Liquid structural parameters

All the complexes XXIa-i are air-sensitive colorless solids or liquids. Structural parameters are available mainly from X-ray structure data (76,266) and from electron diffraction and microwave studies (67-69,71,79,80). In nearly all cases the molecules are monomeric in the solid state, in solution, and... 

Blanken, W. M., Bergh, M. L. E., Koppen, P. L., and van den Eijnden, D.H., High-pressure liquid chromatography of neutral oligosaccharides effects of structural parameters, Anal. Biochem., 145, 322, 1985. 

A model is needed to calculate liquid-liquid equilibrium for the activity coefficient from Equation 4.67. Both the NRTL and UNIQUAC equations can be used to predict liquid-liquid equilibrium. Note that the Wilson equation is not applicable to liquid-liquid equilibrium and, therefore, also not applicable to vapor-liquid-liquid equilibrium. Parameters from the NRTL and UNIQUAC equations can be correlated from vapor-liquid equilibrium data6 or liquid-liquid equilibrium data9,10. The UNIFAC method can be used to predict liquid-liquid equilibrium from the molecular structures of the components in the mixture3. 

Theories of electron mobility are intimately related to the state of the electron in the fluid. The latter not only depends on molecular and liquid structure, it is also circumstantially influenced by temperature, density, pressure, and so forth. Moreover, the electron can simultaneously exist in multiple states of quite different quantum character, between which equilibrium transitions are possible. Therefore, there is no unique theory that will explain electron mobilities in different substances under different conditions. Conversely, given a set of experimental parameters, it is usually possible to construct a theoretical model that will be consistent with known experiments. Rather different physical pictures have thus emerged for high-, intermediate- and low-mobility liquids. In this section, we will first describe some general theoretical concepts. Following that, a detailed discussion will be presented in the subsequent subsections of specific theoretical models that have been found to be useful in low- and intermediate-mobility hydrocarbon liquids. 

The optimum UNIQUAC interaction parameters u, between methylcyclohexane, methanol, and ethylbenzene were determined using the observed liquid-liquid data, where the interaction parameters describe the interaction energy between molecules i and j or between each pair of compounds. Table 4 show the calculated value of the UNIQUAC binary interaction parameters for the mixture methanol + ethylbenzene using universal values for the UNIQUAC structural parameters. The equilibrium model was optimized using an objective function, which was developed by Sorensen [15],... 

Our approach was to study structure reactivity relationships in a number of model reactions and, then, to proceed to the usually more difficult polymerizations using a variety of comonomer pairs. Secondly, we hoped to optimize the various, experimental solid-liquid PTC parameters such as nature and amount of catalyst, solvent, nature of the solid phase base, and the presence of trace water in the liquid organic phase. Finally, we wished to elucidate the mechanism of the PTC process and to probe the generality of solid-liquid PTC catalysis as a useful synthetic method for polycondensation. 

The upper limit for / follows from the hydrogen distribution and aliphatic group distribution derived from proton spin resonance measurements at the temperature of liquid nitrogen (3). Table III shows all structural parameters obtained directly from the second moment H2 (in gauss2) together with H.i/H. 

Methods to Estimate pv from Tb Only The modified Watson correlation [2] applies for liquids and solids in the pv range from 10-7 to 760mmHg. This method is based on the Watson equation (8.5.1) and requires the input of the normal boiling point temperature, Tb, and of AHvb. However, the latter property is itself calculated from Tb and from structural parameters. For compounds with pv between 10 and 760mmHg, a method error of 2.5% has been reported, whereas a considerably higher error has been found for compounds with pv below lOmmHg. The method has been illustrated for benzene and DDT [2]. A large number of other Tb/pv correlations have been discussed by Horvath [17]. 

The second group involves polymers with three-dimensional ordering of side branches (e.g., those forming Mj-phaseXTable 5). On X-ray patterns of these polymers 3-4 narrow reflexes at wide angles are observed. As a rule, the authors define this type of structure as crystalline, or ascribe a smectic type of structure, characteristic for ordered smectics in SE or SH phases. The heats of transition from anisotropic state to isotropic melt are usually small and do not exceed the heats of transition smectic liquid crystal — isotropic melt . The similarity of structural parameters of three-dimensionally ordered smectics and that of crystalline polymers of the type here considered, make their correct identification quite a difficult task. 

In Secs. 13.2-13.3 the principles of toughening of thermosets by rubber particles, and the role of morphologies, interfacial adhesion, composition, and structural parameters on the toughening effect are analyzed. Section 13.4 is devoted to the use of initially miscible thermoplastics for toughening purposes. The effect of core-shell rubber particles is discussed in Sec. 13.5 and, in Sec. 13.6, miscellaneous ways of toughening thermosets (liquid crystals, hybrid composites, etc.), are analyzed. 

The following optimal or feasible conditions and structural parameters were determined liquid to gas flow rate ratio VJVG = 0.85-1.OxlO 3 m3m 3 impinging velocity u0 = 10-15 m-s 1 dimensionless impinging distance S/d0> 4 molar ratio Ca/S = 1.0 for pseudo flue gas without C02 the nozzles were mounted at the outlets of the gas conduits ... 

In order to deal with a coal-derived liquid as a mixture which has a statistically average chemical structure, we choose two measurable structural parameters, aromaticity, fa Car/Ctotal) and the degree of substitution of the aromatic ring, a. To identify major atomic groups of coal-derived liquids which contribute to AHf° and S°, the following assumptions are made. 

Necessary data for estimating the standard heat of formation and the absolute entropy by Equations 3 and 4 are the elemental analysis, structural parameters, fa and a, and the normal boiling point. For a practical purpose, it will be more convenient if we could calculate AHf° and S° only from elemental analysis data and normal boiling point. The aromaticity fa for coal liquids may be estimated by the correlation shown in Figure 1. On the other hand, the value of 0 may be taken as 0.3 for its average value based on the reported data (lf3, 20, 21). Substitution of these relations into Equations 3 and 4 gives... 

Mixtures of hydrocarbons are assumed to be athermal by UNIFAC, meaning there is no residual contribution to the activity coefficient. The free volume contribution is considered significant only for mixtures containing polymers and is equal to zero for liquid mixtures. The combinatorial activity coefficient contribution is calculated from the volume and surface area fractions of the molecule or polymer segment. The molecule structural parameters needed to do this are the van der Waals or hard core volumes and surface areas of the molecule relative to those of a standardized polyethylene methylene CH2 segment. UNIFAC for polymers (UNIFAC-FV) calculates in terms of activity (a,-) instead of the activity coefficient and uses weight fractions... 

Table V shows yields and structural parameters of SP-300 fractions. These fractions were black solid materials like the feed coal, as compared to dark-brown viscous liquids of the HVL-P fractions. The overall average molecular weight of SP-300 was more than three times that of HVL-P. SP-300 fractions have much larger R, RN and //cl than HVL-P fractions. The //cl values disclosed that there were, on the average, 2.8 aromatic clusters per molecule in SP-300, as compared to 1.1 aromatic clusters per molecule in HVL-P. Thus SP-300 fractions are high molecular weight materials,in which the degree of depolymerization is relatively low. This in turn suggests that SP-300 has retained more of the original structures of the parent coal than has HVL-P.

In order to determine whether any direct structural information about coal can be obtained from the liquids used in this study, structural parameter data are compared in Table VII. 

The focus of this study is the chemistry of the partially pyrolyzed and oxidized liquid fuel which survives as pyrolysis and oxidative pyrolysis proceed. The experiments have been designed so that these products are not completely destroyed and can be recovered for analysis. The analyses include measurements of basic nitrogen, average molecular weight, molecular weight distribution and unsubstituted aromatics by gas chromatography, and Hi NMR studies to determine average molecular structure parameters. 

In a search for the defining structural parameter of a composite, the free volume of disperse system proved to be the most sound one from the physical standpoint Presumably, for disperse systems the free volume is a measure of the mobility of filler particles, just as for liquids it is a measure of the mobility of molecules. But as applied to highly-loaded coarse systems of the type solid particles — liquid — gas this notion requires a certain correction. In characterizing the structure of such specific systems as highly-loaded coarse composites, it should be noted that to prevent their settling and separation into layers under the action of vibration, the concentration of the finest filler fraction with the largest specific surface in dispersion medium should be the maximum possible. Because of this and also because of the small size of particles (20-40 pm), the fine fraction suspended in the dispersion medium practically does not participate in the formation of the composite skeleton, which consists of coarser particles. Therefore... 

Equation (1.15), when applied to monoatomic liquids, predicts that the molar surface energy structural parameter m,. If mi is the same for all metals, scale with the quantity Le / Qm. It was shown in (Eustathopoulos et al. 1998) that equation (1.15), valid in principle only at OK, holds also at TF. As Qm is proportional to vm2/3 (vm denoting the molar volume), one obtains ... 

In this equation, Qm is the molar surface area, m i is a structural parameter defined in Section 1.1 (see Figure 1.3) and A is the regular solution parameter of Ni-Si alloy defined by equation (4.3). From the slope of the osL(XNi) curve for XNi— 0, the adsorption energy is found to be E i,(f ) = —8.2 kJ/mole. Thus, in equations (1.2), all the quantities are known (or can be easily estimated), except W and Wf 1 which represent respectively the work of adhesion and the work of immersion of pure liquid Ni in metastable equilibrium with SiC (i.e., for a supposed non-reactive pure Ni/SiC system). The values deduced from equation (1.2) are Wj4 = 3.17 J/m2 and W = —1.35 J/m2 for pure Ni. They are reported in Figure 7.6 along with the corresponding value of contact angle. 

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