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

Volumes d'exces des melanges eau-butaneiols-1,2, -1,3 et -1,4, propanediol-1,3 et pentanediol-1,5

Excess molar volumes of binary mixtures of diols and water

Singular behavior of the static dielectric permittivity of n-alkyloxycyanobiphenyls $({\mathrm{C}}_{n}{\mathrm{H}}_{2n+1}\mathrm{O}\ensuremath{-}\mathrm{P}\mathrm{h}\ensuremath{-}\mathrm{P}\mathrm{h}\ensuremath{-}\mathrm{C}\ensuremath{\equiv}N,$ $n=6,$ 7) was studied above and below the nematic clearing point ${(T}_{I\ensuremath{-}N}).$ On approaching the clearing point, the evolution of principal components of the nematic permittivity tensor, ${\ensuremath{\varepsilon}}_{\ensuremath{\parallel}}$ and ${\ensuremath{\varepsilon}}_{\ensuremath{\perp}},$ is described by the order parameter exponent $\ensuremath{\beta}\ensuremath{\approx}0.25.$ The mean value of the nematic permittivity ${\ensuremath{\varepsilon}}_{\mathrm{mean}}=({\ensuremath{\varepsilon}}_{\ensuremath{\parallel}}+2{\ensuremath{\varepsilon}}_{\ensuremath{\perp}})/3$ exhibits a singular behavior similar to that observed in the isotropic phase and that for the diameter of the coexistence curve in binary mixtures. The derivative of experimental data $d{\ensuremath{\varepsilon}}_{\mathrm{iso}}(T)/dT$ and $d{\ensuremath{\varepsilon}}_{\mathrm{mean}}(T)/dT$ shows the specific-heat-like behavior with universal exponents $\ensuremath{\alpha}={\ensuremath{\alpha}}^{\ensuremath{'}}\ensuremath{\approx}0.5.$ Results obtained confirm the hypothesis of the fluidlike, pseudospinodal, and tricritical behavior of the isotropic to nematic phase transition. [A. Drozd-Rzoska, Phys. Rev. E 59, 5556 (1999)].

Fluidlike behavior of dielectric permittivity in a wide range of temperature above and below the nematic-isotropic transition.

This paper presents the results of studies of the dielectric relaxation of nematic 6CHBT obtained for different values of the angle between the directions of the macroscopic orientation of the sample (director n) and the probing electric field E. Analysis of the evolution of the relaxation spectrum from e*‖(ω) (E‖n) to e*⊥(ω) (E⊥n)allows one to explain the hitherto existing inconsistency in the molecular interpretation of the spectra. A model of the molecular dynamics in the oriented nematics is proposed.

On the molecular interpretation of the dielectric relaxation of nematic liquid crystals

The paper presents the results of measurements of the linear dielectric properties of the compounds from the homologous series of alkylcyanobiphenyls (C n H 2 n + 1 PhPhCN, nCB) in the vicinity of the first order transition (from the isotropic liquid to the crystalline phase) of nonmesogenic nCB's (n = 2-4) and the weakly first order transition (from the isotropic liquid to the nematic phase) of 5CB. The experimental method for the separation of the critical part of the static permittivity derivative and the activation energy for rotation of the mesogenic molecules, in the vicinity of weakly first order phase transition, is proposed. It is shown that the critical temperature dependence of the permittivity and the activation energy can be described with a function of (T -T*) - α type, with the same values of the temperature of virtual transition of the second order (T*) and the critical exponent (α).

Static and dynamic dielectric properties of strongly polar liquids in the vicinity of first order and weakly first order phase transitions.

This paper presents the results of measurements of the principal electric permittivities ∊ ∥*(T, ω and ∊⊥*(T, ω) and the viscosity for 4-(trans-4-n-hexylcyclohexyl)isothiocyanatobenzene (C6H13-CyHx-Bz-N=C=S, 6CHBT). In the nematic phase, the Miesowicz η2 viscosity coefficient was measured in a sample oriented due to the flow. On the basis of the temperature dependence of the static permittivities, using the Maier-Meier equations, the angle β between the dipole moment vector and the long axis of the 6CHBT molecule, the square of the molecular apparent dipole moment μ2 app 2 and the nematic order parameter S(T), were determined. From the temperature dependence of the viscosity and the relaxation time corresponding to the molecular rotation around the short axis, the strength of the nematic potential and the effective length of the 6CHBT molecule (in the isotropic phase) were estimated.

Grzegorz Czechowski

Papers

Excess molar volumes of binary mixtures of diols and water

Fluidlike behavior of dielectric permittivity in a wide range of temperature above and below the nematic-isotropic transition.

On the molecular interpretation of the dielectric relaxation of nematic liquid crystals

Static and dynamic dielectric properties of strongly polar liquids in the vicinity of first order and weakly first order phase transitions.

Dielectric and viscous properties of 6CHBT in the isotropic and nematic phases