The impact of ionic contribution to dielectric permittivity in 11CB liquid crystal and its colloids with BaTiO3 nanoparticles

Abstract

Abstract The report shows the temperature behavior of the real part of dielectric permittivity in the static (dielectric constant) and low-frequency (LF) domains in bulk samples of 11CB and its BaTiO 3 -based nanocolloids. The study covers the isotropic liquid (I), nematic (N), smectic A (SmA), and solid crystal (Cr) phases. For each phase, the dominance of pretransitional fluctuations, significantly moderated by nanoparticles, is shown. The authors consider separate focuses on the dielectric constant $$\varepsilon \left( {\varvec{T}} \right)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>ε</mml:mi> <mml:mfenced> <mml:mrow> <mml:mi>T</mml:mi> </mml:mrow> </mml:mfenced> </mml:mrow> </mml:math> evolution in the static domain, yielding mainly response from permanent dipole moment and its arrangement, and in the low-frequency (LF) domain $$\Delta \varepsilon^{\prime } \left( f \right) = \varepsilon^{\prime } \left( f \right) - \varepsilon$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:msup> <mml:mi>ε</mml:mi> <mml:mo>′</mml:mo> </mml:msup> <mml:mfenced> <mml:mi>f</mml:mi> </mml:mfenced> <mml:mo>=</mml:mo> <mml:msup> <mml:mi>ε</mml:mi> <mml:mo>′</mml:mo> </mml:msup> <mml:mfenced> <mml:mi>f</mml:mi> </mml:mfenced> <mml:mo>-</mml:mo> <mml:mi>ε</mml:mi> </mml:mrow> </mml:math> (where $$\varepsilon^{\prime } \left( {\varvec{f}} \right)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>ε</mml:mi> <mml:mo>′</mml:mo> </mml:msup> <mml:mfenced> <mml:mrow> <mml:mi>f</mml:mi> </mml:mrow> </mml:mfenced> </mml:mrow> </mml:math> is for the real part of dielectric permittivity in the LF domain), which is associated solely with ionic-related polarization mechanisms. All of these led to new experimental evidence concerning I–N, N–SmA, and SmA–solid transitions, focusing on the strength and extent of pretransitional effects, critical exponents, and phase transitions discontinuities. The strong evidence for pretransitional effects near the SmA–Cr transition is notable, particularly regarding $$\Delta \varepsilon^{\user2{^{\prime}}} \left( {{\varvec{f}},{\varvec{T}}} \right)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Δ</mml:mi> <mml:msup> <mml:mi>ε</mml:mi> <mml:mrow> <mml:msup> <mml:mrow/> <mml:mo>′</mml:mo> </mml:msup> </mml:mrow> </mml:msup> <mml:mfenced> <mml:mrow> <mml:mrow> <mml:mi>f</mml:mi> </mml:mrow> <mml:mo>,</mml:mo> <mml:mrow> <mml:mi>T</mml:mi> </mml:mrow> </mml:mrow> </mml:mfenced> </mml:mrow> </mml:math> . Studies are supplemented by the discussion of DC electric conductivity—a parameter also related to the LF domain. Finally, the validity of the relation $$\varepsilon^{\prime } \left( {\varvec{f}} \right) = {\varvec{Af}}^{ - 3/2} + \varepsilon$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>ε</mml:mi> <mml:mo>′</mml:mo> </mml:msup> <mml:mfenced> <mml:mrow> <mml:mi>f</mml:mi> </mml:mrow> </mml:mfenced> <mml:mo>=</mml:mo> <mml:msup> <mml:mrow> <mml:mrow> <mml:mi>Af</mml:mi> </mml:mrow> </mml:mrow> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>3</mml:mn> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mo>+</mml:mo> <mml:mi>ε</mml:mi> </mml:mrow> </mml:math> (where f stands for frequency, and A is a constant parameter), often used for discussing dielectric spectra in LC compound and its nanocolloids in the LF domain, is examined. Graphical abstract

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