Binary entropy function

Scheme 1.1 The molecular information system modeling the chemical bond between two basis functions /=(o,b) and its entropy/information descriptors. In Panel b, the corresponding nonbonding (deterministic) channel due to the lone-pair hybrid 6° is shown. For the molecular input p = (P, Q), the orbital channel of Panel a gives the bond entropy-covalency represented by the binary entropy function H[P). For the promolecular input p° = (1/2,1/2), when both basis functions contribute a single electron each to form the chemical bond, one thus predicts H[p°] = 1 and the bond information ionicity / = 1 — H(P). Hence, these two bond components give rise to the conserved (P-independent) value of the single overall bond multiplicity N = I + S = 1.

In addition to the estimated properties, we measured the thermochemistry of several important vapor species. These measurements were conducted in a Knudsen effusion cell using special line-of-sight vaporization under subambient pressures with flowing O2 and H2O vapor mixtures [4]. The gaseous species over silica [5], manganese oxide [6], lanthana, alumina, and palladium metal were detected and relative partial pressures measured as a function of temperature. These vapor pressure measurements were calibrated by using the known metal atom or binary metal oxide volatility as a calibration source. Oxide species concentrations were measured relative to that of a reference compound, e.g., metal atom. The identification of oxide and hydroxide compounds was facilitated by Ae technique of threshold electron ionization [7]. These data were then evaluated using estimated entropy functions and the third law temperatures. 

This expression accounts for the configurational entropy of an ideal binary mixture with identical molecular sizes, but not for that of a polymer solution, since polymer chains are large and flexible. For that case, more contributions arise from the chain conformational entropy, first considered by Meyer [19] and then derived by Huggins [20] and Flory [21]. In analogy with a nonreversing random walk on a lattice, the conformational contribution of polymer chains to the partition function is given by... 

The regular solution approximation is introduced by assuming definition) that the excess entropy of mixing is zero. This requires that the excess free energy equal the excess enthalpy of mixing. For binary mixtures the excess enthalpy of mixing is ordinarily represented by a function of the form... 

The difference in thermodynamic functions between a non-ideal solution and a comparative perfect solution is called in general the thermodynamic excess function. In addition to the excess free enthalpy gE, other excess functions may also be defined such as excess entropy sE, excess enthalpy hE, excess volume vE, and excess free energy fE per mole of a non-ideal binary solution. These excess functions can be derived as partial derivatives of the excess free enthalpy gE in the following. 

This paper provides a framework for the application of Second Law based design methodology to separation systems. A relationship is derived for the available-energy destruction in a binary separation column as a function of the reflux ratio and the feed and product mass fractions. This derivation is limited to separations in which the entropy production is predominately due to mass transfers. 

The transformation of information from one system to another is often almost entropy-free energy transfer, and the information capacity I in binary units is expressed as a function of the probability P... 

In this section it was shown that the excess entropy and excess enthalpy can be determined from various temperature derivatives of the excess Gibbs energy. These and other excess thermodynamic functions can also be computed directly from derivatives of the activity coefficients. Show that in a binary mixture the following equations can be used for such calculations ... 

Thermodynamic functions have been calculated for liquid binary Ga-Pb alloys in the composition range 10—90 atom % Pb. Enthalpies and excess entropies of mixing at 1000 K were reported. ... 

This chapter deals with experimental methods for determining the thermodynamic excess functions of binary liquid mixtures of non-electrolytes. Most of it is concerned with techniques suitable for measurements in the temperature range 250 to 400 K and the pressure range 0 to 100 kPa. Techniques suitable for lower temperatures will be briefly reviewed. Techniques for measuring the molar excess Gibbs function G, the molar excess enthalpy and the molar excess volume will be discussed. The molar excess entropy can only be determined indirectly from either measurements of (7 and at a specific temperature = (If — C /T], or from the temperature dependence of G m [ S m = The molar excess functions have been defined by... 

Binary mixtures of non-aromatic fluorocarbons with hydrocarbons are characterized by large positive values of the major thermodynamic excess functions G , the excess Gibbs function, JT , the excess enthalpy, 5 , the excess entropy, and F , the excess volume. In many cases these large positive deviations from ideality result in the mixture forming two liquid phases at temperatures below rSpper. an upper critical solution temperature. Experimental values of the excess functions and of Tapper for a representative sample of such binary mixtures are given in Table 1. 

Critical phenomena in binary fluid mixtures are substantially analogous to those in one-component fluids when proper allowance is made for the increase in the number of independent thermodynamic variables by one. Thus any extensive property of a one-component system ie,g. the energy U) can be expressed as a function of three variables, for example the entropy 5, the volume V, and the amount of substance but the binary mixture requires four (e.g. S, V, and 2). For most purposes the size of the system is irrelevant and one reduces the number of variables by one by using molar quantities Um, Sxa, Vm, for the binary mixture three independent variables (e.g. 5m, Im, and a composition variable such as the mole fraction x of the second component) then sufiice. 

It is of interest to estimate the thermodynamic functions of siuface layers of different composition. Since a binary system is considered, it is possible to make thermodynamic calculations for mixtures of different concentrations at different temperatures (Fig. 2.27). This was done using the equation that connects the surface pressure with the change in entropy and enthalpy of the surface layers [232] ... 

Specific interactions in binary blends of ethylene-vinyl acetate copolymer with various low molecular weight terpene-phenol tackifying resins (TPR) were systematically investigated, as a function of the composition of the blend and of the electron acceptor ability of the resin, by using attenuated total reflection FTIR spectroscopy. Molecular acid-base were evidenced between TPR hydroxyl groups and EVA carbonyl groups. Quantitative information on the fraction of acid-base bonded entities, the enthalpy and equilibrium constant of pair formation were obtained. A crystalline transition of the EVA copolymer was observed and discussed in terms of enthalpy and entropy considerations based on FTIR and calorimetric DSC investigations. Fundamental results are then summarised to predict the interfacial reactivity of such polymer blends towards acid or basic substrates. 16 refs. 

Table 5.4.3. Thermodynamic properties of the liquid mixtures used as cosolvents of PMMA. Excess Gibbs function G, and excess entropy S, of the binary mixtures at equimolecular composition (at 25°C). From Prolongo et al. (Copyright by Butterworth-Heineman Ltd., used with permission)...

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