Capillary waves interfacial

The interfacial width obtained from fitting the dPS-LDPE NR profiles is given in Table II. This measured interfacial width is described by a self-consistent mean-field theory, which is broadened by thermally excited capillary waves [2]. The measured interfacial width is given by Gaussian quadrature addition of the intrinsic (unbroadened by capillary waves) interfacial width, Ao, and the interfacial width associated with the capillary waves, Ac. This gives -... 

The fluctuations of the local interfacial position increase the effective area. This increase in area is associated with an increase of free energy Wwhich is proportional to the interfacial tension y. The free energy of a specific interface configuration u(r,) can be described by the capillary wave Hamiltonian ... 

In the past five years, it has been demonstrated that the QELS method is a versatile technique which can provide much information on interfacial molecular dynamics [3 9]. In this review, we intend to show interfacial behavior of molecules elucidated by the QELS method. In Section II, we present the principle and the experimental apparatus of the QELS along with the historical background. The dynamic collective behavior of molecules at liquid-liquid interfaces was first obtained by improving the time resolution of the QELS method. In Section III, we show the molecular collective behavior of surfactant molecules derived from the analysis of the time courses of capillary wave frequencies. Since the... 

The molecular collective behavior of surfactant molecules has been analyzed using the time courses of capillary wave frequency after injection of surfactant aqueous solution onto the liquid-liquid interface [5,8]. Typical power spectra for capillary waves excited at the water-nitrobenzene interface are shown in Fig. 3 (a) without CTAB (cetyltrimethy-lammonium bromide) molecules, and (b) 10 s after the injection of CTAB solution to the water phase [5]. The peak appearing around 10-13 kHz represents the beat frequency, i.e., the capillary wave frequency. The peak of the capillary wave frequency shifts from 12.5 to 10.0kHz on the injection of CTAB solution. This is due to the decrease in interfacial tension caused by the increased number density of surfactant molecules at the interface. Time courses of capillary wave frequency after the injection of different CTAB concentrations into the aqueous phase are reproduced in Fig. 4. An anomalous temporary decrease in capillary wave frequency is observed when the CTAB solution beyond the CMC (critical micelle concentration) was injected. The capillary wave frequency decreases rapidly on injection, and after attaining its minimum value, it increases... 

Dynamic surface tension has also been measured by quasielastic light scattering (QELS) from interfacial capillary waves [30]. It was shown that QELS gives the same result for the surface tension as the traditional Wilhelmy plate method down to the molecular area of 70 A. QELS has recently utilized in the study of adsorption dynamics of phospholipids on water-1,2-DCE, water-nitrobenzene and water-tetrachloromethane interfaces [31]. This technique is still in its infancy in liquid-liquid systems and its true power is to be shown in the near future. 

Levich (L8) has shown that, for capillary waves, the relative increase in interfacial area is given by... 

Recent theoretical studies indicate that thermal fluctuation of a liquid/ liquid interface plays important roles in chemical/physical properties of the surface [34-39], Thermal fluctuation of a liquid surface is characterized by the wavelength of a capillary wave (A). For a macroscopic flat liquid/liquid interface with the total length of the interface of /, capillary waves with various A < / are allowed, while in the case of a droplet, A should be smaller than 2nr (Figure 1) [40], Therefore, surface phenomena should depend on the droplet size. Besides, a pressure (AP) or chemical potential difference (An) between the droplet and surrounding solution phase increases with decreasing r as predicted by the Young-Laplace equation AP = 2y/r, where y is an interfacial tension [33], These discussions indicate clearly that characteristic behavior of chemical/physical processes in droplet/solution systems is elucidated only by direct measurements of individual droplets. 

The electric field experiment shown here can be considered as a test case for the quantitative nature of capillary instability experiments. It shows the precision, with which the capillary wave pattern reflects the underlying destabilizing force. In the case of electric fields, this force is well understood. Therefore, the good fit in Fig. 1.10b demonstrates the use of film instability experiments as a quantitative tool to measure interfacial forces. The application of this technique to forces that are much less well understood is described in the following section. 

Interface between two liquid solvents — Two liquid solvents can be miscible (e.g., water and ethanol) partially miscible (e.g., water and propylene carbonate), or immiscible (e.g., water and nitrobenzene). Mutual miscibility of the two solvents is connected with the energy of interaction between the solvent molecules, which also determines the width of the phase boundary where the composition varies (Figure) [i]. Molecular dynamic simulation [ii], neutron reflection [iii], vibrational sum frequency spectroscopy [iv], and synchrotron X-ray reflectivity [v] studies have demonstrated that the width of the boundary between two immiscible solvents comprises a contribution from thermally excited capillary waves and intrinsic interfacial structure. Computer calculations and experimental data support the view that the interface between two solvents of very low miscibility is molecularly sharp but with rough protrusions of one solvent into the other (capillary waves), while increasing solvent miscibility leads to the formation of a mixed solvent layer (Figure). In the presence of an electrolyte in both solvent phases, an electrical potential difference can be established at the interface. In the case of two electrolytes with different but constant composition and dissolved in the same solvent, a liquid junction potential is temporarily formed. Equilibrium partition of ions at the - interface between two immiscible electrolyte solutions gives rise to the ion transfer potential, or to the distribution potential, which can be described by the equivalent two-phase Nernst relationship. See also - ion transfer at liquid-liquid interfaces. 

First, a typical power spectrum of capillary waves excited at the W/NB interface is shown in Figure 3.4a. The errors on the values of the capillary wave frequency were 0.1 kHz, obtained as the standard deviation of 10 repeated measurements. Capillary wave frequency dependence on CeHsONa is shown in Figure 3.4b. The frequency decreased significantly with increasing CeHsONa concentration. This indicated that interfacial tension was decreased by the interfacial adsorption of CeHsONa. 

In the Current State of the Art we will review some of the recent SANS and reflectivity data from ISIS, which also serve to point to future directions and opportunities. Recent reflectivity measurements, on the adsorption of polymers and polymer/surfactant mixtures at interfaces, surface ordering in block copolymer systems, time dependent inter-diffusion at polymer-polymer interfaces, and the contribution of capillary waves to interfacial widths, will be described. The use of SANS to investigate the dynamic of trans-esterification of polyester blends, the deformation of copolymers with novel morphologies, and the use of diffraction techniques to determine the structure of polymeric electrolytes, will be presented. 

Polymer-polymer interfaces are an important area of study since the interfacial behaviour is fundamental to the bulk properties of the system. This is particularly true when two or more polymers are mixed to form a blend, but the interface also plays a dominant role in areas such as adhesion, welding, surface wetting and mechanical strength. To understand fully polymer behaviour in such applications, the interface must be characterised at a microscopic level. Through deuterium labelling the interface between otherwise indistinguishable polymers can be studied, and neutron reflectivity provides unprecedented detail on interfacial width and shape. In addition to the inherent interdiffusion between polymers at a polymer-polymer interface, the interface is further broadened by thermally driven capillary waves. Capillary waves... 

Typically dynamic techniques (overflowing weirs, cylinders, capillary waves, etc,) will be discussed in sec. 3.7 on Interfacial rheology. 

Let us now briefly mention an approach that is popular among physicists, and which comes down to correlating surface tensions to capillary waves. The underlying idea is that each fluid-fluid interface is subject to a superposition of a large number of thermal waves. The amplitudes of these waves are related to the inter-facial excess energy and the number and frequencies to the interfacial excess entropy, hence the total information obtainable yields F°, and hence y. The idea dates back to Mandelstam and has been taken up by others, including Frenkel and Buff et al. . ... 

Henceforth we shall use the term capillary waves, or capillary ripples for waves that are so small that interfacial tension contributes significantly to their properties. Two types of such waves can be distinguished spontaneous, or thermal waves and those externally applied. The former type is always present they are caused by spontaneous fluctuations cind have a stochastic nature. In secs. 1.10 and 1.15 it was shown how from these fluctuations interfacial tensions and bending moduli could be obtained. Now the second type will be considered. Transverse or longitudinal perturbations can be applied to the interface, for example by bringing in a mechanically driven oscillator (see sec. 3.7). Such waves are damped, meaning that the amplitude Is attenuated. Damping takes place by viscous friction in the... 

Finally, we recall that surface light scattering is another modem technique. Essentially. thermal capillary waves can be studied and this enables us to derive interfacial tensions and binding constants. We discussed this matter in sec. 1.10. 

---