Cluster capacitance

The I U) characteristic of the arrays showed a linear behavior over a broad voltage range. If each cluster is assumed to have six nearest neighbors and a cluster-to-cluster capacitance of 2 x 10 F is implied, the total dot capacitance will be 1.2 x 10 F. A corresponding charging energy can thus be approximated to 11 meV, which is only about half of the characteristic thermal energy at room temperature. This excludes a development of a Coulomb gap at room temperature. 

Solution-phase DPV of Au144-C6S dispersed in 10 mM [bis(triphenylpho-sphoranylidene)-ammoniumtetrakis-(pentafluorophenyl)-borate (BTPPATPFB)/ toluene] [acetonitrile] 2 1 revealed well-behaved, equally spaced and symmetric quantized double-layer charging peaks with AE - 0.270 0.010 V. Applying the classical concentric spheres capacitor model (8) reveals an individual cluster capacitance of 0.6 aF [334, 335]. 

The capacitance of the cluster/substrate-junction was calculated to be 3.9 x 10 F. This value is in agreement with the value of the cluster capacitance previously determined by temperature-dependent impedance measurements. These results are, furthermore, in good agreement with capacitance data obtained from self-assembled gold nanoparticles on a dithiol-modified Au surface, reported by Andres and coworkers.Here tunneling spectroscopy has been performed on 1.8 nm Au particles which were grown in the gas phase and a cluster-substrate capacitance of 1.7 X 10 F was obtained. Thus, the small capacitance enables the observation of Coulomb blockade phenomena at room temperature. 

This relation shows that the core radius and monolayer chain length are the manipulable MPC variables influencing individual cluster capacitances. The cluster capacitance increases with core radius and decreases with monolayer chain length, and these effects are indeed seen in prepared An,44 nanoparticle samples, for both solutions and films. ... 

The Hg/V-methylformamide (NMF) interface has been studied by the capacitance method as a function of temperature.108,294,303 The potential of Hg was measured with respect to the reference electrode Ag/0.05 M AgC104 + 0.05 M NaC104 in water. The specific adsorption of C104 was found to be negligible at a < 6 /iC cm"2. The experimental capacitance data have been discussed in terms of the four-state model,121,291,294 which assumes the presence of both monomers and clusters in the surface layer of the solvent. The model has been found to describe the experimental picture qualitatively but not quantitatively. This is related to the fact that NMF is a strongly associated solvent.108,109,294,303... 

Electric Breakdown in Anodic Oxide Films Physics and Applications of Semiconductor Electrodes Covered with Metal Clusters Analysis of the Capacitance of the Metal-Solution Interface. Role of the Metal and the Metal-Solvent Coupling Automated Methods of Corrosion Measurement... 

From measurement data gained at 90 K, the capacitance of the cluster was determined as 3.9xlO F. Temperature-dependent impedance measurements at the same cluster resulted in a very similar value [23]. 

The capacitance of the cluster was calculated from a fit of the experimental data at 90 K to be 3.9 x 10 F. This value, which is very sensitive toward residual charges and nearby background charges, is close to the value of the microscopic capacitance, which was determined earlier by temperature-dependent impedance measurements [21]. Furthermore these results are found to be in good agreement with the capacitance data obtained on the above-mentioned gold nanoclusters on a XYL-modified Au(l 1 1) surface [13,22]. 

Figure 5. SET on a single ligand-stabilized AU55 cluster at 90 K. The junction capacitance was calculated to be 3 x 10 F by fitting. (Reprinted with permission from Ref. [20], 2004, Springer.)...

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. 

High r factors are, however, not without some other complications since they imply porosity of materials. Porosity can lead to the following difficulties (a) impediment to disengagement of evolved gases or of diffusion of elec-trochemically consumable gases (as in fuel-cell electrodes 7i2) (b) expulsion of electrolyte from pores on gas evolution and (c) internal current distribution effects associated with pore resistance or interparticle resistance effects that can lead to anomalously high Tafel slopes (132, 477) and (d) difficulties in the use of impedance measurements for characterizing adsorption and the double-layer capacitance behavior of such materials. On the other hand, it is possible that finely porous materials, such as Raney nickels, can develop special catalytic properties associated with small atomic metal cluster structures, as known from the unusual catalytic activities of such synthetically produced polyatomic metal clusters (133). 

J. F. Hicks A. C. Templeton S. Chen K M. Shehan R. Jasti R. W. Murray J. Debord T. G. Schaaff R. L. Whetten, The Monolayer Thickness Dependence of Quantized Double-Layer Capacitances of Monolayer-Protected Gold Clusters. Anal. Chem. 1999, 73, 3703-3711. 

The electrochemical characteristics of anthraquinone-derivatized Au clusters prepared by an electroreduction method are similar to those observed on a planar surface. Ho vever, the double layer capacitance values reveal that it is possible to control the charging phenomenon stepwise when multiple redox activity is present. 

Murray has demonstrated that soluble metallic clusters exhibit coulomb staircase-type behaviour [102]. The ionic space charge formed around the dissolved MFCs is reported to contribute to its capacitance, upon charging of the metal core. It is well known that small metal particles exhibit double layer charging (capacitive charging) properties in liquid electrolytes [104]. The sub-attofarad capacitance associated with the MFCs leads to charging of the tiny capacitor by single electron processes in potential intervals of A V that surpass ke T where is the Boltzmann constant and T is the temperature [102, 105]. 

Murray and co-workers have also demonstrated that the variation in Au-core sizes leads to a transition from metal-like double layer capacitive charging for larger sized particles to redox-like charging for smaller particles ranging between 1.1 nm and 1.9 nm diameter [105] (Figure 20.8). Gold particles stabilized with short chain alkanethiolate monolayers have been used in this study. The capacitance of the clusters is calculated using the concentric sphere capacitance model ... 

Other metallic clusters that have been demonstrated to show the QDL effect are palladium [116, 117], silver [118] and copper [119]. Palladium MFCs capped with mixed monolayers of hexanethiolate/dodecanethiolate and ferrocene thiolate ligands are prepared in a manner similar to that employed for gold MFCs. The DPV studies exhibit a quantized charging effect but the current peaks are not as well defined as those observed for Au-MPCs. Capacitance values of the order of 0.35 aF are obtained, indicating smaller core sizes or thicker monolayer dielectrics [116]. 

---