Squeeze mode

An alternative description of membrane stability has been based on hydrodynamic models, originally developed for liquid films in various environments [54-56]. Rupture of the film was rationalized by the instability of symmetrical squeezing modes (SQM) related to the thickness fluctuations. In the simplest form it can be described by a condition [54] d Vdis/dh < where is the interaction contribution related to the dis-... 

The peristaltic force originates from the configurational confinement related to the peristaltic (squeezing) mode of deformation of a fluid bilayer (Figure 5.30b). This mode of deformation consists in flucmation of the bilayer thickness at a fixed position of the bilayer midsurface. The... 

In order to optimize the squeezing effects on the atom, the mode function L (o ) of the squeezed vacuum field should be perfectly matched to the mode function gkj (r,) of the three-dimensional vacuum field coupled to the atoms. Such a requirement of the perfect matching is practically impossible to achieve in present experiments [59]. Therefore, we consider mode functions that correspond to an imperfect matching of the squeezing modes to the vacuum modes surrounding the atoms. In this case, we can write the mode function as... 

Before returning to the derivation of the master equation, we should remark that in the squeezing propagation case in which the squeezed modes lie inside the cone of angle 0m < n, we assume that the modes outside the cone are in their ordinary vacuum state. In practice, the modes will be in a finite-temperature... 

The master equation (97) with parameters (98) is quite general in terms of the matching of the squeezed modes to the vacuum modes and the bandwidth of the squeezed field relative to the atomic linewidths. The master equation is in the... 

B. Scattered Intensity for Films without Long-Range Interaction Forces Bending and Squeezing Modes... 

The contributions of the bending and squeezing modes are given by G0G3 and (2GoG, - G0G3), respectively. The superscript R in indicates... 

Fig. 4.4. Intensity (reflection side) of the light scattered from fluctuations ( i + n) trot s (bending mode) and from fluctuations ( , — n) 2GoG, -G,/ 3 (squeezing mode), where tf— 0 60°, 1.36, and X, =546 nm. (From Ref. 68, courtesy of Elsevier Scientific Publishing Company, Amsterdam.)...

It is only the squeezing mode in our representation of AF that contains a contribution of the interaction free energy V(h). Thus we write, instead,... 

The first term is due to the bending mode and the second one to the squeezing mode. 

From the theory of waves on single surfaces (for a review, see Ref. 85) it was known that for small values of surface wavelength A (i.e., large values of K), the relaxation of the waves was dominated by the action of surface tension. In the case of thin films, also, the effect of interaction forces was expected to influence the relaxation of the film to its mean thickness. Especially, the squeezing mode relaxation, where local thickness fluctuations appear, should show up the influence of colloidal interactions. 

By assuming the existence of squeezing modes, it was found from the conservation of film volume that the amplitude of the mode with wavenumber K relaxes according to... 

A similar equation was found by deGennes. For V" > 0, t is positive, giving rise to an overdamped relaxation. For K" <0 and K<(—2V /yy, r becomes negative, and the squeezing mode will grow in accordance with (4.34), potentially producing film rupture. The maximum value of t is found at K =(- with t- =tJ = -(h y/24v)Kl... 

In the experiments we always deal with film having thickness much less than the wavelength of the observable surface waves (see Section III.A). This means that in the experiments the long-wavelength limit (Iwl) is observed. Since the Iwl corresponds with the conditions Kh<. and w/i bending mode can be found from (5.24) and (5.25) by series expansion of the hyperbolic functions. The result for the squeezing mode is ... 

From (7.3) and (7.4) one sees that the squeezing mode is purely diffusive, whereas the bending mode is propagating. 

The experimental results for the squeezing mode are mainly taken from Ref. 138. 

The squeezing mode experiments were carried out using the homodyne detection scheme with scattering angles within 20° of either the reflected beam ( q=60°) or the transmitted beam. A small region of 4° around either the transmitted or reflected beam was excluded because here a gradual, but not exactly reproducible, transition from homodyne to heterodyne detection is observed. 

Fig. 7.3. Measured autocorrelation function ( + ) of the photocurrent fluctuations. Wavelength of the thickness fluctuation (squeezing mode) A =4.90 ftm. The curve indicates nonlinear least-squares fit to the experimental data according to (7.13). Film was drawn from solution with an ionic strength of 1.9 X 10" mol/dm .

The other three terms on the right-hand side of (7.10) can be neglected in the analysis of the relaxation of the squeezing mode because (F, is... 

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