Mixing rules and the Casimir force between composite systems

Abstract

The Casimir-Lifshitz force is calculated between two inhomogeneous composite slabs, each made of a homogeneous matrix with spherical metallic inclusions. The effective dielectric function of the slabs is calculated using several effective medium approximations and we compare the resulting forces as a function of slab separation and filling fraction. We show that the choice of effective medium approximation is critical in making precise comparisons between theory and experiment. The role that the spectral representation of the effective medium plays in making a Wick rotation to the complex frequency axis is also discussed

Nanolevitation Phenomena in Real Plane-Parallel Systems Due to the Balance between Casimir and Gravity Forces

“…Several trends are found for each model and configuration (panels (a) and (b)), as was previously indicated for metallic inclusions. 39 The three models follow the same trend, predicting stable d eq in panel (a) but providing different distance values with maximum variations of ∼30 nm, depending on the model considered. In contrast, in panel (b) no d eq are obtained since a total force F < 0 for all separation distances is predicted by the Maxwell–Garnett model, while the Cuming and Bruggeman models produce stable positions.…”

“…Figure 6 a shows the total force acting on a SiO 2 matrix as a function of the separation distance, d 0 , and using the effective permittivity provided by Maxwell–Garnett, Bruggeman, and Cuming models in eqs 8 , 9 , and 10 . This strategy was previously considered in ref ( 39 ) to evaluate the effect on the Casimir force with polymer matrices with metallic inclusions inside. Results for the complementary system are displayed in Figure 6 b, and ε eff ( iξ n ) for each model are shown in Figure S9 of the Supporting Information .…”

“…At least 12 mixing formulas have been proposed for calculating the effective permittivity 49 in hybrid systems, and the validity of some of the formulas applied to calculations of the Casimir force has been previously analyzed for polymer matrices with metallic inclusions inside. 39 However, the accuracy of the various theories can be judged only when comparing with experimental data. 50 In this work, we will use the widely employed Maxwell–Garnett (ε eff MG (ω)) and Bruggeman (ε eff Bru (ω)) models for spherical inclusions and compare them with results obtained using the Cuming (ε eff Cum (ω)) model, which does not assume any special geometry for the inclusions, and it has been shown to be valid for large filling fractions.…”

Optical interference effects on the Casimir-Lifshitz force in multilayer structures

“…On this point, different ways to modify not only the intensity and nature (attractive or repulsive) of F (C−L) , but also the Casimir torque, have been proposed [8][9][10][11][12][13][14]. Of special importance, due to their versatility for tuning F (C−L) , are the strategies in which the optical properties of the interacting objects are modified [15][16][17][18][19][20]. According to the fluctuation-dissipation theorem [21], the correlation of quantum fluctuations explicitly depends on the dissipation of the interacting materials, or in other words, the Casimir-Lifshitz force between two separated bodies depends on the absorption properties of the materials involved.…”

Near Field Heat Transfer between Random Composite Materials: Applications and Limitations

“…In the static limit, where there is no dissipation, any effective medium model is bounded above and below by the Hashim-Strickman variational [11] bounds that impose a maximum and minimum value for the effective dielectric function. The variations in the effective models have also been explored in the context of the Casimir effect where Lifshitz model imposes the condition that the effective dielectric function has to satisfy Kramers-Kronig relations [12]. Experimentally, Grundquist and Hunderi [13,14] measured the optical response of Ag-SiO 2 cermet films as well as films made by depositing Au particles on substrate.…”