Viscoelastic properties of composites of calcium alginate and hydroxyapatite

Calcium alginate was reinforced with hydroxyapatite (HA) particles, whose dimensions were a few micrometres, with mass fraction, mf, values in the range 0–0.8. Cylindrical samples of these composite materials were subjected to cyclic compression in the frequency range f = 0.001–20 Hz; in these tests a sinusoidal load of amplitude 1 N was applied either side of a static compression of 2 N. Storage and loss moduli, E′ and E′′, respectively, were found to be independent of particle size; however, E′ increased with frequency consistent with the materials undergoing a glass transition. Above frequencies of about 0.05 Hz, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$E^{\prime}\, > \,E^{\prime\prime}$$\end{document} for all materials. For each frequency, the dependence of the moduli on log10 f could be represented by a third order polynomial; these equations can be used to calculate E′ and E′′ for a range of compositions. Approximate values of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$|E^{\ast}|=\sqrt{{E}^{\prime}{}^{2}+{E}^{\prime\prime}{}^{2}}$$\end{document} are predicted by a Reuss model.