Temperature coefficient of tension

The most remarkable features are the high surface tensions, greater, often many times greater, than those of any other substances and the occasional positive temperature coefficients of tension. There is no obvious correlation between the tension and other physical properties though (except for the last four metals in the table) the surface tension is higher for the metals with the higher melting-points, a fact which indicates that the cohesional forces in the liquid and in the solid state are similar in kind. 

The author knows of no other cases of a positive temperature coefficient of tension, except some rather discordant results of Zickendraht,1 with sulphur, and the observations of Jaeger2 on liquid crystals. In every one of five cases the tension increases abruptly by a small amount, up to... 

This gives the entropy change per unit extension, (dS/dT)j, which occurs in Eq. (4-32), in terms of the temperature coefficient of tension at constant length (9//9T )/, which can be measured. With Eq. (4-38), Eq. (4-32) becomes... 

Joule in 1859, and hence it is called the Gough-Joule effect. The Gough-Joule effect suggests that the temperature coefficient of tension is positive. 

Because the entropy change is = 0 for the adiabatic process, the temperature change of the sample is proportional to the temperature coefficient of tension... 

Corollary 4.—The temperature coefficient of the surface tension of a liquid is inversely proportional to the molecular surface. 

Laplace had previously deduced from his theory that the temperature coefficient of surface tension should stand in a constant ratio to the coefficient of expansion this is in many cases verified, and shows that the effect of temperature is largely to be referred to the change of density (Cantor, 1892). 

The entropy of formation of the interface was calculated from the temperature coefficient of the interfacial tension.304 The entropy of formation has been found to increase with the nature of the electrolyte in the same sequence as the single cation entropy in DMSO.108, 09,329 The entropy of formation showed a maximum at negative charges. The difference in AS between the maximum and the value at ff=ocan be taken as a measure of the specific ordering of the solvent at the electrode/solution interface. Data 108,109304314 have shown that A(AS) decreases in the sequence NMF > DMSO > DMF > H90 > PC > MeOH. 

We are naturally interested in connecting a physical constant, like surface tension, with other physical constants, and one such connection is immediately suggested by the decrease in surface tension caused by an increase in temperature. It is only natural to inquire whether there is any parallelism between this and the most obvious change produced in a liquid by increasing temperature expansion. Measurements have shown that this is indeed the case, and that there is marked parallelism between the temperature coefficient of surface tension, i.e., the decrease caused by a rise in temperature of one degree, represented by the constant a in our first equation, and the coefficient of expansion. 

Van der Waals further finds a relation between the temperature coefficient of surface tension and the molecular surface energy which is in substantial agreement with the Eotvos-Ramsay-Shields formula (see Chapter V.). He also arrives at a value for the thickness of the transition layer which is of the order of magnitude of the molecular radius, as deduced from the kinetic theory, and accounts qualitatively for the optical effects described on p. 33. Finally, it should be mentioned that Van der Waals theory leads directly to the conclusion that the existence of a transition layer at the boundary of two media reduces the surface tension, i.e., makes it smaller than it would be if the transition were abrupt—a result obtained independently by Lord Rayleigh. 

In an extreme case the surface tension of diphenyl is almost double that of benzene at the same temperature and it would be expected that in a mixture of these substances the benzene would be preferentially adsorbed at the surface, and any attempt to find the mean molecular weight of the two would break down. Certain mixtures of aniline and water were found by Worley (J.G.S. ov. 260, 1914) to have positive temperature coefficients of surfiice tension as exemplified in the following data for a 3-3 °/o aniliiie... 

Unlike most liquids, perhaps with the exception of some liquid metals, the temperature coefficients of the surface tension of B203, Ge02, and Si02 are positive (24, 50). Some possible causes of this anomaly are (1) a preferred orientation occurring in the surface layer, and (2) dissociation or... 

The temperature coefficient of surface tension in homologous series. Some insight into the behaviour of molecules at surfaces may be... 

If the positive temperature coefficient of surface tension is a genuine property of the pure metals, it may mean that there is a decrease in the components of kinetic energy, parallel to the surface, as the temperature rises. The matter appears worthy of further investigation. 

The volume of a drop formed by coalescence of two small drops is not exactly the sum of their volumes. The enthalpy, H, is not the sum of the enthalpies of the two small drops. In other words, a sufficiently sensitive measurement would reveal a AV and a AH associated with the coalescence. We can calculate the AH for the process with considerable precision if the drops are very small but large enough to ensure that surface tension is nearly the same as for the liquid in bulk. The calculation involves AH per unit area calculated from the temperature coefficient of surface tension (8) and the area which disappears in the process. (The coalescence of two drops of water at 25° C. each 0.01 cm. in diameter produces a temperature rise of 3.5° X 10 4° C.)... 

In dilute aqueous solution (< 10 m) the behavior of amphiphiles, such as long-chain trimethylammonium, sulfate, and earboxylate salts, parallels that of strong electrolytes. At higher amphiphile concentrations, however, a pronounced deviation from ideal behavior occurs. A generalized diagram for such variations in physical properties as a function of the detergent concentration, C-, is given in Fig. 1. Some of the physical properties which have been found to exhibit this type of behavior are related to interfacial tension, electric conductivity, e.m.f., pH, density, specific heat, temperature coefficients of solubility. 

A matter of practical importance in nonaqueous titrimetry is that, when volumetric equipment is used, errors should be prevented that arise from solvent volatility and from characteristics of viscosity and surface tension that differ from those of water. Temperature coefficients of expansion are often about six times that of water, so careful control of temperature is needed when volumes are being measured. Gravimetric titration techniques are recommended, since they avoid most of these volumetric problems. Details of a gravimetric technique using a syringe have been given. ... 

Teitelbaum and co-workers (2012-2014) describe the use of the temperature coefficient of surface tension to study H bonding in mixtures. The curve of this coefficient against the concentration of one component normally shows a minimum, but for H bonding solutions it has a maximum. With this technique the group proposed hydrates of alcohols, ketones, and some miscellaneous compounds. 

The various terms are interpreted as follows T(dSg/dT)p r represents the heat capacity, Cp r, of the adsorbate at constant pressure and surface occupancy r. The second term represents the mechanical work involved in the expansion of Vg on heating here the coefficient of expansion is relevant ap,r = V (dVg/dT)p r- In the third term we invoke the Maxwell relation that is specified in Eq. (5.2.8) of Table 5.2.1 T(dSg/dP)T,r = -T(dVg/dT)p r = —TVgap p, which again relates to mechanical work associated with the alteration of surface phase volume induced by pressure changes. The fourth term describes the contraction in volume of the surface phase due to the application of pressure. This effect is described by the isothermal compressibility fip.r = — V dVg/dP)T,r- The product —(pdAg obviously deals with the work of expanding the surface area. The sixth term is dealt with by use of the Maxwell relation from (5.2.8) from Table 5.2.1 T(dSg/dAg)T,p,ns = T d

temperature coefficient of the surface tension. We may therefore recast the above equation in the form... 

It follows from [4.6.8ff] that the Interfacicd excess entropy cem in principle be obtained from the temperature dependence of the surface tension. Such experiments require some scrutiny both technically (how to prevent evaporation ) and interpretationally (now to account for the temperature coefficients of chemical potentials at fixed concentrations ). Detailed studies are welcome. However, one striking trend may be mentioned ). Adsorption of (at least some) non-ionics is accompanied by an increase of entropy, whereas for the cationic Cj TMA Br" a decrease is observed. Again, more systematic study seems appropriate, before... 

On the tension-temperature coefficient of natural rubber. Makromol. Chem. 43, 152 (1961). 

The tensions at the optima in Fig. 15 cannot be used to compare the relative magnitudes of the two optima, because (a) they are determined with different single fibers, (b) the number of experiments is small, and (c) different fibers under the same conditions develop very different tensions according to the extent they are denatured. In the experiments of Fig. 8, the tension is measured on the same fibers at different temperatures, and, moreover, on a greater number of fibers. In any case, the correspondence between the temperature coefficients of the tension and hydrolysis rate has not very strict significance, since the one is measured on extended fibers and the other on freely suspended (i.e., contracted) fiber particles (cf. II, 4/). 

Critical surface tension values for various polymers of general interest are given in Table 3 (for a more complete listing, see Ref. ). The temperature coefficient of y is small dyJdT = 0.05 dyne/cm K... 

CONCERNING THE SURFACE TENSION, CRITICAL SURFACE TENSION, AND TEMPERATURE COEFFICIENT OF SURFACE TENSION OF POLYTETRAFLUOROETHYLENE. 

The temperature coefficient of surface tension is plotted versus composition in Figure 8. One recognizes that the blend exhibits the temperature coefficient of PMA as long as PMA is in excess. At lower content of PMA, the coefficient steeply ascends to the temperature coefficient of PEO. This indicates that surface entropy of the blend is ruled by PMA in the range of low content of PEO. 

FIGURE 8 Temperature coefficient of surface tension as a function of blend composition the dotted curve gives Unear variation of temperature coefficient with composition. 

At temperatures near the critical temperature of a hquid, the cohesive forces acting between molecules in the liquid become very small and the surface tension approaches zero. That is, since the vapor cannot be condensed at the critical temperature, there will be no surface tension. A number of empirical equations that attempt to predict the temperature coefficient of surface tension have been proposed one of the most useful is that of Ramsey and Shields ... 

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