Multicomponent systems, properties

Redenti, E., L. Szente, and J. Szejtli (2000). Drug/cyclodextrin/hydroxy acid multicomponent systems. Properties and pharmaceutical applicatiohS harm. Sci., 89 1-8. 

Redenti, E. Szente, L. Szejtli, J. Drug/cyclodextrin/ hydroxy acid multicomponent systems, properties and pharmaceutical applications. J. Pharm. Sci. 2000, 89 (1), 1-8. 

In order to specify fhe size of fhe sysfem, af leasf one of fhese variables ought to be extensive (one that is proportional to the size of the system, like n or the total volume V). In the special case of several phases in equilibrium several extensive properties, e.g. n and Vfor two phases, may be required to detennine the relative amounts of the two phases. The rest of the variables can be intensive (independent of the size of the system) like T,p, the molar volume V = V/n,or the density p. For multicomponent systems, additional variables, e.g. several ns, are needed to specify composifion. 

Synthetic polymers have become extremely important as materials over the past 50 years and have replaced other materials because they possess high strength-to-weight ratios, easy processabiUty, and other desirable features. Used in appHcations previously dominated by metals, ceramics, and natural fibers, polymers make up much of the sales in the automotive, durables, and clothing markets. In these appHcations, polymers possess desired attributes, often at a much lower cost than the materials they replace. The emphasis in research has shifted from developing new synthetic macromolecules toward preparation of cost-effective multicomponent systems (ie, copolymers, polymer blends, and composites) rather than preparation of new and frequendy more expensive homopolymers. These multicomponent systems can be "tuned" to achieve the desired properties (within limits, of course) much easier than through the total synthesis of new macromolecules. 

Conducting Polymer Blends, Composites, and Colloids. Incorporation of conducting polymers into multicomponent systems allows the preparation of materials that are electroactive and also possess specific properties contributed by the other components. Dispersion of a conducting polymer into an insulating matrix can be accompHshed as either a miscible or phase-separated blend, a heterogeneous composite, or a coUoidaHy dispersed latex. When the conductor is present in sufftcientiy high composition, electron transport is possible. 

From the definition of a partial molar quantity and some thermodynamic substitutions involving exact differentials, it is possible to derive the simple, yet powerful, Duhem data testing relation (2,3,18). Stated in words, the Duhem equation is a mole-fraction-weighted summation of the partial derivatives of a set of partial molar quantities, with respect to the composition of one of the components (2,3). For example, in an / -component system, there are n partial molar quantities, Af, representing any extensive molar property. At a specified temperature and pressure, only n — 1) of these properties are independent. Many experiments, however, measure quantities for every chemical in a multicomponent system. It is this redundance in reported data that makes thermodynamic consistency tests possible. 

Hctivity Coefficients. Most activity coefficient property estimation methods are generally appHcable only to pure substances. Methods for properties of multicomponent systems are more complex and parameter fits usually rely on less experimental data. The primary group contribution methods of activity coefficient estimation are ASOG and UNIEAC. Of the two, UNIEAC has been fit to more combinations of groups and therefore can be appHed to a wider variety of compounds. Both methods are restricted to organic compounds and water. 

Problem Solving Methods Most, if not aU, problems or applications that involve mass transfer can be approached by a systematic-course of action. In the simplest cases, the unknown quantities are obvious. In more complex (e.g., iTmlticomponent, multiphase, multidimensional, nonisothermal, and/or transient) systems, it is more subtle to resolve the known and unknown quantities. For example, in multicomponent systems, one must know the fluxes of the components before predicting their effective diffusivities and vice versa. More will be said about that dilemma later. Once the known and unknown quantities are resolved, however, a combination of conservation equations, definitions, empirical relations, and properties are apphed to arrive at an answer. Figure 5-24 is a flowchart that illustrates the primary types of information and their relationships, and it apphes to many mass-transfer problems. 

The material in this section is divided into three parts. The first subsection deals with the general characteristics of chemical substances. The second subsection is concerned with the chemistry of petroleum it contains a brief review of the nature, composition, and chemical constituents of crude oil and natural gases. The final subsection touches upon selected topics in physical chemistry, including ideal gas behavior, the phase rule and its applications, physical properties of pure substances, ideal solution behavior in binary and multicomponent systems, standard heats of reaction, and combustion of fuels. Examples are provided to illustrate fundamental ideas and principles. Nevertheless, the reader is urged to refer to the recommended bibliography [47-52] or other standard textbooks to obtain a clearer understanding of the subject material. Topics not covered here owing to limitations of space may be readily found in appropriate technical literature. 

The interest in this type of copolymers is still very strong due to their large volume applications as emulsifiers and stabilizers in many different systems 43,260,261). However, little is known about the structure-property relationships of these systems 262) and the specific interactions of different segments in these copolymers with other components in a particular multicomponent system. Sometimes, minor chemical modifications in the PDMS-PEO copolymer backbone structures can lead to dramatic changes in its properties, e.g. from a foam stabilizer to an antifoam. Therefore, recent studies are usually directed towards the modification of polymer structures and block lengths in order to optimize the overall structure-property-performance characteristics of these systems 262). 

These processes are very rapid and allow the preparation of inorganic supports in one step. This technique allows large-scale manufacturing of supports such as titania, fumed silica, and aluminas. Sometimes the properties of the material differ from the conventional preparation routes and make this approach unique. Multicomponent systems can be also prepared, either by multimetallic solutions or by using a two-nozzle system fed with monometallic solutions [22]. The as-prepared powder can be directly deposited onto substrates, and the process is termed combustion chemical vapor deposition [23]. 

The National Institute of Standards and Technology (NIST) molten salts database has been designed to provide engineers and scientists with rapid access to critically evaluated data for inorganic salts in the molten state. Properties include density, viscosity, electrical conductance, and surface tension. Properties for approximately 320 single salts and 4000 multicomponent systems are included, the latter being primarily binary. Data have been abstracted from the literature over the period 1890-1990. The primary data sources are the National Bureau of Standards-National... 

In emulsion and foam technology much is known concerning the properties and behavior of systems which involve only two or three components. Given a particular system and data concerning concentration, temperature, and manner of mixing, we can today predict fairly well the properties of the comparatively simple emulsion or foam. However, most emulsions and foams of importance are multicomponent systems and in these systems the predictability of the action or the properties of the emulsion or foam on a theoretical basis often becomes small. 

Choices of precursor(s) may be dictated by solubility, reactivity, or other property. For multicomponent systems, mutual solubility is another factor that must be considered. For such solutions, the solvent selected must facilitate dissolution of all precursors. 

Thermodynamic data (enthalpy of reaction, specific heat, thermal conductivity) for simple systems can frequently be found in date bases. Such data can also be determined by physical property estimation procedures and experimental methods. The latter is the only choice for complex multicomponent systems. 

The average dT/dt is typically an arithmetic average between the value at set pressure and the value at peak allowed pressure. The properties Cp, hfg, i, either can be evaluated at the set conditions or can be taken as the average values between the set condition and the peak allowed pressure condition. Alternatively, the term h/g/t)/g in Eq. (23-95) can be replaced by T(dP/dT)tat via the Clapeyron relation. This holds reasonably well for a multicomponent system of near constant volatility. Such an application permits direct use of the experimental pressure-temperature data obtained from a closed-system runaway VSP2 test. This form of Eq. (23-95) has been used to demonstrate the advantageous reduction in both vent rate and vent area with allowable overpressure (Leung, 1986a). 

The extension of the cell model to multicomponent systems of spherical molecules of similar size, carried out initially by Prigogine and Garikian1 in 1950 and subsequently continued by several authors,2-5 was an important step in the development of the statistical theory of mixtures. Not only could the excess free energy be calculated from this model in terms of molecular interactions, but also all other excess properties such as enthalpy, entropy, and volume could be calculated, a goal which had not been reached before by the theories of regular solutions developed by Hildebrand and Scott8 and Guggenheim.7... 

A or As). It is necessary to first establish a reliable experimental database for the property of interest, and then to fit it, by means of a statistical analysis code, to (usually) three or four of the quantities, appropriately selected, as computed for the molecules in the database. If the interaction involves multicomponent systems, as does solvation, then only one component may vary. For example, a relationship could be developed for a series of solutes in a particular solvent, or a given solute in different solvents. In doing so, we have always sought to use as few of the computed quantities as is consistent with a good correlation, since they can provide insight into the physical factors that are involved in the interaction this becomes obscured if many terms are involved. 

Covalently bonded substructures having compositions distinguishable from their surroundings are formed in multicomponent systems they are called chemical clusters. The adjective chemical defines covalency of bonds between units in the cluster. To be a part of a cluster, the units must have a common property. For example, hard clusters are composed of units yielding Tg domains. Hard chemical clusters are formed in three-component polyurethane systems composed of a macromolecular diol (soft component), a low-molecular-weight triol (hard component) and diisocyanate (hard component). Hard clusters consist of two hard... 

The performance of semiconducting inorganic materials as a photocatalyst depends much on the physical properties of the particles such as crystallinity, size and morphology. The effect can be even more pronounced when using two or more materials together, since an intimate interaction between particles is more important in the multicomponent system (So et al., 2004). 

In recent studies, Friberg and co-workers (J, 2) showed that the 21 carbon dicarboxylic acid 5(6)-carboxyl-4-hexyl-2-cyclohexene-1-yl octanoic acid (C21-DA, see Figure 1) exhibited hydrotropic or solubilizing properties in the multicomponent system(s) sodium octanoate (decanoate)/n-octanol/C2i-DA aqueous disodium salt solutions. Hydrotropic action was observed in dilute solutions even at concentrations below the critical micelle concentration (CMC) of the alkanoate. Such action was also observed in concentrates containing pure nonionic and anionic surfactants and C21-DA salt. The function of the hydrotrope was to retard formation of a more ordered structure or mesophase (liquid crystalline phase). 

Bertrand G. L., Acree W. E. Jr., and Burchfield T. (1983). Thermodynamical excess properties of multicomponent systems Representation and estimation from binary mixing data. J. Solution. Chem., 12 327-340. 

Most multicomponent systems undergo phase separation because of their positive mixing enthalpies coupled with low entropy of mixing. Morphological features have been central to the study of multicomponent systems, because domain sizes, shapes, and interfacial bonding characteristics determine the mechanical properties. A proper understanding of these features often allow synergistic behavior to be developed. 

Two different methods have been presented in this contribution for correlation and/or prediction of phase equilibria in ternary or mul> ticomponent systems. The first method, the clinogonial projection, has one disadvantage it is not based on concrete concepts of the system but assumes, to a certain extent, additivity of the properties of individiial components and attempts to express deviations from additivity of the properties of individual components and attempts to express deviations from additivity by using geometrical constructions. Hence this method, although simple and quick, needs not necessarily yield correct results in all the cases. For this reason, the other method based on the thermodynamic description of phase equilibria, reliably describes the behaviour of the system. Of cource, the theory of concentrated ionic solutions does not permit a priori calculation of the behaviour of the system from the thermodynamic properties of pure components however, if a satisfactory equation is obtained from the theory and is modified to express concrete systems by using few adjustable parameters, the results thus obtained are still substantially more reliable than results correlated merely on the basis of geometric similarity. Both of the methods shown here can be easily adapted for the description of multicomponent systems. 

The discovery of unusual physical or chemical properties in multicomponent systems demands the isolation and chemical and physical characterization of the single component which is responsible for the observed effect. In many instances the resulting search is less than systematic and depends more on serendipity than on careful experimentation. As an example, many of the early attempts to discover the compound responsible for superconducting transition temperatures in the 90K range were sometimes haphazard when viewed in terms of synthetic techniques. 

In many studies the chemisorption and the surface reaction is just the first step in a series of solid state reactions that take place as atoms from the surface move into the bulk. Corrosion, oxide, carbide and other compound formations are generally initiated at the surface and then propagate into the bulk. There may be a concentration gradient of certain constituents at the surface in a multicomponent system that would influence the mechanical or chemical properties of the system. Hardening of materials and other forms of passivation treatment frequently involve introduction of certain substances only in the near surface region. For the investigation of these problems RHEED is a powerful technique. 

Expressions for the transport coefficients suitable for use in computational simulations of chemically reacting flows are usually based on the Chapman-Enskog theory. The theory has been extended to address in detail transport properties in multicomponent systems [103,178]. 

Chapman-Enskog theory provides the basis for the multicomponent transport properties laid out by Hirschfelder, Curtiss, and Bird [178] and by Dixon-Lewis [103]. The multi-component diffusion coefficients, thermal conductivities, and thermal diffusion coefficients are computed from the solution of a system of equations defined by the L matrix [103], seen below. It is convenient to refer to the L matrix in terms of its nine block submatrices, and in this form the system is given by... 

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