Pseudo-Casimir Force

The pseudo-Casimir force in a heterophase system wiU be illustrated with the example of a thin nematogenic film with order-inducing wetting layers on both confining surfaces discussed before. The resulting fluctuation force can be interpreted in terms of two contributions (i) the interaction between the substrates and the phase boundaries and (ii) the interaction between the two phase boundaries. 

Experimental Evidence of Structural and Pseudo-Casimir Forces in Liquid Crystals... 

There are some indications that the pseudo-Casimir force in liquid crystals can be studied systematically with existing experimental techniques [69]. The lower limit for the separation of the substrate between which the force could be studied is roughly given by a molecular size where the system starts to behave as a continuum. The upper limit depends on the sensitivity of the force apparatus which is in the case of standard apparatuses about 10 pN [70]. This means that these apparatuses are precise enough to detect the pseudo-Casimir force at distances up to ss 40 nm [69]. 

Micro- and Macroscopic Theories for Liquid Srystals 239 8.4,2 Pseudo-Casimir Force... 

The name pseudo-Casimir force for the fluctuation-induced interaction is due to the analogy with the Casimir effect [63] at T = 0 quetntum fluctuations of the electromagnetic field in a cavity yield a weak yet measurable attraction between the walls of the cavity. Because the force between the walls is determined by a derivative of the free energy of a system rather than by a derivative of its energy, a similar effect is expected above absolute zero where the interaction is not just due to quantum but also due to thermal fluctuations. In liquid crystals, the fluctuation-induced interaction is due to thermal fluctuations of the order parameter field instead of the electromagnetic field. 

Fig. 8.12. (a) Pseudo-Casimir force in the paranematic heterophase system compared to the structural force as a function of temperature, (b) Pseudo-Casimir force in a hybrid nematic ceU with uniform director field. Labels denote the ratio Xh/ p-... 

Up to now, in the frustrated nematic systems the pseudo-Casimir force has only been determined for the simplest structure with a uniform director field d < dc = Xh Xp, where Ah Ap is the extrapolation length of the honieotropic substrate and Ap the extrapolation length of the degenerate in-plane anchoring which preserves the full rotational symmetry about the substrate normal) [12]. Then, within the bare director description the correlation length in the Hamiltonian (8.28) is constant and the partition function of the fluctuation modes can be derived analytically. The derivation of the force in the bent-director and biaxial structures is more complex due to the deformed equilibrium order. 

The shape of the pseudo-Casimir force in the uniform structure depends on the ratio between the two extrapolation lengths A = Xn/Xp) whereas its magnitude is tuned by the difference between them, dc- For finite but similar extrapolation lengths (H —1) the force is attractive and decreases as d ... 

To conclude, let us point out, that more detailed and target studies of confined LC systems are still required. On the theoretical side, the complete phase diagram of confined nematogens is still needed. Since most of the existing studies correspond to the simplest planar geometry, the more complex and realistic geometries should be considered as well. Here, a microscopic analysis such as MC or molecular dynamics simulations would be welcome to complement the continuum theoretical description. On the experimental side, the main focus should be to extract structural and especially pseudo-Casimir forces from the observed data. 

The force measured in liquid crystals is a superposition of structmal, pseudo-Casimir, and non-structural forces. The non-structural forces include electrostatic and polarization forces, such as the van der Waals force. The behavior of non-structural forces is well-understood [68]. Recently, the improved... 

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