Temperature dependence of surface tension

The highest value for the surface tension of pure compounds is found at the triple point. Between this and the critical point, the surface tension gradually decreases with rising temperature and becomes zero at the critical point [7]. Jasper [8] has reported linear a IT correlation for a variety of compounds  

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Since surface tension vanishes roughly 6 C above the critical temperature rather than at the critical temperature, Ramsay and Shields proposed the following equation for the temperature-dependence of surface tension ... 

Fig. 5. Temperature dependence of surface tension of PS and PVME [23]. The circles represent the experimental data [34], and the lines are the calculated values using the simulated equation-of-state parameters. The dimensionless constant k in Eq. (13) is fixed at a theoretical value of 0.5 such that there is no adjustable parameter...

The surface tension of this system was measured by Lubyova et al. (1997) using the maximum bubble pressure method. The values of constants a and b of the temperature dependency of surface tension, a = a —bt, obtained using the linear regression analysis, together with the values of the standard deviations of approximation, and the values of the surface tension at 823°C for the investigated KF-KBF4 melts are given in Table 6.1. 

The values of constants a and b of the temperature dependency of surface tension, a = a - bt, were obtained using the linear regression analysis, together with the values of the standard deviations of approximation. 

The results of these studies can be summarised as follows. For low concentrated solutions of ionic surfactants, the increase of the temperature leads to a decrease in the equilibrium surface tension. This can be explained by the decrease of the surface tension of the solvent. In the range of medium ionic surfactant concentrations, almost no temperature dependence of surface tension is observed, while at concentrations close to CMC the most common trend is an increase of surface tension with temperature. The rate of surface tension changes usually slightly increase with increasing temperature. 

The data on the temperature dependence of surface tension of surfactant solutions are often used to estimate the thermodynamic characteristics of adsorption and micelle formation. One of such characteristics is the standard free energy of adsorption AG [83, 160, 178-191]. To derive the expression for AG , one can use the relations for the chemical potential in the surface layer and in the solution bulk. The chemical potentials p] depend on the composition of the surface layer and its surface tension y and are given by the relation (2.2), the potentials... 

TEMPERATURE DEPENDENCE OF SURFACE TENSION IN ASSOCIATED LIQUIDS. 

TEMPERATURE DEPENDENCE OF SURFACE TENSION FOR POLY /TETRAFLUORETHYLENE//SUPERCOOLED LIQUID/ ESTIMATED FROM CONTACT ANGLES. 

SURFACE AND VOLUME PROPERTIES OF CHOLESTERYL ESTERS OF HOMOLOGOUS FATTY ACIDS. II. TEMPERATURE DEPENDENCE OF SURFACE TENSION. 

Hershey AV (1939) Ridges in a liquid surface due to the temperature dependence of surface tension. Phys Rev 56 204... 

Table 2.4. Reducing parameters for various polymers, for use with equation (2.5.3) to predict the temperature dependence of surface tension (from Poser and Sanchez...

Figure 1 Effect of S content on (a) surface tension (y) of Fe and (b) temperature dependence of surface tension (dy/dT) of austenitic stainless steels [2],...

Aumann E, Hildemann LM, Tabazadeh A (2010) Measuring and modeling the composition and temperature-dependence of surface tension for organic solutions. Atmos Environ... 

Where trig is the surface tension of the gas-liquid interface, y is a constant, T is the actual terrperature, and crigo is the surface tension at the reference temperature Tq. The temperature dependency of surface tension is the fundamental concept of thermocapillary pumping. 

A strained, solid-like, and well-ordered liquid skin serves as an elastic covering sheet for a liquid drop or a gas bubble formation the skin is covered with locked dipoles due to charge polarization by the densely trapped core electrons. Temperature dependence of surface tension reveals the atomic cohesive energy at the surface the temperature dependence of elastic trtodulus gives the mean atomic cohesive energy of the specimen. 

Fig. 24.4 Temperature dependence of surface tension of a CoSi liquid [57] and b Sn liquid under different oxygen partial pressures [58]. The inflection of the coefflcient results from a competition between the adsorbate-induced compressive stress and the broken-bond-induced tensile stress according to the present understanding (reprinted with permission from [111])...

A huge database has been established regarding the temperature coefficient of siuface tension for metals, alloys, and polymers. Tables 24.1a and 24.1b tabulate the data for some typical samples and includes information derived and discussed later in Sect. 24.4.2. The temperature dependence of surface tension provided an opportunity for one to derive information regarding atomic cohesive energy in the bulk and with possible mechanism for the adsorbate-induced surface stress. The latter could be a challenging topic of research on adsorption of various adsorbates to liquid surfaces of relatively low-Tn, metals. 

Equating Eqs. (24.9)-(24.10) leads to an estimation of the single bond energy Eb(0) the bulk energy density, y Qi)/D, with the measured temperature dependence of surface tension ... 

Figure 24.6 shows the reproduction of the measured temperature dependence of surface tension of (a) liquid Hg [52] and Ni [51], (b) Co [67] and H2O [68], and (c) hexadecane and polyethylene [69]. With the Debye temperature and the thermal expansion coefficient for the corresponding specimens as input parameters, the b(0) is derived. No other parameters are involved. Tables 24.1a and 24.1b summarize information of the estimated results for several specimens. 

Reproduction of the temperature dependence of surface tension. Young s modulus and Raman shift has led to quantitative information regarding the mean bond energy of a specimen in the bulk at 0 K though the accuracy is subject to the involvement of artifacts in measurement. 

The temperature dependence of surface energy density, follows the temperature dependence of surface tension and Young s modulus [17, 18] ... 

If data of surface tension is scarce, data about the temperature dependence of surface tension is even scarcer. In fact we have only found one paper where cr vs. T appears (Yang et al., 2007). Those data are plotted in Figure 38 for the aqueous system with EI M-BF4, which roughly follows a quadratic polynomial equation with temperature (line in the figure). 

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