Capillary wave excitations

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... 

FIG. 3 Power spectra for capillary waves excited at the water-nitrobenzene interface (a) without CTAB molecules and (b) 10s after injection of a CTAB solution (0.5mL, lOmM) into the water phase. 

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. 

FIGURE 3.4. (a) Power spectrum for capillary waves excited at the W/NB interface (238 K). (b) Capillary wave frequency dependence on the concentrations of CsHsONa (283 K). 

The mean field Cahn-Hilliard approach (Eq. 7) describes the intrinsic profile ( >(z) about the internal interface between two coexisting phases. It involves only one dimension, i.e., depth z, as a lateral homogeneity is assumed [7]. Capillary wave excitations may however cause lateral fluctuations of the depth Ie(x,y) at which the internal interface is locally positioned. As a result the effective interfacial width may be broadened beyond its intrinsic value (Eqs. 10 and 12). The mean field theory predicts the temperature dependence of the intrinsic width in a good agreement with experimental data presented here and reported by others (e.g., [76,89] reanalyzed by [88] or [96,129]). Some other experimental results [95,97,98] indicate the width larger than its intrinsic value... 

As mentioned in Sect. 2.2.2, the effective interfacial width wD characterizing the bilayer structure may be broadened beyond its intrinsic value w, yielded by a mean field theory (Eqs. 10 and 12). This is due to the capillary wave excitations causing the lateral fluctuation of the depth Ie(x,y) corresponding to the midpoint of the internal interface between coexisting phases. This fluctuation is opposed by the forces due to external interfaces, which try to stabilize the position Ie(x,y) in the center of the bilayer [6, 224, 225]. It was suggested recently [121] that the spectrum of capillary waves for a soft mode phase should be cut off by qb and y. This leads to the conclusion that the effective interfacial width wD should depend on the film thickness D as (wD/2)2= b2+ bD/4. Experimental data [121] obtained for olefinic blends (at T close to Tc) indeed show remarkable increase of the measured interfacial width from wd(D=160 nm)=14.4(3) nm to wd=45(12) nm for thickness D-660 nm, where wD levels off (because is comparable with lateral sample dimensions). This trend is in qualitative agreement with the formula due to capillary oscillations in the soft mode phase . However... 

In addition, theoretical models extended beyond the standard mean field or self consistent mean field (for systems with sharp concentration gradients) approach can yield predictions which are in quantitative accord with experimental results. For instance, the inclusion of the concept of capillary wave excitations [6, 7] helps to explain the fine details of the concentration profiles observed for the interface between coexisting phases [130] or for the interfacial brush layer [261]. 

In summary, assuming the equilibrium structure of the fluid interface to result from averaging capillary wave excitations on an intrinsic interface, it is found that while the external field does not affect the divergence of the interfacial thickness in the critical region of fluids in three or more dimensions (except, of course, extremely close to the critical point ), its effect is dramatic in two dimensions, where the critical behavior is found to be non-universal, i.e., depending on the external field. Consequently, the relation p = (d-Do>, which links the critical exponents of surface tension and interfacial thickness to the dimension of space and which is most probably correct in d > 3, appears to be incorrect in d = 2, since there co, unlike p, is strongly field-dependent. ... 

Here we briefly present the relevant theory of capillary waves. The thermally excited displacement (r, t) of the free surface of a liquid from the equilibrium position normal to the surface can be Fourier-decomposed into a complete set of surface modes as... 

Recently, the newly developed time-resolved quasielastic laser scattering (QELS) has been applied to follow the changes in the surface tension of the nonpolarized water nitrobenzene interface upon the injection of cetyltrimethylammonium bromide [34] and sodium dodecyl sulfate [35] around or beyond their critical micelle concentrations. As a matter of fact, the method is based on the determination of the frequency of the thermally excited capillary waves at liquid-liquid interfaces. Since the capillary wave frequency is a function of the surface tension, and the change in the surface tension reflects the ion surface concentration, the QELS method allows us to observe the dynamic changes of the ITIES, such as the formation of monolayers of various surfactants [34]. 

There are several experimental techniques suitable for studying e. Some of them are Relaxation after a sudden compression of the monolayer Electrocapillary waves An oscillatory barrier Light Scattering by thermally excited capillary waves. The first two techniques are used in the low - frequency range, below 1 Hz. The last one in the kilohertz range. 

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. 

The products of hybridization are detected through the use of fluorescent labeling. These molecular complexes can either be homogeneously distributed in the liquid core or be bound to the interior surface of the capillary through covalent bonding. In both cases, labeled molecules can be excited either by direct illumination with the leaky modes of the liquid filled core, or by the evanescent waves arising from the guided modes of the capillary wall. Direct excitation is less wasteful of incident photon flux and is the method of choice in conventional fluorometers. Evanescent wave excitation becomes a necessity when direct excitation is either not feasible or results in undesirable sensor performance. Both methods of illumination are possible for the CWBP. 

Stenvot C, Langevin D (1988) Study of viscoelasticity of monolayers using analysis of propagation of excited capillary waves. Langmuir 4 1179-1183... 

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