Rupture of Thin Films

Vrij and others used a linear theory with respect to deviations in the film thickness. Including nonlinear effects, Williams and Davis found that rupture times are typically 10 times shorter [832,833]. Simulations demonstrated that the morphology of structures formed by spinodal dewetting depends sensitively on the precise interfacial forces and the film thickness. But the characteristic length scale is correctly predicted by the theory [834]. For very thin films, also the fact that the viscosity of the film is not constant but changes with the thickness and the specific height position in the film needs to be taken into account [835]. 

An 8 nm thick polystyrene film is spin coated on an oxidized silicon wafer [820]. Immediately after spin coating, the film is in a nonequiUbrium state. However, since polystyrene is a solid material at room temperature, it is practically stable. When heating, the film becomes a viscous liquid and dewets the surface. What is the characteristic size of structures formed. Assume that attractive van der Waals forces dominate and the Hamaker constant is Ah = 2.2 X 10 J. The surface tension of the heated polystyrene is 31 mNm .  

Whether nudeation or spinodal dewetting dominates the rupture of a liquid film depends on the specific system. The A oc Hq dependence predicted by Eq. (7.34) has been observed in polymer [815, 816, 820] and metal ]821] films. For polymer films in many cases, nudeation is faster [818, 820]. For aqueous films on hydrophobic surfaces, small bubbles are generally accepted to initiate nudeation and nudeation dominates ]813, 814]. 

The same formalism was also appUed to describe the rupture of foam and emulsion films [791, 798, 831, 836]. 

Calculate the relative vapor pressure of liquid helium (Mw = 4.00gmol ) 1 m above the reservoir at 1.35 K. Which height corresponds to a relative vapor pressure of 0.5 Do the same for water vapor at 20°C (Mw = 18.0gmol ). 

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The speed of wetting has been measured by running a tape of material that is wetted either downward through the liquid-air interface, or upward through the interface. For a polyester tape and a glycerol-water mixture, a wetting speed of about 20 cm/sec and a dewetting speed of about 0.6 cm/sec has been reported [37]. Conversely, the time of rupture of thin films can be important (see Ref. 38). 

Various surface thermodynamic considerations relevant to supported metal catalysts are presented. They include the thermodynamics of (1) spreading of the active catalyst on the support, (2) crystallite vs. film stability, (3) thin planar patches, (4) the phase separation on the substrate, and (5) the rupture of thin films. These thermodynamic considerations explain a number of phenomena observed during experiments with model catalysts. 

When the lamella between two droplets thins and breaks, the droplets on either side coalesce into a single, larger droplet (41,72). Continuation of this backward" process eventually leads to the disappearance of the dispersion, if it is not balanced by the forward" mechanisms of snap-off and division. Lamellae are thermodynamically metastable, and there are many mechanisms by which static and moving thin films can rupture. These mechanisms also depend on the molecular packing in the film and, thus, on the surfactant structure and locations of the dispersed and dispersing phases in the phase diagram. The stability and rupture of thin films is described in greater detail in Chapter 7. 

The scope of the present paper is to emphasize the role of wetting and spreading in the aging by sintering, and in the redispersion of supported metal catalysts. In the next section, some experimental results regarding the behavior of iron supported on alumina are presented to demonstrate that surface phenomena do play a major role. This is followed by stability considerations which are employed to explain the coexistence of multilayer surface films with crystallites in an oxygen atmosphere and the rupture of thin films into crystallites in a hydrogen atmosphere. 

R. Dhiman, S. Oiandra Rupture of thin films formed during droplet impact, Proc. R. Soc. A, 466, 1229-1245 (2010). 

Several experiments indicate that the life time of a foam film is correlated with the surface elasticity [738, 786, 800]. One explanation is that high surface elasticities dampen fluctuations in the film [786, 791]. Fluctuations are one possible reason for film rupture. For the same reason, surface viscosity influences the stability of Aims [792, 800]. In particular for large surface-active molecules such as proteins, this has been analyzed for emulsion films due to the importance in food science [721, 793]. The rupture of thin films has been extensively studied for liquid films on solid surfaces. Therefore, we describe it in more detail in Section 7.6.3. 

III.B. The Role of Thermal Fluctuations on the Transition from Common Black Films to Newton Black Films. The method described in the previous section will be now applied to thin films with fluctuating interfaces, with the interaction energy calculated as in section II.G. For low values ofthe external pressure, the enthalpy has two metastable minima at Zk and 2c, and a stable one at 2 - 0 (the former two correspond to the Newton and to the common black films, respectively, and the latter implies the rupture of the film), separated by two maxima located at Z and 22 (see Figure 7a). At metastable equilibrium the distances between the surfaces are distributed between 21 and 22 for the Newton black film and between z2 and 2 —°° for the common black film. The stability of the metastable states depends on the chance for a small area S of the interface to reach the... 

This device was used in the study of the kinetics of common thin film thinning [16,106], in the determination of the critical thickness of rupture of macroscopic films having an area of about 1 cm2 as well as in the measurement of black film thickness [107]. In equilibrium films this technique does not give reliable results, since there are difficulties in the evaluation of the capillary pressure in the menisci. 

Study of processes leading to rupture of foam films can serve to establish the reasons for their stability. The nature of the unstable state of thin liquid films is a theoretical problem of major importance (it has been under discussion for the past half a century), since film instability causes the instability of some disperse systems. On the other hand, the rupture of unstable films can be used as a model in the study of various flotation processes. The unstable state of thin liquid films is a topic of contemporary interest and is often considered along with the processes of spreading of thin liquid films on a solid substrate (wetting films). Thermodynamic and kinetic mechanisms of instability should be clearly distinguished so that the reasons for instability of thin liquid films could be found. Instability of bilayer films requires a special treatment, presented in Section 3.4.4. 

Another approach to the rupture of thin liquid films, proposed by Tsekov and Radoev [84,85], is based on stochastic modeling of this critical transition. Autocorrelation functions for steady state [84] and for thinning [85] liquid films were obtained. A method for calculation of the lifetime At and hcr of films was introduced. It accounts for the effect of the spatial correlation of waves. The existence of non-correlated subdomains leads to decrease in At and increase in hcr as a result of the increase in the possibility for film rupture. Coupling of dynamics of surface waves and rate of drainage v leading to stabilisation of thinning films has also been accounted for [86,87]. 

The n(fc) isotherms of different types of foam films are shown in Fig. 7.8. The surfactant (NaDoS) and electrolyte (NaCl) concentrations were the same as those used in the experiments with foams. The equilibrium thickness of thin films and CBF decreased with the increase in pa = II. Films ruptured in a definite range of capillary pressure (marked with arrows on curves 1 and 2). The thickness of NBF did not change and they ruptured at a definite capillary pressure (marked with an arrow on curve 3). 

A film can only break up into droplets after a disturbance the film locally thins to less than t)q)ically 1000 nm (see Fig. 6.40). In this region the interaction force (van der Waals, electrical double layer, for example) between the liquid-solid and liquid-air surface of the film becomes important. Attraction forces can rupture the thin film and a dry patch is nucleated. Such a film is called a non-wetting film. When the interaction between the two film interfaces is repulsive the so-called disjoining pressure (see also p. 162) of the film, i.e. the pressure difference between the film and bulk liquid, is negative. In the other case of negative disjoining pressures, it may also be called conjoining pressure. 

Ruckenstein, E. and Jain, R. K., Spontaneous rupture of thin liquid films, Chem. Soc. London, Faraday Trans. II, Vol. 70, pp. 132-147, 1974. 

The stability of thin films against rupture (Section 13.4.1). 

The critical event in coalescence is the rupture of the film between close fluid particles. A hole can spontaneously form in a film, but in the presence of some surfactant this can only happen if the film is very thin (a few nm). Local thinning of a film may occur because of the development of capillary waves on the film surfaces. These waves are readily damped if the interfacial tension is large, the repulsion between the particles extends over a large distance, and the film is small. This then implies that protein is a very good stabilizer against film rupture, far more so than many small-molecule amphiphiles. 

After the theory of Vrij (1966) surface waves play an important role. The critical thickness for the rupture of thin liquid films derived from the behaviour of surface waves is much smaller than the equilibrium thickness. Fig. 3.17. shows the thinning of a film due to surface waves generated by disturbances with squeesing modes. 

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