Fractional dynamics has experienced a firm upswing during the past few years, having been forged into a mature framework in the theory of stochastic processes. A large number of research papers developing fractional dynamics further, or applying it to various systems have appeared since our first review article on the fractional Fokker–Planck equation (Metzler R and Klafter J 2000a, Phys. Rep. 339 1–77). It therefore appears timely to put these new works in a cohesive perspective. In this review we cover both the theoretical modelling of sub- and superdiffusive processes, placing emphasis on superdiffusion, and the discussion of applications such as the correct formulation of boundary value problems to obtain the first passage time density function. We also discuss extensively the occurrence of anomalous dynamics in various fields ranging from nanoscale over biological to geophysical and environmental systems.

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The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics

This Review covers the recent developments (2005-2015) in the design, synthesis, characterization, and application of thermotropic ionic liquid crystals. It was designed to give a comprehensive overview of the "state-of-the-art" in the field. The discussion is focused on low molar mass and dendrimeric thermotropic ionic mesogens, as well as selected metal-containing compounds (metallomesogens), but some references to polymeric and/or lyotropic ionic liquid crystals and particularly to ionic liquids will also be provided. Although zwitterionic and mesoionic mesogens are also treated to some extent, emphasis will be directed toward liquid-crystalline materials consisting of organic cations and organic/inorganic anions that are not covalently bound but interact via electrostatic and other noncovalent interactions.

Ionic Liquid Crystals: Versatile Materials.

A review of experimental work on freezing and melting in confinement is presented. A range of systems, from metal oxide gels to porous glasses to novel nanoporous materials, is discussed. Features such as melting-point depression, hysteresis between freezing and melting, modifications to bulk solid structure and solid-solid transitions are reviewed for substances such as helium, organic fluids, water and metals. Recent work with well characterized assemblies of cylindrical pores like MCM-41 and graphitic microfibres with slit pores has suggested that the macroscopic picture of melting and freezing breaks down in pores of molecular dimensions. Applications of the surface force apparatus to the study of freezing and melting phenomena in confinement are discussed in some detail. This instrument is unique in allowing the study of conditions in a single pore, without the complications of pore blockage and connectivity effects. The results have confirmed the classical picture of melting-point depression in larger pores, and allowed the direct observation of capillary condensation of solid from vapour. Other results include the measurement of solvation forces across apparently fluid films below the bulk melting point and a solid-like response to shear of films above the bulk melting point. These somewhat contradictory findings highlight the difficulty of using bulk concepts to define the phase state of a substance confined to nanoscale pores.

https://iopscience.iop.org/article/10.1088/0953-8984/13/11/201/pdf

Confinement effects on freezing and melting

Revolutionary developments in the fabrication of nanosized particles have created enormous expectations in the last few years for the use of such materials in areas such as medical diagnostics and drug-delivery, and in high-tech devices. By its very nature, nanotechnology is of immense academic and industrial interest as it involves the creation and exploitation of materials with structural features in between those of atoms and bulk materials, with at least one dimension limited to between 1 and 100 nm. Most importantly, the properties of materials with nanometric dimensions are, in most instances, significantly different from those of atoms or bulk materials. Research efforts geared towards new synthetic procedures for shape and size-uniform nanoscale building blocks as well as efficient self-assembly protocols for manipulation of these building blocks into functional materials has created enormous excitement in the field of liquid crystal research. Liquid crystals (LCs) by their very nature are suitable candidates for matrix-guided synthesis and self-assembly of nanoscale materials, since the liquid crystalline state combines order and mobility at the molecular (nanoscale) level. Based on selected relevant examples, this review attempts to give a short overview of current research efforts in LC-nanoscience. The areas addressed in this review include the synthesis of nanomaterials using LCs as templates, the design of LC nanomaterials, self-assembly of nanomaterials using LC phases, defect formation in LC-nanoparticle suspensions, and potential applications. Despite the seeming diversity of these research topics, this review will make an effort to establish logical links between these different research areas.

Nanoparticles in Liquid Crystals: Synthesis, Self-Assembly, Defect Formation and Potential Applications

Spatial confinement in nanoporous media affects the structure, thermodynamics and mobility of molecular soft matter often markedly. This article reviews thermodynamic equilibrium phenomena, such as physisorption, capillary condensation, crystallisation, self-diffusion, and structural phase transitions as well as selected aspects of the emerging field of spatially confined, non-equilibrium physics, i.e. the rheology of liquids, capillarity-driven flow phenomena, and imbibition front broadening in nanoporous materials. The observations in the nanoscale systems are related to the corresponding bulk phenomenologies. The complexity of the confined molecular species is varied from simple building blocks, like noble gas atoms, normal alkanes and alcohols to liquid crystals, polymers, ionic liquids, proteins and water. Mostly, experiments with mesoporous solids of alumina, gold, carbon, silica, and silicon with pore diameters ranging from a few up to 50 nm are presented. The observed peculiarities of nanopore-confined condensed matter are also discussed with regard to applications. A particular emphasis is put on texture formation upon crystallisation in nanoporous media, a topic both of high fundamental interest and of increasing nanotechnological importance, e.g. for the synthesis of organic/inorganic hybrid materials by melt infiltration, the usage of nanoporous solids in crystal nucleation or in template-assisted electrochemical deposition of nano structures.

https://iopscience.iop.org/article/10.1088/0953-8984/27/10/103102/pdf

Soft matter in hard confinement: phase transition thermodynamics, structure, texture, diffusion and flow in nanoporous media

Dielectric measurements on the antiferroelectric smectic C (SmCPA) and isotropic (I) phases of a substance formed by bent‐shaped molecules were performed in the frequency range from 0.1 Hz to 0.1 GHz. Three absorption ranges, corresponding to a slow collective process, the reorientation of the molecular core around the long axes and the fast dynamics of the terminal groups, were detected in the SmCPA phase, whereas only two ranges, related to the two last processes, appear in the isotropic state. At the I–SmCPA phase transition the process of molecular reorientation around the long axes changes stepwise with respect to the absorption band intensity and the relaxation time, while the activation energy remains practically unchanged. The activation energy for the dynamics of the terminal groups increases at the I–SmCPA transition.

Broadband dielectric investigations on a compound consisting of bent‐shaped molecules

The paper presents the results of the measurements of the dielectric relaxation of nematic 6-CHBT performed for differentvalues ofthe angle between the directions of the macroscopic orientation of the sample (director n) and the probing electricfield E. Analysis ofthe evolution ofthe relaxation spectrum from 4(o) (E n) to i(o) (E I n) allowed one to explainthe inconsistency in the molecular interpretation ofthe spectra A model of the molecular dynamics in the oriented nematicsis proposed.Keywords: dielectric relaxation, neniatic, molecular dynamics 1. INTRODUCTION Studies of the dielectric relaxation in nematic liquid crystals are of a special interest and importance. The possibilityof control of the molecular orientation in the whole nematic sample by an electric I magnetic field or by an appropriatepreparation of the electrodes surface, gives an exceptional opportunity for studies of the molecular dynamics in correlation to the directions of the principal axes of the nematogenic molecule. One could expect that in such advantageous

Molecular model of the dielectric relaxation in nematic liquid crystals

Dielectric relaxation study was carried out for the nematic and isotropic phases of 4-(trans-4'-n-heptylcyclohexyl)isothiocyanatobenzene in the frequency range from 100 kHz to 1 GHz. In the nematic phase two relaxation processes were recorded for the electric permittivity component measured parallel to the molecular orientation (director n) and three relaxation processes — for the perpendicular permittivity component. The strength of the nematic potential and the nematic order parameter were estimated. PACS numbers: 64.70.Md, 77.84.Nh, 77.22.Gm

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Molecular Dynamics of 4-(trans-4'-n-Heptylcyclohexyl)- Isothiocyanatobenzene Studied with Dielectric Relaxation Spectroscopy

Temperature dependence of the shear viscosity measured for isotropic liquids belonging to the three homologous series: 4-(trans-4'-n-alkylcyclohexyl) isothiocyanatobenzenes (C n H 2 n + 1 CyHx Ph NCS; nCHBT, n = 0 + 12), n-alkylcyanobiphenyls (C n H 2 n + 1 Ph Ph CN; nCB, n = 2 + 12) and 1, n-alkanediols (HO(CH 2 ) n OH; 1,nAD, n = 2+10) were analysed with the use of Arrhenius equation and its two modifications: Vogel-Fulcher and proposed in this paper The extrapolation of the isothermal viscosity of 1, n-alkanediols (n = 2 + 10) to n = 1 leads to an interesting conclusion concerning the expected viscosity of methanediol, HOCH 2 OH, the compound strongly unstable in a pure state

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Temperature Dependence of the Viscosity of Isotropic Liquids

Static electric permittivity and dielectric relaxation have been measured in isotropic and nematic phase of 6-OCB and 8- OCB. On the basis of the temperature dependence of the principal static permittivities of nematics, (epsilon) (parallel)(T) and (epsilon) (perpendicular)(T), using the Maier-Meier equations, the following quantities have been obtained: i) the angle between the dipole moment vector and the long axis of mesogenic molecules, ii) the molecule apparent dipole moment square (mu) 2app(T) and iii) the nematic order parameter S(T). From the temperature dependence of the dielectric relaxation time, the activation energy for the molecular rotation around the short axis has been calculated and, taking into account the viscosity data, the effective dimensions of the nematogen molecules have been evaluated.© (1999) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Grzegorz Czechowski

Papers

Broadband dielectric investigations on a compound consisting of bent‐shaped molecules

Molecular model of the dielectric relaxation in nematic liquid crystals

Molecular Dynamics of 4-(trans-4'-n-Heptylcyclohexyl)- Isothiocyanatobenzene Studied with Dielectric Relaxation Spectroscopy

Temperature Dependence of the Viscosity of Isotropic Liquids

Static and dynamic dielectric properties of 6-OCB and 8-OCB