Triangular Pulse

The initial and boundary conditions for a membrane, with x = L taken as the input side, are assumed to be 

(11) leads to an expression for the change in the anodic current in each case. Hence, for pure diffusion control, 

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IFIGI3RE 11.34 Determination of the real evolution of the heat flux at the inside wall surface The temperature condition at the exterior surface is approximated by triangular pulses, and the heat flux response at the interior surface is determined by superposition of the heat flux responses of the individual pulses. 

Methods employing individual linear or triangular pulses (potential-sweep, triangular pulse and cyclic voltammetry, sometimes also called... 

Fig. 5.18 Potentiostatic methods (A) single-pulse method, (B), (C) double-pulse methods (B for an electrocrystallization study and C for the study of products of electrolysis during the first pulse), (D) potential-sweep voltammetry, (E) triangular pulse voltammetry, (F) a series of pulses for electrode preparation, (G) cyclic voltammetry (the last pulse is recorded), (H) d.c. polarography (the electrode potential during the drop-time is considered constant this fact is expressed by the step function of time—actually the potential increases continuously), (I) a.c. polarography and (J) pulse polarography...

Fig. 5.56 Triangular-pulse voltammograms of oxidation of 0.1 m formic acid in 0.5 m H2S04 at various faces of a single-crystal platinum electrode, 22°C, dE/dt =... 

Essentially the same value of n is obtained by comparing the calculated impulse of Aziz et al (quoted in Ref 5) with a triangular pulse to give same area as the area under their P—t curve. Thus it appears that the n based on Gurney is a little higher than the n s of more sophisticated theoretical estimates... 

Triangular Pulse With the triangular pulse method, each side of a membrane is initially held at a constant potential so that permeation occurs in a normal manner [109]. After a steady state is achieved, an anodic or cathodic triangular pulse is applied to the entry side and the change in the oxidation current is measured at the output side. The duration of the pulse is typically 0.01 to 0.03 s. Analytical solutions for the current have been obtained for pure diffusion control and for entry-limited diffusion control. An anodic current peak is obtained in response to the triangular pulse, and the time corresponding to the half-peak width is characteristic of the type of kinetic control. 

Taking many force curves can nowadays be done automatically with commercial instruments. Usually it requires 0.1 to 1 s to take one force curve. To obtain say 64 X 64 force curves lasts 7 to 70 min. To increase the speed, Miyatani and coworkers developed a procedure in which the cantilever is moved in a sinusoidal form rather than a triangular pulse [205]. 

Short (0.5—5 ms) triangular pulses for tetanic muscular contractions, interrupted or with varying amplitude. Interval between pulses 10—25 m. For muscle pain relief, rectangular pulses of length 2 ms and interval 7 ms are used. TENS for pain relief is different. It is based on stimulating afferent nerve fibers with much shorter pulses (e.g., 0.2 ms). 

A symmetrical triangular pulse can be expressed as the superposition of three linear functions as shown. 

FIG. II-5. Conversion of a triangular dynamic pressure into an equivalent static load. peak of the dynamic triangular puke (Pa) P static pressure (Pa) t duration of the triangular pulse (ms) T first excited period of the one-degree-of-freedom structure (ms) iax- tnaximum displacement at failure (m) Ay maximum elastic dkplacement (m) p maximum ductility. 

Figure 21. Oscilloscope picture showing photodiode response (change in optical transmittivity of the cell) to triangular pulses of opposite polarity (4 V peak-to-peak), demonstrating threshold, saturation, memory, and symmetry bistability cf. Fig. 11. The material is DOBAMBC at 60 X. Horizontal scale 1.5 V/div (from [95]).

Another type of a triangular pulse has negligible frontal part but the tail is similarly valuable for determining the time constant of apparatus. However, this saw-tooth pulse may become a welcome tool for possible calibration of reaction dynamics, which would be a desirable instrument regarding a better determinability and characterization of the kinetics of processes. 

The three important inputs discussed above—step, ramp, rectangular pulse—are depicted in Fig. 5.2. Note that many types of inputs can be represented as combinations of step and ramp inputs. For example, a unit height (isosceles) triangular pulse of width tyy can be constructed from three ramp inputs, as shown in Fig. 5.3. In this case, we write a single expression for the triangular pulse function... 

Figure 5.3 How three ramp inputs can be combined to form a triangular pulse.

Cyclic voltammetry (CV) or triangular pulse voltammetry is an important tool to measure quantitatively, the monolayer coverage of the catalyst active sites. Thus, it is possible to find out the electrochemically oofivp ciirface area from the CV output (Pozio et al., 2002). The basic method is shown in Fig. 6. The CV... 

Listing 12.16. Code segment for solution of soliton wave equation. Initial triangular pulse given at x = 2. 

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