Langmuir of

Figure 12.8 PAES spectra for a Si(100) surface covered with 0.3 ML of Au (a) before and (b) after exposure to 400 Langmuir of 02- The oxygen exposure caused a decreas in the Si peak but not the Au peak. This indicates that the positrons are being pushed away from the Si due to selective adsorption of oxygen at exposed Si sites. A schematic drawing indicating this mechanism is shown in Figure 12.9 below.

The stability of this surface against hydroxylation was tested by extensively dosing the surface with up to 10 Langmuir of H2O at 3-10 mbar partial pressure at room temperature. Similarly to the single crystal case, no stmctural effect could be detected. This stands in contradiction with the NiO(l 11) films of poor structural quality made by oxidation of Ni(lll) [132, 140], which were found unstable against hydroxylation. We thus suggest that the reactivity of NiO(l 11) against water takes mainly place at defects (like for MgO), which are almost absent on our surfaces and thin films. 

Equation 6.49 is strictly valid only for the disperse part of the peak (Chapter 2.2.3). Depending on the shape of the isotherm, this is the rear part ( Langmuir ) or the front part ( anti-Langmuir ) of the peak (Fig 2.6). The sharp fronts ( Langmuir ) or tails ( anti-Langmuir ) of the peaks are called concentration discontinuities or shocks. To describe the movement of these shocks, the differential in Eq. 6.49 has to be replaced by discrete differences A, the secant of the isotherm, which describe the amplitudes of the concentration shocks in the mobile and stationary phases ... 

Reaction Mechanism. To understand the size-dependent reactivity of palladium clusters on MgO surfaces in more detail, combined Fourier transform infrared (FTIR) and thermal desorption (TDS) studies were performed. The cluster model catalysts were first exposed to 1 Langmuir of CO at 90 K and subsequently to the same amount of NO. Upon linearly heating the model catalysts, the product molecules C02 and were detected by mass spectrometry as a function of the cluster size for Pd with n < 30. While for Pd4, the formation of C02 is negligible, Pdg and Pdso form C02 at 305 K or 145K and 300K, respectively (Fig. 1.97). 

We now consider the influence of the support material on the reactivity of the three atoms. The experiments show that the coinage metal atom silver remains inert when deposited on the MgO surface and exposing this model system to 1 Langmuir of acetylene at 90 K and detecting benzene as function of temperature (Fig. 1.100). Thus, the electronic structure of Ag is not substantially changed even when trapped at an F center. Calculations... 

Fig. 10. Work function and work-function change vs. exposure in Langmuir of H2 for hydrogen adsorption on clean W(110) at 90 K. (a) shows the region from 0 to 40 L and (b) the entire curve. From [97N].

Langmuir adsorption isotherm A theoretical equation, derived from the kinetic theory of gases, which relates the amount of gas adsorbed at a plane solid surface to the pressure of gas in equilibrium with the surface. In the derivation it is assumed that the adsorption is restricted to a monolayer at the surface, which is considered to be energetically uniform. It is also assumed that there is no interaction between the adsorbed species. The equation shows that at a gas pressure, p, the fraction, 0, of the surface covered by the adsorbate is given by ... 

Although still used the Langmuir equation is only of limited value since in practice surfaces are energetic inhomogeneous and interactions between adsorbed species often occur. 

Fig. ni-14. Cross section of the PLAWM (Pockels-Langmuir-Adam-Wilson-McBain) trough. 

Langmuir [ 146] gave an instructive interpretation to this rule. The work W to transfer one mole of solute from bulk solution to surface solution should be... 

Using Langmuir s principle of independent surface action, make qualitative calculations and decide whether the polar or the nonpolar end of ethanol should be oriented toward the mercury phase at the ethanol-mercury interface. 

There are three forms of the Langmuir-Szyszkowski equation, Eq. III-57, Eq. Ill-107, and a third form that expresses ir as a function of F. (n) Derive Eq. III-57 from Eq. Ill-107 and (b) derive the third form. 

A sketch of Langmuir s film balance is shown in Ref. 7 and a modem version of a film balance, in Fig. IV-5. 

Langmuir also gave needed emphasis to the importance of employing pure substances rather than the various natural oils previously used. He thus found that the limiting area (at the Pockels point) was the same for palmitic, stearic, and cerotic acids, namely, 21 per molecule. (For convenience to the reader, the common names associated with the various hydrocarbon derivatives most frequently mentioned in this chapter are given in Table IV-1.)... 

To resume the brief historical sketch, the subject of monolayers developed rapidly during the interwar years, with the names of Langmuir, Adam, Harkins, and Rideal perhaps the most prominent the subject became one of precise and... 

A belief that solid interfaces are easier to understand than liquid ones shifted emphasis to the former but the subjects are not really separable, and the advances in the one are giving impetus to the other. There is increasing interest in films of biological and of liquid crystalline materials because of the importance of thin films in microcircuitry (computer chips ), there has been in recent years a surge of activity in the study of deposited mono- and multilayers. These Langmuir-Blodgett films are discussed in Section XV-7. 

The equilibrium shape of a liquid lens floating on a liquid surface was considered by Langmuir [59], Miller [60], and Donahue and Bartell [61]. More general cases were treated by Princen and Mason [62] and the thermodynamics of a liquid lens has been treated by Rowlinson [63]. The profile of an oil lens floating on water is shown in Fig. IV-4. The three interfacial tensions may be represented by arrows forming a Newman triangle ... 

The film pressure is defined as the difference between the surface tension of the pure fluid and that of the film-covered surface. While any method of surface tension measurement can be used, most of the methods of capillarity are, for one reason or another, ill-suited for work with film-covered surfaces with the principal exceptions of the Wilhelmy slide method (Section II-6) and the pendant drop experiment (Section II-7). Both approaches work very well with fluid films and are capable of measuring low values of pressure with similar precision of 0.01 dyn/cm. In addition, the film balance, considerably updated since Langmuir s design (see Section III-7) is a popular approach to measurement of V. 

Film pressure is often measured directly by means of a film balance. The principle of the method involves the direct measurement of the horizontal force on a float separating the film from clean solvent surface. The film balance has been considerably refined since the crude model used by Langmuir and in many... 

In the case of Langmuir monolayers, film thickness and index of refraction have not been given much attention. While several groups have measured A versus a, [143-145], calculations by Knoll and co-workers [146] call into question the ability of ellipsometry to unambiguously determine thickness and refractive index of a Langmuir monolayer. A small error in the chosen index of refraction produces a large error in thickness. A new microscopic imaging technique described in section IV-3E uses ellipsometric contrast but does not require absolute determination of thickness and refractive index. Ellipsometry is routinely used to successfully characterize thin films on solid supports as described in Sections X-7, XI-2, and XV-7. 

Interferometry is based on the fact that light reflected from the front and back interfaces of a film travels different distances, producing interference effects. The method has been applied to Langmuir-Blodgett films (Section XV-7) and to soap films (Section XrV-8) [147-149]. 

The external reflection of infrared radiation can be used to characterize the thickness and orientation of adsorbates on metal surfaces. Buontempo and Rice [153-155] have recently extended this technique to molecules at dielectric surfaces, including Langmuir monolayers at the air-water interface. Analysis of the dichroic ratio, the ratio of reflectivity parallel to the plane of incidence (p-polarization) to that perpendicular to it (.r-polarization) allows evaluation of the molecular orientation in terms of a tilt angle and rotation around the backbone [153]. An example of the p-polarized reflection spectrum for stearyl alcohol is shown in Fig. IV-13. Unfortunately, quantitative analysis of the experimental measurements of the antisymmetric CH2 stretch for heneicosanol [153,155] stearly alcohol [154] and tetracosanoic [156] monolayers is made difflcult by the scatter in the IR peak heights. 

The ability to image lateral heterogeneity in Langmuir monolayers dates back to Zocher and Stiebel s 1930 study with divergent light illumination [166]. More recently the focus shifted toward the use of fluorescence microscopy of mono-layers containing a small amount of fluorescent dye [167]. Even in single-corn-... 

A newer and perhaps more useful application of ellipsometry to Langmuir films is their lateral characterization via ellipsometric microscopy [146], A simple modification of the nuU ellipsometer allows one to image features down to 10-/im resolution. Working with a fixed polarizer and analyzer, some domains are at extinction while others are not and appear bright. This approach requires no fluorescent label and can be applied to systems on reflective supports. 

Electron diffraction studies are usually limited to transferred films (see Chapter XV), One study on Langmuir films of fatty acids has used cryoelectron microscopy to fix the structures on vitrified water [179], Electron diffraction from these layers showed highly twinned structures in the form of faceted crystals. 

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