Thermodynamics spread films

The thermodynamics of spread films at the air-water interface can be expressed by the tt-A isotherm, obtained in a Langmuir- or Wilhelmy-type film balance (Figure 14.4a). From the tt-A isotherm, different structures can be deduced for emulsifier monolayers as a function of emulsifier, temperature, and surface density or surface pressure. A phase diagram... 

Evidently if S > 0 then k>+1. Were S>0 so that > o-, + a, this would imply that the solid-gas interface would immediately coat itself with a layer of the liquid phase and replace the supposedly higher free energy per unit area of direct solid-gas contact, cr g, by the supposedly lower sum of the free energies per unit area of solid-liquid and liquid-gas contacts, cr i + cr, thereby lowering the free energy of the system. However, in thermodynamic equilibrium this cannot be realized (Gibbs 1906, Rowlinson Widom 1982). Therefore, for a spreading film in thermodynamic equilibrium k = +1 S = 0), and locally there is a state of mechanical equilibrium at the contact line between the three phases. 

Since the surface pressure of a spread film is the two-dimensional equivalent of pressure, attempts have been made to set down an equation of state for the spread film. All derivations make use of the basic thermodynamic relationship between the surface pressure and the surface area (A) ... 

The scaling law exponents for the relation between surface pressure and surface concentration, i.e., n = where y = 2v/(2v - 1) and v is the excluded volume exponent, the value of which reflects the nature of the thermodynamic interaction between polymer and subphase. The values of v obtained for the copolymers, from the linear region of the isotherm, 0.62, 0.64 and 0.68 for /i75, 25 and n50 respectively, are all very close to the value of 0.75 for spread films of PEO on water [18], indicative of thermodynamically favourable conditions. As the PEO content of the copolymer increases, v increases suggesting that the graft copolymer-water interactions become more favourable and perhaps the grafts become less coiled as the percentage of PEO in the copolymer increases. 

However, the spreading of a surfactant monolayer from a volatile solvent leaves behind a film that may not be in thermodynamic equilibrium with its bulk crystalline form or the aqueous subphase. It has been proposed that this is a result of the relatively high energy barriers to film collapse or dissolution into the subphase as compared with lowered interfacial free energy when a stable, insoluble surfactant monolayer is formed (Gershfeld, 1976). The rate at which a whole system approaches true equilibrium in such a system is often so slow that the monolayer film can be treated for most purposes as though it were at equilibrium with the subphase. 

The question may then be raised as to whether insoluble monolayers may really be treated in terms of equilibrium thermodynamics. In general, this problem has been approached by considering (i) the equilibrium spreading pressure of the monolayer in the presence of the bulk crystalline surfactant, and (ii) the stability of the monolayer film as spread from solution. These quantities are obtained experimentally and are necessary in any consideration of film thermodynamic properties. In both cases, time is clearly a practical variable. 

The surface shear viscosity of a monolayer is a valuable tool in that it reflects the intermolecular associations within the film at a given thermodynamic state as defined by the surface pressure and average molecular area. These data may be Used in conjunction with II/A isotherms and thermodynamic analyses of equilibrium spreading to determine the phase of a monolayer at a given surface pressure. This has been demonstrated in the shear viscosities of long-chain fatty acids, esters, amides, and amines (Jarvis, 1965). In addition,... 

Table 8 gives the results of this thermodynamic analysis for the spreading of film types I and II from the bulk, and the direct transition from film types I and II. It is obvious that the Helmholtz free energies, entropies, and enthalpies are differentiated stereochemically. 

Lipids with a suitable hydrophilic-lipophilic balance (HLB) are known to spread on the surface of water to form monolayer films. It is obvious that if the lipid-like molecule is highly soluble in water, it will disappear into the bulk phase (as observed for SDS). Thus, the criteria for a monolayer formation are that it exhibits very low solubility in water. The alkyl part of the lipid points away from the water surface. The polar group is attracted to the water molecules and is inside this phase at the surface. This means that the solid crystal, when placed on the surface of water, is in equilibrium with the him spread on the surface. A detailed analysis of this equilibrium has been given in the literature (Gaines, 1966 Adamson and Gast, 1997 Birdi, 2009). The thermodynamics allows one to obtain extensive physical data on this system. It is thus apparent that, by studying only one monolayer of the substance, the effect of temperature can be very evident. 

The subscript G specifies elasticity determined from isothermal equilibrium measurements, such as for the spreading pressure-area method, which is a thermodynamic property and is termed the Gibbs surface elasticity, EG. EG occurs in very thin films where the number of molecules is so low that the surfactant cannot restore the equilibrium surface concentration after deformation. 

In printing, a film of ink is formed by wetting the surface with the compression force of the rollers. This force spreads the ink over the surface and into any capillaries that may be present. Spreading and penetration are controlled thermodynamically and kinetically. Measurement of the contact angle can be used to determine the thermodynamics of wetting. This angle can be used also to determine the contribution that polarity and dispersive forces of the liquid make to the wetting of the surface. 

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. 

The figure shows that many of the surface films, spread by the aid of solvents, are not thermodynamically stable, though they are often sufficiently stable in practice to be examined without serious collapse during some hours. The establishment of equilibrium between the film and the crystal is very slow from the film side perhaps this is due to the absence of crystal nuclei of sufficiently large perimeter to allow collapse or condensation on the crystal to occur at an appreciable rate or perhaps the aggregates formed when a film collapses have a considerably higher potential energy than properly formed crystals. 

Adsorption and oil-water potentials. Dean, Gatty, and Rideal2 discuss the thermodynamics and the mechanism of the establishment of interfacial potential differences by the adsorption of ions, or by the adsorption or spreading of a film containing dipoles. They show that, provided that one or more of the charged components can pass the phase boundary and come into equilibrium on both sides, the adsorption of the interfacial film will not by itself change the phase boundary potential. For the electrochemical potentials of those charged components which can pass the boundary are equal, at equilibrium, in the two phases, i.e. 

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. 

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