Volume excess mixing

CUN Cuniberti, C. and Bianchi, U., Thermodyrrarrric of mixing excess volumes in polyiso-butylene-solvent systems, Polymer, 1, 151,1966. 

Since these mixing processes occur at constant pressure, // is the heat evolved or absorbed upon mixing. It is usually measured in a mixing calorimeter. The excess Gibbs free energy, is usually obtained from phase equilibria measurements that yield the activity of each component in the mixtureb and S is then obtained from equation (7.17). The excess volumes are usually obtained... 

Silver ion reacts with excess CN- to form a colorless complex ion, Ag(CN)2, which has a formation constant Kf = 3.0 X 1020. Calculate the concentration of Ag+ in a solution prepared by mixing equal volumes of 2.0 X 10 3 M AgN03 and 0.20 M NaCN. 

After excess water is removed, the sections are covered with 200-300 pi of silver enhancement mixture for 8-11 min at 20°C. The silver enhancement mixture is prepared immediately before use by mixing equal volumes of the enhancer and initiator solutions of the Janssen Intense LM kit. The sections are washed three times for 5 min in distilled water, dehydrated, and mounted. 

Excess volumes on mixing Significantly lower than theory... 

Silver iodide sol. Mix equal volumes of aqueous solutions (10 3 to 10 2 mol dm-3) of silver nitrate and potassium iodide. Separate the sol from larger particles by decantation or filtration. By arranging for the silver nitrate or the potassium iodide to be in very slight excess, positively or negatively charged particles, respectively, of silver iodide can be formed. 

Conversion of solubilities from thex-scale to the mol dm-3 scale, c, and vice versa requires knowledge of the volume change on mixing the components (the excess volume of mixing, VE). If this is ignored, then the approximate relationships ... 

Prepare the titration reaction mix in each reaction tube as shown in the following tables. Add all the components except the main counterion that would mediate folding (Mg2-1- for Mg titration and K+ for K titrations). For each reaction mix, prepare a reference solution of slightly excess volume but with identical reagent concentrations, for blank absorbance measurements. [Note For K+ titrations, prepare two tubes with 10 mM MgCl2 for comparison of the final states of the RNA in highest K+ concentration and in 10 mM Mg2 1.]... 

This excess volume vE is the difference between the mean molar volume of the non-ideal binary solution, v"° dcal = V+ n2), and the mean molar volume of the perfect binary solution vper/ = XjV + x2v2 (the sum of the volume of the two pure substances before mixing... 

We can calculate excess volumes (volume changes of mixing) for methanol(l)/water(2) system at 25°C from the volumetric data of Fig. 1 Equation (13.20) specializes to... 

The NR/PS is of more interest here because of its similarity to poly-butadiene/PS and polyisoprene/PS which are the pairs most widely studied in block copolymer systems. No excess volume of mixing is predicted for this pair, the v values, 1.172 for NR and 1.152 for PS, changing to 1.162 for the mixture at Wi = 0.5. Although Ah, fv and As, fv fail to cancel each other completely, the net sum of the two is still only about 10% of the total A, indicating that here too the contact term is the most important effect giving rise to the incompatibility of the pair. 

Through the understanding of the nonequilibrium changes in the glassy state of miscible blends, the excess volume of mixture is analyzed, and is related to the nonequilibrium enthalpy of mixing. In contrast to the multi-phase systems, the presence of a maximum yield stress in a miscible glassy blend at a critical concentration is predicted as a function of the nonequilibrium interaction. In accordance with Eq. (59), the total volume of a compatible blend is written as... 

The behavior of binary hquid solutions is clearly displayed by plots of M, AM, and In y vs. Xi at constant T and P. The volume change of mixing (or excess volume) is the most easily measured of these quantities and is normally small. However, as illustrated by Fig. 4-1, it is subject to individualistic behavior, being sensitive to the effects of molecular size and shape and to differences in the nature and magnitude of intermolecular forces. 

If the excess volume of mixing is zero, then all the volume fraction multipliers cancel out in these forms, because then (f)i = (1 — 2)- Though the present derivation should provide a basis for doing better, this assumption of zero volume of mixing will be our second assumption here. Then Eqs. (4.44) describe a scaling of second virial coefficients that is natural even though special ... 

Unusual Properties of PDMS. Some of the unusual physical properties exhibited by PDMS are summarized in List I. Atypically low values are exhibited for the characteristic pressure (a corrected internal pressure, which is much used in the study of liquids) (37), the bulk viscosity i, and the temperature coeflScient of y (4). Also, entropies of dilution and excess volumes on mixing PDMS with solvents are much lower than can be accounted for by the Flory equation of state theory (37). Finally, as has already been mentioned, PDMS has a surprisingly high permeability. 

Characteristic pressure, unusually low Bulk viscosity (i ), unusually low Temperature coeflScient of i, unusually low Entropies of dilution, significantly lower than predicted by theory Excess volumes on mixing, significantly lower than predicted by theory... 

In comparison, ab initio calculations of the electronic stmcture of Fe-S and Fe-Si compounds by Sherman (1997) indicate that due to large excess volumes of mixing as little as 2-8 wt.% of sulfur is enough to account for the density deficit in the core. Alfe et al. (1999b) estimated that 9-11 wt.% oxygen is required to explain the density deficit. 

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