Saturated monolayers

It is thus tempting to define the first saturated layer as being one monolayer, and this often done, causing some confiision. One therefore also often uses tenns like saturated monolayer to indicate such a single adsorbate layer that has reached its maximal two-dimensional density. Sometimes, however, the word saturated is omitted from this definition, resulting m a different notion of monolayer and coverage. One way to reduce possible confiision is to use, for contrast with the saturated monolayer, the tenn fractional monolayer for the tenn that refers to the substrate unit cell rather than the adsorbate size as the criterion for the monolayer density. 

When a component of interest is considerably surface active, its adsorbed amount is high even when its bulk concentration is low. The second terms on the right-hand side of Eqs. (4)-(6) are then small and the relative surface excesses are simply taken as the surface excesses, which, in turn, may be seen as the surface concentration. For example, dilaur-oylphosphatidylcholine forms a saturated monolayer in the liquid-expanded state at the nitrobenzene-water interface when its concentration in nitrobenzene is 10 moldm [30]. Then the experimentally obtained value, 1.76 x 10 °molcm, can be considered to be the surface concentration. 

FIG. 10 Vibrational sum frequency spectrum of saturated monolayers of dilauroyl- (DLPQ, dimyristoyl- (DMPC), dipalmitoyl- (DPPC), and distearoyl-phosphatidylcholine (DSPC) at the D2O-CCI4 interface at ambient temperature in the region of the methylene and methyl symmetrical stretches. (From Ref 139, copyright American Chemical Society.)... 

Sorption and desorption are usually modeled as one fully reversible process, although hystersis is sometimes observed. Four types of equations are commonly used to describe sorption/desorption processes Langmuir, Freundlich, overall and ion or cation exchange. The Langmuir isotherm model was developed for single layer adsorption and is based on the assumption that maximum adsorption corresponds to a saturated monolayer of solute molecules on the adsorbent surface, that the energy of adsorption is constant, and that there is no transmigration of adsorbate on the surface phase. 

Figure 4. AFM micrograph of a saturated monolayer of antibodies against p2-microglobulin measured in phosphate buffered saline (PBS) solution using tapping mode. The dark window shows the underlying polystyrene surface obtained by wipping off the antibodies.

Emmert and Pigford (E4), Ternovskaya and Belopol skil (T9-T12), and Tailby and Portalski (T3) have carried out detailed investigations of the effects of surfactants, using several different surfactants, each at a number of concentrations. In nearly all cases it was found that, as the concentration of surfactant was increased, the waves were rapidly damped out as far as some optimum concentration, beyond which there was either little further damping of the waves, or the waviness increased again. Ternovskaya and Belopolskii calculated that the optimum concentrations for wave damping corresponded to quantities of surfactant just sufficient to form a saturated monolayer at the interface (T10). 

The Langmuir and Brumnauer, Emmett, and Teller (BET) models also have been used to describe nonlinear sorption behavior for environmental solids, particularly for mineral dominated sorption (Ruthven, 1984 Weber et al., 1992). The Langmuir model assumes that maximum adsorption corresponds to a saturated monolayer of solute molecule on the absorbent surface, that there is no migration of the solute on the surface phase, and that the energy of adsorption is constant. The BET model is an extension of the Langmuir model that postulates multilayer sorption. It assumes that the first layer is attracted most strongly to the surface, while the second and subsequent layers are more weakly held. 

For molecular systems at surfaces, one must take into account that STM may interfere with natural assembly. That is, the tip-molecule interaction may induce disorder during scanning operation. In other words, defined molecular 2D crystals can be distorted by this method, not allowing true geometric analysis. Again, low temperatures in UHV or saturated monolayer systems, in general, help to circumvent this problem. 

Fig. 15 a M-[7]H forms at 95% of the saturated monolayer CW-rotated pinwheels (top, left) while CCW-rotated pinwheels are observed via STM for P-[7H] (top, right) [44]. At full ML opposite tilt angles of cloverleaf clusters with respect to the adlattice are observed (bottom). Images 10 nm x 10 nm. Reprinted with permission from Wiley, b Model for the M-[7]H cloverleaf structure obtained from MMC. Minimal repulsion is achieved for certain relative azimuthal orientations... 

This is the simplest isotherm equation, proposed in 1916 by I. Langmuir. The Langmuir equation is based on the fact that every active site in the surface acts the same way, and the maximum adsorption occurs at a saturated monolayer of the solutes on the surface. When an adsorbent is added to a solution containing a substance to be removed, the substance adsorbs on the surface of the adsorbent, and equilibrium is established. A fraction a of the adsorbing surface is occupied with adsorbed substance and a fraction (1 - a) of the adsorbing surface will remain unoccupied. The rate of adsorption is proportional to the availability of the adsorbing surface and the concentration [A] of the substance in solution ... 

At small coverages, the change A in the work function is proportional to the surface concentration. At higher coverages, the variation of with Ns becomes less rapid in some cases it may even pass through a maximum before reaching the value for a saturated monolayer. This apparent decrease of the dipole moment is caused by the Coulomb interaction between the adsorbed atoms, which makes large dipole moments unfavorable.62... 

Figure 8 Evolutions of intramolecular vibrations (a) and extramo-lecular phonons, (b) of K-doped Ceo on Ag(l 11) at different dopant concentrations. The lowest curves correspond to the undoped monolayers and the topmost ones to the saturated monolayers. (Reprinted from Silien, Thiry and Caudano, Elsevier 2004)...

In figure 1.12 we illustrate the different ways of plotting for the special case of a model Langmuir Isotherm. The "measuring points" are chosen such as to obey the Langmuir equation [1.1.31, with 0= VA (nion), where V(mon) is the volume adsorbed in a saturated monolayer. It is assumed that the specific surface area (via V(mon)) is not known, hence the data are given as V (in ml at standard p and T)as a function of pressure (in Pa or N m" ). The "original" plot is... 

According to the theories of Smith and Ewart and of Garden, the effect of emulsifiers on the number of polymer latex particles fomied N (and hence on tbe rate of polymerization during Interval II) is determined by the area % which the emulsifier molecule occupies in a saturated monolayer at tbe polymer-water inteiface,... 

A third example illustrating the same type of system involves people in some hot areas, such as Australia, who have tried to conserve precious water supplies in ponds or leikes by covering the surface with a (saturated) monolayer of an insoluble substance, like a fatty alcohol. They hoped in this way to reduce evaporation. For long-term use this method has only been moderately successful, but the fact is established that such monolayers do inhibit water transport. We will return briefly to this in sec. 3.9. 

Einalogy with adsorption on solids, will be used for the moleculcU" area in a saturated monolayer. The subseript 1 can be omitted if no eonfusion arises with a as the radius of a molecule. For condensed monolayers molecular cross-sections cu e usually obtained from breaks in x(A) curves . depending on the number of transitions observed, a variety of corresponding cross-sections can be distinguished. 

Region C is often linear. Constancy of dy/dlnc means constancy of r, at least if the activity constant remains the same, and it is physically realistic to interpret this range as representing the saturated monolayer. Here, I K I is low again (in this situation surfactant is abundant the surface is instantaneously replenished). From the plateau value F ( ) of F as the molecular cross-section per surfactant molecule cam be computed, see [4.6.5],... 

The simulations were designed to mimic as closely as possible the experiments carried by Gasteiger et al. [88]. These authors prepared well-characterized Pt-Ru alloys in UHV before their transfer to the electrochemical cell. The surface consisted of a random mixture of Pt and Ru sites, onto which a saturated monolayer of CO was adsorbed. The monolayer was oxidized in a CO-free electrolyte by stripping voltammetry, and the catalytic activity of the Pt-Ru alloy was studied as a function... 

Figure 19. CO stripping voltammograms of Ru/Au(lll) (solid line) and the baselines obtained on CO free surfaces (dotted line) obtained in 0.1 M FI2 SO4 for (a) a multilayer deposit (b) a saturated monolayer (0.85 ML coverage) (c) a submonolayer deposit (0.15 ML coverage). Reprinted from Ref.12 with permission from Elsevier.

In spite of these quantitative differences, qualitatively the behaviour of the static elasticity curves are similar in Figures 3 and 4 the elasticity achieves a maximum at small concentrations of the order of a saturated monolayer concentration and then decreases very quickly tending to small values for saturated films. 

It is shown that the dependencies of the damping coefficient on surfactant concentration are quite different for the ordinary surfactants and for the polymer films. For the ordinary surfactants the damping coefficient achieves a maximum at concentrations of the order of the concentration of saturated monolayers at higher concentrations the damping coefficient is high and practically constant. For the polymer films the damping coefficient has a low-concentration peak similar to the case of ordinary surfactants and a "plateau"-like maximum at high concentrations. 

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