Surface tension corresponding-states principle

In the new version, Chapter 10 focuses exclusively on van der Waals forces and their implications for macroscopic phenomena and properties (e.g., structure of materials and surface tension). It also includes new tables and examples and some additional methods for estimating Hamaker constants from macroscopic properties or concepts such as surface tension, the parameters of the van der Waals equation of state, and the corresponding state principle. 

CORRESPONDING-STATES PRINCIPLE AND SURFACE TENSION. WATKINSONAP LIELMEZSJ J CHEM PHYS... 

Figure 2.25. The reduced surface tension as a function of the reduced temperature based on the corresponding states principle of Dee and Sauer (1995).

The surface tension can be estimated by the Brock-Bird-Miller equation, which is based on the corresponding states principle [90] ... 

Theories of Homopolymer Surface Tension. More rigorous expressions for predicting polymer surface tension have been derived from equations of state for polymers. Corresponding states principles have been employed to derive expressions for surface tensions in terms of characteristic equation of state parameters and the associated reduced temperature, pressure, and volume. One proposed expression is of the form (14)... 

There are many more methods for estimating the surface tension. Two useful methods are those based on the corresponding-states principle (CSP) and on solubility parameters. 

The temperature and molecular weight dependence of the surface tension for the n-alkanes is correctly predicted and is shown to be related to the dependence of liquid density on chain length. Polymer liquid surface tensions satisfy a corresponding states principle and can be estimated for many polymers with an error of less than 10%. This method of estimating pol3mier surface tensions appears to be the most accurate that is available. 

Another method for predicting polymer surface tensions is based on the empirical relation between the tension and solubility parameters, 6, observed by Hildebrand and Scott for low molecular weight liquids. Slow and Patterson have adapted this empirical relation to pol3miers through the use of the Prigogine corresponding states principle to obtain... 

Generalized Surface Tension Correlations. Use of the principle of corresponding states has provided a practical and accurate method for the estimation of surface tensions. The functional relationship for the surface tension of a pure substance (85) is... 

Before entering into the problem of quantum effects in the theory of surface tension or surface energy, some considerations based on the principle of corresponding states for these quantities will be presented. In order to consider the surface tension from the standpoint of corresponding states, it is not necessary to resort to expressions such as Eq. V.ll. The principle of corresponding states for surface tension can be derived directly from Eq. V.10 for the free energy. If the area of the interface between the liquid and the vapor is A, the surface tension is given by... 

The principle of corresponding states is a special case of the application of scaling laws. In addition io PVT diagrams, transport properties, surface tension, etc., can be modeled [7,8]. Further applications of scaling laws can be found in Sect. 11.4. 

Patterson, D., and Rastogi, A. K., The surface tension of polyatomic liquids and the principle of corresponding states, J. Phys. Chem., 1, 1067-1073, (1970). 

THE SURFACE TENSION OF POLYATOMIC LIQUIDS AND THE PRINCIPLE OF CORRESPONDING STATES. 

All our discussion of theories of polymer surface tensions up to now has relied ultimately on the van der Waals theory in conjunction with some equation of state. There is, however, another possible approach, which starts out from a principle of corresponding states, as was first applied to polymers by Patterson and Rastogi (1970). We start by assuming spherical molecules interacting via an attractive potential, which is described by the depth of the energy minimum (s ) and a hard core or impenetrable radius (r ). The partition function is written in terms of variables scaled by the characteristic energy and length scale and thus all physical properties can be described in terms of these scaled variables. Clear corollaries with the equation of state... 

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