Group contribution models surface tension

This method does not attempt to distinguish between the various energy contributions. The surface tension parameter acts to include all interactions as much as possible. There are a number of algorithms for implementing this method, most of which differ in the means for determining the surface area associated with a particular group. This method is particularly popular for very large molecules, which can only be modeled by molecular mechanics. 

A number of models which can estimate density at atmospheric pressure have recently been reported. For example, Rebelo et al. [63, 64] defined the effective molar volumes of ions at 298.15 K and used the assumption of ideal behavior for the determination of the molar volume of ionic liquids. Yang et al. [65] used a theory based on the interstice model which correlated the density and the surface tension of the ionic liquid. Group contribution models have been reported by Kim et al. [66, 67] for the calculation of the density and C02 gas solubility for 1-alkyl-3-methylimidazolium based ionic liquids as a function of the temperature and C02 gas pressure with reasonable accuracy over a 50 K temperature range however, the... 

SouckovaM, Klomfar J.Patek J (2015) Surface tension and 0.1 MPa density data for l-Cn-3-methylimidazolium iodides with n = 3, 4, and 6, validated using a parachor and group contribution model. J Chem Thermodyn 83 52-60... 

This group of model interpretations refers typically to interfacial tensions, say between condensed phases a and p, and their relations to the individual surface tensions y and y. Intuitively it is felt that such a relation should exist, since, at a given temp>erature and pressure y and y are unique functions of the composition of phases a and p, respectivety, and so is y fully determined by the Interface that is spontaneously formed upon contact between phases a and p. As, however, the interpretation of y in terms of molecular properties of phase a is not so simple (as proven by the preceding part of this chapter), the relation y (y ,y ) is not as obvious either. Nevertheless, a number of semi-empirical relationships have been put forward, and applied with some success. Many of these contain the geometric mean (y y ) or. where y is the contribution to y of dispersion forces. 

Many properties of pure polymers (and of polymer solutions) can be estimated with group contributions (GC). Examples of properties for which (GC) methods have been developed are the density, the solubility parameter, the melting and glass transition temperatures, as well as the surface tension. Phase equilibria for polymer solutions and blends can also be estimated with GC methods, as we discuss in Section 16.4 and 16.5. Here we review the GC principle, and in the following sections we discuss estimation methods for the density and the solubility parameter. These two properties are relevant for many thermodynamic models used for polymers, e.g., the Hansen and Flory-Hug-gins models discussed in Section 16.3 and the free-volume activity coefficient models discussed in Section 16.4. 

When not available, liquid surface tensions (pure compounds and solutions) can be estimated using predictive methods like those based on parachors and group contributions, solubility parametes (including Hansoi solubility parameters) and corresponding states. Alternatively, they can be estimated from thermodynamic models like UNIFAC and SAFT combined with the gradient or the density functional theories. For a review of the latter, see Kontogeorgis and Folas (2010). Some of the most important direct methods for estimating surface tension arc briefly described here. 

The first term on the right-hand side of equation (8.7) is the contribution of the head group repulsion, while the second is the interfacial energy contribution where Ahg is the total surface area of the head groups and (Tmic is the interfacial tension. Within the framework of the Gouy-Chapmann theory, the dressed micelle model allows the estimation of values, which are for sodium dodecyl sulfate (SDS), sodium octyl sulfate, and teradecyltrimethylammonium bromide, 15-16, 11 and 11-14 mN m , respectively (15). Note that these values are up to a factor of 3 lower than those of the pure monomers (cf. Table 8.2). A further decrease of or is possible in the case of emulsions of organic liquids where the interface is saturated with stabilizer. For example, a value of about 4 mN m was determined for a toluene emulsion stabilized with potassium lau-rate (16). 

---