A new study of associating inhomogeneous fluids with classical density functional theory

ABSTRACT

A new density functional for the study of associating inhomogeneous fluids based on Wertheim's first-order thermodynamic perturbation theory is presented and compared to the most currently used associating density functionals. This functional is developed using the weighted density approximation in the range of association of hard spheres. We implement this functional within the framework of classical density functional theory together with modified fundamental measure theory to account for volume exclusion of hard spheres. This approach is tested against molecular simulations from literature of pure associating hard spheres and mixtures of non-associationg and associating hard spheres with different number of bonding sites close to a hard uniform wall. Furthermore, we compare and review our results with the performance of associating functionals from literature, one based on fundamental measure theory and the inhomogeneous version of Wertheim's perturbation theory. Results obtained with classical DFT and the three functionals show excellent agreement with molecular simulations in systems with one hard wall. For the cases of small pores where only one or two layers of fluid are allowed discrepancies between results with classical DFT and molecular simulations were found.     

Specific features of photoisomerization of provitamin D 3 in a nematic liquid crystal

Photoisomerization of provitamin D ₃ (7-dehydrocholesterol) in a nematic liquid crystal (ZLI-1695, Merck) is investigated in detail by UV absorption spectroscopy. It is found that dissolution of chiral molecules of provitamin D ₃ induces the cholesteric phase in a nematic. The spectral kinetics of photoisomerization in this phase changes significantly from that in an ethanol solution. A sharp nonmonotonic dependence of the increase in accumulation of trans isomer tachysterol in a liquid crystal matrix with a decrease in the induced cholesteric pitch from 2200 to 25 μm is revealed.     

Nonlinear “brightening” of a film of nonabsorbing chiral nematic under selective reflection conditions

A strong decrease in the reflection coefficient of a film of a nonabsorbing chiral nematic (cholesteric) is observed experimentally in the region of selective reflection under the action of a powerful beam of circularly polarized light. The independence of the effect from the average power density (and its dependence only on the peak power density) allow it to be attributed to an increase in the pitch of the cholesteric helix to such a degree that it is completely unwound, an effect previously observed only in static and low-frequency electric and magnetic fields, in the strong field of the light wave. These are the first experiments in which, on account of the specially chosen irradiation conditions, the changes produced in the pitch of the helix by the field of the light wave can accumulate over time, so that a nonthermal mechanism can be invoked to explain the nonlinear brightening of a mirror made of a chiral nematic. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 6, 403–407 (25 March 1996)     

Structure,elasticity and phase transitions in liquid crystals with deformations

ABSTRACT

A molecular-statistical theory describing the nematic liquid crystals (LCs) with spherical inclusions (or point defects) is proposed. At given size of inclusions and nematic order parameters at the surfaces of inclusions (zero in the case of point defects) and far from inclusions (where the nematic LC is almost uniform), the distribution of nematic order parameters in the bulk of LC with inclusions was found to be fully determined by the elastic constants of LC. We have found and explained the two-step heat-driven transformation from the nematic phase into the isotropic phase, with the intermediate phase in between. The nematic order parameters and the elastic constants are evaluated in the framework of a unified approach based on the features of pair interaction potentials of the individual LC molecules. It is shown that, in the case of K₃₃ < K₁₁, the point defects should destroy the conventional nematic phase.     

Capillary nematisation of colloidal rods in confinement

ABSTRACT

We confine a colloidal liquid crystal between parallel plates separated down to several times the rod length. By connecting the system to a reservoir we effectively create a grand canonical system, in which the liquid crystal displays an isotropic phase in the reservoir, but upon strong confinement becomes nematic between the parallel plates. This capillary nematisation transition can be followed down to the single particle level by means of laser scanning confocal microscopy. We compare the experimental findings to density functional theories (DFTs), within the Zwanzig model as well as a more advanced DFT, in which the effect of rod flexibility is taken into account.     

New investigation on the tetragonal liquid-crystalline phase or SmQ

Chiral liquid crystals, for which twist and smectic order strongly compete, can exhibit complex architectures. This is the case of the SmQ phase which shows a high degree of 3D order (tetragonal or hexagonal) as well as a liquid signature. We have combined X-ray scattering and optical observations on a new compound exhibiting a SmQ phase to discriminate between the two models proposed by A.M. Levelut et al. (J. Phys. II 7, 981 (1997)) at the molecular level for the phase with the I4₁22 space group.Received: 9 March 2004, Published online: 10 November 2004PACS: 61.30.Eb Experimental determinations of smectic, nematic, cholesteric, and other structures - 61.30.Mp Blue phases and other defect-phases     

Structure of polarization-resolved conoscopic patterns of planar oriented liquid crystal cells

The geometry of distributions of the polarization of light in conoscopic patterns of planar oriented nematic and cholesteric liquid crystal (LC) cells is described in terms of the polarization singularities including C-points (points of circular polarization) and L lines (lines of linear polarization). Conditions for the formation of polarization singularities (C-points) in an ensemble of conoscopic patterns parametrized by the polarization azimuth and ellipticity of the incident light wave have been studied. A characteristic feature of these conditions is selectivity with respect to the polarization parameters of the incident light wave. The polarization azimuth and ellipticity are determining parameters for nematic and cholesteric LC cells, respectively.     

Probing the orientation of porphyrin oligomers in a liquid crystal solvent – a triplet state electron paramagnetic resonance study

ABSTRACT

Linear porphyrin oligomers have found various applications as synthetic molecular wires in the context of light harvesting, solar energy conversion and molecular electronics. In many of these applications a partial ordering of the molecules helps to improve the reaction efficiency or device performance. In this work we study the orientational properties of the building blocks of such porphyrin-based molecular wires, namely a porphyrin monomer and the corresponding butadiyne-bridged dimer. The porphyrins have been embedded in the nematic liquid crystal solvent 4-cyano-4'-pentylbiphenyl (5CB) and the anisotropic properties of their photogenerated triplet states were characterised by transient electron paramagnetic resonance (EPR) spectroscopy. When aligned in strong magnetic fields, the liquid crystal molecules impose their orientational anisotropy onto the solute guest molecules whose orientation-dependent magnetic properties can then be explored. The line shape analysis of the porphyrin triplet state EPR spectra – highly sensitive to small conformational changes – confirms the orientation of the zero-field-splitting (ZFS) tensors previously determined for these molecules by magnetophotoselection experiments. A biaxial distribution function is shown to be necessary to simulate the experimental EPR data. The biaxial behaviour, in conjunction with symmetry considerations, allows an unambiguous assignment of the three ZFS tensor axes to the molecular axes. From the determined orientational distributions of the porphyrins in 5CB, the biaxial order parameters for both molecules were calculated.     

液晶胆甾相中的分子短程关联

向列相液晶的二粒子集团理论被推广应用于研究胆甾相二维模型.手征性分子固定在三维简单立方晶格的格点上,而分子取向限制在二维.理论结果表明,平衡态螺旋波矢依赖于温度的变化,且存在胆甾相到向列相相变.通过考虑分子间短程关联,二粒子集团理论的数值结果较平均场理论更接近Monte Carlo模拟结果.     

Structure factors in a two-dimensional binary colloidal hard sphere system

ABSTRACT

Hard disks are one of the simplest interacting many-body model system in two dimensions (2D). Here, we present a comprehensive set of measurements of the static structure factors for quasi-2D monodisperse fluids and two different binary colloidal hard sphere mixtures: a small size ratio (SSR) system with a negligibly small negative non-additivity and a large size ratio system with a significantly larger non-additivity. We compare the experimental results for the monodisperse and SSR systems to those calculated using density functional theory (DFT) for additive mixtures. Furthermore, we determine the zero-wavevector limits of the static structure factors for the monodisperse and binary hard sphere fluids directly from an analysis of number and concentration fluctuations. For the monodisperse case, this leads to the isothermal compressibility, which agrees very well with DFT, and is consistent with the scaled particle theory equation of state for hard disks. For the binary fluids, the partial static structure factors are used to calculate the Bhatia–Thornton structure factors, and we find qualitative agreement with DFT for the SSR mixture. Finally, the zero-wavevector limits of the Bhatia–Thornton structure factors are determined and directly related to the thermodynamic factor, the dilatation factor and the isothermal compressibility.     

Electron spin resonance of symmetrical three-spin systems in nematic liquid crystals

An E.S.R. line-shape model is developed for fast tumbling three-spin systems in nematic liquid crystals. The line positions are calculated from a spin hamiltonian, which considers Zeeman, exchange, dipolar and hyperfine interactions of the three unpaired electrons. The dominant spin relaxation process, determining the line-widths, is assumed to result from the anisotropy of the zero-field splitting coupled to the molecular motion. The predictions of the theory are tested by comparison with the temperature-dependent E.S.R. spectra of trisverdazyl radicals in 4,4′-azoxydianisole. Good agreement is found between experimental and simulated spectra. A detailed analysis provides values for the solute order parameters [Pbar] ₂ and [Pbar] ₄. They correspond surprisingly well to predictions of the molecular-field theories of nematic liquid crystals.     

The role of enhanced aromatic -electron donating aptitude of the tyrosyl sidechain with respect to that of phenylalanyl in intramolecular interactions

An exhaustive ab initio and DFT search for energetically stable conformers from the topologically possible set was undertaken on the N-acetyl-phenylalanyl-N-methylamide and N-acetyl-tyrosyl-N-methylamide systems. The geometries of all 81 phenylalanyl and 162 tyrosyl possible rotamers, described under the rules outlined by Multi-Dimensional Conformational Analysis (MDCA), were attempted at each of the RHF/3-21G, RHF/6-31G(d) and B3LYP/6-31G(d) levels of theory. A total of 32 and 66 stable conformational minima were found for the phenylalanyl and tyrosyl amino acid diamides, respectively, at the B3LYP/6-31G(d) level. From the tyrosyl set, 33 unique conformers emerge when the orientation of the A _i ³ dihedral angle (p-OH orientation) is disregarded. A total of 31 conformers were common to both sets and showed nearly identical geometries. The comparison of the optimized DFT geometries of the two systems showed near by perfect linear fits with R² values of 0.9997, 0.9994, 0.9997, and 0.9996 for the φ _i , ψ _i , A _i ¹ , and A _i ² dihedral angles, respectively. Relative energies of the matching 31 conformers also fitted to a linear plot with an R² value of 0.9985. The geometric centroid of the aromatic ring in the sidechain of both systems was found to be within 4.1 ?of the H and O atoms of the peptide groups, in 21 and 2 of the conformers, respectively. None of the non-matching conformers showed any such interaction distance ≤4.1 ?. Received 1st February 2002 / Received in final form 28 May 2002 Published online 13 September 2002     

Specific features of the dielectric spectra of the liquid crystal 5CB in the decimeter wavelength range

The dispersion and anisotropy of the permittivity of the liquid crystal 5CB in the solid, nematic, and isotropic phases are investigated at frequencies ranging from 50 to 1000 MHz using discretely tunable hybrid microstrip cavities. Resonance features which grow with increasing temperature are observed in the dielectric spectra. It is found that the section of the dispersion which is due to oriented vibrations of the mesophase molecules covers the frequency range almost up to 300 MHz, and the resonances found could be due to conformational vibrations of the molecules. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 4, 251–253 (25 August 1997)     

The synthesis of the chiral non-mesogenic d-seco estrone derivatives and their influence on the phase transitions of cholesteric liquid crystals

The synthesis of new chiral seco-estrone derivatives is presented, as well as their influence on the phase transition of binary mixtures of cholesteryc liquid crystals. The new chiral derivatives do not posses any liquid crystalline phases and were synthesized in several synthetic steps, starting from estrone. We have studied the mixtures of cholesteryl non-anoate (40%) with cholesteryl myristate (40%) and addition of new chiral derivatives 3 4, or 5 (20%). It was concluded that the addition of chiral derivative 3 to the binary mixture stabilizes smectic A and cholesteric phase and shifts the phase transition temperature with respect to pure binary mixture for about 5°C towards lower temperatures. The extension of the temperature range of the cholesteric phase from 5°C to 15°C was established in the case when the derivatives 3 and 4 are added to the binary mixture of cholesteryl nonanoate with cholesteryl myristate. The phase diagrams of investigated compounds are formed on the basis of data obtained by the optical microscopy. Using X-ray diffraction on the crystalline powder of unoriented samples we have determined the molecular parameters: the thickness of smectic and cholesteric layers and average distance between the long axes of neighboring molecules.     

Equilibrium structures of planar nematic and cholesteric films in electric fields

Liquid crystal layers subjected to an electric or a magnetic field can have several types of instabilities. This paper reviews recent theoretical studies concerning equilibrium structures of planar layers.

Using the Oseen-Frank elasticity theory, the Freedericksz transition and the transition to static periodic domains of planar nematic and cholesteric films are reconsidered. A perturbation treatment of nonlinear torque balance equations for the director is suitable to derive amplitude equations for the film distortions under the action of a field and to predict the topological features of phase diagrams for equilibrium states. The competition between the Freedericksz effect and the formation of periodic distortions is studied varying material and geometrical parameters. Some results are useful to optimize cholesteric mixtures for application in display devices in such a manner, that the occurrence of periodic domains is avoided.     

Equation of state for the Lennard-Jones truncated and shifted fluid with a cut-off radius of 2.5 σ based on perturbation theory and its applications to interfacial thermodynamics

ABSTRACT

An equation of state is presented for describing thermodynamic properties of the Lennard-Jones truncated and shifted (LJTS) potential with a cut-off radius of 2.5 σ. It is developed using perturbation theory with a hard-sphere reference term and labelled with the acronym PeTS (perturbed truncated and shifted). The PeTS equation of state describes the properties of the bulk liquid and vapour and the corresponding equilibrium of the LJTS fluid well. Furthermore, it is developed so that it can be used safely in the entire metastable and unstable region, which is an advantage compared to existing LJTS equations of state. This makes the PeTS equation of state an interesting candidate for studies of interfacial properties. The PeTS equation of state is applied here in two theories of interfaces, namely density gradient theory (DGT) and density functional theory (DFT). The influence parameter of DGT as well as the interaction averaging diameter of DFT are fitted to data of the surface tension of the LJTS fluid obtained from molecular simulation. The results from both theories agree very well with those from the molecular simulations.     

New types of phase behaviour in binary mixtures of hard rod-like particles

The phase behaviour of binary mixtures of hard rod-like particles has been studied using Parsons—Lee theory (Parsons, J. D., 1979, Phys. Rev. A, 19, 1225); Lee, S. D., 1987, J. Chem. Phys., 87, 4972). The stability of the isotropic-nematic (I-N) transition with respect to isotropic—isotropic (I-I), and nematic—nematic (N-N) demixing is investigated. The individual components in the mixtures are modelled as hard cylinders of diameters D_i and lengths L_i (i = 1,2). The aspect ratios k_i = L_i/D_i of the components are kept fixed (with values of k ₁ = 15 and k ₂ = 150), and the phase behaviour of the mixtures is studied for varying diameter ratios d = D ₁/D ₂. When the diameter ratio is relatively large, e.g., for values of d = 50, component 1 may be considered a large colloidal particle, while the second component plays the role of a weakly interacting solvent. This mixture exhibits only an I-N phase transition which is driven by the excluded volume interaction between the large particles (no I-I or N-N demixing is seen). A decrease in the diameter ratio enhances the contribution of the smaller component to the free energy (especially in terms of the unlike excluded volume term), and I-I as well as N-N demixing transitions are observed. The character of the N-N transition is rather unusual, a single region bounded by a lower critical point (in the pressure—composition plane) is seen for a diameter ratio of d = 3.2, while two demixed nematic regions bounded by lower and upper critical points are observed for d = 3.13. A further decrease in the diameter ratio (e.g., to d = 3) leads to systems with a phase behaviour in which the two demixed N-N regions meet, giving rise to a large demixed region with very strong fractionation in composition, and no N-N critical points. The I-I demixing transition is always accompanied by a lower critical point and occurs for systems with intermediate size (diameter) ratios. A diameter ratio of d = 4.5 corresponds to systems with significant like and unlike excluded volume interactions, and in this case the I-N transition takes place over the whole composition range with weak fractionation and one azeotropic point. Surprisingly, the coexisting nematic phase is of lower packing fraction than the isotropic phase for some of the compositions, i.e., an inversion of packing fraction takes place. In addition to this, the longer rods can be less ordered that the shorter rods for certain values of the composition.