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Modelling the Relative Permittivity of Anisotropic Insulating Composites
KTH, School of Chemical Science and Engineering (CHE), Fibre and Polymer Technology.
KTH, School of Chemical Science and Engineering (CHE), Fibre and Polymer Technology.
KTH, School of Chemical Science and Engineering (CHE), Fibre and Polymer Technology.
2011 (English)In: Composites Science And Technology, ISSN 0266-3538, E-ISSN 1879-1050, Vol. 71, no 2, 216-221 p.Article in journal (Refereed) Published
Abstract [en]

Three models have been developed for predicting the dielectric permittivity of insulating composites with inclusions of different lengths (from nm and larger) and different shapes. Firstly, for approximately periodic materials, a finite element model based on a smallest repeating box method was used in order to mimic frameworks with fibres, crystals, clay platelets, foams and lamellar layers. The introduction of parameters for relative aspect ratio, overlap, rotation and packing density made the model very flexible while maintaining its simplicity. Secondly, a finite element composite model with oriented, randomly positioned particles of different shapes was constructed. Thirdly, an analytical relationship to approximate the effective permittivity of two- or three-phase insulators with brick-shaped inclusions was derived. For a wide range of volume fractions, permittivity ratios and packing conditions, this model gave solutions very close to corresponding finite element simulation data for lamellae, much closer than all the other analytical relationships found in the literature. Results obtained by simulation were in agreement with experimental data from the literature for composites of micrometre-sized hollow glass spheres in epoxy and nanocomposites of mica platelets in polyimide, provided that a third (interfacial) component was introduced.

Place, publisher, year, edition, pages
2011. Vol. 71, no 2, 216-221 p.
Keyword [en]
Polymer-matrix composites (PMCs), Electrical properties, Modelling
National Category
Materials Engineering
Identifiers
URN: urn:nbn:se:kth:diva-25417DOI: 10.1016/j.compscitech.2010.11.016ISI: 000286909100020Scopus ID: 2-s2.0-78650877405OAI: oai:DiVA.org:kth-25417DiVA: diva2:358139
Funder
Swedish Research Council, VR-05-6138
Note
QC 20110317 Ändrad från submitted till published 20110317Available from: 2010-10-21 Created: 2010-10-21 Last updated: 2017-12-12Bibliographically approved
In thesis
1. Meso-scale modelling of composites and semi-crystalline polymers
Open this publication in new window or tab >>Meso-scale modelling of composites and semi-crystalline polymers
2009 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis covers the first few steps of a multi-scale computer simulation strategy for predicting physical properties of complex polymers like composites and semi-crystalline polymers. Meso-scale simulations of crystallization and solvent diffusion in polyethylene as well as simulations examining the geometrical impact on the effective permittivity of composites have been performed. These meso-scale models will in the near future be coupled to molecular dynamics models for increased realism and accuracy.  

The first paper was focused on solvent diffusion in spherulitic semi-crystalline polyethylene. Geometrical models of polyethylene spherulites were constructed and Monte-Carlo random walker simulations were used to estimate the geometrical impedance factor as function of volume crystallinity, mean free path and other geometry properties. Novel numerical off-lattice algorithms made it possible to increase the maximum volume crystallinity from 40 to 55%, to decrease the computation time a factor 100 and to use shorter and more realistic diffusion jump-lengths. The simulation results were in good agreement with experimental results and new analytical formulas were found that could be neatly fitted to both simulation data and experimental data. It was noticed that the geometrical impedance factor was proportional to the polymers mean free path length rather than its length/width aspect ratio and that the traditional Fricke formula for oblate spheroids was not able to correctly predict the diffusion behaviour in complex geometries like spherulites at medium-high volume crystal fractions.   

The second paper was focused on the electrostatics of composites. Geometrical models of layered composites were first obtained and the finite element method was then used to calculate the effective composite permittivity as function of particle content, particle shape, degree of mixing and other geometrical issues. Analytical lamellae formulas for 2- and 3-phase composites were formulated with clearly better correlation to corresponding finite element data than all other previously known analytical formulas. The analytical 3-phase formula was successfully compared with experimental data for mica/polyimide and it was noted that the influence of water and air was significant.

Place, publisher, year, edition, pages
Stockholm: KTH, 2009. 53 p.
Series
Trita-CHE-Report, ISSN 1654-1081 ; 2009:54
Keyword
semi-crystalline polymers, simulations, diffusion, electrostatics
National Category
Materials Engineering Computational Mathematics Polymer Chemistry
Identifiers
urn:nbn:se:kth:diva-11296 (URN)978-91-7415-463-4 (ISBN)
Presentation
Rånbyrummet, Teknikringen 56, KTH, Stockholm (Swedish)
Opponent
Supervisors
Available from: 2009-10-19 Created: 2009-10-14 Last updated: 2010-10-27Bibliographically approved
2. Simulations of Semi-Crystalline Polymers and Polymer Composites in order to predict Electrical, Thermal, Mechanical and Diffusion Properties
Open this publication in new window or tab >>Simulations of Semi-Crystalline Polymers and Polymer Composites in order to predict Electrical, Thermal, Mechanical and Diffusion Properties
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Several novel computer simulation models were developed for predicting electrical, mechanical, thermal and diffusion properties of materials with complex microstructures, such as composites, semi-crystalline polymers and foams.

A Monte Carlo model for simulating solvent diffusion through spherulitic semicrystalline polyethylene was developed. The spherulite model, based on findings by electron microscopy, could mimic polyethylenes with crystallinities up to 64 wt%. Due to the dendritic structure of the spherulites, the diffusion was surprisingly independent of the aspect ratio of the individual crystals. A correlation was found between the geometrical impedance factor (τ) and the average free path length of the penetrant molecules in the amorphous phase. A new relationship was found between volume crystallinity and τ. The equation was confirmed with experimental diffusivity data for Ar, CH4, N2 and n-hexane in polyethylene.

For electrostatics, a novel analytical mixing model was formulated to predict the effective dielectric permittivity of 2- and 3-component composites. Results obtained with the model showed a clearly better agreement with corresponding finite element data than previous models. The analytical 3-component equation was in accordance with experimental data for nanocomposites based on mica/polyimide and epoxy/ hollow glass sphere composites. Two finite element models for composite electrostatics were developed.

It is generally recognized that the fracture toughness and the slow crack growth of semicrystalline polymers depend on the concentrations of tie chains and trapped entanglements bridging adjacent crystal layers in the polymer. A Monte Carlo simulation method for calculating these properties was developed. The simulations revealed that the concentration of trapped entanglements is substantial and probably has a major impact on the stress transfer between crystals. The simulations were in accordance with experimental rubber modulus data.

A finite element model (FEM) including diffusion and heat transfer was developed for determining the concentration of gases/solutes in polymers. As part of the FEM model, two accurate pressure-volume-temperature (PVT) relations were developed. To predict solubility, the current "state of the art" model NELF was improved by including the PVT models and by including chemical interactions using the Hansen solubility parameters. To predict diffusivity, a novel free-volume diffusion model was derived based on group contribution methods. All the models were used without adjustable parameters and gave results in agreement with experimental data, including recent data obtained for polycarbonate and poly(ether-etherketone) pressurized with nitrogen at 67 MPa.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2012. 59 p.
Series
Trita-CHE-Report, ISSN 1654-1081 ; 2012:15
National Category
Polymer Chemistry
Identifiers
urn:nbn:se:kth:diva-93519 (URN)978-91-7501-290-2 (ISBN)
Public defence
2012-04-20, F2,, Lindstedtsvägen 28, entréplan, KTH, Stockholm, 10:00 (English)
Opponent
Supervisors
Note
QC 20120420Available from: 2012-04-20 Created: 2012-04-20 Last updated: 2012-04-23Bibliographically approved

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