Bending surface tensions

The dimensionless constants b and 2 were introduced by Leikin [78] they account for the fact that contributions from each monolayer to the bending modulus and the surface tension can differ for the two modes considered. Such effects are probably small so that bi bj I [78]. We note that the electrical potential enters Eqs. (69) and (70) only through the parameter z. 

At this point we should note that, fixing the bending radii, we define the location of the interface. A possible choice for the ideal interface is the one that is defined by the Laplace equation. If the choice for the interface is different, the value for the surface tension must be changed accordingly. Otherwise the Laplace equation would no longer be valid. All this can... 

The bending moduli of the AOT films in the presence ofvarious electrolytes are not known. Experiment showed that19 at low AOT concentrations, the surface tension... 

The chief problem is that plastic deformation effects at the crack tip usually obscure the process of surface formation. The work needed to propagate a crack is utilized not only to form two surfaces and to bend the cleaved material elastically but also for plastic deformation around the crack tip [16]. The energy needed for this plastic deformation is dissipated as heat. Hence the measured quantity, which is called the effective fracture surface tension yntts- is numerically larger than y. Reliable results can only be obtained at temperatures below 150 K when plasticity practically disappears 121,55]. 

Tensions of non-relaxed interfaces are sometimes known by the adjective dynamic dynamic surface tension or dynamic inteifacial tension. The term dynamic is not absolute. It depends on De (i.e. on the time scale of the measurement as compared with that of the relaxation process). Some interfacial processes have a long relaxation time (polymer adsorption-desorption), so that for certain purposes (say the measurement of y] they may be considered as being in a state of frozen equilibrium. This last notion was introduced at the end of sec. 1.2.3. Unless otherwise stated, we shall consider static tensions and interfaces which are so weakly curved that curvature energies, bending moments, etc. may be neglected. 

A variant is the micro-pipette method, which is also similar to the maximum bubble pressure technique. A drop of the liquid to be studied is drawn by suction into the tip of a micropipette. The inner diameter of the pipette must be smaller than the radius of the drop the minimum suction pressure needed to force the droplet into the capillary can be related to the surface tension of the liquid, using the Young-Laplace equation [1.1.212). This technique can also be used to obtain interfacial tensions, say of individual emulsion droplets. Experimental problems include accounting for the extent of wetting of the inner lumen of the capillary, rate problems because of the time-dependence of surfactant (if any) adsorption on the capillary and, for narrow capillaries accounting for the work needed to bend the interface. Indeed, this method has also been used to measure bending moduli (sec. 1.15). 

Owing to the unsymmetrical coating of the typically used cantilevers, these will bend as a result of different surface tensions [Raiteri R, Butt H-J (1995) J Phys Chem 99 15728-15732] or thermal expansion coefficients... 

The elasticity of multilamellar vesicles can be discussed in reference to that of emulsion droplets. The crystalline lamellar phase constituting the vesicles is characterized by two elastic moduli, one accounting for the compression of the smectic layers, B, and the second for the bending of the layers, K [80]. The combination has the dimension of a surface tension and plays the role of an effective surface tension when the lamellae undergo small deformations [80]. This result is valid for multilamellar vesicles of arbitrary shapes [81, 82]. Like for emulsion droplets, the quantity a/S is the energy scale that determines the cost of small deformations. 

Equilibrium tests at the local deformation stage of a sample provide adequate changes of external forces to internal efforts of a material to resist with corresponding static development of the main crack. These tests are most appropriate when using bending or tension of the samples, because the fracture process will be defined by development of a unique breakaway type of crack, which allows determination of the actual surface area of the fracture. This means that the tests correctly provide the real physical processes of fracture of a concrete and the principles of nonlinear fracture mechanics with traditional mechanical characteristics of concrete and allows determination of a set of power and energy parameters of the material fracture. 

Now we discuss briefly the results obtained from the relaxation of the bending mode. As a comparison with the bulk value for the surface indicates (Table I), there is a discrepancy between this surface tension and the surface tension obtained from the bending mode experiments. It should be realized, however, that the film tension value is obtained from experiments on a time scale totally different from the time scale encountered in obtaining the bulk value. This implies the possibility of processes that influence both values in a completely different way, like adsorption and desorption phenomena of surface active materials at the interface. 

Figure 14 shows the knee-shaped curve of solution surface tension vs. concentration characteristic of aqueous surface-active agents the steeper the curve, the more efficient the wetting agent. It is generally assumed that the bend of the curve coincides with the critical micelle concentration (c.m.c.) of the respective compound in the aqueous medium. Since the discontinuities in the slopes of the individual curves of Figure 14 occur in the region of the c.m.c. values reported by various... 

Up till now we considered only flat interfaces. The surface tension aspires to bend the surface. As a result, there is a negative pressure jump as we go through the interface from the side where the centre of curvature is located. The expression for the pressure jump is called the Laplace-Young equation ... 

---