Liquids isotropic

6 Structure of the Isotropic and Nematic Phase 5.6.1 Isotropic Liquid 

This is the other extreme case with respect to crystals. The density correlation function G(r) is spherically symmetric decaying function. It is very instructive to find, at first, the structure factor (5.26) for any function of the spherical symmetry. We should use spherical frame with volume element dV = P smddi d ddr  

we may use the simplest density correlation function for an isotropic unstmctured liquid in the form G r) = where K = is an inverse 

The structure factor and intensity of scattering (5.25) have a spherically symmetric Lorentzian form centered at the zero wavevector q = 0. The fuU width oti the half a maximum (FWHM) is equal to 2k=2/.  

In real liquids there is a short-range positional order because each particular molecule has nearest neighbors forming few so-called coordination spheres. Therefore, each selected molecule feels its nearest neighbors and the G-function oscillates. For simplicity, we can take only the first harmonic of density oscillation and write the density correlation function as follows  

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Given that R, can be arbitrarily chosen as anywhere in the sample volume of an isotropic liquid in the absence... 

Otlier possibilities for observing phase transitions are offered by suspensions of non-spherical particles. Such systems can display liquid crystalline phases, in addition to tire isotropic liquid and crystalline phases (see also section C2.2). First, we consider rod-like particles (see [114, 115], and references tlierein). As shown by Onsager [116, 117], sufficiently elongated particles will display a nematic phase, in which tire particles have a tendency to align parallel to... 

For fluorescence PAH determination in tap water acid-induced cloud point extraction was used. This kind of extraction based on the phase separation into two isotropic liquid phases a concentrated phase containing most of the surfactant (surfactant-rich phase), where the solubilised solutes are exttacted, and an aqueous phase containing a surfactant concenttation closes to the critical micellar concentration. 

The aqueous micellai solutions of some surfactants exhibit the cloud point, or turbidity, phenomenon when the solution is heated or cooled above or below a certain temperature. Then the phase sepai ation into two isotropic liquid phases occurs a concentrated phase containing most of the surfactant and an aqueous phase containing a surfactant concentration close to the critical micellar concentration. The anionic surfactant solutions show this phenomenon in acid media without any temperature modifications. The aim of the present work is to explore the analytical possibilities of acid-induced cloud point extraction in the extraction and preconcentration of polycyclic ai omatic hydrocai bons (PAHs) from water solutions. The combination of extraction, preconcentration and luminescence detection of PAHs in one step under their trace determination in objects mentioned allows to exclude the use of lai ge volumes of expensive, high-purity and toxic organic solvents and replace the known time and solvent consuming procedures by more simple and convenient methods. 

Similarly, N-allcylammonium [28] and alkylphosphonium [29] salts form lamellar phases with smectic bilayer structures. In both cases. X-ray scattering also showed the isotropic liquid not to be completely disordered and still displaying similar features to the mesophase. Buscio et al. [28] showed that in N-allcylammonium chlorides the feature was not only much broader than that observed in the mesophase but increased in width with decreasing chain length. 

The liquid crystalline (LC) state is an intermediary state between isotropic liquid and crystalline solid. It arises from the tendency of rod like or disc like... 

In formulating liquid detergent products with LAS, the carbon chain distribution, phenyl isomer distribution, and DATS level can all contribute to the solubility and viscosity characteristics. Hydrotrope requirements for isotropic liquid detergents can vary widely for different types of commercial LAS. 

Unlike low molar mass liquid crystals, these materials do not undergo a nematic-isotropic transition. Instead, they adopt liquid crystal behaviour throughout the region of the phase diagram for which they are in the melt. Above a particular temperature, rather than adopting an isotropic liquid structure, they decompose. 

Fig. 5. The growth of orientational order for the 64 molecules of 5,5-BBCO during a 300 K quench starting from the isotropic liquid. Data from [104], supplied hy C McBride, University of Durham...

The question arises as to how useful atomistic models may be in predicting the phase behaviour of real liquid crystal molecules. There is some evidence that atomistic models may be quite promising in this respect. For instance, in constant pressure simulations of CCH5 [25, 26] stable nematic and isotropic phases are seen at the right temperatures, even though the simulations of up to 700 ps are too short to observe spontaneous formation of the nematic phase from the isotropic liquid. However, at the present time one must conclude that atomistic models can only be expected to provide qualitative data about individual systems rather than quantitative predictions of phase transition temperatures. Such predictions must await simulations on larger systems, where the system size dependency has been eliminated, and where constant... 

The rapid rise in computer speed over recent years has led to atom-based simulations of liquid crystals becoming an important new area of research. Molecular mechanics and Monte Carlo studies of isolated liquid crystal molecules are now routine. However, care must be taken to model properly the influence of a nematic mean field if information about molecular structure in a mesophase is required. The current state-of-the-art consists of studies of (in the order of) 100 molecules in the bulk, in contact with a surface, or in a bilayer in contact with a solvent. Current simulation times can extend to around 10 ns and are sufficient to observe the growth of mesophases from an isotropic liquid. The results from a number of studies look very promising, and a wealth of structural and dynamic data now exists for bulk phases, monolayers and bilayers. Continued development of force fields for liquid crystals will be particularly important in the next few years, and particular emphasis must be placed on the development of all-atom force fields that are able to reproduce liquid phase densities for small molecules. Without these it will be difficult to obtain accurate phase transition temperatures. It will also be necessary to extend atomistic models to several thousand molecules to remove major system size effects which are present in all current work. This will be greatly facilitated by modern parallel simulation methods that allow molecular dynamics simulations to be carried out in parallel on multi-processor systems [115]. 

Fig. 5. The essential form of the phase diagram for the mesogen GB(3.0, 5.0, 2, 1) the open circles indicate the approximate coexistence lines and the solid circles show the density of the isotropic liquid in equilibrium with the vapour phase...

Both compound I and a mixture of the two derivatives M70 (70% 1 30% II) display the usual monolayer smectic Aj phase on cooling down from the isotropic liquid. At lower temperatures the particular smectic phases (X and X ) showing polar behaviour have been observed [78]. The smectic X phase in... 

The conventional liquid state is described as the isotropic phase. The temperature at which the compound passes from the solid phase into a mesophase is described as the melting point and the transition temperature between a mesophase and an isotropic liquid is described as the clearing point. 

Most solid materials produce isotropic liquids directly upon melting. However, in some cases one or more intermediate phases are formed (called mesophases), where the material retains some ordered structure but already shows the mobility characteristic of a liquid. These materials are liquid crystal (LCs)(or mesogens) of the thermotropic type, and can display several transitions between phases at different temperatures crystal-crystal transition (between solid phases), melting point (solid to first mesophase transition), mesophase-mesophase transition (when several mesophases exist), and clearing point (last mesophase to isotropic liquid transition) [1]. Often the transitions are observed both upon heating and on cooling (enantiotropic transitions), but sometimes they appear only upon cooling (monotropic transitions). 

The introduction of a second chiral atom in the system leads to a reduction in the mesogenic properties and only a monotropic chiral nematic transition is observed for compound 23. However, when this compound is cooled down from the isotropic liquid state at a cooling rate of 0.5 °Cmin , very unusual blue phases BP-III, BL-II and BP-I are observed in the range 103-88 °C. Blue phases usually require pitch values below 500 nm. Hence the pitch value of the cholesteric phase for 23 must be very short, suggesting that the packing of two chiral carbons forces a faster helical shift for successive molecules packed along the perpendicular to the director. 

As indicated above in chiral mesophases, the introduction of a functional group in mesogenic stmctures offers the opportunity to achieve functional LCs. With this aim, mesomorphic crown-ether-isocyanide-gold(I) complexes (26) have been prepared recently [38]. The derivatives with one alkoxy chain show monotropic SmC mesophases at or close to room temperature. In contrast, the complexes with three alkoxy chains behave as monotropic (n = 4) or enantiotropic (n > 4) LCs. The structure of the mesophases could not be fully eluddated because X-ray diffraction studies in the mesophase were unsuccessful and mesophase characterization was made only on the basis of polarized optical microscopy. These complexes are luminescent not only in the solid state and in solution, but also in the mesophase and in the isotropic liquid state at moderate temperatures. The emission spectra of 26a with n=12 were... 

Besides this, the remarkable properties of gold(I) compounds, which often give rise to aurophilic interactions and/or to luminescence, are of interest when these properties are transported into the liquid crystal field. Although there is much still to be studied, it is already clear that luminescence can survive in the condensed but mobile state of a mesophase, and even in the isotropic liquid state of a molten gold compound. It also seems that aurophilicity can contribute in some cases to the formation of mesophases. 

Arias, J., Bardaji, M. and Espinet, P. (2008) Luminescence and Mesogenic Properties in Crown-Ether-Isocyanide or Carbene Gold(I) Complexes Luminescence in Solution, in the Solid, in the Mesophase, and in the Isotropic Liquid State. Inorganic Chemistry, 47, 3559-3567. 

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