Surface tension temperature derivative

There are two useful empirical relationships that have been derived that attempt to quantify the surface tension-temperature relationship. The Eotvos relationship, named after the Hungarian physicist Lorand (Roland) Eotvos (1848-1919), has the form... 

This equation describes the additional amount of gas adsorbed into the pores due to capillary action. In this case, V is the molar volume of the gas, y its surface tension, R the gas constant, T absolute temperature and r the Kelvin radius. The distribution in the sizes of micropores may be detenninated using the Horvath-Kawazoe method [19]. If the sample has both micropores and mesopores, then the J-plot calculation may be used [20]. The J-plot is obtained by plotting the volume adsorbed against the statistical thickness of adsorbate. This thickness is derived from the surface area of a non-porous sample, and the volume of the liquified gas. 

Isoxazole dissolves in approximately six volumes of water at ordinary temperature and gives an azeotropic mixture, b.p. 88.5 °C. From surface tension and density measurements of isoxazole and its methyl derivatives, isoxazoles with an unsubstituted 3-position behave differently from their isomers. The solubility curves in water for the same compounds also show characteristic differences in connection with the presence of a substituent in the 3-position (62HC(17)1, p. 178). These results have been interpreted in terms of an enhanced capacity for intermolecular association with 3-unsubstituted isoxazoles as represented by (9). Cryoscopic measurements in benzene support this hypothesis and establish the following order for the associative capacity of isoxazoles isoxazole, 5-Me, 4-Me, 4,5-(Me)2 3-Me> 3,4-(Me)2 3,5-(Me)2 and 3,4,5-(Me)3 isoxazole are practically devoid of associative capacity. 

It has already been observed in the case of pure liquids such as substituted hydrocarbons that the surface tension was, if not completely defined by the non-polar portions of the molecule, at least not so markedly affected by substituent groups as we should anticipate if no orientation existed. Again, although vaporisation and condensation at a liquid surface such as water at high temperatures takes place with great speed, yet the life of a molecule on the surface is probably long enough to permit of such adjustment as orientation requires. Even more conclusive in favour of the hjq)othesis of at least partial orientation is the evidence derived from a consideration of the latent heats of evaporation and the... 

With short chain derivatives, the forces of repulsion are higher than the ones of attraction the curvature is high and spherical micelles are formed at a concentration called the critical micellar concentration (cmc). This concentration can be detected by a change in the physico-chemical properties of the solution (e.g. surface tension, Fig. 3 a). Above a characteristic temperature (referred as Krafft temperature), the tensio-active molecules are infinitely soluble in the form of micelles (Fig. 3 b). 

Before turning to the surface enthalpy we would like to derive an important relationship between the surface entropy and the temperature dependence of the surface tension. The Helmholtz interfacial free energy is a state function. Therefore we can use the Maxwell relations and obtain directly an important equation for the surface entropy ... 

The derivative of the surface tension with respect to the temperature at constant composition of the double-primed phase is... 

Micelle formation of the nonionic detergent sorbitan monostearate in o-xylene, particularly the temperature dependence of the CMC, has been observed by Brown et al.I6 The data were obtained from surface tension, dye solubilization, and light scattering measurements. With regard to the CMC values the results derived from these techniques agreed reasonably well. The AH- and AS-values evaluated from the remarkable temperature dependence of the CMC cannot claim to be more than an estimate. Two different values of AH and AS at 25 and 45 °C were determined due to the considerable variation of the heat of micellization with temperature. The discrepancies between the values referring to dye solubilization and surface tension measurements are probably reasonable. 

Bhattacharya etal. [73] reported gelation behavior of several L-phenylalanine-based amphiphiles. To explore the impact of molecular structures on gelation of L-phenylalanine derivatives, Bhattacharya and co-workers synthesized as many as twelve L-phenylalanine-based mono- and bi-polar derivatives and solubilized each of these in selected solvents. The formation of gel was found to depend on the concentration of the gelling agent, solvents and the temperature. The SEM and TEM studies suggested the formation of intertwined threads and fibers juxtaposed by slender filaments, which also produced a network with pores, which probably held the solvent molecules due to surface tension in the gel. 

Here ps is the saturated vapor pressure at temperature T, y the surface tension, Vm the molar volume of the liquid, and the curvature radius r is conventionally taken as negative for concave interfaces. Kelvin equation for a non-ideal multicomponent mixture was derived by Shapiro and Stenby (1997). 

A relation between the surface tension y and the surface stress T can be directly derived from the Gibbs-Duhem equation, Eq. (7). At constant temperature, chemical potentials, and electric potential we have... 

Although Gossart claimed that y was the same for substances of the same chemical class (alcohols, acids, esters, some chlorine derivatives), this was not found by Hock. Cantor found that y/a=7/3=2-33, where a=coefficient of expansion Bakker found the ratio 3 6 to 3 7 at the m.p. (except for water and allyl alcohol), and gave the equation y=2a+M5rc, where Tc=cntical temperature. Creighton found that surface tension followed Ramsay and Young s equation ( 8.VIII K) ... 

Hi) Surface excess entropies. Basically, from the temperature dependence of the surface tension S" can be derived. For binary mixtures, this is a complicated procedure (sec. 4.2d). However, for dilute solutions it is easier. Equations 4.2.8a and b) for the Gibbs equation now reduce to... 

---