Nyquist rate calculator

Figure 3.13 (a) Values of charge-transfer resistance of different systems based on carbon, using the redox probe Fe(CN)6 . (b) Nyquist plot of different carbon nanotube composites in the presence of the redox couple, (c) Table with the electron-transfer rate constants calculated from cyclic voltammet data by using Nicholson method. Adapted with permission from Ref [103]. Copyright, 2008, Elsevier. 

In order to compare with the experimentally measured spectrum, one would ideally like to have the spectra simulated with equal or better energy resolution and with a good statistical reliability for the predicted intensity. Therefore, a suitable estimate of these quantities is important, in order to minimise the output to a manageable level (i.e. to output the trajectories and velocities as less as possible). According to the sampling theorem [23], the smallest time step for the Z(co) calculations is a factor of n times larger than MD simulation step which is determined by the maximum frequency, (Omox, of the system to be simulated. Hence the appropriate time step n At is given by the Nyquist sample rate, as ... 

Fe(CN)6] , electrochemically contacted at a photoisomerizable command interface (lla/llb). Figure 7.15 shows the impedance features (as Nyquist plots) of the nitrospiropyran (11a) and protonated nitromerocyanine (lib) electrodes in the presence of [Fe(CN)6] as a redox probe. The impedance spectra show a larger resistance to interfacial electron transfer when the monolayer is in the neutral dinitrospiropyran state (Ret = 60 kll) than when it is in the positively charged protonated merocyanine state (Ret = 48 kQ) (Figure 7.15, curves b and a). The heterogeneous rate constants for electron transfer between the electrode and the redox probe were calculated to be 0.82 X 10" and 1.1 x 10" cm s" for the 11a and 1 lb-monolayer modified Au-electrodes, respectively. 

Within the range of frequency, temperature, shear rate etc. covered by the experiment, all the measured thermal noise levels agreed well with the predictions based on the Nyquist formula. This implies that the thermal noise level could have been calculated from resistivity measurements and also that the noise peaks in the vicinity of Tg and Tm would have appeared in the corresponding resistivity-temperature diagrams. This was actually verified in numerous experimental runs. On the other hand, the measurement of thermal noise has the advantage that no external voltage has to be applied across the sample. This eliminates the possibility that the observed peaks arise from polarization effects (6,7). 

It should be noted that in Figure 4, each Nyquist plot has an inductance at low frequencies. This inductance is related to the number of Oad on the anode surface. The calculations show that the inductance on the SCA anode is 308.9 H/cm whereas that on the general zone anode is only 190.5 H/cm. This means that the adsorbed oxygen atoms on the SCA anode have more difficulty to combine with each other to form oxygen molecules than those on the general zone anode. It is known that the Oad is a strong oxidant it can diffuse across the oxide layer and attack the metal substrate to form more oxide. This accelerates the corrosion rate of the anode. 

Nyquist frequency is the name of the highest frequency that can theoretically be represented in a digital audio system. It is calculated as half of the value of the sampling rate. For instance, if the sampling rate of the system is equal to 44100 Hz, then the Nyquist frequency is equal to 22050 Hz. 

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