Density Functional Theory for Chiral Nematic Liquid Crystals

Even though chiral nematic phases were the first liquid crystals experimentally observed more than a century ago, the origin of the thermodynamic stability of cholesteric states is still unclear. In this Letter we address the problem by means of a novel density functional theory for the equilibrium pitch of chiral particles. When applied to right-handed hard helices, our theory predicts an entropy-driven cholesteric phase, which can be either right- or left-handed, depending not only on the particle shape but also on the thermodynamic state. We explain the origin of the chiral ordering as an interplay between local nematic alignment and excluded-volume differences between left- and right-handed particle pairs

Connectedness percolation of hard deformed rods

Nanofiller particles, such as carbon nanotubes or metal wires, are used in functional polymer composites to make them conduct electricity. They are often not perfectly straight cylinders, but may be tortuous or exhibit kinks. Therefore we investigate the effect of shape deformations of the rodlike nanofillers on the geometric percolation threshold of the dispersion. We do this by using connectedness percolation theory within a Parsons-Lee type of approximation, in combination with Monte Carlo integration for the average overlap volume in the isotropic fluid phase. We find that a deviation from a perfect rodlike shape has very little effect on the percolation threshold, unless the particles are strongly deformed. This demonstrates that idealized rod models are useful even for nanofillers that superficially seem imperfect. In addition, we show that for small or moderate rod deformations, the universal scaling of the percolation threshold is only weakly affected by the precise particle shape.Comment: 7 pages, 8 figures; simplified figures and added to discussion, results unchange

Cooling irrigation as a powerful method for microclimate modification in apple plantation

Irrigation in some countries is a horticultural practice mainly used only to supply water. At the same time the use of microsprinklers have a powerful influence on the changes of temperature in orchards. When the air’s temperature is high (about 20 °C or higher) the evaporative cooling irrigation significantly decreases the plants’ surface temperature and air temperature. The cooling effect is stronger when the air is dryer. By using cooling irrigation regularly, canopy temperature can be decreased so that the beginning of blooming can be delayed. Also if the blooming is early and frost probability is high, serious damages can happen in orchards. The beneficial effect of cooling irrigation is the temperature reduction and frost protection. InMarch 2010, one month earlier than the expected blooming an irrigation system was established to produce anti-frost treatment and regulate the micro-climate of a Gala apple orchard which belongs to the University of Debrecen (Hungary). The objective of sprinklers was to cool the air by increasing water evaporation and relative humidity. The position of the micro-sprinklers was planned in three levels (around the tree trunks, a few cm near to the soil surface, in the crown region and above the crown, a half meter higher). The results showed that the water sprayed in the orchard by micro-jets influenced decisively the temperature of the plantation. At higher temperatures (around 20 °C), the drop of temperature may attain 5–7 °C. A low relative humidity of the air may increase the relative effect. When water was applied at intervals of 15 minutes for ten times a day from 8 am to 18 pm, the air, flowers and bud’s surface temperature could be kept low.At certain days when the temperature was higher than 10 °C, irrigation was used at night time in similar 15 minutes intervals, from 18 pm and 6 am. The beginning of bloom could be delayed for more than ten days. The Gala apple variety blooming dynamics was characterized by a logistic curve in the treated as well as in the control plot. In the treated plot, the curve was steeper than in the control one in spite of the equal temperatures measured in the plots. Under Hungarian climatic conditions, the method was successfully used to delay blooming dates. The main result was the diminution of the frost damage in the spring that assured apple yields

When shape is enough: from colloidal spheres to twisted polyhedra, from icosahedral to chiral order

In this thesis, we study entropy-driven phase transitions in suspensions of colloidal particles. Colloids are small particles, with typical sizes ranging from the nanometer to the micron, dispersed in a medium that is composed of much smaller particles (atoms or molecules). Because of this size difference, colloids experience Brownian motion that allows them to move around the medium, exploring the microscopic configurations available, and possibly arrange themselves in ordered structures. This process is called self-assembly. For example, colloids self-assemble in fluids (disordered arrangements of particles), liquid-crystals (partially ordered), and crystals (fully ordered). The stability and the transitions between these phases, i.e., the phase behaviour, depend both on the interactions between the colloids and on thermodynamic parameters like temperature or density. Here, we focus on systems composed of hard colloidal particles, that are particles that do not have any interactions except for the fact that cannot overlap with each other. By using computer simulations and theory, we show that the particle shape is enough for the formation of several thermodynamic phases. In other words, it is possible to obtain order in complete absence of any attraction in the system, just by increasing the density of the system. These transitions are (fully) entropy-driven since no change in energy is associated to the phase transition but only a change in entropy, that is a quantity related to the number of possible microscopic particle arrangements. In chapter 2 we show that when (tens of) thousands of hard spheres are compressed, while being confined in a spherical cavity, they do not self-assemble into an FCC crystal, that is the equilibrium bulk crystal structure, but rather they form stable icosahedral clusters. In chapter 3, we study hard spherocylinders forming liquid crystals. In chapter 4, we study liquid crystals formed by binary mixtures of colloidal rods and spheres, focusing in particular on the binary smectic phase, that consists in alternating layers of rods and spheres. In chapters 2, 3, and 4 our theoretical and simulation results are compared with experiments performed in our group. In chapter 5, we consider hard rod-like particles with a polyhedral shape and we identify the conditions to form prolate, oblate and biaxial nematic phases. In chapters 6, 7 and 8, we consider colloidal particles with a chiral shape forming chiral liquid-crystal phases. In particular, in chapter 6 we develop a theory to predict the equilibrium cholesteric pitch as a function of thermodynamic state and microscopic details. Applying the theory to hard helices, we observe both right- and left-handed cholesteric phases that depend on a subtle combination of particle geometry and system density. In chapter 7, we introduce particles with a twisted polyhedral shape and obtain, for the first time, a stable fully-entropy-driven cholesteric phase by computer simulations. Our results unveil how the competition between particle biaxiality and chirality is transmitted at a higher level into the nematic phases and new theoretical challenges on the self-assembly of chiral particles are addressed in chapter 8

On the stability and finite-size effects of a columnar phase in single-component systems of hard-rod-like particles

Colloidal rod-like particles self-assemble into a variety of liquid crystal phases. In contrast to the formation of the nematic and smectic phases for which it is well understood that it can be driven by entropy, the stabilisation mechanism of a prolate columnar phase (), observed for example in fd-virus suspensions, is still unclear. Here, we investigate whether or not a phase can exist in a purely entropy-driven single-component system. We perform computer simulations of hard particles with different shapes: spherocylinders, top-shaped rods, cuboidal particles, and crooked rods. We show that the phases observed in previous simulation studies are mere artefacts due to either finite-size effects or simulation boxes that are incommensurate with the stable thermodynamic phase. In particular, we observe that the characteristic layering of the stable smectic or crystal phase disappears when the dimension of the simulation box along the direction of the layers is too small. Such a system-size effect depends both on particle shape and the competing phases, and appears to be more pronounced for less anisotropic particles

Density functional theory and simulations of colloidal triangular prisms

Nanopolyhedra form a versatile toolbox to investigate the effect of particle shape on self-assembly. Here we consider rod-like triangular prisms to gauge the effect of the cross section of the rods on liquid crystal phase behavior. We also take this opportunity to implement and test a previously proposed version of fundamental measure density functional theory (0D-FMT). Additionally, we perform Monte Carlo computer simulations and we employ a simpler Onsager theory with a Parsons-Lee correction. Surprisingly and disappointingly, 0D-FMT does not perform better than the Tarazona and Rosenfeld’s version of fundamental measure theory (TR-FMT). Both versions of FMT perform somewhat better than the Parsons-Lee theory. In addition, we find that the stability regime of the smectic phase is larger for triangular prisms than for spherocylinders and square prisms

Modeling the cholesteric pitch of apolar cellulose nanocrystal suspensions using a chiral hard-bundle model

Cellulose nanocrystals (CNCs) are naturally sourced elongated nanocolloids that form cholesteric phases in water and apolar solvents. It is well accepted that CNCs are made of bundles of crystalline microfibrils clustered side-by-side, and there is growing evidence that each individual microfibril is twisted. Yet, the origin of the chiral interactions between CNCs remains unclear. In this work, CNCs are described with a simple model of chiral hard splinters, enabling the prediction of the pitch using density functional theory and Monte Carlo simulations. The predicted pitch P compares well with experimental observations in cotton-based CNC dispersions in apolar solvents using surfactants but also with qualitative trends caused by fractionation or tip sonication in aqueous suspensions. These results suggest that the bundle shape induces an entropy-driven chiral interaction between CNCs, which is the missing link in explaining how chirality is transferred from the molecular scale of cellulose chains to the cholesteric order. © 2022 Author(s)

On the stability and finite-size effects of a columnar phase in single-component systems of hard-rod-like particles

Colloidal rod-like particles self-assemble into a variety of liquid crystal phases. In contrast to the formation of the nematic and smectic phases for which it is well understood that it can be driven by entropy, the stabilisation mechanism of a prolate columnar phase (), observed for example in fd-virus suspensions, is still unclear. Here, we investigate whether or not a phase can exist in a purely entropy-driven single-component system. We perform computer simulations of hard particles with different shapes: spherocylinders, top-shaped rods, cuboidal particles, and crooked rods. We show that the phases observed in previous simulation studies are mere artefacts due to either finite-size effects or simulation boxes that are incommensurate with the stable thermodynamic phase. In particular, we observe that the characteristic layering of the stable smectic or crystal phase disappears when the dimension of the simulation box along the direction of the layers is too small. Such a system-size effect depends both on particle shape and the competing phases, and appears to be more pronounced for less anisotropic particles