Singleton frequency

An important difference between eqn(7) and eqn(4) is that uj no longer represents the frequency of an adsorbed singleton but rather the frequency of a hypothetical adsorbed molecule isolated from its self-image too. The singleton frequency is given by the limit of eqn(7) as S - 0 ... 

Figure 6. Dependence on distance d from image plane of the image dipole sum V for the ( /TX " / 3)-30o structure ( = 1/3) of CO on Cuflll). Also shown is the frequency shift, = 0 - = 1/3, which depends strongly on the displacement of the singleton frequency to lower values by the self-image.

In order to avoid the influence of lateral interactions on the vibrational frequency of adsorbates, it is common to analyze the frequency of a single adsorbed molecule, i.e., the singleton frequency, which is obtained by extrapolating the adsorbate frequency to zero coverage. For the sake of comparison, the electronic backdonation must be the same for both UHV and electrochemical system. Since in UHV the potential is governed by the work function of the metal, an equivalent potential must be found for the electrochemical system. 

Actually, the absence of reliable values for the potential of zero charge makes this kind of comparison extremely difficult. On the other hand, for Pt(lOO), taking the potential of zero charge based on work function measurements ( = 1.0 V vs. SCE), a value 2045 cm is found for the singleton frequency, which is well below that of the gas phase. Possibly the increasing formation of bridge-bonded CO at low coverages makes the analysis for the Pt(lOO) surface difficult. 

Reliable values of the potential of zero charge are needed for a more precise analysis of this phenomenon. Furthermore, the difference in the singleton frequency for... 

A Stark effect for adsorbed sulfate on Pt electrodes has been reported for the 1200 cm symmetric stretching mode of the adsorbed ion [165]. A quadratic dependence of the band center on the applied electric field is observed (Fig. 60). But this field dependence changes with the degree of coverage. The frequency values extrapolated to zero coverage (singleton frequency) present a linear dependence on the applied electric field (Fig. 61). So we conclude that the second-order Stark effect is induced when the ions are close together on the surface. 

On a Pt(lll) single-crystal surface the effect of the potential on the band position has been evaluated for different coverages [143]. No linear dependence is found for any surface coverage, not even for the singleton frequency. This shows that on Pt(lll) a correction of higher order is necessary and, in this case, the effect is not induced by the presence of neighboring ions alone. 

Fig. 61. Plot of the singleton frequency for the 1200cm mode of adsorbed sulfate on polycrystalline platinum as a function of the applied electric field at the interface.

The microscopic model, however, cannot take into account net coupling of dynamic dipoles oriented parallel to the surface for the thin (microscopic) film. Such coupling in adsorbed monolayers has been shown [57] by probing an otherwise disallowed transition on a metal through a combination band, to result in a red shift from the singleton frequency. This effect of parallel and normal dipole components can be best exemplified by comparison of the RAIRS spectrum of an isotropic physisorbed molecule with a very strong dipole oscillator, v(C-O) in Mo(CO)6, with the gas phase value (singleton frequency) [58]... 

Fig. 18. FT-RAIRS spectra of CO adsorbed at 300K on IML and 20ML films of palladium deposited by metal vapour deposition on TiO2(110) [56]. The switch from a local titania dielectric (transmission band) to that of the metal (absorption band) takes place at about lOML of palladium. The singleton frequency and the coverage dependent dipole shift are similar for both palladium layers indicating little perturbation of the CO adsorption behaviour on the palladium by the Ti02(l 10) substrate.

Figure 7 IR spectra of the stretching vibration of a partial CO coverage on a polycrystalline Pt electrode. The partially filled CO layer is created in a potential sweep of lOOmV/s with varying positive potential limits. All spectra are recorded at SOmVRHE- Spectrum 1 corresponds to a measurement without potential changes. Spectra 2-14 correspond to measurements after a potentiodynamic cycle with changing positive limits from 255 mV to 675 mV. Inset Dependence of the vibrational peak frequency co on the CO coverage. Determination of the singleton frequency cOs by extrapolating to zero CO coverage. (From Ref. 84.)...

Hirschmugl and Williams measured the vibration frequencies of C O diluted by C 0 , and obtained that, for the CO stretch vibrational frequency, the singleton frequency, i/, was 2076cm , the dilution limit, I d, was 2043cm, and the homogeneous limit, Vh, was 2086cm . Thus, they... 

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