Interfacial tension temperature coefficient

Soave m coefficient Solubility parameter at 25°C 0iJ/m ) /2 Temperature n °c Interfacial tension at mN/m Lee Kesier acentric factor... 

Assume that an aqueous solute adsorbs at the mercury-water interface according to the Langmuir equation x/xm = bc/( + be), where Xm is the maximum possible amount and x/x = 0.5 at C = 0.3Af. Neglecting activity coefficient effects, estimate the value of the mercury-solution interfacial tension when C is Q.IM. The limiting molecular area of the solute is 20 A per molecule. The temperature is 25°C. 

The diffusion current Id depends upon several factors, such as temperature, the viscosity of the medium, the composition of the base electrolyte, the molecular or ionic state of the electro-active species, the dimensions of the capillary, and the pressure on the dropping mercury. The temperature coefficient is about 1.5-2 per cent °C 1 precise measurements of the diffusion current require temperature control to about 0.2 °C, which is generally achieved by immersing the cell in a water thermostat (preferably at 25 °C). A metal ion complex usually yields a different diffusion current from the simple (hydrated) metal ion. The drop time t depends largely upon the pressure on the dropping mercury and to a smaller extent upon the interfacial tension at the mercury-solution interface the latter is dependent upon the potential of the electrode. Fortunately t appears only as the sixth root in the Ilkovib equation, so that variation in this quantity will have a relatively small effect upon the diffusion current. The product m2/3 t1/6 is important because it permits results with different capillaries under otherwise identical conditions to be compared the ratio of the diffusion currents is simply the ratio of the m2/3 r1/6 values. 

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. 

In these examples, as one would expect, the interfacial tensions are small and diminish as the critical solution temperature is approached. The differences between the surface tensions of the two phases are generally too small to decide whether the interfacial tension approaches zero asymptotically in all cases although such appears to be the case in the phenol water system we notice however that the temperature coefficient is very small indeed, as is the case for surface tensions of liquids near their critical point, but to a still greater degree. 

The partial derivative of the Gibbs free energy per unit area at constant temperature and pressure is defined as the interfacial coefficient of the free energy or the interfacial tension (y), a key concept in surface and interface science ... 

While phase equilibria for the a-tocopherol/carbon dioxide system at high pressures have been studied by several authors [1-6], only a few measurements of dynamic viscosity [7], thermal conductivity [7] and mass transfer coefficients [3] were carried out. The present study of the interfacial tension in the a-tocopherol/carbon dioxide system at temperatures between 313 and 402 K and pressures from 10 to 37 MPa aims on the one hand at completing characterisation of this system and on the other at contributing to understanding interfacial phenomena in mass transfer processes. 

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. 

Antonoff s rule agrees with the result that the interfacial tension 0 12 is less than the larger (ori) of the two surface tensions, arid it requires that when two partly miscible liquids are in equilibrium the spreading coefficient (contact angle. The value of (7i2 decreases with rise of temperature. 

Intuitively, surface and interfacial tensions may be expected to be related to a number of physical characteristics of the liquid or the liquid-vapour transition. Two of these are the enthalpy and entropy of evaporation, discussed in sec. 2.9. Other parameters that come to mind are the molar volume V, the isothermal compressibility and the expansion coefficient. The combination of certain powers of such parameters and y sometimes leads to products with interesting properties, like temperature independence or additivity. Severed of such scaling rules have been proposed over the past century, mostly with limited quantitative success. A few of these wUl now be discussed. 

The interfacial (excess) heat capacity is another Interfacial characteristic that we decided to disregard. The reason for doing so is not in its intrinsic interest. On the contrary, as with bulk heat capacities, they reflect the structure, or ordering (see e.g. FIGS I, sec. 5.3c). However, it is very difficult to establish these values experimentally. Basically the second derivative of the interfacial tension with respect to the temperature at a constant pressure is needed (see sec. 1.2.7), and to obtain this extremely preeise measurements are needed. The spread in the quadratic coefficient B in [1.12.1) indicates the uncertainty, even for a well-studied liquid like water. Yang and Li showed, by a thermodyncimic ancdysis, that for LL interfaces this heat capacity is related to the two bulk heat capacities, the inter-... 

In Table II, we list the various dimensionless groups defined above and the two criteria for enhancement of the heat transfer coefficient by interfacial tension-driven flow. Calculated values are given for the three mixtures for which we presented experimental data. All values pertain to a temperature difference AT of 10 K. 

Table 8.1 Values of the Interfacial Tension and Its Temperature Coefficient at the Liquid-Air Interface for Selected Polar Solvents at 25°C [2]...

Here k is the thermal conductivity of the liquid in the shallow cavity and kg is a heat transfer coefficient for the gas. Finally, we assume, for simplicity, that the interfacial tension o( T) depends linearly on the interface temperature,... 

Figure 1.23 Variation of the water (shown as hollow symbols) and n-octane (shown as filled symbols) diffusion coefficients DA and Dg [115], the length scale [25], the mean curvature H and the water/oil interfacial tension (jat, as function of the temperature for the system hbO-n-octane-CnEs. Note that at the mean temperature of the three-phase body f the diffusion of water and oil molecules is equal (points to bicontinuity), the length scale runs through a maximum, the curvature change sign and the water/oil interfacial shows an extreme minimum.

A 25-mm-OD copper tube is to be used to boil water at atmospheric pressure, (a) Estimate the maximum heat flux obtainable as the temperature of the copper surface is increased, b) If the temperature of the copper surface is 210°C, calculate the boiling film coefficient and the heat flux. The interfacial tension of water at temperatures above 80°C is given by... 

Figure 4.2. Temperature dependence of the interfacial tension coefficient for PP/PS (data from Kamal et al., 1994) and for PE/PA, LDPE/PS, and PVDE/EP [Luciani et al, 1996].

It seems that Chappelear [1964] was the first who applied this technique to measure the interfacial tension coefficient of polymer blends. Further refinements have been published [Elemans, 1989 Elemans et al., 1990 Elmendorp, 1986]. The method is simple, not requiring special equipment, but the zero-shear viscosity of the investigated polymers at the processing temperature must be known. Typical results obtained this method are shown in Table 4.3. 

The domain size of sequential IPNs (such as shown in Figure 6.2) is controlled by several features the interfacial tension coefficient between the two polymers, y, the volume fraction of polymers 1 and 2, v and v, respectively, effective network concentration of the two polymers and Vj respectively, and the gas constant times the absolute temperature, RT. 

There have been several efforts to provide means for computation of the interfacial tension coefficient from characteristic parameters of the two fluids [Luciani et al., 1996a]. The most interesting relation was that found between the interfacial tension coefficient and the solubility parameter contributions, that are calculable from the group contributions. The relation makes it possible to estimate the interfacial tension coefficient from the unit structure of macromolecules at any temperature. The correlation between the experimental and calculated data for 46 polymer blends was found to be good — the correlation coefficient R = 0.815 — especially when the computational and experimental errors are taken into account. 

Considering melt flow of BC, it is usually assumed that the test temperature is UCST > T > T, where T stands for glass transition temperature of the continuous phase. However, at Tg < T < T g (T g is Tg of the dispersed phase) the system behaves as a crosslinked rubber with strong viscoelastic character. At UCST > T > T, the viscosity of BC is much greater than would be expected from its composition. The reason for this behavior is the need to deform the domain structure and puU filaments of one polymer through domains of the other. Viscosity increases with increase of the interaction parameter between the BC components in a similar way as an increase of the interfacial tension coefficient in concentrated emulsions causes viscosity to rise [Henderson and Williams, 1979]. 

In the method employed in obtaining these data any effect of temperature on the solid-liquid interfacial tension is ignored. For the n-alkanes [66] the amount of xmdercooling was only 12° to 13°C. Hence, applying any reasonable temperature coefficient-e.g., -0.05 dyne per cm. per degree-would not have a significant effect. It is therefore suggested that a satisfactory estimate of the solid-liquid tension for n-decane on solid hydrocarbon surfaces would be 10 dynes per cm. 

Figure 4.13. The interfacial tension between polyst5n-ene and poly(methyl methacrylate). The relative molecular mass of the PMMA was 10000 and the temperature of measurement was 199 °C. The solid line is the prediction of the Broseta equation (Broseta et al. 1990) with x = 0.045. The dashed line is the prediction of the Broseta equation with the coefficient changed from n /6 to 1.35, to bring it into line with the Freed interpolation formula (Tang and Freed 1991), equation (4.3.17), with x = 0.055. Data from Anastasiadis et al. (1988).

As Table 2.1 shows, the concept of the wetting coefficient has been successfully applied in filled polymer blends containing various fillers, such as carbon black [36], silica [26,27,37], or nano-CaCOs particles [38,39]. Limitations of this criterion include strong discrepancies in interfacial tensions, due to the lack of data in the literature regarding polymer/filler interfaces and issues of extrapolation to the appropriate temperature. Also, this criterion assumes that thermodynamic equilibrium has been reached, which is not always the case experimentally due to the limited processing time. 

The coefficient dy/dT of interfacial tension variation with tranpraatuie is assumed to have a constant valne. It is virtually always negative, a typical value being abont -0.1 mN/m K. According to Equation 6.26, developmrait of a temperature gradient along an interface causes flow to arise having shear stresses that balance the lateral force produced by the interfadal tension gradirait. In terms of the coeffidents A, Equation 6.26 becomes... 

---