Interfacial fluctuations

We now evaluate the spectrum of interfacial fluctuations It is the space-time Fourier transfonn of the... 

Then, from equation (A3.3.31) and equation (A3.3.32), we obtain the spectmm of interfacial fluctuations ... 

The interfacial fluctuations broaden laterally averaged profiles. Within the convolution approximation ( B3.6.15) one obtains a profile with the shape of the erfc fimction [49] ... 

Starting point is the description of the interface in terms of the drumhead model [273], i.e. we disregard for the moment the fact that the interface has a non-trivial intrinsic profile with width w0, and treat it like a sharp kink in terms of the local interfacial height h(x,y) only, x,y being coordinates along the lower surface (at z=0). Then the effective free energy functional Heff [h] associated with interfacial fluctuations can be written as [220]... 

Krawczyk (44) investigated the influence of different demulsifiers on the stability of water-in-crude oil emulsions. He defined a partitioning coefficient, KP = Ca/cQ, where Cg refers to the demulsifier concentration in the aqueous phase, and cq to the concentration in the oil phase. He concluded that demulsifiers with K = 1 gives the best results. He also concluded that the interfacial activity and adsorption kinetics of the demulsifier are important parameters. The interfacial region can be expected to be more dynamic, and considerable interfacial fluctuations may occur in the presence of medium-chain alcohols. 

Wang, H., Composto, R.J. Kinetics of surface and interfacial fluctuations in phase separating polymer blend films. Macromolecules 35(7), 2799-2809 (2002)... 

For blends containing diblock copolymers, interface enrichment by the copolymers as well as the potential reduction of the interfacial tension was investigated by Muller and Binder recently (Muller and Binder 2000). For weak segregation, the addition of copolymers led to compatibilization. At high incompatibilities, the homopolymer-rich phase could accommodate only a small fraction of the copolymer before the formation of a copolymer lamellar phase. The analysis of interfacial fluctuations yielded an estimate for the bending rigidity of the interface. The latter quantity is important for the formation of a polymeric microemulsion at intermediate segregation. 

A. Bednorz and M. Napiorkowski, Interfacial fluctuations near the critical filling transition, Phys. Rev. E, 63, 031602 (2001). 

A different approach to the problem of fluid interfacial structure advocates capillary waves, which have no analogue in the bulk, as the proper modes of the interfacial fluctuations. While originally designed for low temperatures, capillary wave theory has been successfully extrapolated into the critical region of three-dimensional fluids. ... 

In order to elucidate the nature of the critical behavior of fluid interfaces in two dimensions and to better determine the special role played by the external field, it will prove instructive to analyze the effect of varying the external field and test some of the current ideas on the nature of interfacial fluctuations, in particular that according to which capillary waves and intrinsic fluctuations should be combined and forced to coexist rather than exclude each other. 

Let us consider an example of thermal interfacial fluctuations at the expense of bending energy. We take as an example a lamellar phase (Fig. 10), where each layer (separation h) may fluctuate about its means position with an amplitude (x, y) where (x, y) denote the position in the horizontal plane. Assuming no tendency for spontaneous curvature (Rq ),... 

Equations (l)-(3) provide a connection between interfacial fluctuations, the surface tension, and intermolecular interactions (expressed by forces). Qualitatively, interactions of water with molecules of the organic liquid increase interfacial fluctuations and reduce the surface tension, compared with the liquid-vapor interface of water. For example, the surface tension of water at 7 = 298 K is 0.0727 N m whereas the surface tension at water-hexane and water-octanol at the same temperature is 0.051 and 0.0085 N m respectively. 

The dynamical aspects of melt-phase behaviour are also governed by interfacial reorganization. It has been recognized theoretically that interfacial fluctuations or corrugations [80-90] play an important role in order-to-order transitions and set the kinetic pathway (or intermediate state) [91-96]. Examples are shown in Figure 4.1 for hex-to-bcc, hex-to-lam, and bcc-to-hex transitions. These are the results obtained using a theory of anisotropic fluctuations [97] introduced to study the stability of ordered phases [80,81]. Experimental evidence for interfacial fluctuations has been presented for the hex-to-bcc transition by 2D-SAXS for well-aligned hex cylinders [86,87]. The presence of interfacial fluctuation was confirmed by transmission electron microscopy (TEM) observations performed by the same authors. 

Figure 4.1 Examples of interfacial fluctuations or corrugations at an OOT (a) hex-to-bcc, (b) hex-to-lam, and (c) bcc-to-hex transitions. (Reproduced from M. Laradji et at. (1997) Macro-molecules, 30 3242-3255, Copyright (1997) with permission from the American Chemical Society.)...

---