Films gaseous

A single substance may, under appropriate conditions of temperature and surface pressure, be obtained as a condensed film, either a liquid- or a vapour-expanded film, but not both, and a gaseous film. The class of vapour-expanded film is rather ill defined, and shades into the gaseous films but the properties of these films are often so different from those of the gaseous films, and so close to the liquid-expanded films, that a separate name seems desirable. The expanded films form a state without any close parallel in three-dimensional matter. So far as is known, they are only found with long-chain aliphatic substances. 

These films will be described in order of decreasing simplicity of structure. 

If the unit of area is the sq. A., k becomes 1 372. The proof of this relation follows exactly, in two dimensions, the lines of the proof of the ordinary gas laws in three, and need not be repeated here.1 

At room temperature the product kT is about 400, in terms of sq. A. per molecule. A perfect gaseous film would thus exert a pressure of 1 dyne at 400 sq. A. It will be seen later that the molecules in gaseous films nearly always lie flat, and since the area occupied by an aliphatic substance containing some sixteen carbon atoms in the chain will be of the order 120 sq. A., the instruments used for investigating the gaseous state of the films must be capable of measuring pressures down to a very small fraction of a dyne, in order that the films may be so dilute that the mole- 

Equation (1) assumes that the molecules move about singly in the surface. If the product of surface pressure and area is approximately constant, and about 400 at room temperature, when the area is sufficiently 

A film at low densities and pressures obeys the equations of state described in Section III-7. The available area per molecule is laige compared to the cross-sectional area. The film pressure can be described as the difference in osmotic pressure acting over a depth, r, between the interface containing the film and the pure solvent interface [188-190]. 

In this model, a gaseous film is considered to be a dilute surface solution of surfactant in water and Eq. in-108 can be put in the form 

The alternative approach is to treat the film as a nonideal two-dimensional gas. One may use an appropriate equation of state, such as Eq. Ill-104. Alternatively, the formalism has been developed for calculating film activity coefficients as a function of film pressure [192]. 

An ideal (bulk) gas will have an equation of state given by the ideal gas law 

Similarly, an ideal gaseous monolayer should follow the corresponding law 

If molecular interactions are taken into consideration. Equation (8.15) can be modified to 

It is tempting to equate Aq directly with the cross-sectional area (in the plane of the surface) of the vertically adsorbed molecule. However, lateral interactions tend to reduce (or in cases of repulsion increase) its value, so that for many films, Ao may be significantly less than or greater than the 

Of course, even more complicated equations of state such as a combination of Equations (8.16) and (8.17) can be devised, as, for example 

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At lower temperatures a gaseous film may compress indefinitely to a liquid-condensed phase without a discemable discontinuity in the v-a plot. 

A n +A2it2, where A and A2 are the molar areas. A particular gaseous film has... 

A third definition of surface mobility is essentially a rheological one it represents the extension to films of the criteria we use for bulk phases and, of course, it is the basis for distinguishing states of films on liquid substrates. Thus as discussed in Chapter IV, solid films should be ordered and should show elastic and yield point behavior liquid films should be coherent and show viscous flow gaseous films should be in rapid equilibrium with all parts of the surface. 

These assumptions have been expanded upon (Shah and Capps, 1968 Lucassen-Reynders, 1973 Rakshit and Zografi, 1980), especially in regard to the application of the ideal mixing relationship in gaseous films (Pagano and Gershfeld, 1972). It has been pointed out that water may contribute to the energetics of film compression if the molecular structures of the surfactants are sufficiently different (Lucassen-Reynders, 1973). It must be noted that this treatment assumes that the compression process is reversible and the monolayer is truly stable thermodynamically. It must therefore be applied with considerable reservation in view of the hysteresis that is often found for II j A isotherms. 

Gas electrodes may also be regarded as electronic-and-ionic electrodes covered with a gaseous film. The electron transfer occurs between the electrode and the gaseous film (2 + 2 eoii H2( >) and the ion transfer occurs between the... 

From these descriptions, it is seen that the films may, under given experimental conditions, show three first-order transition states, such as (i) transition from the gaseous film to the liquid-expanded (Lex), (ii) transition from the liquid-expanded (Lex) to the liquid-condensed (Lco), and (iii) from Lex or Lco to the solid state if the temperature is below the transition temperature. The temperature above which no expanded state is observed has been found to be related to the melting point of the lipid monolayer. 

The very low water adsorption by Graphon precludes reliable calculations of thermodynamic quantities from isotherms at two temperatures. By combining one adsorption isotherm with measurements of the heats of immersion, however, it is possible to calculate both the isosteric heat and entropy change on adsorption with Equations (9) and (10). If the surface is assumed to be unperturbed by the adsorption, the absolute entropy of the water in the adsorbed state can be calculated. The isosteric heat values are much less than the heat of liquefaction with a minimum of 6 kcal./mole near the B.E.T. the entropy values are much greater than for liquid water. The formation of a two-dimensional gaseous film could account for the high entropy and low heat values, but the total evidence 22) indicates that water molecules adsorb on isolated sites (1 in 1,500), so that patch-wise adsorption takes place. 

For a formal kinetic description of vapour phase esterifications on inorganic catalysts (Table 21), Langmuir—Hinshelwood-type rate equations were applied in the majority of cases [405—408,410—412,414,415]. In some work, purely empirical equations [413] or second-order power law-type equations [401,409] were used. In the latter cases, the authors found that transport phenomena were important either pore diffusion [401] or diffusion of reactants through the gaseous film, as well as through the condensed liquid on the surface [409], were rate-controlling. 

A film in which molecules move about independently on the surface and their lateral adhesion for each other is very small. At low surface pressures (Jr i and large area I A), a gaseous film obeys the relation. 7.1 = kT. At higher pressures an equation of the form t, t A - A ) = t k T holds, where, v is a constant. 

This film occupies a much larger area ihan a condensed film, but is still a coherent film. It can form a separate phase from a gaseous film with which it is in equilibrium, and obeys the relation... 

Liquid (L). When compressing a gaseous film, there can be a first-order phase transition to the liquid state. The liquid state is characterized by a significant lateral interaction... 

The principal requirements for an ideal gaseous film are that the constituent molecules must be of negligible size with no lateral adhesion between them. Such a film would obey an ideal two-dimensional gas equation, ttA kT, i.e. the it-A curve would be a rectangular hyperbola. This ideal state of affairs is, of course, unrealisable but is approximated to by a number of insoluble films, especially at high areas and low surface pressures. Monolayers of soluble material are normally gaseous. If a surfactant solution is sufficiently dilute to allow solute-solute interactions at the surface to be neglected, the lowering of surface tension will be approximately linear with concentration - i.e. 

Attraction of Two Spheres—An expression for the attraction between two or more particles, based on collision theory rather than attraction due to the motion of spheres, may be developed by the methods of dimensional analysis. Let the force of attraction between two particles of diameters d and d2 be F and assume that when the particles are close enough so that the gaseous film enveloping each particle coalesces over a region about the point of contact, then the whole attraction is due to a free surface energy a. If the average surface of contact of the particles is denoted by Sc then... 

Coherent films are sometimes solid, the molecules not being free to move about in the film, so that the film cannot flow on the surface unless sufficient force is applied to break it films are more frequently liquid and can flow in the surface, even under considerable compression, fairly freely Whether films are solid or liquid is often decided by small details of distribution of the adhesive forces between adjacent molecules it is the total amount of the lateral adhesion which determines whether the molecules form coherent, or gaseous, films. 

Indications of further complexities in the coherent type of surface films were found by Langmuir, and have been further investigated by Labrouste,1 Adam, and others. It is now well established that there frequently exists a coherent, expanded state in insoluble surface films of fatty substances, intermediate in area between the very closely packed condensed films, and the gaseous films in which the molecules move about independently on the surface. This most interesting type of film will be discussed in 18 and 19. 

Moss and Rideal3 have used, for the investigation of gaseous films at very low pressures, an ingenious instrument shown in Fig. 10. The trough is made... 

The interpretation of surface-pressure and surface-potential measurements.8 Surface pressure F is best plotted against area A, as this shows up the resemblance between the films and three-dimensional PV isothermals. For gaseous films, however, curves with FA as ordinates and F as abscissae are very useful. 

Gaseous films are homogeneous in surface potential if the air electrode is moved over the surface there should be no large fluctuations of potential. 

The main types of film. Langmuir established the existence of one type of coherent film, with insoluble substances, and of the gaseous films, with the adsorbed layers of soluble substances at an air-liquid surface. It is now known that a number of different types of insoluble film can exist with long-chain aliphatic substances these are best classified according to the lateral adhesion between the molecules. These are... 

Dividing (2) by F, it is clear that the area would tend to 85 sq. A. at high surface pressures, if the physical conditions of this part of the curve were maintained (this is not actually the case, as the molecules tilt, and occupy much less space in gaseous films at high compressions). The value of the first constant on the right of (2) is an indication of the area of the molecules lying flat, but it usually gives results which are rather too small. 

The following gaseous films have been found to approach closely to the limiting value of FA = = 400 at great dilution the acetates of long-chain amines l nonoyl trimethoxybenzene,2... 

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