Interfacial forces and Marangoni flow on a nematic drop retracting in an isotropic fluid

Nematic-isotropic interfaces exhibit novel dynamics due to anchoring of the liquid crystal molecules on the interface. The objective of this study is to demonstrate the consequences of such dynamics in the flow field created by an elongated nematic drop retracting in an isotropic matrix. This is accomplished by two-dimensional flow simulations using a diffuse-interface model. By exploring the coupling among bulk liquid crystal orientation, surface anchoring and the flow field, we show that the anchoring energy plays a fundamental role in the interfacial dynamics of nematic liquids. In particular, it gives rise to a dynamic interfacial tension that depends on the bulk orientation. Tangential gradient of the interfacial tension drives a Marangoni flow near the nematic-isotropic interface. Besides, the anchoring energy produces an additional normal force on the interface that, together with the interfacial tension, determines the movement of the interface. Consequently, a nematic drop with planar anchoring retracts more slowly than a Newtonian drop, while one with homeotropic anchoring retracts faster than a Newtonian drop. The numerical results are consistent with prior theories for interfacial rheology and experimental observations.     

Interfacial tension of a nematic liquid crystal/water interface with homeotropic surface alignment

Pendant drop experimental results are presented for the temperature dependence of the interfacial tension between water and the immiscible nematic liquid crystal 4'-pentyl-4-biphenylcarbonitrile (5CB) in the presence of the adsorbed surfactant cetyltrimethylammonium bromide (CTAB). Adsorption of the surfactant lowers the interfacial tension value and is also known from earlier work to induce a transition in liquid crystal surface alignment from planar to homeotropic [Brake et al. Langmuir 2003, 19, 6436.]. Discrepancies exist in the literature regarding the density of 5CB, and the density difference between 5CB and water in any case is very small. However, from the ability to form pendant 5CB drops, one may infer that the density of 5CB exceeds that of water over the entire temperature range studied (28-41 degrees C), in disagreement with the predictions of one earlier report on 5CB. The interfacial tension is shown to exhibit a relative maximum near the bulk 5CB nematic-isotropic transition temperature T(NI), regardless of which published data set of 5CB density values is used to analyze the measurements, with a possible discontinuity in tension occurring at T(NI). The anomalous shape of the interfacial tension curve, depending on the choice of the 5CB density data set, may be quite similar to that recently reported for the interface between 5CB and a hydrophobic, isotropic molten polymer (Rai et al. Langmuir 2003, 19, 7370).     

Interfacial nematodynamics of heterogeneous curved isotropic-nematic moving fronts

The early stages of liquid crystal phase ordering upon thermal quenches of isotropic phases into unstable and metastable temperature ranges is studied using two-dimensional (2D) computational solutions of the governing Landau-de Gennes (L-dG) equations for low molar mass nematic liquid crystals and analysis based on the corresponding interfacial nematodynamic model. The early phase ordering stage, for both unstable and metastable quenches of the isotropic phase, is shown to lead to highly textured nematic spherulites through a mechanism of interfacial defect nucleation. The underlying mechanisms of interface-driven texturing are elucidated using complementary 2D computational parametric studies of the bulk L-dG equation and analysis of the IN model. It is shown that for highly curved nanodomains and realistic elastic anisotropy, sharp interfacial transitions between uniaxial and biaxial states arise and are resolved by interfacial defect nucleation, which upon subsequent migration into the spherulite's interior leads to strong texturing. This paper shows that texture formation in the early stages of phase ordering is interface driven, and due to low interface tension, elastic anisotropy, and large curvature. Interfacial defect shedding in highly curved, low tension, anisotropic interfaces is a significant defect nucleation mechanism that needs to be taken into account when considering texturing processes.     

Thermodynamics of soft anisotropic interfaces

The Gibbs-Duhem equation for interfaces between nematic liquid crystals and isotropic fluids is formulated and shown to be a generic equation for soft anisotropic surfaces. The one-to-one correspondence between the nematic and crystalline surface Gibbs-Duhem equations is established. Consistency between the surface Gibbs-Duhem equation and the classical equations of interfacial nematostatics is shown. Using a phase space that takes into account thermodynamics, liquid crystalline order, and geometric variables, the generalized nematic surface Gibbs-Duhem equation reveals the presence of couplings between shape, adsorption, temperature, and average molecular orientation. Merging the thermodynamic analysis with nematostatics results in a model for morphactancy, that is, adsorption-induced interfacial shape selection. The specific roles of gradient bulk Frank elasticity, interfacial tension, and anchoring energy are elucidated by analyzing particular paths in the thermodynamic-geometric phase space.     

Computational modelling of nematic phase ordering by film and droplet growth over heterogeneous substrates

This paper presents a computational study of defect nucleation associated with the kinetics of the isotropic‐to‐nematic phase ordering transition over heterogeneous substrates, as it occurs in new liquid crystal biosensor devices, based on the Landau–de Gennes model for rod‐like thermotropic nematic liquid crystals. Two regimes are identified due to interfacial tension inequalities: (i) nematic surface film nucleation and growth normal to the heterogeneous substrate, and (ii) nematic surface droplet nucleation and growth. The former, known as wetting regime, leads to interfacial defect shedding at the moving nematic‐isotropic interface. The latter droplet regime, involves a moving contact line, and exhibits two texturing mechanisms that also lead to interfacial defect shedding: (a) small and large contact angles of drops spreading over a heterogeneous substrate, and (b) small drops with large curvature growing over homogeneous patches of the substrate. The numerical results are consistent with qualitative defect nucleation models based on the kinematics of the isotropic–nematic interface and the substrate–nematic–isotropic contact line. The results extend current understanding of phase ordering over heterogeneous substrates by elucidating generic defect nucleation processes at moving interfaces and moving contact lines.     

Study of the surface and interfacial tensions in systems containing a low molar mass liquid crystal

The surface tension of a low molar mass liquid crystal (LMMLC), 4-cyano-4'-n-heptyloxybiphenyl (70CB), was measured as a function of temperature using the pendant drop method, forming drops of different volumes ranging from 5 to 11 mm³. Contact angles formed by drops of 70CB in the nematic and isotropic phases on plates of polystyrene (PS) and of a liquid crystal polymer (LCP), VECTRA A910, were also measured. Only large drops could be used for surface tension analysis. It was shown that in the nematic phase the surface tension of 70CB decreases with increasing temperature, and that in the isotropic phase the surface tension increases with increasing temperature. Using the values of contact angle and of surface tension of 7OCB it was possible to evaluate the interfacial energy between 7OCB and PS and between 7OCB and VECTRA. The interfacial energy between 7OCB and PS, and between 7OCB and VECTRA, decreased with increasing temperature for ranges of temperatures corresponding to both phases of 70CB.     

Influence of the anisometry of magnetic particles on the isotropic–nematic phase transition

The influence of the shape anisotropy of magnetic particles on the isotropic–nematic phase transition was studied in ferronematics based on the nematic liquid crystal (LC) 4-(trans-4-n-hexylcyclohexyl)-isothiocyanato-benzene (6CHBT). The LC was doped with spherical or rod-like magnetic particles of different size and volume concentrations. The phase transition from isotropic to nematic phase was observed by polarising microscope as well as by capacitance measurements. The influence of the concentration and the shape anisotropy of the magnetic particles on the isotropic–nematic phase transition in LC are demonstrated here. The results are in a good agreement with recent theoretical predictions.     

Computational modelling of nematic phase ordering by film and droplet growth over heterogeneous substrates

This paper presents a computational study of defect nucleation associated with the kinetics of the isotropic-to-nematic phase ordering transition over heterogeneous substrates, as it occurs in new liquid crystal biosensor devices, based on the Landau-de Gennes model for rod-like thermotropic nematic liquid crystals. Two regimes are identified due to interfacial tension inequalities: (i) nematic surface film nucleation and growth normal to the heterogeneous substrate, and (ii) nematic surface droplet nucleation and growth. The former, known as wetting regime, leads to interfacial defect shedding at the moving nematic-isotropic interface. The latter droplet regime, involves a moving contact line, and exhibits two texturing mechanisms that also lead to interfacial defect shedding: (a) small and large contact angles of drops spreading over a heterogeneous substrate, and (b) small drops with large curvature growing over homogeneous patches of the substrate. The numerical results are consistent with qualitative defect nucleation models based on the kinematics of the isotropic-nematic interface and the substrate-nematic-isotropic contact line. The results extend current understanding of phase ordering over heterogeneous substrates by elucidating generic defect nucleation processes at moving interfaces and moving contact lines.     

Surface tension of some liquid crystals in the cyanobiphenyl series

The temperature dependence of the surface tension was measured by the pendant drop method for four compounds from the homologous series of alkylcyanobiphenyls (nCB), in the nematic liquid crystal and isotropic phases. For 8CB (octylcyanobiphenyl) the temperature dependence was also measured in the smectic range. Not very close to the isotropic transition temperature, and with the exception of 8CB, the surface tension decreases with increase in temperature in the nematic range. A downward jump at the transition temperature was observed for all liquid crystals studied. The shape of the drop in the smectic A phase of 8CB gives indications of stratification in a system of terraces.     

Interplay between domain microstructure and nematic order in liquid crystalline/isotropic block copolymers

The domain microstructure and the nematic LC mesophase in a series of side-chain liquid crystalline/isotropic (LC/I) diblock copolymers with systematically varied block volume fractions were studied in a broad temperature range (25–170 °C) by DSC, polarized microscopy, and wide and small angle X-ray scattering. At all temperatures the block copolymers are microphase separated. The PSLC block copolymers exhibit order at two length-scales: on one hand, a nematic LC mesophase with characteristic length-scale of 0.43 nm (intermesogen distance); on the other hand, lamellar, hexagonal or cubic domain microstructures with characteristic length-scales of 27–44 nm (lattice parameter). The LC block was either located in the matrix or confined inside the microdomains. The thermotropic behavior is characterized by the sequence g/~35 °C/n/~115 °C/i and is not affected by the domain microstructure and/or dimensions. Analysis of the lamellar dimensions showed that the LC chain is stretched. With increasing temperature, a thermal expansion of both blocks takes place followed by a retraction of the LC chain above T_NI. The phase diagram is asymmetric and does not alter above T_NI. No order-to-order transitions triggered by the nematic-isotropic transition are observed. It was shown that domain microstructures of low interfacial curvature (lamellar and hexagonal) are energetically favored over the geometrically expected ones of high interfacial curvature (micellar cubic) due to the presence of nematic LC mesophase in the matrix or in the microdomains. By comparison to theory a Kuhn segment length of the LC block b_LC=0.86 nm was derived from the location of the lamellar/hexagonal phase boundaries.This paper is dedicated to Prof. Fischer on the occasion of his 75th birthday.     

Phase transitions in mixtures of a side-on-side chain liquid crystalline polymer and low molar mass nematic liquid crystals

Miscibility phase diagrams of mixtures of side-on side chain liquid crystalline polymers (s-SCLCP) and low molar mass liquid crystals (E48 and E44) have been established by means of polarized optical microscopy and light scattering. E48 and E44 are cyanobiphenyl-based eutectic nematic liquid crystal (LC) mixtures with nematic-isotropic transition temperatures of 93 and 105 C, respectively. The phase diagram of the s-SCLCP/E48 system reveals the coexistence of an isotropic nematic region and a single nematic phase in order of descending temperature. The single nematic phase suggests that the pair is miscible in the nematic region. On the other hand, the s-SCLCP/E44 mixture shows liquid liquid and nematic nematic coexistence phases, suggestive of the immiscibility character of the pair. These nematic phase diagrams of the s-SCLCP/E48 and s-SCLCP/E44 have been analysed in the context of the combined Flory-Huggins (FH) free energy for isotropic mixing and the Maier-Saupe (MS) free energy for nematic ordering of the mesogens. This combined FH/MS theory is capable of predicting the observed nematic phase diagrams consisting of liquid liquid, liquid nematic, nematic nematic, and the pure nematic regions. The change of colour accompanying the appearance and disappearance of the inversion walls may be attributed to the temperature dependence of birefringence.     

Study of the surface and interfacial tensions in systems containing a low molar mass liquid crystal

The surface tension of a low molar mass liquid crystal (LMMLC), 4-cyano-4'-n-heptyloxybiphenyl (70CB), was measured as a function of temperature using the pendant drop method, forming drops of different volumes ranging from 5 to 11 mm³. Contact angles formed by drops of 70CB in the nematic and isotropic phases on plates of polystyrene (PS) and of a liquid crystal polymer (LCP), VECTRA A910, were also measured. Only large drops could be used for surface tension analysis. It was shown that in the nematic phase the surface tension of 70CB decreases with increasing temperature, and that in the isotropic phase the surface tension increases with increasing temperature. Using the values of contact angle and of surface tension of 7OCB it was possible to evaluate the interfacial energy between 7OCB and PS and between 7OCB and VECTRA. The interfacial energy between 7OCB and PS, and between 7OCB and VECTRA, decreased with increasing temperature for ranges of temperatures corresponding to both phases of 70CB.     

Loading effect on swelling of nematic elastomers

Externally imposed loading has substantially different effects on the swelling of nematic elastomers in the high-temperature isotropic and low-temperature nematic states. In the isotropic state, the stretching drives a considerably large degree of further swelling, whereas the stretching-induced volume change in the nematic state is significantly suppressed. In the isotropic phase that favors the less anisotropic state, the further swelling occurs to reduce the shape anisotropy caused by the imposed elongation. In the nematic phase, no significant swelling is induced because further swelling decreases the nematic order enhanced by the applied stretching. These different loading effects in the isotropic and nematic states observed in the experiments are qualitatively described by a mean field theory.     

Investigation of the nematic-isotropic transition of a liquid crystalline polymer and determination of molecular diffusion coefficients using gas chromatography

Inverse gas chromatography has been used to study the nematic-isotropic transition of a side chain liquid crystalline polymer (LCP). The mesogenic side groups are laterally attached to a polysiloxane backbone through a flexible spacer. The nematic-isotropic transition of this LCP coated onto a glass capillary column is detected by considering the variation with temperature of the retention volume and of the theoretical plate number for the several probes. The molecular diffusion coefficients, D, of naphthalene, fluorene, pyrene and o-terphenyl have been determined at different temperatures in the nematic phase of the LCP as well as in the isotropic melt. The values ranged between 10(-14) and 10(-12) m2 s(-1) for the polynuclear aromatic hydrocarbon probes tested.     

Theory of the Nematic-Isotropic Transition in a Restricted Geometry

We discuss, using a Landaude Gennes formalism, the nematic-isotropic transition temperature for a system placed between two parallel plates, subject to identical homeotropic or homogeneous boundary conditions at each plate. The temperature at the phase transition may increase or decrease as the inverse sample thickness, D^-1, increases, depending on the nature of the boundary conditions. In all cases the transition terminates at a critical point for sufficiently large D^-1, beyond which the nematic and isotropic phases are no longer distinct. The phase transition temperature is well described by a liquid crystal analogy of the Kelvin equation which can be generalized to give an exact Clausius-Clapeyron relation. Under many circumstances the system behaves from a thermodynamic point of view as though it were in a bulk ordering field. The finite geometry restricts the growth of nematic or isotropic wetting films. We discuss the disjoining pressure experiment of Horn, Israelachvili and Perez [15]. Finally we place our work in the context of recent progress in the statistical mechanics of surfaces and systems in restricted geometries.     

Shape of the nematic-isotropic interface in conditions of partial wetting

A nematic liquid crystal in contact with a solid substrate is studied in the partial wetting regime. Both a mesoscopic Landau-de Gennes theory and a macroscopic effective interface Hamiltonian approach are considered. A generalized Young equation for the balance of forces at the three-phase contact line is derived, which takes into account corrections due to distortions of the nematic director field. It is also shown that the asymptotic form of the separation of the nematic-isotropic interface from the substrate has a logarithmic correction to the usual linear behaviour. The characteristic length scale of this correction is given by the ratio K/(2σ_NI), where K and σ_NI are the average elastic constant and the nematic-isotropic surface tension, respectively, and is of the order of a few hundred angstroms. Then, a simple form of an effective interface Hamiltonian is proposed, and results consistent with the predictions of the Landau-de Gennes theory are obtained. It is shown, in the framework of this macroscopic approach, that the line tension associated with the contact line remains finite, when the thermodynamic limit is taken, if the anchoring at both the nematic-substrate and the nematic-isotropic interfaces is homeotropic. However, in the case of different anchoring directions, the line tension diverges logarithmically with the system size.     

Surface tension of some liquid crystals in the cyanobiphenyl series

The temperature dependence of the surface tension was measured by the pendant drop method for four compounds from the homologous series of alkylcyanobiphenyls (nCB), in the nematic liquid crystal and isotropic phases. For 8CB (octylcyanobiphenyl) the temperature dependence was also measured in the smectic range. Not very close to the isotropic transition temperature, and with the exception of 8CB, the surface tension decreases with increase in temperature in the nematic range. A downward jump at the transition temperature was observed for all liquid crystals studied. The shape of the drop in the smectic A phase of 8CB gives indications of stratification in a system of terraces.     

On the conformational effects of intermolecular interactions in nematics

A perturbation expansion of the pair correlation function is used to derive the molecular field self-consistency equations for non-rigid molecules. The order parameters and the thermodynamic functions are expressed directly in terms of the segmental interaction coupling constants. The values of these constants for the 4-n-alkyl-4'-cyanobiphenyis (NCB) are determined by analysing the orientational order parameters observed by N.M.R. in the nematic phase; they are in reasonable agreement with values obtained from calculations of the nematic-isotropic transition temperatures. It is found that contributions of the isotropic intermolecular interactions to the conformational energy of the alkyl chain are comparable in magnitude to the direct intramolecular contributions.     

H-shaped liquid crystals inducing nematic order in the isotropic liquid

ABSTRACT

We prepared a homologous series of H-shaped liquid crystals I-n and investigated their phase transition properties using optical microscopy and differential scanning calorimetry. All the compounds exhibited a nematic phase at room temperature. The phase transition behaviour is explained in terms of molecular shape anisotropy. Furthermore, those compounds were found to exhibit electro-optical switching in the isotropic liquid in the vicinity of the nematic–isotropic liquid transition, indicating that the microscopic nematic order with a certain coherence length of the molecules exists in the optically isotropic temperature range.     

Magnetic field effects on tactoids of plate-like colloids

We investigate the effect of a magnetic field on the shape and director field of nematic droplets in dispersions of sterically stabilized and charge-stabilized colloidal gibbsite platelets with a negative diamagnetic anisotropy. Depending on the magnetic field strength and tactoid size, we observe with polarized light microscopy several interesting structures, with different shapes and director fields both with and without defects. In particular, our findings provide the first experimental evidence for the existence of the split-core defect structure predicted ten years ago by Mkaddem and Gartland [Phys. Rev. E 62, 6694 (2000)]. The split-core structure is a metastable director-field configuration that can be stabilized by a sufficiently strong externally applied magnetic field but only if the diamagnetic anisotropy of the particles is negative. To account for our observations, we present a calculation of the stability regions of different shapes and director-field structures as a function of tactoid size, anchoring conditions, surface tension, elastic constants, and magnetic field strength. By fitting the experimental data to the theoretically predicted structures, we are able to extract values for the splay elastic constant, interfacial tension, and anchoring strength. Remarkably, we find significant differences between the two systems studied: for sterically stabilized gibbsite in bromotoluene the anchoring strength is one order of magnitude larger than that of aqueous gibbsite, with the latter exhibiting weak and the former strong anchoring of the director field to the interface. The splay elastic constants that we obtain are in agreement with earlier experiments, simulations, and theory, while the interfacial tension and anchoring strength are considerably larger than what was found in earlier experiments.