Nematic Coexistence Research Articles

Phase diagram of a rigid rod system with attractive end groups

We present a molecular dynamics study into the thermotropic liquid crystalline phase behaviour of a coarse-grained model of a rigid bolaamphiphilic molecule. The model consists of 11 spherical beads held in a fixed linear arrangement, where the two opposing terminal beads are self-attracting, mimicking hydrophilic segments and the remaining internal beads, as well as cross-bead interactions, are softly repulsive, mimicking hydrophobic organic segments. The effect of the model’s end bead self-attraction strength on liquid crystalline phase behaviour is studied. Coexistence points between the smectic A, nematic and isotropic phases exhibited by the model are determined following a thermodynamic integration pathway, using equations of state constructed by multiple histogram reweighting of simulation data. Variants of Gibbs–Duhem integration are used to trace pressure–temperature coexistence curves. Under isobaric conditions, the effect of increasing the end-group self-attraction on the nematic–isotropic coexistence temperature is relatively small; however, the nematic phase stability is reduced at the expense of a significant increase in the smectic A–nematic coexistence temperature. Lower temperature simulations show the approximate smectic A–crystalline transition temperature to be only weakly dependent on the strength of the end-group self-attraction.

Nanodrops of Discotic Liquid Crystals: A Monte Carlo Study.

We study the morphologies of nematic nanodrops in a vapor of a discotic nematogen by Monte Carlo simulations. The fluid interactions are modeled by a Gay-Berne model with molecular elongations of κ = 0.3 and 0.5 and different values of the energy anisotropy parameter κ' in the range of temperature T in which the nematic coexists with a vapor phase. We considered nanodrops of N = 4000 and 32 000 particles. For κ > κ', we observe that nanodrops are quite spherical (even for N = 4000 nanodrops), with a homogeneous director field for κ = 0.3 and a bipolar nematic configuration with tangential anchoring for κ = 0.5. By increasing the value of κ', nanodrops change from spherical to lens-shaped for κ = 0.3, and for κ = 0.5, spherical nanodrops with homeotropic anchoring and a disclination ring located on its equatorial plane are observed. Although no radial nanodrops are observed, isotropic liquid nanodrops with a paranematic shell and radial texture are observed for temperatures slightly above the vapor-isotropic-nematic triple point when the vapor-isotropic interface is completely wet by the nematic phase.

Freeze-Thaw Cycling Induced Isotropic-Nematic Coexistence of Amyloid Fibrils Suspensions.

Amyloid fibrils are charged semiflexible assemblies with very large aspect ratio (length to diameter, L/D). Because of this large aspect ratio, the isotropic (I) and nematic (N) phase coexistence expected from the first-order thermodynamic nature of the I-N phase transition, as predicted from the Onsager's theory, is vanishingly small and, in practice, challenging to experimentally observe. In this study we present a remarkable widening of the I + N biphasic region in β-lactoglobulin fibrils suspension via freeze-thaw (F-T) cycling. The demixing behavior can be induced and controlled by a slow growth of propagation front of the ice crystals, which grow by excluding the amyloid fibrils from the crystal phase and thus concentrating them in the liquid phase. The growth of the ice crystals is accompanied by the formation of concentrated and elongated tactoid-like structure in the liquid phase. During the subsequent thawing cycling, at large tactoid domains, the mismatch in density caused by the presence of amyloid fibrils is sufficient to generate a sedimentation of the N phase at the bottom of the vial, coexisting with an I phase on the top. We reason why, despite the remarkable stability of the coexisting I and N phases observed over several weeks after F-T cycling, the biphasic region is understood to be a nonequilibrium, metastable state. Yet, the results in this study suggest that the F-T treatment is an effective approach to stabilize multiphase coexistence of liquid crystalline phases in colloidal suspensions of anisotropic particles without the need of additives, such as depleting agents, needed to modify interaction potentials.

Multiphase coexistence in mixed suspensions of large and small hard platelets

The phase behaviour of mixed suspensions of large and small hard platelets is treated by osmotic equilibrium theory. Depending on the size ratios of the small and large platelets, three distinct phase behaviour scenarios appear: isotropic–isotropic–nematic, isotropic–nematic and isotropic–nematic–nematic coexistence regions, in agreement with computer simulations. The experimental multiphase coexistence observed in mixed suspensions of large Titanate platelets and small Laponite platelets can be reproduced semi-quantitatively using osmotic equilibrium theory calculations.

Glass transition of repulsive charged rods (fd-viruses)

It has recently been shown that suspensions of long and thin charged fibrous viruses (fd) form a glass at low ionic strengths. The corresponding thick electric double layers give rise to long-ranged repulsive electrostatic interactions, which lead to caging and structural arrest at concentrations far above the isotropic-nematic coexistence region. Structural arrest and freezing of the orientational texture are found to occur at the same concentration. In addition, various types of orientational textures are equilibrated below the glass transition concentration, ranging from a chiral-nematic texture with a large pitch (of about 100 μm), an X-pattern, and a tightly packed domain texture, consisting of helical domains with a relatively small pitch (of about 10 μm) and twisted boundaries. The dynamics of both particles as well as the texture are discussed, below and above the glass transition. Dynamic light scattering correlation functions exhibit two dynamical modes, where the slow mode is attributed to the elasticity of helical domains. On approach of the glass-transition concentration, the slow mode increases in amplitude, while as the amplitudes of the fast and slow mode become equal at the glass transition. Finally, interesting features of the "transient" behaviors of charged fd-rod glass are shown as the initial caging due to structural arrest, the propagation of flow originating from stress release, and the transition to the final metastable glass state. In addition to the intensity correlation function, power spectra are presented as a function of the waiting time, at the zero-frequency limit that may access to the thermal anomalities in a charged system.

Non-equilibrium nature of two-dimensional isotropic and nematic coexistence in amyloid fibrils at liquid interfaces

Two-dimensional alignment of shape-anisotropic colloids is ubiquitous in nature, ranging from interfacial virus assembly to amyloid plaque formation. The principles governing two-dimensional self-assembly have therefore long been studied, both theoretically and experimentally, leading, however, to diverging fundamental interpretations on the nature of the two-dimensional isotropic-nematic phase transition. Here we employ single-molecule atomic force microscopy, cryogenic scanning electron microscopy and passive probe particle tracking to study the adsorption and liquid crystalline ordering of semiflexible β-lactoglobulin fibrils at liquid interfaces. Fibrillar rigidity changes on increasing interfacial density, with a maximum caused by alignment and a subsequent decrease stemming from crowding and domain bending. Coexistence of nematic and isotropic regions is resolved and quantified by a length scale-dependent order parameter S(2D)(d). The nematic surface fraction increases with interfacial fibril density, but depends, for a fixed interfacial density, on the initial bulk concentration, ascribing the observed two-dimensional isotropic-nematic coexistence to non-equilibrium phenomena.

Structural arrest and texture dynamics in suspensions of charged colloidal rods

There is an abundance of experiments and theories on the glass transition of colloidal systems consisting of spherical particles. Much less is known about possible glass transitions in suspensions of rod-like colloids. In this study we present observations of a glass transition in suspensions of very long and thin rod-like, highly charged colloids. We use as a model system fd-virus particles (a DNA strand covered with coat proteins) at low ionic strength, where thick electric double layers are present. Structural arrest as a result of particle-caging is observed by means of dynamic light scattering. The glass-transition concentration is found to be far above the isotropic–nematic coexistence region. The morphology of the system thus consists of nematic domains with different orientations. Below the glass-transition concentration the initial morphology with large shear-aligned domains breaks up into smaller domains, and equilibrates after typically 50–100 hours. We quantify the dynamics of the transitional and the equilibrated texture by means of image time-correlation. A sharp increase of relaxation times of image time-correlation functions is found at the glass-transition concentration. The texture dynamics thus freezes at the same concentration where structural arrest occurs. We also observe a flow instability, which sets in after very long waiting times (typically 200–300 hours), depending on the rod concentration, which affects the texture morphology.

Non-linear dielectric behaviour of 4,4′-n-hexylcyanobiphenyl near the nematic–isotropic phase transition

The non-linear dielectric spectra of 4,4′-n-hexylcyanobiphenyl (6CB) were recorded in the frequency range 1–100 MHz in the presence of a strong static electric field E 0 = 1 × 107 V/m. The measurements were performed in the isotropic phase and the isotropic and nematic coexistence temperature region. Two absorption bands, related to intermolecular interactions (chemical bands), were observed in the non-linear dielectric relaxation spectra. The dynamic phenomena of the band which appears in the frequency region below 10 MHz in the vicinity of the phase transition between the isotropic and nematic phases were interpreted within the framework of the Landau–de Gennes theory for weakly first-order phase transitions. The second effect, with relaxation times 2–20 ns (about one order of magnitude lower, as in a process where the molecules are involved in pseudonematic domains), is expected to characterise the interaction processes of individual molecules.

Phase behaviour of binary mixtures of diamagnetic colloidal platelets in an externalmagnetic field

Using fundamental measure density functional theory we investigate paranematic–nematic andnematic–nematic phase coexistence in binary mixtures of circular platelets with vanishingthicknesses. An external magnetic field induces uniaxial alignment and acts on the plateletswith a strength that is taken to scale with the platelet area. At particle diameter ratioλ = 1.5 the system displays paranematic–nematic coexistence. Forλ = 2, demixing into two nematic states with different compositions also occurs, between anupper critical point and a paranematic–nematic–nematic triple point. Increasing thefield strength leads to shrinking of the coexistence regions. At high enough fieldstrength a closed loop of immiscibility is induced and phase coexistence vanishes ata double critical point above which the system is homogeneously nematic. Forλ = 2.5, besides paranematic–nematic coexistence, there is nematic–nematic coexistence whichpersists and hence does not end in a critical point. The partial orientational orderparameters along the binodals vary strongly with composition and connect smoothly foreach species when closed loops of immiscibility are present in the corresponding phasediagram.

Arrested phase separation of colloidal rod–sphere mixtures

Sterically stabilised colloidal rod–sphere mixtures were prepared by mixing sepiolite rods of an average length L = 860 nm and aspect ratio L/D = 40 with silica spheres of average diameter d = 620 nm. Whereas most previous studies have addressed low or high L/d ratios, the present study has an intermediate ratio of 1.4. Samples were studied at rod concentrations from 3 to 9 wt%, in the isotropic–nematic coexistence region. No dramatic effects were seen on adding spheres, except for two samples at low rod concentrations where a rapid (local) phase separation resulted. This is ascribed to formation of nematic tactoids, separated by layers of spheres. Samples at higher rod concentrations did not show any rapid phase separation. Microscopy using fluorescent rods however showed a fine network of rods formed in this case. Macroscopic phase separation into sphere-rich and rod-rich phases was not observed in any sample, nor was any rapid clustering of spheres as seen previously in mixtures with L/d = 0.3. The late stage sediment density can be described well by approximating the osmotic pressure of the colloidal rods at second virial level. Whilst the absence of macroscopic phase separation suggests that these mixtures do not reach chemical equilibrium and instead remain stuck in a range of long-lived metastable states, the observations on the sediment density show that nevertheless local mechanical equilibrium is attained.

Advances in generalised van der Waals approaches for the isotropic–nematic fluid phase equilibria of thermotropic liquid crystals–an algebraic equation of state for attractive anisotropic particles with the Onsager trial function

In this contribution we provide a review and reformulation of perturbation theories (generalised van der Waals approaches) for the description of the fluid phase behaviour and orientational ordering transitions of thermotropic nematic liquid crystals. Free-energy functionals of the basic Onsager form are used as the platform for the development of a general formulation that reduces to the specific forms of the various theories that have found common use. A novel closed analytical description of the thermodynamic properties and degree of nematic order is then obtained by employing the Onsager trial function to represent the orientational distribution function in terms of a single parameter. The latter essentially constitutes an algebraic equation of state for the nematic phase appropriate for use in engineering applications. The description of ordering transitions with scaled-Onsager theories and suitable trial functions has already been illustrated by its application to systems of hard spherocylinders (HSCs), indicating that the approach provides an excellent representation of the orientational order of the hard-core (athermal) system [Mol. Phys. 106, 649 (2008)]. Here, the hard-body model is extended to account for attractive interactions (treated at the van der Waals level) of a general isotropic/anisotropic form (e.g., Lennard-Jonesium (LJ), square-well (SW), Maier–Saupe (MS), etc.). The adequacy of our generalised van der Waals–Onsager theory is exemplified by an analysis of the vapour–liquid, liquid–nematic, and vapour–nematic phase equilibria for hard spherocylinders with attractive square-well interactions (HSC-SW). The effect of the potential range and molecular aspect ratio on the vapour–liquid–nematic equilibria and orientational ordering transitions is examined to investigate the van der Waals limit (corresponding states) of the ordering phase behaviour. In the case of systems with an aspect ratio of ∼5 the corresponding-states limit is reached when the range is about 16 times the molecular diameter. For progressively longer molecules with an attractive range that follows their long dimension, the fluid–nematic equilibrium is enhanced to the point that the vapour–liquid boundary becomes metastable relative to fluid–nematic equilibria. In the case of molecules of very large aspect ratio (∼50), an additional region of nematic–nematic coexistence is exhibited by the system.

Partitioning of charged and neutral dextran-dye derivatives in biphasic cellulose nanocrystal suspensions

The partitioning behaviour of dye-labeled dextrans of high molecular weight in aqueous suspensions of native cellulose nanocrystals was studied. Cellulose concentrations lie in the isotropic–nematic coexistence region. Blue dextrans of various molecular weights and degrees of substitution of dye molecules (anionic Cibacron blue 3G-A) were investigated. Increasing the total concentration of blue dextran and degree of dye substitution led to increasing partition coefficients. Increasing dextran molecular weight resulted in higher partition coefficients, in agreement with theory. Partition coefficients were larger than predicted theoretically using a second virial coefficient approximation. Electrostatic and entropic contributions to the partition coefficient of blue dextran are discussed. Dextrans labeled with neutral fluorescein isothiocyanate did not partition preferentially in this system.Key words: partition coefficient, cellulose nanocrystals, dextrans, degree of substitution, polyelectrolyte.

Control over phase behavior and solution structure of hairy-rod polyfluorene by means of side-chain length and branching

We present guidelines on how the solution structure of pi -conjugated hairy-rod polyfluorenes is controlled by the side-chain length and branching. First, the semiquantitative mean-field theory is formulated to predict the phase behavior of the system as a function of side-chain beads (N). The phase transition at N=N{ *} separates a lyotropic phase with solvent coexistence (N<N{ *}) and a metastable membrane phase (N>N{ *}). The membrane phase transforms into the isotropic phase of dissolved rodlike polymers at the temperature T_{mem}{ *}(N), which decreases both with N and with the degree of side-chain branching. This picture is complemented by polymer demixing with the transition temperature T_{IN}{ *}(N), which decreases with N . For N<N{ *}, the lyotropic phase turns isotropic with increasing T at T_{IN}{ *} . For N>N{ *}, stable membranes are predicted for T_{IN}{ *}<T<T_{mem}{ *} and metastable membranes with nematic coexistence for T<T_{IN}{ *}. Second, in experiment, samples of poly(9,9-dialkylfluorene) with N=6-10 were mixed in methylcyclohexane. For N=8 the side-chain branching was controlled by (9,9-dioctylfluorene)/(9,9-bis(2-ethylhexyl)fluorene) (F8/F2/6) random copolymers. The proportion of F8 to F2/6 repeat units was 100:0, 95:5, 90:10, 50:50, and 0:100. In accordance with the theory, lyotropic, membrane, and isotropic phases with the corresponding phase transitions were observed. For N<N{ *} approximately 6 only the lyotropic phase is present for attainable temperatures. The membrane and isotropic phases are present for N>N{ *}. T_{mem}{ *}(N) decreases from 340 K to 280 K for N > or = 8 . For copolymers, the membrane phase is found when the fraction of F8 units is at least 90%, T_{mem}{ *} decreasing with this fraction. The membrane phase contains three material types: loose sheets of two polymer layers, a better packed beta phase, and dissolved polymer. For N > or = 7 and T<T_{mem}{ *} the tendency for membrane formation becomes stronger with increasing temperature.

Kinetics of photopolymerization-induced phase separation and morphology development in mixtures of a nematic liquid crystal and multifunctional acrylate

Photopolymerization behavior and reaction kinetics for a series of multifunctional acrylate monomer(s) and eutectic liquid crystal blends were investigated with particular emphasis on determination of the reaction rate coefficients for propagation and termination steps of photopolymerization. Reaction rate coefficients were determined via real-time infrared spectroscopy and compared with those obtained by photo-differential scanning calorimetry. Effects of various parameters such as LC concentration, light intensity, and monomer functionality on the kinetics were investigated. Phase transition temperature versus composition phase diagrams were established by means of optical microscopy and differential scanning calorimetry for mixtures of triacrylate/liquid crystal (LC) before photopolymerization and after exposing to ultra violet (UV) irradiation under various reaction times. The snapshot phase diagram of the reacting mixtures exhibited isotropic gel, isotropic liquid+nematic, and narrow pure nematic coexistence regions. These coexistence regions were further confirmed by morphological changes of the polymer dispersed liquid crystal films as functions of temperature and concentration using polarized optical microscopy.

Capillary nematization of hard colloidal platelets confined between two parallel hardwalls

We use density functional theory to study the capillary phase behaviour of a discoticsystem of colloidal platelets that are confined in a planar slit pore. The model plates havecircular shape, continuous orientations and vanishing thickness; they interact via hard-corerepulsion with each other and with the walls which induces homeotropic wall anchoring ofthe nematic director. We find that the isotropic–nematic capillary binodal is shifted tolower values of the chemical potential as compared to bulk isotropic–nematic coexistence.Capillary isotropic–nematic coexistence vanishes below a critical wall separationdistance which is significantly larger than it is in a reference system of thin hard(Onsager) rods confined between two parallel hard walls that act on the particlecentres.

Phase behavior of symmetric rod–plate mixtures revisited: Biaxiality versus demixing

The phase behavior of symmetric binary rod–plate mixtures has been investigated by numerical minimization of a free energy functional derived by Parsons [J. D. Parsons, Phys. Rev. A 19, 1225 (1979)] and Lee [S. D. Lee, J. Chem. Phys. 87, 4972 (1987)]. Both rod and plate molecules are represented by hard cylinders, with aspect ratios chosen so that the molecular and pair excluded volumes are equal; in this way symmetric phase diagrams in composition are found. The subtle competition between the packing entropy and the entropy of mixing rules out the possibility of a uniaxial nematic–biaxial nematic phase transition and instead favors a demixing phase transition between a rod-rich and a plate-rich nematic phase. It is shown that the biaxial nematic phase is unstable relative to demixing even for symmetric mixtures of very long rod and very flat plates, where the Parsons–Lee theory becomes identical with the Onsager theory. The contradictory predictions obtained in recent studies regarding the stability of the biaxial nematic phase have been resolved by examining the lowest aspect ratio of the rods (κ2) where the Parsons–Lee and Onsager theories become equivalent. It turns out that neglecting the lower order terms in the excluded volumes (so-called end effects) leads to a favoring of the biaxial nematic phases. Only two types of phase transitions are observed in this work: isotropic–nematic phase coexistence and demixing transitions involving either two isotropic or two nematic phases. The stability of the nematic region on mixing is found to be very sensitive to the aspect ratios of the molecules: for moderate aspect ratios of the rods (5&amp;lt;κ2&amp;lt;10), a destabilization of the nematic phase is observed relative to the isotropic phase, while for κ2&amp;gt;10 the opposite tendency is found. A demixing transition between rod-rich and plate-rich nematic phases takes place for all of the systems studied with a widening coexistence region for increasing aspect ratio. Isotropic–isotropic demixing is also observed for aspect ratios κ2&amp;gt;65.5. For the larger values of κ2 the regions of isotropic–isotropic and nematic–nematic demixing broaden, while the isotropic–nematic coexistence is progressively suppressed.

Phase behavior, photopolymerization, and morphology development in mixtures of eutectic nematic liquid crystal and photocurable monomer

Phase behavior and photopolymerization-induced morphology development in mixtures of eutectic nematic liquid crystals (LC) (designated E44) and photocurative monomers (designated NOA65) have been investigated by means of optical microscopy and light scattering. The observed phase diagram of the E44/NOA65 system prior to photopolymerization is of an upper critical solution temperature (UCST) type overlapping with the nematic–isotropic transition of E44. It displayed isotropic liquid, isotropic liquid+isotropic liquid, isotropic liquid+nematic, and pure nematic coexistence regions that were verified experimentally. Using the phase diagram as a guide, photopolymerization-induced phase separation experiments were performed in the isotropic region in order to examine the morphology development in multicomponent LC (E44)-based system in comparison with that of a single component LC (K21)-based system. Of particular interest is that the emerging LC droplets turned out to be unevenly distributed in the E44/NOA65 system as opposed to the K21/NOA65 system where the droplet size was uniform. The non-uniform distribution of the droplets in the E44/NOA65 system may be attributed to compositional fractionation associated with different affinities of the constituent LC in E44 to the NOA65 networks.

Morphology Development and Dynamics of Photopolymerization-Induced Phase Separation in Mixtures of a Nematic Liquid Crystal and Photocuratives

Dynamics of photopolymerization-induced phase separation (PIPS) and morphology development in mixtures of low molar mass nematic liquid crystal (LC) 4-n-heptyl-4‘-cyanobiphenyl (designated K21) and photocuratives (designated NOA65) have been investigated by means of optical microscopy, light scattering, and differential scanning calorimetry. The equilibrium phase diagram of the LC/monomer (uncured NOA65) system was first established theoretically on the basis of the Flory−Huggins/Maier−Saupe theory. The calculated phase diagram displayed isotropic, liquid + liquid, liquid + nematic, and pure nematic coexistence regions in conformity with experiment. The effect of photopolymerization on the phase diagram was examined through comparison of the calculated phase diagrams of LC/linear polymer with LC/cross-linked polymer mixtures. Photopolymerization of the LC/monomer mixtures resulted in phase separation due to instability caused by an increase in molecular weight and subsequent network formation. Photopolymerization initiated in the isotropic phase gave uniformly distributed polygonal-shaped LC droplets in contrast to photopolymerization initiated in the two-phase region. Of particular interest is that the size of the phase-separated LC droplet increases with LC concentration. The network morphology is reminiscent of an interconnected thread seemingly running through the interstices of the polygonal droplets. Temporal evolution of structure factors was analyzed in the context of dynamical scaling law.

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.

Phase Diagram and Photopolymerization Behavior of Mixtures of UV-Curable Multifunctional Monomer and Low Molar Mass Nematic Liquid Crystal

A miscibility phase diagram of mixtures of UV-curable multifunctional thiolene-based optical adhesive (NOA65) and low molar mass 4-n-heptyl-4-cyanobiphenyl nematic liquid crystal (K21) has been established using light scattering, optical microscopy, and differential scanning calorimetry. The emergence of phase morphology was investigated during the heating and cooling cycles to identify various coexistence regions. A teapot phase diagram was obtained in which an upper critical solution temperature (UCST) overlapped with the nematic−isotropic transition of the liquid crystal. The phase diagram exhibited liquid + liquid, liquid + nematic, and pure nematic coexistence regions. Photopolymerization was carried out on various mixtures of NOA65 and K21 to fabricate polymer/liquid crystal composites by initiation in the one-phase and two-phase regions of the phase diagram. The rate constants for propagation and termination reactions (kp and kt) were determined as functions of temperature and conversion. On the ba...