature to enhance material densification.PARIS-Arts et Métiers (751132303) / SudocSudocFranceF

Moulage par microinjection des polymères semi-cristallins

La miniaturisation des pièces est une étape importante pour la progression de la microtechnologie dans plusieurs domaines (connectique, médical, optique, microsystèmes mécaniques). Pour cela, le moulage par microinjection, semble être la solution clé pour la production à grande échelle de micro-composants de polymères. Pour les polymères semi-cristallins, la cristallisation, sous fort taux de cisaillement et sous des vitesses de refroidissement élevées (about 100 K/s), induit des morphologies et des propriétés spécifiques. Elle prend donc une importance considérable dans le processus de microinjection par rapport au moulage par injection classique où les épaisseurs injectées sont généralement supérieures à 1 mm. Ces microstructures ont une grande influence sur les propriétés mécaniques du produit final. La prédiction de ces propriétés à partir de la description de la microstructure est un défi technique et scientifique. Durant cette thèse, deux polymères semi-cristallins ont été microinjectés, le polyéthylène haute densité et le polyamide 12. Les analyses obtenues par la microscopie otiques montrent que les morphologies cristallines varient entre les micro- et les macro-pièces. Tandis que la morphologie de peau-cœur' est présente dans les macropièces, les micropièces présentent une morphologie plutôt particulière. Les analyses combinées de diffusion et de diffraction des rayons X (SAXS et WAXS) avec un microfaisceau synchrotron, nous ont permis de déterminer la microstructure induite par le processus de microinjection dans toute l'épaisseur des pièces. Nous avons constaté que la morphologie et les orientations cristallines induites sont très dépendantes des conditions d'injection ou de microinjection. Une diminution de l'épaisseur, de la vitesse et de la température du moule, augmente l'orientation cristalline en limitant la relaxation des chaînes de polymères.The components miniaturization is an important step in the evolution of micro technology in several domain (connectivity, medical, optical, mechanical, microsystems). For this purpose, the micro-injection molding seems to be the key solution for the large-scale micro-polymer components production.The crystallization of the semi-crystalline polymers under high shear and cooling rates (about 100 K / s), induces specific properties and morphologies, consequently, it takes a substantial importance in the process of micro-injection compared to conventional injection molding where the usually injected thicknesses is over 1 mm. These micro-structures have a great influence on the mechanical propertie of the final product. The prediction of the final product's properties based on the illustration of the micro-structure is a technical and scientific challenge. In this thesis, two semi-crystalline polymers were micro-injected, the high density polyethylene and the polyamide 12. The obtained analyzes with the use of an optical microscope showed that the Morphology of Crystals vary between micro-and macro-pieces. While the morphology of 'peau-cœur' is present in the macro-pieces, the micro-parts have a particular morphology. The combined analysis of diffusion and X-ray diffraction (WAXS and SAXS) along with the synchrotron microbeam, has allowed us to determined the micro-structure induced by the micro-injection process throughout the thickness of the pieces.We have identified that the morphology and the induced crystal's orientation are very dependent on the conditions of injection or micro-injection. The decrease of the thickness,speed and temperature of the mold will increase the crystal orientation by limiting the relaxation of the polymer chains.PARIS-Arts et Métiers (751132303) / SudocSudocFranceF

Role of the inter‐ply microstructure in the consolidation quality of high‐performance thermoplastic composites

Consolidation of Carbon Fiber (CF)/high-performance thermoplastic compos-ites is much less understood than the one of their thermoset counterparts. It isusually assumed that the consolidation quality is directly linked to the removalof voids within the sample during consolidation, leading to mechanical proper-ties suitable for aerospace applications. A systematic study of the temporalevolution of CF/polyetherketoneketone (PEKK) samples' microstructure con-solidated under low pressure in a rheometer is related to the increase in inter-laminar shear strength. The results show that despite similar void contentswell-below 1 vol%, samples can present significant differences in ILSS values,from 80 to 95 MPa for cross-ply samples, and from 98 to 112 MPa for unidirec-tional (UD) ones. A microstructural analysis shows that, for these materials,consolidation quality is rather related to a reorganization of the inter-ply, aresin-rich ( 70 vol%) region of typical thickness 10μm which is slowly repo-pulated in fibers during consolidation

Experimental and numerical analysis of the selective laser sintering (SLS) of PA12 and PEKK semi-crystalline polymers

A dual experimental-numerical approach was carried out to estimate thermal cycles and resulting fusion depths obtained during the selective laser sintering (SLS) of two polymers: PA12 and PEKK. The validation of thermal cycles was obtained by considering fusion depths on single layers for different experimental conditions and temperature measurements with IR thermal camera. It was shown that a simple Beer-Lambert’s heat deposit equation incorporating an extinction coefficient determined experimentally, and an efficiency ratio including both laser absorption and diffusion in the powder bed were sufficient for determining accurately fusion depths, and heat cycles for the two polymers. This allowed determining optimum process conditions for manufacturing additive layers on a specifically-designed SLS set-up.FUI Fadiplas