Hole nucleation

The dependence on film thickness is attributed to the dewetting nucleation, which occurs in the 2.5-4.5 nm thickness range via the formation of randomly distributed droplets rather than the formation of holes. When the initial film thickness exceeds 4.5 nm, dewetting is trigged via nucleation of holes instead of droplets, and for film thickness above 10 nm, dewetting develops slowly via hole nucleation at defects. The different dewetting processes observed for different initial film thicknesses can be explained in terms of the variation of disjoining pressure and the inability of the polymer to spread on its own monolayer. 

Let us consider a circular puddle of liquid, L, on solid, S, in the presence of liquid vapor, V. The puddle is of radius Rq and small initial thickness Bq. We assume that holes nucleate spontaneously in the puddle and grow with radius r(t) as time t passes because the equilibrium contact angle. Go, is nonzero. The liquid is unstable as a wetting film. Equilibrium thickness of a film, < is given by [27,28]... 

Rgure 5.2. Scheme of the hole nucleation process and variation of the energy cost with hole radius r. 

At a microscopic scale, a single coalescence event proceeds through the nucleation of a thermally activated hole that reaches a critical size, above which it becomes unstable and grows [29]. We shall term E(r) the energy cost for reaching a hole of size r. A maximum of E occurs at a critical size r, E r ) = Ea being the activation energy of the hole nucleation process (Fig. 5.2). 

Eqs. (3.110) and (3.111) show that both the nucleus size and nucleation work become infinitely large if A// = 0, i.e. if C = Ce Physically, this means that formation of nucleus holes in the bilayer is then impossible. Accordingly, the bilayer is then truly stable (and not metastable) in respect to rupture by hole nucleation. It must be emphasised that the bilayer also retains this true (or infinite) stability for A/r < 0, i.e. for C > Ce, since both terms in Eqs. (3.108) and (3.109) are then positive and W, can only increase with increasing i (Fig. 3.84). Thus, as it requires more and more work to be done, the overgrowth of the randomly formed holes is then suppressed and the bilayer cannot rupture despite the presence of a certain population of holes in it. 

The molecular model of amphiphile bilayers can also be used for describing the process of hole nucleation by the classical nucleation scheme [408,409] as resulting from a series of bimolecular reactions characterised by the nucleation rate J (s 1) which is the frequency with which the / -sized nucleus holes become supemucleus holes of size / +1. For steady-state nucleation, J is known to be [408,409]... 

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... 

Calculated values of the fitting constants A, B and C, and of other parameters of hole nucleation in NaDoS foam bilayers of radius 250 pm at different temperatures [414]... 

Table 3.13 shows that the kinetic factor A increases with temperature. This fact cannot be explained without knowing the concrete mechanism of formation of the holes in the foam bilayer. A possible explanation is the occurrence of hole nucleation on preferred sites, for example along line defects (such as domain boundaries) in the bilayer. A similar preferential nucleation of voids on structural defects is known to occurs in crystals [422], If the density N0 of these preferred sites in the bilayer decreases with increasing temperature, according to Eq. (3.125). A will increase with Tprovided oKT) dependence is not significant. 

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. 

Rupture of emulsion bilayers. Experimental verification of the theory [399,402,403] of hole nucleation rupture of bilayer has also been conducted with emulsion bilayers [421]. A comparative investigation of the rupture of microscopic foam and emulsion bilayers obtained from solutions of the same Do(EO)22 nonionic surfactant has been carried out. The experiments were done with a measuring cell, variant B, Fig. 2.3, a large enough reservoir situated in the studied film proximity was necessary to ensure the establishment of the film/solution equilibrium. The emulsion bilayer was formed between two oil phases of nonane at electrolyte concentration higher than Cei,cr-... 

In conclusion, let us outline some more important aspects of the hole-nucleation theory for stability of amphiphile bilayers of Kashchiev-Exerowa and its experimental support. The outlined theoretical and experimental investigations of the stability and permeability of foam, emulsion and membrane bilayers represent a new approach towards... 

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. 

It is well known that water dispersions of amphiphile molecules may undergo different phase transitions when the temperature or composition are varied [e.g. 430,431]. These phase transitions have been studied systematically for some of the systems [e.g. 432,433]. Occurrence of phase transitions in monolayers of amphiphile molecules at the air/water interface [434] and in bilayer lipid membranes [435] has also been reported. The chainmelting phase transition [430,431,434,436] found both for water dispersions and insoluble monolayers of amphiphile molecules is of special interest for biology and medicine. It was shown that foam bilayers (NBF) consist of two mutually adsorbed densely packed monolayers of amphiphile molecules which are in contact with a gas phase. Balmbra et. al. [437J and Sidorova et. al. [438] were among the first to notice the structural correspondence between foam bilayers and lamellar mesomorphic phases. In this respect it is of interest to establsih the thermal transition in amphiphile bilayers. Exerowa et. al. [384] have been the first to report such transitions in foam bilayers from phospholipids and studied them in various aspects [386,387,439-442]. This was made possible by combining the microscopic foam film with the hole-nucleation theory of stability of bilayer of Kashchiev-Exerowa [300,402,403]. Thus, the most suitable dependence for phase transitions in bilayers were established. 

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. 

In order to apply the hole-nucleation theory of bilayer stability of Kashchiev-Exerowa [27] involving quantitative interpretation of the W(C) dependence (probability for observation of black films vs. surfactant concentration), the black films from amniotic fluid should be bilayer films. This is proved experimentally by two dependences Y hw) (Fig. 11.1) and hw(Cei) (Fig. 11.2). As it can be seen in Fig. 11.1, the equivalent film thickness is 8 nm and does not change with the increase in IT (which is the difference between the pressures in the... 

Let us summarise the conditions of formation of a microscopic foam film in order to serve the in vivo situation. These are film radius r from 100 to 400 pm capillary pressure pa = 0.3 - 2.5-102 Pa electrolyte (NaCl) concentration Ce 0.1 mol dm 3, ensuring formation of black films (see Section 3.4) and close to the physiological electrolyte concentration sufficient time for surfactant adsorption at both film surfaces. Under such conditions it is possible also to study the suitable dependences for foam films and to use parameters related to formation and stability of black foam films, including bilayer films (see Section 3.4.4). For example, the threshold concentration C, is a very important parameter to characterise stability and is based on the hole-nucleation theory of bilayer stability of Kashchiev-Exerowa. As discussed in Section 3.4.4, the main reason for the stability of amphiphile bilayers are the short-range interactions between the first neighbour molecules in lateral and normal direction with respect to the film plane. The binding energy Q of a lipid molecule in the foam bilayer has been estimated in Section 11.2. 

In contrast, the transient behavior measured in the system Ag(lll)/Pb, CIO4 , Na-acetate, Na2H-citrate (Fig. 3.49) can only be interpreted by 2D nucleation and growth. It was suggested that Me UPD on S, modified by a previously formed anion monolayer, can be controlled by pitting (hole) nucleation and growth [3.94]. 

In a first attempt to interpret the reductive adsorption transients of BP-based self-assembled monolayer s, we analyzed the experimental data displayed in Fig. 2IB with the diagnostic Avrami equation (Eq. 2), which is based on the Bewick-Fleischmann-Thirsk model of (hole) nucleation and growth [165,166]... 

We anticipate that the entanglement density in the dry spin-coated films is lower than in an equilibrated bulk system. Such a departure fi om equilibrium most likely generates residual stresses. As one consequence, we tentatively attribute the observed hole nucleation, which initiated the dewetting process of holes, to the presence of such residual stresses within the film [165]. In this way, rupture can be related to the spin-coating process used to prepare thin polymer films. 

L. holes nucleated immediately upon heating to 125 C in films cast... 

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