Enthalpy composition dependency

The Fp correction factor for each enthalpy interval depends both on the assumed value of Xp and the temperatures of the interval on the composite curves. It is possible to modify the simple area target formula to obtain the resulting increased overall area A etwork for a network of 1-2 exchangers ... 

Fig. 1 Composition dependence of the thermal transition parameters, Tg, Tm, and AFZf, estimated by DSC for CA-g-PLA samples (acetyl DS = 2.15). Data for Tm (melting temperature) and AHf (enthalpy of fusion) were obtained in the first run, while Tg was evaluated in the second. (Quoted from [23] with an adequate modification)...

Here the main iteration variables are the stage temperatures and inter-stage phase rates. The temperatures are paired with the combined constitutive and phase equilibrium equations, and the phase rates with the enthalpy and total mass balances. Unfortunately, this pairing is effective only for relatively narrowboiling systems, hence the method frequently fails for wide-boiling systems. Further, the computational procedure involves a lag of the K-value composition dependence from iteration to iteration, which makes the method unsuitable when the composition dependence is strong. 

A,B K-value or temperature dependence parameters a,b Activity coefficient composition dependence parameters C,D Vapor enthalpy temperature dependence parameters E,F Liquid enthalpy temperature dependence parameters F Total feed molar flow rate... 

Generating the derivatives is the most difficult part of the method. Writing analytical derivatives of composition-dependent K-values and enthalpies can be very difficult, especially if a method such as UN1QUAC and NRTL is being used. The alternative is numerical derivatives. For any independent variable, these can be found by ... 

The column section can be solved by simultaneous solution of the component mass balance and energy balance equations and the vapor-liquid equilibrium relations. Additional equations include the temperature, pressure, and composition dependence of the equilibrium coefficients and enthalpies. The equations for stage j are as follows ... 

These are rigorous, composition-dependent methods, generally based on equations of state and liquid activity coefficients (Chapter 1). The /f-values and enthalpies are ultimately functions of temperature, pressure, and composition ... 

Bol] investigated thermodynamic properties of the phases in the CoSi-FeSi and CoSi2-FeSi2 sections by chemical vapor transport methods. For the first section the composition dependences of enthalpy, entropy and heat capacity were given. 

Mar] Marinelli, R, Guillermet, A.F., Sade, M., The Enthalpy Change of the hep —> fee Martensitic Transformation in Fe-Mn-Co Alloys Composition Dependence and Thermal Cycling Effects , Mater. Sci. Eng. A, 373(1-2), 1-9 (2004) (Experimental, Phase Relations, Phys. Prop., Thermodyn., 30)... 

It can be recognized that different temperature dependencies are observed for the two compounds involved, caused by the different sign of the partial molar excess enthalpies. While the activity coefficient for ethanol decreases, the activity coefficient for water increases with increasing temperature in the temperature range covered. But as can be seen from Figure 5.17 the temperature dependence of the partial molar excess enthalpies strongly depends on composition. For example, for compositions Xj <0.1 negative partial molar excess enthalpies for ethanol would result. 

The separation factors mainly depend on composition and temperature. The correct composition dependence is described with the help of activity coefficients. Following the Clausius-Clapeyron equation presented in Section 2.4.4 the temperature dependence is mainly influenced by the slope of the vapor pressure curves (enthalpy of vaporization) of the components involved. But also the activity coefficients are temperature-dependent following the Gibbs-Helmholtz equation (Eq. (5.26)). This means that besides a correct description of the composition dependence of the activity coefficients also an accurate description of their temperature dependence is required. For distillation processes at moderate pressures, the pressure effect on the activity coefficients (see Example 5.7) can be neglected. To take into account the real vapor phase behavior, equations of state, for example, the virial equation, cubic equations of state, such as the Redlich-Kwong, Soave-Redlich-Kwong (SRK), Peng-Robinson (PR), the association model, and so on, can be applied. 

To assess how the presence of specific interactions affects the physical aging behavior, Robertson and Wilkes carried out volume relaxation measurements on PMMA/SAN blends as a function of blend composition (Robertson and Wilkes 2001). In this system, there are no attractive interactions between the components, and miscibility is a result of the so-called copolymer repulsion effect. The dependence of the volume relaxation rate on blend composition was found to be consistent with the enthalpic measurements of Mijovic et al. (1989) on the same system both values of volume and enthalpy relaxation rates were intermediate for the blends compared to the pure components and composition dependent except for... 

Ethylene-co-vinyl acetate Permittivity measurements single Eg and negative enthalpy of mixing (Righetti et al. (2002)) II had 70 % vinyl acetate composition dependent miscible when blend contained >25 % II Rellick and Runt (1986), Righetti et al. (2002)... 

Phase composition depends on mixture temperature T (K), which is found by the enthalpy budget ... 

PCT has been blended with other miscible or compatible polymers in order to decrease its melting temperature and to improve its processability. Hwang (132) blended it with an aromatic amorphous copolyester made from bisphenol A and isophthalic/tere-phthalic acids, which is called Polyarylate (PAR). These blends were miscible in all range of compositions, as demonstrated by the existence of a single, composition dependent T. A decrease in melting temperature and enthalpy was observed for increasing amounts of PAR in the blend. PCT was also miscible with polycarbonate of bisphenol A, as revealed by DSC and solid state deuterium NMR spectroscopy (133). The crystallization of PCT /PC blends in microlayers and blends has been also studied (134). 

As was the case for the A cuprates, problems are encountered with consistency of the measured data. One of the reasons for this is the occurring nonstoichiometry. Whereas data obtained from solution calorimetry refer to the chosen composition, enthalpies and entropies of formation from redox EMF measurements relate in general to one of the two hmiting compositions depending on whether the R cuprate in question appears as the oxidized or reduced product in the actual redox system investigated. As a consequence of this, redox EMF data may give widely different temperature dependences of standard... 

Consideration of the composition dependence requires the introduction of a further set of thermodynamic quantities. So far it has been assumed that the enthalpies, entropies, and Gibbs energies of formation are the molar quantities for the formation of the compound from the component elements. These are termed the integral quantities. However, for experimental as well as practical reasons, the corresponding partial quantities must be defined. The partial molar quantities, say AZb, are related to the integral quantity by the formula ... 

Fig. 9. Pressure and polymer solution composition dependences of the enthalpy of the mixing, AH, for the TD/PS polymer solutions at the indicated temperature (the inserted figure shows pressure dependences of the enthalpy of the mixing, AH, for the TD/PS polymer solutions with fixed composition and temperature).

Figure 8 shows a strong compositional dependence of both the absolute conductivity values at a given temperature as well as the activation enthalpy (derived from the slope of the presented lines). The values of the activation enthalpy A/fjc of the dc conductivity as well as of the pre-exponential factors of the Arrhenius law ff(jcT = Adc exp[—AT/dc/C nF)] are summarized in table III of [40]. 

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