Correlation between topological features and surface tension of binary liquid mixtures

Summary The excess surface tension of a large number of binary liquid mixtures has been correlated with their topological features quantified in terms of the molecular connectivity indices. The agreement between the calculated and experimental ^E values is reasonably well for all the mixtures. A simple correlation has also been proposed between ^E and molar excess volume (V ^E ) of a binary mixture. The correlation is quite useful in correlating ^E data even for the mixtures where either one or both the components are associated in the pure state and/or there is interaction between them.

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Korrelation zwischen topologischen Gegebenheiten und Oberflächenspannung von binären flüssigen Mischungen

Zusammenfassung Die Exzeß-Oberflächenspannungen einer großen Anzahl von binären flüssigen Mischungen wurden mit der Topologie ihrer Komponenten in Form der molekularen Konnektivitätsindices korreliert. Die Übereinstimmung zwischen den ^E -Werten ist für alle Mischungen relativ gut. Es wurde ebenfalls eine einfache Korrelation zwischen ^E und den molaren Exzeß-Volumina (V ^E ) der binären Mischungen vorgeschlagen. Diese Korrelierung ist nützlich, um die ^E -Werte sogar dann für die Korrelation von Mischungen verwenden zu können, wenn entweder eine oder beide Komponenten im Reinzustand assoziiert sind und/oder eine Wechselwirkung zwischen ihnen besteht.

     

Correlation between surface tension and void fraction in ionic liquids

An effort to systematize published and new data on the surface tension gamma of ionic liquids (ILs) is based on the hypothesis that the dimensionless surface tension parameter gamma V v (2/3)/ kT is a function of the void fraction x v = V v/ V m. The void volume V v is defined as the difference between the liquid volume V m occupied by an ion pair (known from cationic and anionic masses and liquid density measurements) and the sum V (+) + V (-) of the cationic and anionic volumes (known from crystal structures), while kT is the thermal energy. Our hypothesis that gamma V m (2/3)/ kT = G( x v) is initially based on cavity theory. It is then refined based on periodic lattice modeling, which reveals that the number N of voids per unit cell (hence the dimensionless surface tension) must depend on x v. Testing our hypothesis against data for the five ILs for which surface tension and density data are available over a wide range of temperatures collapses all of these data almost on a single curve G( x v), provided that slight (4%) self-consistent modifications are introduced on published crystallographic data for V (+) and V (-). An attempt to correlate the surface tension vs temperature data available for inorganic molten salts is similarly successful, but at the expense of larger shifts on the published ionic radii (8.8% for K; 3.3% for I). The collapsed G( x v) curves for ILs and inorganic salts do not overlap anywhere on x v space, and appear to be different from each other. The existence of a relation between gamma and x v is rationalized with a simple capillary model minimizing the energy. Our success in correlating surface tension to void fraction may apply also to other liquid properties.     

Calculation of surface tension of metals using density gradient theory and PC-SAFT equation of state

The Cahn-Hilliard theory was combined with PC-SAFT equation of state (EOS), in order to describe both the phase behaviors and the surface tension of different types of metals (Li, Na, K, Rb, Cs, Mg, Ca, Sr, Ba, Fe, Zn, Cd, In, Sn, Pb, and Bi). The only two inputs of the theory are the Helmholtz free-energy density and the influence parameter. The PC-SAFT equation of state was applied to determine Helmholtz free-energy density and bulk properties. The influence parameter is obtained by fitting to the experimental data of surface tension. The results show a useful possibility to calculate surface tensions which are in satisfactory agreement with experimental data.     

The surface tension of liquid copper

The surface tension of liquid copper of 99.999 mass per cent purity has been measured by the sessile drop method in the temperature range 1373 to 1861 K. The least-squares equation expressing the surface tension σ as a function of temperature T is:

$\text{σ(}\text{Cu}\text{)/}\text{mN m}{}^{\mathrm{?}}\text{= (1552±35) ? (0.176±0.023)T/}\text{K}$

The linear correlation of excess surface enthalpy $\text{H}{}^{\mathrm{\sigma }}\text{A}{}^{\mathrm{\sigma }}$ and excess surface entropy $\text{S}{}^{\mathrm{\sigma }}\text{A}{}^{\mathrm{\sigma }}$ per unit area among σ(T) from the literature is also demonstrated. Estimation of $\text{S}{}^{\mathrm{\sigma }}\text{A}{}^{\mathrm{\sigma }}$ via the statistical electron-gas theory of Zadumkin and Pugachewich yields an equation for the calculation of recommended values for the surface tension of molten copper as a function of temperature:

$\text{σ(}\text{Cu}\text{)/}\text{mN m}{}^{\mathrm{?}}\text{= 1497 ? 0.174(T/}\text{K}\text{)}$

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Empirical equation for predicting the surface tension of some liquid metals at their melting point

A new empirical equation is proposed for predicting the surface tension of some pure metals at their melting point. The investigation has been conducted adopting a statistical approach using some of the most accredited data available in literature. It is found that for Ag, Al, Au, Co, Cu, Fe, Ni, and Pb the surface tension can be conveniently expressed in function of the latent heat of fusion and of the geometrical parameters of an ideal liquid spherical drop. The equation proposed has been compared also with the model proposed by Lu and Jiang giving satisfactory agreement for the metals considered.     

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.     

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.     

Relationship between surface tension and surface coverage

Surfactant action is caused in part by a dramatic reduction in surface tension. Using surface excess measurements from a radioactive surfactant, it was possible to show that (a) the surface tension declines only slightly when the occupancy of the air/water interface increases from 0 to 60% of the maximum and (b) the steep drop in surface tension in region B (Figure 1 ), frequently observed to be linear, begins at about 80% occupancy. Surfactant continues to enter the interface cooperatively up to and past the critical micelle concentration. Linearity in region B is not indicative of surface saturation despite a seemingly constant surface excess throughout the region. The disparity between interfacial areas determined by surface tension and by other methods is discussed in terms of these results.     

Estimation of physicochemical properties of ionic liquid C6MIGaCl4 using surface tension and density

An ionic liquid (IL) C6MIGaCl4 (1-methyl-3-hexylimidazolium chlorogallate) was prepared by directly mixing GaCl3 and 1-methyl-3-hexylimidazolium chloride with molar ratio of 1/1 under dry argon. The density and surface tension of the IL were determined in the temperature range of 283.15-338.15 K. The ionic volume and surface entropy of the IL were estimated by extrapolation, respectively. In terms of Glasser's theory, the standard molar entropy and lattice energy of the IL were estimated, respectively. By use of Kabo's method, the molar enthalpy of vaporization of the IL, Delta lgHm0 (298 K), at 298 K was estimated. According to the interstice model, the thermal expansion coefficient of IL C6MIGaCl4, alpha, was calculated and in comparison with experimental value; their magnitude order is in good agreement.     

Surface tension of pure liquid lanthanide and early actinide metals

A systematic theoretical study of the surface tension of liquid rare earth metals and early actinides is performed. An equation, based on the theoretical considerations suggested by Eyring, enables one to calculate the surface tension of elementary substances in a wide temperature range from melting to boiling points. The results of temperature-dependent surface tension calculations of a pure liquid terbium (1629–1880?K) are fitted as γ?=?845?0.1 (T???T _m) (mJ?m²), where the surface tension decreases linearly with temperature. The surface tension was also calculated, at melting points, for all the liquid rare earth metals from La to Lu and for the first six metals of the actinide series from Ac to Pu. It is observed that the lanthanides may be divided into three groups in accordance with their electronic structure. Mostly, the calculated results agree well with available experimental data.     

Surface tension of liquid metals and alloys — Recent developments

Surface tension measurements are a central task in the study of surfaces and interfaces. For liquid metals, they are complicated by the high temperatures and the consequently high reactivity characterising these melts. In particular, oxidation of the liquid surface in combination with evaporation phenomena requires a stringent control of the experimental conditions, and an appropriate theoretical treatment. Recently, much progress has been made on both sides. In addition to improving the conventional sessile drop technique, new containerless methods have been developed for surface tension measurements. This paper reviews the experimental progress made in the last few years, and the theoretical framework required for modelling and understanding the relevant physico-chemical surface phenomena.     

Measurement of the surface tension of liquid marbles

The capillary rise and Wilhelmy plate methods have been used to study the "surface tension" of water marbles encapsulated with polytetrafluoroethylene (PTFE) powders of 1-, 35-, and 100-μm particle size. With the capillary rise technique, a glass capillary tube was inserted into a water marble to measure the capillary rise of the water. The Laplace pressure exerted by the water marble was directly measured by comparing the heights of the capillary rise from the marble and from a flat water surface in a beaker. An equation based on Marmur's model was proposed to calculate the water marble surface tension. This method does not require the water contact angle with the supporting solid surface to be considered; it is therefore a simple but efficient method for determining liquid marble surface tension. The Wilhelmy method was used to measure the surface tension of a flat water surface covered by PTFE powder. This method offers a new angle for investigating liquid marble shell properties. A discussion on the nature and the realistic magnitude of liquid marble surface tension is offered.     

Estimation of the surface tension of liquid carbon dioxide

The surface tension of liquid carbon dioxide has practical significance in material science, environmental science and chemical engineering separation processes as well as in the secondary or tertiary recovery of petroleum. The surface tension of liquid carbon dioxide is estimated by semi-empirical and statistical formulae and the results are compared and analysed with experimental data. It is shown that the methods proposed by Brock, Hakim, Miqueua and Zuo are better methods for estimating the surface tension of liquid carbon dioxide and have relatively less percentage deviation from experimental data.     

离子液体水合物反应液表面张力的研究

表面张力是衡量水合物动力学促进剂促进效果的主要参数,为了探究离子液体应用于水合物生成促进的可行性,实验合成了具有表面活性功能的离子液体[HMIPS]DBSA、[MIMPS]DBSA、[PIPS]DBSA和[PYPS]DBSA,并分别测定了在不同浓度及温度条件下的表面张力。结果表明:四种离子液体的最低表面张力相较于纯水均降低了一半以上,其中[MIMPS]DBSA的降幅最小;各离子液体的表面张力随着浓度的升高而降低并达到一定值,其中[MIMPS]DBSA的CMC浓度为700 ppm左右,其余三种离子液体的CMC浓度则均在900 ppm以上;此外,各离子液体的表面张力随着温度的升高而逐渐降低,但相较于浓度对其的影响,降幅要小得多。这说明浓度是影响水合物反应液表面张力的主要控制因素。可以发现所合成的离子液体与当前最好的促进剂SDS相比,有待于进一步优化。但离子液体的高度可设计性及生物可降解性给水合物促进剂的研发提供了广阔的发展空间,具有很好的发展前景。     

Effect of surface wettability on liquid density, structure, and diffusion near a solid surface

Molecular dynamics and Langevin dynamics simulations are used to elucidate the behavior of liquid atoms near a solid boundary. Correlations between the surface wettability and spatial variations in liquid density and structure are identified. The self-diffusion coefficient tensor is predicted, revealing highly anisotropic and spatially varying mass transfer phenomena near the solid boundary. This behavior affects self-diffusion at a range of time scales. Near a more-wetting surface, self-diffusion is impeded by strong solid-liquid interactions that induce sharp liquid density gradients and enhanced liquid structure. Conversely, near a less-wetting surface, where solid-liquid interactions are weaker, the liquid density is low, the atoms are disordered, and diffusion is enhanced. These findings suggest that altering the wettability of a micro- or nanochannel may provide a passive means for controlling the diffusion of select targets towards a functionalized surface and controlling the reaction rate in diffusion-limited reactions.     

Liquid–liquid phase behaviour,liquid–liquid density,and interfacial tension of multicomponent systems at 298 K

Experimental liquid–liquid phase diagrams are presented for the multicomponent systems isooctane–benzene–(80 mass% methanol + 20 mass% water)–5 mass% isobutyl alcohol (2-methyl-1-propanol) and isooctane–benzene–(80 mass% methanol + 20 mass% water)–15 mass% isobutyl alcohol, at 298.15 K. The density and interfacial tension of conjugate phases of concentration located in the isothermal binodal have been determined at 298.15 K for the partially miscible systems: isooctane–benzene–methanol, isooctane–benzene–(80 mass% methanol + 20 mass% water), isooctane–benzene–(80 mass% methanol + 20 mass% water)–5 mass% isobutyl alcohol, and isooctane–benzene–(80 mass% methanol + 20 mass% water)–15 mass% isobutyl alcohol. The experimental tie-line data define the binodal or coexistence curve of the two studied multicomponent systems and depending on the initial isobutyl alcohol concentration the liquid–liquid phase diagram is either of type II, with low alcohol concentration, or type I, with high concentration of alcohol, which is a clear indication that the solubility of the partially miscible systems is greatly enhanced via the co-solvency phenomenon. It is observed that both the density of each conjugate phase and the interfacial tension of each tie-line are valuable indicators of the degree of solubility of the multicomponent systems. Furthermore the experimental tie-lines data were correlated with the NRTL and UNIQUAC solution models with satisfactory quantitative results.