Foam bilayers vacancies

Parameters of hole nucleation and molecular characteristics of bilayers. Theoretically, the fitting constants A, B and Ce in Table 3.12 contain important information. Using their values in Eqs. (3.107), (3.110), (3.111), (3.126) and (3.129), the following characteristic parameters of the process of hole nucleation in the foam bilayers can be evaluated nucleation work W, number C of surfactant vacancies in the nucleus hole, specific... 

To verify whether the rupture of a-particle-irradiated foam bilayers can also occur by the hole mechanism the experimental TjC) dependence for NB foam films of NaDoS has been analysed using Eq. (3.132) [415]. The circles in Fig. 3.88 show the experimental data, and the solid line is drawn according to Eq. (3.132) as a result of the best fit in the range C = 3 to 6T0 4 mol dm 3. The % value of 2-10 11 J m 1 obtained is in good agreement with the % value for spontaneous rupture. The size of the smallest irradiation-active hole is i = 3, and nucleus hole consists of = 12 to 83 NaDoS vacancies. The abrupt rise of the slope in the... 

The conclusion is, therefore, that both spontaneous and forced rupture of foam bilayer by a-particles are mediated by microscopic holes of surfactant vacancies and can be described from a unified point of view with the aid of the nucleation theory of bilayer rupture [399,402,403]. However, studying the effect of a-particle irradiation of the bilayer lifetime is an independent way of proving the applicability of the hole mechanism of bilayer rupture. 

Adsorption isotherm of surfactant vacancies in foam bilayers. As discussed above, the investigation of the stability of foam bilayers at different temperatures allow determination of the binding energy Q of a surfactant molecule in the bilayer. At the highest temperatures of 30°C the Q value for a NaDoS molecule in the foam bilayer (Q 6kT) is high enough to ensure the occurrence of 2D first-order phase transition in the bilayer. Theoretically Q > 8kT is known to be the condition for such a transition in the most frequently encountered 2D lattices [423],... 

The adsorption isotherms of NaDoS vacancies calculated in [424], from Eq. (3.13) with the aid of the values of Q and Co given previously are shown in Fig. 3.90 for 10°C (curve 1), 22°C (curve 2) and 30°C (curve 3). The equilibrium NaDoS concentrations Ce above which NaDoS foam bilayers of infinitely long lifetime are to be obtained are marked by arrows. In practice, this cannot be achieved because CMC < Ce. The hatched area shows the investigated concentration interval in which the gas of NaDoS vacancies in the foam bilayer undergoes a 2D first-order phase transition from a dilute phase (existing metastable bilayer) into a condensed phase (ruptured bilayer). 

Fig. 3.90. Calculated dependence of the degree of filling of the foam bilayer by surfactant vacancies on...

Fig. 3.91 displays the dependence of the density n of NaDoS vacancies in the foam bilayer on the concentration C of NaDoS in the solution for the three temperatures investigated 10°C (curve 1), 22°C (curve 2) and 30°C (curve 3). This dependence is calculated [424] using the formula... 

Fig. 3.91. Calculated dependence of the density of surfactant vacancies in the foam bilayer on the...

The experimental results discussed pertain to foam and emulsion bilayers formed of surfactants of different kinds and provide information about quantities and effects measurable in different ways. It is worth noting that analysing the observed effect of temperature on the rupture of foam bilayers enables the adsorption isotherm of the surfactant vacancies in them to be calculated. This isotherm shows a first-order phase transition of the vacancy gas into a condensed phase of vacancies, which substantiates the basic prerequisites of the theory of bilayer rupture by hole nucleation. 

Hole-nucleation rupture of foam bilayers was considered on the basis of formation of nucleus-holes from molecular vacancies existing in the film in Section 3.4.4. The experimentally determined parameters of film rupture along with the hole-nucleation theory of rupture of amphiphile bilayers of Kashchiev-Exerowa [300,301,354,402] made it possible to evaluate the coefficient of lateral diffusion of vacancies in foam bilayer. 

Microscopic foam films are most successfully employed in the study of surface forces. Since such films are small it is possible to follow their formation at very low concentrations of the amphiphile molecules in the bulk solution. On the other hand, the small size permits studying the fluctuation phenomena in thin liquid films which play an important role in the binding energy of amphiphile molecules in the bilayer. In a bilayer film connected with the bulk phase, there appear fluctuation holes formed from vacancies (missing molecules) which depend on the difference in the chemical potential of the molecules in the film and the bulk phase. The bilayer black foam film subjected to different temperatures can be either in liquid-crystalline or gel state, each one being characterised by a respective binding energy. 

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