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Motivated by recent experimental observations of power-law statistics both in spectral diffusion process and fluorescence intermittency of individual semiconductor nanocrystals (quantum dots), we consider two different but related problems: (a) a stochastic lineshape theory for the Kubo–Anderson oscillator whose frequency modulation follows power-law statistics and (b) photon counting statistics of quantum dots whose intensity fluctuation is characterized by power-law kinetics. In the first problem, we derive an analytical expression for the lineshape formula and find rich type of behaviors when compared with the standard theory. For example, new type of resonances and narrowing behavior have been found. We show that the lineshape is extremely sensitive to the way the system is prepared at time t=0 and discuss the problem of stationarity. In the second problem, we use semiclassical photon counting statistics to characterize the fluctuation of the photon counts emitted from quantum dots. We show that the photon counting statistics problem can be mapped onto a Le´vy walk process. We find unusually large fluctuations in the photon counts that have not been encountered previously. In particular, we show that Mandel’s Q parameter may increase in time even in the long time limit. [Copyright &y& Elsevier]

Fo¨rster–Dexter theory for excitation energy transfer (EET) is generalized for the account of short time nonequilibrium kinetics due to the nonstationary bath relaxation. The final rate expression is presented as a spectral overlap between the time dependent stimulated emission and the stationary absorption profiles, which allows experimental determination of the time dependent rate. For a harmonic oscillator bath model, an explicit rate expression is derived and model calculations are performed in order to examine the dependence of the nonequilibrium kinetics on the excitation–bath coupling strength and the temperature. Relevance of the present theory with recent experimental findings and possible future theoretical directions are discussed. [Copyright &y& Elsevier]

Molecular dynamics simulation is employed to study graphene supercapacitors. Four different ionic liquids are considered as an electrolyte, each of which is combination of the same cation 1-ethyl-3-methylimidazolium([emim] + ), and different, cyano-containing anions, thiocyanate ([SCN] – ), dicyanamide ([N(CN) 2 ] – ), tricyanomethanide ([C(CN) 3 ] – ), and tetracyanoborate ([B(CN) 4 ] – ), respectively. In particular we investigate how electric double layer structure and electrical properties are affected by the structure of cyano containing anions. Cations and anions make alternating structure near charged electrode. Differential capacitances in four ionic liquids are found to have a maximum value at negative potential. The maximum capacitances are comparable to each other, but the corresponding potential shifts to the negative side as more cyano groups are attached to the anion. Starting from the interfacial layer, the effects of the further ionic layers on differential capacitance are systematically investigated. Comparing charges of the electrode and those of ionic layers, we find that differential capacitance behavior mainly stems from the ion exchange between electric double layer and bulk region. The ion exchange behaviors are decomposed into cation and anion contributions. The differential charging mechanisms of the system are strongly dependent on the electric potential. The maximum capacitances are consequence of rapid desorption of respective anions. [ABSTRACT FROM AUTHOR]

Supercapacitors with graphene electrodes are studied via molecular dynamics simulation. As an electrolyte, we consider three different room-temperature ionic liquids (RTILs), each of which is made up of the same anion BF 4 − , and different cations, 1-C n (n = 2,4,6)-3-methylimidazolium, respectively. We investigate how the alkyl chain length of the cation affects their interfacial structure and electrical properties for electric double layer capacitors. As a whole, cations and anions make layering structures between two parallel electrodes. Cations in the nearest layer orient predominantly in parallel to the electrode. Imidazolium rings of cations form π-stacking with graphene, then the alkyl chains of cations align parallel to the electrode. Differential capacitances in three RTILs are found to decrease with an increase of the magnitude of electrode potentials. The ion size and orientation affect both structure and capacitance behavior. The parallel orientations of cations become stronger with an increase of the alkyl chain length for the considered RTILs. The differential capacitance tends to decrease with raising the alkyl chain length over a wide range of the electrode potential. This is ascribed to a steric effect caused by larger cation size. It is also found that anodic capacitance is higher than cathodic one due to a higher screening efficiency by small anions, and an asymmetry in the peak of capacitance biased to the cathodic side becomes weaker as the alkyl chain length increases. Comparing electrode charge with ion numbers near the electrodes, with respect to their changes in response to the electrode potential, we find that the interfacial layer of the electrolyte mainly governs capacitive behavior of the systems. [ABSTRACT FROM AUTHOR]