Modelling the chemically induced liquid crystalline phases in mixtures of disc-shaped mesogens: the phase diagram of quadrupolar Gay-Berne discs revisited

We investigate the phase behaviour of pure systems and mixtures of quadrupolar Gay-Berne discs. The interaction potential mimics that of disc-shaped molecules which exhibit chemically induced phases with a structure based on columns of alternately stacking species. The phase diagram of the pure system is determined over a range of pressures, and the phase sequence is shown to include tilted columnar and nematic phases. The mixtures, in which the species have equal but opposite quadrupole moments, are investigated over a range of pressures using semigrand canonical simulations, such that the composition of the system is allowed to change. The fact that the composition is not fixed is especially important at the phase transitions, where the compositions of the coexisting phases may not necessarily be the same. In this situation, preparation of a system in the ‘biphasic region’ will lead to phase separation into the two distinct phases of differing compositions. The resulting phase diagram obtained using semigrand canonical simulations indicates that the columnar nematic phase observed in previous fixed composition simulations of this model [Liq. Cryst.,24, 229 (1998)] is not stable with respect to phase separation into an isotropic phase rich in a single component and a hexagonal columnar phase composed of roughly equal quantities of the two components. The structure of the columnar phase for the mixture is shown to be based on the alternate stacking of the different species. The relative concentrations of the different species in this phase may deviate up to approximately 60 : 40 mol%, after which any further material added will separate into the pure isotropic state.     

Atomistic simulations of liquid crystal mixtures of alkoxy substituted phenylpyrimidines 2PhP and PhP14

We study liquid crystal mixtures of alkoxy substituted phenylpyrimidines 2-[4-(butyloxy)phenyl]-5-(octyloxy)pyrimidine (2PhP) and 2-[4-(tetradecyloxy)phenyl]-5-(tetradecyloxy)pyrimidine (PhP14) using molecular dynamics simulations at the all atom level. The molecular length of PhP14 is 1.8 times that of 2PhP, resulting in an interesting binary mixture phase diagram. Our simulations are composed of 1000-1600 molecules for a total of 80,000-130,000 atomic sites, with total simulation times of 60-100 ns. We first show that a pure 2PhP system self-assembles into isotropic, nematic, smectic A and smectic C phases, and a pure PhP14 system self-assembles into isotropic and smectic C phases. Binary mixtures of PhP14 and 2PhP display a stabilization of the smectic A phase at the expense of the smectic C and nematic phases. We determine that the concentration-induced phase transition from the smectic C to the smectic A phase in the mixture is driven by an out-of-layer fluctuation arrangement of the molecules. We also observe that the tilt angle in the smectic C phases formed in the mixtures is concentration dependent. The results of our simulations are in good agreement with the experimental findings of Kapernaum et al. [J. Org. Chem. 5, 65 (2009)], thus showing that atomistic simulations are capable of reproducing the phase behavior of liquid crystal mixtures and can also provide microscopic details regarding the mechanisms that govern phase stability.     

Phase equilibrium of poly(n-butyl acrylate) and E7

The experimental equilibrium phase diagram of mixtures of linear poly(n-butyl acrylate) of molecular mass M_w = 112000 g mol^-1 and the low molecular mass LC mixture E7 has been established using polarized optical microscopy and light scattering techniques. The diagram is found to be reminiscent of an upper critical solution temperature system. Two independent series of samples with the same composition were studied, yielding consistent results. A region of nematic and isotropic coexisting phases and a region of a single isotropic phase were identified in the composition-temperature phase diagram. The results were analysed within a theoretical model combining the Flory-Huggins lattice theory for isotropic mixing and the Maier-Saupe theory for nematic ordering. Interestingly, no region of isotropic coexisting phases was observed in our experiments. This is probably due to the fact that the nematic interaction overwhelms the isotropic interaction in the region where (I + I) coexisting phases could appear. A preferential solubility of certain constituents of the LC mixture in the polymer could possibly be a reason for this behaviour.     

Mesophase formation in a system of top-shaped hard molecules: density functional theory and Monte Carlo simulation

We present the phase diagram of a system of mesogenic top-shaped molecules based on the Parsons-Lee density functional theory and Monte Carlo simulation. The molecules are modeled as a hard spherocylinder with a hard sphere embedded in its center. The stability of five different phases is studied, namely, isotropic, nematic, smectic A, smectic C, and columnar phases. The positionally ordered phases are investigated only for the case of parallel alignment. It is found that the central spherical unit destabilizes the nematic with respect to the isotropic phase, while increasing the length of the cylinder has the opposite effect. Also, the central hard sphere has a strong destabilizing effect on the smectic A phase, due the inefficient packing of the molecules into layers. For large hard sphere units the smectic A phase is completely replaced by a smectic C structure. The columnar phase is first stabilized with increasing diameter of the central unit, but for very large hard sphere units it becomes less stable again. The density functional results are in good agreement with the simulations.     

Phase equilibrium of poly(n-butyl acrylate) and E7

The experimental equilibrium phase diagram of mixtures of linear poly(n-butyl acrylate) of molecular mass M_w = 112000 g mol^-1 and the low molecular mass LC mixture E7 has been established using polarized optical microscopy and light scattering techniques. The diagram is found to be reminiscent of an upper critical solution temperature system. Two independent series of samples with the same composition were studied, yielding consistent results. A region of nematic and isotropic coexisting phases and a region of a single isotropic phase were identified in the composition-temperature phase diagram. The results were analysed within a theoretical model combining the Flory-Huggins lattice theory for isotropic mixing and the Maier-Saupe theory for nematic ordering. Interestingly, no region of isotropic coexisting phases was observed in our experiments. This is probably due to the fact that the nematic interaction overwhelms the isotropic interaction in the region where (I + I) coexisting phases could appear. A preferential solubility of certain constituents of the LC mixture in the polymer could possibly be a reason for this behaviour.     

Complete phase diagrams of mixtures of a nematic liquid crystal with n-alkanes

The full experimental phase diagrams of mixtures of the nematic liquid crystal 4.4'-azoxyanisole, (PAA), and n-tetracosane and of PAA and n-octadecane are given. Equilibria of a nematic phase with an isotropic phase, of two isotropic phases, and a reentrant isotropic phase could be observed directly. The experimental phase diagram is in qualitative agreement with the result derived from the Flory lattice model adopted for thermotropic systems.     

Smectic, nematic, and isotropic phases in binary mixtures of thin and thick hard spherocylinders

A second-virial Onsager theory, based on Parsons-Lee rescaling and suitably extended to deal with multicomponent systems and smectic phases, has been used to calculate the phase diagram of a collection of binary mixtures of thin and thick hard spherocylinders. In particular, two types of phase diagrams are investigated. First, a number of binary mixtures where the two components have the same total length have been considered; in addition, the phase diagram of a binary mixture where the two components have the same volume has been calculated. For the particles of one of the two components, the length of the cylindrical part and the diameter have always been set equal to 5 and 1, respectively. Spherocylinders of the same total length and different diameter tend to demix considerably as soon as the diameter ratio deviates from unity. This happens especially at high pressures, when at least the phase richer in the thicker component is smectic. In the case where the two components have equal volumes, demixing is further increased due to the disparity not only in particle diameter but also in particle lengths. The incorporation of inhomogeneous layered phases is seen to alter significantly the phase diagrams calculated if only homogeneous phases are allowed, since transitions to a smectic phase often preempt those to a nematic or an isotropic phase. The apparent versatility of the recent experimental techniques suggests that the phase diagram features predicted by the theory might be also observed in real systems.     

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 equilibria in liquid crystalline systems based on polypropylenimine dendrimer

The thermodynamic characteristics of infinitely dilute solutions of saturated hydrocarbons in the columnar and isotropic polypropylenimine dendrimer phases were studied by gas chromatography. The contribution of the entropy Gibbs energy component to the solution of sorbates in a liquid crystalline solvent at a positive deviation from ideality was found to be predominant. A phase diagram of the binary system consisting of the dendrimer and nematic p-amyloxy-p′-cyanobiphenyl was constructed. The effect of the chemical nature and shape of component molecules on the mesomorphism of the mixtures is discussed.     

Phase equilibria and photopolymerisation-induced phase transitions of mesogenic diacrylate monomer and low molecular mass liquid crystal mixture

Experimental phase diagrams of binary mesogenic mixtures of reactive mesogenic diacrylate (RM257) monomer and low molar mass liquid crystals (E7) were determined by means of differential scanning calorimetry and optical microscopy. The combined free energy densities of Flory–Huggins for liquid–liquid demixing, Maier–Saupe for nematic ordering, and phase field free energy for crystal solidification was proposed to describe the phase diagrams of the starting E7/RM257 mixtures. The phase diagram thus constructed is an ideal mixing type, exhibiting a narrow loop of isotropic + nematic (I + N) coexistence region followed by the crystal + nematic (Cr1 + N) region in descending order of temperature. Of particular interest is the permanent fixation of the mesophase structures upon photopolymerisation of neat RM257 in the corresponding nematic and crystalline phases. Upon photopolymerisation of a low RM257 content mixture in both isotropic and nematic states, the nematic–isotropic transition of E7 was found to persist. The permanent structural anchoring is seen upon photo-curing of the 90/10 RM257/E7 mixture in the crystalline state.     

Reentrant isotropic phase in a discotic liquid crystal mixture

We have used X-ray diffraction and optical microscopy to study binary mixtures of 2,3,7,8,12,13-hexa-n-tetradecanoyloxy- and 2,3,7,8,12,13-hexa(4-n-undecyloxybenzoyloxy) truxenes. Our measurements confirm the existence of a reentrant isotropic phase, which is however always preceded by a mixed phase region rather than by a pure columnar phase. The nematic N_D phase displays an anomalously negative thermal expansion coefficient. We speculate on mechanisms for reentrancy in discotic mesogens.     

Phase behaviour and structure of a non-ionic discoidal amphiphile in water

The phase behaviour and structure of mixtures of a novel non-ionic discoidal amphiphile, 2,3.6,7,10,11-hexa-(1,4,7-trioxaoctyl)-triphenylene, and water have been investigated using deuterium NMR spectroscopy and X-ray diffraction. The feature of special interest is the occurrence of a nematic phase, intermediate to an isotropic micellar solution at higher temperatures and a columnar hexagonal phase at lower temperatures. This nematic phase exists over wide concentration (0.1 to 0.5 volume fraction of amphiphile) and temperature intervals. The molecules are stacked in columnar (rod-shaped) aggregates. In the isotropic micellar solution and nematic phase the length of the micelle is of the order of the centre-to-centre separation.     

Calorimetric studies of poly (2-phenoxyethylacrylate)/5CB mixtures

The thermophysical properties of mixtures of poly (2-phenoxyethylacrylate) and 4-cyano-4'-pentyl-biphenyl, 5CB, are investigated using polarizing optical microscopy (POM) and differential scanning calorimetry (DSC). The polymer has a molar mass M w = 181 000 g mol -1 ; the low molecular mass liquid crystal exhibits a nematic to isotropic transition at 35.3°C and crystallizes below 23°C. The phase diagram exhibits miscibility gaps in certain regions of temperature and composition where coexisting nematic and isotropic phases are found. From a practical point of view when considering the electro-optical applications of these systems, it proves to be useful to know precisely the amount of small liquid crystal molecules dissolved in the polymer matrix and the concentration of polymer in the nematic phase. The former quantity has a mechanical impact due to a plasticizing effect, an optical impact since it changes the polymer refractive index, while the polymer in the nematic phase shifts the transition temperatures influencing the electro-optical response of the liquid crystal. The present work addresses these important aspects using POM and DSC.     

Calorimetric study of phase transitions in a liquid-crystal-based microemulsion

A lyotropic inverse micelle phase composed of water, thermotropic liquid-crystal octylcyanobiphenyl (8CB), and surfactant (DDAB) was studied by using high-resolution calorimetry on several mixtures with 3%, 8%, and 15% micelle concentration. Calorimetric results show strong depression of the isotropic to nematic (I-N) phase-transition temperature. Broad heat-capacity anomalies show the existence of a wide coexistence range of isotropic, nematic, and smectic-A phases, which mimics the behavior of a new nearly stable thermodynamic phase. An observation of the rather sharp almost bulklike nematic to smectic-A (N-A) transition at low-temperatures indicates that our heat capacity results are consistent with the phase separation scenario in which significant number of micelles is expelled during I-N conversion leaving almost pure nematic phase at lower temperatures. It was found that micelles get almost completely remixed on heating the mixture back to the isotropic phase.     

Monte Carlo simulation of the self-assembly and phase behavior of semiflexible equilibrium polymers

Grand canonical Monte Carlo simulations of a simple model semiflexible equilibrium polymer system, consisting of hard sphere monomers reversibly self-assembling into chains of arbitrary length, have been performed using a novel sampling method to add or remove multiple monomers during a single MC move. Systems with two different persistence lengths and a range of bond association constants have been studied. We find first-order lyotropic phase transitions between isotropic and nematic phases near the concentrations predicted by a statistical thermodynamic theory, but with significantly narrower coexistence regions. A possible contribution to the discrepancy between theory and simulation is that the length distribution of chains in the nematic phase is bi-exponential, differing from the simple exponential distribution found in the isotropic phase and predicted from a mean-field treatment of the nematic. The additional short length-scale characterizing the distribution appears to arise from the lower orientational order of short chains. The dependence of this length-scale on chemical potential, bond association constant, and total monomer concentration has been examined.     

Observation of a re-entrant isotropic phase in a pure disc-like liquid crystal

We report the observation of an optically isotropic phase in the new disc-like mesogen 2,3,7,8,12,13-hexa(octadecanoyloxy)truxene. On cooling, this optically isotropic phase goes over into a nematic phase, while on heating a columnar phase grows in. To our knowledge this is the first example of a pure discotic mesogen exhibiting an isotropic phase below the temperature existence of a columnar phase. Our findings are supported by refractive index measurements of this compound as a function of temperature.     

Calorimetric studies of poly (2-phenoxyethylacrylate)/5CB mixtures

The thermophysical properties of mixtures of poly (2-phenoxyethylacrylate) and 4-cyano-4′-pentyl-biphenyl, 5CB, are investigated using polarizing optical microscopy (POM) and differential scanning calorimetry (DSC). The polymer has a molar mass M _w = 181 000 g mol ^-1 the low molecular mass liquid crystal exhibits a nematic to isotropic transition at 35.3°C and crystallizes below 23°C. The phase diagram exhibits miscibility gaps in certain regions of temperature and composition where coexisting nematic and isotropic phases are found. From a practical point of view when considering the electro-optical applications of these systems, it proves to be useful to know precisely the amount of small liquid crystal molecules dissolved in the polymer matrix and the concentration of polymer in the nematic phase. The former quantity has a mechanical impact due to a plasticizing effect, an optical impact since it changes the polymer refractive index, while the polymer in the nematic phase shifts the transition temperatures influencing the electro-optical response of the liquid crystal. The present work addresses these important aspects using POM and DSC.     

Computer simulation studies of anisotropic systems XXIX. Quadrupolar Gay-Berne discs and chemically induced liquid crystal phases

Liquid crystal phases can be induced chemically by mixing compounds whose specific interactions are such that the transition temperature for the induced phase is higher than the melting points of the two compounds. A particularly dramatic example of such behaviour is the creation of a columnar nematic and a hexagonal columnar phase on mixing discotic multiynes with 2,4,7-trinitrofluorenone. Although the intense colour of the mixture indicates a strong charge-transfer band, it is uncertain as to whether the charge-transfer interaction between unlike molecules is enough to stabilize the induced liquid crystal phases. An alternative explanation for the formation of such phases involves an electrostatic quadrupolar interaction between the components,whose quadrupole moments differ in sign. This interaction weakens the face-to-face attraction for like particles while strengthening it for unlike particles. We have explored this possible explanation for chemically induced liquid crystal phases in discotic systems by modelling the basic interaction between discs with a Gay-Berne potential, to which is added a point quadrupolar interaction. We have determined the phase behaviour of the pure systems and their binary mixtures with constant pressure Monte Carlo simulations. It would seem that the quadrupolar interaction can account for many of the features of chemically induced liquid crystals.     

Nanospheres in a nematic liquid crystal solvent: the influence of particle size

We use Monte Carlo simulations to investigate a simple lattice model for nematic liquid crystals containing nanospheres. The influence of particle size on the phase behaviour is studied using two different sized particles. The phase diagram is found to be topologically equivalent for both particle sizes, with a large biphasic region corresponding to coexistence between a rod-rich nematic and a rod-poor isotropic phase. For small spheres, the rod-rich nematic phase is stable for relatively large volume fractions of spheres (up to a maximum of about 16%). In contrast, the nematic phase for the system with larger spheres is constrained to a much narrower region of the phase diagram.