wwceramics. org/ACT Polymer-Ceramic Composites of 0-3 Connectivity 419 gm角C0 )C composites with BST loading100,组a%,的60m% and(d) BSTa-COC with BST Fig 3. SEM images Hu et al). BST, BaossSross Tio 2. Modified Lichtnecker equation lar. 33 among these equations, the Lichtnecker equation is the most com- log er =log Em +ur(l-m)log(=i)(2) monly used relation for predicting the permittivity of the composites. The Lichtnecker logarithmic rule con- 3. Series mixing formulas siders the composites as a random mixture of nearly spherical inclusions. In general, the theoretical predic (3) tions are valid for low filler contents and deviations from predictions increase with increasing filler contents. This 4. Maxwell-Wagner equation: ramic particles at higher filler contents and also due to 2Em +Ei+2 ur(E-Em) 2cm+1-(1-Em) (4) porosity or air enclosed by the composite. The theoret- ical predictions do not consider the matrix-filler inter 5. Effective medium theory(EMT) hase interactions and are valid for a composite made of a filler and a matrix with nearly the same relative per- tr(E-Em) mittivity values. The modified Lichtnecker eq Em 1+ Em +n(1-urEi-Em (5) cludes a fitting factor n, which repr between the filler and the matrix. In polyethelene- where Eeff, E;, and Em are the permittivity of the com- Sm2 Si2O, and polystyrene-Sm2Si2O7, the relative per posites, filler, and matrix, respectively, Ve is the volume mittivity calculated using the modified Lichtnecker fraction of the ceramic, and n is the fitting parameter or equation showed good agreement with experimental the morphology factor. The Jayasundere-Smith equa- data as shown in Fig. 4 for a filler up to 0.4 vol% tion is only valid for a filler content up to 0.3 vol%. This The deviations at higher volume fractions can be attrib is due to the fact that it considers the interactions be- uted to inhomogeneity in the filler distribution in the tween neighboring spheres. The Maxwell-Wagner polymer matrix and air entrapment in the composite In rule is generally valid when the properties of the two addition, it has been reported that the fitting fact2. Modified Lichtnecker equation51: log eeff ¼ log em þ vfð1 nÞlog ei em ð2Þ 3. Series mixing formula51: 1 eeff ¼ vf ei þ ð1 vfÞ em ð3Þ 4. Maxwell–Wagner equation33: eeff ¼ em 2em þ ei þ 2 vf ðei emÞ 2em þ ei vf ðei emÞ ð4Þ 5. Effective medium theory (EMT)51 eeff ¼ em 1 þ vf ðei emÞ em þ nð1 vfÞðei emÞ   ð5Þ where eeff, ei, and em are the permittivity of the com￾posites, filler, and matrix, respectively, Vf is the volume fraction of the ceramic, and n is the fitting parameter or the morphology factor. The Jayasundere–Smith equa￾tion is only valid for a filler content up to 0.3 vol%. This is due to the fact that it considers the interactions be￾tween the neighboring spheres. The Maxwell–Wagner rule is generally valid when the properties of the two phases in the composite are similar.33 Among these equations, the Lichtnecker equation is the most com￾monly used relation for predicting the permittivity of the composites. The Lichtnecker logarithmic rule con￾siders the composites as a random mixture of nearly spherical inclusions. In general, the theoretical predic￾tions are valid for low filler contents and deviations from predictions increase with increasing filler contents. This is mainly due to the imperfect dispersion of filler ce￾ramic particles at higher filler contents and also due to porosity or air enclosed by the composite. The theoret￾ical predictions do not consider the matrix–filler inter￾phase interactions and are valid for a composite made of a filler and a matrix with nearly the same relative per￾mittivity values. The modified Lichtnecker equation in￾cludes a fitting factor n, which represents the interaction between the filler and the matrix. In polyethelene– Sm2Si2O7 and polystyrene–Sm2Si2O7, the relative per￾mittivity calculated using the modified Lichtnecker equation showed good agreement with experimental data as shown in Fig. 440 for a filler up to 0.4 vol%. The deviations at higher volume fractions can be attrib￾uted to inhomogeneity in the filler distribution in the polymer matrix and air entrapment in the composite. In addition, it has been reported that the fitting factor n is Fig. 3. SEM images of BSTc-COC composites with BST loading (a) 10 vol%, (b) 40 vol%, (c) 60 vol%, and (d) BSTa-COC with BST loading of 10 vol% (after Hu et al.24). BST, Ba0.55Sr0.45TiO3. www.ceramics.org/ACT Polymer–Ceramic Composites of 0–3 Connectivity 419