Fundamental harmonics

This means that the quantity a is determined as the full amplitude of the fundamental harmonic. 

Fig. 3.41. Sinusoidal AC polarography. (a) measuring principle, (b) fundamental harmonic ac polarogram (i included).

Fig. 3.42 represents the symmetric bell shape curve of 7, i.e., the genuine fundamental harmonic ac polarogram, which means the curve of only 7F discriminated for 7C, e.g., by means of phase-selective ac polarography. The term "fundamental is related to the character of the polarographic cell as a non-linearized network whose response is not purely sinusoidal but consists of the sum of a series of sinusoidal signals at first harmonic (o>) response, besides that of the second harmonic (2a>), the third harmonic (3a>), etc. 

Fig. 4.1. Schematic diagram of the second harmonic generation experimental apparatus with the sample in the reflection geometry. The polarization analyzers are set to transmit p-polarized light at the frequency labeled in the figure. The (co/2co) filters transmit the (fundamental/harmonic) light while blocking the (harmonic/fundamental) light. For phase measurements, a quartz plate is mounted on a translation stage for movement towards the sample at a distance L.

Figure 6. Relative fundamental harmonic amplitude as a function of z-oscillation amplitude. (1) Ar = 0.25 when Az = 0. (2) Ar = 0.05 when Az = 0. (Reproduced with permission from Ref. 33. Copyright 1986 Elsevier Science Publishers B.V.)...

Figure 3.5 Conventional (bottom), fundamental-harmonic AC, and second-harmonic AC polarograms for a reversible couple at a dropping-mercury electrode. Curves represent the envelope of the upper limits of the current oscillations.

Figure 1. Upper inset tilted potential U(q) [Eq. (5)] solid maximal tilt, t = 1 dashed minimal tilt, e = 0 [Eq. (4)]. Lower inset U (e = 0) is approximated by a binding potential for energies below Urn, since tunneling is negligible U (e = 1) is divided into the same binding potential and a perturbation V < 0, allowing tunneling. Main figure (a) the coupling spectrum Gn i2 ( ) and the modulation function J t= 4r0 (oo) (multiplied by 2) with n = I /ojo and To = 5n, where loo is the fundamental (harmonic) oscillation frequency in the well (b) idem, with Gn=is(u>), Ti = 0.3/loo, and Ft=iTO(uo) (times 4).

The current output has d.c. as well as a.c. components at the input frequency, to (the fundamental harmonic), and at higher harmonics. The shape of an a.c. polarogram (fundamental harmonic) for a reversible system resembles the first derivative of a d.c. polarogram (Fig. 1). The equations describing the peak current (I )-potential relationship (wave shape) and current-frequency relationship are complex but reduce to simpler expressions in limiting cases. Table 1 summarizes the results for the reversible case. 

Figure 1. Calculated fundamental-harmonic a.c. polarograms tor quasireversible electron transfer.

Figure 4. Calculated fundamental harmonic a.c. polarograms for two electron-transfer reactions. Dotted line gives value of concerted single-step two-electron process. A, AE = — 100 mV ...

Figure 20 shows the incidence angle dependence of SHG intensity at pp fundamental - harmonic beam polarization configuration for a vacuum evaporated BAG thin film, showing very similar dependence as poled polymers with point symmetry oomm. This dependence can be well described by the formulas derived for this symmetry [50]. The fact that the measured quadratic NLO susceptibilities... 

A model containing higher-order term contributions in Eqs. (130)-(131) to fundamental harmonic impedances was recently discussed by Darowicki and Diard et Taking into account that (see Section... 

We realize that, as for the DM noise calculation, from the viewpoint of the noise envelope and its required attenuation, only the fundamental harmonic really counts. The current caused by this is... 

Theoretical and experimental fundamental harmonic a.c. cyclic voltammograms for cis-Cr(CO) (dpm) system as described in Figure 8 but with T = 293 K,ki =... 

Figure 25. Peak cot - il/2 data for the Cd2+ system in the presence OTd Asence of 1-octanol using the SCW (o, ) and NPPW (+,X) d.c. scans. System 1.01x10-3 M Cd2+ at the Hg-aqueous 1.0 Na2S04 0.36 H2SO4 interface, 25 C, where 0 = SCW with no added 1-octanol f+ X 1 = 2 0x10" 1-octanol added. Applied pseudo-random odd-harmonic a.c. waveform with 1.5 mV per frequency component, 35 total components, 195.3 Hz fundamental harmonic superimposed on SCW or NPPW d.c. scans. Pulse width = 61.5 ms NPPW Ei = +0.10 (+) and -0.45 (X) V. Measured peak cot9 at 5.0 s in the life of Hg drop, using five replicates and no FFT digital filtering.

Figure 30. In-phase fundamental-harmonic a.c. polarographic peak current vs. concentration profiles for reserpine and methyltestosterone. System (A) CH3CN 2,4,6,8,10 x 10"5 M reserpine at DME, 2s drop life, 0.01 TEAPFB in CH3CN, (A) DMF 2,4,6,8,10 x lO" M reserpine at DME, 2s drop life, 0.01 M TEAPFB in DMT, (A) Methanol-water 0.01 M TBAOH 2,4,6,8,10 x lO" M reserpine at DME, 2s drop life, 0.01 M TBAOH in 60% methanol-40% water, (B) CH3CN 2,4,6,8,T0 x 10-5 M methyl-testosterone at DME, 2s drop life. 0.01 M TEAPFB in CH3CN, (B) DMF 2,4,6,8,10 x lO" M methyl testosterone at DME, 2s drop life, 0.01 M TEAPFB in DME, (B) Aqueous Base 2,4,6,8,10 x 10" methyl testosterone at DME,...

Figure 31. Fundamental-harmonic a.c. polarograms of a methyl-testosterone standard and a tablet extract. System ...

Fundamental-harmonic a.c. polarograms of a reserpine standard and a tablet extract. System (A) 1.62 x 10"5 M reserpine standard. (B) 1.65 x lO" M reserpine extracted from a tablet, at DME, 0.01 W TEAPFB-ACN interface, 2s drop life, room temperature, 25 +2 C. Applied pseudo-random, odd-harmonic a.c. waveform,... 

Figure 33. In-phase fundamental harmonic a.c. polarographic peak...

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