Transition time constant

The measured value of r at known i (or better, the values of obtained at various currents) can be used to determine n. A, Cq or Dq. For a well-behaved system, the transition time constant, is independent of i or Cq. A lack of constancy in this... 

This equation applies to the totally mass-transfer-limited condition at the RDE and predicts that //c is proportional to Cq and One can define the Levich constant as which is the RDE analog of the diffusion current constant or current function in voltammetry or the transition time constant in chronopotentiometry. 

On the other hand, the thickness of the slab in the Lagrangian system is the constant Ah = Axq, so for a Lagrangian shock velocity of C, the transit time is... 

The transition state theory rate constant can be constructed as follows. The total flux of trajectories across the transition state dividing surface will be equal to the rate of transition times the population of reactants at equilibrium N, or... 

Although the effects of dielectric constant change and strain have a strong effect on the current during wave transit time, the current at a time about j transit time is close to the value for the linear relation. Thus, based on Eq. 5.7, the wavespeed can be computed from the measured current and the measured polarization data. The approximate agreement between currents calculated from the polarization data and the wavespeed data confirms that the wavespeed values currently available are reasonable. 

Biisslcr et ai [110-113] treated charge recombination in organic LEDs in terms of chemical kinetics. The probability of recombination depends on the ratio of recombination rate ynp-np (where y represents a bimolecular rate constant) and the transition time (itr=dlpE) of the charge carriers through the device. 

The time constant r, appearing in the simplest frequency equation for the velocity and absorption of sound, is related to the transition probabilities for vibrational exchanges by 1/r = Pe — Pd, where Pe is the probability of collisional excitation, and Pd is the probability of collisional de-excitation per molecule per second. Dividing Pd by the number of collisions which one molecule undergoes per second gives the transition probability per collision P, given by Equation 4 or 5. The reciprocal of this quantity is the number of collisions Z required to de-excite a quantum of vibrational energy e = hv. This number can be explicitly calculated from Equation 4 since Z = 1/P, and it can be experimentally derived from the measured relaxation times. 

The case of the prescribed material flux at the phase boundary, described in Section 2.5.1, corresponds to the constant current density at the electrode. The concentration of the oxidized form is given directly by Eq. (2.5.11), where K = —j/nF. The concentration of the reduced form at the electrode surface can be calculated from Eq. (5.4.6). The expressions for the concentration are then substituted into Eq. (5.2.24) or (5.4.5), yielding the equation for the dependence of the electrode potential on time (a chronopotentiometric curve). For a reversible electrode process, it follows from the definition of the transition time r (Eq. 2.5.13) for identical diffusion coefficients of the oxidized and reduced forms that... 

The reciprocals of the time constants, x, and x2, are the rate constants k, and k2. The weights of the exponentials (ii and w2) are complicated functions of the transition rates in Eq. (6.25). Flowever, the rate constants are eigenvalues found by solving the system of differential equations that describe the above mechanism. A, and k2 are the two solutions of the quadratic equation ... 

While in vivo studies assess absorption rates as process-lumped time constants from blood level versus time data, these rate parameters encompass the kinetics of dosage-form release, GI transit, metabolism, and membrane permeation. The use of isolated tissue and cellular preparations to screen for drug absorption potential and to evaluate absorption rate limits at the tissue and cellular levels has been expanded by the pharmaceutical industry over the past several years. For more detail in this regard, the reader is referred to an article by Stewart et al. [68] for references on these preparations and for additional details on the various experimental techniques outlined below. 

Figure 3.43 Schematic illustration of the transition time t in a constant-current (chronopotentin-metric) electrolysis experiment (see text for details).

In the frame of the present review, we discussed different approaches for description of an overdamped Brownian motion based on the notion of integral relaxation time. As we have demonstrated, these approaches allow one to analytically derive exact time characteristics of one-dimensional Brownian diffusion for the case of time constant drift and diffusion coefficients in arbitrary potentials and for arbitrary noise intensity. The advantage of the use of integral relaxation times is that on one hand they may be calculated for a wide variety of desirable characteristics, such as transition probabilities, correlation functions, and different averages, and, on the other hand, they are naturally accessible from experiments. 

Before finding the Laplace-transformed probability density wj(s, zo) of FPT for the potential, depicted in Fig. A 1(b), let us obtain the Laplace-transformed probability density wx s, zo) of transition time for the system whose potential is depicted in Fig. Al(c). This potential is transformed from the original profile [Fig. Al(a)] by the vertical shift of the right-hand part of the profile by step p which is arbitrary in value and sign. So far as in this case the derivative dpoints except z = 0, we can use again linear-independent solutions U(z) and V(z), and the potential jump that equals p at the point z = 0 may be taken into account by the new joint condition at z = 0. The probability current at this point is continuous as before, but the probability density W(z, t) has now the step, so the second condition of (9.4) is the same, but instead of the first one we should write Y (0) + v1 (0) = YiiOje f1. It gives new values of arbitrary constants C and C2 and a new value of the probability current at the point z = 0. Now the Laplace transformation of the probability current is... 

Chronopotentiometry has also been used to determine chloride ions in seawater [31]. The chloride in the solution containing an inert electrolyte was deposited on a silver electrode (1.1 cm2) by the passage of an anodic current. The cell comprised a silver disc as working electrode, a symmetrical platinum-disc counter-electrode and a Ag-AgCl reference electrode to monitor the potential of the working electrode. This potential was displayed on one channel of a two-channel recorder, and its derivative was displayed on the other channel. The chronopotentiometric constant was determined over the chloride concentration range 0.5 to 10 mM, and the concentration of the unknown solution was determined by altering the value of the impressed current until the observed transition time was about equal to that used for the standard solution. 

It should be noted here that the ultra thin-layer cells (UTLC) which result from the close approach of an STM tip to a conducting substrate may have important electroanalytical applications in studies other than STM imaging (64). This is because extremely large current densities should be attainable in such cells, and also because of the fast transit times (e.g., 50 nsec for d - 10 nm) for reactants across the cell. Thus, such UTLC s might facilitate the determination of fast heterogeneous rate constants or the study of reactive electrochemical intermediates (64). 

The second problem to be tackled is data reconciliation for applications in which the dominant time constant of the dynamic response of the system is much smaller than the period in which disturbances enter the system. Under this assumption the system displays quasi-steady-state behavior. Thus, we are concerned with a process that is essentially at steady state, except for slow drifts or occasional sudden transitions between steady states. In such cases, the estimates should be consistent, that is, they should satisfy the mass and energy balances. 

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