Affiliations: [a] Departmet of Physics, Faculty of General Studies, Gunma University, Maebashi 371, Japan | [b] Department of Polymer Science, Faculty of Technology, Gunma University, Kiryu 376, Japan
Note: [] Accepted by: Editor S. Oka
Abstract: The bulk modulus of a dilutely dispersed system of spherical shell structures is obtained taking into account interfacial tensions at both the interfaces of the shell as follows:
κ∗=κQ+43cμQ′Q−cQ′
where Q=K′Km−ΔK′ΔMA3, Q′=K′ΔK−ΔK′KA3, Km=3κm+4μ−2γ/a, ΔK=3κm−3κ−2γ/a, ΔM=4μm−4μ+2γ/a, K=4μm+3κ+2γ/a, K′=3κ′+4μm−2γ′/a′, ΔK′=3κm−3κ′+2γ′/a′, A = a′/a, a and a′ are the outer and the inner radii of the shell, γ and γ′ the interfacial tensions at r = a and r = a′, in which r is the radial distance from the origin at the center of the shell structure, κ and μ the bulk modulus and the rigidity of the medium, in which the prime and the subscripts m denote the quantities for the inside (r<a′) and the shell (a′<r<a) regions, respectively, and c the volume concentration of shell structures.
