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

The analysis of temperature dependence of the shear viscosity of freely flowing nematic liquid crystals shows that the anisotropic fluid adopts such a manner of flow, which corresponds to the minimum of its viscosity at given conditions. We postulate that the principle is of general significance, i.e. it concerns any fluid in the flow.

http://iopscience.iop.org/article/10.1088/0953-8984/13/12/101/pdf

The shear viscosity minimum of freely flowing nematic liquid crystals

The anchoring of nematic molecules on magnetic particles in some types of ferronematics

The paper presents the shear viscosity data for the isotropic phase of the homologous series of mesogenic n-alkylcyanobiphenyls (CnH2n+1PhPhC⋮N, nCB) for n = 2−12.

Viscosity of the Homologous Series of n-Alkylcyanobiphenyls

Temperature dependences of the static dielectric permittivity and its derivative, obtained for isotropic mesogenic liquids composed of the molecules of different polarity in relation to the basic thermodynamic quantities (internal energy, entropy, and Helmholtz free energy), are analyzed. A role of the molecular polarity in the dielectric behavior of the liquids in the vicinity of the isotropic to nematic phase transition is discussed.

Prenematic behavior of the electric-field-induced increment of the basic thermodynamic quantities of isotropic mesogenic liquids of different polarity.

Mesogenic compounds belonging to the two well-known -cyanophenyl, and -isothiocyanatophenyl homologous series, which distinctly differ in the molecular polarity (-C identical with N, 5D; -N=C=S, 2.5D), show an essential difference in the pretransitional dielectric behavior in the vicinity of the isotropic to nematic (I-N) phase transition. Taking into account the results presented in Phys. Rev. E 67, 041705 (2003), the features of the I-N transition observed for the less polar mesogens are characteristic for the first order phase transition, whereas in the case of the strongly polar ones, the I-N transition is undoubtedly close to the second order.

Grzegorz Czechowski

Papers

The shear viscosity minimum of freely flowing nematic liquid crystals

The anchoring of nematic molecules on magnetic particles in some types of ferronematics

Viscosity of the Homologous Series of n-Alkylcyanobiphenyls

Prenematic behavior of the electric-field-induced increment of the basic thermodynamic quantities of isotropic mesogenic liquids of different polarity.

Static and dynamic dielectric behavior of mesogenic compounds of different polarity in the vicinity of the isotropic to nematic phase transition.