Compositional mixture experiments

Compositional mixture experiments involve some specialist techniques and a whole range of considerations must be made before designing and analysing such experiments. The principal consideration is that die value of each factor is constrained. Take, for example, a du-ee component mixture of acetone, methanol and water, which may be solvents used as the mobile phase for a chromatographic separation. If we know diat diere is 80 % water in the mixture, there can be no more than 20 % acetone or methanol in die mixture. If there is also 15 % acetone, die amount of methanol is fixed at 5 %. In fact, aldiough there are three components in die mixtures, these translate into two independent factors. 

The parameter g,j is an energy parameter characteristic of the i-j interaction. The parameter an is related to the non-randomness in the mixture. The NRTL model contains three parameters which are independent of temperature and composition. However, experience has shown that for a large number of binary systems the parameter al2 varies from about 0.20 to 0.47. Typically, the value of 0.3 is set. 

It should be pointed out that to obtain a second-order model we have to do 66 trials, or 10 with pure components, 45 of binary composition, 10 internal points and one centroid point. However, the 21 compositions out of 31 mixtures from a screening experiment are simultaneously a part of the design of 66 design points for a second-order model. This shows that even in mixture experiments we may deal with the principle of upgrading/augmenting a design of experiments. 

Feng, Kostrov and Stewart (1974) reported multicomponent diffusion data for gaseous mixtures of helium (He), nitrogen (N2) and methane (CH4) through an extruded platinum-alumina catalyst as functions of pressure (1 to 70 atm), temperature (300 to 390 K), and terminal compositions. The experiments were designed to test several models of diffusion in porous media over the range between Knudsen and continuum diffusion in a commercial catalyst (Sinclair-Engelhard RD-150) with a wide pore-size distribution. 

The above discussion is confirmed by an experiment (Table 5) Potassium nitrate composition shows a very different character from others the combustion is quite unstable, and we cannot pick up general rules from these data. We have no experimental data here concerning black powder type compositions (mixture of potassium nitrate, charcoal and sulphur) and metal powder compositions, but the burning of such compositions is quite stable and their critical wind velocities seem to be very high. 

The dimensionless extra term 0 principally depends on the difference between the vapour and liquid compositions and is always positive, due to the reduction in heat transfer in the mixture. Experiments with numerous mixtures yielded a linear relationship... 

The notion of a semigrand ensemble arises when this decision is made in the context of mixture composition variables. Experience tells us that mole numbers or mole fractions are the most natural way to specify a mixture composition, and indeed anyone unfamiliar with the formalism of thermodynamics may not conceive that there exists an alternative. Of course, the component chemical potentials provide just this alternative, and their selection as independent thermodynamic variables in lieu of mole numbers is no less valid than the substitution of the pressure for the volume. In fact there are very familiar physical manifestations of semigrand ensembles in Nature. For example, in osmotic systems the amount of one component is not fixed, but takes a value to satisfy equality of chemical potential with a solvent bath. Another example is seen in systems undergoing chemical reaction, where the amounts of the various components are subject to chemical equilibrium. 

The bulk phase diagrams of pure hydrocarbons and mixtures are well known from the experiments. In the work by Sage et al. [3], the bubble point pressures of methane + n-butane mixtures are determined experimentally from the discontinuity of isothermal compressibility of constant-composition mixture at the point of phase transition. The composition of vapor phase is determined in that work from the residual specific volume of gas. Later experiments employ phase recirculation techniques [4] to achieve vapor-Uquid equilibrium [5, 6], and the phase compositions are analyzed by more advanced methods such as gas chromatography. 

Figure A2.5.31. Calculated TIT, 0 2 phase diagram in the vicmity of the tricritical point for binary mixtures of ethane n = 2) witii a higher hydrocarbon of contmuous n. The system is in a sealed tube at fixed tricritical density and composition. The tricritical point is at the confluence of the four lines. Because of the fixing of the density and the composition, the system does not pass tiirough critical end points if the critical end-point lines were shown, the three-phase region would be larger. An experiment increasing the temperature in a closed tube would be represented by a vertical line on this diagram. Reproduced from [40], figure 8, by pennission of the American Institute of Physics.

They then compared measured and predicted fluxes for diffusion experiments in the mixture He-N. The tests covered a range of pressures and a variety of compositions at the pellet faces but, like the model itself, they were confined to binary mixtures and isobaric conditions. Feng and Stewart [49] compared their models with isobaric flux measurements in binary mixtures and with some non-isobaric measurements in mixtures of helium and nitrogen, using data from a variety of sources. Unfortunately the information on experimental conditions provided in their paper is very sparse, so it is difficult to assess how broadly based are the conclusions they reached about the relative merits oi their different models. 

In general, tests have tended to concentrate attention on the ability of a flux model to interpolate through the intermediate pressure range between Knudsen diffusion control and bulk diffusion control. What is also important, but seldom known at present, is whether a model predicts a composition dependence consistent with experiment for the matrix elements in equation (10.2). In multicomponent mixtures an enormous amount of experimental work would be needed to investigate this thoroughly, but it should be possible to supplement a systematic investigation of a flux model applied to binary systems with some limited experiments on particular multicomponent mixtures, as in the work of Hesse and Koder, and Remick and Geankoplia. Interpretation of such tests would be simplest and most direct if they were to be carried out with only small differences in composition between the two sides of the porous medium. Diffusion would then occur in a system of essentially uniform composition, so that flux measurements would provide values for the matrix elements in (10.2) at well-defined compositions. 

A mixture of methyl paraben, ethyl paraben, propyl paraben, diethyl phthalate, and butyl paraben is separated by HPLC. This experiment emphasizes the development of a mobile-phase composition capable of separating the mixture. A photodiode array detector demonstrates the coelution of the two compounds. 

Scott and Kucera [4] carried out some experiments that were designed to confirm that the two types of solute/stationary phase interaction, sorption and displacement, did, in fact, occur in chromatographic systems. They dispersed about 10 g of silica gel in a solvent mixture made up of 0.35 %w/v of ethyl acetate in n-heptane. It is seen from the adsorption isotherms shown in Figure 8 that at an ethyl acetate concentration of 0.35%w/v more than 95% of the first layer of ethyl acetate has been formed on the silica gel. In addition, at this solvent composition, very little of the second layer was formed. Consequently, this concentration was chosen to ensure that if significant amounts of ethyl acetate were displaced by the solute, it would be derived from the first layer on the silica and not the less strongly held second layer. 

Scott and Beesley [2] measured the corrected retention volumes of the enantiomers of 4-benzyl-2-oxazolidinone employing hexane/ethanol mixtures as the mobile phase and correlated the corrected retention volume of each isomer to the reciprocal of the volume fraction of ethanol. The results they obtained at 25°C are shown in Figure 8. It is seen that the correlation is excellent and was equally so for four other temperatures that were examined. From the same experiments carried out at different absolute temperatures (T) and at different volume fractions of ethanol (c), the effect of temperature and mobile composition was identified using the equation for the free energy of distribution and the reciprocal relationship between the solvent composition and retention. 

Four different material probes were used to characterize the shock-treated and shock-synthesized products. Of these, magnetization provided the most sensitive measure of yield, while x-ray diffraction provided the most explicit structural data. Mossbauer spectroscopy provided direct critical atomic level data, whereas transmission electron microscopy provided key information on shock-modified, but unreacted reactant mixtures. The results of determinations of product yield and identification of product are summarized in Fig. 8.2. What is shown in the figure is the location of pressure, mean-bulk temperature locations at which synthesis experiments were carried out. Beside each point are the measures of product yield as determined from the three probes. The yields vary from 1% to 75 % depending on the shock conditions. From a structural point of view a surprising result is that the product composition is apparently not changed with various shock conditions. The same product is apparently obtained under all conditions only the yield is changed. 

The shock-modified composite nickel-aluminide particles showed behavior in the DTA experiment qualitatively different from that of the mixed-powder system. The composite particles showed essentially the same behavior as the starting mixture. As shown in Fig. 8.5 no preinitiation event was observed, and temperatures for endothermic and exothermic events corresponded with the unshocked powder. The observations of a preinitiation event in the shock-modified mixed powders, the lack of such an event in the composite powders, and EDX (electron dispersive x-ray analysis) observations of substantial mixing of shock-modified powders as shown in Fig. 8.6 clearly show the first-order influence of mixing in shock-induced solid state chemistry. 

With Freon 112 or 113 as a solvent, fluonnation of pnmary butyl halides with bromine trifluonde can give mixtures of primary and secondary fluorides When 1,4 dibromobutane is the substrate, 93% l-bromo-4-fluorobutane and 1% 1-bro-mo-3-fluorobutane is obtained, with 1,4 dichlorobutane, the product contains 65% l-chloro-3-fluorobutane and 35% 1-chloro 4 fluorobutane When 4-bromo- or 4-chlorobutyl trifluoroacetate is used, the ratio of 4-fluorobutyl tnfluoroacetate to 3 fluorobutyl trifluoroacetate is 1 4 The effect of solvent is measured in another set of experiments When the reaction of bromine trifluonde and l,3-dichloro-2-fluoropropane in either Freon 113 or hydrogen fluoride is allowed to proceed to 40% conversion, the product mixture has the composition shown m Table 1 [/O] When 1 chloro 2,3-dibromopropane is combined with one-third of a mole of bromine trifluonde, both 1 bromo 3 chloro-2-fluoropropane and l-chloro-2,3-di-fluoropropane are formed [//] (equation 10)... 

Styrene-based polymer supports are produced by o/w suspension polymerization of styrene and divinylbenzene. Suspension polymerization is usually carried out by using a monomer-soluble initiator such as benzoperoxide (BPO) or 2,2-azo-bis-isobutylnitrile (AIBN) at a temperature of 55-85°C (19). A relatively high initiator concentration of 1-5% (w/w) based on the monomer is used. The time required for complete monomer conversion must be determined by preliminary experiments and is usually between 5 and 20 h, depending on the initiator concentration, the temperature, and the exact composition of the monomer mixture (11-18). 

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