Multicomponent mixing

Although acrylonitrile manufacture from propylene and ammonia was first patented in 1949 (30), it was not until 1959, when Sohio developed a catalyst capable of producing acrylonitrile with high selectivity, that commercial manufacture from propylene became economically viable (1). Production improvements over the past 30 years have stemmed largely from development of several generations of increasingly more efficient catalysts. These catalysts are multicomponent mixed metal oxides mostly based on bismuth—molybdenum oxide. Other types of catalysts that have been used commercially are based on iron—antimony oxide, uranium—antimony oxide, and tellurium-molybdenum oxide. 

These reactions have been studied in detail for materials such as silica, and understanding of reaction mechanisms, as well as of the role of the precursor and catalyst (acid or base), has been well documented.63,64 Similar studies have been carried out in other material systems, most notably, lead zirconate titanate [Pb(Zr,Ti)03 PZT].52,65-68 For multicomponent (mixed-metal) systems such as those noted, prehydrolysis of less reactive alkoxides is sometimes employed to improve solution compositional uniformity. Other synthetic strategies to achieve molecular level mixing of reagents have also been employed. Here, synthesis of mixed-metal alkoxides has been a focus of investigators.40-42 A key point is to restrict the amount of water and to control how it is added to form solubalizable precursor species, rather than to induce precipitation.1,52,69,70... 

The pseudo-phase separation approach has been successfully applied in developing a generalized nonideal multicomponent mixed micelle model (see I4) and it is Interesting to consider whether this same approach can be used to develop a generalized treatment for adsorbed nonideal mixed surfactant monolayers. The preferred form for suoh a model is that it be suitable (at least in principle) for treating multiple components and be extendable to other interfaoes and properties of interest suoh as oontaot angles. Earlier models (5, 18, 27) based on the pseudo-phase separation approach and... 

The oxidation of ethane to acetic acid is believed to proceed via the intermediate formation of ethylene (Equation Al). The catalysts are multicomponent mixed oxides, having optimized compositions for ethane oxydehydro-genation (Mo-V oxides) and ethylene oxidation (Pd, Nb oxide). Reported... 

The obtained equations can be applied to numerous cases involving multicomponent solutions. In the present paper, we examine the gas solubilities and the solubilities of solid nonelectrolytes in multicomponent mixed solvents. 

Solubility of a Solid. For the solubilities of poorly soluble crystalline nonelectrolytes in a multicomponent mixed solvent, one can use the infinite-dilution approximation and consider that the activity coefficient of a solute in a mixed solvent is equal to the activity coefficient at infinite dilution. Therefore, one can write the following relations for the solubility of a poorly soluble crystalline nonelectrolyte in a ternary mixed solvent and in two of its binaries i2,i3... 

Solubility of drugs in aqueous solutions Part 3 Multicomponent mixed solvent... 

The results obtained previously by Ruckenstein and Shulgin [Int. J. Pharm. 258 (2003a) 193 Int. J. Pharm. 260 (2003b) 283] via the fluctuation theory of solutions regarding the solubility of drugs in binary aqueous mixed solvents were extended in the present paper to multicomponent aqueous solvents. The multicomponent mixed solvent was considered to behave as an ideal solution and the solubility of the drug was assumed small enough to satisfy the infinite dilution approximation. 

Keywords Solubility of drugs Multicomponent mixed solvent Fluctuation theory... 

The two previous papers (Ruckenstein and Shulgin, 2003a, b) of this series were focused on the solubility of a solid (particularly a drug) in binary mixed (mainly aqueous) solvents. The present paper extends the method suggested in the above publications to the solubility of drugs in ternary and multicomponent mixed solvents. 

For the solubility of a solid (solute, component 2) in a (n - 1) multicomponent mixed solvent one can write the following equation (Acree, 1984 Prausnitz et al, 1986) ... 

When the solubility of the solute is small (which is typical for drugs in aqueous mixed solvents), one can write the following expressions (see Eq. (1)) for the solubility of a solute in the above multicomponent mixed solvents ... 

Ruckenstein, E., Shulgin, I., 2003c. Solubility of drugs in aqueous solutions. Part 3. Multicomponent mixed solvent. Int. J. Pharm. 267, 121-127. 

The paper is organized as follows first, the thermodynamic relations for the solubility of poorly soluble solids in pure and multicomponent mixed solvents are written. Second, an equation for the activity coefficient of a solute at infinite dilution in a binary nonideal mixed solvent [23) is employed to derive an expression for its solubility in terms of the properties of the mixed solvent. Third, various expressions for the activity coefficients of the cosolvents, such as Margules and Wilson equations [19), are inserted into the above equation for the solubility. The obtained equations are used to correlate the HOP solubilities in binary aqueous mixed solvents and the results are compared with experiment. Finally, the case of an ideal multicomponent solvent is considered and used for ternary and higher mixed solvents. 

Expression for the Solubility of a Poorly Soluble Solid in a Multicomponent Mixed Solvent. By inserting into Equation 22 the expressions of y" , and... 

Solute Multicomponent mixed solvent MPDiA MPD, MPDi MPD2... 

The prediction of the solubility of poorly soluble substances of environmental significance in multicomponent (ternary and higher) aqueous mixed solvents is a difficult task because it requires the knowledge of the activity coefficient of a solute in a multicomponent mixed solvent. The method most often used for the solubility of a solid in ternary and multicomponent mixed solvents is the combined nearly ideal binary solvent/Redlich - Kister equation (33). That equation was applied to the solubility of a solid in ternary... 

Rohm, H. J., The Simulation of Steady State Behavior of the Dephlegmation of Multicomponent Mixed Vapors, Int. J. Heat Mass Transfer, 23, 141-146 (1980). 

Scheme 3. Proposed Mechanism of Propane Ammoxidation using a Paraffin Activating Catalyst, e.g.,NiaCobMcMoOx and a Multicomponent Mixed Metal Molybdate Olefin Ammoxidation Catalyst, e.g., CSaKbNicMgdMeBif SbgMOhOx, where M = Ce, Cr, or Fe [15].

An eluent container can be a Mariotte flask that produces constant hydrostatic pressure, and thus it can serve for the generation of the gravitational eluent transport in the chromatographs of the first generation. Simple solvent tanks, or even open vessels, are used as eluent containers in the instruments provided with efficient pumping systems. The preferential evaporation effects, however, should be prevented when working with multicomponent, mixed eluents. 

Part II Multicomponent Mixed Conductors Under Closed Circuit Conditions... 

What is clearly needed is a working model for multicomponent, mixed-conducting electrolytes, one which would be applicable to closed as well as open circuit conditons and yet would be relatively... 

Figure 6. Direct current (dc) analog for a multicomponent mixed conducting...

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