Mixtures of very similar components

In Section 4.4 we showed that in a mixture of very similar components, the chemical potential of each component has the form... 

One can effectively reduce the tliree components to two with quasibinary mixtures in which the second component is a mixture of very similar higher hydrocarbons. Figure A2.5.31 shows a phase diagram [40] calculated from a generalized van der Waals equation for mixtures of ethane n = 2) with nomial hydrocarbons of different carbon number n.2 (treated as continuous). It is evident that, for some values of the parameter n, those to the left of the tricritical point at = 16.48, all that will be observed with increasing... 

It is worth noting here that this difference between the interface and in the bulk is not specific to surfactant mixtures. While oil mixtures of very similar substances, such as n-alkanes, exhibit a linear mixing rule written in terms of equivalent alkane carbon number or EACN [62-64], mixtures of oils containing substances with very different polarities behave in a non-ideal way and exhibit a segregation near the interface, which results in an accumulation most polar oil components close to the interface [65]. 

The studies described above illustrate the difficulties in predicting the effects of mixtures, even when all components are chemically similar. In these studies, exposures to lipophilic mixtures of very similar compounds produced expected effects in one study and unanticipated effects in different body organs in the other studies. These studies, as well as others describing the effects of lipophile/hydrophile mixtures, point out the need to limit exposures to aromatic hydrocarbons. 

An interesting question, which is closely related to the VPIE, is the deviation of isotopic mixtures from the ideal behavior. Isotopic mixtures, that is, mixtures of isotopic molecules (e.g., benzene and deuterated benzene), have long been considered as textbook examples of ideal solutions statistical theory predicts that mixtures of very similar species, in particular isotopes, will be ideal the only truly ideal solutions would thus involve isotopic species molecules which differ only by isotopic substitution... form ideal solutions except for isotope mixtures, ideal solutions will occur rather rarely we expect binary solutions to have ideal properties when the two components are isotopes of each other. ... 

For liquid crystal displays, mixtures of liquid crystals are always used. Therefore, there is an essential interest in models that predict the rotational viscosity of mixtures from the rotational viscosities of the pure components. With the exception of mixtures of very similar compounds, the dependence of the shear viscosity of isotropic liquids on the mixture composition is normally complex. Due to the additional dependence on the order parameter, one cannot expect a simple concentration dependence for the rotational viscosity of liquid crystals. Figure 20 shows the rotational viscosities of a series of mixtures between the ester LCl... 

DOSY is a technique that may prove successful in the determination of additives in mixtures [279]. Using different field gradients it is possible to distinguish components in a mixture on the basis of their diffusion coefficients. Morris and Johnson [271] have developed diffusion-ordered 2D NMR experiments for the analysis of mixtures. PFG-NMR can thus be used to identify those components in a mixture that have similar (or overlapping) chemical shifts but different diffusional properties. Multivariate curve resolution (MCR) analysis of DOSY data allows generation of pure spectra of the individual components for identification. The pure spin-echo diffusion decays that are obtained for the individual components may be used to determine the diffusion coefficient/distribution [281]. Mixtures of molecules of very similar sizes can readily be analysed by DOSY. Diffusion-ordered spectroscopy [273,282], which does not require prior separation, is a viable competitor for techniques such as HPLC-NMR that are based on chemical separation. 

Second, Raoult s equation is based on the assumption that the liquid behaves as an ideal solution. Ideal-solution behavior is approached only if the components of the liquid mixture are very similar chemically and physically. 

This method provides the exact solutions for ideal systems at constant temperature and pressure. It is successful in describing diffusion flow in (i) nearly ideal mixtures, (ii) equimolar counter diffusion where the total flux is zero (Nt = 0), (iii) diffusion of one component through a mixture of n — 1 inert components, and (iv) pseudo-binary case and the diffusion of two very similar components in a third. 

For notational convenience, we shall discuss a two-component mixture of A and B. The generalization for multicomponent system is quite straightforward. We consider a system of two components in the T, P, NA, NB ensemble. We have chosen the T, P, NA, NB ensemble because the isothermal-isobaric systems are the most common ones in actual experiments. By very similar components, we mean, in the present context, that the potential energy of interaction among a group of n molecules in a configuration X is independent of the species we... 

For a mixture of components that behaves ideally, it can be derived that there is no change in enthalpy when the components are mixed, i.e., no heat is released nor consumed. The decrease in free energy due to mixing then is purely due to an increase in entropy. Such a situation may occur for two components of very similar properties, for instance for a mixture of closely related triglycerides. However, if one of the components is a solid at the temperature of mixing, it has to melt, and this means an increase in enthalpy, equal to the enthalpy of fusion AH( (the enthalpy of mixing is still assumed to be zero). This implies that there is a limited solubility (xs), given by the Hildebrand equation,... 

The entries in Tables 8.6-2 and 8.6-4 are interesting in that they show that the partial molar volume and partial molar enthalpy of a species in a mixture are very similar to the pure component molar quantities when the mole fraction of that species is near unity and are most different from-the pure component values, at infinite dilution, that is, as the species mole fraction goes to zero. (The infinite dilution values in Tables 8.6-2 and... 

Usually, peak capacity is defined as the number of peaks per unit time, see Eq. (3.5). The peak capacity as a separation criterion proves to be important when very similar components have to be separated, such as components of a homologous series, for example, ohgomers in this case, one expects equidistant spacing of the peaks. With similar components, we can hardly expect different interactions and thus a good selectivity. The situation is similar in the case of complex mixtures and/or a difficult matrix. Again, realistically here we do not come any further via selectivity. A separation in this case will be possible, when the many (similar ) components can be eluted distributed as narrow peaks throughout the chromatogram. 

A procedure called chromatography automatically and simply applies the principles of these fractional separation procedures. Chromatography can separate very complex mixtures composed of many very similar components. The various types of chromatographic instrumentation... 

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