Transition thickness

Fig. 4.1. The La line of the H atom and its structure in the constant electric field (a) and the rotational structure of the vibrational transition (b). Wavy arrows show collision-induced transitions, thick horizontal arrows indicate the optical transitions that mutually interfere.

As already mentioned, stepwise transitions in foam films are observed, as a rule, at thicknesses less then 60 - 70 nm. The number of transitions increases with the increase in surfactant concentration. Manev et al. [351] have observed up to 10 transitions when the NaDoS concentration in the initial aqueous solution was raised to 0.5 mol dm 3 (in the absence of additional electrolyte). Upon increasing the ionic strength (addition of electrolyte or ionic surfactants) the differences in the transition thicknesses decrease. In some cases [351-353] electrolyte inhibits stratification. 

Ellipsometry Spectroscopic ellipsometry Imaging ellipsometry Adsorbed amounts/coverages phase transitions thickness and refractive indices. Identification of interfacial molecules. Domain formation eind shape (coexisting phases) internal structure of condensed phases resolution O (1 gm). For interpretation in terms of molecular structure model profiles across the Interface are needed. Problems mono-layer anisotropy, and different profiles may match the experimental data additional (independent) information required. 

Figure 9. Phase diagram from MC simulations showing the liquid—gas transition (thick line), the liquid-liquid transition (squares) and the temperature of maximum density (TMD). Emanating from the LLCP (full circle) is the locus of maxima of (crosses), the locus of maxima of...

In Equation 5.271, h is the so-called transitional thickness at which the increase of free energy due to the increased film area and the decrease of free energy due to the van der Waals interaction in the thinner part (Figure 5.36d) compensate for each other. At h, the most rapidly growing fluctuation (the critical wave) becomes unstable. The transitional thickness obeys the following equation " " " ... 

Problem 1 Use the data in Table 14.2 to rank the plastics in terms of the transition thickness tc for plane strain fracture (Eq. 9.21), and comment on why polyethylene is preferred to the other polymers. 

The dependence of the transitional distance hf on the siu-factant concentration, calculated with the help of Eq. (61), is shown in Fig. 14 the three ciuves correspond to three fixed values of the mean drop radius a. The calculations are carried out for the system with SDS + 0.1 M NaCl in the aqueous phase (see Table 4) the oil phase is dodecane. One sees that the increase in siufactant concentration leads to a decrease in transitional thickness, which corresponds to a greater stability of the emulsion against coalescence. Physically this is related to the damping of the fluctuation cap-... 

As aheady mentioned, the transition from stability to instability occurs when the thickness of the gap between two colliding emulsion drops decreases down to a transitional thickness hf. Vox hf> h> the film continues to thin, while the instabilities grow, until the film ruptures at the critical thickness h = h. ... 

Equation (82) shows that the disjoining pressure significantly influences the transitional thickness The effect of surface mobility is characterized by the parameter d, see Eq. (53) in particular, d = 0 for tangentially immobile interfaces. Equation (82) is valid for H < 2o/u, i.e., when the film thins and ruptures before reaehing its equilibrium thickness, eorresponding to H = 2o/a [cf Eqs (42), (43), and (59)]. 

The ealculation of the transitional thickness is a prerequisite for computing the critical thickness h, whieh can be obtained as a solution to the equation (95, 96) ... 

To describe mathematically the process of thin liquid film instability the shape of the corrugated film surfaces is presented as a superposition of Fourier-Bessel modes, proportional to Jo(kr/R), for all possible values of the dimensionless wave number k (Jo is the zeroth order Bessel function). The mode, which has the greatest amplitude at the moment of film breakage, and which causes the breakage itself, is called the critical mode, and its wave number is denoted by cr- The stability-instability transition for this critical mode happens at an earlier stage of the film evolution, when the film thickness is equal to Atr - the so-called transitional thickness, h r > her (Ivanov 1980). The theory provides a... 

Our tentative interpretation is that the thin PTFE layers are patchy. Then, for liquid crystal layers thinner than the crossover thickness, the molecules on top of the patches will be perpendicular to the surface, while those between patches will be parallel. (We disregard here the case of very thin layers discussed above, when all molecules are parallel.) With increasing liquid crystal thickness, however, the elastic bend energy in the transition between the two orientations becomes gradually more important, and at some transition thickness a single orientation, parallel to the surface, may become energetically favored. Conceivably, a compromise inclined orientation could also be the results. 

Many more functional characteristics beyond the discussed selection exist. For instance, the influence of the composition of the membrane on activity has been almost completely ignored. This includes important topics such as membrane fluidity, phase transition, thickness (and hydrophobic matching), surface potentials 4 0 (and Gouy-Chapman theory), partitioning, heterogeneity ( rafts ), or swelling and shrinking in response to stress. 

Figure 7 Typical Jablonski diagram of an organic chromophore showing the electronic ground state So, radiative transitions (thick vertical arrows), nonradiative deactivations (wavy arrows), and mtersystem crossing (ISC, curved thick arrow) from the first singlet excited state (Si) to the first triplet excited state (Ti)...

Seifert and Lipowsky [47] used the above scheme to calculate phase diagrams for the unbinding of a vesicle adsorbed to a substrate. In Fig. 21, an example of such a phase diagram as calculated by Seifert and Lipowsky is shown [47,48]. In this example, 1/Rq = 0. the volume V and surface area A are kept constant, and the unbinding transition (thick solid lines and thick dashed line) is located as a function of the reduced volume v= [(367tF )//l ] and reduced substrate adhesion energy, [(<7— )A]l Ank). 

Figure 44 Dependence of the critical thickness of rapture, he and the transitional thickness, h on the film radius, R. Curve 1—experimental data for aniline films stabilized by dodecanol [420] curve 2—theoretical calculation on the basis of Eq. (267) curves 3 and 4—the transitional thickness calculated from Eqs. (265) and (271), respectively.

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