Predicting the surface tension of liquid metals

The recent availability of more complete and reliable surface tension data for molten metals has led the authors to seek a general surface tension correlation which would include other fundamental properties of the molten metals. The relationship proposed has a thermodynamic basis and relates the surface tension of a molten metal to its heat of vaporiza3ion and ionic radius. Based on data reported by several investigators, the error in the calculated value of surface tension is less than ten per cent in the melting point region.     

Theoretical consideration of the anomalous temperature dependence of the surface tension of pure liquid gallium

The surface tension of pure liquid gallium in the temperature range 303–503 K (303 K is the melting point) was previously measured using the noninvasive method of capillary wave spectroscopy (CWS). The result of this experiment showed that the value of surface tension increases from 303 to 345 K indicating a negative surface excess entropy (S ^σ), and decreases linearly from ~345 to 503 K confirming a negative slope, and thus a positive S ^σ. This unusual behavior of Ga is not known for other liquid metals such as Bi, Pb, Hg, Sn and Al. The reported experimental behavior is modeled here. A theoretical equation for calculating the surface tension of liquid Ga, based upon formulating a proper partition function that includes the rotational part, is derived and described. The theory predicted no maximum in the temperature-dependence of the surface tension, as seen in the experiment, where the analysis was done over a large temperature range (325–503 K). The value obtained from this mathematical expression indicates that the temperature variation of surface tension has no positive slope within the temperature range 303–345 K. At T > 345 K, the surface tension shows the usual linear temperature-dependence with a negative slope. Therefore, the equation is only applicable for the latter temperature range. A comparison between the theoretical and experimental values of surface tension of liquid Ga is discussed.     

The character of the temperature dependence of the surface tension coefficient of a liquid phase

The analysis performed showed that several well-known equations used to determine the surface tension coefficient reduce to a particular mathematical model.     

The temperature dependence of surface tension and critical micelle concentration of egg lysolecithin

Summary The surface tension of egg lysolecithin-water solutions has been investigated using a modified Wilhelmy technique in a temperature scanning mode. Use of this method has allowed a thorough analysis of both the surface conformational properties of the monomer, and the temperature dependence of the critical micelle concentration of the lipid, from 20– to 80 °C. Assuming that the lysolecithin is a non-ionic (zwitterionic) surfactantH _mic. has been calculated from the CMC values. The variation of log₁₀ CMC with temperature was complex and a least squares analysis had to be done over three overlapping temperature ranges.H _mic calculated from log₁₀ CMC versus 1/T plots, also showed a complex dependence on temperature.In the CMC concentration region experimental results were complicated by an apparent temperature dependent increase in the solubility of the micellar phase. This resulted in desorption from the surface, with a resultant increase in surface tension.

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Zusammenfassung Die Oberflächenspannung von wäßrigen Lösungen von Eilysolecithin wurde mittels einer modifizierten Wilhelmymethode bei kontinuierlicher Temperaturänderung untersucht. Die Benutzung dieser Methode gestattet eine sorgfältige Analyse sowohl der Konformationsänderungen an der Oberfläche als auch der Temperaturabhängigkeit der kritischen Mizellkonzentration des Lipids von 20°–80 °C. Die EnthalpieänderungH _mic der Mizellbildung wurde aus den Werten der kritischen Mizellkonzentration (CMC) berechnet. Der Verlauf von log₁₀ CMC mit der Temperatur erwics sich als komplex, so daß eine Analyse kleinster Fehlerquadrate über drei sich teilweise überschneidende Temperaturintervalle durchgeführt werden mußte.H _mic zeigte infolgedessen ebenfalls einen komplizierten Verlauf der Temperaturabhängigkeit.Im Bereich der kritischen Mizellkonzentration verursachte eine temperaturabhängige Zunahme der Löslichkeit der Mizellarphase eine Desorption von der Oberfläche und infolgedessen eine Erhöhung der Oberflächenspannung.

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With 5 figures and 2 tables     

Temperature dependence of the surface tension of indium

Original data on the temperature dependence of the surface tension of indium, obtained using two independent approaches (a large sessile drop and the maximum pressure in a drop) are presented. The focus is on analyzing possible methodological shortcomings of experimental studies in which the surface tension values of a number of pure metals are obtained that are considerably higher than the results from measuring surface tension by traditional means. It is found that cleaning the investigated metal surfaces through bombardment with heavy ions of inert gases can lead to violations of the thermodynamic equilibrium conditions of a surface with its own saturated vapor, and to the ensuing consequences.     

Concentration dependence of the surface tension of ternary systems

A surface tension isotherm equation for ternary systems was derived based on general thermodynamic expressions with consideration for the concentration dependence of the molar surface area. Within the experimental errors, the equation describes the properties of ternary systems with smooth surface tension isotherms.     

New approach to defining thermodynamic surface tension of solids

Using either the chemical potential of the immobile component of a solid dissolved in a fluid phase or the corresponding component of the tensor of chemical potential in solid phase, a new concept of the grand thermodynamic potential of solid-fluid two-phase system is proposed. For a planar interfacial surface, this makes it possible to generalize the notion of thermodynamic surface tension σ introduced by Gibbs that has the meaning of the formation work of a unit surface. This tension is determined as the specific surface excess of the grand thermodynamic potential. This definition of the thermodynamic surface tension does not depend on the position of the dividing surface and is common for fluids and solids. It is shown that, at the arbitrary position of dividing surface, the difference between thermodynamic σ and mechanical @[gamma] surface tensions for solid surface is determined by the nonuniformity of the tensor of chemical potential in a solid, as well as by its anisotropy in the bulk of solid phase.     

Anomalous temperature dependence of interfacial tension in water-hydrocarbon mixtures

An experimental study of the interfacial tension (IFT) as a function of temperature for three water-hydrocarbon mixtures is reported. The interfacial tension rises with increasing temperature for all mixtures studied, which contradicts the Antonov rule.     

Surface tension and its temperature coefficient for liquid metals

Temperature-dependent surface tension gamma(lv)(T) and its temperature coefficient (T) [=dgamma(lv)(T)/dT] for liquid metals are thermodynamically determined on the basis of an established model for surface energy of crystals. The model predictions correspond to the available experimental or theoretical results. It is found that for metallic liquids gamma(lv)(T(m)) proportional, variant H(v)/V(m)(2/3), gamma(lv)(T) proportional, variant T, and (T) proportional, variant T over a certain temperature range (including T < T(m) and T >/= T(m)), where H(v) and V(m) are the liquid-vapor transition enthalpy at boiling temperature T(b) and the atomic volume at melting temperature T(m), respectively. Furthermore, T(m)(T(m))/gamma(lv)(T(m)) almost remains constant, which gives a way to estimates of (T(m)) values when T(m) and gamma(lv)(T(m)) are known.     

Thermodynamic approach to calculating the surface tension of single-component liquids by computer simulations

A thermodynamic method for computing the surface tension at a flat liquid-vapor interface by the Monte Carlo or molecular dynamics methods over a wide temperature range was proposed. The approach is based on the Gibbs separating surface method; it does not require information on the mechanical state of the surface layer.     

Surface tension as a function of temperature for some molten metals

Results are given for Sn, In, and Ge from the melting points up to 1700 C, for Pb up to 1400 C, for Tl up to 1100 C, for Bi up to 1300 C, and for Cd up to 600 C. In every case the surface tension is a linear function of temperature. Estimates are made of the critical temperatures of Cd and Ge. It is shown that deductions on the structure of the melts can be drawn from surface-tension data.     

Temperature dependence of viscosity and relation with the surface tension of ionic liquids

Viscosities of ionic liquids were correlated with two linear relations. The first one presents the temperature dependence of imidazolium-, pyridinium-, pyrrolidinium-, quaternary ammonium-, and nicotinium-based ionic liquids with high accuracy. The second one is a linear relation between logarithm of surface tension and fluidity involving the characteristic exponent ?, and fits the ionic liquids uniquely with ? = 0.30. Our previously measured surface tension data of ionic liquids and literature's were used in this study. The dependence of surface tension–fluidity relation of the imidazolium-based ionic liquids on the anion type is likely disappeared as alkyl chain length increases.     

Experimental studies on the geometrical characteristics determining the system behavior of surface tension autooscillations

Autooscillation of the surface tension is a phenomenon related to Marangoni instability periodically arising and fading by dissolution of a surfactant droplet under a water-air interface. A detailed experimental investigation was performed to clear up the influence of the system geometry on development and characteristics of autooscillations. It was found that the aspect ratio is an additional dimensionless parameter that determines the system behavior equally to the Marangoni number. The influence of the cell diameter, capillary immersion depth, and droplet radius on the autooscillation period and amplitude was studied as well.     

Relation between the temperature coefficient of surface tension and phase diagrams

An equation determining the relation between the temperature coefficient of surface tension and crystallization temperature was obtained. The equation was substantiated experimentally for solutions of NaOH and ZnCl₂. The rule governing the alternation of structures in phase diagrams was found. A relation between phase diagram structures and structures in adsorbed surface layers of liquid solutions at microconcentrations of surface-active components was derived.     

New combinatorial approach for the investigation of kinetics and temperature dependence of surface reactions in thin organic films

In this paper we present a new, simple, and reproducible method for the rapid determination of the temperature dependence of solution phase surface reactions of organic thin films on solid supports. Instead of estimating the extent of reaction for many separate samples for many different temperatures sequentially, we exploit in our new high throughput combinatorial approach surface reactions carried out under a thermal gradient followed by position-resolved contact angle (CA) measurements. The reaction kinetics, activation energies, and entropies are, thus, accessible on the basis of measurements on a very limited set of samples that differ in reaction times. The kinetics and temperature dependence of surface reactions of the previously studied alkaline hydrolysis of 11,11'-dithiobis(N-hydroxysuccinimidylundecanoate) (NHS-C10) self-assembled monolayers (SAMs) on gold, as well as the ester hydrolysis in SAMs of the novel disulfide 11,11-dithiobis(tert-butylundecanoate) (t-Bu-C10), were investigated in detail using the conventional sequential and the new combinatorial approach. The reaction kinetics, corresponding apparent rate constants k, and activation energies Ea, as well as activation entropies deltaS double dagger, determined according to both approaches agree well with each other to within the experimental error. Hence, these parameters can be quantitatively determined using the described combinatorial approach. A comparison of the reactions of the two model systems indicated that the transition state is tighter for the acid-catalyzed ester hydrolysis in SAMs of the novel disulfide t-Bu-C10 compared to the hydrolysis of the ester groups in SAMs of NHS-C10 on gold.     

A syringe for surface tension measurements at constant temperature

The drop volume method can give precise results for the surface tension of liquids if a certain number of precautions are taken. One of the most important is the temperature control. A drop volume syringe fitted with a jacket is described; water at constant temperature circulates in the jacket. The syringe is introduced in a brass chamber and the whole system immersed in a thermostat. The closed chamber eliminates evaporation and allows the surface tension to be determined in an inert atmosphere.     

Correlation between the temperature coefficient of the surface tension and the partial entropy

The author’s correlation equation relating the temperature coefficient of the surface tension to the partial entropy and the adsorption value is supported by measurements of the surface tension in alkali solutions. The oscillatory character of partial entropy changes is explained by the formation of crystalline hydrates.     

Correlation between surface tension, density, and sound velocity of liquid metals

The inter-relationship of surface tension sigma, density rho, and sound velocity c has been examined for forty-one liquid metals. Sound velocities correlate with the equation, log c=0.5526log(sigma/rho)+5.4364. Unknown sound velocities may be estimated using surface tension and liquid density values.