We review the current state of knowledge of phase separation and phase equilibria in porous materials. Our emphasis is on fundamental studies of simple fluids (composed of small, neutral molecules) and well-characterized materials. While theoretical and molecular simulation studies are stressed, we also survey experimental investigations that are fundamental in nature. Following a brief survey of the most useful theoretical and simulation methods, we describe the nature of gas‐liquid (capillary condensation), layering, liquid‐liquid and freezing/melting transitions. In each case studies for simple pore geometries, and also more complex ones where available, are discussed. While a reasonably good understanding is available for phase equilibria of pure adsorbates in simple pore geometries, there is a need to extend the models to more complex pore geometries that include effects of chemical and geometrical heterogeneity and connectivity. In addition, with the exception of liquid‐liquid equilibria, little work has been done so far on phase separation for mixtures in porous media.

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Phase separation in confined systems

Advanced Mathematical Methods for Scientists and Engineers

Aspects of Scientific Explanation: and Other Essays in the Philosophy of Science

We present a review of experimental, theoretical, and molecular simulation studies of confinement effects on freezing and melting We consider both simple and more complex adsorbates that are confined in various environments (slit or cylindrical pores and also disordered porous materials) The most commonly used molecular simulation, theoretical and experimental methods are first presented We also provide a brief description of the most widely used porous materials The current state of knowledge on the effects of confinement on structure and freezing temperature, and the appearance of new surface-driven and confinement-driven phases are then discussed We also address how confinement affects the glass transition

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Effects of confinement on freezing and melting.

With the maturation of the information display field, liquid-crystal materials research is undergoing a modern-day renaissance. Devices and configurations based on liquid-crystal materials are being developed for spectroscopy, imaging and microscopy, leading to new techniques for optically probing biological systems. Biosensors fabricated with liquid-crystal materials can allow label-free observations of biological phenomena. Liquid-crystal polymers are starting to be used in biomimicking colour-producing structures, lenses and muscle-like actuators. New areas of application in the realms of biology and medicine are stimulating innovation in basic and applied research into these materials.

Liquid-crystal materials find a new order in biomedical applications.

Liquid-crystalline blue phases exhibit exceptional properties for applications in the display and sensor industry. However, in single component systems, they are stable only for very narrow temperature range between the isotropic and the chiral nematic phase, a feature that severely hinders their applicability. Systematic high-resolution calorimetric studies reveal that blue phase III is effectively stabilized in a wide temperature range by mixing surface-functionalized nanoparticles with chiral liquid crystals. This effect is present for two liquid crystals, yielding a robust method to stabilize blue phases, especially blue phase III. Theoretical arguments show that the aggregation of nanoparticles at disclination lines is responsible for the observed effects.

http://samo.kralj.fnm.uni-mb.si/clanki/a10c4.pdf

Nanoparticle-induced widening of the temperature range of liquid-crystalline blue phases

Liquid crystals in complex geometries formed by polymer and porous networks

The self-organizing properties of nematic liquid crystals can be used to align carbon nanotubes dispersed in them. Because the nanotubes are so much thinner than the elastic penetration length, the alignment is caused by the coupling of the unperturbed director field to the anisotropic interfacial tension of the nanotubes in the nematic host fluid. In order to relate the degree of alignment of the nanotubes to the properties of the nematic liquid crystal, we treat the two components on the same footing and combine Landau-de Gennes free energies for the thermotropic ordering of the liquid crystal and for the lyotropic nematic ordering of carbon nanotubes caused by their mutually excluded volumes. The phase ordering of the binary mixture is analyzed as a function of the volume fraction of the carbon nanotubes, the strength of the coupling and the temperature. We find that the degree of ordering of the nanorods is enslaved by the properties of the host liquid and that it can be tuned by raising or lowering the temperature or by increasing or decreasing their concentration. By comparing the theory to recent experiments, we find the anchoring energy of multiwalled carbon nanotubes to be in the range from 10 -10 to 10 -7 Nm -1 .

Alignment of carbon nanotubes in nematic liquid crystals.

We present a calorimetric study of the phase behavior of octylcyanobiphenyl (8CB) liquid crystal confined to a controlled-pore glass (CPG). We used CPG matrices with characteristic void diameters ranging from 400 to 20 nm. In bulk we obtain weakly first-order isotropic to nematic (I-N) phase transition and nearly continuous character of the nematic to smectic-A (N-SmA) phase transition. In all CPG matrices the I-N transition remains weakly first order, while the N-SmA one becomes progressively suppressed with decreasing CPG pore radius. With decreased pore diameters both phase transition temperatures monotonously decrease following similar trends, but increasing the stability range of the N phase. The heat-capacity response at the weakly first order I-N and continuous N-SmA phase transitions gradually approaches the tricritical-like and three-dimensional XY behavior, respectively. The main observed features were explained using a bicomponent single pore type phenomenological model.

Calorimetric study of octylcyanobiphenyl liquid crystal confined to a controlled-pore glass.

We study the biaxial structure of both line and point defects in a nematic liquid crystal confined within a capillary tube whose lateral boundary enforces homeotropic anchoring. According to Landau--de Gennes theory the local order in the material is described by a second-order tensor $\mathbf{Q},$ which encompasses both uniaxial and biaxial states. Our study is both analytical and numerical. We show that the core of a line defect with topological charge $M=1$ is uniaxial in the axial direction. At the lateral boundary, the uniaxial ordering along the radial direction is reached in two qualitatively different ways, depending on the sign of the order parameter on the axis. The point defects with charge $M=\ifmmode\pm\else\textpm\fi{}1$ exhibit a uniaxial ring in the plane orthogonal to the cylinder axis. This ring is in turn surrounded by a torus on which the degree of biaxiality attains its maximum. The typical lengths that characterize the structure of these defects depend both on the cylinder radius and the biaxial correlation length. It seems that the core of the point defect does not depend on the far nematic director field in the bulk limit.

http://samo.kralj.fnm.uni-mb.si/clanki/a99c1.pdf

Samo Kralj

Papers

Nanoparticle-induced widening of the temperature range of liquid-crystalline blue phases

Liquid crystals in complex geometries formed by polymer and porous networks

Alignment of carbon nanotubes in nematic liquid crystals.

Calorimetric study of octylcyanobiphenyl liquid crystal confined to a controlled-pore glass.

Biaxial torus around nematic point defects.