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The Dominance of Pretransitional Effects in Liquid Crystal-Based Nanocolloids: Nematogenic 4-methoxybenzylidene-4′–butylaniline with Transverse Permanent Dipole Moment and BaTiO_{3} Nanoparticles

^{*}

## Abstract

**:**

_{3}nanoparticles (spherical, d = 50 nm). MBBA (4-methoxybenzylidene-4′–butylaniline) is a liquid crystalline compound with a permanent dipole moment transverse to the long molecular axis. The distortions-sensitive analysis of the dielectric constant revealed its hidden pretransitional anomaly, strongly influenced by the addition of nanoparticles. The evolution of the dielectric constant in the nematic phase shows the split into two regions, with the crossover coinciding with the standard melting temperature. The ‘universal’ exponential-type behavior of the low-frequency contribution to the real part of the dielectric permittivity is found. The critical-like pretransitional behavior in the solid phase is also evidenced. This is explained by linking the Lipovsky model to the Mossotti catastrophe concept under quasi-negative pressure conditions. The explicit preference for the ‘critical-like’ evolution of the apparent activation enthalpy is worth stressing for dynamics. Finally, the long-range, ‘critical-like’ behavior of the dissipation factor (D = tgδ), covering the isotropic liquid and nematic phases, is shown.

## 1. Introduction

_{3}nanoparticle nanocolloids. 12CB is the LC material with the Solid (S)–Smectic A (SmA)–Isotropic Liquid (I) mesomorphism. The dominant impact of fluctuations was observed in pure LC compounds and related nanocolloids. It manifested via the following pretransitional effects [26]:

_{3}, C

_{60}fullerenes) preserved the form of Equation (2) with the exponent $\alpha =1/2$. The mentioned mechanism should be absent for rod-like molecules with the transverse (perpendicular) dipole moment with respect to the long molecular axis. The classic example is MBBA (4-methoxybenzylidene–4′–butylaniline), for which linear changes of dielectric constant are observed in the isotropic liquid on approaching the I–N transition [3,6,35,36,37,38,39,40,41,42].

_{3}nanoparticles. MBBA is the LC compound with the transverse orientation of the permanent dipole moment. So far, such studies have been carried out only for nanocolloids based on LC molecules with the parallel arrangement of dipole moment. The results presented also offer new results for low frequency-related dielectric properties, still constituting a cognitive challenge.

## 2. Materials and Methods

_{3}nanopowder (paraelectric, diameter $d=50\mathrm{n}\mathrm{m}$) was purchased from US Research Nanomaterials, Inc.: see ref. [53] showing the link to the characterization of these nanoparticles. Mixtures of the liquid crystal and nanoparticles were sonicated at a temperature above the isotropic–nematic phase transition for 4 h to obtain homogeneous suspensions. Studies were carried out for nanocolloids with nanoparticle concentrations of 0.05%, 0.1%, 05%, and 1% weight (mass) fractions. Our experience shows that significant nanoparticle sedimentation can occur at concentrations above 1% in such systems [32,33]. It can be avoided by introducing a macromolecular surfactant [8,9,10], but it significantly distorts the dielectric response by introducing the molecular admixture, which can also lead to a shift in the clearing temperature ([7] and refs therein). The preparation of nanocolloids with such few nanoparticles is always a laboratory challenge. It requires a large amount of expensive (high-purity) liquid crystalline material.

## 3. Results and Discussion

_{3}nanoparticles ($d=50\mathrm{nm}$) can create a unique endogenic permanent orientation of rod-like LC molecules in bulk [30,31,32,33]. It is reached without any strong external field (electric, magnetic). This report follows this path by focusing on tests in a bulk LC compound subjected solely to the impact of nanoparticles in an LC nematogenic compound with a transverse location of the permanent dipole moment.

_{3}($d=50\mathrm{nm}$) nanoparticles, the appearance of super-paraelectric elements on the surface was suggested [55,56]. This may lead to a preference for Coulombic interactions with permanent dipole moments coupled to LC molecules, creating different local arrangements of LC molecules with the parallel and transverse positions of the permanent dipole moment.

#### 3.1. Dielectric Constant Changes in the Isotropic Liquid Phase

#### 3.2. Dielectric Constant Changes in the Nematic Phase

_{3}nanoparticles, notable is the increase in the average value of the dielectric constant, reaching $21\%$ for $x=1\%$ nanocolloid. A similar behavior was observed in 5CB, 8OCB, 11CB, and 12CB nanocolloids with paraelectric BaTiO

_{3}nanoparticles [26,27,28,29,30,31,32,33]. All these suggest that paraelectric BaTiO

_{3}nanoparticles can introduce an endogenic arrangement of dipole moment associated with molecules, leading to significant changes in dielectric constant, both in the nematic mesophase and isotropic liquid phase.

#### 3.3. Dielectric Constant Changes in the Solid Phase

#### 3.4. Dielectric Permittivity in the Low-Frequency Domain

_{3}nanoparticles for selected frequencies in the LF domain. There is a very strong increase in ${\epsilon}^{\prime}\left(f\right)$ when lowering the monitoring frequency below the static reference adopted for f = 126 kHz in the given case. The average value of ${\epsilon}^{\prime}\left(f\right)$ also increases the addition of nanoparticles.

#### 3.5. Dynamic Properties in MBBA and Related Nanocolloids

_{3}nanoparticles in the Arrhenius scale ${{log}_{10}\sigma}^{-1}$ vs. $1/T$, where the basic Arrhenius dependence, with the activation energy ${E}_{\sigma}=const.$, is associated with the linear behavior. The addition of nanoparticles increases the electric conductivity (decreases ${\sigma}^{-1}$), which is particularly visible for $x=0.5\%$ and $x=1\%$ concentrations. Generally, the rise and decrease in electric conductivity are evidenced in different LC-based nanocolloids [8,9,10,97,98]. The authors of this report noted that for nCB doped with BaTiO

_{3}nanoparticles, both patterns, depending on the concentration of nanoparticles, appeared [31]. Explanations of the phenomenon recall the most common definition of DC electric conductivity as the ability to transport direct electric current, depending on the number of free electrons or ionic species within the material and their mobility. In liquid crystalline systems, they are heuristically called ‘residual ionic contaminations’ and are linked to the post-manufacturing remaining or consequences of material/s degradation [8,9,10,97,98]. This means that they are not precisely defined and differ from the basic LC molecules. Consequently, it is stated that some nanoparticles can ‘supplement’ or ‘trap’ residual ions to explain the above behavior [8,97,98]. Is such an explanation, essentially general and heuristic, in agreement with the basic experimental evidence? In the opinion of the authors, the answer is not clear.

_{3}nanoparticles in the Arrhenius scale ${{log}_{10}\sigma}^{-1}$ vs. $1/T$ where the basic Arrhenius dependence, with the activation energy ${E}_{\sigma}=const$, manifests via a linear behavior. The behavior visible in Figure 12 is explicitly non-linear, suggesting the super-Arrhenius (SA) pattern with the temperature-dependent activation energy. It is most often parameterized by the Vogel–Fucher–Tammann (VFT) dependence, namely [99,100,101,102]:

## 4. Conclusions

_{3}nanoparticles (spherical, d = 50 nm). The distortions-sensitive analysis of the dielectric constant revealed the hidden anomaly of the dielectric constant, strongly influenced by the addition of nanoparticles, which finally leads to the ‘anomalous’ pretransitional anomalies for x = 0.5% and x = 1% concentrations of NPs. The evolution of the dielectric constant in the nematic phase indicates its split into two regions, with the crossover related to the standard ‘equilibrium, hidden melting temperature. Notable is the finding of the exponential behavior of the low-frequency contribution to the real part of the dielectric permittivity, which has been not reported so far. The next issue is the critical-like pretransitional behavior in the solid phase and the strong rise in this effect when adding nanoparticles. For dynamics, the explicit preference for the ‘hyperbolic’ or ‘critical’ evolution of the apparent activation enthalpy is worth stressing, leading to the preference for the ‘activated & critical’ equation introduced recently [102]. Finally, worth stressing is the long-range empirical ‘critical-like’ behavior of the dissipation factor (D = tgδ).

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

**Figure A1.**The imaginary part of the complex dielectric permittivity as a function of frequency. Spectra collected in the isotropic liquid, nematic, and solid phases of MBBA liquid crystal and its colloids doped with paraelectric BaTiO

_{3}nanoparticles. Characteristic features of spectra (DC electric conductivity and primary relaxation processes) are indicated.

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**Figure 1.**The frequency spectrum of the real part of dielectric permittivity in the nematic phase of MBBA and MBBA + BaTiO

_{3}nanocolloids. The behavior associated with characteristic frequency domains is indicated. LF stands for low-frequency, and the static domain is related to the dielectric constant.

**Figure 2.**The frequency spectrum of the real part of dielectric permittivity in the solid phase of MBBA and MBBA + BaTiO

_{3}nanocolloids, close to the N–S transition. Note the log-log scale. The skeletal formula for MBBA is also shown in the picture.

**Figure 3.**The frequency spectrum of the real part of dielectric permittivity in the solid phase of MBBA and MBBA + BaTiO

_{3}nanocolloids, remote from the N–S transition.

**Figure 4.**Dielectric constant temperature changes in MBBA and its nanocolloids, for nanoparticle concentrations given in the plot. Dashed arrows indicate transitions between the isotropic liquid and nematic phases, and solid arrows indicate nematic–solid phase transitions.

**Figure 5.**Temperature changes in dielectric constant derivatives of MBBA and its nanocolloids with BaTiO

_{3}nanoparticles. Concentrations are given in the plot. Dashed arrows indicate transitions between the isotropic liquid and nematic phases, and solid arrows indicate nematic–solid phase transitions. Values of ${T}_{I\u2013N}$ and ${T}_{N\u2013S}$ temperatures are given in Table 1. Dotted arrows indicate phase transition in the solid phase, with ${T}_{S1},{T}_{S2},{T}_{S3}$ phase transition temperatures. The dashed-dotted arrow (in grey) indicates the transformation within the nematic phase, associated with ${T}_{cross.}\approx 295.3\mathrm{K}$.

**Figure 6.**The focused insight on the behavior of dielectric constant in the isotropic liquid phase in MBBA and related nanocolloids for small concentrations of nanoparticles. Solid curves are associated with the parameterization via Equation (5). Reference data are taken from Figure 4. The dashed arrows indicate the clearing temperatures, their colors correspond to the colors of the data series.

**Figure 7.**The focused insight for the behavior of dielectric constant in the isotropic liquid phase in MBBA-based nanocolloids for larger concentrations of nanoparticles. Solid curves are associated with the parameterization via Equation (5). Reference data are taken from Figure 4. The gray dashed arrow indicates the isotropic-nematic phase transition temperature ${T}^{C}$. Note: the transition occurs within the isotropic liquid phase, which suggests the liquid-liquid transition (${I}_{2}\leftarrow {I}_{1}$)—indicated by the dotted arrow.

**Figure 8.**The pretransitional changes in dielectric constant in the solid phase of MBBA and its nanocolloids with BaTiO

_{3}nanoparticles. Solid curves are associated with Equation (8), with singular temperature ${T}_{m.f}^{*}$ in the liquid phase at $~{T}_{m,f}+0.5$. The arrow indicate the nematic-solid phase transition temperature.

**Figure 9.**Temperature changes in the real part of dielectric permittivity in the isotropic liquid and nematic phases of MBBA and its nanocolloids with BaTiO

_{3}nanoparticles for concentration (in mass fractions) frequencies given in the plot. The latter extends from the static to the low-frequency domain. For each figure, the same ranges are presented.

**Figure 10.**Temperature evolutions of the difference ${\mathsf{\Delta}\epsilon}^{\prime}={\epsilon}^{\prime}\left(f\right)-\epsilon $, where $\epsilon ={\epsilon}^{\prime}\left(f=116\mathrm{kHz}\right)$ is for dielectric constant—related to the static domain. Note the link to Equation (10). Dashed lines show the ‘average’ position of the clearing temperature for all concentrations.

**Figure 11.**Results from Figure 10, presented as ${\mathsf{\Delta}\epsilon}^{\prime}\left(T\right)={\epsilon}^{\prime}\left(f\right)-\epsilon $ dependencies for MBBA and its nanocolloids with BaTiO

_{3}in the semi-log scale. The plots reveal the hidden exponential behavior (Equation (11)) of ${\mathsf{\Delta}\epsilon}^{\prime}\left(T\right)$ in the low-frequency domain. Dashed lines show the ‘average’ position of the clearing temperature for all concentrations.

**Figure 12.**The temperature evolution of DC electric conductivity in the isotropic liquid and nematic phases of MBBA and nanocolloids with BaTiO

_{3}nanoparticles. Arrows indicate clearing temperatures for pure MBBA and related nanocolloids, with given concentrations of nanoparticles.

**Figure 13.**The temperature evolution of the reciprocal of the apparent enthalpy (definition in the plot), and alternatively, the steepness index for DC electric conductivity in MBBA and related nanocolloids with $0.1\%$ BaTiO

_{3}nanoparticles. Note the link to Equation (13). The plot recalls the analysis introduced in ref. [102] for ‘glassy’ dynamics.

**Figure 14.**Temperature evolutions for $tg\delta $ loss factor (frequency $f=1.23\mathrm{MHz}$) in MBBA and related nanocolloids with BaTiO

_{3}nanoparticles.

**Figure 15.**Temperature evolutions for $tg\delta $ loss factor (frequency $f=1\mathrm{kHz}$) in MBBA and related nanocolloids with BaTiO

_{3}nanoparticles. The solid green curve is related to Equation (18) with the exponent $\varphi \approx 2.8$.

**Figure 16.**Temperature evolutions for $tg\delta $ loss factor (frequency $f=12\mathrm{Hz}$) in MBBA and related nanocolloids with BaTiO

_{3}nanoparticles. The solid green curve is related to Equation (18) with the exponent $\varphi \approx 4$.

**Table 1.**Basic phase transition temperatures in MBBA and its nanocolloids with BaTiO

_{3}nanoparticles. ${T}_{I\u2013N}$ is for the weakly discontinuous Isotropic–Nematic (I–N) transition temperature (clearing temperature) and ${T}_{N\u2013S}$ is for the strongly discontinuous Nematic–Solid (N–S) transition temperature. Concentrations are given in mass fraction: $x\%=\left[{m}_{NPs}/\left({m}_{NPs}+{m}_{MBBA}\right)\right]\times 100\%$ and the volume fraction: ϕ% $=\left[{V}_{NPs}/\left({V}_{NPs}+{V}_{MBBA}\right)\right]\times 100\%$. The latter is associated with pure MBBA clearing temperature.

System: MBBA + NPs | ${\mathit{T}}_{\mathit{I}\u2013\mathit{N}}\left(\mathbf{K}\right)$ | ${\mathit{T}}_{\mathit{N}\u2013\mathit{S}}\left(\mathbf{K}\right)$ |
---|---|---|

MBBA (x%, ϕ% = 0) | 314.4 | 271.2 |

+0.01% (x%); +0.17 (ϕ%) | 306.3 | 276.5 |

+0.05% (x%); +0.008% (ϕ%) | 303.3 | 276.1 |

+0.1% (x%); +0.017% (ϕ%) | 296.6 | 269.1 |

+0.5% (x%): +0.088% (ϕ%) | 292.9 | 275.1 |

+1%(x%): +0.17% (ϕ%) | 293.7 | 276.6 |

System | $\mathit{a}$ | $\mathit{C}$ | ${\mathsf{\Delta}\mathit{T}}^{\mathbf{*}}\left(\mathbf{K}\right)$ | α |
---|---|---|---|---|

MBBA | −0.0101 | 9.14 × 10^{−4} | 0.8 | $1/2$ |

+0.01% | −0.0117 | 3.13 × 10^{−3} | 1.3 | $1/2$ |

+0.5% | −0.011 | −6.91 × 10^{−3} | 3.0 | $1/2$ |

+1% | −0.013 | −6.12 × 10^{−3} | 3.4 | $1/2$ |

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**MDPI and ACS Style**

Drozd-Rzoska, A.; Łoś, J.; Rzoska, S.J.
The Dominance of Pretransitional Effects in Liquid Crystal-Based Nanocolloids: Nematogenic 4-methoxybenzylidene-4′–butylaniline with Transverse Permanent Dipole Moment and BaTiO_{3} Nanoparticles. *Nanomaterials* **2024**, *14*, 655.
https://doi.org/10.3390/nano14080655

**AMA Style**

Drozd-Rzoska A, Łoś J, Rzoska SJ.
The Dominance of Pretransitional Effects in Liquid Crystal-Based Nanocolloids: Nematogenic 4-methoxybenzylidene-4′–butylaniline with Transverse Permanent Dipole Moment and BaTiO_{3} Nanoparticles. *Nanomaterials*. 2024; 14(8):655.
https://doi.org/10.3390/nano14080655

**Chicago/Turabian Style**

Drozd-Rzoska, Aleksandra, Joanna Łoś, and Sylwester J. Rzoska.
2024. "The Dominance of Pretransitional Effects in Liquid Crystal-Based Nanocolloids: Nematogenic 4-methoxybenzylidene-4′–butylaniline with Transverse Permanent Dipole Moment and BaTiO_{3} Nanoparticles" *Nanomaterials* 14, no. 8: 655.
https://doi.org/10.3390/nano14080655