Liquid lattice model dispersivity

The Flory theory discussed in the next section is another important theory on rigid liquid crystalline polymers. Because of its clear picture of the lattice model and the incorporation of the Onsager theory, it has become a basic method for the theoretical study of liquid crystalline polymers. As a result of the constant efforts of Flory and his co-workers, the theory has been applied to binary and poly-disperse systems and also includes the soft interactions. 

This type of liquid is characterized by direction independent, relatively weak dispersion forces decreasing with r-6, when r is the distance between neighbouring molecules. A simple model for this type of liquid, which accounts for many properties, was given by Luck 1 2> it is represented by a slightly blurred lattice-like structure, containing hole defects which increase with temperature and a concentration equal to the vapor concentration. Solute molecules are trapped within the holes of the liquid thus reducing their vapor pressure when the latter is negligible. 

LATTICE SPIN MODELS OF POLYMER-DISPERSED LIQUID CRYSTALS... 

Abstract Monte Carlo simulations of lattice spin models are a powerful method for the investigation of confined nematic liquid crystals and allow for a study of the molecular organization and thermod3mamics of these systems. Investigations of models of polymer-dispersed liquid cr3rstals are reviewed devoting particular attention to the calculation of deuterium NMR spectra from the simulation data. 

We have described lattice spin models for the simulation of polymer-dispersed liquid crystals. The biggest advantage of Monte Carlo simulations is the possibility of investigating the system at a microscopic level, and to calculate thermodynamic properties and their specific order parameters suitable for different types of PDLC. Molecular organizations can be investigated by calculating the order parameters point by point across the droplet. Moreover, it is possible to calculate experimental observables like optical textures and, as discussed here, NMR line shapes. We have given an overview of the method and some applications to models of PDLC with radial and bipolar boundary conditions, and considered the effect of orientational and translational diffusion on the spectra. We have examined in particular under what conditions the NMR spectra of the deuterated nematic can provide reliable information on the actual boundaries present in these submicron size droplets. 

The most successful statistical theory of liquids is that derived by Simha and Somcynsky. The model considers liquids to be mixtures of voids dispersed in solid matter, i.e., a lattice of unoccupied and occupied sites. The occupied volume fraction, y (or its counterpart the free volume fraction f = 1 - y), is the principal variable y = P, T). From die configurational partition function the configurational contribution to the Helmholtz molar free energy of liquid i was expressed as [3] ... 

The authors [13] also proposed a multiphase mass transport model for toluene nitration, the details of, which are given in Fig. 2.4. It is based on the formation of a thin aqueous film aroimd the hydrophilic catalyst particles, which are dispersed in toluene medium. The model also accounted for the existence of vapor phase over the liquid-liquid-solid reaction medium. The major mass transfer resistances are offered by the liquid film around the catalyst particles and in the catalyst pores. The aqueous film and the liquid in the pores constitute the micro environment necessary to facilitate the desired level of lattice transformation in the catalyst particles. Figure 2.4 also shows the concept of the microenvironment within and around the catalyst particle. These studies have demonstrated that shape selectively effect of zeolite Beta catalyst is significantly enhanced by the specific microenvironment created within and around the catalyst particles. This has significantly enhanced the para-selectivity from 0.7 to 1.5. The microenvironment has also improved the accessibility of reactant molecules to the catalyst active sites. 

Simple models aside, if we choose to perform a self-consistent DFT calculation in which we explicitly treat the ionic lattice with, for example, a PP or full potential treatment, what level of accuracy can we expect to achieve As always, the answer depends on the properties we are interested in and the exchange-correlation functional we use. DFT has been used to compute a whole host of properties of metals, such as phonon dispersion curves, electronic band structures, solid-solid and solid-liquid phase transitions, defect formation energies, magnetism, superconducting transition temperatures, and so on. However, to enable a comparison between a wide range of exchange-correlation functionals, we restrict ourselves here to a discussion of only three key quantities, namely, (i) (ii) ao, the... 

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