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Gibbs mixing function

For binary polymer-solvent, the Gibbs mixing function, AGm, can be written, without approximation, as the sum of a combinatorial term plus an interactional term... [Pg.3]

The thermodynamic state of a polymer- solvent system is completely determined, as it was analized before, at fixed temperature and pressure by means of the interaction parameter g. This g is defined through the noncombinatorial part of the Gibbs mixing function, AGm- The more usual interaction parameter, x, is defined similarly but through the solvent chemical potential, A xi, derived from AGm-... [Pg.38]

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,... [Pg.38]

An alternative review of excess Gibbs mixing function and combining rules is provided by Voutsas et al and it is clear that each cubic equation of state has limitations. [Pg.111]

Mass spectrometric studies (1.-5) of the equilibrium gases over pure KOH(cr, t) and mixed KOH-NaOH condensed phases have unequivocally identified the vapor species as monomer and dimer in the temperature range 600-700 K. Absolute partial pressures for KOH(g) and K2(OH)2 (g) have been determined from peak intensity data by Porter and Schoonmaker (3 ) and Gusarov and Gorokhov (5). These data are analyzed by the 3rd law method with JANAF Gibbs energy functions (6) in order to evaluate an enthalpy of dimerization at 298 K. The adopted value is A H (298.15 K) = -45.3 t 3.0 kcal mol" for the reaction 2 KOH(g) = K2(0H)2 (g). [Pg.1222]

Phase relationships in equilibrium are determined by the free enthalpy (Gibbs free energy) of the system. The thermodynamic bdiaviour of polymer solutions can be very well described with the free enthalpy of mixing function derived, independently, by Florv (6,7) and Huggins (8—10) on the basis of the lattice theory of the liquid state. For the simplest case conceivable — a solution of a polydisperse polymer in a single solvent quasi-binary system) — we have... [Pg.3]

Figure C2.1.10. (a) Gibbs energy of mixing as a function of the volume fraction of polymer A for a symmetric binary polymer mixture = Ag = N. The curves are obtained from equation (C2.1.9 ). (b) Phase diagram of a symmetric polymer mixture = Ag = A. The full curve is the binodal and delimits the homogeneous region from that of the two-phase stmcture. The broken curve is the spinodal. Figure C2.1.10. (a) Gibbs energy of mixing as a function of the volume fraction of polymer A for a symmetric binary polymer mixture = Ag = N. The curves are obtained from equation (C2.1.9 ). (b) Phase diagram of a symmetric polymer mixture = Ag = A. The full curve is the binodal and delimits the homogeneous region from that of the two-phase stmcture. The broken curve is the spinodal.
A.ctivity Coefficients. Activity coefficients in Hquid mixtures are directiy related to the molar excess Gibbs energy of mixing, AG, which is defined as the difference in the molar Gibbs energy of mixing between the real and ideal mixtures. It is typically an assumed function. Various functional forms of AG give rise to many of the different activity coefficient models found in the Hterature (1—3,18). Typically, the Hquid-phase activity coefficient is a function of temperature and composition expHcit pressure dependence is rarely included. [Pg.236]

Let us apply Equation (6.8) to the two-phase liquid-vapor equilibrium requirement for a pure substance, namely p = p T) only. This applies to the mixed-phase region under the dome in Figure 6.5. In that region along a p-constant line, we must also have T constant. Then for all state changes along this horizontal line, under the p—v dome, dg = 0 from Equation (6.8b). The pure end states must then have equal Gibbs functions ... [Pg.142]

In the case of reciprocal systems, the modelling of the solution can be simplified to some degree. The partial molar Gibbs energy of mixing of a neutral component, for example AC, is obtained by differentiation with respect to the number of AC neutral entities. In general, the partial derivative of any thermodynamic function Y for a component AaCc is given by... [Pg.290]

The way we wrote 3G in Equation (5.13) suggests the chemical potential // is the Gibbs function of 1 mol of species i mixed into an infinite amount of host material. For example, if we dissolve 1 mol of sugar in a roomful of tea then the increase in Gibbs function is /x,sugar> - An alternative way to think of the chemical potential // is to consider dissolving an infinitesimal amount of chemical i in 1 mol of host. [Pg.215]

It is easy to visualize these conditions by plotting the pressure as a function of chemical potentials (ji and Re) for both components of the mixed phase. This is shown in Figure 8. As should be clear, the above Gibbs conditions are automatically satisfied along the intersection line of two pressure surfaces (dark solid line in Figure 8). [Pg.236]

Figure 1. Chemical potentials of the three phases of matter (H, Q, and Q ), as defined by Eq. (2) as a function of the total pressure (left panel) and energy density of the H- and Q-phase as a function of the baryon number density (right panel). The hadronic phase is described with the GM3 model whereas for the Q and Q phases is employed the MIT-like bag model with ms = 150 MeV, B = 152.45 MeV/fm3 and as = 0. The vertical lines arrows on the right panel indicate the beginning and the end of the mixed hadron-quark phase defined according to the Gibbs criterion for phase equilibrium. On the left panel P0 denotes the static transition point. Figure 1. Chemical potentials of the three phases of matter (H, Q, and Q ), as defined by Eq. (2) as a function of the total pressure (left panel) and energy density of the H- and Q-phase as a function of the baryon number density (right panel). The hadronic phase is described with the GM3 model whereas for the Q and Q phases is employed the MIT-like bag model with ms = 150 MeV, B = 152.45 MeV/fm3 and as = 0. The vertical lines arrows on the right panel indicate the beginning and the end of the mixed hadron-quark phase defined according to the Gibbs criterion for phase equilibrium. On the left panel P0 denotes the static transition point.
For the industrially important class of mixed solvent, electrolyte systems, the Pitzer equation is not useful because its parameters are unknown functions of solvent composition. A local composition model is developed for these systems which assumes that the excess Gibbs free energy is the sum of two contributions, one resulting from long-range forces between ions and the other from short-range forces between all species. [Pg.86]

The Entropy and Gibbs Function for Mixing ideai Gases... [Pg.228]

Determine the relationship for Gibbs free energy of mixing as a function of composition at 9.7°C (282.7 K) for both liquid and solid solutions. [Pg.148]


See other pages where Gibbs mixing function is mentioned: [Pg.267]    [Pg.267]    [Pg.487]    [Pg.169]    [Pg.48]    [Pg.228]    [Pg.90]    [Pg.223]    [Pg.2524]    [Pg.65]    [Pg.328]    [Pg.329]    [Pg.167]    [Pg.167]    [Pg.166]    [Pg.167]    [Pg.63]    [Pg.77]    [Pg.89]    [Pg.274]    [Pg.354]    [Pg.228]    [Pg.378]    [Pg.427]    [Pg.99]    [Pg.169]    [Pg.281]    [Pg.520]    [Pg.327]    [Pg.194]   
See also in sourсe #XX -- [ Pg.3 , Pg.38 ]




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