Interfacial tension as a function

Electrocapillarity is the study of the interfacial tension as a function of the electrode potential. Such a study can provide useful insight into the structure and properties of... 

Figure 15.12. (a) Interfacial tension as a function of solubility)38) (b) Induction period as a function of initial... 

The Measurement of Interfacial Tension as a Function of the Potential Difference across the Interface... 

We start this chapter with electrocapillarity because it provides detailed information of the electric double layer. In a classical electrocapillary experiment the change of interfacial tension at a metal-electrolyte interface is determined upon variation of an applied potential (Fig. 5.1). It was known for a long time that the shape of a mercury drop which is in contact with an electrolyte depends on the electric potential. Lippmann1 examined this electrocapillary effect in 1875 for the first time [68], He succeeded in calculating the interfacial tension as a function of applied potential and he measured it with mercury. 

Electrocapillary is the study of the interfacial tension as a function of the electrode potential. Such a study can shed useful light on the structure and properties of the electrical double layer. The influence of the electrode-solution potential difference on the surface tension (y) is particularly pronounced at nonrigid electrodes (such as the dropping mercury one, discussed in Section 4.5). A plot of the surface tension versus the potential (like the ones shown in Fig. 1.13) is called an electrocapillary curve. 

Figure 3.24 Left emulsion type depending on the temperature and surfactant concentration (C- 2E5) for a constant tetradecane/water ratio of 1 1. Right interfacial tension as a function of the temperature of the system tetradecane/water/C Es.

Figure 4. Relative increase in interfacial tension as a function of droplet contact angle for increasing NaCl concentrations. Series C films, Cl counterion...

Figure 2. Interfacial tension as a function of Figure 3. Interfacial tension as a function of pressure at all nine temperatures investi- density of pure carbon dioxide at all nine gated. temperatures investigated.

Figure 6. The interfacial tension as a function of sodium acetate concentration. Composition of the systems. (G 1086 + Arlacel 83, HliB = 9.3) 8% aqueous phase (water + sodium...

Measurement of the partition of the cosurfactant between the oil and the interface is not easy. A simple procedure to select the most efficient cosurfactant is to determine the oil/water interfacial tension as a function of cosurfactant concentration. In this case, the lower the percentage of cosurfactant required to reduce /q/w rn the better is the candidate. 

The variation of the interfacial tension as a function of T for the Eusapon OD system shows the typical V-shape. The full curve corresponds to a theoretical description in terms of bending energy [164,165], The minimum of the interfacial tension correlates well with the mean temperature of the system and is located at interfacial tension between water and oil near the degreasing temperature corresponds to aab = 0.43 mN m. Although the interfacial tension between water and triolein is high compared to efficient microemulsion systems, it is still two orders of magnitude lower than the pure water oil interfacial tension (50 mN m 1). 

Mesoscale simulations of various types also provide the ability to estimate the interfacial tension as a function of time in an evolving system, as summarized below. 

Figure 7.5. Representative results from dissipative particle dynamics simulations studying nonionic diblock surfactant adsorption onto oil-water interfaces [34], (a) A water film between two layers of oil, showing that the surfactant molecules have preferentially migrated to the interfaces and oriented themselves such that their hydrophilic portions are pointed towards the water layer while their hydrophobic portions are pointed towards the oil layers. See the insert showing the colored figures for a better view, (b) Final interfacial tension as a function of the bulk concentration of surfactant, (c) Evolution of the interfacial tension as a function of time (as represented by the simulation steps), for two different concentrations (5% and 15%) by volume of the surfactant. Dr. Brace Eichinger, from Accelrys, Inc., kindly provided this figure. Copyright (2001) Taylor Francis for Figure 7.5(c).

FIG. 13 Polymer solution/cyclohexane interfacial tension as a function of polymer concentration and pH for HMPAA (Pemulen TR 2). (Reprinted from Colloids and Surfaces A Physicochem Eng Aspects, 88, Lochhead RY, Rulinson CJ, An investigation of the mechanism by which hydrophobically modified hydrophilic polymers act as primary emulsifiers for oil in water emulsions. 1. Poly(acrylic acids) and hydroxethyl celluloses. 27-32, Copyright (1994), with permission from Elsevier Science.)... 

Interfacial Tension as a Function of Added Oleic Acid 0.01 M Sodium Oleate, 0.1 M Sodium Chloride,... 

Figure 8 shows the values of electrophoretic mobility and interfacial tension as a function of the NaOH concentration for the Long Beach crude oil which has been equilibrated with the alkaline solution. This figure shows that the electrophoretic mobility increases and then decreases with increasing caustic concentration. It should be noted that the maximum in electrophoretic mobility appears to correspond to a minimum in interfacial tension. This finding is consistent with our recent results for surfactant systems (6) and those of Shah and Walker (21). 

The solubilisation of oil or water in a micellar solution of non-ionic surfactant, a) two-phase diagram (O - oil, W - water, 0, - oil in micellar solution, - water in inverse micellar solution, D - phase separation temperature region), b) interfacial tension as a function of T, according to Shinoda Friberg 1975... 

This paragraph will briefly present the most frequently used methods for measuring the surface and interfacial tensions as a function of time the maximum bubble pressure, drop volume, growing bubble/drop, bubble/drop shape, and other methods. 

A drop of a certain volume, corresponding to a certain interfacial tension (y) value, is expelled rapidly, and the time necessary for the interfacial tension to fall to such a value that the drop becomes detached is measured. This procedure is repeated for differing drop sizes, i.e. for different values of the interfacial tension. A plot of the interfacial tension as a function of time (t) can then be made, as seen in Figure 1. This... 

The value of cq can also be obtained independently from the work reported in Ref 28. In this work, among other things, the droplet radii and the interfacial tensions as a function of the cosurfactant concentration for the same system as used in Ref 55 were measured. For the system containing 19% pentanol, which is closest to the 20% used by van Aken [55], we estimate y = 0.02 mN/m = 0.00487 r nm , and R32 = 12 nm. Substituting these values into Eq. (49) and using the fact that K = kT for this system, we obtain co = 0.029kT nm, which is remarkably close to the value of 0.035/ T nm used in Fig. 6. (Moreover, it is expected that Cq indeed increases with increasing cosurfactant concentration.)... 

It means that the knowledge of the interfacial tension as a function of any electrode potential and the chemical potential of the electrolyte, that is, of its concentration, enables one to determine all other interfacial quantities by differentiation (Eqs. (3) and (5)). 

Note that the simple arguments of section 2.1, being essentially static and mechanical in character, fail to make any prediction about the dependence of the interfacial tension on temperature. We shall see that the determination of surface or interfacial tensions as a function of temperature can give considerable insight into the equilibrium thermodynamics of the interface, therefore the accurate measurement of surface and interfacial tension becomes of some significance. 

Figure 6.24. The reduction in interfacial tension as a function of the bulk volume fraction of a copolymer for three different architectures, calculated by self-consistent field theory. The total degree of polymerisation of the copolymers was 600 and their composition was symmetrical. The homopolymer degrees of polymerisation were 100 and the interaction parameter % = 0.1. After Lyatskaya et al. (1995).

A material that is strongly adsorbed at an interface may be termed a surface active material (a surfactant ), and will normally produce a dramatic reduction in interfacial tension with small changes in bulk phase concentration. In dilute solution, it is assumed that the activity coefficient of a material, 72, can be approximated as unity so that the last term in Equation (9.15) can be substituted for by the molar concentration, C2. The practical applicability of this relationship is that the relative adsorption of a material at an interface, its surface activity, can be determined from measurement of the interfacial tension as a function of solute concentration ... 

Fig. 4.16 Interfacial tension as a function of added maleic anhydride for PE/PA-6 blend...

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