Following the terminology of conventional micromechanics models, we still use CTE in this section. The two-phase composite consisting of matrix and short fiber is of perfect interfaces at phase boundaries. Therefore, it is impossible for the two components, i.e., the matrix and short fiber, to separate at their interfaces when the composite is loaded or heated. Additionally, PXD101 concentration only macro-composites are considered, namely the scale of the reinforcement is large compared to that of the atom size or grain size so that composite properties can be modeled by continuum methods. This assumption may be reasonable here since the

present MWCNT is comparatively large in diameter. Finally, the composite properties are an appropriate average of those of the components. The CTE of a composite with short-fiber orientation distribution function f(φ), which is independent of dimension, can be given by [18] (1) For nanocomposites which contain a uni-directionally aligned reinforcement phase (e.g., MWCNT), f(φ) = 1, and therefore, the

CTE of the nanocomposites is (2) If MWCNTs are randomly orientated, the orientation distribution function f(φ) = 1/n, where n represents the number of different orientations of the MWCNTs in the matrix. If n is the number of possible orientations, the CTE of the nanocomposites is (3) In the above equations, the nomenclatures for the parameters are as follows: α, CTE V, volume fraction E, Young’s Torin 2 in vitro modulus ν, Poisson’s ratio

and the subscripts NVP-BSK805 in vivo are as follows: c, nanocomposite m, the matrix f, the reinforcement phase (MWCNT here) Note that Poisson’s ratio of the nanocomposites, v c in Equation 3, was directly obtained from the rule of mixture and the data in Table 2. For 1 ~ 5 wt% addition of CNTs, v c ranges from 0.338 (1 wt%) to 0.333 (5 wt%). Experimental measurements In the present experiments, MWCNTs were made via chemical vapor deposition, with purity above 99.5% (Hodogaya Chemical Co., Ltd., Tokyo, Japan). The detailed data have been listed in Tables 1 and 2. An insulating bisphenol-F epoxy resin (JER806, Japan Epoxy Resins Acyl CoA dehydrogenase Co., Ltd., Tokyo, Japan) and an amine hardener (Tomaido 245-LP, Fuji Kasei Kogyo Co., Ltd., Osaka, Japan) were used as matrix. The MWCNT/epoxy nanocomposites were prepared by mixing the epoxy and the hardener using a planetary mixer (AR-100, THINKY Co., Ltd., Tokyo, Japan) at 2,000 rpm for 30 s. Then, the MWCNTs were added into the mixture and mixed again at 2,000 rpm for 10 min. The final mixture was poured into a silicon mold and cured in a vacuum oven at 80°C for 2 h. This nanocomposite fabrication method was the same with that in the authors’ previous experimental work [19–21], in which very good dispersion states of the MWCNTs under 3 and 5 wt% loading were identified (see image from scanning electron microscope observation in Figure 8 for the fractured surface of a 3 wt% sample).