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Cottrell’s equation

Rearrangement of the equation to make an expression for tm will show the reader the similarity between Cottrell s equation for a diffusion-controlled current as a function of time at constant potential and Sand s equation for the time at which, under diffusion control at constant current, the potential takes off to seek a new supply of charge carriers for its electron stream. [Pg.508]

The measurement of limiting currents is probably the simplest and most widely applicable method for measuring the diffusion coefficients of redox species. In agreement with Cottrell s equation, the value of D, can be obtained from the plot of... [Pg.75]

The linear relationship between the current density and reciprocal square root of time is observed for chronoamperograms with applied potential below -1.7 V (Figure 4.5.12, insert). The cathodic current density for a reversible process involving soluble species can be expressed by Cottrell s equation [24] ... [Pg.269]

Myland, J.C. Oldham, K.B. (2004). Cottrell s Equation Revisited An Intuitive, but Unreliable, Novel Approach to the Tracking of Electrochemical Diffusion. Electrochemistry Communications. Vol.6, No.4, (February 2004), pp. 344-350, ISSN 1388-2481... [Pg.18]

Fig. 10.9 Chronoamperometry at a potential corresponding to Co(0,t) = 0 (a) perturbation signal (b) concentration profiles at increasing times (c) signal recorded i =f(t) according to Cottrell s equation normalization in (b) is performed by dividing Co(x,t) by Cq with respect to the bulk concentration, which is quite common practice... Fig. 10.9 Chronoamperometry at a potential corresponding to Co(0,t) = 0 (a) perturbation signal (b) concentration profiles at increasing times (c) signal recorded i =f(t) according to Cottrell s equation normalization in (b) is performed by dividing Co(x,t) by Cq with respect to the bulk concentration, which is quite common practice...
The Cottrell s equation indicates that the current is at any time proportional to the bulk concentration of the electroactive species, which potentially makes chronoamperometry a technique suitable for quantitative determinations. Actually, it is not so often directly used to this purpose, due to low sensitivity at times not short enough and poor selectivity exhibited in many situatimis. However, it is at the basis of a not so often used, maybe underestimated technique, namely the voltammetry with periodical renewal of the diffusion layer. This technique very often furnishes comparable information in respect to the more sophisticated voltammetry making use of the rotating disk electrode, requiring a much less sophisticated experimental setup. Although different initial conditions hold, the responses of pulse techniques described in the following are also based on chronoamperometric decays. [Pg.262]

IEC 41, 78-81(1949) (Equation of state. Generalized correlation applicable to all phases) B) S. Paterson J. Davidson, jChemPhys 22, 150(1954) CA 48, 4911 (1954) [Cottrell-Paterson equation of state (see item d, above) was applied to various expls covering a wide range of loading d and reaction energy. The calcd velocities agreed well with exception of expls of low reaction heat at low loading d] C) T. [Pg.298]

Derive the Cottrell equation by combining Fick s first law of diffusion with the tune-dependent change of the concentration gradient during a potential-step experiment. [Pg.99]

The product D0 (dCo/dx)x=0 t is the flux or the number of moles of O diffusing per unit time to unit area of the electrode in units of mol/(cm2 s). (The reader should perform a dimensional analysis on the equations to justify the units used.) Since (3Co/3x)x=01 is the slope of the concentration-distance profile for species O at the electrode surface at time t, the expected behavior of the current during the chronoamperometry experiment can be determined from the behavior of the slope of the profiles shown in Figure 3. IB. Examination of the profiles for O at x = 0 reveals a decrease in the slope with time, which means a decrease in current. In fact, the current decays smoothly from an expected value of oo at t = 0 and approaches zero with increasing time as described by the Cottrell equation for a planar electrode,... [Pg.57]

When substituted into Fick s first law (Appendix B, (B.9)), (7.16) becomes the Cottrell equation, which describes the variation of the diffusion limiting current with time exactly,... [Pg.206]

Both of these methods may be applied to nonplanar electrodes if the results are obtained at electrolysis times sufficiently short that the diffusion layer remains thin in comparison to the radius of curvature of the nonplanar electrode surface. For example, the spherical hanging-mercurcy-drop electrode provides chronoamperometric data that deviate less than 1-2% from the linear-diffusion Cottrell equation out to times of about 1 s. With solid wire electrodes of cylindrical geometry, similar conclusions apply, but at short times surface roughness effects yields a real surface area that is larger than the geometric area. [Pg.218]

Since the surface concentration of O becomes zero (Eq. 37), the rate of the reduction of O will be mass-transport-controlled or rather diffusion-controlled, as the migration and convection terms can be neglected. Thus, the experiment can be described by use of Tick s first and second laws (Eqs. 38 and 34, respectively). The substrate O is the only species initially present in the cell (Eq. 35) and because the electrode area A is small compared to the cell volume V in electroanalytical experiments, the bulk concentration can be assumed to be unchanged during the experiment (Eq. 36). Should a preparative conversion of O to R be the goal, a large A/V ratio would have been desirable. Equations 34-38 can be solved with the Laplace transformations this affords the Cottrel equation (Eq. 39). [Pg.508]

This is the so-called Cottrell equation. The minus sign on the r.h.s. is to a certain extent a matter of taste. In the present situation, where z is counted from the surface, it means that the transport takes place in the negative z-direction. If C (0,t) = 0 the profile c.(z,t) reads... [Pg.509]

When conventional electrodes with diameters between 0.1 and 2 mm are used, the latter quantity has usually decayed to zero after 0.5 ms or less and may be neglected in experiments lasting 1 ms or more. This decay time is reduced to the microsecond time regime when ultramicroelectrodes are used [94,125,202]. According to Eq. (64), which for i = 0 is known as the Cottrell equation, the current approaches zero when the time approaches infinity. However, undisturbed linear diffusion can be maintained only over rather short time intervals unless special precautions are taken (see Sec. II.D.l), and the measurements of current-time curves, called chronoamperometry (CA), are often complicated by additional modes of transport. Therefore, the use of properly shielded electrodes [140] should be considered in chronoamperometric experiments exceeding approximately 1 s. The mathematical formalism for chronoamperometry has been developed also for the application of ultramicroelectrodes [203]. [Pg.139]

The current is now controlled solely by the mass transfer to the electrode (region c in Fig. 36) and the equation reduces to the so-called Levich equation, Eq. (88), which may be used together with the Cottrell equation, Eq. (64), in the experimental determination of S [252]. [Pg.150]

Diffusion coefficients were taken from the literature or measured using chronocoulometry (5). The area of the electrode. A, was measured using FefCN) " in a solution of 0.004 m K3Fe(CN)5 in 0.1 m KCl, for which the diffusion coefficient is given as 762 + 0.01 x 10" cm sec" (S). It was found from six measurements to be 0.242 cm + 0.005 this value was then used to determine diffusion coefficients for species of interest (from the integrated Cottrell equation. Equation 5.9.1 in Reference 5). [Pg.342]

Limitations due to convection. At longer times the buildup of density gradients and stray vibrations will cause convective disruption of the diffusion layer, and usually result in currents larger than those predicted by the Cottrell equation. The time for the onset of convective interference depends on the orientation of the electrode, the existence of a protective mantle around the electrode, and other factors (1, 2). In water and other fluid solvents, diffusion-based measurements for times longer than 300 s are difficult, and even measurements longer than 20 s may show some convective effects. [Pg.163]

In most chronoamperometry, with measurement times of 1 ms to 10 s, the diffusion layer is several micrometers to even hundreds of micrometers thick. These distances are much larger than the scale of roughness on a reasonably polished electrode, which will have features no larger than a small fraction of a micrometer. Therefore, on the scale of the diffusion layer, the electrode appears flat the surfaces connecting equal concentrations in the diffusion layer are planes parallel to the electrode surface and the area of the diffusion field is the geometric area of the electrode. When these conditions apply, as in Figure 5.23a, the geometric area should be used in the Cottrell equation. [Pg.167]

Integrate the Cottrell equation to obtain the total charge consumed in electrolysis at any time, then calculate the value for f = 10 s. Use Faraday s law to obtain the number of moles reacted by that time. If the total volume of the solution is 10 mL, what fraction of the sample has been altered by electrolysis ... [Pg.222]

Figure 7.1.3 is an illustration of the current-time curves for several drops as predicted by the Ilkovic equation. Immediately apparent is that the current is a monotoni-cally increasing function of time, in direct contrast to the Cottrell decay found at a stationary planar electrode. Thus, the effects of drop expansion (increasing area and stretching of the diffusion layer) more than counteract depletion of the electroactive substance near the electrode. Two important consequences of the increasing current-time function are that the current is greatest and its rate of change is lowest just at the end of the drop s life. As we will see, these aspects are helpful for applications of the DME in sampled-current voltammetric experiments. [Pg.264]

In a potential-step experiment, the potential of the working electrode is instantaneously stepped from a value where no reaction occurs to a value where the electrode reaction under investigation takes place and the current versus time (chronoamperometry) or the charge versus time (chronocoulometry) response is recorded. The transient obtained depends upon the potential applied and whether it is stepped into a diffusion control, in an electron transfer control or in a mixed control region. Under diffusion control the transient may be described by the Cottrell equation obtained by solving Tick s second law with the appropriate initial and boimdary conditions [1, 2, 3, 4, 5 and 6] ... [Pg.1929]


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See also in sourсe #XX -- [ Pg.118 , Pg.173 ]




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