Binary mixed solvent

The Kirkwood—Buff integrals Gu and G13 can be calculated from the characteristics of the protein-free mixed solvent (binary mixture 1—3) using the expressions " " ... 

The properties of a copolymer can be viewed as hybrids of the properties of the separate homopolymers. Because of this, a good deal of refinement can be introduced into these properties by the use of copolymers. The situation is analogous to the use of pure liquids or binary solutions as solvents. The number of binary combinations, n(n - l)/2 as noted above, greatly exceeds the number of pure liquids, and any one of these combinations can be prepared over a range of compositions. Just as mixed solvents offer a wider range of properties than... 

Most of what we know about solvent effects is a result of studies in which the reactivity is compared in a series of solvents. There are two main types of experimental design in one of these the reaction is carried out in different pure solvents in the other design the reaction is studied in mixed solvents, often a binary mixture whose composition is varied across the entire range. Experimental limitations often... 

The bulk properties of mixed solvents, especially of binary solvent mixtures of water and organic solvents, are often needed. Many dielectric constant measurements have been made on such binary mixtures. The surface tension of aqueous binary mixtures can be quantitatively related to composition. ... 

When the range of chemieal types is restricted, regular behavior is often observed. For example, one might choose to study a series of hydroxylic solvents, thus holding approximately constant the H-bonding capabilities within the series. This is a motivation, also, for solvent studies in a series of binary mixed solvents, often an organic-aqueous mixture whose composition may be varied from pure water to pure organic. Mukerjee et al. defined a quantity H for hydroxylic and mixed hydroxyiic-water solvents by Eq. (8-17). 

Figure 7 shows the FOM of an AA cell and the PC content in EC/PC binary mixed-solvent electrolytes. With an increase in PC content, the lithium cycling efficiency (Eff) obtained with Li cycling on a stainless steel substrate increases. However, the FOM of the AA cell reaches its maximum value at EC/PC=1 9 [82], This result arises from the interaction between EC and the a-V205-P205 cathode. 

The equation of Krichevsky and Ilinskaya can readily be extended to high-pressure solutions of a gas in a mixed solvent, as shown by O Connell (01) and discussed briefly by Orentlicher (03). This extension makes it possible to predict the behavior of simple multicomponent systems using binary data only. 

Preferential solvation of ions in binary mixed solvents. S. Janardhanau and C. Kalidas, Rev. Inorg. Chem., 1984, 6, 101,(91). 

The physical reason for the inherent lack of incentive for mixing in a polymer-polymer system is related to that already cited in explanation of the dissymmetry of the phase diagram for a polymer-solvent binary system. The entropy to be gained by intermixing of the polymer molecules is very small owing to the small numbers of molecules involved. Hence an almost trivial positive free energy of interaction suffices to counteract this small entropy of mixing. 

Special care has to be taken if the polymer is only soluble in a solvent mixture or if a certain property, e.g., a definite value of the second virial coefficient, needs to be adjusted by adding another solvent. In this case the analysis is complicated due to the different refractive indices of the solvent components [32]. In case of a binary solvent mixture we find, that formally Equation (42) is still valid. The refractive index increment needs to be replaced by an increment accounting for a complex formation of the polymer and the solvent mixture, when one of the solvents adsorbs preferentially on the polymer. Instead of measuring the true molar mass Mw the apparent molar mass Mapp is measured. How large the difference is depends on the difference between the refractive index increments ([dn/dc) — (dn/dc)A>0. (dn/dc)fl is the increment determined in the mixed solvents in osmotic equilibrium, while (dn/dc)A0 is determined for infinite dilution of the polymer in solvent A. For clarity we omitted the fixed parameters such as temperature, T, and pressure, p. 

Where binary, ternary or quaternary gradient elution (p. 91) is required, a microprocessor controlled low-pressure gradient former is the most suitable (Figure 4.31(c)). The solvents from separate reservoirs are fed to a mixing chamber via a multiport valve, the operation of which is preprogrammed via the microprocessor, and the mixed solvent is then pumped to the column. For the best reproducibility of solvent gradients small volume pumps (< 100 gl) are essential. 

In Eq. (88), dn0/dl expresses how the refractive index % of the binary solvent alone varies with its composition expressed as volume fraction 4>y of liquid-1. Clearly, if liquids 1 and 3 are iso-refractive or nearly so, then M = M2, that is, a LS experiment will yield the true molecular weight irrespective of the composition of the mixed solvent. This situation is exemplified133) by the system polystyrene -ethyl-acetate (l)-ethanol (3) for which the molecular weight in mixed solvents of different 0i is the same as that obtained in pure ethylacetate (Fig. 40). The values of dn /d0j for the mixed solvents are only of the very small order of ca. 0.01, whilst the values of dn/dc for the polymer solutions are large (ca. 0.22 ml/g). 

Another type of ternary electrolyte system consists of two solvents and one salt, such as methanol-water-NaBr. Vapor-liquid equilibrium of such mixed solvent electrolyte systems has never been studied with a thermodynamic model that takes into account the presence of salts explicitly. However, it should be recognized that the interaction parameters of solvent-salt binary systems are functions of the mixed solvent dielectric constant since the ion-molecular electrostatic interaction energies, gma and gmc, depend on the reciprocal of the dielectric constant of the solvent (Robinson and Stokes, (13)). Pure component parameters, such as gmm and gca, are not functions of dielectric constant. Results of data correlation on vapor-liquid equilibrium of methanol-water-NaBr and methanol-water-LiCl at 298.15°K are shown in Tables 9 and 10. 

The study of solute-solvent and solvent-solvent interactions in mixed solvents has been gaining significance in recent years61-64, because of the increasing application of these solvents. Casassas and collaborators67 have used the Kamlet-Taft multiparametric equation for the correlation of dissociation constants of acids in 1, 4-dioxane-water mixtures. They found that when the main solvent is retained the property does not involve significant changes in the cavity volumes and, in those cases, the pK in binary solvents can be described by equation 8 ... 

Natural equality constraints exist in many real systems. For example, consider a chemical reaction in which a binary mixed solvent is to be used (see Figure 2.15). We might specify two continuous factors, the amount of one solvent (represented by X,) and the amount of the other solvent ( 2). These are clearly continuous factors and each has only a natural lower bound. However, each of these factors probably should have an externally imposed upper bound, simply to avoid adding more total solvent than the reaction vessel can hold. If the reaction vessel is to contain 10 liters, we might specify the inequality constraints... 

Solubilities, in water, ethanol, and ethanol-water mixtures, have been reported for [Fe(phen)3]-(0104)2, [Fe(phen)3]2[Fe(CN)6], and [Fe(phen)3][Fe(phen)(CN)4]. Solubilities of salts of several iron(II) iiimine complexes have been measured in a range of binary aqueous solvent mixtures in order to estimate transfer chemical potentials and thus obtain quantitative data on solvation and an overall picture of how solvation is affected by the nature of the ligand and the nature of the mixed solvent medium. Table 8 acts as an index of reports of such data published since 1986 earlier data may be tracked through the references cited below Table 8, and through the review of the overall pattern for iron(II) and iron(III) complexes (cf. Figure 1 in Section 5.4.1.7 above) published recently. ... 

A review is presented of techniques for the correlation and prediction of vapor-liquid equilibrium data in systems consisting of two volatile components and a salt dissolved in the liquid phase, and for the testing of such data for thermodynamic consistency. The complex interactions comprising salt effect in systems which in effect consist of a concentrated electrolyte in a mixed solvent composed of two liquid components, one or both of which may be polar, are discussed. The difficulties inherent in their characterization and quantitative treatment are described. Attempts to correlate, predict, and test data for thermodynamic consistency in such systems are reviewed under the following headings correlation at fixed liquid composition, extension to entire liquid composition range, prediction from pure-component properties, use of correlations based on the Gibbs-Duhem equation, and the recent special binary approach. 

Here 113 is completely defined by the variables Z and N3. For any given values of Z and N3, the reference of the activity coefficient will be chosen as the extremely dilute state (N3 = 0) of the given solute in a binary mixed solvent of the same composition Z. By the definition, the chemical potential of the reference state varies with Z. Hence, one obtains for the 1-1 salts... 

The salt effects of potassium bromide and a series office symmetrical tetraalkylammonium bromides on vapor-liquid equilibrium at constant pressure in various ethanol-water mixtures were determined. For these systems, the composition of the binary solvent was held constant while the dependence of the equilibrium vapor composition on salt concentration was investigated these studies were done at various fixed compositions of the mixed solvent. Good agreement with the equation of Furter and Johnson was observed for the salts exhibiting either mainly electrostrictive or mainly hydrophobic behavior however, the correlation was unsatisfactory in the case of the one salt (tetraethylammonium bromide) where these two types of solute-solvent interactions were in close competition. The transition from salting out of the ethanol to salting in, observed as the tetraalkylammonium salt series is ascended, was interpreted in terms of the solute-solvent interactions as related to physical properties of the system components, particularly solubilities and surface tensions. 

With the use of thermodynamic relations and numerical procedure, the activity coefficients of the solutes in a ternary system are expressed as a function of binary data and the water activity of the ternary system. The isopiestic method was used to obtain water activity data. The systems KCl-H20-PEG-200 and KBr-H20-PEG-200 were measured. The activity coefficient of potassium chloride is higher in the mixed solvent than in pure water. The activity coefficient of potassium bromide is smaller and changes very little with the increasing nonelectrolyte concentration. PEG-200 is salted out from the system with KCl, but it is salted in in the system with KBr within a certain concentration range. 

The first quantitative theory of the reentrant collapse was developed in Ref. [49], The theory explained the phenomenon of the simple reentrant collapse which was observed in Refs. [14, 41]. A more general theory of swelling and collapse of charged networks in the binary solvent was developed in Ref. [31] and described in Sect. 2.4.1. We have seen that one of the most essential features of the swelling behavior in mixed solvents is a redistribution of solvent molecules within the network giving a different solvent composition in the gel and the external solution. This redistribution is more pronounced for the collapsed gel, because the probability of contacts of the molecules of the solvent with polymer links in the collapsed gel is higher than in the swollen gel. 

The kinetics of the reaction between bromopropionate and thiosulfate ions have been studied at 10-40 °C in various ethanol-water mixtures.107 Activation parameters were evaluated as a function of ionic strength and dielectric constant of the medium. The medium effect of mixed solvents on the rate constants of the Menshutkin reaction of triethylamine with ethyl iodide has been studied for binary mixtures of cyclohexane with benzene or ethyl acetate,108 and with chlorobenzene or dimethoxyethane.109 Rates were measured over the temperature range 293.1-353.1 K, and activation parameters were determined. 

These equations are used whenever we need an expression for the chemical potential of a strong electrolyte in solution. We have based the development only on a binary system. The equations are exactly the same when several strong electrolytes are present as solutes. In such cases the chemical potential of a given solute is a function of the molalities of all solutes through the mean activity coefficients. In general the reference state is defined as the solution in which the molality of all solutes is infinitesimally small. In special cases a mixed solvent consisting of the pure solvent and one or more solutes at a fixed molality may be used. The reference state in such cases is the infinitely dilute solution of all solutes except those whose concentrations are kept constant. Again, when two or more substances, pure or mixed, may be considered as solvents, a choice of solvent must be made and clearly stated. 

In ternary systems composed of one polymer and two liquids or of two polymers and one solvent, the total Gibbs mixing function of the system can be written in terms of the g interaction parameters of the corresponding binary pairs, according to the I lory - Huggins formalism [11], When studying polymers in mixed solvents, it has been customary to introduce an additional interaction parameter, called ternary,... 

Reactive absorption processes occur mostly in aqueous systems, with both molecular and electrolyte species. These systems demonstrate substantially non-ideal behavior. The electrolyte components represent reaction products of absorbed gases or dissociation products of dissolved salts. There are two basic models applied for the description of electrolyte-containing mixtures, namely the Electrolyte NRTL model and the Pitzer model. The Electrolyte NRTL model [37-39] is able to estimate the activity coefficients for both ionic and molecular species in aqueous and mixed solvent electrolyte systems based on the binary pair parameters. The model reduces to the well-known NRTL model when electrolyte concentrations in the liquid phase approach zero [40]. 

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