Adsorption phenomena and anchoring energy in nematic liquid by Giovanni Barbero, Luiz Roberto Evangelista
By Giovanni Barbero, Luiz Roberto Evangelista
Regardless of the massive volume of phenomenological details about the bulk houses of nematic section liquid crystals, little is known concerning the starting place of the outside strength, really the outside, interfacial, and anchoring homes of liquid crystals that impact the functionality of liquid crystal units. Self-contained and certain, Adsorption Phenomena and Anchoring strength in Nematic Liquid Crystals presents an account of latest and demonstrated effects spanning 3 a long time of study into the issues of anchoring strength and adsorption phenomena in liquid crystals. The booklet incorporates a distinctive dialogue of the beginning and attainable assets of anchoring power in nematic liquid crystals, emphasizing the dielectric contribution to the anchoring power specifically. starting with primary floor and anchoring houses of liquid crystals and the definition of the nematic part, the authors clarify how selective ion adsorption, dielectric strength density, thickness dependence, and bias voltage dependence impact the uniform alignment of liquid crystals and impact the functionality of liquid crystal units. additionally they speak about primary equations regulating the adsorption phenomenon and the dynamic features of ion adsorption phenomenon in liquid crystalline structures. Adsorption Phenomena and Anchoring power in Nematic Liquid Crystals serves as an exceptional resource of reference for graduates and researchers operating in liquid crystals, complicated fluids, condensed subject physics, statistical physics, chemical engineering, and digital engineering, in addition to offering an invaluable normal creation to and history details at the nematic liquid crystal section.
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Extra info for Adsorption phenomena and anchoring energy in nematic liquid crystals
100) is equivalent to Tc , b K(z) = [Kb − K(z) = Kb (1 + ∆e−z/ξ )2 . 102) we obtain = 1 Kb ∞ 0 (1 + ∆e−z/ξ )2 − 1 dz. 102) 1, which implies S0 not very diﬀerent from Sb , from 1 ξ = 2∆ . , in the macroscopic range, as experimentally observed [1, 49]. The total extrapolation length is the sum of the diﬀerent contributions analyzed above. 105) and Lelast = Kb Kb + . 106) Consequently, the total extrapolation length can be rewritten as LT = Kb Kb Kb + + Weu + Wiu Wb Wξ Kb . 107) This simple result shows that the weak anchoring is mainly due to the spatial variation of the scalar order parameter.
1 Stochastic contribution to the anchoring energy The eﬀect of a stochastic contribution to the surface energy, coming from the direct interaction between an orienting ﬁlm and a solid substrate, indicates that, in the hypothesis in which the NLC orientation coincides with the ﬁlm orientation, the Rapini-Papoular expression for the anisotropic part of the surface energy has to be modiﬁed. There are two important modiﬁcations: (1) the ﬁrst one is a renormalization of the anchoring strength coeﬃcient, connected with the square of the sine of the deformation angle; (2) the second one is the presence of an additional contribution, proportional to the fourth power of the same quantity.
57) µij (r)xα xβ dS . 57) one derives Niαβ = Niβα . 47), it follows that Mijαβ = Mjiαβ = Mijβα = Mjiβα . 60) The meaning of the diﬀerent terms introduced before is very simple. f0 (m) is the surface energy density of a uniformly oriented ﬁlm (m position independent), whereas L, N , and M play the role of elastic constants. Tensors L, N , and M have to be decomposed in terms of the elements of symmetry of the ﬁlm. In the present case, in which the ﬁlm is assumed to be ﬂat, the elements of symmetry are the geometrical normal k (parallel to the z−axis) and the vector m (see details in ).