Foam bilayers lifetime

A premiss for such quantification is the theory of a foam-bilayer lifetime (43). The main notions of this theory are similar to the theory of Deijaguin and coworkers (44, 45). However, the theory (43) is specified for amphiphile foam films, it is elaborated in detail, and is proven by experiment with water-soluble amphiphiles, such as sodium dodecyl sulfate (47). As the dependence of the mpture of the emulsion film on surfactant concentration is similar to that for a foam film, the modification of theory with respect to emulsions may be possible. Although this modification is desirable the specification of a theory for a given surfactant will not be trivial, since the parameters in the equation for the lifetime (45) are unknown and their determination is not easy. As the theory (43, 47) is proposed for amphiphiles and since a wider class of chemical compounds can stabilize, emulsions, the fihn-mpture mechanism (44) is not universal regarding emulsions. 

The molecular model of amphiphile bilayers with holes in them is a good basis also for the description of the rupture of NB foam films by a-particle irradiation [331,415,416]. The mean lifetime ra of the foam bilayer shortens dramatically under irradiation, and probability considerations [416] show that only a small area Sh S of the bilayer is active for the passage of the a-particles. Assuming that 5 is the overall area of those holes in the foam bilayer which are large enough to be irradiation-active makes it possible to represent Sh as... 

Thus, the foam bilayer can indeed be regarded as a system of two amphiphile monolayers adsorbed onto each other. In view of the strong effect of the concentration C of surfactant in the solution on the bilayer lifetime T, it is very convenient to use the t(C) dependence for experimental verification of the theory [399,402,403] of hole-mediated rupture of bilayers. 

Dependence of the lifetime of foam bilayers on the concentration of dissolved surfactant. The stability of foam, emulsion and membrane bilayers can be characterised by their mean lifetime r which is the time elapsing form the moment of formation of a bilayer with a given radius until the moment of its rupture. Obviously, this is a kinetic characteristic of the bilayer stability and can only be applied to thermodynamically metastable bilayers. 

The z(C) dependence has been investigated with the help of microscopic foam bilayers of both ionics and nonionics [419,420]. Due to the fluctuation character of the film rupture, the film lifetime is a random parameter. Experimentally, the film mean lifetime r has been determined by averaging from a great number of measurements. Because of the assumption that the monomer and the total surfactant concentrations are practically equal, in all t(C) dependences given below, C refers to the total concentration. Using Eq. (3.120) to analyse the experimentally obtained time dependence of the probability P(t) of film rupture it was found... 

Rupture of foam bilayers by a-particle irradiation. By means of a-particle irradiation a controlled external influence can be exerted on the rupture of black foam films [331,415,416]. The measuring cell in which the studied microscopic foam bilayer is formed is shown in Fig. 2.10. The a-source is placed at a distance of 3.5 cm away from the bilayer the Bragg distance at which the particle energy is almost constant. The statistical character of bilayer rupture is evidenced in experiments at different irradiation rates [416]. The bilayer mean lifetime ra is therefore an appropriate parameter for assessing the destructive action of the a-particles. 

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. 

Effect of temperature on the stability of foam bilayers. The effect of temperature on the rupture of foam bilayers has also been studied [414] with the help of microscopic NaDoS NB films with a radius of 250 pm. The dependence of the bilayer mean lifetime ton the surfactant concentration C in the presence of 0.5 mol dm 3 electrolyte (NaCI) at 10, 22 and 30°C has been obtained, the temperature being kept constant within 0.05°C. As in the above mentioned case, the NB foam films formed via black spots and the measurements were carried out after a sufficiently long time in order to allow equilibration of the system. At each of the NaDoS concentrations used and at the corresponding temperature, x was determined statistically and the comparison of the experimental with the theoretical x Q dependences was done by means of non-linear optimisation of the constants A, B and Ce. 

The analysis of the effect of temperature on the mean lifetime of foam bilayers provides further evidence for the applicability of the theory of bilayer rupture by hole nucleation [399,402,403]. The experiments show that the foam bilayers become less stable with increasing temperature, due both to the Boltzmann-type thermal activation of the hole nucleation and to the decreasing work of a nucleus hole formation. 

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). 

One of the most important theoretical predictions is the existence of truly (i.e. infinitely) stable bilayers for C > Ce provided Ce < CMC. By fitting theoretical to experimental rfC) dependences it is possible to determine the equilibrium amphiphile concentration Ce and thus to judge whether in a given C range a bilayer, and in some cases, the corresponding disperse system, can be infinitely stable. BLMs, for example, are known to live for months and years. Thermodynamically, there is no difference between foam bilayers and BLMs so that the long lifetime of BLMs is apparently due to their existence in contact with amphiphile solutions of concentrations C either slightly bellow or above Cr. 

It is shown in Section 3.4.4. that microscopic foam bilayers (NBF) can be used to measure different parameters characterising their rupture. A time dependence J(t) expressed as a ratio of the number of films ruptured within the interval t + (/ + At) to the total number of films with lifetime longer than t, was derived to evaluate Dv. It is clearly seen in Fig. 3.114 that for all NaDoS films studied the J(t) dependence has a non-steady-state character. 

The systematic study of foam bilayers from phospholipids [28,38-40] reveals that they do not rupture spontaneously at any concentration allowing their formation. That is why in the case of phospholipid foam bilayer the dependence of their mean lifetime on the bulk amphiphile concentration cannot be measured in contrast to foam bilayer from common surfactants [41,42], This infinite stability of phospholipid foam bilayers is the cause for the steep W(d) and W(C) dependences. In the case of AF foam bilayers this high stability was confirmed by a very sensitive method [19,43] consisting of a-particle irradiation of foam bilayers. As discussed in Sections 2.1.6 and 3.4.2.2, the a-particle irradiation substantially shortens the mean lifetime of foam bilayers. The experiments showed that at all temperatures and dilutions studied (even at d,), the foam bilayers from AF did not rupture even at the highest intensity of irradiation applied, 700 (iCi. 

Fig. 3.85. Bilayer mean lifetime vs. total surfactant concentration for NaDoS NB foam films in the...

Dependence of the probability of observing a bilayer in a foam film on the concentration of dissolved surfactant. Experimental verification of the theory [399,402,403] of hole-mediated rupture of bilayers has also been conducted [382] by analysing data for the W(C) dependence with the help of Eq. (3.128). Studying this dependence is possible and particularly convenient at lower C values when the bilayer mean lifetime t is comparable with tr (see Eq. (3.122)). A characteristic feature of W, according to Eq. (3.128), is its sensitivity to changes of C only in a very narrow range. 

Muller et. al. [421] have studied the behaviour of emulsion Newton bilayer films and compared it to that of foam films. They determined the dependence of the lifetime on surfactant concentration of emulsion films stabilised with 22-oxythylated dodecyl alcohol (see Section 3.4.1). Experimental data for both kinds of films proved to be in conformity with the theory of bilayer stability (see Section 3.4). The values of the equilibrium concentrations Ce calculated for emulsion films were higher (Ce 10 3 mol dm 3) than those for foam films (Ce 3 1 O 5 mol dm 3). It is worth noting that Ce value of foam films from certain surfactants is lower than CMC (C < CMC) while for emulsion films - Ce > CMC. That is why it is impossible to obtain thermodynamically stable films in the latter case. This result is of particular importance for the estimation of stability of aqueous emulsions with bilayer films between the drops of the organic liquid. 

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