The surface tension of pure liquids

For pure liquids the description becomes much simpler. We start by asking, how is the surface tension related to the surface excess quantities, in particular to the internal surface energy and the surface entropy  

One important relationship can be derived directly from Eq. (3.29). For pure liquids we choose the Gibbs dividing plane such that T = 0. Then the surface tension is equal to the free surface energy per unit area  

Let us turn to the entropy. We start with Eq. (3.31). For pure liquids the position of the interface is chosen such that Na = 0. For homogeneous systems we also know that s 7 = S7/A = dS17/dA. Putting everything together we find 

The surface entropy per unit area is given by the change in the surface tension with temperature. In order to determine the surface entropy one needs to measure how the surface tension changes with temperature. 

Question If the volume of the interface is zero, why is the condition important that P is constant Reason A change in pressure might change the quality of the interface and thus its entropy. This equation is generally valid, not only within the Gibbs formalism. 

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Jasper, J. J. (1972) J. Phys. Chem. Ref. Data 1, 841. The surface tension of pure liquids. 

II.7 The following data were obtained for the work of adhesion between the listed liquids and carbon black. Use these data, together with the surface tensions of pure liquids from Appendix 4 (or from additional sources as necessary), to calculate the spreading coefficients for the various liquids on carbon black. 

The temperature dependence of the surface tension of pure liquid is given by the Eotvos-Ramsay equation ... 

J. J. Jasper, The Surface Tension of Pure Liquid Compounds. Journal of Physicatand Chemical Reference Data 1, No. 4 (1972), pp. 841-1009. 

J.J. Jasper. The Surface Tension of Pure Liquid Compounds, J. Phys. Chem. Ref Data 1 (1972) 841-1010. (Extensive tabulations, mostly as a function of temperature. Linearized plots are given, valid for at least part of the y(T) range between 0 and 100 C, see fig. 1.27.)... 

As shown in Equation (6), we need the value of the surface tension CTx of pure solid X, but the precise information on the value of cr nd its temperature dependence are insufficient.From the data reported in some references, " the value of of pure solid at the melting point is found to be 25% larger than the surface tension of pure liquid on the average. Equation (10) is, therefore, assumed to express the sur-... 

However, other solid materials can also be used as capillary tubes when required.) It has been observed experimentally that there is an inverse proportionality between the height of the liquid present in the capillary tube and the radius of the tube (see also Section 6.1). Capillary rise was found to result from the adhesion interactions between the liquid and the capillary wall, which are stronger than the cohesion interactions within the liquid. This is a method used to measure the surface tension of pure liquids. During the measurement, the capillary tube must be very clean, placed completely vertical and be circular in cross section with accurately known and uniform radius. 

If we further increase the temperature towards the critical temperature, Tc, the restraining force on the surface molecules diminishes, and the vapor pressure increases, and when Tc is reached, the surface tension vanishes altogether (y= 0). There are several empirical approaches using critical properties and molar volume to predict the surface tension of pure liquids. By comparing the surfaces on the basis of the number of similarly shaped and symmetrically packed molecules per unit area, Eotvos derived an equation in 1886,... 

Numerous methods have been proposed to estimate the surface tension of pure liquids and liquid mixtures. One of the simplest is the empirical formula proposed by MacLeod in 1923. It expresses the surface tension of a liquid in equilibrium with its own vapor as a function of the liquid- and vapor-phase densities as ... 

The values in parenthesis are the surface tensions of pure liquids given at 20 °C in mN m . ... 

Padday JF, Russel DR. 1960. The measurement of the surface tension of pure liquids and solutions. J Colloid Sci 15 503-511. 

However, narrow bore tubes are difficult to clean and there are difficulties in ensuring that the cross-section is circular, but the method gives reliable values for the surface tension of pure liquids and, by using a U-tube, is readily adapted for measuring the variation of 7 with temperature. 

It has been argued that the ring method is suitable only for measuring the surface tension of pure liquids. The applicability of the method for the measurement of surface tension of surfactants has been debated [328,367-369]. 

The dependence of the surface tension on temperature is largely influenced by the fact that the interface between the liquid phase and the gas phase disappears at the critical temperature (i.e., the temperature above which the liquid state no longer exists regardless of pressure). Thus, the surface tension of liquids is reduced to zero at this temperature. Consequently, the surface tension of pure liquids must decrease with increasing temperature. The surface tension data for the elements most commonly used in solder alloys are given in Table 4, where the expression ... 

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