Composition conception

The fact that crystalline polymers are multiphase materials has prompted a new approach in characterizing their internal structure (lamellar thickness, perfection, etc.) and relating it to the hardness concept (volume of material locally deformed under a point indenter). In lamellar PE microhardness is grossly a given increasing function of lamellar thickness. In using the composite concept care must be exercised to emphasize and properly account for the non-crystalline phase and its various... 

The second is based on the local composition concept and represents work in progress. 

Among the various models incorporating the local composition concept for short-range interactions, the NRTL equation is adopted in this study. Electrolyte systems are characterized by extraordinarily large heats of mixing. 

Two activity coefficient models have been developed for vapor-liquid equilibrium of electrolyte systems. The first model is an extension of the Pitzer equation and is applicable to aqueous electrolyte systems containing any number of molecular and ionic solutes. The validity of the model has been shown by data correlation studies on three aqueous electrolyte systems of industrial interest. The second model is based on the local composition concept and is designed to be applicable to all kinds of electrolyte systems. Preliminary data correlation results on many binary and ternary electrolyte systems suggest the validity of the local composition model. 

But the potentiality of molecular structure could not be successfully pursued until the atomic weights were reliably established and the number of atoms in the molecules could be reliably known. This was not accomplished until fifty years later, by Stanislao Cannizzaro, through a rigorous application of Avogadros hypothesis first published in 1811. Since this long complex story does not involve any change in the compositional concepts introduced by Dalton, it is appropriate to offer only a brief account. 

Two classes of reactive secondary amines (XX and XXI) were synthesized [90] for the thermoset version of the In Situ Molecular Composite concept. The thermoset chemistry of the bisnadimide (XX) involved that of PMR systems (polymerization of monomeric reactants) [95], The secondary amine (XXI) embodied the more recent ringopening polymerization of benzocyclobutene (BCB) [96]. Polymerization exotherms for both thermoset amines occurred with an onset at 225 °C, maximizing at approximately 260 °C as evidenced by DSC at a heating rate of 10 °C/m. 

Model polyamicdialkylamides were prepared by the reaction of the secondary amines (XX) and (XXI) with the polyisoimide (XVII) in DMAC at room temperature. Unfortunately, the resultant polyamicdialkylamides only exhibited limited softening behavior for processing into bulk specimens. The inability to provide molded specimens prevented the validation of the In Situ Molecular Composite concept. Research is currently being carried out at a number of academic and industrial institutions on new thermoset chemistry, polyamices-ters, and extended chain polyimides. 

Ramakrishna S., Ramaswamy S., Teoh S.H., et al., Application of textiles and textile composites concepts for biomaterials development Int. Conf. New Textiles for Composites, TEXCOMP 3 Conference Series, Aachen, Germany, 1996, 1-27. 

It should be noted that distribution coefficients Ki comprise both fugacities in the gas phase and activity coefficients in the liquid phase. These coefficients are determined by the three-parametric Electrolyte-NRTL method. The latter is based on the local composition concept and satisfactorily represents physical interactions of this multicomponent electrolyte system [46]. 

We can estimate the activity coefficients by using the excess Gibbs energy models. Based on the local composition concept, the Wilson, NRTL, and UNIQUAC models for excess Gibbs energy provide relations for activity coefficient... 

MoUerup, J. A note on excess Gibbs energy models, equations of state and the local composition concept. Fluid Phase Equilib. 1981, 7, 121-138. 

The activity coefficient models mentioned above depend on the overall space-averaged composition of the solution. On the other hand the range of intermolecular forces acting in an ordinary liquid mixture is rather short and is limited to a few molecular diameters. Consequently, it has been proposed that one use a local composition around the molecules that could be different from the overall composition of the solution. A thorough analysis of the local composition concept can be found... 

Excluded are principles no. 8 and 12, which state rules that govern the construction of compositional concept names they do not apply to the C EDM, as we do not utilize such compositional terms. Principle no. 13 is debatable It advices to avoid ambiguous words in concept definitions, such as which may , indicates , characterizes , etc. While we certainly tried to define concepts as precisely as possible, words like characterize and indicates have been used regularly, in order... 

Heil and Prausnitz proposed an FH/UNIQUAC-type model, which has been applied to a number of ternary liquid-liquid PS-mixed solvent systems. Satisfactory results were obtained for the ternary systems using solely two parameters per binary. These results show the potential of local composition concept (UNIQUAC, UNIFAC) for multicomponent polymer systems. The required binary parameters were estimated from solvent-polymer VLE data. 

No known model for g meets all the above criteria. As with PVTr equations of state, the choice of an expression for g for en eagineering calculation is frequently uiede on en ed hoc basis. We discuss in the next two sections two classes of expressions commonly employed for practical work classical empirical expressions for g and more recent expressions for g based on the local-composition concept. 

Wilson (1964) brought the first major contribution in the field of modem liquid activity models by developing the local composition concept. This is related to the segregation caused by different interaction energies between pairs of molecules. Thus, the probability of finding a species 1 surrounded by molecules of species 2, relative to the probability of being surrounded by the same species 1, is given by the expression ... 

NRTL (non-random two-liquids) model developed by Renon and Prausnitz (1968) is an extension of the local composition concept that accounts for the non-randomness of interaetions. The following expression for is obtained ... 

The Wilson equation can be extended to immiscible liquid systems by multiplying the right-hand side of (5-41) by a third binary-pair constant evaluated from experimental data. However, for multicomponent systems of three or more species, the third binary-pair constants must be the same for all constituent binary pairs. Furthermore, as shown by Hiranuma, representation of ternary systems involving only one partially miscible binary pair can be extremely sensitive to the third binary-pair Wilson constant. For these reasons, application of the Wilson equation to liquid-liquid systems has not been widespread. Rather, the success of the Wilson equation for prediction of activity coefficients for miscible liquid systems greatly stimulated further development of the local composition concept in an effort to obtain more universal expressions for liquid-phase activity coefficients. 

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