Normal red blood cells' shape stabilized by membrane's in-plane ordering.

Red blood cells (RBCs) are present in almost all vertebrates and their main function is to transport oxygen to the body tissues. RBCs' shape plays a significant role in their functionality. In almost all mammals in normal conditions, RBCs adopt a disk-like (discocyte) shape, which optimizes their flow properties in vessels and capillaries. Experimentally measured values of the reduced volume (v) of stable discocyte shapes range in a relatively broad window between v ~ 0.58 and 0.8. However, these observations are not supported by existing theoretical membrane-shape models, which predict that discocytic RBC shape is stable only in a very narrow interval of v values, ranging between v ~ 0.59 and 0.65. In this study, we demonstrate that this interval is broadened if a membrane's in-plane ordering is taken into account. We model RBC structures by using a hybrid Helfrich-Landau mesoscopic approach. We show that an extrinsic (deviatoric) curvature free energy term stabilizes the RBC discocyte shapes. In particular, we show on symmetry grounds that the role of extrinsic curvature is anomalously increased just below the nematic in-plane order-disorder phase transition temperature.

Theoretical and experimental study of the nanoparticle-driven blue phase stabilisation.

We have studied theoretically and experimentally the effects of various types of nanoparticles (NPs) on the temperature stability range [Formula: see text] T (BP) of liquid-crystalline (LC) blue phases. Using a mesoscopic Landau-de Gennes type approach we obtain that the defect core replacement (DCR) mechanism yields in the diluted regime [Formula: see text] T (BP)(x) [Formula: see text] 1/(1 - xb) , where x stands for the concentration of NPs and b is a constant. Our calculations suggest that the DCR mechanism is efficient if a local NP environment resembles the core structure of disclinations, which represent the characteristic property of BP structures. These predictions are in line with high-resolution ac calorimetry and optical polarising microscopy experiments using the CE8 LC and CdSe or aerosil NPs. In mixtures with CdSe NPs of 3.5nm diameter and hydrophobic coating the BPIII stability range has been extended up to 20K. On the contrary, the effect of aerosil silica nanoparticles of 7.0nm diameter and hydrophilic coating is very weak.

Inhomogeneous bulk nematic order reconstruction.

A two-dimensional model within the Q-tensor description of liquid crystals is used to describe the inhomogeneous order reconstruction in a nematic cell driven by tony modulation in the anchoring conditions. Homogeneous and inhomogeneous reconstruction are contrasted: the former is defectless, the latter is defect mediated. While the transition thresholds are comparable in both cases and in good agreement with experimental data, the biaxial wall breaking is considerably slower in the inhomogeneous transition than in the homogeneous one. The shape of the signal given by the electric current flowing through the cell allows us to distinguish the actual path followed by the transition.

Periodic saddle-splay Freedericksz transition in nematic liquid crystals.

By use of a local stability criterion recently introduced, we predict the existence of a periodic saddle-splay Freedericksz (PSSF) transition that adds to the existing class of classical Freedericksz transitions driven in a nematic cell by an external field. Occurrence of the PSSF transition requires a saddle-splay elastic constant with a large enough magnitude and different anchoring strengths at the plates confining the nematic cell. Otherwise, either the PSSF transition does not occur at all, or it requires a field higher than that associated with the classical aperiodic splay Freedericksz (ASF) transition, in which case it is not observable. Here, we determine the threshold field for which the PSSF precedes the ASF transition, as well as the structure of the destabilizing mode.

Electric field induced order reconstruction in a nematic cell.

We have experimentally observed the biaxial switching between two topologically distinct textures of a nematic liquid crystal cell submitted to a strong electric field. The effect is deduced from optical and electrical measurements across the cell. Above a static threshold, a bulk order reconstruction is observed, where the final nematic orientation in the centre becomes perpendicular to its initial one, inducing a total pi change of orientation across the cell. Using short electric field pulses, a higher dynamical threshold is observed. These experiments are explained by a Landau-de Gennes-Khalatnikov model. The threshold implies the local exchange of two eigenvalues of the nematic order tensor through intermediate biaxial states. The onset of the effect in a thin splay-bend wall decreases the static threshold by almost an order of magnitude. The model explains reasonably well the static and dynamic measurements within the present description of nematic biaxiality.

Dynamics of dissipative ordered fluids.

A variational principle is proposed that allows to derive the equations of motion for a fluid with a general microstructure described by a tensorial order parameter. The only constitutive ingredients are the densities of the free energy and the dissipation, both subject to appropriate invariance requirements. As an illustration, it is shown how the hydrodynamic theory for uniaxial nematic liquid crystals can be derived within this setting.

Biaxial torus around nematic point defects.

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 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=+/-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.