Regular solutions mixing functions

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... 

Perhaps the most important term in Eq. (5.2-3) is the liquid-phase activity coefficient, and mathods for its prediction have been developed in many forms and by many workers. For binery systems die Van Laar [Eq. (1.4-18)]. Wilson [Eq. (1.4-23)]. NRTL (Eq. (1.4-27)], and UNIQUAC [Eq. (1.4-3 )] relationships are useful for predicting liquid-phase nonidealities, but they require some experimental data. When no data are available, and an approximate nonideality correction will suffice, the UNiFAC approach Eq-(1.4-31)], which utilizes functional group contributions, may be used. For special cases Involving regular solutions (no excess entropy of mixing), the Scatchard-Hiidebmod mathod provides liquid-phase activity coefficients based on easily obtained pane-component properties. 

In the model of regular solution (or its extension to polymer mixtures), the Aj2 term is purely enthalpic and Ajj is thus a true constant. In a real mixture, Aj is a function of T, p, and the composition of the mixture, but the utility of Eq. (1) relies on the fact that the dependence of Ajj on these variables is only moderate in most cases. Only in the case of the systems exhibiting LCST behavior is the temperature dependence of Aj2 appreciable. The strong concentration dependence of Xi2> often found with dilute polymer solutions, is not encountered with polymer mixtures. This is mainly due to the fact that the mean-field approximation, as stated earlier, is fairly satisfactory and the entropy of mixing two polymeric components is reasonably well represented by the combinatory entropy term. 

A regular solution may be defined as that solution of which the enthalpy of mixing is different from zero, but the entropy of mixing is the same as for an ideal solution. The various mixing functions of a binary regular solution A-B may be written as... 

Figure 8. Free enthalpy of mixing G of binary solid solutions (regular) Ca,. (PO ) OH F as a function of x at W/2.303 RT = 1.4.

Fig. 2 The construction of a polymer-cushioned lipid bilayer membrane. (A) Architecture constructed in a sequential way first, onto the functionalized substrate a polymer layer (cushion) is deposited by adsorption from solution and covalent binding, followed by the (partial) covalent attachment of a lipid monolayer containing some anchor lipids as reactive elements (B) able to couple the whole monolayer to the polymer cushion. (C) Alternatively, a lipopolymer monolayer, organized, e.g., at the water-air interface can be co-spread with regular low-mass amphiphiles and then transferred as a mixed monolayer onto a solid support, prefunctionalized with reactive groups, able to bind covalently to the polymer chains of the lipopolymer molecules, (B). (D) By a fusion step (or a Langmuir Schaefer transfer) the distal lipid monolayer completes the polymer-tethered membrane architecture...

Figure 7.2 shows a functional block diagram of a conventional DFMC system. The regular arrows and the bold arrows represent the mechanical (or fluid) connections and the electrical connections, respectively. A pump sends methanol aqueous solution, normally 0.5 to 1.5 M (1 M methanol solution contains about 3% wt of methanol, and the remaining 97% is water), to the stack from a methanol mixing tank the anode exhaust, a mixture of methanol, CO2, and water, is pumped back to the methanol mixing tank where the... 

The term general solution was introduced by Flory to characterize polymer solutions whose enthalpy of mixing is not zero. The model of general solutions borrows the formula of excess enthalpy from regular systems and the excess entropy from athermal solutions. Thus, a treatment of non-ideal polymer solutions arises which is simpler than the conventional methods applied to real systems this allows the deduction, on the basis of the known relationships, of the expressions of functions of deviation from ideality. Thus, for the activity coefficients of components in a binary system the following relations were established ... 

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