An eigenfunction expansion-variational method in prediction of the transverse thermal conductivity of fiber reinforced composites considering interfacial characteristics

An eigenfunction expansion-variational method based on a unit cell is developed to deal with the steady-state heat conduction problem of doubly-periodic fiber reinforced composites with interfacial thermal contact resistance or coating. The numerical results show a rapid convergence of the present method. The present solution provides a unified first-order approximation formula of the effective thermal conductivity for different interfacial characteristics and fiber distributions. A comparison with the present high-order results, available experimental data and micromechanical estimations demonstrates that the first-order approximation formula is a good engineering closed-form formula. An engineering equivalent parameter reflecting the overall influence of the thermal conductivities of the matrix and fibers and the interfacial characteristic on the effective thermal conductivity, is found. The equivalent parameter can greatly simplify the complicated relation of the effective thermal conductivity to the internal structure of a composite. (c) 2010 Elsevier Ltd. All rights reserved.

A four-phase confocal elliptical cylinder model for predicting the effective thermal conductivity of coated fibre composites

A four-phase confocal elliptical cylinder model is proposed from which a generalised self-consistent method is developed for predicting the thermal conductivity of coated fibre reinforced composites. The method can account for the influence of the fibre section shape ratio on conductivity, and the physical reasonableness of the model is demonstrated by using the fibre distribution function. An exact solution is obtained for thermal conductivity by applying conformal mapping and Laurent series expansion techniques of the analytic function. The solution to the three-phase confocal elliptical model, which simulates composites with idealised fibre-matrix interfaces, is arrived at as the degenerated case. A comparison with other available micromechanics methods, Hashin and Shtrikman's bounds and experimental data shows that the present method provides convergent and reasonable results for a full range of variations in fibre section shapes and for a complete spectrum of the fibre volume fraction. Numerical results show the dependence of the effective conductivities of composites on the aspect ratio of coated fibres and demonstrate that a coating is effective in enhancing the thermal transport property of a composite. The present solutions are helpful to analysis and design of composites.

Estimation of Transverse Thermal Conductivity of Doubly-periodic Fiber Reinforced Composites

For steady-state heat conduction a new variational functional for a unit cell of composites with periodic microstructures is constructed by considering the quasi-periodicity of the temperature field and in the periodicity of the heat flux fields. Then by combining with the eigenfunction expansion of complex potential which satisfies the fiber-matrix interface conditions, an eigenfunction expansion-variational method (EEVM) based on a unit cell is developed. The effective transverse thermal conductivities of doubly-periodic fiber reinforced composites are calculated, and the first-order approximation formula for the square and hexagonal arrays is presented,which is convenient for engineering application. The numerical results show a good convergency of the presented method, even through the fiber volume fraction is relatively high. Comparisons with the existing analytical and experimental results are made to demonstrate the accuracy and validity of the first-order approximation formula for the hexagonal array.

Scaling and the thermal conductivity of the Frenkel-Kontorova model

We have studied the dependence of the thermal conductivity kappa on the strength of the interparticle potential lambda and the strength of the external potential beta in the Frenkel-Kontorova model. We found that the functional relation can be expressed in a scaling form, kappa(proportional to) lambda 3/2/beta(2 center dot). This result is first obtained by nonequilibrium molecular dynamics. It is then confirmed by two analytical methods, the self-consistent phonon theory and the self-consistent stochastic reservoirs method. The thermal conductivity kappa is therefore a decreasing functon of beta and an increasing function of lambda.

Relaxation time and conductivity of comb-like gel polymer electrolytes

Using the copolymer of acrylonitrile (AN), methyl methacrylate (MMA), and poly(ethylene glycol) methyl ether methacrylate as a backbone and poly(ethylene glycol) methyl ether (PEGME) with 1100 molecular weight as side chains, comb-like gel polymers and their Li salt complexes were synthesized. The dynamic mechanical properties and conductivities were investigated. Results showed that the gel copolymer electrolytes possess two glass transitions: alpha-transition and beta-transition. Based on the time-temperature equivalence principle, a master curve was constructed by selecting T. as reference temperature. By reference to T-0 = 50 degrees C, the relation between log c, and c was found to be linear. The master curves are displaced progressively to higher frequencies as the content of plasticizer is increased. The relation between log tau(p) and the content of plasticizer is also linear.

Enhanced electrical conductivity of highly crystalline polythiophene/insulating-polymer composite

Poly(3-butylthiophene) (P3BT)/insulating-polymer composites with high electrical conductivity have been prepared directly from the solution. These composites exhibit much higher conductivity compared to pure P3BT with the same preparation method provided that P3BT content is higher than 10 wt %. Morphological studies on both the pure P3BT and the composites with insulating polymer show that P3BT highly crystallizes and develops into whisker-like crystals. These nanowires are homogeneously distributed within the insulating polymer matrix and form conductive networks, which provide both extremely large interface area between conjugated polymer and insulating polymer matrix and highly efficient conductive channels through out the whole composite. In contrast, the conductivity enhancement of P3HT/PS composite is not so obvious and drops down immediately with increased PS content due mainly to the absence of highly crystalline whisker-like crystals and much larger scale phase separation between the components. The results presented here could further illuminate the origin of conductivity formation in organic semiconducting composites and promote applications of these polymer semiconductor/insulator composites in the fields of organic (opto-)electronics, electromagnetic shielding, and antistatic materials.