Small Potassium Clusters

While the dipole absorption features [114, 124] and photodissociation dynamics of small sodium clusters are rather well known [112, 113, 126, 127, 407-409], there is very little knowledge about potassium clusters larger than the dimer. The lack of experimental data might be caused by ultrafast fragmentation processes within the potassium clusters, so that conventional stationary spectroscopic techniques might fail. Hence, the goal of this section is to determine the photodissociation probability of small potassium clusters as a function of cluster size as well as excitation energy. 

Special Features of the Experimental Setup. Brechnignac s investigations [111] encouraged the study of the photodissociation dynamics of K for three different excitation energies. Employing a two-color TPI experiment, the potassium clusters were excited at 1.47 eV and 2.94 eV, while with one-color TPI spectroscopy these clusters were excited at 2eV. Therefore, two 

In the two-color experiments the pulses of the Tiisapphire laser (1.47 eV) were frequency-doubled by a 1 mm BBO crystal with a conversion efficiency of 15%. A dichroic mirror separated the fundamental from the second harmonic (2.94 eV). For convenience, a positive delay here means the pump beam is the second harmonic at 2.94 eV and the probe beam is the fundamental at 1.47 eV. For negative delay times the energies of the pump and probe pulses are interchanged. 

The one-color experiment was performed with pump and probe pulses of the same photon energy (2.00eV). In this case a synchronously pumped femtosecond optical parametric oscillator was used (see Sect. 2.1.1). At A = 1.3 im the signal wave s maximum output reached more than 400 mW, corresponding to 20% conversion efficiency. The signal wave was frequency-doubled by a BBO crystal (60 mW). By measuring an interferometric autocorrelation 

To describe the shape of the curves, the extended fragmentation model (Sect. 2.2.2) was again applied. The analysis was performed analogously to that for the sodium clusters (Sect. 4.3). The function n on t) was fitted to the experimental data by means of a least-squares routine. This function is shown in Figs. 4.15 and 4.16 as solid lines. Obviously there is an excellent agreement between measured and fitted curves. 

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One of the first published cluster compounds of the heavier group 13 elements was the closo-dodecaaluminate K2[Ali2iBui2] 54 (Figure 2.3-10) [79], which possesses an almost undistorted icosahedron of 12 aluminum atoms with short Al-Al distances (268-270 pm). Up until today, it remained the only homonuclear cluster compound of the elements aluminum to indium which, with respect to structure and cluster electron count, is completely analogous to any boronhydride (see Chapters 1.1.2, 1.1.3, 1.1.5.2, and 2.1.5.6) (in this case doso-[Bi2H12]2 ). Compound 54 was formed in small quantities by the reaction of di(isobutyl)aluminum chloride with potassium and was isolated as dark red crystals (Figure 2.3-10). 

Here, w = m, n, and S. V represents the membrane potential, n is the opening probability of the potassium channels, and S accounts for the presence of a slow dynamics in the system. Ic and Ik are the calcium and potassium currents, gca = 3.6 and gx = 10.0 are the associated conductances, and Vca = 25 mV and Vk = -75 mV are the respective Nernst (or reversal) potentials. The ratio r/r s defines the relation between the fast (V and n) and the slow (S) time scales. The time constant for the membrane potential is determined by the capacitance and typical conductance of the cell membrane. With r = 0.02 s and ts = 35 s, the ratio ks = r/r s is quite small, and the cell model is numerically stiff. The calcium current Ica is assumed to adjust immediately to variations in V. For fixed values of the membrane potential, the gating variables n and S relax exponentially towards the voltage-dependent steady-state values noo (V) and S00 (V). Together with the ratio ks of the fast to the slow time constant, Vs is used as the main bifurcation parameter. This parameter determines the membrane potential at which the steady-state value for the gating variable S attains one-half of its maximum value. The other parameters are assumed to take the following values gs = 4.0, Vm = -20 mV, Vn = -16 mV, 9m = 12 mV, 9n = 5.6 mV, 9s = 10 mV, and a = 0.85. These values are all adjusted to fit experimentally observed relationships. In accordance with the formulation used by Sherman et al. [53], there is no capacitance in Eq. (6), and all the conductances are dimensionless. To eliminate any dependence on the cell size, all conductances are scaled with the typical conductance. Hence, we may consider the model to represent a cluster of closely coupled / -cells that share the combined capacity and conductance of the entire membrane area. 

The parameters of Table III suggest that the higher reaction rates on Pt/Sn/KLTL zeolite and Pt/Sn/K/Si02 may be attributed to the stabilization of adsorbed species on the small Pt/Sn clusters within the zeolite micropores and/or stabilization by the presence of potassium. For example, equilibrium constants for hydrogen adsorption at the average temperature of... 

Instead of cupric or ferric ions, other zeolite-encapsulated oxidants have also been studied for the polymerization of pyrrole. These include small SnOa particles and oxygen-covered Pd clusters residing in potassium L zeolite. The structure of the clusters was elucidated using x-ray absorption spectroscopy, and ESR and IR data as well as the observation that more monomer than oxidant was present led to the conclusion that the pol5unerization reaction might proceed in a catalytic fashion, involving air oxidation. 

In a similar process, platinum supported on the potassium-ion-exchanged zeolite L (Pt/K-L) has been found to be an excellent catalyst for the aromati-sation of hexane and heptane. This is thought to be due to its ability to support small clusters of platinum metal that act as a molecular die . The lack of acidity in this catalyst is important because it prevents side reactions, including cracking. ... 

Figure 3 A representation of the crystal structure of the V12 cluster (1). The vanadium ions are shown as black spheres, the arsenate ions by dark gray spheres and the potassium ion by the large light gray sphere. The small white spheres are oxygen atoms and the smaller white spheres are hydrogen atoms.

As discussed in Part 1-A, the small-angle x-ray scattering data reveal the absence of any centers with diameter in the neighborhood of 8 A in ammonia solutions of potassium, sodium, and lithium of concentration of about 0.8M but do show the presence of larger centers. At this concentration, one would expect to have mostly dimer clusters or two-electron cavities. Since Schmidt s measurements cannot give information about centers with diameters less than 6 A, one cannot conclude that two-electron cavities, which would be expected to have nearly the same radius as one-electron cavities, are definitely absent. On the other hand, the observed presence of scattering centers of diameters as large as 13,16, and 32 A in solutions of potassium, sodium, and lithium, respectively, does indirectly support the... 

In this book the real-time photodissociation dynamics of small sodium (Nan=3...io) and potassium (Kn=3...9) clusters are studied as a function of cluster size as well as excitation wavelength (Sects. 4.2-4.4). The ratio of dissociative to radiative decay is a measure of the predissociation of an electronic state [122, 133]. For the C state of Naa the electronic predissociation dynamics and especially the localization of its onset are analyzed in detail by ultrafast spectroscopy (Sect. 4.1). 

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