Polymer composites models

Capiati N J and Porter R S (1975) Concept of one polymer composites modeled with high-density polyethylene, J Mater Sci 10 1671-1677. 

Nassehi, V., Kinsella, M. and Mascia, 1.., 1993b. Finite element modelling of the stress distribution in polymer composites with coated fibre interlayers. J. Compos. Mater. 27, 195-214. 

Lipatov et al. [116,124-127] who simulated the polymeric composite behavior with a view to estimate the effect of the interphase characteristics on composite properties preferred to break the problem up into two parts. First they considered a polymer-polymer composition. The viscoelastic properties of different polymers are different. One of the polymers was represented by a cube with side a, the second polymer (the binder) coated the cube as a homogeneous film of thickness d. The concentration of d-thick layers is proportional to the specific surface area of cubes with side a, that is, the thickness d remains constant while the length of the side may vary. The calculation is based on the Takayanagi model [128]. From geometric considerations the parameters of the Takayanagi model are related with the cube side and film thickness by the formulas ... 

Recently, Teymour and coworkers developed an interesting computational technique called the digital encoding for copolymerization compositional modeling [20,21], Their method uses symbolic binary arithmetic to represent the architecture of a copolymer chain. Here, each binary number describes the exact monomer sequence on a specific polymer chain, and its decimal equivalent is a unique identifier for this chain. Teymour et al. claim that the... 

Gel Permeation Chromatography (CPC) is often the source of molecular wei t averages used in polymerization kinetic modelling Q.,2). Kinetic models also r uire measurement of molecular weight distribution, conversion to polymer, composition of monomers in a copolymerization rea tion mixture, copolymer composition distribution, and sequence length distribution. The GPC chromatogram often reflects these properties (3,. ... 

For the transformation of the macrocomposite model to a molecular composite model for the ultimate strength of the fibre the following assumptions are made (1) the rods in the macrocomposite are replaced by the parallel-oriented polymer chains or by larger entities like bundles of chains forming fibrils and (2) the function of the matrix in the composite, in particular the rod-matrix interface, is taken over by the intermolecular bonds between the chains or fibrils. In order to evaluate the effect of the chain length distribution on the ultimate strength the monodisperse distribution, the Flory distribution, the half-Gauss and the uniform distribution are considered. 

Saturated complex polyesters, particularly, poly (butylene terephthalate) (PBT) are used as engineering thermoplastics possesing good thermo - and wearstability, excellent moulding. These properties also allow to use them as matrix material for polymer composites [1], One of the perspective ways of search of effective catalysts for such systems is kinetic study of the reesterification model reaction, performed in the presence of various catalysts and comparison it with the results of the similar reaction without catalyst. Clarification on the example of model system of the most effective catalysts list allows to use them for obtaining both filled and nonfilled PBT and compare catalytic activity of various catalysts. The purpose of the... 

Chen, C.-C.., 1993, A Segment Based Local Composition Model for the Gibbs Energy of Polymer solutions. Fluid Phase Equilibria, 83, 301. 

The possible fatigue failure mechanisms of SWCNT in the composite were also reported (Ren et al., 2004). Possible failure modes mainly include three stages, that is, splitting of SWCNT bundles, kink formation, and subsequent failure in SWCNTs, and the fracture of SWCNT bundles. As shown in Fig. 9.12, for zigzag SWCNT, failure of defect-free tube and tubes with Stone-Wales defect of either A or B mode all resulted in brittle-like, flat fracture surface. A kinetic model for time-dependent fracture of CNTs is also reported (Satapathy et al., 2005). These simulation results are almost consistent with the observed fracture surfaces, which can be reproduced reasonably well, suggesting the possible mechanism should exist in CNT-polymer composites. 

Henstenburg, R.B. and Phoenix, S.L. (1989). Interfaeial shear strength studies using the single-filament-compositc test, part II, A probability model and Monte Carlo simulation. Polym. Composites 10, 389-408. 

Lacroix, Th., Tilmans, B., Keunings, R., Desaeger, M. and Verpoest, F. (1992). Modelling of critical fiber length and interfacial debonding in the fragmentation testing of polymer composites. Composites Sci. Technol. 43, 379-387. 

Methylene blue was used as a model drug, and matrices were based upon crosslinked copolymers of sodium acrylate or polymer composites of ferrite. 

Fig. 10. A composite model for a polymer film in which crystallites are surrounded by the amorphous phase...

To develop a comprehensive model for the polymerization mechanism which accounts for the dependence of polymer composition, polymerization rate, and polymer molecular weight on synthesis conditions. 

The methods quoted under a) above give bulk information only although they may be used in conjunction with composite models to test theories of the microstructure. The methods under b) are more closely related to structural elements. It is an interesting fact that even at the atomic level, displacement and therefore strain can be measured by several means (although average values are of course obtained) yet loads are only measurable in terms of the secondary effects they produce, for example elastic or inelastic displacements, strain-related optical effects or electronic transitions detectable by optical or infrared spectroscopy. The problem of load transference in a polymer is of great interest, yet very few methods exist by which it may be studied. 

Gray and McCrum735 used the Hashin-Shtrikman theory to explain the origin of the y relaxation in PE and PTFE, Maeda et al.745 have given exact analyses of several two phase models for semi-crystalline polymers and Buckley755 represented a biaxially oriented sheet of linear polyethylene by a two phase composite model. 

The gas-polymer-matrix model for sorption and transport of gases in polymers is consistent with the physical evidence that 1) there is only one population of sorbed gas molecules in polymers at any pressure, 2) the physical properties of polymers are perturbed by the presence of sorbed gas, and 3) the perturbation of the polymer matrix arises from gas-polymer interactions. Rather than treating the gas and polymer separately, as in previous theories, the present model treats sorption and transport as occurring through a gas-polymer matrix whose properties change with composition. Simple expressions for sorption, diffusion, permeation and time lag are developed and used to analyze carbon dioxide sorption and transport in polycarbonate. 

In Section I we introduce the gas-polymer-matrix model for gas sorption and transport in polymers (10, LI), which is based on the experimental evidence that even permanent gases interact with the polymeric chains, resulting in changes in the solubility and diffusion coefficients. Just as the dynamic properties of the matrix depend on gas-polymer-matrix composition, the matrix model predicts that the solubility and diffusion coefficients depend on gas concentration in the polymer. We present a mathematical description of the sorption and transport of gases in polymers (10, 11) that is based on the thermodynamic analysis of solubility (12), on the statistical mechanical model of diffusion (13), and on the theory of corresponding states (14). In Section II we use the matrix model to analyze the sorption, permeability and time-lag data for carbon dioxide in polycarbonate, and compare this analysis with the dual-mode model analysis (15). In Section III we comment on the physical implication of the gas-polymer-matrix model. 

Keywords Recycling Recycling as resources Polyolefins Quality Degree of degradation Polymer composition Low molecular weight compounds NIR DSC MAE Chromatography Multivariate modelling... 

S. Bawiskar and J. L. White, A Composite Model for Solid Conveying, Melting, Pressure and Fill Factor Profiles in Modular Co-rotating Twin Screw Extruders, Int. Polym. Proc., 12, 1331 (1997). 

---