The rigid rod model for nematic polymers: Testing closure approximations with bifurcation analysis

A numerical investigation is conducted into the flow of a dilute suspension of rigid rod-like particles between parallel flat plates, driven by a uniform pressure gradient. The particles are assumed to be small relative to lengthscales of the flow with the effect that particle orientations evolve according to the local velocity gradient; the particles are also assumed to be small in an absolute sense, with the consequence that Brownian motions are of consequence. The calculations are performed using a novel approach, with a theoretical basis that has been developed previously in a companion paper (Szeri & Leal 1992). The new approach permits one to solve flow problems of microstructured fluids (such as suspensions, liquid crystals, polymer solutions and melts) without ‘pre-averaging’ or closure approximations. In the present work, the new approach is used to expose previously unknown pathological, non-physical predictions in various constitutive models derived using closure approximations. This appears to have passed unnoticed in prior work. In addition, the new approach is shown to possess several computational advantages. The determination of the orientation distribution of particles is self-adaptive; this leads, in effect, to a very efficient solution of the associated Smoluchowski (or Fokker–Planck) equation. Moreover, the new approach is highly suited to parallel (and vector) implementation on modern computers. These issues are explored in detail in the context of the example flow.

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Simulation of Long Semi-Flexible Fiber Orientation During Injection Molding

Volume 1: Processing ◽

10.1115/msec2016-8577 ◽

2016 ◽

Author(s):

Hongyu Chen ◽

Peter Wapperom ◽

Donald G. Baird

Keyword(s):

Mechanical Properties ◽

Injection Molding ◽

Fiber Orientation ◽

Fiber Length ◽

Simple Shear Flow ◽

Orientation Model ◽

Rod Model ◽

Flexible Fibers ◽

Rigid Rod ◽

Long Fibers

Fiber orientation simulation is conducted for the Center-Gated-Disk (CGD) geometry and compared with experimental data. Long-fiber thermoplastic composites (LFTs) possess competitive advantages over short glass fiber composites in terms of their mechanical properties while retain the ability to be injection molded. Mechanical properties of LFTs are highly dependent on the microstructural variables imparted by the injection molding process including fiber orientation and fiber length distribution. As the fiber length increased, the mechanical properties of the composites containing discontinuous fibers can approach those of continuous fiber materials. Several researchers have reported that flexural, creep and charpy impact properties increase as fiber length increases, while tensile modulus will plateau for glass fibers above 1 mm in length. Fibers less than the 1 mm threshold have been considered to be short while fibers with lengths greater than 1 mm are considered long. For long fibers, they will have the ability to deform, bend and even break during any stage of polymer processing. There is a lack of knowledge about the effects of fiber length and fiber length variation on fiber orientation kinetics. This lack of information provides an opportunity to understand the length effect inherent to long fibers systems. The Bead-Rod fiber orientation model takes into account the flexibility of semi-flexible fibers that show small bending angles. In this model, a flexibility parameter representing the resistive bending potential is fiber length dependent (detailed explanation can be found in the reference)1. This work is concerned with the effect of fiber length on the performance of the Bead-Rod fiber orientation model which takes into account the flexibility of semi-flexible fibers. Different averaging techniques are used to represent the average fiber length for the population of fibers, which give different fiber length parameters for the Bead-Rod model. The sensitivity of the Bead-Rod model is evaluated with regard to the fiber flexibility parameter, k, and length parameter, lb. The other phenomenal parameters within the orientation model are obtained via basic rheological measurements using simple shear flow. As the value of average fiber length Lav increases and the corresponding flexibility parameter value decreases, the core regions become wider and the flow direction orientation gradually decreases especially near the walls for the Bead-Rod model predictions. In addition, as the parameters favor longer fiber lengths, the predicted extent of fiber bending increases. The simulation results are also compared with the experimental obtained fiber orientation at different flow length along the thickness direction. The Bead-Rod model shows improvement over the rigid rod model.

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Bifurcation analysis of a molecular model for nematic polymers in shear flows

Journal of Non-Newtonian Fluid Mechanics ◽

10.1016/0377-0257(95)01363-z ◽

1995 ◽

Vol 59 (1) ◽

pp. 73-91 ◽

Cited By ~ 18

Author(s):

P.L. Maffettone ◽

S. Crescitelli

Keyword(s):

Bifurcation Analysis ◽

Shear Flows ◽

Molecular Model ◽

Nematic Polymers

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Polarizable force field for molecular dynamics simulations of silver nanoparticles

Kharkov University Bulletin Chemical Series ◽

10.26565/2220-637x-2019-32-03 ◽

2019 ◽

Cited By ~ 1

Keyword(s):

Molecular Dynamics ◽

Polarization Effect ◽

Md Simulations ◽

Water Molecules ◽

Interfacial Water ◽

Silver Surface ◽

Polarizable Force Field ◽

Rod Model ◽

Adsorption Of Water ◽

Rigid Rod

Contact of silver metal surfaces with water, ions and organic ligands experiences induced charges, leading to attractive polarization. These forces play an important role at inorganic/organic interfaces and complement other non-bonded surface interactions. Despite the importance of these interactions, it, however, remains difficult to implement polarization effects to classical molecular dynamics (MD) simulations. In this contribution, we first present an overview of two popular polarizable models, such as Drude oscillator and the rigid rod model, which are utilized to mimic the polarizability of bulk metals. Second, we implemented the rigid rod model to the polarizable force field (FF) for a silver atom, which was further adapted for atomistic MD simulations of silver nanoparticles (AgNPs) composed of 1397 atoms. In our model, induced charge polarization is represented by the displacement of a charge-carrying virtual site attached rigidly to an original Ag atom. To explore the role of polarization, we compared the performance of the classical nonpolarizable FF and the new polarizable model in the MD simulations of adsorption of water and ions onto quasi-spherical AgNP and the flat crystalline silver surface. The analysis of the radial distribution function of Ag-Ag atoms demonstrated that the introduction of the polarization effect had minor effects on face-centered cubic (fcc) packing of silver atoms of bare and water-solvated AgNPs. We found that the polarizable FF causes some increase in attractive interactions between the silver surface and water molecules and Na+ ions. As a crucial test of the developed polarizable model, the structure of adsorbed interfacial water molecules was analyzed. Our data suggest that the environment-induced polarization of the silver surface contributes significantly to the structure of adsorbed interfacial water layers and it also plays an important role in the adsorption of positive ions. However, it was also found out that the polarization effect has a rather short-range effect, so that a minor contribution of silver polarization was seen for adsorption of water molecules and ions from distant solvation shells.

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