Ferroelectric nanoparticles

The aforementioned frequency of the use of these nanomaterial shapes is best attributed to two factors (1) the ease with which these nanoparticle shapes can be synthesized in the laboratory and (2) the availability of these nanomaterials from commercial sources. It cannot be the aim of this review to cover all of the different nanomaterials used so far, but some of the most commonly investigated will be introduced in more detail. For zero-dimensional nanoparticles, emphasis will be put on metallic nanoparticles (mainly gold), semiconductor quantum dots, as well as magnetic (different iron oxides) and ferroelectric nanoparticles. In the area of onedimensional nanomaterials, metal and semiconductor nanorods and nano wires as well as carbon nanotubes will be briefly discussed, and for two-dimensional nanomaterials only nanoclay. Finally, researchers active in the field are advised to seek further information about these and other nanomaterials in the following, very insightful review articles [16, 36-45]. 

In addition to lowering V th, ferroelectric nanoparticles such as BaTi03 or Sn2P2S6 [144, 156, 318-323] have also been shown to increase the nematic-to-isotropic phase transition temperature (TN/Iso) and the order parameter of the nematic host [142, 320, 324-326], which are thought to have their origin in a coupling of the electric dipole moment of the particles with the orientational order of the surrounding nematic molecules (Fig. 6). 

Fig. 6 (a) Cartoon of a nanoparticle with no electric dipole moment in the isotropic phase, (b) Cartoon of a ferroelectric nanoparticle with electric dipole moment, which produces an electric field that interacts with orientational order of the nematic phase [327], (Copyright 2009, American Physical Society)... 

Lopatina and Selinger recently presented a theory for the statistical mechanics of ferroelectric nanoparticles in liquid crystals, which explicitly shows that the presence of such nanoparticles not only increases the sensitivity to applied electric fields in the isotropic liquid phase (maybe also a possible explanation for lower values for in the nematic phase) but also 7 N/Iso [327]. Another computational study also supported many of the experimentally observed effects. Using molecular dynamics simulations, Pereira et al. concluded that interactions between permanent dipoles of the ferroelectric nanoparticles and liquid crystals are not sufficient to produce the experimentally found shift in 7 N/ so and that additional long-range interactions between field-induced dipoles of nematic liquid crystal molecules are required for such stabilization of the nematic phase [328]. 

A method to obtain nano-particles at air/water interfaces has been described in [287]. Spreading of surfactant-coated metallic, semi-conducting, magnetic and ferroelectric nanoparticles on water surfaces results in the formation of monoparticulate thick films which then can be transferred, layer by layer, to solid substrates. These films can find potential applications in advanced electronic and electro-optical devices. Here and further, we give only typical examples of using surfactants in novel technologies. A more detailed description can be found in a new edition of Surfactants Science Series [288]. 

The introduction of ferroelectric nanoparticles in polymeric matrices seems attractive for improving the dielectric permittivity of polymeric-based materials. New pyro-and piezoelectric systems have been proposed, and better efficiency has been obtained by using ferroelectric particles with d 700 nm. However, the understanding of correlations between structure and macroscopic properties needs to be improved. Nevertheless, it is interesting to note that smart hybrid materials have been prepared by combining organic and inorganic phases, which illustrates the versatility of such nanocomposites. 

L.M. Lopatina, J.V. Selinger, Theory of ferroelectric nanoparticles in nematic liquid crystals. Phys. Rev. Lett. 102, 197802 (2009)... 

Finally it is worth to mention the paper, which deals with electric analog of superparamagnetism, i.e. superparaelectricity. Namely, the paper predicts the conditions of superparaelectric phase appearance in the ensemble of noninteracting ferroelectric nanoparticles [113]. The authors [113] introduced superparaelectricity... 

T, R) is the temperature and size dependent dielectric permittivity of incipient ferroelectric nanoparticles of radius R, (x is the fermion effective mass, is the effective permittivity of the particle environment, 8q is the dielectric permittivity of vacuum (in SI units). Due to the high values of e(r, R) the radius (T, R) > 5 nm is much higher than the lattice constant a = 0.4 nm, proving the validity of the effective mass approximation as well as the self-consistent background for the introduction of dielectric permittivity in the continuous medium approach [60]. 

The conditions (l)-(5) determine the conditions of emergence and physical properties of superparaelectric phase in the ensemble of ferroelectric nanoparticles of radius Rcr[Pg.264]

Subsequently we calculate the dependence of correlation radius on the temperature, particle radius, as well as on ferroelectric material parameters. Namely, these are the potential barrier of polarization reorientation in ferroelectric nanoparticle and polarization dependence on electric field. 

Note that open circuit electrical boundary conditions for single ferroelectric nanoparticles of different shapes were considered by Naumov and co-workers [120-122] and Slutsker et al. [123], The various types of domain structures were found, including vortices [121]. However when the boundary conditions tend to short circuit, the nanoparticle becomes single domain [121]. Since only individual nanoparticles were considered in Refs. [120-123], the depolarization field outside the particles was ignored despite partial screening should lead to its appearance. With respect to the fact that the depolarization field is responsible for electrostatic interaction between nanoparticles in the ensemble, the partial screening may lead to the formation of superstructures inside the ensemble. Since we aim to consider the conditions of superparaelectric phase appearance, we restrict our model to the case... 

Fig. 4.35 (a) Ensemble of non-interacting ferroelectric nanoparticles covered outside by the ambient free charges a. AH particle radii R are less than the correlation radius so that the dipole moments inside the particle are aligned due to the correlation effects, (b) A given nanoparticle, where the arrows inside the particle indicate the absolute value of dipole moments in different points [117]... 

Therefore, the condition 0 < AF T,R) < ksT determines the superparaelectric phase emergence in ferroelectric nanoparticles of radius Rcr(T) potential barrier the external electric field could partially or fully align the nanoparticles dipoles as considered below. 

The favorable conditions for the superparaelectricity observation in small ferroelectric nanoparticles at room temperatures are small Curie-Weiss constants, high nonlinear coefficients an and narrow distribution function of particles radii. The ensemble of noninteracting ferroelectric nanoparticles could be realized in nanoporous nonferroelectric matrix with the pores filled at least partly by some ferroelectric material. Another type of composite material can be considered also. Namely, it is the material with cylindrical geometry of nanopores in the nonferroelectric matrix filled with ferroelectric nanorods. However some difference in polar behavior for this geometry in comparison with spherical case can be expected. 

The hydrothermal synthesis of ferroelectric nanoparticles like BaTiOs is an industrial concern. This method is a powerful tool for fabricating ultrafine, homogeneous powders of high purity for a large variety of multi-cation oxides [73] as compared to methods based on the decomposition of solid precursors. The main advantage of hydrothermal synthesis is the improved control of the chemical and granular... 

Fig. 5.9 Technological flowsheet for microemulsion synthesis of the ferroelectric nanoparticles...

Lin Y, Boker A, Sill K, Xiang H, Abetz C, Li X, Wang J, Emrick T, Balazs AC, Russell TP (2005) Self-directed self-assembly of nanoparticle/copolymer mixtures. Nature 434(1 ) 55-59 Lopatina LM, Selinger JM (2011) Maier-Saupe-type theory of ferroelectric nanoparticles in nematic liquid crystals. Phys. Rev E 84 041703/1-041703/7 Lorenz A, Zimmermann N, Kumar S, Evans DR, Cook G, Martinez ME, Kitzerow H-S (2013) X-ray scattering of nematic liquid crystal nanodispersion with negative dielectric anisotropy. Appl Opt 52(22) E1-E5... 

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