Interfacial curvature measurement

Interfacial Curvature Measurement Comparison Between LSCM and TRLS. 141... 

There are several methods for interfacial tension measurement. However, at high temperatures, the choice of the measurement technique is limited. Since most high temperature liquids are corrosive and often non-transparent to visible light, the sessile drop technique can rarely be used. However, by the use of the X-ray beam, the shape of sessile drops immersed in another liquid may be determined. This technique was used by Utigard and Toguri (1985) in the measurement of interfacial tension of aluminum in cryolite melts. On the basis of the curvature of the drop and the density difference between the metal and the salt. X-rays lead to a fuzzy outline of the drop shape and together with the sensitivity of the drop outline on the interfacial tension, this technique is limited to an accuracy of about 5-10%. 

H. Jinnai, Y. Nishikawa, R J. Spontak, S. D. Smith, D. A Agard, and T. Hashimoto, "Direct Measurement of Interfacial Curvature Distributions in a Bicontlnuous Block Copolymer Morphology," Phys Rev. Lett 84, 518-521 (2000). 

Choi, S.M., Chen, S.H., Sottmann, T., and Strey, R. 1997 Measurement of interfacial curvatures in microemulsions using small-angle neutron scattering, Physica B Condens. Mat. 241—243 976—978. 

Direct Measurement of Interfacial Curvature Distributions in a Bicontinuous Block Copolymer Nanostructure... 

D visualization of bicontinuous morphologies in block copolymer systems has been achieved [26-27] by TEMT (see Sect 2.2). This technique affords the real-space structural analysis of complex nanoscale morphologies without a priori synunetry or surface assumptions [97]. Application of numerical methods developed [39, 98] to measure interfacial curvatures from 3D LSCM images of SD polymer blends (see Sects. 3.2.3 and 4.3.3) to a TEMT reconstruction of the G morphology yields the first experimental measurements of interfacial curvature distributions, as well as (H) and an, in a complex block copolymer nanostructure. 

Interfacial curvature distributions, F(H,X), were evaluated from the 3D morphologies in Fig. 27 according to the SFM. The value of RI computed for the TEMT data analyzed here is 0.12. If RI is less than 0.2 in the curvature distribution measurements, a 5% error is expected [98]. 

Due to the fact that freezing point temperature and vapor pressure of a substance vary with interfacial curvature in a pore, the determination of pore size and pore size distribution can be achieved by observing solid-liquid or liquid-vapor transition in pores. Thermoporometry is a technique involving the measurement of freezing point depression of a liquid in membrane pores using a sensitive differential scanning calorimetry (Table 15.3e). The principle of thermoporometry is described by Gibbs-Thomson equation [174] ... 

Israelachvili and coworkers [64,69], Tirrell and coworkers [61-63,70], and other researchers employed the SFA to measure molecular level adhesion and deformation of self-assembled monolayers and polymers. The pull-off force (FJ, and the contact radius (a versus P) are measured. The contact radius, the local radius of curvature, and the distance between the surfaces are measured using the optical interferometer in the SFA. The primary advantage of using the SFA is its ability to study the interfacial adhesion between thin films of relatively high... 

It is probable that numerous interfacial parameters are involved (surface tension, spontaneous curvature, Gibbs elasticity, surface forces) and differ from one system to the other, according the nature of the surfactants and of the dispersed phase. Only systematic measurements of > will allow going beyond empirics. Besides the numerous fundamental questions, it is also necessary to measure practical reason, which is predicting the emulsion lifetime. This remains a serious challenge for anyone working in the field of emulsions because of the polydisperse and complex evolution of the droplet size distribution. Finally, it is clear that the mean-field approaches adopted to measure > are acceptable as long as the droplet polydispersity remains quite low (P < 50%) and that more elaborate models are required for very polydisperse systems to account for the spatial fiuctuations in the droplet distribution. 

Of all local motions, v(r), of an interface that pass the same amount of volume from one side to the other, the motion that is normal to the interface with magnitude proportional to the weighted mean curvature, v f) oc /c7n, increases the interfacial energy the fastest. However, fastest depends on how distance is measured. How this distance metric alters the variational principles that generate the kinetic equations is discussed elsewhere [14]. 

Microemulsions consist of oil, water and an oil-water interfacial Him. DLS and SLS have been used to determine the translational diffusion coefficient and the interaction potential of microemulsions [45—47). The thickness of the inter-facial film and its curvature were measured by the contrast variation method in neutron scattering [48,491. This method is based on changing the scattering strength by changing the relative amount of light and heavy water in the microemulsion. 

The best fit for M = 64 corresponds to an interfacial energy at the micelle-water interface of y = 52 erg cm in agreement with the measured value of y, at the bulk oil-water interface. The interfacial energies of liquid hydrocarbon-water interfaces vary from about 50 to 54 erg cm (from section 4 with the spherical approximation, the best fit y was 37 erg cm- ). With a 20 A, the value of K2 corresponds to a hydrophobic energy of 13 300 cal mol Curvature corrections (see below) reduce this to about 12 000 cal mol close to the expected value deduced in section 4. 

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. 

From a fundamental point of view this method is very attractive because it attempts to measure the capillary pressure directly. So, if the radii of curvature are known in one point of the Interface, the interfacial tension can be computed. In principle, the contact angle does not have to be known. However, in practice a number of problems have to be surmounted. 

Basically, all the methods for measuring interfacial tensions described so far have in common that the Helmholtz energy for extending an interface is determined. Upon this extension, the interfacial tension should not vary, otherwise the quantity y would become ill-defined. One of the changes that might be incurred could result from strong curving of the interface. In the present chapter this issue was avoided because we have only considered macroscopic interfaces with radii of curvatures above 0(10-100 nm). Already in sec. 1.2.23c we showed that y is then still independent of curvature. 

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