Simulation mixture

W. Windig, P. G. Kistenmaker, and J. Haverkamp, Chemical interpretation of differences in pyrolysis—Mass spectra of simulated mixtures of biopolymers by factor analysis with graphical rotation, J. Anal. Appl. Pyrolysis 3(3), 199-212 (1981/1982)... 

The matrix of extinction coefficients for the components of product PI can be assembled by arranging the vectors of extinction coefficients into the rows of Epi = [ j,e5,e6, , ]. The matrix of concentrations, C, for the subset of active species in product PI is given in the right-hand side of Table 8.19, or in matrix form, C = [C1( C5, C6, C7, C9], According to the Beer-Lambert law in Equation 8.79, the product of these two matrices gives the matrix of simulated mixture spectra, A, for the calibration set, where the path length, l, is assumed equal to 1. 

Try to simulate mixture experiments with single component isotherms. 

Chen et al [12] and Bertola et al [8] simulated mixtures consisting of A1+1 phases by use of algebraic slip mixture models (ASMMs) which have been combined with a population balance equation. Each bubble size group did have individual local velocities which were calculated from appropriate algebraic slip velocity parameterizations. In order to close the system of equations, the mixture velocity was expressed in terms of the individual phase velocities. The average gas phase velocity was then determined from a volume weighted slip velocity superposed on the continuous phase velocity. Chen et al [12] also did run a few simulations with the ASMM model with the same velocity for all the bubble phases. 

Subsequent applications of semigrand methods have been numerous, as species-identity changes have become a standard practice when simulating mixtures. We would fail in an attempt to mention all such uses, so instead we will sample some of the more interesting applications and extensions. Hautman and Klein [22] examined, by molecular dynamics a breathing Lennard-Jones fluid of fluctuating particle diameter the breathing modes are introduced to better model molecules that are treated as LJ atoms. Liu... 

Try to simulate mixture e q)eriments with single-component isotherms Determine component interactions only if necessary Check agreement between theoretical and e5q)erimental chromatograms Static methods... 

The accuracy and precision of the substoichiometry were evaluated by determining U(VI) in a simulated mixture containing a known amount of U(VI) and large amounts of diverse ions together with phosphoric acid. After a preliminary extraction of U(VI) from 6M nitric acid into 2% TBP in toluene, the substoichiometric extraction was applied. The high precision of 0.23% RSD and the high accuracy of -b 0.5% relative... 

Figure 10.2. Snapshots at different times of a jelly-bean representation of a simulated mixture of water and Nafion in protonated form (at water content A = 5). Dark Red regions denote polymer, grey, blue and yellow regions denote water, hydronium and sulfonate groups, respectively, in the aqueous phase. The indicated box corresponds to a length of 4.5 nm. Note that the jelly-bean surfaces hide a large number of molecules [72].

Nataraj, S.K., Hosamani, K.M. and Aminabhavi, T.M. 2009. Nanofiltration and reverse osmosis thin film composite membrane module for the removal of dye and salts from the simulated mixtures, 249 12-17. 

Table 6.9.2 Evaluation of the concentration of three rare earth elements in a simulated mixture at 773 K...

Sample recovery Some reactions will not allow the spiking of the reaction and/ or process mixture with SM without rapidly converting it to product. In these cases, a quenched reaction or process simulation mixture may be used as a substitute. Process simulation mixtures are used for IPC samples that are only stable for a few hours, or spike recovery cannot be performed in the reaction or process matrix. A process simulation sample is made using the same chemical reagents in the reaction. The components of the process simulation matrix should be determined in -collaboration with the process chemist. The stability of the process simulation mixture should be determined before the initiation of the formal method validation. 

Figure 15-1 Simulated mixtures (a) perfect mixture (b) random mixture. (From Williams, 1986.)...

From the analytical results, it is possible to generate a model of the mixture consisting of an number of constituents that are either pure components or petroleum fractions, according to the schematic in Figure 4.1. The real or simulated results of the atmospheric TBP are an obligatory path between the experimental results and the generation of bases for calculation of thermodynamic and thermophysical properties for different cuts. 

Distillation simulated by gas chromatography is a reproducible method for analyzing a petroleum cut it is appiicabie for mixtures whose end point is less than 500°C and the boiling range is greater than 50°C. The results of this test are presented in the form of a curve showing temperature as a function of the weight per cent distilled equivalent to an atmospheric TBP. 

The CS pressures are close to the machine calculations in the fluid phase, and are bracketed by the pressures from the virial and compressibility equations using the PY approximation. Computer simulations show a fluid-solid phase transition tiiat is not reproduced by any of these equations of state. The theory has been extended to mixtures of hard spheres with additive diameters by Lebowitz [35], Lebowitz and Rowlinson [35], and Baxter [36]. 

The Gibbs ensemble method has been outstandingly successfiil in simulating complex fluids and mixtures. 

Vlugt T J H, Krishna R and Smit B 1999 Molecular simulations of adsorption isotherms for linear and branched alkanes and their mixtures in silicalite J. Phys. Ohem. B 103 1102-18... 

Panagiotopoulos A Z, Quirke N, Stapleton M and Tildesley D J 1988 Phase equilibria by simulation in the Gibbs ensemble. Alternative derivation, generalization and applioation to mixture and membrane equilibria Mol. Phys. 63 527-45... 

Deutsoh H-P and Binder K 1993 Mean-field to Ising orossover in the oritioal behavior of polymer mixtures—a finite size sealing analysis of Monte Carlo simulations J. Physique II 3 1049... 

As shown in section C2.6.6.2, hard-sphere suspensions already show a rich phase behaviour. This is even more the case when binary mixtures of hard spheres are considered. First, we will mention tire case of moderate size ratios, around 0.6. At low concentrations tliese fonn a mixed fluid phase. On increasing tire overall concentration of mixtures, however, binary crystals of type AB2 and AB were observed (where A represents tire larger spheres), in addition to pure A or B crystals [105, 106]. An example of an AB2 stmcture is shown in figure C2.6.11. Computer simulations confinned tire tliennodynamic stability of tire stmctures tliat were observed [107, 1081. 

A second case to be considered is that of mixtures witli a small size ratio, <0.2. For a long time it was believed tliat such mixtures would not show any instability in tire fluid phase, but such an instability was predicted by Biben and Flansen [109]. This can be understood to be as a result of depletion interactions, exerted on the large spheres by tire small spheres (see section C2.6.4.3). Experimentally, such mixtures were indeed found to display an instability [110]. The gas-liquid transition does, however, seem to be metastable witli respect to tire fluid-crystal transition [111, 112]. This was confinned by computer simulations [113]. 

Oykstra M, van Roi] R and Evans R 1999 Direot simulation of the phase behaviour of binary hard-sphere mixtures test of the depletion potential desoription Phys. Rev. Lett. 82 117-20... 

We tested our recipe on many trial densities by Monte Carlo simulation, c. g., on the normal mixture tajrget densities of Jones et al. [14]. Examples of pair potentials U r) = Wy q r)) reconstructed in this way are given in Figure 3. 

One application of the grand canonical Monte Carlo simulation method is in the study ol adsorption and transport of fluids through porous solids. Mixtures of gases or liquids ca separated by the selective adsorption of one component in an appropriate porous mate The efficacy of the separation depends to a large extent upon the ability of the materit adsorb one component in the mixture much more strongly than the other component, separation may be performed over a range of temperatures and so it is useful to be to predict the adsorption isotherms of the mixtures. 

A7 Ethane/methane selectivity calculated from grand canonical Monte Carlo simulations of mixtures in slit IS at a temperature of 296 K. The selectivity is defined as the ratio of the mole fractions in the pore to the ratio of mole fractions in the bulk. H is the slit width defined in terms of the methane collision diameter (Tch,- (Figure awn from Crackncll R F, D Nicholson and N Quirke 1994. A Grand Canonical Monte Carlo Study ofLennard-s Mixtures in Slit Pores 2 Mixtures of Two-Centre Ethane with Methane. Molecular Simulation 13 161-175.)... 

The breaking up of azeotropic mixtures. The behaviour of constant boiling point mixtures simulates that of a pure compound, because the composition of the liquid phase is identical with that of the vapour phase. The composition, however, depends upon the pressure at which the distillation is conducted and also rarely corresponds to stoichiometric proportions. The methods adopted in practice will of necessity depend upon the nature of the components of the binary azeotropic mixture, and include —... 

Solvents exert their influence on organic reactions through a complicated mixture of all possible types of noncovalent interactions. Chemists have tried to unravel this entanglement and, ideally, want to assess the relative importance of all interactions separately. In a typical approach, a property of a reaction (e.g. its rate or selectivity) is measured in a laige number of different solvents. All these solvents have unique characteristics, quantified by their physical properties (i.e. refractive index, dielectric constant) or empirical parameters (e.g. ET(30)-value, AN). Linear correlations between a reaction property and one or more of these solvent properties (Linear Free Energy Relationships - LFER) reveal which noncovalent interactions are of major importance. The major drawback of this approach lies in the fact that the solvent parameters are often not independent. Alternatively, theoretical models and computer simulations can provide valuable information. Both methods have been applied successfully in studies of the solvent effects on Diels-Alder reactions. 

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