Oscillation of potential

Fig. 7.11. The ground-state vibrational wave funetion of the anharmonic oscillator (of potential energy V2) is asymmetric and shifted towards positive values of the displacement when compared to the wave function for the harmonic oscillator with the same force constant (the potential energy Vi).

It was found that electropolishing occurs in systems which, under anodic dissolution, exhibit a limiting current characteristic of diffusion control, i.e., currents are dependent on flow rate of the electrolyte past the anode, as shown in Figure 24. Over a certain range of potentials at the limiting current plateau, at which maximum brilliance is obtained, oscillations of potential occur at a virtually constant current density, with an amplitude of over 0.40 V, and without appreciable damping. Also, a significant photoelectrochemical effect is found. 

Fig. 1. Optimization of the Onsager-Machlup action for the two dimensional harmonic oscillator. The potential energy is U(x,y) = 25i/ ), the mass is 1...

Figure 1.13 Plot of potential energy, V(r), against bond length, r, for the harmonic oscillator model for vibration is the equilibrium bond length. A few energy levels (for v = 0, 1, 2, 3 and 28) and the corresponding wave functions are shown A and B are the classical turning points on the wave function for w = 28...

Aside from merely calculational difficulties, the existence of a low-temperature rate-constant limit poses a conceptual problem. In fact, one may question the actual meaning of the rate constant at r = 0, when the TST conditions listed above are not fulfilled. If the potential has a double-well shape, then quantum mechanics predicts coherent oscillations of probability between the wells, rather than the exponential decay towards equilibrium. These oscillations are associated with tunneling splitting measured spectroscopically, not with a chemical conversion. Therefore, a simple one-dimensional system has no rate constant at T = 0, unless it is a metastable potential without a bound final state. In practice, however, there are exchange chemical reactions, characterized by symmetric, or nearly symmetric double-well potentials, in which the rate constant is measured. To account for this, one has to admit the existence of some external mechanism whose role is to destroy the phase coherence. It is here that the need to introduce a heat bath arises. 

It is left to reader to verify that, under Lee .s discrete mechanics, both free particles and particles subjected to a constant force, behave in essentially the sa e way as they do under continuous equations of motion. Moreover, the time intervals At = t-i i — ti are all equal. While the spatial behavior for non-constant forces (ex particles in a harmonic oscillator V potential) also remains essentially... 

A thorough insight into the comparative photoelectrochemical-photocorrosion behavior of CdX crystals has been motivated by the study of an unusual phenomenon consisting of oscillation of photocurrent with a period of about 1 Hz, which was observed at an n-type CdTe semiconductor electrode in a cesium sulfide solution [83], The oscillating behavior lasted for about 2 h and could be explained by the existence of a Te layer of variable width. The dependence of the oscillation features on potential, temperature, and light intensity was reported. Most striking was the non-linear behavior of the system as a function of light intensity. A comparison of CdTe to other related systems (CdS, CdSe) and solution compositions was performed. 

Bohannan, E. W., Huang, L. Y Miller, F. S., Shumsky, M. G. and Switzer, J. A. (1999) In situ electrochemical quartz crystal microbalance study of potential oscillations during the electrodeposition of CU/CU2O layered nanostructures. Langmuir, 15, 813—818. 

The Oscillation of Membrane Potential or Membrane Current Kohji Maeda and Sorin Kihara... 

The oscillation of membrane current or membrane potential is well-known to occur in biomembranes of neurons and heart cells, and a great number of experimental and theoretical studies on oscillations in biomembranes as well as artificial membranes [1,2] have been carried out from the viewpoint of their biological importance. The oscillation in the membrane system is also related to the sensing and signal transmission of taste and olfaction. Artificial oscillation systems with high sensitivity and selectivity have been pursued in order to develop new sensors [3-8]. 

The oscillation at a liquid liquid interface or a liquid membrane is the most popular oscillation system. Nakache and Dupeyrat [12 15] found the spontaneous oscillation of the potential difference between an aqueous solution, W, containing cetyltrimethylammo-nium chloride, CTA+CK, and nitrobenzene, NB, containing picric acid, H" Pic . They explained that the oscillation was caused by the difference between the rate of transfer of CTA controlled by the interfacial adsorption and that of Pic controlled by the diffusion, taking into consideration the dissociation of H Pic in NB. Yoshikawa and Matsubara [16] realized sustained oscillation of the potential difference and pH in a system similar to that of Nakache and Dupeyrat. They emphasized the change of the surface potential due to the formation and destruction of the monolayer of CTA" Pic at the interface. It is... 

A. Oscillation of the Membrane Potential Difference Under an Appiied Current [22,23]... 

Two aqueous phases separated by a liquid membrane, EM, of nitrobenzene, NB, were layered in a glass tube, which was equipped with Pt counterelectrodes in W1 and W2 and reference electrodes in three phases as in Eq. (1). Reference electrodes set in W1 and W2 were Ag/AgCl electrodes, SSE, and those in LM were two tetraphenylborate ion selective electrodes [26,27], TPhBE, of liquid membrane type. The membrane current, /wi-w2 was applied using two Pt electrodes. The membrane potential, AFwi-wi recorded as the potential of SSE in W2 vs. that in W1. When a constant current of 25 /aA cm was applied from W1 to W2 in the cell given as Eq. (1), the oscillation of membrane potential was observed as shown in curve 1 of Fig. 1. The oscillation of AFwi-wi continued for 40 to 60 min, and finally settled at ca. —0.40 V. 

The positive limit and negative limit of the amplitude in the oscillation of AFlm/w2 (cf-curve 3 in Fig. 1) agreed with the potential of the maximum wave (indicated by A) and that of the final descent (indicated by B), respectively, at —35/iAcm in the voltammogram (Fig. 3). When TMA was used instead of Cs" ", the positive limit of the oscillation amplitude was ca. 0.12 V more positive than that with Cs" ". The difference corresponds to that in the potential difference of the maximum wave between TMA and Cs. The negative limit of the amplitude observed when TBA or TPrA was employed in place of TPA was more positive than that with TPA+, since the final descent due to the transfer of TBA+ or TPrA from LM to W2 is more positive than that for TPA" " transfer, as in Fig. 3. 

B. Oscillation of Membrane Current Under an Applied Membrane Potential [24,25]... 

Curve 1 in Fig. 5 gives an example of the oscillation of membrane current observed with the liquid membrane system as in Eq. (3) by applying a constant AFwi-w2 of —0.48 V and measuring the time course of the current through the LM, /wi-w2- The cell used was the same as that used for the measurement of the potential oscillation, except a tetraphenyl-arsonium ion selective electrode [26,27], TPhAsE, was employed as a reference electrode in LM of NB ... 

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