Nonideal solutions entropy

A particular type of nonideal solution is the regular solution which is characterized by a nonzero enthalpy of mixing but an ideal entropy of mixing. Thus, for a regular solution,... 

The other limiting case of nonideal solutions is when AGe —TASe, in which case the deviation from ideality is mostly due to the excess entropy of mixing AHe 0. In this case, using (8.4.17) in... 

One of the simplest and most widely used models for the thermodynamic characterization of a nonideal solution is the so-called simple solution model . In this model the excess free energy of mixing, accounting for deviations from the ideal entropy of mixing, is taken as an expression that is proportional to the product of the mole fractions of the constituents. 

We concluded the last section with the observation that a polymer solution is expected to be nonideal on the grounds of entropy considerations alone. A nonzero value for AH would exacerbate the situation even further. We therefore begin our discussion of this problem by assuming a polymer-solvent system which shows athermal mixing. In the next section we shall extend the theory to include systems for which AH 9 0. The theory we shall examine in the next few sections was developed independently by Flory and Huggins and is known as the Flory-Huggins theory. 

This approach to solution chemistry was largely developed by Hildebrand in his regular solution theory. A regular solution is one whose entropy of mixing is ideal and whose enthalpy of mixing is nonideal. Consider a binary solvent of components 1 and 2. Let i and 2 be numbers of moles of 1 and 2, 4>, and 4>2 their volume fractions in the mixture, and Vi, V2 their molar volumes. This treatment follows Shinoda. ... 

Many workers have offered the opinion that the isokinetic relationship is confined to reactions in condensed phase (6, 122) or, more specially, may be attributed to solvation effects (13, 21, 37, 43, 56, 112, 116, 124, 126-130) which affect both enthalpy and entropy in the same direction. The most developed theories are based on a model of the half-specific quasi-crystalline solvation (129, 130), or of the nonideal conformal solutions (126). Other explanations have been given in terms of vibrational frequencies involving solute and solvent (13, 124), temperature dependence of solvent fluidity in the quasi-crystalline model (40), or changes of enthalpy and entropy to produce a hole in the solvent (87). 

The solvophobic model of liquid-phase nonideality takes into account solute—solvent interactions on the molecular level. In this view, all dissolved molecules expose microsurface area to the surrounding solvent and are acted on by the so-called solvophobic forces (41). These forces, which involve both enthalpy and entropy effects, are described generally by a branch of solution thermodynamics known as solvophobic theory. This general solution interaction approach takes into account the effect of the solvent on partitioning by considering two hypothetical steps. First, cavities in the solvent must be created to contain the partitioned species. Second, the partitioned species is placed in the cavities, where interactions can occur with the surrounding solvent. The idea of solvophobic forces has been used to estimate such diverse physical properties as absorbability, Henry s constant, and aqueous solubility (41—44). A principal drawback is calculational complexity and difficulty of finding values for the model input parameters. 

In the event that the molar volumes of solute and solvent are not comparable, and the thermal agitation is not adequate to achieve maximum entropy of mixing, a nonideal entropy of mixing exists (Bustamante et al., 1989). Two equations that account for the nonideal entropy of mixing have been derived by considering the partial molal volurfiA,and the volume fraction, occupied by each solution component. The L rst was developed by Flory and Huggins (Hildebrand, 1949 Kertes, 1965) ... 

Nonideal thermodynamic behavior has been observed with polymer solutions in which A Hm is practically zero. Such deviations must be due to the occurrence ofa nonideal entropy, and the first attempts to calculate the entropy change when a long chain molecule is mixed with small molecules were due to Flory [8] and Huggins [9]. Modifications and improvements have been made to the original theory, but none of these variations has made enough impact on practical problems of polymer compatibility to occupy us here. 

The Flory-Huggins model differs from the regular solution model in the inclusion of a nonideal entropy term and replacement of the enthalpy term in solubility parameters by one in an interaction parameter x- This parameter characterizes a pair of components whereas each S can be deduced from the properties of a single component. 

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. 

A so-called regular solution is obtained when the enthalpy change (AHmix) is nonideal (i.e., non-zero, either positive or negative) but the entropy change (A mix) is still ideal. So on the molecular level, while an ideal solution is one in which the different types of molecules (A and B, for example) behave exactly as if they are surrounded by molecules of their own kind (that is, all intermolecular interactions are equivalent), a regular solution can form only if the random distribution of molecules persists even in the presence of A-B interactions that differ from the purely A-A and B-B interactions of the original components A and B. This concept has proved to be very useful in the development of an understanding of miscibility criteria. 

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