Gibbs monolayers

If the surface tension of a liquid is lowered by the addition of a solute, then, by the Gibbs equation, the solute must be adsorbed at the interface. This adsorption may amount to enough to correspond to a monomolecular layer of solute on the surface. For example, the limiting value of in Fig. Ill-12 gives an area per molecule of 52.0 A, which is about that expected for a close-packed 

Such a monolayer may be considered to exert a film pressure ir, such that 

It must be kept in mind that both pictures are modelistic and invoke extrather-modynamic concepts. Except mathematically, there is no such thing as a two-dimensional gas, and the solution whose osmotic pressure is calculated is not uniform in composition, and its average concentration depends on the depth assumed for the surface layer. 

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The deviation of Gibbs monolayers from the ideal two-dimensional gas law may be treated by plotting xA// 7 versus x, as shown in Fig. III-15c. Here, for a series of straight-chain alcohols, one finds deviations from ideality increasing with increasing film pressure at low x values, however, the limiting value of unity for irAfRT is approached. 

The succeeding material is broadly organized according to the types of experimental quantities measured because much of the literature is so grouped. In the next chapter spread monolayers are discussed, and in later chapters the topics of adsorption from solution and of gas adsorption are considered. Irrespective of the experimental compartmentation, the conclusions as to the nature of mobile adsorbed films, that is, their structure and equations of state, will tend to be of a general validity. Thus, only a limited discussion of Gibbs monolayers has been given here, and none of such related aspects as the contact potentials of solutions or of adsorption at liquid-liquid interfaces, as it is more efficient to treat these topics later. 

The preceding evidence for orientation at the interface plus the considerations given in Section III-3 make it clear that the polar end is directed toward the water and the hydrocarbon tails toward the air. On the other hand, the evidence from the study of the Gibbs monolayers (Section III-7) was that the smaller molecules tended to lie flat on the surface. It will be seen that the orientation... 

Antonow s rule can be understood in terms of a simple physical picture. There should be an adsorbed film or Gibbs monolayer of substance B (the one of lower surface tension) on the surface of liquid A. If we regard this film as having the properties of bulk liquid B, then y A(B) is effectively the interfacial tension of a duplex surface and would be equal to [Y a(b> + Yb[Pg.37]

The critical micelle concentration (cmc) in block copolymer solutions can be determined by measurement of the surface tension (y) as a function of concentration. The method detects completion of the Gibbs monolayer at the air/water interface, and is a secondary indicator of the onset of micellization. The cmc for solutions of monodisperse polymers is indicated by a fairly sharp decrease in y versus log(c). 

If there is still a significant proportion of the amphiphile dissolved in the liquid we talk about Gibbs monolayers. Solubility in water is increased by using molecules with short alkyl chain or a high polarity of the headgroup. In this case T is determined from the reduction of the surface tension according to the Gibbs adsorption isotherm (Eq. 3.52). 

At low surface excess, Gibbs monolayers can often be described as two-dimensional gases. This description is based on the observation that, at low concentration, the surface tension decreases linearly with the concentration of the added amphiphile c ... 

Highly Fluorinated Langmuir, Langmuir-Blodgett and Gibbs Monolayers... 

These three Illustrations (to whieh more could be added) have in common that they deal with very thin (down to moleeular scale) layers of molecules at fluid-liquid interfaces. In this way they serve to Introduce the subject matter of this, and the following chapter, namely Langmuir- and Gibbs monolayers, respectively. 

Besides the obvious difference in prepciration, there is a difference in principle between these two categories. Langmuir monolayers are at thermal equilibrium with the liquid subphase, but not with respect to the exchcuige of material. So in this case the liquid should, strictly speaking, not be called solvent. On the other hand, Gibbs monolayers are both in thermal and material exchange equilibrium. 

By contrast, Gibbs monolayers are continually at equilibrium with the subphase which, in this case, may be called a solution. Surface tension and concentration are related through Gibbs law, so that the surface pressure can be related to the solution concentration. By analogy with [II. 1.1.6 and 7J we have for a single adsorbed component in an ideal solution... 

The distinction between Langmuir and Gibbs monolayers resembles that between an ideally polarizable and an ideally relaxed electrified interface (sec. 1.5.5b). An interface is polarizable when no charges (ions or electrons) can cross it it is reversible when such transport takes place until equilibrium between electrode and solution has been attained. In the former case the potential across the interface has to be applied from an external source so that it is an independent variable. For a relaxed interface this is not the case the potential is spontaneously established by preferential adsorption or desorption of ionic species. 

With regard to the surface pressure, for ideeilized Langmuir monolayers 7t is an independent, externally applied veirlable, whereas for idealized Gibbs monolayers n is determined by adsorption of molecules. The obvious question is whether surface equations of state are identical between Langmuir and Gibbs monolayers. The answer is, in principle, yes. Relations between n, A and r are completely determined by the numbers of, and Interactions between, the molecules in the monolayer, irrespective of whether or not equilibrium with an adjacent phase has been established. The statistical derivation underlines this. The two-dimensional pressure can be obtained canonically from... 

For the preparation of Langmuir monolayers, a detour is required, except when such layers can be made from Gibbs monolayers, by changing the composition of the substrate after adsorption hcis taken place, for example by changing the pH. The need for a detour is typical and requires some form of spreading. By this technique the amount of molecules at the interface is known and the interfacial tension or pressure are basicalty measurable. Hence, Jt[A] curves are obtainable. 

Let us illustrate the last point. For Gibbs monolayers the obvious thermody-... 

Through the vehicle of partition functions expressions can be derived for macroscopic quantities from molecular parameters. Examples of such qucintities cire the surface pressure, and, for Gibbs monolayers, the adsorbed amount. Fluctuations in extensive quantities, like the number density or the interfacial excess energy, may also be obtained (sec. 1.3.7). 

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