Thermodynamics of Binary Systems

Polymers are often synthesized or used in solutions as mixtures with low-molecular-weight solvents. More recently, a number of polymer blends (mixtures of different polymers) with desirable properties have been commercialized. The ability of a polymer to dissolve in a solvent or to mix with another polymer to form a single-phase mixture depends on the free energy change AG upon mixing the two components. At a temperature T, thermodynamics allows us to express AG as 

AS is the change of entropy upon mixing AH is the change of enthalpy upon mixing 

The change of volume upon mixing is denoted by AV and is usually quite small. For a polymer to dissolve in a solvent or another polymer, it is necessary to have AG 0. If AG 0, the mixing of a polymer with a solvent (or with another polymer) will result in two phases, each containing predominantly one of the two components. In Chapter 3, we will discuss phase separation in polymer solutions and blends. Here, we describe a simple thermodynamic analysis that helps to understand the basis of these phase separations in polymers. 

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The vacancy flux and the corresponding lattice shift vanish if bA = bB. In agreement with the irreversible thermodynamics of binary systems i.e., if local equilibrium prevails), there is only one single independent kinetic coefficient, D, necessary for a unique description of the chemical interdiffusion process. Information about individual mobilities and diffusivities can be obtained only from additional knowledge about vL, which must include concepts of the crystal lattice and point defects. 

Saam, W.F. (1970) Thermodynamics of binary systems near the liquid-gas criticeil point, Phys. Rev. A 2, 1461-1466. 

Copp, J. L. Findlay, T. J. V. Thermodynamics of binary systems containing amines. Part 4 Trans. Faraday Soc. 1960,56, 13-22... 

A large number of thermodynamic studies of binary systems were undertaken to find and determine eventual intermolecular associations for thiazole Meyer et al. (303, 304) discovered eutectic mixtures for the following systems -thiazole/cyclohexane at -38.4°C, Wt = 0.815 -thiazole/carbon tetrachloride at -60.8°C, Mt = 0.46 -thiazole/benzene at -48.5°C, nr = 0.70. 

The general thermodynamic treatment of binary systems which involve the incorporation of an electroactive species into a solid alloy electrode under the assumption of complete equilibrium was presented by Weppner and Huggins [19-21], Under these conditions the Gibbs Phase Rule specifies that the electrochemical potential varies with composition in the single-phase regions of a binary phase diagram, and is composition-independent in two-phase regions if the temperature and total pressure are kept constant. 

Critical assessment of phase-diagram data employing the thermodynamics of the phase equilibria in the form of phase-diagram modeling provides consistent thermochemical data (including also the liquid solution) for binary metal-boron systems such as V—B Cr—B, Mn—B, Fe —B, Co—B, Ni—Mo—B and Nb—B, W—B, A1 — B Despite these efforts, reinvestigation of binary systems is... 

Levitskii V. A., Golovanova Yu. G., Popov S. G., and Chentsov V. N. (1975). Thermodynamics of binary oxide system Thermodynamic properties of nickel orthosilicate. Russ. J. Phys. Chem., 49 971-974. 

The (liquid 4- liquid) equilibria diagram for (cyclohexane + methanol) was taken from D. C. Jones and S. Amstell, The Critical Solution Temperature of the System Methyl Alcohol-Cyclohexane as a Means of Detecting and Estimating Water in Methyl Alcohol , J. Chem. Soc., 1930, 1316-1323 (1930). The G results were calculated from the (vapor 4- liquid) results of K. Strubl, V. Svoboda, R. Holub, and J. Pick, Liquid-Vapour Equilibrium. XIV. Isothermal Equilibrium and Calculation of Excess Functions in the Systems Methanol -Cyclohexane and Cyclohexane-Propanol , Collect. Czech. Chem. Commun., 35, 3004-3019 (1970). The results are from M. Dai and J.-P.Chao, Studies on Thermodynamic Properties of Binary Systems Containing Alcohols. II. Excess Enthalpies of C to C5 Normal Alcohols + 1,4-Dioxane , Fluid Phase Equilib., 23, 321-326 (1985). 

An excellent discussion of the thermodynamics of LLE systems has been given by Sorensen and Arlt (1979,1980) and Sorensen et al. (1979). The following section is adapted from these references. Consider a binary liquid mixture of + n2 moles at fixed temperature and pressure. The necessary and sufficient condition for equilibrium is that the total Gibbs free energy of mixing, AG, for the mixture is a minimum with respect to all possible changes... 

For oxide electrocrystallization, the last condition is the most strenuous, sine many oxides are insulating non-stoichiometric compounds, however, are sufficient conductive. When two (or more) substances are codeposited, certain specific feature of the crystallization can be expressed for both cathodic and anodic processes on th basis of the thermodynamics of binary (or more complex) systems. If stabl multicomponent phases exist, then it is their deposition (not the deposition of mixture of simpler products) that preferentially proceeds in a certain potential regioi In such cases, intermetallic compounds are deposited in cathodic processes, and th deposition of mixed oxides takes place in anodic processes. These products ca represent both chemical compounds and solid solutions. 

The second kind of binary systems contain benzene (B), hexafluorobenzene (HFB), toluene (TL), and cyclohexane (CH) HFB/B (for five different temperatures), HFB/TL, HFB/CH, B/TL, and B/CH. In contrast to the first group, these systems have small deviations from idealitybut some of them have more complex thermodynamic behaviors such as double azeotropy. The information about these mixtures is listed in Table 2. 

Gaw, W. J. Swinton, F. L. Thermodynamic properties of binary systems containing hexafluorobenzene. Part 4. Excess Gibbs free energies of fhe three systems hexafluorobenzene -I- benzene, fouene, and /)-xylene. Trans. Faraday Soc. 1968, 64, 2023-2034. 

Eor thermodynamic calculations and analyses of phase diagrams of binary systems whose components form a binary compound, partially or totally dissociating at melting, it is necessary to know the enthalpies of fusion of the components of the binary compounds, and of both eutectic mixtures, as input quantities. When these data cannot be found in the literature, it is possible to estimate them using entropy or enthalpy balances. 

For thermodynamically stable binary systems the second derivative of the Gibbs free energy with respect to the mole fraction x is positive... 

We shall now recall the considerations lying at the basis of this equation. Thermodynamic analysis of the phase diagrams of binary systems provides the most suitable instrument for obtaining information about the interactions in the solid dissolved substance-liquid system. Let us consider the similar dependence for interactions in a binary system. 

An accurate equation of state of fluids is used to test the combining rules for the interaction energy uy of mixtures derived from the theories of London energy between small or large (chain) molecules. The tests are based mostly on comparisons with the thermodynamic excess functions of binary systems at P = 0. For long chains the parameter r)/k, determining the dependence of u/k on the temperature, depends on the reduced density p = V°/V of the system (where V° is the close-packed volume) and /k—>0 when P > 0.75 (solid state). 

Thermodynamic Research Center, National Institute of Standards and Technology, TRC Thermodynamic Tables, . Sangster, J., Phase Diagrams and Thermodynamic Properties of Binary Systems of Drugs," / Phys. Chem. Ref. Data 28, 889,1999. 

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